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Internationall 

Symposium on 

Magnetic 

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Technology 

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NASA Conference Publication 3152 

Part 1 

International 

Symposium on 

Magnetic 

Suspension 

Technology 

Edited by 

Nelson J. Groom 

NASA Langley Research Center 

Hampton, Virginia 

Colin P. Britcher 

Old Dominion University 

Norfolk, Virginia 

Proceedings of an international symposium sponsored by the 

National Aeronautics and Space Administration, 

Washington, D.C., and held at 

Langley Research Center 

Hampton, Virginia 

August 19-23, 1991 

NI\5J\ 

National Aeronautics and 

Space Administration 

Office of Management 

Scientific and Technical 

Information Program 

1992 
INTRODUCTION 

An International Symposium on Magnetic Suspension Technology was held at the Langley Research 

Center in Hampton, Virginia, on August 19-23, 1991. The symposium was sponsored by the Langley 

Research Center in coordination with the office of Aeronautics, Exploration, and Technology (OAET) 

in NASA Headquarters and was hosted by the Spacecraft Controls Branch at Langley Research Center. 

The symposium was chaired by the following people: 

Nelson J. Groom, Co-Chairman 

NASA 

Langley Research Center 

Hampton, VA 23665-5225 

Dr. Robert A. Kilgore, Co-Chairman 

NASA 

Langley Research Center 

Hampton, VA 23665-5225 

Dr. Colin P. Britcher, Technical Program Co-Chairman 

Dept. of Mechanical Engineering and Mechanics 

Old Dominion University 

Norfolk, VA 23529-0247 

Dr. James R. Downer, Technical Program Co-Chairman 

SatCon Technology Corporation 

12 Emily Street 

Cambridge, MA 02139-4507 

Emily E. Kornegay, Administrative Chairman 

NASA 

Langley Research Center 

Hampton, VA 23665-5225 

The goal of the symposium was to examine the state of technology of all areas of magnetic suspension 

and to review related recent developments in sensors and controls approaches, superconducting magnet 

technology, and design/implementation practices. The symposium included 17 technical sessions in 

which 55 papers were presented. The technical sessions covered the areas of bearings, sensors and 

controls, microgravity and vibration isolation, superconductivity, manufacturing applications, wind 

tunnel magnetic suspension systems, magnetically levitated trains (MAGLEV), space applications, and 

large gap magnetic suspension systems. A list of attendees appears at the end of the document. 

iii 

PRECEDING P'AG€ BlANK NOT FILMED 
Cenain materials and processes are identified in this publication in order to adequately specify 

procedures. In no case does such identification imply recommendation or endorsement by the 

govenunent, nor does it imply that the materials or processes are the only or best ones available 

for the purpose. 

iv 
Session 4 - Microgravity and Vibration Isolation 1 

Chairman - Mike Scott, NASA Langley Research Center 

A Six Degree-of-Freedom Magnetic Bearing for Microgravity Vibration Isolation 

A. Peter Allan, Carl R. Knospe 

A Six Degree-of-Freedom Lorentz Force Vibration Isolator with Nonlinear Controls 

Ralph C. Fenn, Michael Gerver, and Bruce Johnson 

Session 5 - Superconductivity 1 

Chairman - Jim Downer, SatCon Technology Corporation 

2091,/ 

219v' 

Recent Progress Towards Developing a High Field, High-T c Superconducting Magnet for 

Magnetic Suspension and Balance Systems . . . . . . . . . . . . . . . . . . . . . . . . . 247 vi' 

L. Pierre de Rochemont, Carlton E. Oakes, Michael R. Squillante, Hong-Min Duan, 

Allen M. Hermann, Robert J. Andrews, Roger B. Poeppel, Victor A. Maroni, 

Ingrid A. Carlberg, and Warren C. Kelliher 

Levitation of YBa2Cu307-x Superconductor in a Variable Magnetic Field 

Alexander N. Terentiev and Anatoliy A. Kuznetsov 

Hybrid Superconducting Magnetic Bearing (HSMB) for High Load Devices 

C. K. McMichael, K. B. Ma, M. A. Lamb, M. W. Lin, L. Chow, R. L. Meng 

P. H. Hor, and W.-K. Chu 

267.( 

279~ 

Characterization of Superconducting Magnetic Bearings (Dynamic stiffness and damping 

coefficients in axial direction) .............................. 289 V 

Ryoichi Takahata, Hirochika Ueyama, and Tsutom Yotsuya 

Session 6 - Bearings 2 

Chairman - Claude Keckler, NASA Langley Research Center 

Feasibility of Magnetic Bearings for Advanced Gas Turbine Engines 

David Hibner and Lewis Rosado 

Low Power Magnetic Bearing Design for High Speed Rotating Machinery 

P. E. Allaire, E. H. Maslen, R. R. Humphris, C. K. Sortore, and P. A Studer 

Progress of Magnetic Suspension Systems and Magnetic Bearings in the USSR 

A. V. Kuzin 

Session 7 - Sensors and Controls 2 

Chairman - Monique Gaffney, SatCon Technology Corporation 

Extended H2 Synthesis for Multiple Degree-of-Freedom Controllers 

R. David Hampton and Carl R. Knospe - University of Virginia 

vi 

299/ 

31ti 

........ 363 J 
CONTENTS 

Introduction . . . . . . . . . . . . . . . 

Session 1 - Introductions and Review Papers 

Chairman - Robert A. Kilgore, NASA Langley Research Center 

Overview of Magnetic Suspension Research at NASA Langley Research Center 

Nelson J. Groom 

Professor Jesse W. Beams and the First Practical Magnetic Suspension 

Paul E. Allaire, Robert R. Humphris, and David W. Lewis 

Large-Gap Magnetic Suspension Systems 

Colin P. Britcher 

Session 2 - Bearings 1 

Chairman - Paul E. Allaire, University of Virginia 

Magnetic Bearings: A Key Technology for Advanced Rocket Engines? 

J. Ph. Girault 

Active Magnetic Bearings-As Applied to Centrifugal Pumps 

Lev Nelik, Paul Cooper, Graham Jones, Dennis Galecki, Frank Pinckney, 

and Gordon Kirk 

Precision Magnetic Suspension Linear Bearing . . . 

David L. Trumper and Michael A. Queen 

Modelling and Design for PM/EM Magnetic Bearings . . . . . 

D. Pang, J. A. Kirk, D. K. Anand, R. G. Johnson, and R. B. Zmood 

Session 3 - Sensors and Controls 1 

Chairman - Mark Motter, NASA Langley Research Center 

iii 

25 V'" 

7Yi 

8~ 

105) 

Application of Narrow Band Control to Reduce Vibrations in Magnetic Bearing Systems ..... 123J 

Monique S. Gaffney and Bruce G. Johnson 

Dynamics and Control of High Precision MagneticaUy Levitated Vibration 

Isolation Systems . . . . . . . . . . . . . . . . . . . . . . . . . 

K. Youcef-Toumi and T-J Yeh 

Stability and Performance of Notch Filter Controllers for Unbalanced Response 

Carl R. Knospe 

v 

149/ 

........ 181 ~ 
Experimental Results in Nonlinear Compensation of a One Degree-of-Freedom Magnetic 

Suspension ................................ . 

David L. Trumper, James C. Sanders, Tiep H. Nguyen, and Michael A. Queen 

Control Concepts for Active Magnetic Bearings ................ . 

R. Siegwart, D. Vi scher, R. Larsonneur, R. Herzog, A. Traxler, H. Bleuler, and G. Schweitzer 

Computer Aided Design of a Digital Controller for Radial Active Magnetic Bearings 

Zhong Cai, Zupei Shen, Zuming Zhang, and Hongbin Zhao 

Session 8 - Microgravity and Vibration Isolation 2 

Chairman - Ralph Fenn, SatCon Technology Corporation 

385~ 

401./" 

A Microgravity Vibration Isolation Rig ..... . ......... 435'V' 

Bibhuti B. Banerjee, Carl R. Knospe, and Paul E. Allaire 

Vibration Damping of Elastic Waves in ElectricaUy Conducting Media Subjected to 

High Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . 

T. G. Horwath 

Coarse-Fine Residual Gravity Cancellation System with Magnetic Levitation 

S. E. Salcudean, H. Davis, C. T. Chen, D. E. Goertz, and B. V. Tryggvason 

Attendees 

Session 9 - Superconductivity 2 

Chairman - Warren C. Kelliher, NASA Langley Research Center 

Magnetic Suspension Using High Temperature Superconducting Cores 

R. G. Scurlock 

45"/ 

....... 507 

Effect of Flux Penetration on the Load Capacity of Passive Superconducting Bearings . . . . . . 519 

Dantam K. Rao 

Application of Ceramic Superconductors in High Speed Turbines .............. 535 

C. K. McMichael, M. A. Lamb, M. W. Lin, K. B. Ma, and W. K. Chu 

Cryogenic Test Rig with an Aerodynamic Magnetically Levitated Carriage . . . . . . . . . . . 547 

Sergey Yu. Borisov, Anton L. Iskra, and Anatoly P. Philatov 

Session 10 - Bearings 3 

Chairman - Jim Downer, SatCon Technology Corporation 

The Bearingless Electrical Machine 

J. Bichsel 

·Part 2 is presented under separate cover. 

vii 

......... 561 
Wide Gap, Permanent Magnet Biased Magnetic Bearing System ............... 575 

Karl Boden 

Force Analysis of Magnetic Bearings with Power-Saving Controls . . . . . . . . . . . . . . . 595 

Dexter Johnson, Gerald V. Brown, and Daniel J. Inman 

Session 11 - Manufacturing Applications 

Chairman - Nelson J. Groom, NASA Langley Research Center 

Manipulation and Identification of Objects by Magnetic Forces . . . . .. . ....... 617 

Benjamin Joffe 

Precise Positioning and Compliance Synthesis for Automatic Assembly Using 

Lorentz Levitation ................................... 639 

R. L. Hollis and S. Salcudean 

Session 12 - Bearings 4 

Chairman - Timothy Hawkey, SatCon Technology Corporation 

Development of a Differentially Balanced Magnetic Bearing and Control System for use 

with a Flywheel Energy Storage System . . . . . . . . . . . . . . . . . . .. ..... 657 

Mark A. Higgins, David P. Plant, Douglas M. Ries, James A. Kirk, and Davinder K. Anand 

Design of Bearings for Rotor Systems Based on Stability . . . . . . . . 

D. Dhar, L. E. Barrett, and C. R. Knospe 

..... 673 

An Evaluation of Some Strategies for Vibration Control of Flexible Rotors . . . . . . . . . . . 691 

C. R. Burrows 

Session 13 - Wind Tunnel Magnetic Suspension Systems 

Chairman - Robert A. Kilgore, NASA Langley Research Center 

Propulsion Simulator for Magnetically Suspended Wind Tunnel Models 

P. B. Joshi, M. R. Malonson, G. P. Sacco, C. L. Goldey, K. Garbutt, M. Goodyer, 

and P. Lawing 

....... 709 

Present Status of the MITINASA Langley 6 inch MSBS ................... 741 

Timothy Schott, Thomas Jordan, and Taumi Daniels 

Progress of Magnetic Suspension and Balance Systems for Wind Tunnels in the USSR . . . . . . 765 

A. V. Kuzin, Y. D. Vyshkov, and G. K. Shapovalov 

Wind Tunnel Magnetic Suspension Systems at the University of Southampton, England ..... 775 

Michael J. Goodyer 

viii 
Session 14 - Magnetically Levitated Trains (MAGLEV) 1 

Chairman - Colin P. Britcher, Old Dominion University 

Attractive and Repulsive Magnetic Suspension Systems Overview .. 

David B. Cope and Richard R. Fontana 

. ........ 791 

Change in the Coil Distribution of Electrodynamic Suspension System ............. 813 

Hisashi Tanaka 

The Concept of the Mechanically Active Guideway as a Novel Approach to Maglev . . . . . . . 827 

T. G. Horwath 

Session 15 - Space Applications 

Chairman - Nelson J. Groom, NASA Langley Research Center 

Space Applications of Diamagnetic Suspensions . . . . . . . . . . . . . ...... . . 847 

Ronald E. Pelrine 

Magnetic Bearing Wheels for Very High Pointing Accuracy Satellite Missions ......... 857 

J. P. Roland 

An Electrostatically Suspended, Micro-Mechanical Rate Gyroscope .... . . . . . . . . . . 873 

Timothy Hawkey and Richard Torti 

Session 16 - Magnetically Levitated Trains (MAGLEV) 2 

Chairman - Colin P. Britcher, Old Dominion University 

Battery Cars on Superconducting Magnetically Levitated Carriers--One Commuting 

Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 

B. Mike Briggs and Henry Oman 

Knolle Magnetrans, A Magnetically Levitated Train System 

Ernst G. Knolle 

•............... 907 

Computation of Magnetic Suspension of Maglev Systems Using Dynamic Circuit Theory . . . . . 919 

J. L. He, D. M. Rote, and H. T. Coffey 

Session 17 - Large-Gap Magnetic Suspension Systems 

Chairman - Nelson J. Groom, NASA Langley Research Center 

Large-Gap Magnetic Positioning System Having Advantageous Configuration . . . . ... 941 

Paul Chong, Colin Commandeur, Harold Davis, and Lome Whitehead 

Performance of a Superconducting Large-Angle Magnetic Suspension . . . . . . . . . . 955 

James R. Downer, Dariusz A. Bushko, Vijay Gondhalekar, and Richard P. Torti 

ix 
The Large-A1lg1e Magnetic Suspension Test Fixture . . . . . . . . . . . . . . . . . . . . . 971 

Colin P. Britcher, Mehran Ghofrani, Thomas C. Britton, and Nelson J. Groom 

Attendees ........... 987 

x 
Part 1 

Session 1 

INTRODUCTIONS AND REVIEW PAPERS 

Chairman - Robert A. Kilgore 

NASA Langley Research Center 

1 
~ 

N92-27722' 

OVERVIEW OF MAGNETIC SUSPENSION RESEARCH 

AT LANGLEY RESEARCH CENTER 

Nelson J. Groom 

PRECEDING PAGE BLANK NOT FILM!D 3 
SUMMARY 

An overview of research in small- and large-gap magnetic suspension systems at Langley 

Research Center (LaRC) is presented. The overview is limited to systems which have been 

built as laboratory models or engineering models. Small-gap systems applications include 

the Annular Momentum Control Device (AMCD), which is a momentum storage device 

for the stabilization and control of spacecraft, and the Annular Suspension and Pointing 

System (ASPS), which is a general purpose pointing mount designed to provide orientation, 

mechanical isolation, and fine pointing of space experiments. These devices are described and 

control and linearization approaches for the magnetic suspension systems for these devices 

are discussed. Large-gap systems applications at LaRC have been almost exclusively wind 

tunnel magnetic suspension systems. A brief description of these efforts is also presented. 

INTRODUCTION 

Research in small-gap magnetic suspension systems at Langley Research Center (LaRC) 

began in the early 1970's with the development of the Annular Momentum Control Device 

(AMCD) concept. The AMCD is a momentum storage device with applications to the 

stabilization and control of spacecraft (ref. 1). This research was continued with the 

development of the Annular Suspension and Pointing System (ASPS) concept. The ASPS 

is a derivative of the AMCD and is a general purpose pointing mount designed to provide 

orientation, mechanical isolation, and fine pointing of space experiments (refs. 2 and 3). 

These devices will be described, and control and linearization approaches for the magnetic 

suspension systems for these devices will be discussed. 

Research in large-gap magnetic suspension systems at LaRC began in the early 1960's 

and has been focused almost entirely on wind tunnel systems. The research began with the 

development of a single degree-of-freedom demonstration system (ref. 4) and has continued to 

the present with design studies of large-scale systems with superconducting magnets (ref. 5). 

A brief description of the wind tunnel magnetic suspension system efforts at LaRC will be 

presented. 

SMALL-GAP SUSPENSION SYSTEMS 

Annular Momentum Control Device (AMCD) 

Magnetic suspension has historically been viewed as a promising solution to several problems encountered in the long-term utilization of momentum storage devices for spacecraft 

control. However, earlier efforts toward the application of magnetic suspension technology 

were focused on developing a direct physical replacement for the mechanical bearings of 

conventional shaft-driven and suspended-steel flywheels. The conventional approach, using 

a central hub with a shaft to provide support for both translational forces and rotational 

moments, was motivated in part by the need to keep the bearings self-contained and as 

small as possible so that bearing surface speed and drag effects could be kept to acceptable 

levels. With magnetic suspension there are no contacting surfaces and, with proper design, 

PRECEOfNG PAC*: BLANK NOT FIL.MED 

5 
6 

drag losses can be made relatively small. Therefore, bearing surface speed ceases to be a 

constraint. A reexamination of conventional approaches to the design of momentum storage 

devices on both a device and system level, without the bearing surface speed constraint, led 

to the concept of the AMCD (ref. 6). The basic concept of the AMCD consists of a spinning 

annular rim suspended by a minimum of three non contacting magnetic suspension stations 

and is driven by a noncontacting electromagnetic spin motor. The use of a thin annular rim 

provides the maximum momentum-to-mass ratio for any material since the spinning mass is 

concentrated at the largest mean radius. Significant improvements in this ratio can be obtained by using lightweight, high strength, composite materials since, for a rim, the stresses 

due to rotation are predominantly circumferential. The utilization of noncontacting suspension and driving elements eliminates mechanical wear and lubrication subsystem failures 

and results in system reliability characteristics equal to those of the magnetic suspension 

and rim drive motor electronics. A further advantage of the magnetic suspension system is 

that it can be tuned to provide for effective isolation of vibrations, generated by the rotating 

rim, from the vehicle and its scientific payloads. In addition, the magnetic suspension can 

produce smooth forces without threshold type nonlinearities (i.e., no mechanical breakout 

forces). The advantage of this characteristic is that small, precision, precessional torques 

can be generated by "gimbaling" the rim in the magnetic gaps. 

In order to investigate technology requirements and evaluate certain design approaches, 

the AMCD was implemented as a laboratory test modeL The laboratory model, shown in 

figure 1, consists of a graphite/epoxy composite rim, three magnetic suspension stations, 

three spin motor stator element pairs (one pair per suspension station), and six pneumatic 

backup bearings (required for laboratory use only). The suspension assemblies are attached 

to an aluminum base plate. A vacuum cover fits over the suspension-motor-rim-backup 

bearing assembly and bolts to the base plate for high-speed spin tests. The rim is 1. 7m 

(5.5 ft) in diameter, weighs 22.68 kg (50 lb), and is designed to rotate at 2,741 rpm. The 

rim momentum at this speed is 4,068 N-m-s (3,000 ft-Ib-sec). A detailed description of the 

AMCD laboratory test model, as delivered, is given in reference 7, and preliminary test 

results are presented in reference 8. Additional information related to the laboratory model 

is available in references 9-16. Potential applications of the AM CD concept are presented 

in references 17-22. 

Annular Suspension and Pointing System (ASPS) 

The ASPS was developed to meet the need for a multipurpose experiment pointing 

platform which was established during NASA Earth-orbital systems technology guidance 

and control planning activities in the early 1970's. The ASPS is a derivative of the AMCD 

and uses a similar magnetic bearing design and suspension technique. However, the two are 

very different in purpose and operation (refs. 23-24). The ASPS (fig. 2) consists of a vernier 

assembly, which uses magnetic suspension, and a mechanical gimbal assembly, which uses 

conventional de motor technology. The magnetic suspension of the vernier assembly provides 

high accuracy pointing (0.01 arcsec) and isolation from carrier motion disturbances. The 

mechanical gimbal assembly allows for system deployment, target acquisition and tracking, 

retargeting, and can serve as a backup, at reduced performance levels, in case of vernier 

assembly failure. A typical payload-ASPS-carrier vehicle configuration is shown in figure 3. 
In order to demonstrate the very high accuracy pointing and control capability of the 

ASPS concept, a decision was made to fabricate and test an engineering model of the ASPS. 

The ASPS vernier assembly engineering model, with payload plate removed, is shown in 

figure 4. The payload plate bolts to the annular rotor which is suspended by five magnetic 

bearing actuators (MBA's) that provide control over three translational axes and rotations 

about the two transverse axes. Control about the roll axis is provided by a segmented 

ac induction motor. Power and data to and from the payload are provided by a rotary 

transformer and an optical coupler, respectively. Therefore, the only connection between 

payload and carrier vehicle is through the stiffness of the MBA servo loops which, because 

of the decoupling scheme used (ref. 2), acts through the payload's center of mass. 

Additional information on the ASPS design and development and related analyses and 

simulations are presented in references 25-31. 

SMALL-GAP ACTUATOR LINEARlZATION 

AND CONTROL APPROACHES 

In order to define the basic type of small-gap magnetic bearing actuator which will 

be discussed in this paper, the simplified schematic of figure 5 is introduced. Shown are 

upper and lower electromagnets with currents Iu and IL, producing forces Fu and FL on 

a suspended element positioned in the center between the electromagnets at a gap distance 

Go from the top electromagnet pole face. Since an electromagnet of the type being discussed 

produces an attractive force only, two are required to produce a bidirectional force capability. 

A position sensor is shown which measures the displacement G s of the suspended element 

with respect to the centered position Go. Position information is required for active control 

of the suspended element and is also required for some of the linearization approaches to be 

discussed. Under ideal assumptions, the force produced by a given electromagnet is directly 

proportional to the square of the coil current and inversely proportional to the square of the 

electromagnet gap (ref. 10) and can be written as 

(1) 

Two approaches have been investigated for controlling this type of actuator. One 

approach involves controlling the upper and lower electromagnets differentially about a bias 

flux. The bias flux can either be supplied by permanent magnets in the magnetic circuit 

or by bias currents. In the other approach, either the upper electromagnet or the lower 

electromagnet is controlled depending on the direction of the force required. 

Bias Flux Linearization and Control Approaches 

Permanent Magnet.- The original control approach used for the laboratory model AMCD 

magnetic actuators was permanent magnet flux biasing. The operation of a permanent 

magnet flux-biased magnetic actuator can be described by referring to figure 6. This figure 

is a simplified schematic which shows a single actuator, for control along a single axis, which 

consists of a pair of magnetic bearing elements with permanent magnets mounted in the 

cores. The bearing elements are shown connected in a differential configuration. That is, for 

7 
8 

a given input, the amplifier driver shown in the figure produces current in a direction to aid 

the permanent-magnet-produced flux: in one element and, at the same time, produces equal 

current in a direction to subtract from the permanent-magnet-produced flux: in the other 

element. This change in flux: results in a net force produced on the suspended mass in a 

direction dependent on the polarity of the input to the amplifier driver. The force produced 

by this type actuator as a function of current, I, and gap, G, can be written as (from ref. 10) 

(2) 

where Kl, xo, and 10 are constants (defined in ref. 10). 10 can be thought of as an equivalent 

constant bias current provided by the permanent magnets. Figure 7 shows the composite 

forc~current characteristic of this type actuator with the suspended mass centered in the 

gaps. This figure illustrates a linear electromagnet gain of the actuator at a giiven gap 

position. By performing a first order linearization of equation 2 about a fixed operating 

point, the actuator force as a function of differential coil current and displacement can be 

written as 

F=KBI+KMG (3) 

where K B is an equivalent electromagnet gain and K M is an equivalent bias flux: stiffness 

(for more detail see ref. 10). These gains would be different for different operating points. 

Variable Bias Current.- A variation of the permanent-magnet flux: bias approach W:i:l.S developed for the ASPS in order to provide a linear actuator characteristic over a wide gap range. 

This approach uses variable bias currents to provide the bias flux:. Figure 8 is a simplified 

block diagram of the variable bias current approach that was implemented for the ASPS. 

As can be seen by working through the block diagram, the bias current and control currents 

of the upper and lower electromagnets are adjusted so that the bias force produced by each 

and the net force produced by a given command force are equal regardless of the suspended 

mass's location in the gap. The unbalanced bias-flux: stiffness is thus eliminated and the 

electromagnet gain is constant. A detailed description of this implementation is given in 

reference 25. 

Flux: Feedback.- When considering simplicity, efficiency, and controllability of force around 

zero, the permanent magnet flux: bias approach trades off better than the other magnetic 

bearing control and linearization approaches that were discussed in the previous sections. 

Disadvantages of this approach include a minimum bandwidth requirement for stability 

(ref. 8) and linear operation over a restricted gap range about a fixed operating point. 

The variable bias current approach used in the ASPS suspension system was d«~veloped 

to overcome these disadvantages. However, since current is the controlled variable, the 

implementation of this approach is relatively complicated and requires actuator core material 

and rotor material with very low hysteresis in order to provide a sufficiently accurate forc~ 

output to forc~command transfer characteristic (ref. 25). By using flux: feedback (fig. 9), 

the complex current calculation, with the attendant requirement for gap compensation, is no 

longer required. In addition, the nonlinear transfer characteristic between electromagnet coil 

current and flux is included in the forward loop of a feedback system with very high open loop 

gain. This reduces the sensitivity of the forc~output to for~input transfer characteristic 

to a negligible level as long as the actuator is operated below the saturation flux density of 
the electromagnet core material and rotor material. Bias flux can be supplied by either fixed 

bias currents or permanent magnets in the flux feedback approach. In most applications, 

permanent magnet flux bias is the preferred approach because of power consumption and 

actuator heating issues. 

The force produced by a given electromagnet, as a function of current and gap, is given 

by equation 1. Under the same assumptions, the force produced by a given electromagnet, 

as a function of flux in the electromagnet gap, can be written as (ref. 16) 

(4) 

where 4> is flux and K is defined in reference 16. Using figure 5 and the associated 

nomenclature again, the force produced by the upper and lower elements becomes 

(5) 

For a bearing element pair with differential control of flux, the total force becomes 

(6) 

With differential control about a bias flux, 4>0, the flux in the upper and lower gaps becomes 

4>u = 4>0 + 4>e, 4> L = 4>0 - 4>e (7) 

where 4>e is flux command. Substituting equation 7 into equation 6 results in 

FT = K([4>~ + 24>04>e + 4>~1 - [4>~ - 24>04>e + 4>~]) (8) 

which simplifies to 

(9) 

By defining 4>e = Fe and K F = 4K 4>0, the total actuator force output, FT, as a function of 

command force input, Fe, can be written as 

Single Element Linearization 

and Control Approaches 

(10) 

As mentioned above, single element control involves controlling either the upper or lower 

electromagnet (shown in fig. 5), depending on the direction of the force required. Controlling 

the electromagnets in this way results in a highly nonlinear force-current characteristic. 

This is illustrated by figure 10 which shows the composite force-current characteristic of a 

magnetic actuator with individual element control and with the suspended mass centered 

in the actuator gaps. It should be noted that this curve is based on ideal assumptions, and 

that in practice, because of hardware considerations, the smooth crossover at zero is difficult 

to achieve. 

9 
10 

Two linearization approaches have been investigated for individual element control. One 

approach, which has been implemented for the laboratory model AMCD, utilizes the analog 

solution of the force equation for a given element. Figure 11 is a simplified block diagram of 

this implementation which uses analog multipliers and square root modules. The equations 

for upper and lower elements are included in the figure. A detailed description of this 

implementation is given in reference 12. This approach proved to be very sensitive to bearing 

element calibration and alignment accuracy. 

The other linearization approach investigated for individual element control is microprocessor based and uses a table lookup to generate control signals. This approach was bench 

tested but has not been used in the AM CD laboratory model suspension system. Figure 12 

is a block diagram representation of the laboratory implementation. In this approach, actual 

calibration data for a given bearing element pair are used to build a lookup table which is 

stored in the memory of a microprocessor system. Using the force command and gap position as input data, the correct value of current input to the coil, for the suspended element 

centered in the actuator gaps, is obtained by using a table lookup routine. This current 

is compensated for displacement from center by multiplying by the calculated gap. This 

approach is described in more detail and test results are presented in reference 15. 

LARGE-GAP SYSTEMS 

Interest in large-gap magnetic suspension systems at NASA Langley began in the early 

1960's. The principal goal was the elimination of aerodynamic support interference in wind 

tunnel testing, which can cause significant corruption of wind tunnel results, as illustrated 

in figure 13. A single degree-of-freedom demonstration suspension system was operational in 

1964 (ref. 4) and is shown in figure 14. The suspension coil was 16 inches in overall diameter, 

water cooled and split into two independent windings, and fed from a de "bias" supply and 

a unipolar SCR power amplifier. Figure 15 is a schematic of the major circuit components. 

For almost a decade, the principal LaRC MSBS activity was through grants and contracts 

with the Massachusetts Institute of Technology (MIT) and the University of Virginia (UVA). 

Information on these efforts is presented in references 32 and 33. An extensive list of related 

publications can be found in reference 34. MIT constructed two small-scale MSBSs and used 

them for a variety of testing at subsonic and supersonic speeds. The MIT 6-inch system 

was a relatively sophisticated and successful design and was eventually moved to LaRC in 

1980. The system is now operated by the Instrument Research Division, principally to aid 

in the development of more accurate position sensors and force calibration techniques. A 

schematic diagram of the system is shown in figure 16. UVA also constructed two systems; 

the superconducting system is believed to be the first superconducting suspension system of 

any type. The system was decommissioned in the late 1970's and the electromagnet array 

is now kept at LaRC for historical interest. 

LaRC also supported research at the University of Southampton from the late 1970's 

until recently (refs. 34-35). Notable achievements were the development of a digital control 

system, demonstration of roll control techniques (providing control of the sixth degree-offreedom), and the construction of a superconducting model core (ref. 36) which is the small 

model shown in figure 17. 
The LaRC 13-inch MSBS was originally constructed at AEDC, TUllahoma, TN and was 

transferred to LaRC in 1979. Since then, almost all the original hardware has been replaced, 

including the control system (now digital), position sensors, and main electromagnets. The 

system is installed in a low-speed wind tunnel, illustrated in figure 18, and has been used 

for extensive aerodynamic testing (refs. 37-38). For many years, this system was the largest 

air-gap suspension system known, but it has recently been surpassed by other wind tunnel 

systems in the U.S.S.R. and Japan. 

Under various contracts with General Electric Company and Madison Magnetics Incorporated (MMI), a series of design studies of large-scale MSBSs were completed (ref. 5). MMI 

also designed and constructed a second-generation superconducting solenoid model core, 

which is the large model shown in figure 17. 

CONCLUDING REMARKS 

An overview of research in small- and large-gap magnetic suspension systems at Langley 

Research Center has been presented. The overview was limited to systems which have 

been built as laboratory models or engineering models. Small-gap systems applications have 

been focused on space applications and include advanced spacecraft control actuators and 

experiment isolation and pointing mounts. Large-gap systems applications have been almost 

exclusively wind tunnel magnetic suspension systems. A comprehensive list of references 

which provides more details on the systems discussed in the overview was also presented. 

REFERENCES 

1. Anderson, Willard W.; and Groom, Nelson J.: The Annular Momentum Control Device 

(AMCD) and Potential Applications. NASA TN D-7866, March 1975. 

2. Anderson, Willard W.; and Joshi, Suresh M.: The Annular Suspension and Pointing (ASP) System for Space Experiments and Predicted Pointing Accuracies. NASA 

TR R-448, December 1975. 

3. Anderson, Willard W.; Groom, Nelson J.; and Woolley, Charles T.: The Annular 

Suspension and Pointing System. Journal of Guidance and Control, Vol. 2, No.5, 

September-October 1979, pp. 367-373. 

4. Hamlet, Irving L.; and Kilgore, Robert A.: Some Aspects of an Air-Core Single-Coil 

Magnetic Suspension System. Presented at the ARL Symposium on Magnetic Wind 

TUnnel Suspension and Balance Systems. April 1966. 

5. Boom, Roger W.; Abdelsalam, Mustafa K.; Eyssa, Y. M.; and McIntosh, G. E.: Magnetic 

Suspension and Balance System Advanced Study-Phase II. NASA CR-4327, November 

1990. 

6. Anderson, Willard W.; and Groom, Nelson J.: Annular Momentum Control Device. U.S. 

Letters Patent No. 3,915,416; October 28 1975. 

7. Ball Brothers Research Corporation: Annular Momentum Control Device (AMCD). 

Volume I: Laboratory Model Development. NASA CR-144917, 1976. 

11 
12 

8. Groom, Nelson J.; and Terray, David E.: Evaluation of a Laboratory Test Model Annular 

Momentum Control Device. NASA TP-1142, March 1978. 

9. Groom, Nelson J.: Fixed-Base and Two-Body Equations of Motion for an Annular 

Momentum Control Device (AMCD). NASA TM-78644, March 1978. 

10. Groom, Nelson J.: Analytical Model of An Annular Momentum Control Device (AMCD) 

Laboratory Test Model Magnetic Bearing Actuator. NASA TM-80099, August 1979. 

11. Groom, Nelson J.; and Waldeck, Gary C.: Magnetic Suspension System for a Laboratory 

Model Annular Momentum Control Device. Presented at the AIAA Guidance and Control 

Conference, Boulder, Colorado, August 1979. (Available as AIAA Paper 79-U55). 

12. Sperry Flight Systems: Magnetic Suspension System for an Annular Momentum Control 

Device (AMCD). NASA CR-159255, December 1979. 

13. Woolley, Charles T.; and Groom, Nelson J.: Description of a Digital Computer Simulation 

of an Annular Momentum Control Device (AM CD) Laboratory Test Model. NASA TM81797, 1981. 

14. Groom, Nelson J.; Woolley, Charles T.; and Joshi, Suresh M.: Analysis and Simulation 

of a Magnetic Bearing Suspension System for a Laboratory Model Annular Momentum 

Control Device. NASA TP-1799, March 1981. 

15. Groom, Nelson J.; and Miller, James B.: A Microprocessor-Based Table Lookup 

Approach for Magnetic Bearing Linearization. NASA TP-1838, 1981. 

16. Groom, Nelson J.: A Magnetic Bearing Control Approach Using Flux Feedback. NASA 

TM-100672, March 1989. 

17. Ball Brothers Research Corporation: Annular Momentum Control Device (AMCD). 

Volume II: Application To A Large Space Telescope. NASA CR-144917, 1976. 

18. Nadkarni, Arun A.; and Joshi, Suresh M.: Optimal Maneuvering and Fine-Pointing 

Control of a Large Space Telescope with a New Magnetically Suspended, Single Gimbaled, 

Momentum Storage Device. Proceedings of the 15th IEEE Conference on Decision and 

Control, Clearwater Beach, FL, December 1-3, 1976. 

19. Nadkarni, Arun A.; Groom, Nelson J.; and Joshi, Suresh M.: Optimal Fine Pointing of a 

Large Space Telescope using an Annular Momentum Control Device. Proceedings of the 

IEEE Southeastcon 77, Williamsburg, VA, April 4-6, 1978. 

20. Joshi, Suresh M.; and Groom, Nelson J.: A Two-Level Controller Design Approach for 

Large Space Structures. Proceedings of the 1980 Joint Automatic Control Conference, 

San Francisco, CA, August 13-15, 1980. 

21. Joshi, Suresh M.; and Groom, Nelson J.: Modal Damping Enhancement in Large Space 

Structures Using AMCD's. Journal of Guidance and Control, Vol. 3, No.5, SeptemberOctober 1980, pp. 477-479. 

22. Joshi, Suresh M.: Damping Enhancement and Attitude Control of Large Space Structures. 

Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, NM, 

December 10-12, 1980. 

23. Anderson, Willard W.; and Groom, Nelson J.: Magnetic Suspension and Pointing System. 

U.S. Letters Patent No. 4,088,018, May 9, 1978. 
24. Anderson, Willard W.; and Groom, Nelson J.: Magnetic Suspension and Pointing System. 

U.S. Letters Patent No. 4,156,548, May 29, 1979. 

25. Cunningham, D. C.; Gismondi, T. P.; and Wilson, G. W.: System Design of the Annular 

Suspension and Pointing System (ASPS). Presented at the AIAA Guidance and Control 

Conference, Palo Alto, California, August 1978. (Available as AIAA Paper 78-1311). 

26. Cunningham, David C.; et. al.: Design of the Annular Suspension and Pointing System 

(ASPS). NASA CR-3343, October, 1980. 

27. Keckler, Claude R; Kibler, Kemper S.; and Rowell, Larry F.: Determination of ASPS 

Performance for Large Payloads in the Shuttle Orbiter Disturbance Environment. NASA 

TM-80136, October, 1979. 

28. Keckler, Claude R: ASPS Performance with Large Payloads Onboard the Shuttle 

Orbiter. AIAA Journal of Guidance, Control, and Dynamics, Vol. 5, No.1, pp. 32-36, 

January-February 1982. 

29. Hamilton, Brian J.: Vibration Attenuation Using Magnetic Suspension Isolation. Presented at the Joint Automatic Control Conference, Charlottesville, VA, June 17-19, 1981. 

30. Hamilton, Brian J.: Laboratory Evaluation of the Pointing Stability of the ASPS Vernier 

System. NASA CR-159307, June, 1980 

31. Sperry Flight Systems: The Development of the ASPS Vernier System. Final Report 

under Contract No. NASl-15008, June, 1983. 

32. Covert, E. E.; Finston, M.; Vlajinac, M.; and Stephens, T.: Magnetic Balance and 

Suspension Systems for Use with Wind Thnnels. Progress in Aerospace Sciences, Volume 

14, 1973. 

33. Zapata, R N.: Development of a Superconducting Electromagnetic Suspension and 

Balance System for Dynamic Stability Studies. NASA CR-132255, February 1973. 

34. Thttle, M. H.; Moore, D. L.; and Kilgore, R A.: Magnetic Suspension and Balance 

Systems-A comprehensive, annotated, bibliography. NASA TM-4318, August 1991. 

35. Britcher, C. P.: Progress toward Magnetic Suspension and Balance Systems for Large 

Wind 'funnels. AIAA Journal of Aircraft, Volume 22, April 1985. 

36. Britcher, C. P.; Goodyer, M. J.; Scurlock, R G.; and Wu, Y. Y.: A Flying Superconducting Model and Cryostat for Magnetic Suspension of Wind Thnnel Models. Cryogenics, 

April, 1984. 

37. Dress, D. A.: Drag Measurements on a Laminar-Flow Body of Revolution in the 13-inch 

Magnetic Suspension and Balance System. NASA TP-2895, April, 1989. 

38. Britcher, C. P.; and Alcorn, C. W.: Interference-Free Measurements of the Subsonic 

Aerodynamics of Slanted-Base Ogive Cylinders. AIAA Journal, April, 1991. 

13 
ORIG INAL Pi-GE 

BLACK AND WHITE PHOTOGRAPH 

Figure 1. AMCD laboratory model. 

14 
PAYLOAD 

MOUNTING 

PLATE 

ROLL RESOLVER 

38 INCHES 

VERNIER LATCH/ __ -+----t~~/r BATTERY RECHARGE 

CONNECTOR 

VERNIER 

POINTING 

ASSEMBLY 

ROTARY 

TRANSFORMER 

AXIAL 

MAGNETIC 

BEARING 

ASSEMBLY 

PAYLOAD SUPPORT 

BATTERY 

~ 

~~LATERAL GIMBAL 

tS" , c , r, I) '\ 

o 

ASSEMBLY 

ELEVATION GIMBAL 

ASSEMBLY 

MOUNTING/DEPLOYMENT 

ASSEMBLY 

ANNULAR SUSPENSION AND POINTING SYSTEM 

(ASPS)-EXPLODED VIEW 

Figure 2. ASPS configuration. 

15 
16 

DEPLOYED 

Figure 3. Typical payload ASPS carrier vehicle configuration. 

Radial magnetic bearing 

actuator assembly(2) 

Figure 4. ASPS vernier assembly engineering model. 

ORIGINAL rf,GE 

BLACK AND WHITE PHOTOGRAPH 
ositio 

Sensor 

G 

Luspended 

Element 

Figure 5. Magnetic bearing actuator. 

I 

III 

Position tzz tz2 Sensor 

'iT I IT. t I I I I I I 

''::'~,:.:~-=.:~;:'/ 

-- -- ..,-:, ---=--:. -~" 

I I I I I I 

I~I '...I...' 

rz Z2 

III 

I 

Go 

j 1~ 

Amplifier 

Driver 

r 

Figure 6. Penn anent magnet flux-biased magnetic actuator. 

17 
18 

Force t 

! 

Upper Magnet 

Characteristic 

Net Force-Current 

Characteristic 

Lower Magnet 

Characteristic 

Current 

Figure 7. Force-current characteristic of a penn anent magnet flux-biased magnetic actuator. 

Fe --+-------., 

F K Fe 

lu 

G From Position 

Sensor 

Figure 8. Variable biased current approach for magnetic actuator control. 
Fco---", 

Permanent 

magnets 

--------- ---, , , , 

, 

'- - - - - -~ -~~II-~ffect sensor 

1_ & amplifier .- - - - - - - - - - - -. , 

, 

, 

, 

, 

, 

Figure 9. Flux feedback approach. 

Lower Magnet 

Characteristics 

Force t 

12 

F=K -

G2 

Upper Magnet 

Characteristics 

Current 

For Linear Force 

Characteristic 

I=GYFC/K 

Figure 10. Force current characteristic of a magnetic actuator with individual element control. 

19 
G 

20 

lu 

.----:::-------, , 

Top Element 

Driver 

I~ F = K - • Gu=(Go-G) u Gt 

~-- G From Sensor 

Bottom 

Element 

Driver 

It. 

FL = K GL • GL=(Go+G) 

Figure 11. Analog solution of the force equation for individual element control. 

-

AID 

L....-...o 

Microprocessor 

r-----------------------------------..., 

I 

: Force-Current I Table (Gap-centered) I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

T 

Signl 

Fc 

l 

~ I 

1-

Compute Gu or G L 

Based on Sign of F c 

I Gu.L· I 

I 

r 

I 

Gu,L I 

I 

I 

I 

I 

I I 

~----------------------------------~ 

Figure 12. Table look-up approach for individual element control. 

-

D/A --1 Cur.rent I Driver 

-
• Afterbody drag 

£r----(jj_~ , 

• Trim & tail loads 

+ 

...- ---- ...-

...-

0 -1 -2 

.6 .8 1.0 1.2 M 

& • YaW' damping 

+ --- / -

o S 

a 

,,'----

10 

~ 

Figure 13. Examples of model support problems. 

it 

Figure 14. Photograph showing model supported in Langley magnetic suspension system. 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

21 
Figure 15. Schematic of major circuit components. 

Figure 16. NASA LaRC/MIT 6-inch magnetic suspension and balance system. 

22 
Power 

supplies 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

Figure 17. Superconducting solenoid. 

room 

Electromagnets (5) 

~ 

It 

Figure 18. Thirteen inch magnetic suspension laboratory. 

Intake 

23 
N92-27723 

PROFESSOR JESSE W. BEAMS AND THE FIRST PRACTICAL MAGNETIC SUSPENSION 

P. E. Allaire 

R. R. Humpbris 

D. W. Lewis 

Mechanical and Aerospace Engr. Dept., University of Virginia, Charlottesville, VA 22901 

PRf.cEDING PAGE BLANK NOT FilMED 2S 
INTRODUCTION 

Dr. Jesse W. Beams developed the first practical magnetic suspension for high speed rotating 

devices [1-2]. These devices included high speed rotating mirrors, ultracentrifuges and high 

speed centrifugal field rotors. Figure 1 shows a photograph of Dr. Beams in his laboratory. 

Dr. Beams employed magnetic suspension as a means to carry out extensive experiments on 

physical properties in areas of isotope separation, biophysics, materials science, and gravitational 

physics. Typically, he thought of ways to modify and improve experiment equipment. The 

improved equipment then gave much better experimental results. Building on this advance, he 

then thought of some new type of experiment that could be performed with the technological 

advance in equipment and capabilities. 

ORIG! N/\L ~GE 

BLACK AND WHITE PHOTOGRAPH 

Fig. 1 Professor Jesse W. Beams, 1898-1977 

EARLY AXIAL MAGNETIC SUSPENSION FOR ULTRACENTRIFUGES 

The interest in high speed rotating devices extended to centrifuges. Around 1924, practical 

centrifuges were being developed in Sweden. Heavy particles in suspension will settle out more 

rapidly than light particles. This process can be speeded up by putting the suspension in a high 

speed centrifuge. However, convection currents caused by friction heating of the rotor surface 

due to the air outside caused problems. Beams removed this difficulty by placing the rotor in a 

vacuum. 

Originally, the rotor was supported axially by compressed air. This was replaced by a 

magnetic suspension system. A vertical shaft in the centrifuge rotor was attracted upward by a 

27 
28 

magnetic solenoid coaxial with it. The centrifuge was then radially stable, but axially unstable. 

Beams and two colleagues, Sheppard Black and Fred Holmes [3--6], devised a system of sensing 

the vertical position of the centrifuge rotor with a photoelectric cell. The position of the rotor 

was maintained by changing the current in the solenoid as needed. This type of system is now 

called automatic feedback control. 

The principle was reported in [3]. Figure 2 illustrates the approach employed. "Solenoid 1 

carries a steady direct current producing a magnetic field sufficiently strong to support a large 

fraction of the weight of the needle, N, and the attached cylindrical vane V. A source of light, S, 

is roughly focused on the upper edge of V so that some of the light passes over V and strikes a 

photo--cell P. The current from P operates a two-stage d.c. amplifier whose output is fed into a 

solenoid 2. Thus if N drops too low, the amount of light striking P is increased and the magnetic 

field is increased: if N rises too high, the field is decreased. In this way, if adequate damping 

is supplied, N may be automatically maintained at its equilibrium position." Figure 3 gives the 

circuit diagram for controlling solenoid 2. 

x 

oS 

N = rotating needle 

V = attached vane 

1 = steady solenoid 

2 = control solenoid 

S = source of light 

L = lens 

P = photocell 

o = damping plate 

Fig. 2. Schematic of Vertical Magnetic Suspension System Employed by Beams, et. al. [3] in 

1937. 

p= photocell, P J23 

R = resistor, 5 meg ohm 

R1 = resistor, 40 kilo ohm 

Tl = vacuum tube, 27 

T2 = vacuum tube, 2A3 

2 = control solenoid 

Fig. 3. Control Circuit [3] Feeding Solenoid 2 in Figure 1. 

In a short period of time, the magnetic suspension was employed in an ultracentrifuge and a 

paper [5] published in 1939 showed the schematic diagram of Figure 4. " ... The rotating parts 

consist of the centrifuge C, an armature D of the electric motor, a small iron rod S, and a flexible 

shaft A which connects them together. The shaft A passes through vacuum tight oil glands G 1, 

which seals the vacuum chamber, and G2, which serves to center D in the field F." 

" ... The rotating members are supported by an electromagnet consisting of an iron core M 

and windings L. The current through L is so adjusted that the magnetic attraction between M 

and the small iron rod S, rigidly attached to and coaxial with A, is just greater than necessary 

to lift S, A, D, and c." 

The new magnetic suspension system had several advantages. First, the vertical rotor position 

was controlled to such an extent that no vertical motion could be detected by a 100 power 
microscope. Second, the power losses were so low that very high rotating speeds could be 

produced. Figure 5 shows a photograph of the magnetically supported centrifuge. In 1940, 

Skarstrom and Beams reported on an improved ultracentrifuge [6] as shown in Fig. 6. A viscous 

damper was added at the bottom to reduce lateral shaft vibrations. Figure 7 shows machinist P. 

Sommer in Dr. Beams' laboratory standing next to an ultracentrifuge. 

As early as 1937, Beams and colleagues showed that the isotopes of elements could be 

purified by centrifuges. Further work was reported in [6]. During World War II, the Department 

of Physics conducted work on a long cylindrical centrifuge for the separation of uranium isotopes. 

A pilot plant was operated at Bayway, NJ starting early in the war for separating uranium 235 

from uranium 238. However, this method was not employed for production of uranium 235 

during the war. After the war, Dr. Beams continued to work with a classified project at the 

University to develop the centrifuge for eventual use in the production of uranium supplied to 

electric power reactors. The project continued unti11988. 

Figure 5. Photograph of Early Ultracentrifuge. 

Figure 4. Drawing of Vacuum-Type 

Self-Ba.lancing and Magnetically 

Supported Ultracentrifuge (1939). 

C = centrifuge rotor 

D = motor armature 

S = iron rod 

M = electromagnet 

iron core 

L = electromagnet 

windings 

A = flexible shaft 

G1 = oil gland 

G2 = oil bearing 

F = field for rotation 

N = clutch 

D = motor a.rma.t ure 

R = mag. support core 

M = em iron core 

L = support solenoid 

C = rotor 

A = shaft 

G1 = oil bearing 

G2 = oil bearing 

G3 = oil bearing 

G4 = viscous damper 

P = pick up coil 

F = motor sta.tor 

V = vacuum chamber 

Fig. 6. Drawing of Assembled Electric Ultracentrifuge in 1940. 

29 
30 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAf'h 

Fig. 7. Beams' Machinist, P. Sommer, with Early Version of Magnetically Supported Ultracentrifuge 

In 1968, the National Medal of Science was presented to Dr. Beams by President Lyndon 

Johnson for his gas centrifuge work. Also, the Atomic Energy Commission in 1972 cited Dr. 

Beams for his outstanding contributions to the U. S. atomic energy program. 

MAGNETIC SUSPENSION FOR mGH CENTRIFUGAL FIELDS 

Dr. Beams' interest in centrifugal effects continued after World War ll. Small steel balls, 

in this case 1/32 of an inch, were spun up to 386,000 revolutions per second [7]. In other 

works [8,9,10,11], he reported small balls rotating at speeds up to 800,000 revolutions per 

second. He and his co-workers filed for a patent on this device [12]. The electronic circuitry 

was constructed of vacuum tubes. He later received another patent with a rotational speed of 

4,000,000 revolutions per second. 

It may be noted that this work was not without risk of personal injury. During one experiment, 

the metal ball came out of support while spinning at an extremely high speed. The ball went 

through a railroad tie that was employed as the stationary barrier and through Dr. Beams' neck, 

just missing the carotid artery. He might easily have been killed. However, he was treated at 

the local hospital and was back at work in a few days. 
CONCLUSIONS 

While many others had speculated on the development of magnetic suspension of rotating 

devices, Dr. Beams was the first researcher to develop a practical magnetic suspension system. 

Work in his laboratory on magnetic bearings went on for many years. The later works of Dr. 

Beams and the laboratory that he founded in the Physics Department at the University of Virginia 

are not discussed in this brief paper. 

On the morning of July 23, 1977, Dr. Beams had an idea and described to his wife, in great 

detail, how to construct what he felt would be the best gyroscope in the world. After dinner, he 

discussed current research with colleagues. At eight o'clock, he died. He lived a very full life. 

Currently, magnetic suspension research continues at the University of Virginia in the Physics 

Department under Beams' colleague, Rogers Ritter. In the Nuclear Engineering and Engineering 

Physics Department, there is a strong program on magnetically supported medical devices, 

conducted by former student George Gilles. Also, the Mechanical and Aerospace Engineering 

Department has continued the work on magnetic bearings for rotating machines. This research 

program has become the Center for Magnetic Bearings. 

For his pioneering work in the field, Dr. Jesse W. Beams deserves to be called the "Father 

of Magnetic Bearings." 

BIOGRAPHY 

In Jesse Beams was born in . He obtained a Ph. D. from the 

Department of Physics at the University of Virginia in 1925. After three years at Yale University, 

he returned to the University of Virginia as an Associate Professor of Physics. He became a 

Professor in 1930, Chairman of the Physics Department in 1948, and Smith Professor of Physics 

in 1953. He retired as Professor Emeritus in 1969 and continued to work in his laboratory at 

the University until his death on July 23, 1977. 

Professor Beams was a kind and gentle man, always willing to discuss technical questions with 

anyone. Many of his experiments required intricate machining. He listened to his machinists' 

suggestions and often listed them as co-authors. He authored or co-authored 246 articles. 

The bibliographical records on Dr. Beams in the University library indicate 2.75 meters of 

information, including 14 patents. 

Beams first worked on the timing of the emission of light by atoms excited by electric 

discharge in a device called a Kerr cell. He made improvements on a rapidly rotating mirror 

employed to detect the light. His first paper on this subject appeared in 1930. 

REFERENCES 

1. "Jesse Wakefield Beams," Obituary, 1977. 

2. Leyh, C. H., "A Brief History for the Precision Measurement Group at the University 

of Virginia," Proceedings of 1983 Symposium on Precision Measurement and Gravity 

Experiment, Taipei, China, 1983. 

3. Holmes, F. T., "Axial Magnetic Suspensions," Review of Scientific Instruments, VoL 8, 

Nov. 1937, pp. 444 447. 

4. Holmes, F. T. and Beams, J. W., "Frictional Torque of an Axial Magnetic Suspension," 

Nature, VoL 140, July 3, 1937, pp. 30-31. 

5. Beams, J. W., and Black, S. A., "Electrically-Driven Magnetically-Supported VacuumType Ultracentrifuge," VoL 10, Feb. 1939, pp. 59--63. 

31 
6. Skarstrom, C. and Beams, J. W., "The Electrically·Driven Magnetically Supported 

Vacuum Type Ultracentrifuge," Review of Scientific Instruments, Vol. 11, Dec. 1940, 

pp. 398-403. 

7. Beams, J. W., Young, J. L., and Moore, J. W., "The Production of High Centrifugal 

. Fields," Journal of Applied Physics, Vol. 17, Nov. 1946, pp. 886-890. 

8. Beams, J. W., "Experiments With High Speed Rotors," Science, Vol. 107, 1948, p. 646. 

9. Dillon, J. F., and Beams, J. W., "An Improved Axial Magnetic Suspension," Physics 

Review, Vol. 74, 1948, p. 117. 

10. Beams, J. W., "Magnetic Suspension Balance," Physics Review, No. 78. 1950, p. 471. 

11. Beams, J. W., "Magnetic Suspension for Small Rotors," Review of Scientific Instruments, 

Vol. 21, No.2, 1950, pp. 182-184. 

12. Beams, J. W., Kinsey, E. E., and Snoddy, L. E., "Magnetically Supported Rotating 

Bodies," U.S. Patent No. 2,691,306, 1951. 

32 
N92-27724 

LARGE-GAP MAGNETIC SUSPENSION SYSTEMS 

Colin P. Britcher 

Department of Mechanical Engineering and Mechanics, Old Dominion University 

33 
SUMMARY 

This paper will address the classification of magnetic suspension devices into small-gap and large-gap 

categories. The relative problems of position sensing, control systems, power supplies, electromagnets and magnetic 

field or force analysis will be discussed. The similarity of all systems from a controls standpoint will be qualified. 

Some applications where "large-gap" technology is being applied to systems with a physically small air-gap will be 

mentioned. Finally, the applicability of some other suspension approaches, such as electrodynamic or 

superconducting, will be addressed briefly. 

INTRODUCTION 

The majority of research concerning magnetic suspension devices has concentrated on systems and 

applications where the air-gap between suspended object and suspension elements has been relatively small. This 

has been especially true in recent years, with the strong growth of interest in, and application of, magnetic bearings. 

In turn, the predominant technical approach used to date for bearings has been the feedback-controlled 

electromagnet/ferromagnetic suspended element type. There are applications, however, where large air-gaps are 

essential; perhaps the longest-standing of these being Magnetic Suspension and Balance Systems for wind-tunnel 

models (MSBS) and magnetically-levitated trains (Maglev), both illustrated in Figure 1. Other applications are now 

emerging where large-gap systems are of interest or where the design approaches used in large-gap systems are 

applicable. Some examples of these applications are multi-degree-of-freedom microgravity vibration isolation and 

large-angle space-based gimballing and pointing systems, illustrated in Figure 2. From a controls standpoint, the 

large- and small-gap systems prove to be quite similar, but in most other respects can be dramatically different. 

FIELDS AND FORCES 

This section will start with some simple analysis of small-gap systems, leading to consideration of largergaps, highlighting some of the important trends involved. Small-gap systems are frequently designed, at least in the 

preliminary stages, using magnetic circuit theory. A sketch of a representative two-pole suspension system is shown 

in Figure 3. The important features are the uniform air-gap, and the presence of iron yokes and/or back-iron. 

Examining the magnetic circuit, it is clear that the reluctance of the circuit is dominated by the air-gap, which is, 

PRECED!NG PAGE BLANK NOT FILM£D 35 
in turn, the parameter being controlled. Using standard formulations, chiefly: 

- it is easily shown that: 

F B2 

A - 2 flO 

flo A (NI)2 

F= 2 

4h 

- (1) 

- (2) 

A fringing factor is usually introduced to account for flux non-uniformity but is not necessary here. The total flux 

linking the coil is : 

flo (NI) A 1 

<P= 2h <XIi" 

The stored energy in the system can be calculated from : 

B2 

E = -2- * Vol 

flo 

- (3) 

- (4) 

- where this expression is appropriate for linear material characteristics and is only large in the air region for this 

problem. The energy/force ratio is important and is found to be (see also Figure 4) : 

- (5) 

It is now argued that this is a crucial factor distinguishing small-gap and large-gap systems. Large-gap systems 

involve considerable stored energy, tending to lead to large, highly stressed electromagnets and large, expensive 

power supplies. Typically, the natural frequencies of the suspension system will tend to be reduced, principally due 

to the associated high inductance of the electromagnets, since: 

- (6) 

Continuing with classical analysis and following established magnetic bearing terminology, the position and current 

stiffnesses can be found by differentiation of equation (2) : 

Kx = _ 0::)0 = _ flo ; ~~I)2 - (7) 

OF) flo A N2 I 

KI = m 0 = 2 h2 - (8) 

It is seen that the position stiffness is completely determined by the geometric configuration and is independent of 

the coil design. The current stiffness of course depends on the choice of the number of turns in the coil. Additional 

practical details include the effective magnetic "pressure" in the air-gap, found to be approximately 1 atmosphere 

36 
for B=O.5T, using (1). It is clear from (1-4) that the efficient transmission of large forces requires a small air-gap 

and large pole face area. It is also clear that this simple suspension configuration exhibits severe non-linearities with 

respect to gap and current. 

In large-gap systems it is a practical impossibility to generate uniform flux penetrating the suspended 

object. The simple formulae shown above are therefore not applicable, though several options are available. First, it 

is recognized that (1) is merely the normal component of Maxwell stress. For large-gap systems, the Maxwell 

stresses on arbitrary surfaces completely enclosing the suspended object can be integrated to yield the total force 

(and moment) on the object [1], but normal and shear stresses must both be considered: 

- 1 - F = Tl J T ... dS 

'-0 S IJ 

where T .. = IJ - (8) 

2 

The terms on the leading diagonal of the stress tensor, Tij are recognized as constituting the 2

BJ.lo term which in 

turn leads to the form of (1). Alternatively one may use: 

F = J ( M . V' ) B dV 

V 

and T = f( M x B) dV 

V 

- (9) 

The latter forms may be quite convenient for permanent magnet suspended elements and are usable, though 

inconvenient, for soft-iron elements. In this application, B in equation 9 may be taken as the "external" or applied 

field; the field that would exist if the magnetization of the suspended element were removed from the problem. This 

is easily calculated in the case of permanent magnet suspended elements, slightly more difficult for soft-iron, 

provided that there is negligable magnetization of suspension electromagnet cores by the suspended element. This is 

only likely to be the case with large-gap systems. 

It should be clear that field gradients are the key factors in the production of forces, either directly through 

the V' B term in (9) or indirectly via integration over the closed surface in (8). It can be noted that a gradient 

exists in Figure 1, due to the reversal in sign of flux relative to the suspended object. That is, entering on one side 

and leaving on the other, although the magnitude of the flux is relatively uniform in the region of each pole face. 

No simple formula exists for "position stiffness", due to the presence of numerous field and field gradient 

terms. Previous work [2,3] has resulted in linearized models for suspended permanent magnet elements under 

certain restrictive conditions, from which current and position stiffnesses can be found. As a point of interest, if the 

suspended object has a permanent magnet core then the current stiffness can be deduced directly: 

37 
SOME ASPECTS of the TECHNICAL DEVELOPMENT of WIND TUNNEL MSBSs 

With the local air-gap as the controlled variable in small-gap systems, each suspension station becomes a 

quasi-one-degree-of-freedom subsystem. With a rotor, for example, a minimum of five bearings would be needed for 

full control, typically a vertical and horizontal bearing at each end of the shaft, plus a single axial "'thrust" bearing. 

This arrangement facilitates relatively straightforward decoupling between degrees-of-freedom. Extra complications 

do arise due to geometrical or mass asymmetries and due to structural flexibility, and are the subject of 

considerable research. Many microgravity or vibration isolation systems have been designed with this "built-in" 

decoupling. 

The earliest, widespread application of large-gap suspension was to wind tunnel MSBSs. There is evidence 

that the early thinking with MSBSs was consistent with the point actuator viewpoint. For instance see Figure 5 

[4,5], where the suspension systems are seen to resemble a bearing supported shaft. Further, many early MSBS 

control systems were configured so that the current in each electromagnet was controlled on the basis of the 

distance of the model from that electromagnet, i.e. the local airgap, just as in the magnetic bearing case. As the 

complexity of systems increased, and as the geometry of the suspended object became less like that of a slender 

shaft, this approach failed. MSBSs developed in the early to mid-1960s were generally based on "coupled" control 

systems, that is sensors were placed wherever convenient, signals were mixed to sensible degrees-of-freedom (usually 

the principal axes of the suspended element) with a distribution network to allocate control demand among suitable 

electromagnets. An alternative interpretation is a double coordinate transformation, from sensor axes to object 

axes, then from suspended object axes to electromagnet axes. This inevitably leads to the development of an 

entirely different set of governing equations, based directly on field and field gradient components in space, rather 

than point forces, as discussed earlier. 

The next phase of development of design approaches is represented by the MIT 6-inch system, illustrated in 

Figure 6, where considerable efforts were made to ensure that separate field and field gradient components were 

generated independently, and also with good spatial uniformity, by separate sets of electromagnets [6]. Each of 

these sets was then wired in series and fed from an individual power supply. This again provides for controller 

decoupling, albeit in suspended object axes rather than MSBS axes, and considerably simplifies the force 

calibration, but has some disadvantages. Notably the maximum force capability of the electromagnet assembly 

cannot be realised, since individual electromagnets cannot be run up to their respective current limits 

independently, as shown in Figure 7. 

Contemporary thinking is therefore to distribute an array of general-purpose electromagnets around the 

wind tunnel test section and operate each independently. This will provide the maximum possible force and 

moment capability at all attitudes, but can lead to complex calibration procedures; still a subject of considerable 

research [7]. 

38 
SCALING of MAGNETIC SUSPENSION SYSTEMS 

The subject of scaling laws has been addressed previously [8,9]. It is found that in many systems, where a 

limit to the maximum field intensity exists and is important (such as a superconductor critical field, permanent 

magnet coercive field and so on), scale such that the magnetic force varies as length squared, rather than as the 

volume of magnetic material as is often assumed. Relevant to previous discussions, the system stored energy will 

then scale as length cubed, leading to the expected result -

Stored energy I 

Force Max. field limited 

L3 ex: L 2 ex: L ex: Air-gap 

CONTROL and RELATED PROBLEMS 

In large-gap systems the number of "actuators" (controlled currents) frequently exceeds the number of 

degrees-of-freedom to be controlled. This results in the equilibrium point (and the control problem in general) being 

underdetermined, i.e. an infinite set of solutions for suspension currents, more particularly current distribution, 

exist. This poses two problems, determination of a suitable current distribution to generate the required forces and 

torques, and the determination of the maximum force and moment capability, such as where hard electromagnet 

current limits exist. 

The first problem can be overcome by physical argument, as used in Reference 7, where a systematic 

scheme was developed for "allocating" demand ina hierarchical. manner, such that the most effective electromagnets 

took the largest load. Alternatively, matrix theory may be brought to bear in the following manner. If the forces 

and moments generated by the electromagnet array can be written in the linear form shown: 

Ty 

KZl KZ2 KZ3 KZ4 KZ5 

T KYI z 

Fx Kxxl - (3) 

Fy KXYI 

Fz 

KxzI 

- otherwise written as : 

A I = F 

- then the problem is to find a pseudoinverse A-I that satisfies sensible physical constraints. The classical 

pseudoinverse (Moore-Penrose) yields a solution such that the 2-Norm of the solution curren't vector is minimized. 

39 
This corresponds to the Illllllmum sum of squares of electromagnet currents, in other words the minimum power 

solution for conventionally conducting electromagnets, also the minimum stored energy solution in all cases, though 

perhaps requiring some scaling in the case of different sized electromagnets. An alternative inverse will give the 

minimum oo-Norm, corresponding to the maximum value of an individual current being a minimum, and by 

inference to the maximum force and moment capability. This is more appropriate in the case of superconducting 

electromagnets, or where hard current limits are important. A residual problem is that this latter solution has been 

shown to exhibit discontinuities as a function of some variable, such as suspended object orientation [9]. 

POSITION (or RATE) SENSING 

A wide variety of sensing systems have been used for both small-gap and large-gap systems. Some, chiefly 

optical systems, are usable at all air-gaps, some are relatively specific to one size gap or the other. For example, 

commercial capacitive or inductive sensors are only suitable for small gaps. Rather than attempt a comprehensive 

survey of all techniques, a few technical observations relevant to large-gap systems will be made. 

The most common approach used has been the analog optical obscuration approach. The X-ray system 

used in the AEDC MSBS was conceptually similar [5]. Although this approach is capable of picking off a single 

motion from one point of a suspended object, multi-degree-of-freedom systems become quite complex (Figure 8), 

extremely sensitive to detail geometry of the suspended object and prone to couplings between degrees-of-freedom. 

Nevertheless, the fact that high sensitivity can be achieved easily is a strong positive factor, and the approach 

remains the first choice for many experimental systems. 

A significant refinement is the use of linear scanning photo-diode arrays as the light sensors. This greatly 

improves system linearity, repeatability and environmental tolerance, but does not overcome other objections 

mentioned above [10]. The way forward appears to be camera-based sensing, where some form of target is 

monitored by an array of cameras (presumably solid-state), illustrated in Figure 9. Existing camera technology is 

already adequate for low-to-medium frame rates, though the image processing requirements are formidable. 

Processing hardware capable of useful data rates is only just becoming available [11]. 

OTHER SUSPENSION APPROACHES 

This paper has concentrated on the feedback-controlled electromagnet/ferromagnetic suspended element 

type of system. Numerous alternatives exist, including A.C. or eddy current methods, many variations 

incorporating diamagnetic material, or permanent magnets in repulsion. More comprehensive treatment and 

discussion can be found in Reference 12. Many of the alternative approaches could be applied to large-gap systems. 

However, in the context of the anticipated applications, all alternatives appear to have serious shortcomings. 

40 
Notably, in applications involving pointing and manipulation, set-point control is needed, which open-loop 

suspensions cannot easily provide. In many other applications, such as wind tunnel MSBSs or certain types of 

vibration isolation, heavy damping of suspended element motion is required. With the stored energy of all types of 

suspension system rising with increasing air-gap, it is not clear how good motion damping, implying dissipation of 

large quantities of energy, can be arranged. Further research and development will improve matters, as is clearly 

the case with the ElectroDynamic Suspension system (EDS), for Maglev trains. This system [13] is, by all resonable 

measures, a large-gap suspension. That is, air-gap size is not small with respect to system scale. 

A FEW FINAL THOUGHTS 

The fringing fields generated by large-gap suspension systems are sometimes cited as a serious obstacle to 

their use in certain applications, perhaps particularly spaced-based applications. The production of powerful fields 

(possibly time-varying) in the region surrounding the suspension system is certainly a problem, but can be 

overstated. 

It is noted here that since the field sources are essentially dipoles (current-loops or permanent magnets), the 

magnetic field strength in the far-field will decay at least as the cube of distance. Further, since the net strength of 

suspension system dipoles is often zero, the decay can be even faster, and the resultant force and torque in uniform 

external field (such as the earth's field) will be zero. 

ACKNOWLEDGEMENTS 

This work was partially supported by NASA Grant NAG-I-1056, Technical Monitor Nelson J. Groom. 

REFERENCES 

1. Lowther, D.A.; Silvester, P.P.: Computer-Aided Design in Magnetics. Springer-Verlag. 

2. Groom, N.J.: Analytical Model of a Five Degree-of-Freedom Magnetic Suspension and Positioning 

System. NASA TM-I00671, March 1989. 

3. Groom, N.J.; Britcher, C.P.: Stability Considerations for Magnetic Suspension Systems Using 

Electromagnets Mounted in a Planar Array. NASA CP-I0066, March 1991. 

4. Moreau, R.: Use of Magnetic Suspension in O.N.E.R.A. Wind Tunnel. In ARL Symposium on 

Magnetic Wind Tunnel Model Suspension and Balance Systems. Dayton, OH, 1966. ARL-66 

-0135, July 1966. 

41 
5. Crain, C.D.; Brown, M.D.; Cortner, A.H.: Design and Initial Calibration of a Magnetic Suspension 

System for Wind Tunnel Models. AEDC-TR-65-187, September 1965. (In abbreviated form in 

ARL Symposium on Magnetic Wind Tunnel Model Suspension and Balance Systems. Dayton, 

OH, 1966. ARL-66-0135, July 1966) 

6. Stephens, T.: Design, Construction and Evaluation of a Magnetic Suspension and Balance System 

for Wind Tunnels. MIT-TR-136, NASA CR-66903, November 1969. 

7. Parker, D.H.: Techniques for Extreme Attitude Suspension of a Wind Tunnel Model in a Magnetic 

Suspension and Balance System. NASA CR-181895, October 1989. 

8. Zapata, R.N.: Magnetic Suspension for Large-Scale Aerodynamic Testing. In Wind Tunnel Design and 

Testing Techniques, AGARD CP-174, March 1976. 

9. Britcher, C.P.: Some Aspects of Wind Tunnel Magnetic Suspension Systems with Special 

Application at Large Physical Scales. NASA CR-172154, September 1983. 

10. Schott, T.D.; Tcheng, P.: The New Electro-Optical Displacement Measuring System for the 13-inch 

MSBS. In NASA Workshop on Aerospace Applications of Magnetic Suspension Technology, 

NASA CP-10066, March 1991. 

11. Welch, S.S.; Clemmons, J.I.; The Optical Position Measurement System for a Large-Gap 

Suspension System. In NASA Workshop on Aerospace Applications of Magnetic Suspension 

Technology, NASA CP-10066, March 1991. 

12. Jayawant, B.V.: Electromagnetic Levitation and Suspension Techniques. Edward Arnold, 1981. 

13. Society of Automotive Engineers. Magnetic Levitation Technology and Transportation Strategies. SAE SP-834, 

August 1991. 

42 
Figure 1 - Established Applications for Large-Gap Magneti c Suspensions 

- Maglev and wind tunnel MSBSs 

43 
Shuttle Orbiter Acceleration Environment 

10 -· ,r----------------------------------------------------------, 

'-- "-"- RCS Thcu"ers 

103 

Frequency, Hz 

Figure 2 - Potential Applications for La rge-Gap Magnetic Suspensions 

- low fr equency mi crogravity isolation, space-based pointing or payload manipulation 

44 
NI 

--........ 

'\ 

\ \ 

A 

I +x r-~--~I------------------r---+JI \ \,------) / ~ 

" ----- / --

Figure 3 - Schematic Diagram of a 2-Pole Small-Gap Suspension 

Energy (JjN) Force 

# ___ ~ Iron energy 

Fringing 

h (m) 

Figure 4 - Energy/Force Relation for a 2-Pole Small-Gap Suspension 

45 
Airflow 

46 

ONERA M5BS 

Suspension Electromagnets 

.... --Mlrror 

""'r'T------r-:----I......-- Model A \ ~ l~hl Source and Photocell 

Gravity \\ 

S3 \:\ 51 

AEDC MSBS 

Figure 5 - Design Details of Early MSBSs 

- ONERA and AEDC 
~ 

~----

...-' 

/

MAGNITUDE OF 

H DUE TD+lIIMAGNITUDE I OF H , I 

' .... ..... - - I "J~_,__ -I I /'~~ 

"MAGNITUDE OF 

HI DUE TO+I .. 

,/ "< '> "DRAG" WINDINGS 

,~ 1/ tt tttt t:,/!Wft"rtttitt'tt -lI"f---'---

-~NITUDE 

y - aXi 

+ , .. oail 

MAGNETIC FLUX PATH IN 

FORWARD COIL ASSEMBLY 

DUE TO LIFT CURRENT,I .. 

z-axis 

~ ~:G~, 

AXIAL PROFILE OF H, DUE TO 1 .. , ON AXIS 

SIDE a LIFT FORCE 

SUBASSEMBLIES 

WIND 

AXIS .. I I II I 

X- axis 

Figure 6 - Magnetic Configuration of the MIT 6-inch MSBS 
48 

Southampton MSBS 

TRANSLATOR 

@ :; ...... ~K-----I Allocate demand _ ) among available 

electromagnets 

Multiple electrom:;.nety 

and power SUPPIi/ 

Force and 

moment 

demonds 

STABILIZATION pMOdO' Usually series 

leod-Iag 

Multiple 

position 

f----tro- and 

attitude 

sensors 

PRE-FILTER 

I--__ ~ ___ ./ Decouple to 

model degrees 

of freedom 

Position and 

attitude 

information 

Operator 

demonds 

Figure 7 - Example of Contemporary Thinking Regarding MSBS Configuratio~ 
Horizontal (beams) laser 

AEDCjNASA LaRC 

13-inch MSBS 

Figure 8 - Layout of Optical Position Sensing System for NASA 13-inch MSBS 

Diffuse Illumination of Targets 

CID Cameras 

(14) 

Target Indentifier 

Fine Tracking Target 

Figure 9 - Conceptual Layout of Advanced Optical Position Sensing System 

/ 

49 
Session 2 

BEARINGS 1 

Chairman - Paul E. Allaire 

University of Virginia 

PR~CEO!I\iG flAGE BLAm{ NOT FILMED 

51 
· , 

N92-27725 

MAGNETIC BEARINGS: A KEY TECHNOLOGY 

FOR ADVANCED ROCKET ENGINES? 

J.Ph. Girault 

Societe Europeenne de Propulsion 

Vernon - France 

PRECEDING PAGE BlAr~K NOT Fl!..M!D 

53 
SUMMARY 

For several years, Active Magnetic Bearings CAM B) have demonstrated their capabilities in 

many fields, from industrial compressors to control wheel suspension for spacecrafts. Despite 

this broad area, no significant advance has been observed in rocket propulsion 

turbomachinery, where size, efficiency and cost are crucial design criteria. 

To this respect, Societe Europeenne de Propulsion CSEP) has funded for several years 

significant efforts to delineate the advantages and drawbacks of AMB applied to rocket 

propulsion systems. Objectives of this work, relative technological basis and improvements are 

described in this paper, illustrated' by advanced turbopump layouts. 

Profiting from the advantages of compact design in cryogenic environment, the designs show 

considerable improvements in engine life, performances and reliability. However, these 

conclusions should still be tempered by high recurrent costs, mainly due to the space-rated 

electronics. Development work focused on this point and evolution of electronics show the 

possibility to decrease production costs by an order of magnitude. 

PRECEDING PAGE BLANK NOT FilMED 55 
INTRODUCTION 

Every designer in Rotating Turbomachinery has already encountered difficulties in 

obtaining proper compromise between the machine specifications and the actual bearing 

capabilities. This is particularly true for Rocket Engine Turbopump (TIP) designs, where size, 

efficiency and costs are crucial design aspects, resulting in complex turbomachines with very 

high specific power (about 100 kW/kg for high efficiency engines) and rotational speed (up to 

120,000 rpm), with a life limited to a few hours. 

Thus the bearings appear to be key components in successful design, as well as imposing 

major limitations to further improvements in engine performance and life. 

The figure 1 illustrates part of this assertion, reporting current and foreseen values for the 

bearing D.N. product, where D is the shaft diameter (in mm), and N the rotational speed (in 

rpm). It is clear that significant increase in one of these parameters, as dictated by advanced 

designs to improve TIP efficiencies and/or dynamic behaviour, exceed the rolling element 

bearing capabilities and call for innovative solutions. 

Among other aspects, it is well-known that the use of on-board cryogenic propellants for 

cooling these bearings does not offer sufficient viscosity for lubrication, and consequently 

limits strongly the service life. 

300 

250 • SSME (LH2) V 2000 kN (LOX) 

o SSME (LOX) • 40 kN (LH2) 

• HM7B (LH2) • 70 kN (LH2) 

E 200 .Vulcain (LH2) A 70 kN (LOX) 

S 

I 

E 150 .!! 

0 

:: 

6! • 

III 100 

0 

50 

'~ ----B-

~ • . " 

0 ----'----< 

0 50000 100000 150000 200000 250000 

-+- 1 E6 -- 3 E6 -& 6 E6 

Rot'ltional Speed (rpm) 

Figure 1 : Bearing D.N. Values for various TIP Designs 

56 
Consequently, the bearings, highly stressed by large static and dynamic loads, require 

careful analysis during the project, contribute predominantly to the failure mode allocations 

for the TIP, as illustrated figure 2 for a typical liquid hydrogen (LH2) turbopump, and involve 

expensive development tests and maintenance programs. 

Following from this, rocket engine manufacturers have been studying for about two decades 

the capabilities and drawbacks of alternative bearings without any surface contact, i.e. fluid 

film bearing and magnetic bearings. 

The former technique (fluid bearing) has been studied extensively for its noticeable 

advantages, with various practical concepts (hydrodynamic, hydrostatic and hybrid bearings) 

to minimize inherent drawbacks, such as rubbing in transients, complex dynamic behaviour 

and tight clearances. Actual turbopumptes~ have been performed (refs. 1, 2, 3) with positive 

results, but the few applications to space propulsion are biased toward storable propellants 

and low thrust engines (ref. 4). 

Space applications of the second technique (mag bearing) have mainly concerned spacecraft 

attitude control (ref. 5, 6), with at least one degree of freedom (DOF) actively controlled. 

Despite numerous applications in industrial compressors and a growing interest in aerospace 

propulsion (refs. 7, 8), no practical work has been observed, although studies in jet engines 

are emerging. 

In this field, this paper presents the objectives one can expect to meet by implementing 

such technology in aerospace propUlsion together with the required analysis tools and 

technological basis for successful design, as the results of studies funded by Societe 

Europeenne de Propulsion (SEP) since 1986, and team work with Rocketdyne, Division of 

Rockwell International Corporation (RD) (Ref 9). 

Other (25,0%) 

Seals (20,0%) 

Bearings (35,0%) 

Pump (5,0%) 

Turbine (15,0%) 

Figure 2 : Faifure Mode Allocation for the VULCAIN LH2 Turbopump 

57 
TIP DESIGN & FUNCTIONAL FEATURES 

Key features and corresponding TIP limitations can be pointed out on the figure 3, showing 

the strong interaction between the TIP design and the bearings specifications, as well as the 

inherent iterative process to finalize the TIP architecture. 

This is particularly true by using Active Magnetic Bearings (AMB), where the link between 

the shaft (i.e. the bearings rotors) and the TIP housing (Le. the bearings stator) is represented 

by the transfer functions, themselves function of the bearing specifications (speed, loads). The 

resulting bearing and associated controller change in turn the shaft assembly, stiffnesses and 

dampings, which leads to some modifications to the TIP design, thus changing the bearing 

specifications, until obtention of the final compromise. 

Such TIP designs are illustrated in figure 4, reporting LH2 TIP layouts for a 40 kN thmst 

LOXJLH2 expander cycle rocket engine, and LOX TIP layouts for a 2000 kN thrust gas 

generator cycle engine. Main features of these designs and associated magnetic bearings are 

reported in table 1. 

LIFE 

i BEARING 

58 

---C> 

--c. 

~ 

NUMERICAL ANALYSIS 

DESIGN TO COST CRITERIA 

DESIGN ACTIVmes 

& TECHNOLOGIES 

c:::J- -

Figure 3 : TIP Design Methodology 

• 8 

CONTROLLER 
--T~~'--

,-_~_II "" j iii 

t ~--Jr-\--,I~ -~ i ! 

U'~ ! "'~ I ~~.J I . 

,,,I ~ i v----- ~-

2000 kN ENGINE 40 kN ENGINE 

Figure 4. Advanced TIP Designs with AMB 

59 
60 

TABLE 1 : MAIN FEATURE) OF ADVANCED ROCKET ENGINE TIP 

AND ASSOCIATED MAGNETIC BEARINGS (AMB) 

ENGINE THRUST - T/P 40 kN/LH2 60 kN/LH2 2000 kN/LOX 

TiP CHARACTERISTICS 

· Pressure rise (MPa) 24 11 28 

· Shaft Power (kW) 670 610 17.000 · Rotor Speed (rpm) 190.000 60.000 30.000 · Overall Length (m) 0.25 0.35 1.0 

· Weight (kg) 4.8 28 260 

AMB CHARACTERISTICS 

· Load (N) (max) 65 475 4.600 

· Stator 0.0. (mm) 60 75 210 

· Shaft 0.0. (mm) 12 25 91 

· Airgap (mm) 0.2 0.2 0.1.j· 

· Materials (rotor) Fe-Si Fe-Si Fe-Si 

or Fe-Co or Fe-Co 

· Materials (stator) Fe-Co Fe-Co Fe-Co 

· Weight (kg) 0.6 - 30 (w/axial) · Power consumption (W) 500 400 5.000 
The use of AMB in these Advanced TIP designs resul~in high rotational speed for optimal 

pump efficiencies and reduced TIP size and weight. Thrust modulation and dynamic control is 

also facilitated by high damping over a large operating speed range, including the first two or 

three critical speeds. Unbalance requirements can be also relaxed to some extent to simplify 

assembly procedures and minimize production costs. Finally. the AMB Control System means 

the existence of Health and Control Monitoring (HCM) integrated in the TIP at the earliest 

steps of the design, making the development easier, safer and less expensive. 

The results have been substantiated by comparison with alternative TIP designs fitted with 

fluid film bearings andlor rolling element bearings. This has shown important simpliflcation of 

the fuel (Lf.[2) TIP originally designed with ball bearings (e.g. 2 stages pump instead of 4 

stages with ball bearings, and inboard bearing with overhanging turbine disc) but minor or no 

significant advantage for the oxidiser (LOX) TIP. For this latter, the viscous losses at the 

bearings increase drastically,as illustrated in figure 4. The high fluid density (about 16 times 

more for the LOX than for the LH2) leads also to moderate pump tip speeds, thus reducing 

interest in high peripheral speed at the AMB airgap. compared to LH2 cases. 

Thanks to the cryogenic environment (between 40 and 100 K) in both cases, the bearing 

stator size can be reduced by more than 2, compared to ambient temperature applications, 

thus improving bearing integration. 

Figure 4 : Normalizes viscous losses as a function of 

speed at the airgap, fluid and bearing size 

61 
Trade-off between the AMB features and the clearances required along the shaft (with 

provision for misalignment and unbalance responses) generally results in a 0.2 mm 

(200 I'm) airgap for engine thrust up to about 100 kN. This is 5 to 10 times more than the 

clearance required for fluid film bearings, thus facilitating inactive long-term storage in space 

and misalignment tolerance. 

On the other hand, the small LH2 flowrate required to chill down the bearing and maintain 

cryogenic temperatures improves the pump efficiency and reduces shaft power losses. leading 

to LH2 saving. Numerical values as reported (table 2)iIIustrate this point. For cumulated duty 

cycles in space, long-term storage and/or long duration propelled missions, this allows 

considerable LH2 tank size and mass reduction. For a gas generator (GG) cycle engine, in this 

thrust range, this will save between 30 and 50 kg of LH2 per hour. For expander cycle engine, 

this allows slight increase of the chamber pressure, increasing the engine specific impulse. 

TECHNOLOGICAL BASIS 

In parallel with design studies, technological effort was aimed at validating the bearing 

design and improving the current state-of-the-art. 

This effort has been oriented along two axis: the bearing materials and the controller size 

reduction. 

Bearing materials 

Earlier work has been reported in 1988 (ref. 8), and the results are here completed. They 

are mainly driven by cryogenic aspects, compatibility with liquid and gaseous oxygen and 

hydrogen, and improvements of mechanical and magnetic characteristics. 

Silicon-iron rotor laminations have been the traditional choice for industrial bearings. This 

cheaper material offers good mechanical properties in cryogenic conditions: a yield stress 

higher than 500 MPa, high fatigue limit (better than 120 MPa at 107 cycles), together with 

reasonable flux density (up to 1.5 Tesla). 

. Moreover, a GH2 brittleness experimental study, performed with disc burst tests as depicted, 

figl4re 5, have shown classical behaviour, with disappearance of GH2 brittleness in cryogenic 

conditions (fig. 6). 

62 

Standard tests to check compatibility with LOX or GOX (bomb test, adiabatic 

compressions) confirm suitability for use in TIP environment. 

Accordingly. most of the T/P designs briefly presented here have used iron/silicon alloys for 

the rotor laminations and conventional iron/colbalt alloys for the stator laminations. 

Nevertheless, to further improve future designs, new iron-cobalt alloys have been carefully 

studied. This kind of alloy traditionally exhibits very high flux density (up to 2.2 Tesla) 

together with poor mechanical properties (low yield stress, limited to 200 MPa and excessive 

brittleness). However, metallurgical progress has renewed interest in such alloys, exhibiting 
TABLE 2 : COMPARISON BETWEEN MAGNETIC AND HYDROSTATIC 

BEARINGS FOR A 40 kN THRUST ENGINE LH2 TIP 

MAGNETIC HYDROSTATIC 

Flow rate (g/s) 5 30 

Decrease in 1 % 5 % 

pump efficiency 

Viscous losses (W) 450 800 (shaft centered,E 

at the bearing 2500 (E = 0,5) 

Load capacity (N) 65 800 (at E = 0.5) 

LH2 saving + 30 kg/hour 

= O) 

63 
GH2 EMBRITTLEMENT ON FeSi SAMPLES 

,, --"""'" ". S' ,e .. /' 

• 'S f' " 

:::;. 

,< '0' ~ .. 

- L .. t!f rl.l~ ' 

2- ---

.:.. 

6 

• 'tf 

-,I ! , 

- ! Q) 

~ / 0 / I u 

- / I 0' 

0 • i 

-------- u.. 

00 100 - 200 30r 400 

Disk Tempera ture (V) 

• V = 0, 1 MPaimn ' V = 10 MPa/mn 

Ce document est la propnele de la SEP. II ne peut ~t e reprodUl1 au communique sans son aulonsatlon prealable et ecrlh 

Figure 5 : Disc burst test for GH2 brittleness study 

2 ~ 

Q) 

5 

~ 

GJ 

6 

'--" 

'+- + '+-

Q) 

0 • 

u 

OJ 

0 

'---

l.L 

00 lOO 200 300 400 

Disk Temperature (K) 

• v - 0 , l MPa /mn + V = lO MPa / mn 

Figure 6 : Results of GH2 brittleness studies on Fe-Si laminations 

64 
more than 900 MPa for the yield stress in cryogenic conditions, together with high flux density 

(up to 2 Tesla). Hysteresis losses are higher than iron/silicon alloys at low frequencies and/or 

low magnetic field, but similar for higher values. 

This alloy can then reduce by 30 % to 50 % the bearing length, or increase in the same 

proportions the load capacity, providing the AMB with a higher load factor (up to 

190 N/cm2). 

Regarding coil wire materials and insulations, tests performed with copper and copperberyllium alloys, as well as fluorine polymers, has allowed final material selection, wire 

diameters decrease with thin insulation (less than 50 I'm) and production optimisation. 

Controller 

A significant step toward a flightweight controller (including power amplifiers and control 

PC boards) has been made by producing a space-rated power amplifier, whose electrical 

characteristics meet Upper Stage Engine LH2 Turbopump requirements. 

This program has been focused on the power amplifier size reduction, due to the fact that 

they represent about 80 % of the controller size and weight, and almost 100 % of the power 

consumption of the board. Accordingly, joint effort between S2M, subsidiary of SEP and SEP 

personnel involved in space mechanism electronics has been funded to design, fabricate and 

test space-rated Pulse Width Modulation (PWM) power amplifiers. Trade-off studies have 

shown a significant gain in slightly decreasing the output voltage (from 120V to 100y) and 

increasing the current (from 6A to 7 A) in order to meet component rating for space 

qualification. On the other side, design of PC board including two power amplifiers on the 

same card has been preferred for size reduction, thermal control and EMI requirements. 

This concept is illustrated figure 7, with controller characterics reported table 3. 

Those power amplifiers can be driven by analogic or digital control PC boards, the latter 

solution being preferred for easier TIP development and integration of health and control 

monitoring (including Expert System). The former solution offers cheaper development and 

production costs, as well as full availability of space qualified components. 

This prototype has highlighted the high recurrent costs resulting for the electronics, mainly 

due to the space-rated components and necessary quality management, with an order of 

magnitude of 100 k $/kg. 

This result is similar to existing electronics onboard rocket engines (e.g. the SSME flight 

controller), but progress in this field indicates that decrease by a factor of 10, consistent with 

reliability and life specifications, could be achieved (e.g. keeping the existing MTBF of 10.000 

hours for life requirements limited to launch and transfer missions, and increasing up to 

40.000 hours for long duration propelled mission). 

65 
66 

TABLE 3 : 700 W AMB controller characteristics 

Volume (1) 

Mass (kg) 

Power cons. (W) 

Industrial 

120 V 

78 

35 

-

/ 6A 

+ current 

* project 

ORIGINAL PAGE 

Space-rated 

100 V / 7A 

15 ( + ) 10 

9 (+) 6 

30 -

BLACK AND WHITE PHOTOG RAf'H 

(* ) 

(*) 

Figure 7. PC Board Prototype for Space-rated Power Amplifiers 
A TYPICAL EXAMPLE 

To further illustrate the magnetic bearing abilities, detailed design and studies of a 

demonstrative turbopump has been performed. 

This machine (in battleship configuration) is illustrated, figure 8, showing a concept similar 

to LH2 TIP for Upper Stage Engine with two radial AMB. A retractable ball bearing is used to 

absorb axial loads during the transients. 

Detailed rotordynamic analyses have been done during the design stage, both to optimise 

the design as explained previously, and to check consistency of the bearing specifications and 

machine behaviour. 

During the iterative design process, modifications have been applied to bearing dimensions, 

as well as to the bearing impedances (modulus and phase), as reported, fig. 9. Explanations of 

the method and analysis tool can be fund in ref. 10. 

The nominal point has been placed slightly before the seventh mode (2nd shaft bending 

mode) at a speed of 200,000 rpm. Associated critical speed map and damping coefficient 

evolutions are reported figures 10 and 11. Reliability improvement is illustrated by the figure 

12, where the bearing failure mode allocation becomes negligible compared to other potential 

failure sources (not improved here). 

Different control modes have been simulated (axis by axis or plane by plane) as well as 

special features, such as notch filters or Automatic Balancing Control (ABC). Effect of such a 

feature is illustrated figure 13, showing drastic decrease in bearing synchronous load. 

Figure 8. Turbomachine Design for AMB Qualification 

67 
68 

z: 

z: ~08 

iC 

" ;>1 -::; 

~ 

:t: 

'0 

18El 

ll! 

!:! 

'. ' 

I t ---- t-- --

I ! 

+---------~----+---------~----~--------~----+---------~---~ 

1f1 

- ---------r 

- PIiASE ':IE n I'll N J1l'1i 

-PIiASE DE FT ,2M :6 l ')e 

500 lflBfI 

Pulsation in rad/s 

SfH3'3f1 1 BBBBB 

i --II-----------T-------

----L ___ -----l I 

PHASE I I! ! ! I, I 

d 1 - - - i -- 1, : I I I 

I ii' ------l-----r--------f--- T-- ~~-~ M,I. 

--- -- -- --+ ---t- ------- ~ - ~:i=-~~---- - --- I I /- -- ,/ " : --.... - \ \. I , - I ~ ----r ,:/- \ I.: i .. ~ \\ I,', I 

_ I I i I 

&. -36 1----- -4---~/ - '+-------1---t--- \ \ ,--j I I' '- ""--J 

~--I--t- .--- i : I \ \ : 

--- --- ------- -- --+- --- __ +_1___ -f---t- --i \1 I 

I 

! 

: I I : " i I I I " ' i ' , ''-,J 

I ' 

-12e+,----------4---_+----------4-~-+----------4---_+----------+---~ 

10 S0 seE! IElBEl 

Pulsation in rad/s 

Figure 9. AMB Transfer Function 
", 

-1,(,-

I 

I~ J rl HII 

t1J1,! 

I' q}[Ji 

,+ fllPI 

I fJIII; 

I" , 

I " t nl!l; 

pn0~ 

I II!!~ 

, III L~ 

.. ,' 

./ 

/ 

/ ~ Ih, _,n! ' u.s lLo, ,l.- II ''1)r'j I,', 0 ~nr,' ,,~ 

" rl1I!1 -'V " nil,' hi, 

" "I1[!, 4[, !11l)1 ,'> 

'I " "IJul ',,, r JJII. ,". 

w ["JIll! 'o! jJIlJi iij.; • IIJlLI 'ltll-' oli11! J '-, 'r1 • h 1 I ~I' ~ (I " I ..... , • 

Figure 10. Critical Speed Map 

"" \.2.SES 

~-=====:::: ,=" :..--=-:=-----"'=: "- " -

~--=====lt===::::::!======::!=====_-__ • • 

,~-----­

... -===--=: ---------~------ a a ___ -eBf---------ea--------e----- _---<l 

~- • • • • • • 

"- • nltlf JI. 0 ~lJlll h~ 

i' "1111t 4~ " mOl .)11 A~fW I PfD1d i ,:W'1C T fI)/ T~. "I.l~ IJf vu'nT JIlN, 

,"' 'I)IJI ~rJ 11.Jll! ,'~ ~'1JP I ~ll.t - PPI ':nr'TPA INH '0 • 'NTP(! UllNT'i , ~: " "111'1 ',I' 11101 'I' f lU[,[ ',IJIo? PI"" I , ~?M ~, .1 d)A 'NIA J-Ill l-jUPtP 

Figure 11. Damping eoemcients vs Rotational Speed 

I 

69 
70 

Mag Suspension (0,4%) 

Pump (7,7%) 

Turbine (23,0%) 

Stat. Sealings (23,0%) 

" .• J )' '." 

te.~ , 

~.oe f 

S.08 

7.08 

6.88 

Axial Balancing (15,3%) 

Dyn. Sealings (30,7%) 

Newton 

Figure 12. Typical Failure Mode Allocations with AMB 

(for a duty cycle of 600 s) 

5.98 _.,. . ... ..... ...-'. ................. .. ...... _ ..... ~_ .... ___ .... ~..... . .. ~ ......... __ .~. __ ._. ____ .. ~ ...... _._ .... . 

•. 88 •.. ' ." ... ... ..... , ......... , ........... ; .......... ;.......... wI ABC ....... l ............. , 

, " 3.88 ... , ............. : ............. ~ ........... + ............ : 

:: I·········,.~········,.,.······,"········I········,p·····,I····,F,iI······,:~ 

Figure 13. Effect of Automatic Balancing Control on 

the Bearing Dynamic Load 
CONCLUSIONS 

Advanced Turbopump (TIP) Designs implementing Active Magnetic Bearings (AM B) have 

been presented in this paper, together with associated technological basis and rotordynamic 

analysis. Objectives of such integration have been emphasized, as well as the availability of the 

required hardware and sophisticated numerical tools. 

As a result, it is clear that AMB Technology offers important improvements in 

turbomachine performances, life and reliability. This is particularly true for Liquid Hydrogen 

TIP, where the low fluid density does not limit the AMB capabilities. 

Integrated Health Monitoring and throttleability are offered, as well as long-term andlor 

repetitive space storage or propulsion. 

The production cost, estimated according to fabrication of space-rated power amplifiers, 

appears high today. Nevertheless, this feature can be favourably balanced in space or flight 

applications, especially with the expected evolutions in electronic components and avionics. 

References : 

[1] J.M. Reddecliff, J.H. Vohr, Hydrostatic Bearing for Cryogenic Rocket Engine Turbopumps, 

Pratt & Whitney A., Journal of Lubrication Technology, Juky 1969, pp. 557-575 

[2] C.E. Nielson, Hybrid Hydrostatic/Ball Bearings in High-Speed Turbomachinery, 

Rocketdyne Division, NASA-CR-168124, January 1983 

[3] P.S. Buckmann, N.R. Shimp, and F. Viteri, M. Proctor, Design and Test of an Oxygen 

Turbopump For a Dual Expander Cycle Rocket Engine, Aerojet TechSystems & NASA Lewis 

R.C., AIAA Paper 89-2305, July 1989 

[4] R.L. McMillion, T.J. Treinen, S.L. Stohler, Component Evaluations for the XLR-132 

Advanced Storable Spacecraft Engine, Rocketdyne Division, AIAA Paper 85-1228, July 1985 

[5] A. Nakajima, Research and Development of Magnetic Bearing Flywheels for Attitude 

Control of Spacecraft, Japanese National Aerospace Laboratory, Proceedings of the 1st 

International Symposium on Magnetic Bearings, Zurich, June 1988, pp.3-12 

[6] J.P. Roland, Magnetic Bearing Wheels for Very High Pointing Accuracy Satellite Missions, 

Aerospatiale, Proceedings of the Int. Symposium on Magnetic Suspension Technology, NASA 

Langley R.C., August 1991 

71 
72 

[7] J.P. Girault, Implementation of Active Magnetic Bearings in Advanced Rocket Engine 

Turbopumps, Societe Europeenne de Propulsion, Proceedings of the 1st International 

Symposium on Magnetic Bearings, Zurich, June 1988, pp.199-210 

[8] D. Hibner and L Rosado, Feasibility of Magnetic Bearings for Advanced Gas Turbine 

Engines, Pratt & Whitney and Wright laboratory, Proceedings of the Int. Symposium on 

Magnetic Suspension Technology, NASA Langley R.C., August 1991 

[9] J.P. Girault and K.W. Lang, Long Life and Reliability : Expectations for Advanced 

Turbomachinery in Space, Societe Europeenne de Propulsion and Rocketdyne Division, AIAA 

Paper 91-2416, 27th Joint Propulsion Conference, Sacramento, June 1991 

[10] C. Brune, Rotordynamics and Active Magnetic Bearings, Societe Europeenne de 

Propulsion, 8th annual ROMAC Industrial Research Conference, June 1988 
N92-27726 

ACl'IVE MAGNEl'IC BFARINGS - AS APPLIED '10 CENl'RIFUGAL RJMPS 

Lev Nelik 

Paul QJoper Irgersoll-Rarrl carpany (IR) 

Graham Jones 

Gas-COOled Reactor Asscx::iates (GCRA) 

Dermis Galecki Frank pinckne o 01 'Y Magnetl.C Bearll"gS I Inc. (MBI) 

Gordon Kirk 

Virginia Polytedmic Institute & state University (VPI&SU) 

73 
Application of magnetic bearings to boiler feed p.mps presents various 

attractive features, such as lOnJer bearing life, lCMer maintenance costs, arrl 

inproved ~ility through control of the rotordynamics. 

Magnetic bearings have been fitted to an eight-stage, 600 hp boiler feed pump, 

lNhich generates 2600 ft of head at 680 gpn arrl 3560:rpn. In addition to the 

varied arrl severe operat~ enviroranent in steady state operation of this pump 

in a power plant, it is also subjected to transient loads dur~ frequent starts 

arrl stops. '!hese loads can now be measured by the in-built instrumentation of 

the magnetic bearings. '!he pump was facto:ry tested, including the adjusbnent 

(tuning) of magnetic bearings. FollCM~ site installation, a follCM-up bearing 

tune-up was perfonned, arrl pump transient response test~ was corrlucted. '!he 

bear~ response was c:c:atpletely satisfacto:ry, ensur~ trouble-free pump 

operation even in the range of reduced load. '!he experience gained so far 

through design arrl testing proves feasibility of magnetic bearings for boiler 

feed p.mps, which sets the stage for application of even higher energy 

centrifugal p.mps equipped with magnetic bearings. 

PRECEDING PAGE BLANK NOT FILMED 7S 
76 

utilization of magnetic bearirgs in p.mIpS is a natural developtent considering 

the successes of these bearings in large (35,000 Hp) centrifugal carpressors. 

sane notable. capabilities of magnetic bearings, namely (1), 

o 'lheoretically infinite bearing life potential, 

o Control of rotordynamical behavior, 

o Rapid response to load variations so as to maintain shaft position, 

o EliJnination of oil system, 

o Mea.surene1t of bearirg static an:i dynamic loads as a diagnostic IronitorinJ tool 

are becan.irg nore sought after for various types of heavy machinery. In 

particular, for p.mIpS of significant pc:JWer levels, the eliJnination of 

lubrication systems that would otherwise be needed for corwentional bearinJs am 

the atterrlant reduction of maintenance are benefits that arise from claiming 

these capabilities. 

It is the p.n:pose of this paper to shaw haw these benefits of magnetic bearings 

were ciJtained for a 600 HP boiler feed p,nrp. SUch p.mIpS often operate with close 

int.en1al. clearances an:i flexible shafts, am the ability to adjust the stiffness 

an:i danpinJ of magnetic bearings can inprove rotordynamics. Increased 

availability an:i reduction in operatinJ an:i maintenance costs were pro:jected, 

lea<iinJ to a favorable evaluation (2) . 

'!he design of a nultistage boiler feed p,nrp allows sufficient clearance for 

shaft flexure an:i thennal distortion an:i minimizes clearances to increase the 

efficiency of the iJlt:leller rinJs am the shaft sealinJ system. 

Ideally the bearings would be lrOUIlted closer together than current practice 

dictates, allawinJ a smaller tolerance on shaft mJVement. If su1:::merged magnetic 

bearings were used, this could be accarplished by eliJninatinJ the outboard 

(norrlrive errl) seal an:i p.rttinJ the inboard bearinJ between the first-stage 

iJlt:leller am the inboard seals. '!he shaft could be held within 0.003 in (0.076 

DIn) at all times by the magnetic bearings (3). 
'lhere are lilenanena unique to pt1I1pS that CXlUld affect magnetic bearing 

perfonnance. 'lhese include stall effects· caused by nonuniform flow 

interruptions or reversals that occur in a IXJI11P .iItq:leller am diffuser when 

c:perating at reduced flow rates (4,5). 'lhese effects introduce unsteady, raman, 

radial am axial loads that are often aoc:::arpmied am exacerbated by cavitating 

flow; wear of the iIt'peller neck rings (or adjacent casing rings) which leads to 

loss of stabilization am, therefore, to adverse changes in rotordynamical 

behavior. '!he above lilenanena am the oorresporrling mechanical responses becane 

IOOre evident am critical in pt1I1pS of high en&gy level; Le., those of IOOre 

ooncentrated am higher power. It was therefore inportant to gain further 

insight into magnetic bearing behavior in such pt1I1pS in general, to access their 

ability to harxUe these othenrise detrimental situations, am to measure the 

actual instantaneous loads that might be encamtered. 

since the current in a magnetic bearing is related to the load, readings of 

current vs t:ilne, speed am IXJI11P flow rate provided the needed insight into the 

stall effects. Scaling of the loads involved is fairly reliable am enables one 

to make a IOOre infonned estimate of the loads for a still-higher-power 

sul:nerged-magnetic-bearing (carmed) IXJI11P. Also, the ability of the magnetic 

bearings to cope with the rotordynamic uncertainties mentioned above has been 

revealed am could be analyzed for the future sul:nerged-bearing application. 

MAGNEl'IC BEARINGS 

Figure 1 shows both active magnetic bearing assemblies am their relation to the 

boiler feed IXJI11P. '!he magnetic bearings for the boiler feed pump require a 

radial load capacity of 280 lbs (127 kg) steady state am an additional 280 lbs 

(127 kg) for transient oorrlitions. For the magnetic thrust bearings, the 

required load capacities are 1000 lbs (454 kg) steady state am an additional 

1000 lbs (454 kg) for transient oorrlitions. In the design of active magnetic 

bearing systems, it is prudent to include load capacity margins to aa::omroodate 

prooess-irrluced surge loads, abno:rmal imbalance or hydrodynamic loads. 

77 
78 

'lhrough the use of st:.arx3ardized magnetic bearing designs, which provided further 

margins over conventional practice, the resulting magnetic radial bearings 

provide a maximum steady state load capacity of 800 lbs (364 kg) am will 

IOOdulate a force of 400 lbs (181 kg) at a frequency of 60 Hz (boiler fee.d pump 

nmning speed). '!he magnetic tluust bearing provides a maximum steady state 

load capacity of 4000 lbs (1814 kg) am will IOOdulate a force of 1000 lbs (454) 

kg) at a frequency of 60 Hz. 

'!he. magnetic bearing assembly for the. norrlrive. ern of the. boiler feed pump is 

shown on Figure 2. '!he. c:x::.q>le.ted stator assembly consists of two magnetic 

thrust bearirg stators am an axial position sensor, a magnetic radial bearirg 

stator (consisting of four e.lectranagnets) am radial position sensor, a speed 

pick-up, am an auxiliary (emergency back-up) bearing. Additionally, the bearing 

wintings are e.qui~ with resistive te.rrperature devices (RI'Ils) which can be 

USEd to m:>nitor CJlerating temperatures. '!he entire assembly provides the 

radial/tluust forces for the norrlrive ern of the pump. '!he drive ern radial 

bearing is similar to that of the non-drive ern. 

'!he radial forces are transferred fran the bearing assembly to the shaft via two 

2.5 in (63.5 I\1l1) by 6 in. (152.4 I\1l1) diameter laminated silicon-stee.l rotors 

fitted as sleeves at each ern of he shaft. '!he tluust forces are transmitted to 

the shaft through an interference-fitted 1 in (25.4 I\1l1) by 11.25 in (285.8 I\1l1) 

diameter disc. '!he shaft position is controlled by the magnetic bearing system 

which uses two irrlucti ve radial position sensors am one irrluctive axial 

position sensor. '!he radial position sensors (referred to as collocated 

sensors) are adjacent to the radial bearing lamination stacks am the axial 

position sensor is at the ern of the machine. '!he radial sensors are designed 

to minimize rotor runout or other inperfections that would cause position sensor 

signal noise. 
'!he control cabinet is self-contained with power conversion, signal processirg, 

operation logic am alantVtrip :nv:>nitorirg of critical functions necessaty for 

the active magnetic system. '!he air-cooled cabinet measures 52 in. (1321 nun) 

high, 21 in (533 nun) wide, am 20 in 508 nun) deep. '!he cabinet power SUWly 

requires 208 VAC, 3 p,ase (1.4 KVA) as irp.rt am is equiwed with a battery 

backup which will power the system for ten minutes. 

After ten minutes, the system will maintain ~tion, but the bearirg load 

capacity may be diminished. '!he magnetic radial bearil'gs are powered with eight 

120V/15A power anplifiers am the magnetic thrust bearirg is powered with two 

120V/30A power anplifiers. Should the power to the magnetic bearirgs be lost, 

the reserve power is provided by the battery backup system. '!he auxiliaty 

bearirg at the nomrive ern of the machine is a duplexed pair of an;JUlar-contact 

ball bearil'gs. '!he bearirg provides radial am axial load capability if the 

pump were required to coast to a stop because of a loss of both primaty am 

backup power to the magnetic bearirgs. '!he auxiliaty bearirg at the drive ern of 

the machine is a Conrad-type sinJle radial bearirg. '!he magnetic air gap for 

the radial bearil'gs is 0.020 in (0.5ll11m), am the thrust bearinJ magnetic air 

gap is 0.028 in (0.71 mm). '!he auxiliaty bearil'gs are designed to prevent the 

shaft fran novirg past half the magnetic air gap clearance, hence the auxiliaty 

bearirg air gap for the radial am axial bearirgs is 0.010 in (0.25 nun) am 

0.014 (0.36 nun) respectively. 

With the use of auxiliaty bearirgs, protection is assured against sustained loss 

of magnetic levitation as well as against arry upset corrlition that might occur 

as a consequence of pump ~tion in the power plant envirornnent. In addition, 

rotor bushirgs am inpeller rirgs provide additional rotor danpinJ, am further 

enhance the overall system reliability. 

79 
roIDR DYNAMICS 

'!he p.nrp response to unbalance excitation was investigated usin;J the recently 

developed AMB forced response carputer program (6). '!his new carputer code can 

include the influence of sensor axial location in addition to iIrpeller am seal 

rin;J cross-couplin;J am direct stiffness am dant>in;J. '!he response of the pulll> 

rotor for a 0.5 oz-in unbalance placed at midspan is given in Table 1 for normal 

design corrlitions considerinj both clly am wet corrlitions. '!his level of 

unbalance correspon:ls to the API 4WjN balance specification. '!he results for 

clly running corrlitions irrlicate little influence of sensor position when 

operatinj at or near design speed. A greater influence of sensor position is 

irrlicated when operation is near the critical speed. '!he largest midspan 

response is for outboard sensor, smallest for inboard sensor. '!he predicted 

vibration levels at design speed are insensitive to sensor position for the 

normal wet corrlitions. '!he midspan response is inticated to be awroximate1y 

3-4 times the sensor lcx::::ation vibration. '!he forced response analysis predicts 

that the p.nrp rotor could withstarrl just over 150 times this unbalance force am 

still have a response anplitude of less than 1.2 mil at the sensors am only 3.3 

mils at midspan. For reference, the 0.5 oz-in unbalance correspoms to a force 

of 11.5 lbf for a rotor speed of 3560 rpm. 

'!he clly first critical speed was predicted to be 1605 rpm, with the secorrl 

critical at a speed of 5798 rpm. When the wet corrlition is considered, the 

forced response versus speed irrlicates that the first critical speed (5900) is 

critically danped as sha"m in Figure (3). 

'!he stability of the p.nrp was calculated considering varioos corrlitions of 

pre-swirl at the entrance to the front rinjs, center am outer bushings. A 

surmnary of the results are given in Table 2. For a zero preswirl, the p.nrp 1st 

critical speed was predicted to be stable with a log decrement of 9.13. For 50% 

preswirl, the rotor first critical was also predicted to be stable with a log 

decrement of 15.5. If the iIrpeller coefficients are not considered the 50% 

preswirl case lCXJ decrement reduces to 14.2. Actual test starn operation 

gave no irrlication of instability. '!he calculation of the actual seal inlet 

pre-swirl am the eccentric dynamic seal coefficients is not a proven capability 

for actual p.nrp operatinj corrlitions. '!he results for this p.nrp are not very 

sensitive to this influence. 

80 
'!he conclusions of the rotor dynamics analysis irrlicate that the pump design is 

acceptable for forced response excitation. '!he pump design, as built, can 

resist strong unbalance caused by hydraulic excitation forces which is much nore 

important in pump design than the possibility of small self-excited vibration. 

'!he pump is predicted to have very gocx:l stability margins arrl may only resporxi 

to non-synchronous hydraulic excitation during off-design operation. '!he pump 

will not experience self-excited subsynchronous vibration during operation. 

FACIORY AND ON-SITE TES'l'ING 

Prior to factory testing, the magnetic bearing controls had to be tuned to the 

characteristics of the shaft, with the pump in the wet corxlition. '!his took 

significantly less tilne than had been experienced on other projects, arrl was 

c::arpleted in Ul'rler a week, by a team of UNo. 

'!he factory tests, with the exception of an unplanned shutdown onto the battery 

backup as a result of a thunjerstonn, were uneventful. It was noticed, however, 

that one of the m::>tor-errl journal bearing poles was showing a fairly high load. 

'!his was attributed to misaligrnnent due to the temporary nature of the baseplate 

aligmnent for the test, arrl it was agreed to nonitor this further on-site. 

Figure 4 shows the pump installed in the power plant. '!he site 

start-up was uneventful, with the exception that the high bearing load 

I'lOt:ad above rea~ on the same m::>tor-end bearing, but on a different pole. 

'!his seemed to confino. that it was an alignment load. By adjusting the coupling 

to be a little nore flexible, the load was significantly reduced. 

High loads were noted during the nm up to full speed which took only about 2 

secorrls. '!hese levels needed to be unjerstood better,arrl a secorrl retuning with 

test was perfonned, nonitoring bearing loads over all representative rurming 

corxlitions. '!his secorrl tuning took place 4 nonths later together with testing 

of the pump through start-up, shutdown arrl part load operations. nrring this 

testing, no irrlications of hydraulic arrl/or rotordynamic instability were 

obsel:ved. Bearing currents am shaft displacements were stored on a high speed 

"Mre" recx>1:"der for detailed analysis. '!he key results of this operation were 

that after sate tuning adjust:Ioonts, the pump rotor was held both axially am 

radially within about 1 mil during all transient am steady state operations. 

81 
Figures 5 (before tunin:J) am 6 (after tunin:J) show two traces of the shaft 

radial displacement as a function of tirre dur~ the run up to full speed. 

Figure 5 shows displacements of the order of 5 mil, where the bear~ did not 

fully control the shaft displacement. Figure 6 shows that the shaft is held 

gearetrically to within 1 mil dur~ the whole transient. Provided that the 

operati.rq transients are all covered in the specification, this awroach should 

ensUre satisfactory lifetirre operation. 

Conventional bear~s can often abso:rb higher than design loads, accatpanied 

with increased wear rate, but not necessary leadi.rq to immediate failure. 

However, a magnetic bear~ that reaches its design point where the 

electranagnet is saturated, will not resist any additional load am the shaft 

will make contact with whatever backup bearing device is provided. ArTy 

additional load will roN be transferred to this auxiliary SUWOrt system, am 

the shaft will be about 10 mil out of aligrnnent on one or I1'Ore axes. 

For the reasons stated above it is absolutely essential for any prototype 

equipnent nmning on magnetic bear~s that this procedure of nmning the 

machine through all its operation transients am docI.noonting the shaft response 

is carried out before p.ltt~ the equipnent into service. 

Olecking of the power constnnption of the magnetic bearirg feed p.mp against a 

conventional bearirg machine purchased at "the same tirre, am with the same rotor 

design showed a slight reduction in power consunption for the same feern>later 

flow. '!his was fairly consistent over a lorg tirre period. 

Operator Acx::eptance - After an initial period of enthusiastic but cautious use 

of the p.mp, the operators' confidence has increased to the point where it is 

be~ operated as confidently as any other similar equipnent. 

Availability Experience - Fran studies referenced above, expectations for 

availability have been developed. To date, there have been no events on site 

that would irrlicate that these targets cannot be met even with the prototype 

unit. However, a lorger tirre frame of several years will be needed to fully 

justify sud1 high availability claims. 

82 
CXlNCIUSIONS 

Boiler feed p.nnps in an electric utility may benefit fran the expected life am 

lOIN maintenance advantages of magnetic bearings. '!hese p.nnps can provide a 

cxxrprehensive platfonn for evaluating the feasibility of magnet bearing 

technology mrler a variety of severe operating corxlitions that can inp:>se strol19' 

am rarrlan loads on the rotating elements. 

SUccessful in-plant am on-site denK>nstrations of a 600 hp, 

magnetic-bearing-equiwed, eight-stage volute-type boiler feed pump were 

comucted. No effects on pump operation were experienced that could be 

attributed to hydraulic aOOjor rotordynamic instability. Fran the starrlpoint of 

the user, experience gained so far has denK>nstrated that a pump equiwed with 

magnetic bearings can be characterized as follOlNS: 

1. '!he bearings operate satisfactorily. 

2. Equipnent is reliable. 

3. '!he pump is operable. 

4. Provides J1eW' data, not available in the past: bearing loads 

am positions. 

5. Requires less attention. 

6. Requires less maintenance. 

By nonitoring the operation of the 600 hp pump, whidl has the magnetic bearings 

lOOUl1ted external to the pump casing am running in air, it should be possible to 

gain the rotordynamica1 insights needed to design improved, higher-pOINer 

madlines with these bearings submerged in fluid within the interior of the 

casing. An order of magnitude nore power, e.g. 10,000 hp, should be the next 

step. 

A one-year test, nonitoring am benefits evaluation program on two side-by-side 

J1eW' p.nnps - one with magnetic bearings; the other, with conventional bearings -

is continuing through the remairrler of 1991. To date the pump is fulfilling all 

the expectations that acx::ompanied the initiation of the project, am provides a 

SO\.lI'rl basis for future developments. 

83 
84 

Specifically, we expect to develop availability estimates, spa:res requ.irenart:s, 

rurm.i.rg costs, arrl design specification requ.irenart:s for future utility 

awlications. We expect to have all hIt the availability estimates oc:rrplet.ed at 

the ern of the first year of operation, that is by November 1991. '!he 

availability data will need to be acquired over several years of operation to be 

statistically significant, arrl until we have that data the experience in other 

irrlustries is the only yardstick that we have. But that experience awears to 

be very encouragiD;J arrl could provide an alternate technology to the utility 

i.ndusb:y resultiD;J in lower forced ootages, higher availability an:l IrOre 

efficient operations. 

REF'ERENCES 

1. Hen:1rickson, T .A.; I.eanani, J .S.; an:l Weise, D.A.: "Application of Magnetic 

BeariD;J Teclmology to Vibration Free RotatiD;J Machinery." Naval Engineers 

JCIlln1al, May 1987, W. 107-111. 

2. Olson, E.A.J.; et al: "Applications for Magnetic BeariD;Js on Electrical 

GeneratiD;J Plant Equipnent." Final:report on EmI Researdl Project 

2079-22, prepared for EmI, ESEERCO, GCRA an:l Public Service of O::>lorado by 

the S.M. Stoller Corp. an:l Novacorp International ConsultiD;J Ltd., EmI 

Report RP 2079-21 & -22, December 1988. 

3. Baxter, B.Z.; Burger, J.M.; an:l Jones, G.: ''Magnetic BeariD;J Develc:::tp1Slt 

for the utility Ind:ustJ:y." Prooeedi.n:Js of the Arlerican Pc1Ner Conference, 

April 1990. 

4. Cooper, P.; WotriD;J, T.L.; Makay, E.; an:l Corsi, L.: ''Minimum Continuous 

stable Flow in Feed PlmpS." 5ynposium Proceed.i.rgs: Pc1Ner Plant Pumps, 

EmI CS-5857, June 1988, W. 2-97 to 2-132. 

5. Cooper, P.: ''Hydraulics an:l cavitation." 5ynposium Prooeedi.n:Js: Pc1Ner 

Plant PlmpS, EmI CS-5857, June 1988, W. 4-109 to 4-149 

6. Rawal, D., J. Keesee, an:l R. G. Kirk, "Critical Speed an:l Forced Response 

Solution for Active Magnetic BeariD;J Tu:rbanachinery", Part 1 an:l 11, NASA 

Workshop on Aerospace Applications of Magnetic SUSpension Technology, 

I..argley Researdl Center, september 25-27, 1990. 
TABIE 1 RES:roNSE 'ID 0.5 oz-in at MIOOPAN (at design speed of 3560 RIM) 

Corrlition 'Ihrust end MidsPan QQ!ml· Errl 

a. ~ (nuI-pp) (nu-r-pp) 11riIT-P8T 

collocated sensor .010 

outboard sensor .062 

inboard sensor .064 

b. wet 

(c = 0.010 in.- wear rirgs am bushings) 

collocated sensor 

outboard sensor 

.006 

.006 

.384 

(21.0 at N-cr) 

.380 

(42.0 at N-cr) 

.392 

(14.4 at N-cr) 

.022 

.022 

.056 

.056 

.038 

.008 

.008 

TABlE 2 STABILITY RESULTS SUMMARY for :ruMP ROIOR ~ CRITICAL SPEEIlS 

Corrlition 

a. dry 

No Influence of 

liquid seals 

b. wet 

(zero preswirl) 

c. wet 

(50nreswir1) 

reallyart (sec 

-0.76 

-145. 

-19.5 

-323.5 

-118.7 

-198.7 

-349.1 

-118.2 

-197.2 

d. wet 

(50nreswirl 

no ilTpaller Characteristics) -677.3 

-120.2 

-197.3 

Eigenvalue aamoed critical 

1830 

3807 

6462 

2126 

5549 

6276 

1350 

5552 

6256 

2882 

5541 

6323 

(cpn) lQg decrement 

0.03 

1.49 

0.18 

9.13 

1.28 

1.89 

15.5 

1.28 

1.89 

14.2 

1.30 

1.88 

85 
FIGURE 1 KJLTISTAGE VOIl1I'E RJMP FTITED WI'lH ~C BEARINGS. I -H. IUMP IDDEL 

4X10m-8 WI'IH RADIAL BFARING ON OOIVE END AND RADIAL AND l00AL 

BEARINGS ON NONOOIVE END. 

FIGURE 2 RADIAL AND AXIAL ~C BFARING ON NONIRrVE END OF IUMP. 

FIGURE 3 

86 

30.00 ~---r----,-----,------r------'--'-' 

25.00 

o 

L. 2000 :i . 

§. i 15.00 

a. 

~ 10.00 

5.00 

Midspan /,,"'------

Coupling End 

--- --~---~ Thrus1 End 

0010.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 

Frequency (rpm) ("11)2) 

RESR:lNSE FUR 0.5 OZ-IN AT MIOOPAN INCIlJDING WEAR RINGS, RlSHINGS, AND 

~-COLIDCATED AMB SENSORS. 
ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

FIGURE 4 MULTI -STAGE oonER FEED fUMP WI'IH MAGNEI'IC BFARINGS INSTAllED AT NEW 

YORK STATE EIECIRIC AND GAS ro-lER PIANI' 

87 
!/) 

E 

Q) 

"0 

:::J 

.t::: 

a. 

E 

<t: 

!/) 

E 

88 

Unacceptable Transient 

Bearing Response 

1 mil radial movement 

I I 

0 2 

Time, seconds 

FIGURE 5 UNACCEPI'ABIE 'mANSIEN!' BEARING RESfONSE 

Acceptable Transient 

Bearing Response 

~ mil radial movement 

o 1 2 

Time, seconds 

FIGURE 6 ACCEPI'ABIE 'mANSIENI' BEARING RESR:>NSE 

I 

3 

3 
N92-27727 

Precision Magnetic Suspension Linear Bearing 

David L. Trumper, Michael A. Queen 

Dept. of Electrical Engineering 

Univ. of N. Carolina at Charlotte 

Charlotte, NC 28223 

89 
1 Introduction 

Magnetic bearings represent a promising approach for achieving positioning with nanometer 

resolution. The first author has constructed a high-precision linear bearing which 

demonstrates 5 nm short-term position stability. This system represents the experimental 

implementation of an idea presented in [1] and has been investigated as part of the first 

author's Ph.D. thesis [2]. 

This study was initiated with support from the Molecular Measuring Machine (M3) 

project at the National Institute of Standards and Technology [3]. The form-factor of the 

bearing was thus chosen such that it was compatible with the M3 crossed-slide design. The 

bearing technology is also highly suitable for other precision applications, such as in stages for 

photolithography and diamond turning machines; these application areas provide the focus for 

our current research. 

As shown in Figures 1-4, a 10.7 kg platen measuring 125 mm by 125 mm by 350 mm is 

suspended and controlled in five degrees of freedom by seven electromagnets, labelled as B1 

through B7. Five capacitive probes located in the bearing centers measure position with 

nanometer resolution. The seven points at which the bearing forces act on the platen are 

shown as arrows and the five points at which the position measurements are taken are 

indicated as dots in Figure 1. The scale of Figures 2, 3, and 4 is indicated by the 100 mm 

reference shown in Figure 2. 

The suspension acts as a linear bearing, allowing linear travel of 50 mm in the long axis 

of the platen. In previous work [2,4]' the long-travel degree of freedom is not actively 

controlled. Efforts are currently directed at achieving control of this degree of freedom with 

50 mm travel through a novel magnetic suspension linear motor. This motor consists of an 

array of permanent magnets attached to the moving platen and a stator array of coils 

attached to the fixed machine frame as shown in Figs. 2-4. Prototypes of this linear motor 

are currently under construction. Position in this degree of freedom is transduced by a laser 

interferometer. For simplicity, optics for this interferometer are not shown in the figures. 

The key feature of the linear motor is that it affords control of forces in two degrees of 

freedom, one parallel to the air gap and lying on the axis of the magnet array and one 

perpendicular to the air gap. Thus it is possible to simultaneously control translation and 

suspension with a single motor structure. The motor design and control are the focus of this 

PR6CEDING PAGE BLANK NOT FltM!D 91 

Q-:2.. 
./ BEARING FORCES 

• POSITION MEASUREMENTS 

Figure 1: Points at which bearing forces are applied to platen, and points at which platen 

position is measured. 

92 

MA GNET 

AR RAY 

~ 

PRIMARY SUPPORT BRACKET 

_1 

I I 

j., ~ 

t- '-

B3 L ~~ ~~~ ~ 

PlATEN 

~~~~~~~~~ 

~ \ I I I ......................... ,.. ..................................... ............. _ STATOR "-

\_ 100nvn OPTICAl TABLE 

Figure 2: Side view of bearing and linear motor assembly. 
PLATEN 

---r-- I B3 082 I _-rr--

: JOtCt .g:: [ : 

B5 B7 __ ..J.J-- I I --..1- __ 

Figure 3: Top view of bearing and linear motor assembly. 

- r--

I I 

1 1 

r------

.., f 

1 B1 1 

l- I 

w Iii 

" //>. lo:: ~ 

V ~ 0 ~ 

~ --11- - v ~ 

CD -..rr -- 1/ CD 

!i: I ~ 1 !i: 

~ 1 ~ I 0 

n. 

186 ~ I n. n. 1/ ~ _ _ .J..r-- -

B4 """\..L __ ~ 

(/) (/) ~ > > a: V PLATEN V a: 

< A < 

STATO~ I MAGNET c ::i: z a: I I. I -p.-- ARRAY 0 n. 0 

w 

(/) 

OPTICAL TABLE 

Figure 4: End view of bearing and linear motor assembly. 

93 
paper. 

The paper is organized as follows. In the next section, the electromechanical 

characteristics of the linear motor are developed, and an example design is presented. With 

these results in hand, it is then shown how two degrees of freedom can be controlled using this 

linear motor. Following this, the conceptual design for a precision X-V stage driven by four 

such motors is described. It is anticipated that this stage can achieve nanometer motion 

control, with travel in X and Y of several hundred millimeters. Finally, suggestions for further 

work are presented. 

2 Motor fields and forces 

To calculate the electromagnetic forces, the motor is idealized as a two dimensional structure 

as shown in Figure 5. Here, the motor is assumed to have a depth of w into the paper and to 

extend indefinitely in the ±z-direction. The stator is fixed in the laboratory frame x, y, z. 

The primed coordinate frame x', y', z' is fixed in the layer of magnetization, and is displaced 

from the unprimed frame by (xo + ~)ix + zoiz. 

The magnet array is modeled by a half-infinite region of sinusoidally distributed, 

x-directed magnetization Mx = ReMoe-ikz'. The magnetization layer is referred back to the 

unprimed frame by substituting z' = z - Zo into Mx which gives Mx = ReM e-ikz, with 

complex amplitude M = Moeikzo . 

The stator is modeled by a sinusoidally distributed, y-directed current density 

Jy = Re}e-ikz, in a layer from x = 0 to x = ~. The complex amplitude) is a function of the 

winding density TJo, and the two phase currents, II and 12 • Specifically, Re} = 11TJO and 

1m} = 12TJo. Throughout this discussion, the complex amplitudes indicated by a tilde 

represent the temporal variations in both amplitude and spatial phase. 

The model is idealized in several ways. First, while the stator current in the real motor is 

distributed down the axis of the motor in a spatial square-wave, in the model the current 

density is sinusoidally distributed at the spatial fundamental of the actual stator current 

distribution. Further, although the real magnets are of finite thickness and distributed in a 

spatial square-wave of magnetization, we model the magnetized region as of half-infinite 

extent and with the magnetization distributed sinusoidally in space at the spatial 

fundamental of the actual magnetization distribution. It is reasonable to model only the 

fundamental components of magnetization and current, as these are responsible for the bulk 

of the motor force production. The additional harmonics present in the actual motor can 

readily be added as Fourier series components built upon the solution we develop herein. 

The fields and forces for the finite-thickness stator in Figure 5 are obtained by first 

studying a simpler model as shown in Figure 6, in which the excitation consists of a current 

sheet (spatial impulse). Then, with the finite-thickness stator current distribution written as 

an integral of spatially-distributed current sheets, the linearity of the solution is exploited to 

write the forces on the finite thickness stator in the form of a convolution integral. This 

integral is readily solved, yielding the forces on the finite thickness stator. 

The analysis follows the techniques and notation from [5], chapters 2, 3, and 4. The 

94 
Mx=l<.eN'lfle- ""'"" JAL 

I II 

x x' 

Figure 5: Geometry which represents the current density model of linear motor. 

x x' 

Mx = ReMoe-jkz' 

~~y' z.lW (c) 

(d) 

u 

(e) 

_..r...... __ -I. J----------.---"""T'"--

(f) Y Z rf 

Ky=Ke-jkz 

Figure 6: Geometry which represents current sheet model of linear motor. 

95 
magnetic field is given as the gradient of the magnetic scalar potential H = - \l'IjJ. Fields and 

potentials are represented as the real part of a complex amplitude multiplied by a complex 

exponential in z. Superscripted letters denote a quantity evaluated at the corresponding 

boundary. 

At the magnetization boundary the potential is continuous, ~c = ~d, and the normal field 

is discontinuous by the magnetization, fI~ - fI; = -it. At the current sheet, normal H is 

continuous, fI; = fI!, and the tangential field is discontinuous by the value of the surface 

current, fI: - fII = -f<, or alternatively ~e - ~1 = j~. These boundary conditions are 

summarized below 

~c -d 'IjJ 

fIe -1 x H::c 

~e _ ~1 .f< 

)-k 

fIe _ fId x x -it 

Applying the transfer relations from Section 2.16 of [5] yields the following four equations 

among the field and potential complex amplitudes at the boundaries. 

fIc ::c k 'ljJc 

-d 

Hx 

-d k -e 

-k coth( ku) 'IjJ + sinh( ku) 'IjJ 

fIe -k - - ::c sinh( ku) 'ljJd + k coth( ku) 'ljJe 

-1 

Hx _k~1 

where u = Xo + ~. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

Together, equations (1 )-(8) form a set of eight equations in eight unknowns, which are 

driven by the sources Mx and Ky. 

In order to calculate the normal and tangential forces exerted on the platen, the potential 

and normal field at boundary (d) are calculated from equations (1)-(8) as: 

(9) 

and 

(10) 

The tangential field fI: is related to the potential ~d by the negative of the gradient with 

respect to z. Thus 

(11) 

The force acting on a volume of the magnet array is given by the integral of the Maxwell 

stress tensor over the surface enclosing this volume. For a spatially-periodic structure, the 

96 
I"" I • ~ I"" ' • I"" I"" ~ S2 

I 

I 

~ I Tzz 

T I I In! ! l;4 I I 

L... ...I....-c:----r----

r 

Txx Sl 

Tzx 

Txz 

Jl 

x 

y z 

Figure 7: Showing the components of the Maxwell stress tensor acting on a surface which is 

used to find the forces acting on the magnet array. 

Commutation 

Laws 

Current 

Amplifier 

Figure 8: Two degree of freedom control loop block diagram. 

x 

z 

97 
integration is simplified if the volume encloses a single spatial period. The components of the 

stress tensor acting on such a volume are shown in Figure 7. The integrals of Txx and Tzx on 

surface 83 are found to equal zero. Also, the Txz and Tzz components on 82 and 84 cancel, 

since these surfaces are one spatial wavelength apart. The only non-zero contribution is on 81. 

Over an integer number of spatial periods, this force can be written as the spatial average on 

~ multiplied by the area of the surface. Specifically, the normal force acting on one spatial 

period of the magnet array is given by 

(12) 

where the expression (-) z stands for the spatial average with respect to z and Am = w27r / k is 

the area of one spatial period of the motor. Similarly, the tangential force is given by 

(13) 

The minus signs in these expressions are accounted for by the direction of the stress tensor 

components acting on 81 which is the bottom surface. 

The stress tensor for magnetically-linear materials derived from the Korteweg-Helmholtz 

force density ([5], section 3.10) is 

J1. 7' .l.IJ .. -

- r II.H·H· 1 J - -fJ··HkH 2 IJ k (14) 

using the Einstein summation convention where since the k's appear twice in the same term 

they are to be summed from one to three. A final useful identity is the averaging theorem ([5], 

section 2.15). 

(ReAe-jkzReBe-jkZ) z = ~ReAB*. (15) 

Applying equations (12)-(15) with the results (10) and (11), the forces are found to be 

and 

(17) 

Thus we have derived the forces acting on the magnet array due to a sinusoidally distributed 

current sheet separated from the magnet array by a distance u. 

Returning to the finite thickness of sinusoidally distributed current density shown in 

Figure 5 the forces acting on the magnet array in this case can be determined by summing the 

forces due to multiple current sheets of the form shown in Figure 6. That is, we integrate 

from x = 0 to x = ~ the force on the magnet array resulting from a current sheet at location 

x with intensity j{ = Jdx. Specifically, . 

(18) 

98 
and 

(19) 

In writing these integrals, the separation distance ~ + Xo - x between the differential current 

element and the magnet array lower surface has been used to replace u in (16) and (17). Since 

within the stator J is independent of x, evaluating these integrals gives 

Fx = A;;o (Im(i)Re(M) - Re(i)Im(M)) e-kx0 (1_ e-k~) (20) 

and 

(21 ) 

As stated earlier, the current density J is driven by two phase currents Rei = 11 'Tfo and 

Imi = 12 'Tfo, The forces in terms of these phase currents are found by using these relations 

and substituting the earlier derived result M = Moeikzo into (20) and (21). In matrix 

notation, the resulting equations are 

[ Fx 1 = oMoGe-kxo [-sin(kzo) c~s(kzo) 1 [ II 1 

Fz 'Tf cos(kzo) szn(kzo) h 

where several constants have been collected into G = Ar;lo (1 - e-k~). The Xo and Zo 

dependencies are explicitly retained since these variables represent motion of the magnet 

array relative to the stator. This completes the derivation of the motor force equations. 

3 Commutation and control 

(22) 

In operation, the motor will be used under closed-loop control. A loop controlling two degrees 

of freedom with a single linear motor is shown in block diagram form in Figure 8. Here we 

assume that a single linear motor is attached to a mass M which is allowed to move in only 

two degrees of freedom x and z. This is the same as assuming that the motor drives through 

the center of mass. If this assumption is not met, then the model will be more densely 

interconnected, but the control issues remain essentially unchanged. The linear motor 

currents II and 12 are assumed to be driven by a current amplifier. The current setpoints lsI 

and 1s2 are generated by the block labelled Commutation Laws. The function of this block is 

to determine these setpoints such that the motor applies forces Fx and Fz which are equal to 

the desired forces Fdx and Fdz' If this is properly accomplished, then the system appears 

linear and decoupled from inputs Fdx and Fdz to outputs x and z, and can be controlled by 

two independent linear compensators which act on errors ex and ez. 

The commutation laws which achieve this decoupling are derived by inverting (22) to 

yield 

[

lsI 1 e

kxo 

[-sin(kzo) cos(kzo) 1 [ Fx 1 (23) 

1s2 - 'TfoMoG cos(kzo) sin(kzo) Fz ' 

This system of equations takes the desired normal and tangential forces and maps them to the 

currents needed to produce these forces. To the extent that the commutation laws are 

accurate, this decouples the two degrees of freedom. 

99 
4 Power dissipation 

In a specific implementation, the maximum available force is limited by power dissipation in 

the stator windings. To develop the thermal limits imposed on the motor design, the power 

dissipation for a single sinusoidally distributed phase is calculated as follows. The power 

density in a region of conductivity (j carrying current density J is 

J2 P = -. (24) 

u 

In general, the current density is 

J = ReJe-ikz = Re(J) cos(kz) + Im(J) sin(kz). 

With only a single phase excited, J becomes 

J = 117]0 cos( kz). 

The differential power element is 

127]2w~ 

dP = 1 0 cos2 (kz)dz 

u 

The power dissipation PA per spatial wavelength ). = 2; is determined by integrating 

equation (27) over this wavelength. Thus 

2,.. 12 2 J\ 

P -iT 17]owu 2(k)d A - cos Z z. 

o u 

Evaluating this integral gives I2'112w~). P

A 

= _1=--·.:....;:/0 __ 

2u 

A prototype linear motor stator of length 1= 50.8 X 10-3 , width W = 0.102m, depth 

~ = 7.62 X 1O-3m, spatial wavelength), = 50.8 X 1O-3m, and winding density 

(25) 

(26) 

(27) 

(28) 

(29) 

7]0 = 4.4 X 106 turns/m2 was constructed using number 26 copper wire. When supplied with 

approximately 10 W, this stator experiences a temperature rise of 50°C. This experiment 

provides an estimate of 5°C /W for the stator temperature coefficient in this geometry. 

For a two-phase motor of these dimensions, with a phase current II = lA, equation (22) 

yields a force level of 33.8 N. This force is sufficient to accelerate a 10 kg platen at more than 

0.3 times the acceleration of gravity. At this current, equation (29) yields a power dissipation 

of 6.8 W. Using the temperature coefficient developed above, this results in a tempera.ture rise 

of 34°C. 

This temperature rise is well within the thermal limits of the motor materials, but is still 

a large power dissipation in the context of a precision machine, as the resulting thermal 

expansion can destroy machine accuracy. This problem can be addressed by taking advantage 

of the force/power scaling laws. Specifically, since power increases as the square of current, 

and force increases linearly with current, if the motor area is increased by a factor of n, then 

the current required to achieve a given force is reduced by this factor. However, with this 

reduced current, the power density is reduced by n2 , and thus the total power is reduced by n. 

Thus it is likely that a larger motor will be used in the final design. 

100 
Position 

Transducers 

Roll, Pitch, Yaw, 

and three translations 

referred to platen center 

of mass 

Motor 

Commutation 

and Power Amp 

Motor 

Commutation 

and Power Amp 

Coil Currents 

Motor 

Commutation 

and Power Amp 

Force Commands 

(Stator Frame) 

Modal Setpoints 

Compensate 

Geometric 

Nonlinearities 

Forces and torques in Platen frame 

Linear Modal Compensator 

Figure 9: X-Y stage block diagram. 

z L X 

Motor 

Commutation 

and Power Amp 

101 
5 Magnetic bearing X-Y stage 

Given a magnetic suspension linear motor as developed above, various stage geometries are 

possible. One such geometry is shown in Figure 9. Here, four linear suspension motors are 

combined to act on the top surface of a platen to implement an x-Y stage suitable for 

photolithography. The stators are labelled 31 through 34 and drive against four magnet 

arrays which are shown as grey rectangles. Stators 51 and 53 drive the platen in the 

Y-direction and stators 32 and 34 drive the platen in the X-direction. The four stators are 

driven appropriately to control the remaining four platen degrees of freedom. 

The Linear Modal Compensator block consists of separate lead/lag compensators for 

each of the six degrees of freedom. The Compensate Geometric Nonlinearities block inverts 

the kinematic relations to translate forces and torques specified in the platen frame (where 

the system appears as linear) into forces specified in the stator frame (where they are actually 

applied to the platen). The Motor Commutation and Power Amp blocks each implement (23) 

for their respective stator assembly and contain power amplifiers for each of the stator phases. 

This X-Y stage represents the long-term focus of our design efforts. In order to gain 

experience with the construction and control of the linear motor, the linear bearing system of 

Figs. 2-4 will be used as a test-bed for a single linear suspension motor. The design will be 

refined here before advancing to the X-Y system shown in Fig. 6. 

6 Conclusions and suggestions for further work 

We have shown the design and analyzed the electromechanics of a linear motor suitable for 

independently controlling two suspension degrees of freedom. This motor, at least on paper, 

meets the requirements for driving an X-Y stage of 10 kg mass with about 4 m/sec2 

acceleration, with travel of several hundred millimeters in X and Y, and with reasonable 

power dissipation. A conceptual design for such a stage has been presented. 

However, this design has not yet been verified experimentally. A prototype of the linear 

motor is in construction and will be tested shortly. Initial testing is expected to take the form 

of operating the linear motor on a multi-axis load-cell in order to determine the ext.ent to 

which the actual motor operation matches the theory developed herein. The commutation 

laws can then be modified based upon experimental data. Once the motor operation is 

verified experimentally, a single linear motor will be attached to the linear bearing as shown 

in Figures 2-4, in order to gain experience with control issues. After satisfactory testing on 

the linear bearing, the system shown in Figure 9 will be constructed in order to achieve the 

end goal of control of planar motion with 200 mm travel. 

The systems described above can be improved in several ways. Currently, the Hnear 

bearing operates with purely linear control of the seven support electromagnets. The 

large-signal closed-loop performance of the bearing could be improved by including nonlinear 

compensation of the electromagnet force characteristic, as described in [6]. Additionally, the 

background noise of the five capacitive sensors currently limits the position stability. Thus it 

would be fruitful to investigate improved sensor techniques. Also, further work is needed in 

102 
developing sufficiently accurate and robust control techniques for the multivariable bearing 

system. Here, mechanical and electrical noise sources, uncertainties in the plant parameters, 

quantization of signals in the discrete-time controllers, saturation of power amplifiers and 

other non-idealities need to be considered as they impact the overall system performance. 

Finally, the magnet array technology developed by Halbach for linear accelerators [7,8] 

appears to be highly applicable to the linear motor magnet array. These magnet arrays use 

rotated blocks of magnets to provide a highly sinusoidal magnetic field concentrated on only a 

single side of the magnet array and thus a stronger fundamental component to interact with 

the stator winding. A magnet array using Halbach's topology is currently in design. 

In conclusion, this paper has demonstrated the theoretical feasibility of linear and planar 

bearings using single or multiple magnetic suspension linear motors. It remains to 

demonstrate this feasibility experimentally, and we are proceeding in this direction. 

References 

[1] Slocum, A.H., and Eisenhaure, D.B., "Design Considerations for Ultra-Precision Magnetic 

Bearing Supported Slides," NASA Magnetic Suspension Technology Conference, Hampton, 

Va. Feb. 2-4, 1988. 

[2] Trumper, D.L., "Magnetic Suspension Techniques for Precision Motion Control," Ph.D. 

Thesis, Dept. of Elec. Eng. and Compo Sci., M.I.T., Camb., Mass., Sept., 1990. 

[3] Teague, E.C., "The National Institute of Standards and Technology molecular measuring 

machine project: Metrology and precision engineering design," Journal of Vacuum Science 

Technology, B7 (6), Nov IDec, 1989, pp. 1898-1902. 

[4] Trumper, D.L., and Slocum, A. H., "Five-Degree-of-Freedom Control of an Ultra-Precision 

Magnetically-Suspended Linear Bearing," NASA Workshop on Aerospace Applications of 

Magnetic Suspension Technology, NASA Langley Research Center, Hampton, VA, 

Sept. 25-27, 1990. 

[5] Melcher, J.R., Continuum Electromechanics , MIT Press, Camb., Mass., 1981. 

[6] Trumper, D.L., "Nonlinear Compensation Techniques for Magnetic Suspension Systems," 

NASA Workshop on Aerospace Applications of Magnetic Suspension Technology, Hampton, 

VA, Sept. 25-27, 1990. 

[7] Halbach, K., "Design of Permanent Multipole Magnets with Oriented Rare Earth Cobalt 

Material," Nuclear Instruments and Methods, 169, 1980, pp. 1-10, North-Holland Publishing 

Co. 

[8] Halbach, K., "Physical and Optical Properties of Rare Earth Cobalt Magnets," Nuclear 

Instruments and Methods, 187, 1981, pp. 109-117, North-Holland Publishing Co. 

103 
N92-27728 

MODELLING AND DESIGN FOR l'M/EM MAGNETIC BEARINGS 

D. Pang, J. A. Kirk, D. K. Anand, R. G. Johnson 

Department of Mechanical Engineering 

University of Maryland, College Park, MD 20742, U. S. A 

R. B. Zmood 

Department of Communication and Electrical Engineering 

Royal Melbourne Institute of Technology, Melbourne, Victoria 3000, Australia 
SUMMARY 

This paper presents a mathematical model of a permanent magnet/electromagnet [PMIEM] 

radially active bearing. The bearing is represented by both a reluctance model and a stiffness 

model. The reluctance model analyzes the magnetic circuit of the PMIEM bearing. The stiffness 

model uses force equilibrium equations to present the behavior of the bearing. By combining the 

two models the performance of the bearing can be predicted given geometric dimensions, 

permanent magnet strength, and the parameters of the EM coils. 

The overall bearing design including the PM and EM design is subject to the performance 

requirement and physical constraints. A study of these requirements and constraints is discussed. 

The PM design is based on the required magnetic flux for proper geometric dimensions and 

magnet strength. The EM design is based on the stability and force slew rate consideration, and 

dictates the number of turns for the EM coils and the voltage and current of the power amplifier. 

An overall PMIEM bearing design methodology is proposed and a case study is also 

demonstrated. 

INTRODUCTION 

A magnetic bearing design combining permanent magnets and electromagnetic coils has the 

advantages of compact size, high efficiency and low heat generation. Permanent magnets 

containing mainly rare earth material have a high energy density and contribute the major magnetic 

flux in the bearing. The electromagnetic coils offer the additional magnetic flux to enhance the 

desired performance of the bearing. This design can decrease the size of the bearing, reduce the 

power consumption, and generate less heat in the bearing. There are various PMIEM bearing 

designs; this paper will discuss the PMIEM bearing developed in the University of Maryland for a 

flywheel energy storage system [1]. 

The PMIEM magnetic bearing shown Figure 1 is a passive axial support and radial active control 

design. The permanent magnets generate a bias flux across the air gap and support the axial load 

but create a destabilized force in the radial direction if the flywheel is not centered. A feedback 

control system senses the position of the flywheel and sends the appropriate control current into 

the EM coils. This generates the necessary corrective force to stabilize the system. The bearing's 

function is to magnetically suspend and center a rotating flywheel that can store kinetic energy. 

The mathematical model of the PMIEM bearing can be represented by both a reluctance model 

and a stiffness model. The former applies the magnetic circuit theory and geometric dimensions of 

the bearing to analyze the magnetic flux in the air gap. The latter evaluates stiffness equations and 

force equilibrium equations to present the behavior of the bearing. By combining both models the 

bearing performance can be predicted and designed. There are some physical restrictions for the 

PRECEDING PAGE BLANK NOT FILMED 107 
mathematical model such as magnetic saturation, size limitation and electrical constraints that will 

be discussed later. 

RELUCfANCE MODEL 

In Figure 2 there is a typical hysteresis loop for the permanent magnetic material [2]. The 

permanent magnet inherits a flux density Br, remanence, at zero magnetizing force. If a negative 

magnetizing force is applied to the magnet until the flux density reduces to zero, that magnetizing 

force is called the coercive force He. For most applications the permanent magnet operates in the 

second quadrant of the B-H curve between Br and He. The slope of the B-H curve (the ratio ofB 

to H) is denoted the permeability. The most commonly used permeability is the recoil 

permeability JLr, which is the slope of the minor hysteresis loop. It is approximately equal to the 

slope of the B-H curve at zero magnetizing force and is usually presented as a relative value to the 

permeability of the air. 

For an ideal permanent magnet having a strong intrinsic coercive force the B-H curve is a straight 

line between Br and He shown in Figure 3. The minor hysteresis loop will follow the B-H curve 

and the recoil permeability is the ratio of Br and He. The equation for the B-H curve is 

Bm = JL<>JLrHm + Br (1) 

In a static magnetic field condition, magnetic circuit theory is used to analyze the magnetic flux by 

solving an equivalent electrical circuit. The reluctance of a magnetic flux path, which is analogous 

to an electrical resistance, is a function of its length L, cross section area A and permeability JL, 

R = U(p.A) 

The permanent magnet can be simulated as a battery of voltage BrAmRm with an internal 

resistance Rm or a current source HmLm with a shunt reluctance Rm [3]. The EM coils can be 

treated as voltage sources of quantity NI. 

(2) 

Figure 4( a) shows a magnetic circuit containing a permanent magnet, a core material of high 

(assumed mfinite) permeability and an electromagnetic coil. There is a magnetic flux generated by 

the permanent magnet and the EM coil. When the magnetic flux passes through the air gap, it is 

separated into two paths: one is the air gap flux path directly across the pole faces and the other is a 

leakage flux path around the air gap flux path. The reluctance of the air gap and the leakage path 

are Rg and RL. The total reluctance RT is the combination of both reluctances. The equivalent 

electrical circuit can be plotted as Figure 4(b). 

By applying the Ampere's circuital law, the magnetic flux equation and the reluctance equations, 

the magnetic circuit can be presented as the following: 

HmLm + BgAgRg = NI (3) 

BmAm = BgAg(Rg/RT) (4) 

Rg = go/(}LoAg) (5) 

Rm = Lm/(}LoJLrAm) (6) 

From equation (1), (3), (4) and (6), the operating flux density of the magnet can be written as 

Bm = (BrRm + NIIAm)l(Rm + RT) (7) 

The operating flux density has been changed due to the magnetizing force from the EM coils. 

Figure 3 illustrates the load line of the magnet shifted parallel from its original load line. For the 

PM/EM bearing, the magnet will mainly operate at near zero magnetizing force so the operating 

flux density can be treated as a constant value of Bm with a variation ABm. Furthermore, the 

permanent magnet design and the EM coil design can be studied independently as long as the 

108 
operating point of the magnet is along the straight line of the B-H curve. Equation (7) can be 

rewritten as the following: 

Bm = BrRm/(Rm + RT) (8) 

dBm = (NI/Am)/(Rm + RT) (9) 

In the PMIEM bearing the magnetic flux from one permanent magnet passes the one air gap to the 

return ring of the flywheel and return through the other air gap. The equation for the reluctance 

of the air gap is doubled, 

Rg = 2go/JLOAg (10) 

The bias flux generated by the permanent magnet is 

Bu = (BmAm/ Ag)(RT/Rg) (11) 

The permanent magnet design is statically undetermined because there are five equations: (1), (6), 

(8), (10) and (11) with 12 variables: Bm, Br, Bu, Hm,J£r, Lm, go, Am, Ag, RT, Rm and Rg. 

In the magnetic bearing design there are four EM coils of the same axis connected in parallel to the 

power amplifier. The magnetomotive force of the EM coils in each axis is NImax. The flux density 

generated by the EM coils across the air gap is 

BEM = JLONImax/( 4go) (12) 

STIFFNESS MODEL 

The stiffness model for the magnetic bearing assumes the properties of the bearing to be linear 

over the operating range except the control current to the EM coils in the control system. The 

control current is linear until saturation of the power amplifier, after which it is held constant. The 

reason for the limitation of the control current is to avoid a magnetic saturation of the materials. 

The static behavior of the bearing can be represented by force equilibrium equations. In the axial 

direction, the bearing passively supports the axial load of the flywheel. 

FA = Kzdp (13) 

In the radial direction, the flywheel is affected by two forces: the destabilizing force from 

permanent magnets and the corrective force from electromagnetic coils. The combined restoring 

force of the bearing is 

Frad = KiI - KxX (14) 

Figure 5( a) represents the radial forces of the bearing including the destabilizing force, the 

corrective force, and the restoring force. Figure 5(b) shows the control current output from the 

power amplifier. The corrective force reaches its peak when the power amplifier becomes 

saturated and cannot supply more current. Simultaneously the restoring force also reaches the 

peak and begins to decline as the destabilizing force continues to increase and the corrective force 

stays constant. When the net restoring force is zero, the corrective force equals the destabilizing 

force. The maximum displacement of flywheel is defined as the maximum stable range and given 

by 

Xstb = KiImax/Kx (15) 

There is a maximum displacement range the flywheel can travel without current saturation. The 

maximum range Xlin is called the linear range of the bearing, which is dependent on the 

current/displacement ratio C of the control system. 

Xlin = Imax/C. (16) 

In the linear range, the force equilibrium equation (14) can also be written as 

109 
Frad = KaX = KiI - KxX 

This active stiffness of bearing can be represented by 

Ka = CKi - Kx 

(17) 

(18) 

The linear range, the maximum restoring force and the active stiffness are determined not only by 

the maximum control current to the EM coils but by the current/displacement ratio C of the control 

system. A lower current/displacement ratio means a larger linear range, lower active stiffness and 

smaller maximum restoring force. A higher current/displacement ratio has the opposite effects. 

For a magnetic bearing, a larger linear range, higher active stiffness and greater maximum restoring 

force are desired so there is a conflicting interest for the choice of the C. The bearing must balance 

all these performance requirements. 

The geometric dimensions of the bearing such as the length and the cross section area of the air 

gap have major effects on the magnetic flux and the magnetic force because the flux directly across 

the air gap of two pole faces helps to support the weight as welI as center the flywheel. The bias 

flux from the permanent magnet contributes the axial stiffness Kz and the passive radial stiffness 

Kx. The flux from both the permanent magnet and EM coils influences the force/current 

sensitivity Ki. The Kz, Kx and Ki values can be obtained from experimental or a theoretical 

analysis. 

The axial stiffness of the magnetic bearing derived by Sabnis [4] using the Schwartz-Christoffel 

transformation shows that 

Kz = 4Bu2Rmean/j£<) (19) 

The passive radial stiffness and the force/current sensitivity can be derived as the following [1]: 

Kx = 2pBu2Rmeantpf/(J.wgo) (20) 

Ki = 2BuRmeantpfN/go (21) 

PERMANENT MAGNET DESIGN 

Permanent magnetic materials have greatly progressed in last decade due to the development of 

rare earth magnets [5]. Rare earth magnets such as samarium-cobalt and neodymium-iron-boron 

magnets have very high coercive forces combining with high remanence. Figure 6 shows the B-H 

curves of the rare-earth magnets compared to some older magnet types such as Alnico and ceramic 

magnets. The B-H curves for the rare-earth magnets are nearly straight lines in most of the second 

quadrant. The energy products of the rare earth magnet are four or five times values of older 

magnet types. It means smaller magnets can now generate same magnetic flux. A straight B-H 

curve also means the recoil lines of minor hysteresis loops wilI closely follow the B-H curve. The 

magnets can handle the external magnetizing force and any variation of the air gap in the magnetic 

circuit without degrading the performance. Thus, the rare earth magnets induce an easier 

magnetic circuit design with more dynamic applications. 

Although there are many rare earth magnets, the commercially available magnets are generally 

separated into three groups: SmCos, Sm2Co17, and NdFeB. SmCo.s magnets are the first type of 

rare earth magnets and produce an energy product of 16 to 23 MGOe with very high intrinsic 

coercive force, which can resist strong adverse magnetizing fields. They have a high curie 

temperature at 7500C but the intrinsic coercive force drops off as the temperature increases. 

SmCos magnets can only be used to about 2500C. Sm2Co17 magnets have a higher energy product 

of 20 to 30 MGOe and a higher remanence of 9.5 to 12 KG. Some types of Sm2Co17 have a lower 

intrinsic coercive force that results in a knee in the B-H curve. Sm2Col1 magnets have slightly 

better temperature performance than SmCos and are useful to about 3500C. NdFeB magnets 

have the highest energy product of 25 to 40 MGOe and a remanence of 11 to 12.8 KG. NdFeB 

110 
magnets only have a curie temperature of 30()oC and are useful only below 1500C. NdFeB is the 

cheapest rare earth component due to the vast amounts of the material resources currently 

available. NdFeB has a corrosion problem, however, and SmxCox magnets should not be used at 

the radiation environments. All three magnets are very hard and brittle and should be protected 

from large mechanical stresses. 

The PM design has 5 equations with 12 variables as suggested from the reluctance model. Three 

dependent variables Hm, Rm and Rg can be eliminated using equations (1), (6) and (10). Three 

variable Bu, Ag and go are determined by the axial drop, axial load and radial load requirements. 

If the fundamental geometry of the magnetic circuit is known, the useful flux ratio (RT/Rg) is 

approximated. For the current PMJEM bearing design, the useful flux ratio is in the range of 30% 

to 40%. The relative recoil permeability 1.Lr for the rare earth magnets is around 1.05. The PM 

design problem has been simplified into 2 equations, (8) and (11), with 4 variables: Bm, Br, Lm and 

Am. 

For a maximum energy output from the permanent magnet, the operating flux density should be 

half its remanence. This design can also minimize the volume of the magnet and its material cost, 

and equates to 

Bm = Br/2 or Rm = RT (22) 

This may not be feasible due to other geometric constraints on the length and cross section area of 

the magnet. To avoid underestimation of the reluctance in the magnetic circuit or increase of the 

air gap, the operating flux density Bm is always designed above its calculated value (half the 

remanence ). However, the Bm/Br ratio is a good efficiency index for the magnet design. This 

Bm/Br ratio can be used to choose an appropriate permanent magnet strength form the 

manufacturer catalog at a preliminary design. 

Any two of the five variables: Bm, Br, Lm, Am and Bm/Br can be chosen to solve the following 

equations derived from Equation (8) and (11), 

Br = (BuAglAm)(Rg/RT)(Br/Bm) 

Lm/Am = (p.rgo/Ag)(RT/Rg)/«Br/Bm) - 1) 

Am = BgAgLm(Rg/RT)/(BrLm -J.LrBggo) 

(23) 

(24) 

(25) 

PM design is one of the most difficult in the magnetic bearing because all the magnetic flux paths 

should be carefully calculated. The rare earth magnets are expensive and usually made to order 

for a specific configuration. If there is error in the design, the magnets most likely will be wasted. 

ELECTROMAGNETIC COIL DESIGN 

The EM coil design is based on the stability and the force slew rate considerations to choose the 

number of turns for the coil, and the voltage and current for the power amplifier. The stability 

consideration is derived from the nonlinear control system analysis used to remove the limit cycle 

oscillation and to improve the robustness of the bearing. The force slew rate consideration is 

derived form the dynamics requirements of the magnetic bearing for the external force or mass 

unbalance conditions. From both the experimental results and theoretical analysis the power 

amplifier voltage and the number of turns (inductance) of the EM coils have greater roles in 

stabilizing the bearing and responding to any disturbance. 

Zmood et al [6] found, when the power was connected, the flywheel not only failed to self-suspend 

but often broke into self-sustaining oscillation unless the mechanical touchdown gap was well 

adjusted. Also, the magnetic bearing flywheel system broke into limit cycle oscillation due to a 

111 
large disturbance. The source of the oscillations is due to the combined effects of the power 

amplifier saturation, bearing radial stiffness Kx, the touchdown gap Xtd and the inductance of the 

EM coil. A simplified nonlinear control system model shown in Figure 7 has been built to study 

the self-suspension and limit cycle oscillation phenomenon observed in the experiment. The 

model makes the following assumptions: 

!

lj The back e.mJ. induced in the EM coils can be neglected; 

2 The EM coil resistance can be neglected; 

3 When the flywheel collides with the touchdown bearing the velocity and acceleration drop to 

zero; 

!

4j There is no external disturbance force so the equation (14) can be applied; 

5 There are only the current and displacement feedback loops; 

6 The bearing actuator can be approximately modelled by a first order differential equation. 

The equation for the stability condition of the bearing can be written as the following 

1 Kia' 

-+--

4 KxXtd 

where a' = Vcc/(Wm'Lind) and Wm' = (Kx/M)1!2. 

(26) 

For a stable system the parameters of the control system, ex and Ci, should be chosen to satisfy the 

inequality equation (26). To increase the robustness of the control system and to relax the 

restriction on these parameters the right hand part of the inequality equation should be as large as 

possible. This part can also be viewed as the relative stability ratio 8 of the control system. For 

our magnetic bearing there are four EM coils connected parallel together to the power amplifier at 

one axis. The magnetic flux from the EM coils will pass four air gap so the inductance becomes 

Lind = J.LOAgNl/( 4go) (27) 

From equation (26) and (27) the number of turns for the EM coil can be written as an inequality 

form. 

4{2go Va; 1 

N < Jt2BuRmcantpf Wm'Xtd 82 - 8 (28) 

Maslen et al [7] studied the effects of the force slew rate on the dynamic performance of the 

bearing. If the bearing operates about its center, X = 0, the force slew rate can be derived from 

the radial force equation (14) as 

dF /dt = Ki( dl/dt) (29) 

The force slew rate can also be written as the function of the applied voltage and the inductance of 

the EM coils. 

dF /dt = KiV cc/Lind (30) 

For a step force input FR or a mass unbalance at a rotational speed of w rad/s with a distance X 

from the center, the force slew rate is proven to be 

dF/dt > (2FR3/3MX)1!2 

dF/dt > Mw3X 

The number of turns for the EM coils presented as the function of the force slew rate becomes 

N 8{2BuVcc 

< dF 

Jtllo dt 

112 

(31) 

(32) 

(33) 
The maximum supply current for the EM coils can be calculated using equation (12), 

Imax = 4BEMgo/p.oN (34) 

The power amplifier of the control system can be chosen based on the its voltage and current 

reqUIrements. 

PMJEM MAGNETIC BEARING DESIGN 

The flowchart for the design methodology of the PMIEM bearin~ is shown in Figure 8. The design 

procedures start with design requirements for the magnetic bearIng including the mass of the 

flywheel, the axial force, the radial force and the linear operating range. There are some initial 

inputs such as the saturation flux density of the magnetic material, the recoil permeability of the 

PM material, the operating point of the permanent magnet, the useful flux ratio, and power 

amplifier voltage. These values can be updated or changed with the choice of the specific materials 

and designs. 

The bearing design is an iterative processes so the number of steps just shows a possible sequence. 

These procedures are used for the magnetic bearing flywheel energy storage system and designer 

can revise the procedures for other applications. 

(1) Flux density consideration 

The flux densities in any section of the magnetic bearing are limited by the saturation value of 

the magnetic material so the combined flux densities from the PM and EM are less than the 

saturation value. If there are equal flux densities from the PM and EM, the bearing can 

generate a maximum force. In most applications the flux density from the PM is greater than 

that from the EM. 

(2) Geometric relationship consideration 

Our PMIEM bearing is a small gap suspension design so the linear range is less than 15% of the 

air gap. To avoid large leakage flux and cross-talk between the pole faces of the magnet plates 

and return ring, the pole face thickness is at least 3 times of the air gap. Also, there is a 

minimum thickness for the PM to prevent too much leakage between the two magnet plates. 

(3) Axial drop, axial load, and radial force consideration 

The magnetic bearing is designed to satisfy the force requirements by choosing the flux 

densities and the geometric dimensions. Because of our radial active bearing design the load 

capability in the axial direction is weaker than the radial direction. If the bearing is used to 

handle the same force in both directions, the axial force requirement becomes dominate. To 

avoid the possibility that a larger axial drop may worsen the magnetic properties of the bearing 

the ratio of the axial drop and the pole face thickness is limited to 20%. 

(4) Selection of a feasible design 

After satisfying the performance requirement and physical constraints a feasible design is 

chosen including the flux densities from the PM and EM, the mean radius, the air gap, the pole 

face thickness, and other dimensions. 

(5) Permanent magnet design 

Using the information from the previous step the parameters of the permanent magnet design 

such as the magnet strength, thickness and cross section area can be decided by applying the 

equation (23), (24) and (25). 

(6) Electromagnetic coil design 

Based on the stability and force slew rate considerations the number of turns for the EM coils 

as well as the voltage and current for the power amplifier can be decided. 

113 
(7) Characteristics of the PMIEM bearing 

The performance parameters such as Xstb, XIin, Ka, C, Kz, Kx and K.i for the bearing can be 

calculated using the equation (15), (16), (17), (18), (19), (20) and (21). 

(8) Optimization design 

A optimization method for the PMIEM bearing design has been developed at the University of 

Maryland [8]. The designer can define an objective function with all equality and inequality 

constraints to find an optimum design. 

After finishing the preliminary design the bearing needs a detailed study such as a finite element 

model for magnetic circuit agreement and dynamic simulation. Also, the control system and 

overall bearing flywheel system need further investigation but these are beyond the scope of this 

paper. 

EXAMPLE 

An example for the pancake magnetic bearing design is presented to demonstrate the proposed 

design methodology. Assume a pancake magnetic bearmg for the energy storage system having a 

flywheel weight of 8 lbs. The bearing is designed to handle at least 16 lbs force at both axial and 

radial direction with an axial drop of no more than 20% of its pole face thickness. The magnetic 

bearing should allow at least 0.006 inch for the radial displacement before being limited by the 

mechanical touchdown bearing. The magnetic material for the bearing is nickel iron which has a 

saturation flux density of 1 Tesla. The maximum radius for the bearing is limited to 2 inch and the 

minimum height of the permanent magnet is 0.3 inch. The power amplifier of the control system 

has a voltage 24 volts and a maximum supply current 1.5 Ampere. The useful flux ratio is assumed 

to be 40% for this design. 

(1) Design Requirements & Physical Constraints 

The performance requirement and physical constraints of the magnetic bearing are rewritten as 

the following: 

M = 8lbs 

FA > 16lbs 

FR > 16lbs 

Bsat = 1 Tesla 

Rmean < 2 in 

Xtd = 0.006 inch 

dp/tpf < 0.2 

Lm > 0.3 inch 

Vee = 24 V 

Imax < 1.5 Amp 

RT/Rg = 0.4 

(2) Flux Density Consideration 

The flux density generated by the permanent magnet across the air gap is assumed lto be 50% of 

the saturation value of magnetic material. The flux density from the EM coils is 40% of the 

saturation value. 

Bu = 0.5 Bsat = 0.5 Tesla 

BEM = 0.4 Bsat = 0.4 Tesla 

(3) Geometric Relationship 

The touchdown gap is designed to be 15% of the air gap and the pole face thickness is three 

time of the air gap. 

go = Xtd/0.15 = 0.04 in 

114 
tpf = 3 go = 0.12 in 

(4) Axial Drop, Axial Load and Radial Force Requirement 

The axial stiffness equation is used to find the mean radius for the magnetic bearing. 

dp = W A/Kz = 0.2 tpf = 0.024 in 

Rmean = 2.89 in > 2 in (Failure!) 

Because the calculated radius is larger than the allowable size the above design must be 

changed. One way is to choose the bearing radius as the maximum allowable value and to find 

the required flux density at the air gap which can satisfy the requirement. 

Rmean = 2in 

Bu = 0.6 Tesla 

BEM = 0.3 Tesla 

FA = 20.91bs > 16lbs (OK!) 

FR = 25.11b > 16lbs (OK!) 

(5) Permanent Magnet Design 

The permanent magnet is chosen to use the rare earth Recoma 20 material which has a 

remanence of 0.85 Tesla and a recoil permeability of 1.05. The length of the permanent 

magnet is assumed to be 0.3 in. The cross section area for the air gap is calculated to be 0.377 

in2. The radius and the operating flux density of the magnet can be calculated as the below 

Am = 0.829 in2 

Rm = 0.94 in 

Bm = 0.68 Tesla 

(6) Electromagnetic Coil Design 

The radial passive stiffness of the bearing is calculated to be 1567 lb/in. If the relative stability 

ratio is assumed to be 2, the number of turns for the EM coil can be calculated using the 

stability criteria 

N < 1790 turns 

If the bearing is assumed to handle a step input force of 16lbs at the touchdown gap. The 

force slew rate and the number of turns for the coil are: 

dF/dt = 31254 N/s 

N < 1320 turns 

Finally the number of turns for the EM coil is chosen to be 1000 turns so the maximum supply 

current is 0.97 ampere which satisfies the constraint of the power amplifier. 

(7) Characteristics of Pancake Magnetic Bearing 

The performance parameters for the bearing are listed as the following: 

Kx = 1567 lb/in 

Ki = 29.1Ib/Amp 

Ka = 2667 lb/in 

Kz = 332 lb/in 

C = 146 Amp/in 

Xstb = 0.018 in 

Xlin = 0.0066 in 

DISCUSSION AND CONCLUSION 

In light of the demands of modern technology for more efficient and economic energy conversion, 

magnetic bearings certainly fit the requirements. The various magnetic bearings differ in function 

and form but a major commonality between them should be the theory that governs all physical and 

magnetic behavior. Although the specific numbers of these mathematical m~dels for a flywheel 

115 
magnetic bearing are unique, the design methodology and magnetic developments encompass all 

such devices. As always, one must be careful to study the physical constraints and boundary 

conditions placed on the problem. University of Maryland has been successful in developing two 

different sizes of bearings and an operational combination of two bearings in a stack configuration. 

The success has come from proposmg, modifying, and verifying the mathematical models presented 

here. A few grey areas remain, such as the crosstalk between magnetic flux paths and harmonic 

disturbances, which were beyond the scope of this paper. Future methodology will indude 

dynamic effects, digital rather than analog control, and finite element analysis of the magnetic 

circuitry. As the system becomes more complex, so do the questions that are raised about its 

optimization. 

Ag: 

Am: 

BEM: 

Bm: 

Br: 

Bsat: 

Bu: 

Bg: 

C: 

Cx: 

Ci: 

Dm: 

dp: 

FA: 

FR: 

Frad: 

go: 

He: 

Hm: 

Imax: 

Ka: 

Ki: 

Kx: 

Kz: 

Lind: 

Lm: 

M 

N: 

Rg: 

RL: 

Rm: 

RT: 

Rmean: 

tpf: 

Xlin: 

Xstb: 

Xtd: 

Vee: 

Jlo: 

Jlr: 

116 

SYMBOLS AND ABBREVIATIONS 

Cross Section Area of Air Gap; for PMJEM Bearing = 1tRmeantpf/2 

Cross Section Area of Permanent Magnet = 1tDm2/4 

Flux Density by Electromagnet at Pole Face 

Operating Flux Density of Permanent Magnet 

Remeance of Permanent Magnet 

Saturation Value of Magnetic Material 

Useful Flux Density by Permanent Magnet at Pole Face 

Flux Density Across Air Gap 

CurrentlDisplacement Ratio of Control System 

Displacement Feedback Gain in Control System 

Current Feedback Gain in Control System 

Diameter of Permanent Magnet 

Axial Drop of Flywheel 

Maximum Axial Force 

Maximum Radial Force at X = Xtd 

Restoring Radial Force = KiI -KxX 

Air Gap 

Coercive Force of Permanent Magnet 

Magnetizing Force of Permanent Magnet 

Maximum Control Current to Electromagnetic Coils 

Active Stiffness of Magnetic Bearing = CKi - Kx 

Force/Current Sensitivity of Electromagnetic Coils 

Passive Radial Stiffness of Magnetic Bearing 

Passive Axial Stiffness of Magnetic Bearing 

Inductance of Electromagnetic Coils 

Length of Permanent Magnet 

Mass of Flywheel 

Number of Turns of One Electromagnetic Coils 

Reluctance of Air Gap at Pole Face 

Reluctance of Leakage Flux 

Reluctance of Permanent Magnet 

Total Reluctance = RgRL/(Rg+RL) 

Mean Radius of Middle Point of Air Gap 

Pole Face Thickness 

Linear Range of Magnetic Bearing 

Stable Range of Magnetic Bearing = Xlin (1 +Ka/Kx) 

Touchdown Gap 

Amplifier Supply Voltage 

Permeability of Free Space = 41txlO-7 Him 

Recoil Permeability of Permanent Magnet 
dF. 

dt' 

~Bm: 

Force Slew Rate 

Varying Flux Density of Pennanent Magnet 

REFERENCE 

1. Iwaskiw, A. P., "Design of a 500WH Magnetically Suspended Flywheel Energy Storage System", 

Master Thesis, University of Maryland, College Park, 1987. 

2. McCaig, M., Clegg A. G., "Permanent Magnets in Theory and Practice", John Wiley & Sons, Inc., 

New York, 1987. 

3. Parker, R. J., "Advances in Permanent Magnetism", John Wiley & Sons, Inc., New York, 1990. 

4. Sabnis, A. V., " Analytical Techniques for Magnetic Bearings" PhD Dissertation, Univ. of 

California, Berkeley, 1974. 

5. Strnat, K. J., "Modern Permanent Magnets for Applications in Electro-Technology", Proceedings 

of International Workshops on Rare-Earth Permanent Magnets and Applications, Pittsburgh, 

Penn., 1990. 

6. Zmood, R. B., Pang D., Anand D. K., Kirk, J. A., "Improved Operation of Magnetic Bearings for 

Flywheel Energy Storage System", Proceedings of 25th Intersociety Energy Conversion 

Engineering Conference, Reno, Nevada, 1990. 

7. Maslen, E., Hermann, P., Scott, M., Humphris, R. R., "Practical Limits to the Performance of 

Magnetic Bearings: Peak Force, Slew Rate, and Displacement Sensitivity", Proceedings of 

NASA Workshop on Magnetic Bearings, Langley, Virginia, 1988. 

8. Pang, D., Kirk, J. A., Anand, D. K., Huang, c., "Design Optimization for Magnetic Bearing", 

Proceedings of 26th Intersociety Energy Conversion Engineering Conference, Boston, Mass., 

1991. 

8(T) Q STATOR 

H (Am-1 ) 

o .L.-_-

Fig. 1 PM/EM Magnetic Bearing Fig. 2 PM Hyseteresis Loop 

117 
H 

118 

B 

Br 

Bm 

_ I~Bm 

He 

Fig. 3 Ideal PM B-H Curve 

«1>= ~ BmAm r- -- -I .-----------~._----1 

rPM 1 

1 

Ni 

Fig. 4 PM/EM Magnetic Circuit 

+ «I>g 1 

1 

Rg 1 RT 

L _____ I 
Linear Region Saturation Region 

{kA/m] 

1.4 800 600 400 200 0'4 Radial Forceo 

B B 

1.2 12 

{T] [kG] 

1.0 10 ~--v:;"':---~"'c---- Flywheel Displacement From the Center 

0.8 8 

0.6 6 

0.4 4 

0.2 2 

0 12 00 

ControlOurent lz: (oj 

Imu-CX!in - - _.__--

1 

""-__ ----'1:-______ Flywheel Displacement 

Prom the Center (b) 

Fig. 5 Magnetic Bearing Radial Forces Fig. 6 Various PM B-H Curves 

Power Actuator 

Amplifier Coil 

x(t) 

Fig. 7 Simplified Bearing Control System 

119 
Start 

Flux Density Consideration: 

Bu, BEM 

Axial Drop, Axial Load & Radial Force: 

Rmean, tpf, go 

Select a Feasible Design 

Permanent Magnet Design: 

Electromagnetic Coils Design: 

N, Imax, Vee 

Characteristics of PM/EM Bearing: 

Kx, Ki, Ka, C, Kz, Xstb, Xlin 

Detail Design of PM/EM Bearing 

Control System Design 

Overall System Design 

Finish 

Fig. 8 PM/EM Bearing Design Flowchart 

120 
Session 3 

SENSORS AND CONTROLS 1 

Chairman - Mark Motter 

NASA Langley Research Center 

121 
N92-27729 

Application of Narrow Band Control to Reduce Vibrations in Magnetic Bearing Systems 

Monique S. Gaffney 

Bruce G. Johnson 

SatCon Technology Corporation 

12 Emily Street 

Cambridge, MA 02139 

PRECEDING PAGE BLANK NOT FilMED 123 
The goal of this paper is to illustrate the benefits of narrowband control theory for simple, 

open-loop stable systems, then discuss how the control approach changes for magnetic bearing 

systems, which are open-loop unstable. Magnetic bearing systems are good applications for 

narrowband control theory. This paper discusses two sources of synchronous forces, the 

measurement error and the magnetic unbalance. Both the measurement error and the magnetic 

unbalance manifest themselves as synchronous disturbances (ref. 1). As will be shown, narrowband 

control theory for simple, open-loop stable systems provides excellent performance and good 

stability robustness. Because magnetic bearing systems are open-loop unstable, the narrowband 

control approach becomes more complex. Disturbance accommodating control (DAC) theory is 

introduced herein as an effective approach to reduce vibrations in magnetic bearing systems. It is 

used to develop a control/estimation scheme that enables the rotor to spin about its center of mass, 

in the presence of the measurement error disturbances. 

OVERVIEW 

o Magnetic bearing systems are narrowband control applications 

o Narrowband control theory for open-loop stable plants 

o Narrowband control theory for magnetic bearing systems 

o Satcon magnetic bearing system background 

o Results from a disturbance accommodating controller 

PRECEDING PAGE BLANK NOT FILMfD 125 
Active control enables magnetic bearings to reduce vibrations in rotating machinery. One 

method of reducing the synchronous vibrations of a rotating system is to enable the rotor to spin 

about its true inertial axis. No synchronous forces are generated when the rotor spins about its 

center of mass because the acceleration of the center of mass of the rotor is zero. The figure below 

is a simplified free body diagram showing the forces acting between the rotor and stator in a 

magnetic bearing system. The figure presents an axial cross-section of the gap in a magnetic 

bearing system. For simplicity, the effects of gravity are neglected; nevertheless with gravity the 

conclusions are the same. Similarly, the angular motion is neglected, therefore the distance 

between the forces on the free body diagram is immaterial. The translational equation of motion 

for the rotor in one radial direction is, 

rnX = Fb + Fd 

The system will produce no net force on the rotor when, 

Fb + Fd = 0 

From the first equation, the acceleration of the center of mass of the rotor, X, must be zero for the 

second equation to be true. If the rotor spins at a constant speed about an axis other than its 

inertial axis, the center of mass is accelerated due to the changing direction of its velocity vector. 

This implies that when the axis of rotation is the inertial axis, such that x = 0, then there is no net 

force generated by the bearing system because the acceleration of the center of mass is zero, 

namely x = O. In summary, spinning the rotor about its inertial axis eliminates the vibratory forces 

generated by the bearing system. However, the bearing control force Fb is not necessarily zero 

because it acts to "cancel" any other force Fdd. 

126 

SPIN ABOUT THE CENTER OF MASS 

ROTOR 

Rotor/Stator Force Interaction 

Fb is the bearing force 

Fd is any force acting directly between the rotor and base 

ie. magnetic unbalance force 

Equations of Motion 

mx = Fb + Fd 

want F b + F d = 0 

Bearing force "cancels" disturbance force for no vibrations 
The figure below consists of a radial cross-section of a magnetic bearing system. The center 

of mass (M) is situated on the inertial axis of the rotor. Although its position is unknown, the 

inertial axis is the desired axis of rotation in order to minimize system vibrations as discussed 

previously. The measurement center (S) is defined by the position measurement sensors. The 

position sensors are mounted on the bearing housing and measure the distance to the rotor surface, 

or in other words, the gap. To give a physical perception of this center, the measurement center 

is the geometric center of the rotor, assuming an ideal surface measurement, (ie. the rotor surface 

is perfectly smooth and the material is perfectly homogenous). The line segment (€s) in the figure 

below is the unknown distance between the position the sensors measure and the position of the 

center of mass of the rotor. In conventional bearing systems, this distance is the mass imbalance. 

Consequently, (€s) is termed the measurement error because it is the amount of synchronous 

corruption of the center of mass position signal by the measurement system. Also from the figure, 

the kinematic relationship relating the center of mass to the measurement center, using complex 

coordinates, is 

zs = z + € S e

jOt 

The effect of the measurement error or "mass imbalance" is to produce an additive 

disturbance at the output of the plant. The output disturbance is also a function of the synchronous 

frequency. 

MEASUREMENT ERROR MODELLING 

Goal - vibration reduction ==> spin about the center of mass 

Problem - cannot measure the center of mass 

M - rotor center of mass 

S • rotor measurement center ... rotor geometric center 

Kinematic relationship (complex notation) Zs = Z + es elm 

Additive output disturbance 

127 
The following figure is a simple block diagram of a magnetic bearing system, illustrating how 

the measurement error is an additive plant output disturbance that corrupts the center of mass 

position. Because the feedback signal, the measured position, is a combination of the inertial 

position and the measurement error disturbance, the controller drives the rotor to spin about its 

measurement center. As a result, the rotating system generates vibratory forces. 

128 

BLOCK DIAGRAM WITH MEASUREMENT ERROR 

Desired 

Rotor 

Position 

+ 

Force 

+ --~'\....J'---1~ Controller .....---tM J----.t 

Plant 

Measurement 

Error 

Disturbance 

Actual 

Position + 

Measured 

Position 

+ 
Another synchronous disturbance source is the magnetic unbalance. A magnetic center (F) 

is located axially along the rotor at each rotor/stator set, for example at the bearings and motor. 

All the rotor/stator sets on the shaft contribute to a resultant magnetic center. This center is the 

point of equilibrium for the resultant unstable spring force. In other words, if the rotor spins about 

its magnetic center, the change in magnetic gap (oG) would be zero. This center depends mainly 

upon the geometry of the rotor. Given a system with the 

bearings as the only source of side-loading forces, the magnetic center is the measurement center 

(or geometric center), assuming an ideal rotor surface measurement, with a smooth rotor surface 

and homogenous material properties. Consequently, the position of the magnetic center at each 

bearing is known from the position sensors. However, if the rotor has other electric components 

on it, such as an induction motor, the position of the magnetic center at these components cannot 

be extracted simply from information via sensors at the bearings. Therefore, the resultant magnetic 

center is unknown and is different than the measurement center. The point (F) in the figure 

below represents the magnetic center of the rotor at one rotor/stator set. As the rotor spins about 

its center of mass (M), the distance (€p) rotates with angular velocity (n). The kinematic 

relationship between the center of mass and the magnetic center, in complex coordinates, is given 

by _ ~int zp - z + €p t7 

MAGNETIC UNBALANCE MODELLING 

Electric machine interaction ==> radial attractive force ==> function of gap 

M - rotor center of mass 

F - magnetic (field) center ... rotor geometric center 

Linearized constitutive relation 

F = K .6Za K < 0, negative stiffness 

F = K ZF assuming no base motion 

Kinematic relationship (complex notation) 

ZF = Z + EF elm 

F = K ZF = K Z + KEF elm ==> additive input disturbance 

129 
The linearized constitutive relation for the side-loading forces from either the bearings or the motor 

IS 

F = - K 6z g 

Assuming the rotor/stator set in question is located axially at the center of mass initially to 

avoid the angular terms, and also assuming no baseplate motion, 

F = Kzp 

because the change in magnetic gap is represented by a change in position of the magnetic center, 

where (6zp) = -( 6zg). Thus, combining this equation with the kinematic relation, the expression for 

the unstable spring force becomes 

F = K z + K € P ei°t 

As shown in the block diagram below, the synchronous magnetic unbalance disturbances manifests 

itself as an additive input disturbance. 

130 

BLOCK DIAGRAM WITH BOTH DISTURBANCE INPUTS 

Desired 

Rotor 

Position 

Magnetic 

Unbalance 

Disturbance 

+ Force 

+ --..... ~ ____ Controller 1---111>1. J-----at 

Plant 

Measurement 

Error 

Disturbance 

Actual 

Position + 

Measured 

Position 

+ 
Narrowband control theory for open-loop stable plants can provide excellent performance 

with good stability robustness for systems with periodic disturbances. As will be shown, the system 

is phase stable at the disturbance frequency and gain stable everywhere else. High levels of 

disturbance attenuation can be obtained. For simple cases, (SISO, linear, open-loop stable, and a 

constant disturbance frequency) the compensator design parameters consist of the plant gain and 

phase at the disturbance frequency. The resulting low-order filter is easy to implement. 

NARROWBAND CONTROL ATTRIBUTES 

(open-loop stable) 

Stability robustness 

o phase stable at disturbance frequency 

o gain stable everywhere else 

Excellent performance 

o high levels of attenuation 

Simple design and implementation 

o model consists of plant gain and phase at disturbance frequency 

o low order filter for coding 

131 
Numerous approaches exist to the narrowband disturbance control problem, including 

classical feedback and adaptive feedforward. An excellent survey of the different types of 

narrowband control approaches is found in (ref. 2). The performance of these algorithms, however, 

can be made similar, at least for the relatively simple problem of controlling a SISO, linear, openloop stable plant that has a constant disturbance frequency. The implementation of these control 

algorithms, however, can differ significantly. 

NARROWBAND CONTROL APPROACHES 

Feedback 

o classical control, bandpass filtering 

o modern control, frequency-shaped cost functionals 

o disturbance accommodating control 

Feedforward 

o knob turning 

o adaptive feedforward filtering 

o higher harmonic control 

Others 

132 

o good survey in Sievers, L.A., von FLotow, A.H., "Comparison and Extensions 

of Control Methods for Narrowband Disturbance Rejection". NCA-VoI.8, 

A.S.M.E. Winter Annual Meeting, Dallas, Texas, November 1990 
In the classical feedback approach, shown in the block diagram below, the compensator gain 

H(s) is made infinite at the disturbance frequency Wd and small elsewhere. Typically this is 

implemented with a second-order filter, an undamped oscillator. The transfer function is shown 

below, where k is the compensator gain and Wd is the disturbance frequency. Because the feedback 

gain is infinite, the net error will be driven to zero, if the system is stable. 

The stability of this narrow-band controller is easily analyzed with the use of a Bode plot of 

loop gain. On the following page is a loop transfer function that assumes a constant gain plant 

(G(s) = g). This plot can be roughly divided into two frequency ranges, frequencies near the 

disturbance frequency and frequencies not near the disturbance frequency. At the disturbance 

frequency, the loop gain becomes infinite and changes phase by 180 degrees, because of the 

undamped oscillator poles in the compensator. At frequencies not close to the disturbance 

frequency, the loop gain is small, well below 0 db. As a result of these small gains elsewhere, the 

system stability is determined only by the loop gain near the disturbance frequency. The loop 

phase changes from + 90 degrees to -90 degrees at the disturbance frequency because of the zero 

in the compensator transfer function. Thus the phase margin, which is the amount the plant phase 

can change before the system becomes unstable, is seen to be ± 90 degrees. The gain margin, 

which is the amount the plant gain can change before the system becomes unstable, is theoretically 

infinite. 

CLASSICAL FEEDBACK APPROACH 

d(s) 

+ 

+ ." 

G(S) --.... ~ 

e(s) 

-H(s) 

Best performance 

s H(s) = k --- (:J + 1 

= (:J + 1 

Best stability 

133 
These good stability margins were derived for a particularly simple plant that has constant 

gain. However, many of these good stability properties remain even under significantly relaxed 

assumptions about the plant. For a more general plant all we need know to design the 

compensator and analyze its stability properties is the maximum gain of the plant Gmax and the 

phase of the plant at the disturbance frequency LGGtLld). At frequencies away from the disturbance 

frequency, we can guarantee stability if the loop gain is kept below 0 db independent of the plant 

phase, that is we "gain stabilize" the plant at these frequencies. If the loop gain is less than one (0 

db) it can never encircle the minus one point on the Nyquist plot, which is the stability condition 

for this system. At frequencies near the disturbance frequency, the loop gain becomes infinite and 

the best stability robustness will be achieved if the loop gain changes from + 90 to -90 degrees. The 

undamped poles in the compensator will contribute a change in loop phase of -180 degrees to the 

loop gain at the disturbance frequency. Therefore at the disturbance frequency we want the plant 

phase and the numerator portion of the compensator to contribute + 90 degrees of phase. This 

stability definition was shown on the previous page (ref. 3). The numerator of the compensator, 

is therefore designed to satisfy this equation, once the plant angle at the disturbance frequency is 

known. The angle of the compensator can be changed by changing the zero structure or, with a 

discrete time implementation, by the use of a pure time delay. The gain of the compensator is 

chosen so that the maximum loop gain in frequency ranges not close to the disturbance frequency 

gives a desired gain margin. 

134 

LOOP TRANSFER FUNCTION 

10' 

~ :::l 

~ 1~ ~------------------~r-------------------, 

:if 

::::E 

'0 

~ 

~ 

:2. 

10-'1 

Frequency (Hz) 

100 

100 

0 

J -100 

a.. 

-1~.~----~--~----~~~;===================~ 10' Frequ'&icy (Hz) 1 ~ 
More explicitly, the closed-loop performance of the compensator is given by the sensitivity 

transfer function below. If we assume for simplicity that the plant transfer function G(s) is a simple 

unity gain, the closed-loop transfer function between the periodic disturbance d(s) and the net 

output error e(s) is given in the figure below. As expected, the error will be zero at the disturbance 

frequency, because of the infinite gain in the feedback compensator at this frequency. Note that 

although the shape of the closed-loop disturbance to error transfer function of the figure below is 

in general a function of the plant gain G(s), it will always be zero at the disturbance frequency Wd 

independent of the plant gain at this frequency G(jWd). This is assuming that the plant is reasonably 

well behaved at the disturbance frequency, in particular that it does not have undamped zeros at 

the disturbance frequency. The relatively simple compensator, therefore, exhibits "perfect" 

performance in rejecting the disturbance force, if it is stable. 

10' 

100 

10-' ; 

~ ~ 

~ 

10--

10' 

CLOSED LOOP TRANSFER FUNCTION 

e(s} = 

des} 

1 

1 + G(s)H(s) 

(,)d 

10-

:: 

-

:; 

:: 

-

10:5 

135 
One application of this classical feedback narrowband control theory is to actively control 

a Stirling-cycle cryocooler compressor to cancel the higher harmonic forces produced by the linear 

motor (ref. 3). The linear motor is driven at a fundamental frequency of 40 Hz and produces 

higher harmonics that exceed the desired force vibration levels, as shown by the dotted plot in the 

figure below. The narrowband feedback compensation consists of five undamped oscillators, in 

parallel, at the higher harmonics of 80, 120, 160, 180, and 220 Hz. As shown in the figure, the 

forces at the target higher harmonics were driven into the noise floor of the force dynamometer, 

with over 40 db reduction at the 80 Hz harmonic. 

AXIAL VIBRATION FORCE SPECTRA USING SELF-CANCELING CONFIGURATION: 

136 

10' 

FIVE HARMONICS CANCELED 

Uncontrolled 

Actively Controlled 

10-3 L------''----''----'_---'-_---'-_---'-_---'-_---'-_--'-_---' 

o 50 100 150 200 250 300 350 400 450 500 

Frequency (Hz) 
The previous discussion on narrowband control theory was assuming an open-loop stable 

plant. Attractive force magnetic bearings, however, are open-loop unstable. As a result, the loop 

transfer function cannot have small gains everywhere besides the disturbance frequency, as in the 

open-loop case, and still remain stable. There are numerous narrowband control approaches for 

synchronous vibration reduction of magnetic bearing systems, several of those are listed below (ref. 

4,5,6). The remaining discussion will describe a SatCon hardware demonstration and introduce 

disturbance accommodating control theory as an effective narrowband approach for open-loop 

unstable plants. 

NARROWBAND CONTROL FOR MAGNETIC BEARING SYSTEMS 

o magnetic bearing systems are open-loop unstable plants 

o gain margin approach breaks down for open-loop stable plants breaks down 

Approaches 

o Notch filter 

o Open-loop dynamic balancing 

o LQ frequency shaping 

o Disturbance accommodating control 

o Others 

137 
The following discussion applies specifically to a hardware demonstration developed by 

SatCon Technology Corporation (ref 7). The system, shown in the figure below, is a one-fifth 

scaled model (by mass) of a cryogenic alternator. The figure is an axial cross-section of the shaft 

and several important components, namely the magnetic thrust and journal bearings, the motor and 

the flywheels. The magnetically suspended rotor/shaft assembly mass is approximately 82 

kilograms. The axis of rotation is in the vertical direction, therefore its weight is supported entirely 

by the thrust bearings. The induction motor spins the entire rotor/shaft assembly at a maximum 

working rotational speed of 3600 rpm (60 Hz). The flywheel components are simply cylindrical 

masses that simulate the inertial effects of the exciter and generator on the full scale cryogenic 

alternator. During cryogenic operation, the lower radial and axial actuators and the corresponding 

sensors are immersed in liquid nitrogen to demonstrate working bearings at 77· K. 

138 

CROSS-SECTION OF ROTOR/SHAFT ASSEMBLY 

'----..,TOR AXiAl MAOJETIC ACll.IATCR (WARM ENJ) 

FLYwt£EL (FtaD WtN)lIrG) 

~IIAD'''' "'''N;T,C ACTUATOR (COlD ..." 

AXiAl lAAOfr£TlC ACTl..lltTOR (CCLD 91)) 

mass = 82 kg 

shaft length = 1.2 m (47 in) 

rotational speed = 3600 rpm (60 Hz, 377 rad/sec) 

thrust bearing force (max) ert 800 N per bearing 

radial bearing force (max) ert 400 N per bearing 
The figure below is a photograph of the actual shaft, again showing the important 

components. The rotor is equipped with a adjustable mass system. The mass imbalance distance 

is increased by dropping a small weight down an access hole in the center of the shaft. When the 

shaft spins, the weight moves up a plugged-end channel, which is cut into the large flywheel, and 

thereby increases the mass imbalance. 

ORIGINAL PAGE 

BLACK AND WHiTE PHOTOGRAPH 

139 
A photo of the testbed structure is presented in the figure below. The shaft is vertical to 

accommodate for the cryogenic demonstration. As shown, a support stand provides the principal 

support and positioning of the entire system. A thick steel plate is bolted to the top of the stand. 

From this plate are hung the magnetic actuators, the rotating assembly, and the cryostat. During 

cryogenic operation, a level sensing system feeds liquid nitrogen to the cryostat from an external 

storage bottle. As a result, the bottom radial and axial magnetic actuators are submerged in liquid 

nitrogen and reach a constant temperature of 77 0 K. The magnetic actuator assembly consists of 

upper and lower housing structures which hold and accurately position the axial and radial actuators 

by the spacer also shown in the figure. Touch-down surfaces are also integrated into these housings 

in the event of interruption of power to the actuators. Various sensor systems including capacitive 

sensors for measuring radial and axial distances and accelerometers for measuring relative housing 

vibration are integrated into each housing. 

ORIGINAL PAGE 

140 BLACK AND WHiTE PHOTOGRApH 
Disturbance accommodating control (DAC) theory is used to design controllers and 

estimators for systems with disturbances having waveform structure (ref. 8). The control of 

magnetic bearings is a natural application of DAC theory because the dominant disturbances are 

non-stochastic functions of the synchronous frequency, as previously described. DAC theory is used 

in the following discussion to develop a disturbance model of the measurement error. By 

combining the plant and disturbance models, an accurate estimate of the true center of mass 

position is created. Then the corresponding controller feeds back an uncorrupted estimate of the 

center of mass position, which results in the desired behavior of spinning about the center of mass. 

DISTURBANCE ACCOMMODATING CONTROL (DAC) 

Applications 

o disturbances have "waveform" structure 

o non-stochastic methodology 

Approach 

o develop disturbance model 

o combine plant and disturbance models to design estimator 

o given this structure, use appropriate tools to design controller 

Attributes 

o good in rotor dynamic problems 

o does not affect stability 

o quick convergence of estimates 

141 
A block diagram of the closed loop DAC system is presented in the figure below. The 

system consists of the actual plant, the plant and disturbance models and the controller. The plant 

and disturbance models make up the DAC estimator. The disturbance model represents the 

measurement error disturbance at each sensor. The disturbance estimates are injected at the plant 

model output, thereby producing estimates of the corrupted measurements. The differences in the 

estimated and actual measurements are fed back through the estimator gains to drive the plant and 

disturbances estimation errors to zero. The purpose of the disturbance model is to be able to 

distinguish between the plant and disturbance states, in the presence of disturbances. By feeding 

back the estimated inertial positions, uncorrupted by the synchronous disturbances, the rotor will 

spin about its inertial axis. For a variable speed system, the rotational speed is fed to the controller 

to update the disturbance model. Hence, the oscillator will track the rotational speed and reduce 

the vibrations as the speed changes. 

142 

Desir 

Rot 

Posit 

ed 

or 

ion 

+ .... 

Y-f 

... 

..... 

r' 

BLOCK DIAGRAM OF DAC SYSTEM 

.... Controller .... r' ... Actual Plant 

+ ., , + 

Estimator .... f' .... -,... Plant Model 

Gains r' 

+ 

Estimator ..... Disturbance 

Gains ... Model 

... 

Actual 

Position 

Measurement 

Error 

Disturbance 

£ ejrlt 

s 

+ + ., ... r r' .... 

Measured 

Position 

+ ... 

r' ,,, 

Estimated ~II' + 

Inertial 

Position 

Estimated 

Measurement 

Error 

+ ", ..., 

.... , 

Estimation 

Error 
The figure below is a plot of the singular values of the closed loop transfer function matrix 

from the measurement error disturbance inputs to the inertial position outputs. The area of interest 

is at 60 Hz, the rotational frequency. The infinite notch at 60 Hz illustrates that the measurement 

error disturbance is completely removed from the system. It is important to note that both the 

maximum and the minimum singular values are zero at 60 Hz, resulting in complete ideal 

attenuation of the measurement error disturbances. 

SINGULAR VALUE PLOT 

FROM MEASUREMENT ERROR DISTURBANCE TO INERTIAL POSITION 

102 

101 

........ 

f! 

.2l 100 G) 

E 

? 

G) 

+' 10- G) 1 

.s 

G) 

" .a 'c 

0> 

0 

::::E 

Frequency (Hz) 

143 
The notch does not occur in the transfer function between the commanded input and the 

inertial output as shown in the figure below. The DAC estimator, unlike a notch filter, rejects the 

synchronous disturbances without attenuating the control signals at 60 Hz. The system is therefore 

stable at all rotational speeds. 

SINGULAR VALUE PLOT 

FROM COMMANDED INPUT TO INERTIAL POSITION 

10° 

--- CIl 

.... 

~ (1) 

E 

--CIl 

.... 

~ (1) 10-1 E 

'-' 

(1) 

"0 

B 

'2 

0.0 

cd 

::;; 

Frequency (Hz) 

144 
The figure presented below is the time simulation of the inertial position response 

to the measurement error disturbance input. At negative time, the rotor is spinning around its 

geometric center because the feedback variables are the measured positions. Then at time t = 0, 

the DAC estimator is turned on and the feedback variable becomes the estimated center of mass 

position. As a result of the DAC estimator, the rotor quickly reaches the desired steady-state 

position, spinning about its inertial axis. This graph represents the motion of the inertial positions 

in the X plane. Due to symmetry, the Y plane is identical, 90 degrees out of phase. 

CENTER OF MASS POSITION RESPONSE TO MEASUREMENT 

ERROR DISTURBANCE 

0.04r------,r----:-=---,-----.-----,----.,...---,.-----. 

i 

w 

::: 

0.01 ................................. 

:'=~~i ='1= 

; ................ 

.•. ~:I~=;;F1=····F··=r···~:· .;. ...............•.................... .;. .......................................... .;. ................. . 

~ 0 ............ ..1. .............. 1 .............. ..1. ............. ;... ........... 0+ i I ~ i i 

~ -0.01 ·········t .... .. . ... ··t--1""-1··-1··-··I··· 

I ~:.:: •••••••.. ]... ..] ~=:: r=:~I·I::· .. r::::=r=-~~ I I . I I I I 

-0.04 '--_-...1 __ --1. __ --'-__ --1.... __ --'--__ ..1.-__ .1...-_----1 

-0.06 -0.04 -0.02 o 0.02 0.04 0.06 0.08 0.1 

TIME (SECONDS) 

145 
The bearing force response to the measurement error disturbance is shown in the figure 

below, again illustrating the dynamics of the X plane. The DAC estimator is turned OIn at time t = 0, 

hence the feedback variables are changed from the corrupted measurement positions to the 

estimated inertial positions. As shown, the forces on the rotor are reduced significantly. 

CENTER OF MASS FORCE RESPONSE TO MEASUREMENT 

ERROR DISTURBANCE 

800r-----~----~----~------~----~----~----~ . . . . LEA[)'~G i 

600 -" .. "" .. """." .. i""F1·""""""·: ....... " .. "." ....... 1-"" .. "" ... """".1"." .............. ""j,,, ... ,,",, .... ,,,, .... 1.. ........ ,, ..... ,,"-

f\ I ~ I I I I ., 400 ·'t ·····lr~···lrl--r·llg 200 ". .,," """'l ".". "."""" I~~ ·"""·""""·l"·""""·"·~~J'''''''''''''·''·''''''l''·''''''''''''''''''''·t''''''''""""".". Gj : IV \ : : 1 1 

i -20: : ..•••• ~. ~.i .•••••••••. -:[[[-;.f ........ --t ...... _-= 

-400 ".""""".l~ L"."""l~ .".1."""."."""""".["""""".""""..1"""""""",,,.,,.1..,,,,,,,,,,,,,,.,,,,,,.1.."".""""""." vi V i I I i I -600~----~----~----~~----~----~----~----~ 

-0.04 -0.02 o 0.02 0.04 0.06 0.08 0.1 

TIME (SECONDS) 

146 
References 

1. Gaffney, M.S. "Synchronous Vibration Reduction In Magnetic Bearing Systems". S.M. 

Thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts, June 1990. 

2. Sievers, L.A., vonFlotow, A.H., "Comparison and Extensions of Control Methods for 

Narrowband Disturbance Rejection". NCA-VoI.8. A.S.M.E. Winter Annual Meeting, Dallas, Texas, 

November 1990 

3. Johnson, B.G., Gaffney, M.S. "Demonstration of Active Vibration Control on the JPL 

Cryocooler Vibration Testbed". SatCon Technology Corporation Final Report R30-91, Cambridge, 

MA, August 1991 

4. Johnson, B.G, Hochney, R.L., Misovec, KM. "Active Synchronous Response Control of 

Rigid-Body Rotors". IMechE 4th International Conference on Vibrations Machinery, September, 

1988 

5. Humphris, R.R., Knospe, C.R., Sundaram, S. "Dynamic Balancing With Open Loop Control 

of Magnetic Bearings". 26th Annual IECEC, Boston, MA, August 1991 

6. Gaffney, M.S., Johnson, B.G., "Application of Disturbance Accommodation Control to 

Reduce Vibrations in Magnetic Bearing Systems". NCA-VoI.8. A.S.M.E. Winter Annual Meeting, 

Dallas, Texas, November 1990 

7. Downer, J.R., et. aI., "Cryogenically-Cooled Magnetic Journal Bearings". SatCon Final 

Report R08-91, Cambridge, MA, March 1991 

8. Johnson, C.D., "Theory of Disturbance Accommodating Controllers, Chapter 7, Control and 

Dynamic Systems Vol. 12 (D.T. Leondes, Ed.), Academic Press, New York, 1976 

147 
N92-27730 

Dynamics and Control of High Precision 

Magnetically Levitated Vibration Isolation Systems 

K. Youcef-Toumi and T-J Yeh 

Department of Mechanical Engineering 

Massachusetts Institute of Technology 

Mailing Address: 

Kamal Youcef-Toumi 

M.I.T. Room 35-233 

77 Massachusetts A venue 

Cambridge, Massachusetts 02139 

Telephone: (617) 253-2216 

PRECEDING PAGE BLANK NOT FILMED 

149 
Abstract 

Vibration control of flexible structures has received a great deal of interest in recent years. Several 

authors have investigated this topic in the areas of robot manipulators, space structures and flexible 

rotors. Key issues associated with the dynamics and control of vibration isolation systems are 

addressed in this paper. 

Among other important issues to consider in the control of such systems, the location and 

number of actuators and sensors are essential to effectively control and suppress vibration. In 

this paper, we first address the selection of proper actuator and sensor locations leading to a 

controllable and observable system. The Rayleigh-Ritz modal analysis method is used to develop 

a lumped-parameter model of a flexible vibration isolation table top. This model is then used to 

investigate the system's controllability and observability including the coupling effects introduced 

by the magnetic bearing. This analysis results in necessary and sufficient conditions for proper 

selection of actuator and sensor locations. These locations are also important for both controller 

system's complexity and stability point of views. A favorable pole-zero plot of the open loop 

transfer functions is presented. Necessary and sufficient conditions for reducing the controller 

complexity are derived. The results are illustrated by examples using approximate mode shape 

functions. 

Contents 

1 Introduction .152 

2 Problem Formulation .153 

3 Controllability and Observability . 156 

3.1 Analysis without the Coupling Effect of Actuator Dynamics . 156 

3.2 Analysis with the Coupling Effect of Actuator Dynamics . . 159 

3.3 Examples of Locating Actuators (Sensors) to Achieve Controllability (Observability) 16~ 

4 Control System Characteristics for Collocated and N oncollocated Configurations ...... . 164 

5 Effects of Damping .172 

6 Conclusion .173 

A Rayleigh-Ritz method .173 

PRECEDING PAGE BLANK NOT FILMED 151 
152 

1 Introduction 

Sensitive instruments and precision machines have made it possible to investigate phenomena 

with dimensions of the nanometer scale. For example, current Michelson-type optical heterodyne 

interferometer can measure displacement with a resolution in the nanometer range [1]. Scanning 

Tunneling Microscopes (STM's) which use flexure linkage structures have Angstrom resolution 

and range of motion on the order of one micron r2]. In these and other applications, vibration 

from ground motion and other distrubances, which may be in the micrometer level, will seriously 

degrade the overall system performance. 

Traditional vibration isolation techniques can be generally divided into two categories: 1) 

passive and 2) active. Passive vibration isolation often involves the use of metal springs, elastomers, 

rubber, air springs or other passive elements to either absorb or dissipate vibration energy [3]. 

Passive techniques offer simple, inexpensive and reliable means to protect mechanical systems from 

environmental vibration. However, it is not possible for the passive vibration isolation methods to 

influence the system dynamics and adapt in real time. On the other hand, active vibration isolation 

techniques which use force generators that are adaptable to excitation and response characteristics 

of the system can actively counteract and cancel the undesirable vibration. In additiion, the active 

system provides significantly superior vibration isolation performance. The control force is often 

realized by pneumatic or electromechanical actuators. For example, Sandercock [4] proposed to 

combine both the active controlled electromechanical actuators and passive elastomers in building 

a dynamic antivibration system and has already become a commercialized product. In this system, 

the electromechanical actuators offer the damping force proportional to the absolute velocity of 

the table top while the elastomers provide the required compliance. This system is said to achieve 

3J.lgs (3 mgal) RMS acceleration isolation performance [5]. 

In addition to the isolation of ground vibration, the suppression of induced vibration of work 

surface ( or the table top plate) is also an important factor in vibration isolation system design. 

Since the table plate is not a perfect rigid body and thus considered flexible, the resonant frequencies 

of the table can be excited by the environmental disturbances such as acoustic noise, payload 

change, or the motion of a positioning system on the table top. In this case, the vibration modes 

of the table top will be excited and the performance of the system may degrade. 

The use of actively controlled magnetic bearings is considered to not only achieve ultra high 

performance vibration isolation from the environment but also to suppress the induced vibration 

of the table top. Because of the unstable nature of the magnetic bearing, robust control scheme 

is needed to guarantee the performance. But prior to the control system design, the sensors and 

magnetic actuators should be properly located so that the vibration can be reduced effectively. 

As far as the flexibility of the top plate is concerned, this is related to the mode shapes of different vibration mode. This paper focuses on the actuator and sensor locations from the system 

controllability and observability points of view. 

Controllability and observability of distributed systems has been investigated by Hughes and 

Skelton (6J, and Yang and Mote [7J. In [6J the controllability and observability condition of linear 

matrix-second-order systems are discussed. But since the orthogonality of mode shape functions 

wasn't used, no direct relationship between the node line and the condition of controllability and 

observability is derived. In [7J, although the locations of actuators and sensors were related to 

the modeshape functions, the examples discussed are the axially moving string with clamped ends 

and rotating circular disk with clamp rim and thus the rigid body motion is not considered. Also 

the sensors assumed in their derivation are the position and velocity sensors. 

In this paper, it is of interest to investigate the controllability and observability of rigid body 

motion of a magnetically suspended vibration isolation table top. In the case, the table top 

will be modelled as a rectangular plate with free edges. Due to the importance of the inertial 

acceleration feedback in vibration isolation systems, the accelerometer outputs are also included 

in the derivation of the observability condition. Since the prototype design uses magnetic bearings 

for levitation and vibration control, the unstable nature of the actuators is coupled to the overall 
system dynamics. The controllability and observabiJity analysis presented in this work takes this 

fact into account. In order to apply the results to the system design, normalized frequencies and a 

map depicting the node lines corresponding to table top were approximated using the Rayleigh-Ritz 

method. 

Improper placement of actuators and sensors can lead to complex control system designs even 

though these locations may correspond to a controllable and observable system. For example, a 

conventional flexible arm has zeros in the right half plane if the actuator and sensor are noncollated. 

This nonminimum phase nature adds additional phase lag to the system and results in poor system 

performance [8]. Such issues have motivated us to investigate the relationship between proper 

actuator/sensor locations and favorable open loop system behavior. 

In this paper, the problem formulation is presented in section 2. The selection of proper 

actuator and sensor locations leading to a controllable and observable system is then discussed 

in section 3. A lumped-parameter model of a flexible vibration isolation table top is used to 

investigate the system's controllability and observability including the coupling effects introduced 

by the magnetic bearing. This analysis results in necessary and sufficient conditions for proper 

selection of actuator and sensor locations. Section 4 presents a favorable pole-zero plot of the open 

loop transfer functions. Necessary and sufficient conditions for reducing the controller complexity 

are derived. The results are illustrated by examples using approximate mode shape functions. 

Such information is important for the overall design of ultra high performance vibration isolation 

systems. For example, critical frequency regions in the transmissibility curves can be identified 

and taken into account in the control system design. 

2 Problenl Formulation 

Consider a thin rectangular table top plate with free edges as shown in Figure 1, assuming that 

the plate is made of homogeneous, isotropic material, then the equation of motion is [9], 

phw(x, y, t) + D \74 w(x, y, t) = I(x, y, t) (1) 

where p is the density of the plate, h is the plate thickness, w(x, y, t) is the transverse deflection, 

D is the flexural rigidity of the plate and is equal to 12(i~sV')' E is the Young's modulus, II is 

Poisson's ratio and \74 represents the biharmonic operator. Moreover, since we will first deal 

with the controllability and observability issues in this paper, only the control force is taken into 

account and other forces such as gravity and disturbances are not included. Therefore, in such 

a case I(x, y, t) denotes the control force per unit area of the plate. Because there is no lateral 

constraint, the boundary conditions of the plate are given by [10], 

( i) £,rw(x, y, t) + IIfl,rW(X, y, t) = 0 I < < 

y O_x_a for y = O,y = b 

( ii) ~w(x, y, t) + (2 - IIhy

&;x' w(x, y, t) = 0 IO$x$a for y = O,y = b 

( iii) fl.rw(x, y, t) + II~W(X, y, t) = 0 IO<y<b for x = 0, x = a (2) 

( iv) &' &' pw(x,y,t) + (2 - 1I)&x&y2 w(x,y,t) = 0 IO$y$b for x = O,x = a 

The physical meaning of these four boundary conditions is that the bending moments, twist moments, and shear forces along the four edges are equal to zero. 

In order to develop and implement a finite dimensional controller, a lumped parameter model 

of the system is needed for the distributed system described by Equation (1). Because the equation 

is a partial differential equation, in order to apply the control law, the system should be discretized 

to obtain a lumped-parameter model. To achieve this we consider only n modes in the dynamic 

equations and assume that the influence of the higher modes is negligible. The transverse deflection 

153 
154 

~ 

y 

/ 

/ 

W(X,Y,t) § 

___ ~x 

a ~I 

~ Actuator § Sensor 

Figure 1: Thin rectangular plate with free edges 

w(X, y, t) can be represented by means of a series of n mode shape functions <Pi(X, y) of the system 

and expressed in the following form, 

n 

w(x,y,t) = Lai(t)<Pi(X,y) = aT(t)~(x,y) (3) 

i=l 

where ai(t) (i = 1,2, .... , n) are the generalized coordinates. We further assume that the table is 

supported by m discrete point force actuators located at (Xi, yd and i = 1, 2, ... , m. Therefore the 

control force can be expressed as, 

m 

f(x, y, t) = L !i(t)Oi(X, y) = fT (t)d(x, y) (4) 

i=l 

where fi(t) is the control force exerted by the ith actuator and Oi(X, y) is the impulse function 

at (Xi, Yd. Using Equation (3), the kinetic energy T and potential energy V of the plate can be 

written in terms of generalized coordinates and mode shape functions as [9], 

T = !fAPhw2(x,y,t)dA = !fAPh[L:7=lai(t)<Pi(x,y)]2dA 

= ~ fA ph(aT~(x, y))2dA = ~aT(t)Ma(t) (5) 

where the inertia matrix M is given by, 

M = ph i ~(x, y)~T(x, y)dA 

and 

V 
D r [(aT(t)~xx)2 + (aT(t)~yy)2 + 2I1aT(t)~xx~;ya(t) 2 JA +2(1-1I)(aT(t)~Xy)2]dA 

= ~aT (t)Ka(t) 

where the stiffness matrix K is given by , 

K D 1 (~xx~;x + ~yy~;y 

+211~xx~;y + 2(1 - 1I)~xy~;y)dA 

Also the virtual work due to the m point force actuators is: 

8W 

where 

1 f(x,y,t)8w(x,y,t)dA 

1 fT (t)~(x, y)~T (x, y)8a(t)dA 

fT (t) [1 ~(x, y)~T (x, Y)dA] 8a(t) 

fT (t)R8a(t) 

R= 

(6) 

(7) 

and <fJ1 indicates that the ith mode shape is evaluated at location (Xj,Yj), that is ¢i(Xj,Yj). Substituting Equations (5), (6), (7) into the variation indicator of the system and applying Hamilton 

principle, the equations of motion are obtained as, 

Ma(t) + Ka(t) = RTf(t) (8) 

To transform Equation (8) into a state space form, a state vector xT = [aT (t) aT (t)] is introduced 

so that Equation (8) can be written as, 

x = Ax+ Bf (9) 

where the matrices A and B of orders 2n x 2n and 2n x m respectively are given by, 

(10) 

Now that the system equations are formulated, we turn to the system outputs. We consider k 

sensors located at (Xi,Yi)1 (i = 1,2, ... ,8). Assuming that the first p sensors are position sensors, 

(p+ 1 )th to (p+ q)th sensors can measure the velocity of the individual points, and the last 8 - p- q 

sensors are accelerometers. The outputs from the position sensors can be written as: 

n 

Yj(t) = Lai(t)¢i(Xj,Yj) i=1,2, ... ,p (11) 

i=1 

1 Even though we use the same notation (Xi,y;)'S to represent the locations for both actuators and sensors, t.he 

point (Xi,yo) for ith actuator may not be the same as the point (Xi, yo) for ith sensor. 

155 
156 

The outputs from the velocity sensors are: 

n 

Yj(t) = Lai(t)q,i(Xj,Yj) j=p+1,p+2, ... ,p+q (12) 

i=l 

Finally, the accelerometer outputs are: 

n 

Yj(t) = Lai(t)q,i(Xj,Yj) j = p + q + 1,p + q + 2, ... , s (13) 

i=l 

Note that ai(t) and ai(t) represent the first and second time derivatives of the generalized coordinate 

ai(t). The overall output equations can now be expressed in matrix form using Equation (11), (12) 

and (13), 

y = [~ ~ 1 x(t) + [ ~ la(t) 

= [ : ~ 1 x(t) + [ ~ 1 ret) -SM- 1K 0 M- 1RT 

Cx+Df (14) 

where 

[ ¢l q,~ 

¢~ 1 [ ¢i+' q,~+1 ~+1 

1 

q,I q,~ q,~ qJ{+2 ~+2 ~+2 

P

pxn 

= q,:r; . , Q,x. = </1,'+. q,~ ~ ~+q ~+q 

[ W'+' ~+q+1 ... 

W'" 1 qJ{+q+2 ~+q+2 ... ;.+.+, 

S.xn = . . .. 

q,! q,; q,~ 

Equation (9) and (14) can now be analyzed in order to determine the conditions of controllability 

and observability. These isssues are addressed in the following section. 

3 Controllability and Observability 

3.1 Analysis without the Coupling Effect of Actuator Dynamics 

The 2nth order system described by Equations (9) and (14) is controllable if and only if 

rank(C) = rank [B AB ... A2n- 1B] = 2n 

and the system is observable if and only if 

(15) 

(16) 

In order to simplify the problem and deal with diagonal M and K matrices, the orthogonality of 

the eigenfunctions is used [11]. Under this assumption, the n x n inertia and stiffness matrices take 
the form, 

~ · 

· 1 K . = [ ~l . · . Mn 0 in 1 (17) 

o o 

where M;, K; ~ O. The matrix M-l K is also diagonal with diagonal components corresponding 

to the system eigenvalues, 

o 

(18) 

o 

The eigenvalues Al, A2, ... , An are equal to the square of natural frequencies of the system. 

Because a thin plate with free edges is considered, the first three eigenvalues are equal to zero, 

i.e., Al = A2 = A3 = O. The modes associated with these eigenvalues correspond to the translation 

parallel to the z axis and rigid body rotations along x and y axes. In the following discussion, it is 

assumed that n > 3 so that the vibration modes are taken into account and all other eigenvalues A4, 

As, ... , An are positive. In order to investigate the condition for this system to be controllable and 

observable, the controllability and observability matrices are calculated and discussed as follows. 

In our case , the controllability matrix has the form, 

c=[~ H 0 JH 0 In-lH ] (19) 0 JH 0 ... In-lH 0 

where 

M-'RT = [ 

1 <pl 1 <p2 

*~r 1 lr, 1 lr, 1 

1 <pl 1 <p2 1 <pm 

Hnxm 

Jr, 2 l1; 2 Jr, 2 

1 <pl 1 <p2 1 <pm Mn n Mn n Mn n 

0 0 0 0 0 0 

0 0 0 0 0 0 

0 0 0 0 0 0 

J nxn = -M-lK = 0 0 0 -A4 0 0 

0 0 0 0 -AS 0 

0 0 0 0 0 -An 

Since there are 2n states ( n position components and n velocity components), the controllability 

matrix should have rank 2n which means that 2n rows must be linearly independent. It is obvious 

that the upper n x 2mn matrix and the lower n x 2mn matrix are almost the same except that 

they are shifted by a series of n x m 0 matrices. Therefore , if n linearly independent rows can 

be obtained from the upper n x mn submatrix, the lower n x mn matrix will also have n linearly 

independent rows and these two sets of n linearly independent rows are linearly independent to 

each other. If we interchange the columns of the upper submatrix and put all the 0 columns to 

the right hand side without changing the rank of the submatrix, we can deduce that the system is 

controllable if and only if the n x mn matrix L has rank n, where 

L = [H JH ... In-lH] (20) 

157 
158 

Therefore, the system is controllable if and only if rank(L) = n. Due to the diagonal structure of 

J matrix, the conditions for the L matrix to have rank n are [12] : 

1. For Ai with no repeated eigenvalues, the ith row of the H matrix should be a nonzero vector. 

2. For repeated eigenvalues of multiplicity i, Ai+l = Ai+2 = ... = AiH, the (i + 1)th, (i + 2)th, 

... , (i + i)th rows of H should be linearly independent. 

On the other hand, the observability matrix takes the form, 

[ pT 0 JST 0 JQT 0 0 JnQT 0 

0= 0 QT 0 pT 0 JST ... In-lpT 0 JnST 

To investigate the rank of this matrix, we rearrange it as follows: 

I [PT JST JQT JnQT 0 0 0 0 ] o -- 0 0 0 0 pT QT JST JnST 

For the system to be observable, the following two conditions must be satisfied, 

rank [pT JST JQT 

where H' = [pT JST JQT], and 

rank [pT QT JST 

] (21) 

(22) 

(23) 

(24) 

where H" = [pT QT JST]. By substituting the P, Q, and S matrices, the H', H" matrices in 

Equation (23) and (24) can be represented as, 

4>1 4>i 0 0 0 0 

4>~ 4>~ 0 0 0 0 

I 4>! 4>~ 0 0 0 0 

H = 4>~ 4>~ ( -A4)4>~+1 ( -A4)~+q ( -A4)4>~+q+l ( -A4)4>4 (25) 

4>~ <Pn ( -An)4>~+l ( -An)<Pn+q ( -An)4>~+q+l ( -An)4>~ 

and 

4>1 4>i 4>i+1 4>i+q 0 0 

4>~ 4>~ 4>~+1 ~+q 0 0 

/I 4>~ 4>~ 4>~+1 ~+q 0 0 

H = 4>~ 4>~ 4>~+1 ~+q ( -A4)4>~+q+l ( -A4)4>4 (26) 

4>~ <Pn 4>~+1 <Pn+q (-An)4>~+q+l (-An)4>~ 

Due to the similarity between the observability Equations (23), (24) and the controllahility 

Equation (20), the system is observable if both H' and H" matrices satisfy conditions (1) and (2). 

Therefore, the relation between the location of actuators (sensors) and controllability (observability) can be obtained. These results are summarized in the following theorems. 

Theorem 3.1 If the kth mode is controllable (observable), then there exists st least one actuator 

(sensor) not located on the corresponding node loci. 

Proof: In condition (1), the ith row vector of H (H', H") should be a nonzero vector. This corresponds to the situation that for every mode shape function 4>i(X, Y) with ~o repeated eigenvalue, 

there exists one actuator (sensor) location (Xj,Yj) such that 4>i(Xj,Yj) = 4>; is nonzero. 0 
Theorem 3.2 i modes with the same natural frequency (AHi = AH2 = ... = Ai+i) are controllable 

(observable) if there exists at least i actuators (sensors) located at points (Xj"" Yj,,) (a = 1,2, .... i) 

such that 

[ 01 •• 

ifJh 

01.. 1 Hi ... 

det : : #:0 (27) ... 

ifJh ifJj2 ifJ jl 

Hi i+l i+l 

where ifJi+i, ifJi+2, ... ,ifJi+l are the mode shape functions or the eigenfunctions corresponding to this 

natural frequency. 

Proof: In condition (2), the (i + l)th, (i + 2)th, ... , (i + i)th rows of H (H', H") are linearly 

independent if there are i linearly independent columns in the submatrix formed by the i + Ith, 

i + 2th, ... , i + ith rows of H matrix. This corresponds to the situation for which every set of i 

mode shape functions ifJi+i, ... , ifJi+i corresponding to same eigenvalue AHi = AH2 = ... = AHi, 

there should exist a set of (x j" , Yj,,) (a = 1, 2, ... i) such that Equation (27) is satisfied. 0 

A direct application of this result is that there should be at least a actuators (sensors) not located 

at the intersections of all the node lines of the same natural frequencies to make these modes 

controllable (observable). 

Theorem 3.3 The modes of a flexible plate cannot be controlled (observed) with less than three 

actuators (position sensors) I nor is it possible to control (observe) them with more than three 

collinear actuators (sensors). 

Proof: Since there are three zero eigenvalues corresponding to rigid body motion, it can therefore 

be concluded that there should exist a set of three actuator ( or position sensor, due to the 

o submatrix in the upper-right corners of H' and H" matrices) locations (Xj" Yit), (xh' Yh), 

(xj"Yh) so that, 

[ 

ifJ{l ifJ{2 ifJ{' 

det ifJ{l ifJ{2 ifJ{' 

ifJ~l ifJ~2 ifJ~' 

for some it,jz,h between 1 and m(p) (28) 

ifJi(X, Y), ifJ2(X, y) and ifJ3(X, y) denote the first three mode shape functions of the plate which 

correspond to one parallel translation and two rigid body rotations. Assuming ifJi(X, y) = 1, 

<h(x, y) = x, <hex, y) = y, Equation (28) implies that there exists three actuator ( position sensor) 

locations (Xj.,Yj.) (i = 1,2,3) such that, 

det [ X~l Yit 

1 

for some it, jz, h between 1 and m (p) (29) 

which means that these three points are not collinear. [J 

Corollary 3.1 The minimum number of properly located actuators (sensors) necessary to control 

(observe) the modes of a flexible plate is equal to max { 3, multiplicity of eigenvalue of the modes 

to control (observe) }. 

Proof: This is the direct result from the previous three theorems. 0 

3.2 Analysis with the Coupling Effect of Actuator Dynamics 

In the previous discussion of controllability and observability, no actuator dynamics were considered 

in the system state equation. Since we are interested in using magnetically levitation techniques 

to control the vibration, the unstable nature of magnetic forces should be taken into account. This 

159 
160 

instability comes from the negative stiffness existing between the levitated object and the magnetic 

bearing pole face. The introduction of magnetic bearings into the system will significandy affect 

the dynamic behavior. Therefore, in this section we reformulate the problem and invest:igate the 

influence of magnetic bearings on the controllability and observability conditions. In general, the 

nonlinear magnetic force equation is linearized about an equilibrium point. The incremental force 

can then be represented by, 

(30) 

where kz is the unstable stiffness, z is the air gap distance, ki is the current stiffness constant and 

i is the control current. Assuming m magnetic bearings are used as actuators in the vibration 

isolation system, then Equation (30) is written in vector form as, 

(31) 

In this equation, f, z, i denote the m x 1 force, air gap distance, and control current vectors. Kz 2 

and Ki are both nonsingular , m x m diagonal matrices. The diagonal elements of Kz represent the 

unstable stiffness of each magnetic bearing while those of Ki are the corresponding current stiffness 

constants. Substituting Equation (31) into Equation(9) and using the relation that z = [R O]x, 

we can get the new state equation as, 

x=A'x+B'i (32) 

where 

(33) 

Using the same procedure as discussed previously, t~e system is controllable if and only if the 

matrix 

L' = [HKi (J + HKzR)HKi (J + HKzR)2HKi 

(J + HKzRt-lHKi] (34) 

has rank n. A first result is stated in the following lemma. 

Lemma 3.1 Given an integer p and matrices J, Hand W such that p E Z, J E Rnxn, H E R nxm 

and W E Rmxm , The column space of the matrix JPHW is spanned by the column vectors of the 

matrix JPH. 

Proof: Assuming that the matrix H = [hI h2 

H. Let the elements of W be Wij, then 

h m ] where the h;'s are column vectors of 

JPHW JP [hI h2 hm]W 

JP [f>.h m 

). } L wo}. 2ho } tw;,.h;] 

j=1 j=1 j=1 

[t W

'

JPh m 

LW·2 tw JPh] JPho }. } }. } }.n J 

j=1 j=1 j=1 

Because JPH can be expanded as [JPhl J Ph 2 JPhm]' it is obvious that the column space 

of JPHW is spanned by the column vectors of JPH. 0 

Now we state a controllability theorem for magnetically levitated vibration isolation syst.em .. 

2Due to the instability of the magnetic bearing, Kz is a positive definite matrix. 
Theorem 3.4 The system described by Equation (9) is controllable if and only if the system described by Equation (32). 

Proof: In order to show this, we need to prove that the rank of L' is the same as that of L. Since 

Ki is a common factor in each element of L', we can factor it out and write the L' matrix as, 

L' L"Kj 

where L" = [H (J + HKzR)H (J + HKzR)2H (J + HKzR)"-lH] . Since Kj is a nonsingular diagonal matrix, L" has the same rank as the matrix L'. We perform the algebraic 

manipulation on column vectors to reduce the L" matrix into the same form as the L matrix. 

From the lemma for the case of p = 0, we can use the columns of H, which is the first element of 

L" to eliminate HKzRH in the second element so that only the columns of JH remains. Then 

expand the third element as J 2H + JHKzRH + HKzRJH + HKzRHKzRH. The lemma again 

allows us to use the the columns of first element H and the new second element JH to reduce 

the third element into J 2H. Applying the same column reduced procedure to the 4th, 5th, ... , nth 

elements of L" matrix. We can reduced the L" into the same matrix as L. The algebraic manipulation of column vectors doesn't change the rank of the matrix L", therefore we conclude that. the 

L" matrix and the L matrix have the same rank, which implies L' matrix has the same rank as 

L. 0 

A direct application of the theorem is that the introduction of the magnetic bearings dynamics wouldn't influence the controllability condition discussed previously. And all the theorems 

mentioned before can be applied to the magnetic levitated vibration isolation systems. 

For the observability part, using the same argument, we can prove the magnetic bearing dynamics wouldn't change the observability condition if there are m position sensors collocated with 

those m magnetic bearings. This is because if the m position sensors collocated with those m 

magnetic bearings used, the m x 1 output vector becomes y = [R 0] x. Using Equation (32), 

the observability condition can be deduced and is in fact similar to the controllability condition of 

Equation (34). 

3.3 Examples of Locating Actuators (Sensors) to Achieve Controllability (Observability) 

To apply the results obtained in the previous section, the eigenfunctions or the mode shape functions of the system need to be determined. Since there is no analytical solution for a flexible plate 

with free edges [13], approximate mode shape functions are found using with the Rayleigh-Ritz 

method. These mode shape functions allow us to get the node loci, which are the locus of points 

on the plate with zero amplitude corresponding to the normalized natural frequency. For the case 

of a square plate, the node loci of different normalized natural frequencies are shown in Figure 2. 

From the relationships obtained from the previous section, to control and observe the vibration of 

the plate, it can be inferred that we have to choose the actuators and sensors not located on the 

node loci associated with the desired frequency. Therefore, Figure 2 can be used as a guide line 

to properly locate the actuators and sensors so that the modes of interest may be controlled (observed) efficiently. Of course, it is necessary to check whether these locations satisfy the condition 

of linear independence for the modes with the same natural frequency. 

In order to apply the results obtained from the discussion of controllability and observability, 

the first 9 node loci together as a node map are shown in Figure 3. Some examples of locating the 

actuators and sensors are illustrated as follows: 

In Figure 4, the three actuators (sensors) are located in a straight line. Therefore, the rigid 

body rotation of the plate about this line cannot be controlled (observed). 

As shown in Figure 5, although the three actuators (sensors )aren't collinear, they are all placed 

on the node line of the sixth mode. Therefore, this mode cannot be controlled (observed). 

161 
162 

~=O 

I 

1 

1 

----~-----

1 

1 

1 

1 

I 

~ = 14.07 

I 

1 

----,----

1 

1 

1 

1 

----t-----

1 

~ = 36.29 

f-----------

, 

, 

, 

~=O 

, / 

X 

/ , 

/ 

/ 

/ 

/ , 

/ , 

/ , 

1 

1 

1 

~ = 19.01 

1 1 

f---L----L1 1 

1 1 

1 1 

1 1 

~ = 36.29 

1 

: 

1 

1 

1 

1 

1 

1 

! 

~=O 

~ = 24.62 

1 '1 f---r----r1 1 

1 1 

1 1 

1 1 

--t-----t--

1 1 

~ = 66.82 

Figure 2: The node loci of the first nine normalized frequencies 
/ 

1 

1 

~------I------+ 

I"" 1 //1 

I" 1 / 1 

1 " 1 / 1 

1 "" 1 // 1 

1 "" 1 // 1 

----~-----~------~---- 1 /1" 1 

1 // 1 "" 1 

1 / I" 1 

1 / 1 " 1 

1 // 1 "" 1 

1 / 1 " 1 --- ~-----~------

/ 

/ 

/ 

/ 

/ 

1 

1 

Figure 3: Node map of the first 9 modes of vibration 

• Actuator/Sensor 

Figure 4: Uncontrollability (unobservability) due to three collinear actuators (sensors) 

163 
164 

• Actuator/Sensor 

Figure 5: Uncontrollability (unobservability) of the sixth mode due to actuators (sensors) located 

on the node line of this mode 

In Figure 6, since one actuator (sensor) is not located on any node line of the nine modes, it 

seems that all the nine modes are controllable (observable). However, due to the fact that the 

other two actuators and/or sensors are located at the intersections of the node line corresponding 

to the normalized frequency w· = 36.29, the condition for repeated eigenvalues makes these two 

modes uncontrollable (unobservable). 

Figure 7 shows four actuators (sensors) placed in symmetrical arrangement on the node line of 

the fourth mode. Therefore, the fourth mode is uncontrollable (unobservable). 

Figure 8 shows three actuators (sensors) which are located unsymmetrically on the plate. All 

of the nine modes in this are controllable (observable) because none of the actuators (sensors) are 

located on the node lines. 

4 Control System Characteristics for Collocated and N oncollocated Configurations 

In this section, we will examine proper actuator/sensor locations leading to a favorable open-loop 

system behavior. We will investigate the influence of the collocated and noncollocated actuator/sensor configuration on the control system characteristics, and then provide guide lines for 

achieving a favorable system behavior. 

The open loop transfer function matrix of the 2nth order system described by Equations (9) 

and (14) is, 

G(s) = C(sI - A)-lB (35) 

In the following analysis, it is assumed that only position sensors are used which corresponds to 

that C = [P 0]. If the corresponding elements of matrices A, Band C are substituted into the 
• Actuator/Sensor 

Figure 6: Uncontrollability (unobservability) of the seventh and eighth modes 

• Actuator / Sensor 

Figure 7: Uncontrollability (unobservability) of the fourth modes 

165 
166 

• Actuator\Sensor 

Figure 8: Controllability (observability) using three actuators (sensors) 

right hand side of Equation (35), then the (i,j)th element of the G(s) matrix takes the form, 

= n 4>~i 4>~j 

{; Mk(s2 +wn 

"n [¢:';::j TIn (2 2)] L.....k=l k l=l,l¢k s + Wl 

(36) 

gi,j(S) denotes the transfer function from the jth actuator at location (xaj , YaJ to the i,th sensor 

at location (x." y.;). 

The transfer function gi,j (s), if without pole-zero cancellation, always has poles at ±jwl, ±jw2, 

... , ±jwn . If with pole-zero cancellation is possible, we can skip those cancellation pairs and focus 

only on the uncancelled ones. The numerator of Equation (36) has to be expanded as an 2( n - 1 )th 

degree polynomial and solved for the 2( n - 1) zeros. Because the coefficients of this polynomial are 

real and the Laplace variable s always appear with even power, if there is any complex root 0' + j,S, 

then 0' - jp, -0' + jJ3 and -0' + jp are also the roots of the polynomial. Therefore, for the transfer 

function to be nonminimum phase, the zeros can't be any positive or complex numbers. This 

implies that the zeros, like the poles, should be on the imaginary axis. Although such information 

may be known, there are still many ways to locate the zeros. In order to decide on the most 

favorable type of pole-zero plot, the merits of a conventional PD controller are evaluated. The 

following lemma and theorem allow us to compare the relative performances of different types of 

pole-zero plots. 

Lemma 4.1 For a system with the transfer function in the form of Equation (36), if thf ith pole 

located at ±jwi is stabilized by a PD controller and there are 2li zeros at ±jPl, ±jP2, ... , ±jPli 

such that Pl < P2 < ... < Pl; < Wi , then Ii - i = 2qi - 1 where qi is an arbitrary integer'. 

Proof: To prove this lemma, we look at the angle of departure of the ith pole. The angle of 

departure O'i of the ith pole is equal to 1800 -(sum of the angles of vectors to this poles from other 
Im(s) 

ith pole 

-------u~U-~~----------~Re(s) 

Figure 9: Calculation of the angle of departure for a PD controller 

poles)+(sum of the angles of vectors to this pole from zeros) [14). For the pole-zero plot shown in 

Figure (9), it can be shown that, 

fr; 180° - [(n + i-I) x 90° - (n - i) x 90°) + [8; + (n - 1 + £) x 90° - (n - 1 - £) x 90°) 

180° + 8; + (2£ - 2i + 1) x 90° (37) 

Because a stable PD controller is used, 0 < 8 < 90°, which means 180° + (2£ - 2i + 1) x 90° < 

fr; < 270° + (2£ - 2i + 1) x 90°. It is obvious that if the root locus of the ith pole goes to the 

stable region, then 90° ~ fr; ~ 270°. Equation (37) can satisfy this angle condition only when 

2£ + 2i + 1 = 4qi - 1, that is , £; - i = 2qi - 1. 0 

Theorem 4.1 If all 2n poles ±jw1, ±jw2, ... , ±jwn in Equation (36) are stabilized by a PD 

controller, then there should be one and only zero located between two consecutive poles jw;, jWi+1 

or-jw;, -jWi+1 fori = 1,2, ... , n-l. And the pole-zero plot should be the same as the one shown 

in Figure (10). 

Proof: For all the poles to be stablized by a PD controller, Lemma 4.1 should be true for all 

poles. Take the poles located at jw;, jWi+1 or -jw;, -jWi+1 for example, the necessary condition 

becomes, 

£;+1 - (i + 1) 

£; - i 

(a) 

(b) 

If (b) is substracted from (a), we get £;+1 - £; = 2(q;+1 - q;) + 1 which implies that £;+1 - £; is an 

odd number. Since £;+1 - £; represents the number of zeros between these two poles and can't be 

a negative number. From above arguments, £;+1 - £; has to be greater than or equal to 1. This 

means that there is at least one zero between two poles jw;, jWi+1 or -jw;, -jw;+l' Because there 

is only 2( n - 1) zeros for this transfer function and we have to place at least one zero in each of 

167 
168 

Im(s) 

-------+------~ Re(s) 

Figure 10: A favorable pole-zero plot 

the 2(n -1) intervals between consecutive poles jw" jwi+l or -jw" -jWi+l for i = 1, 2, ... , n, the 

only pole-zero type can be achieved is the alternating pole-zero plot shown in Figure (10). 0 

Now we have proved that the only type of non minimum phase pole-zero plot can be stabilized 

by a conventional PD controller is the alternating pole-zero plot. In what follows, we limit ourselves 

to this case and investigate the condition on the transfer function to have such a dynamic behavior. 

This condition can be obtained from the following theorem, 

Theorem 4.2 The transfer function of Equation (36) has an alternating pole-zero plot as in Figure 

(10) if and only if either one of the following conditions is true, 

(i) 

p+q 

and 2: 

"=p+l 

or 

( ii) 

p+q 

and 2: 

k=p+l 

l/J~il/J:j 

M" 

[1/J~il/J:j ] 

M" 

I/J~i I/J:j 

M" 

[1/J~il/J:j ] 

M" 

> 0 

> 0 

< 0 

< 0 

for any kth mode with no repeated eigenvalues 

for p+ lth, p+ 2th, ... , p+ qth modes with same 

repeated eigenvalues 

for any kth mode with no repeated eigenvalufs 

forp+lth, p+2th, ... , p+qth modes with same 

repeated eigenvalues 

Proof: To simplify the notation, a" 's are used to denote rt>:;:? and all the eigenvalues are 

different. This condition will be relaxed later. Then the numerator Z(s) of Equation (36) can be 

written as, n n 

Z(s) = 2: a" II (s2 + wi) (38) 

"=1 l=l,li''' 
The 2(n - 1) roots of Z(s) which are represented by ±jZI, ±jz2, ... , ±jzn-l correspond to the 

zeros of the transfer function. For the system to have alternating pole-zero plot, we should have 

Wk < Zk < Wk+l for k = 1, 2, ... , n - 1. The necessary and sufficient condition for the above 

arguments to be true is, 

n n 

l=l,ltk l=l,ltk+l 

for k = 1, 2, ... , n - 1 (39) 

Since WI < W2 < ... < W n , the following product must be negative, 

n n 

sgn[ II (-w~ + wi) II (-W~+l + wi)] 

l=l,ltk l=l,ltk+l 

-1 

(40) 

If this result is substitubed into Equation (39), the necessary and sufficient condition becomes 

akak+1 > 0 for k = 1, 2, ... , n - 1. This condition is the same as either ak > 0 or ak < 0 for any 

k, which means that all the ak's have the same sign. If there are p + lth, p + 2th, ... , p + qth with 

the same natural frequency, then in Equation (36), all the p + lth, p + 2th, ... , p + qth can be 

summed up together so that there is no repeated poles in the transfer function. As the case of no 

eigenvalue multiplicity and using ap to represent L:1~!+1 [q,\t:j] and follow the same procedure, 

we can still conclude that ak for k = 1, ... , p, p+q + 1, ... , n, should be have the same sign. Even 

though we only discussed the case of one eigenvalue with multiplicity, if there are other repeated 

eigenvalues, the conclusion is the same as what stated in this theorem. 0 

Remark: q,'iq,4j + q,'iq,4j 1.If any ~ or L:1=!+1[~] in Equation (38) is equal to zero, pole-zero cancellation occurs 

for the pole jWk or jwp 

2.For the special case of a collocated actuator and sensor pair, ¢>~i = ¢>:j, for k = 1, 2, ... , n. The 

ith condition is obviously satisfied. Therefore, the collocated system always has an alternating 

pole-zero plot as that of Figure (10). 

Finally, we prove the next theorem to guarantee the stability of a PD controller applied to the 

alternating pole-zero plot of the system in Equation (36). 

Theorem 4.3 The transfer function of Equation (36) has an alternating pole-zero plot if and only 

if it can be stabilized by a PD controller. 

Proof: The necessary condition of this theorem has already been proved in Theorem 4.1. For the 

sufficient part, first we formulate the closed loop characteristic equation as, 

( 41) 

where /{pd is the gain of the PD controller and -c < 0 is the zero introduced by the controller. In 

addition, the ak's have the same meaning as in Theorem 4.2. We have already shown in Theorem 

4.1 that alternating pole-zero plot will make the angle of departure of all open loop poles pointing 

to the left hand plane. If we can prove that the root locus of this plot with a PD controller never 

cross the imaginary axis for any finite gain I/{pdl < 00, then the stability is always guaranteed. 

Assuming the root locus crosses the imaginary axis at jw. By substituting s = jw into Equation 

(41) and equate both the real and imaginary parts to zero, we have, 

169 
170 

(42) 

and 

(43) 

Equation (43) is true only when 

w o 

or t [ak IT (_W2 + wi)] 

k=1 l=1,l;tk 

o 

For the former case, if w = 0 is substituted into Equation (42), then the equation becomes, 

n n n 

IT w~ + KpdC L ak IT wi = 0 

k=1 k=1 l=l,l;tk 

Since all ak's have the same sign and if a /(pd of suitable sign is used, the equation can never be 

equal to zero. Therefore, 0 is not on the root locus. In the latter case, the solution of w corresponds 

to the open loop zeros of the system. Then the equation is substituted into Equation (42) again. 

Equation (42) is true only when /(pd = 00 or /(pd = -00 with the sign dependent on the sign 

of the ak's. This is due to the fact if finite value of Kpd is used, the first term of Equation (42) 

becomes zero while the second term is nonzero because of the alternating pole-zero plot ( the open 

loop zeros can never be equal to the open loop poles). From above argument we have proved that 

the alternating pole-zero plot can always be stabilized by PD controller, which is the sufficient 

condition of this theorem. 0 

In order to apply the above theorem and illustrate the consequence of a given actuator/sensor 

system configuration, we consider only the first vibration mode. Because the first three modes 

correspond to the rigid body motion with eigenvalue equal to zero, it can be shown from Theorem 

4.2 that the transfer function between the ith input and jth output will have an alternating polezero plot if and only 

or 

(i) 

( ii) 

(i) 

(ii) 

(44) 

(45) 

In order to gain more insight, the mode shape functions obtained from the Rayleigh-Ritz 

method are substituted in the above equations. Consider the case of a rectangle plate, if the 

length-to-width ratio % is between 0.65 and 1.54, the first four mode shape functions can be calculated as ¢1(X, y) = I, ¢2(X, y) = /b2(Y)' ¢3(X, y) = fa2(X), ¢4(X, y) = fa2(X)!h2(Y) and M1 = M2 

= M3 = M4. If they are substituted, Equation (44) and (45) can be rearranged as, 

(i) 112 + [~(x •• - ~), tcy.; - ~)l [~«Xaj - ~), tcYaj - ~)l ~ 0 

(ii) (~-x • .)(~-xaJ(~-Y • .)(~-YaJ~O (46) 
A 

• actuator 

o sensor 

Figure 11: Case 1 for locating the actuator and sensor to achieve desirable alternating pole-zero 

type 

and 

(i) 112 + [~(X'i - ~), HY'a - !)] [H(xaj - ~), HYaj - !)] ~ 0 

(ii) (I-x.a)(~-XaJ(~-Y.')U-YaJ ~O (47) 

Conditions (i) of Equation (46) and (47) can be interpreted geometrically as comparing /2 with the 

inner product of two vectors. These two vectors have starting points at the center of the plate and 

end points at the locations at the actuator or sensor, but their x and Y components are normalized 

with respect to a and b individually. If the rectangle plate are divided into four quadrants by the 

lines x = ~ and y = i, then condition (ii) of Equation (46) is satisfied if the actuator and sensor 

are in the same quadrant or they are in opposite quadrant individually. However, condition (ii) 

of Equation (47) is satisfied if the actuator and sensor are in the adjacent quadrants individually. 

Therefore, for the transfer function to have an alternating pole-zero plot, there are basically three 

ways to locate the actuator and sensor. These three cases are described below . 

• Case 1 : Locate actuator and sensor in the same quadrant as shown in Figure (11). Condition 

(i) of Equation (46) is satisfied automatically because the inner product of the two normalized 

vectors are always greater than zero. If either the actuator or sensor is located at the node 

lines of ¢>4(X, y) which are composed of the lines x = ~ and y = ~, then the zeros cancel the 

two poles symmetrically on the imaginary axis and there are only two poles at the origin. 

• Case 2 : Locate actuator and sensor in the opposite quadrants individually and check if 

condition (i) of Equation (46) is satisfied. For the special case of a square plate as shown in 

Figure (12), if the sum of ~~ and the inner porduct of vectors OA and 013 is greater than 0, 

then the condition is satisfied. Also when the sum is equal to zero, then the zeros cancel the 

two poles at the origin and there are only two poles symmetrically on the imaginary axis. 

171 
172 

A 

• actuator 

o sensor 

B 

Figure 12: Case 2 for locating the actuator and sensor to achieve desirable alternating pole-zero 

type 

• Case 3 : Locate actuator and sensor in the adjacent quadrants individually and check if 

condition (i) of Equation (47) is satisfied. By the same argument in case 2, if the plate is 

square, the sum of ~; and the inner product of vectors OA and DB of Figure (13) should be 

less than O. One obvious result is that the angle between the two vectors has to be greater 

than 90 degrees. Also as in case 2, when the sum is equal to zero, then the zeros cancel the 

two poles at the origin and there are only two poles symmetrically on the imaginary axis. 

5 Effects of Damping 

In the above discussion, we assume that there is no energy dissipation or system damping in the 

vibration of a flexible plate. But damping normally exist in the physical systems. Especially in 

the vibration isolation table, damping is a favorable effect because with proper damping mechanism (e.g. viscoelastic material), the higher frequency vibrations that reach the table top can be 

attenuated rapidly. 

For the case of weak damping effects, it can be guaranteed that the controllability and observability conditions obtained in Section 3 are still acceptable. This is because the controllability and 

observability are preserved under sufficient small perturbation such as the damping effect [15, 16]. 

However, when the damping is not negligible, the modes will couple with each other. Therefore, 

certain modes originally uncontrollable (unobservable) in the case of no damping may become 

controllable (observable) [6]. If the system damping is sufficiently large. It is also pointed out in 

[6] that the number of actuators (sensors) to achieve controllability (observability) are expected to 

be reduced because of the significant coupling effect. 

On the other hand, the influences of damping on the system pole-zero plot is that the open loop 

poles are now placed in the left hand plane instead of being on the imaginary axis. The larger the 

damping, the further the poles are from the imaginary axis. Therefore damping tends to stabilize 
B 

0 ____ ..D 

~A 

• actuator 

o sensor 

Figure 13: Case 3 for locating the actuator and sensor to achieve desirable alternating pole-zero 

type 

the overall system and make the controller easier to implement. 

6 Conclusion 

This paper investigated the relationships between actuator and sensor locations and the dynamics 

and control characteristics of a magnetically levitated vibration isolation system. The problem 

was formulated using orthogonal mode shape functions based on the Rayleigh-Ritz method. A 

lumped-parameter model of a flexible vibration isolation table top is used to investigate the system's controllability and observability including the coupling effects introduced by by the magnetic 

bearing. The selection of proper actuator and sensor locations leading to a controllable and observable system were discussed. Necessary and sufficient conditions were derived for proper selection 

of actuator and sensor locations, and for reducing the controller complexity. The results are illustrated by examples using approximate mode shape functions. Such information is important for 

the overall design of ultra high performance vibration isolation systems. 

A Rayleigh-Ritz method 

Assuming that the plate is vibrating with a mode shape <1>( x, y) and frequency w , the Rayleigh-Ritz 

method proceeds by calculating the maximum potential energy from Equation (6), 

(48) 

173 
174 

2 

1 

0 

"0 

:::l 

...... 

. -- 0 0.. 

a 

< 

-1 

-2 

0 0.2 0.4 0.6 0.8 1 

Nonnalized Length 

Figure 14: The first three modeshape functions of prismatic beam with free ends 

Also the maximum kinetic energy from Equation (5) is given by, 

D 2 ( 2 

Tmax = "2Phw fA tP dA (49) 

By equating the above two equations, an expression for the frequency w is obtained, 

2 ph Vmax 

w = '2 fA tP2dA (50) 

The Rayleigh-Ritz method assumes that the mode shape functions can be expanded by a linear 

series of "admissible" functions and adjusts the coefficients in the series to minimize Equation 

(50). For the case of rectangle plate with length a and width b, the mode shape function tP(x,lI) is 

expanded as : 

3 3 

tP(x,y) = E E Amnlam(x)lbJy) (51 ) 

where the function 1/3. (.) is the ith mode shape function of a prismatic beam with free ends and 

length {3. The first three mode shape functions are plotted in Figure 14. We can write these "first 

three modeshape functions as : 1/31 ({) = 1, 1/3~ ({) = V3(1-7f), 1/33 ({) = cosh( 4.;3f,) - cos( 4.;3f,)_ 

0.983[sinh(~) - sin(4.;3{)]. By substituting these into Equation (51), Equation (50) becomes 

a function or Amn . Then we minimize it by taking the partial derivative with respect to each 

coefficient and equating to zero then follow the same procedure as in [17], we arrive at a set of 

equations each of which has the form, 

3 3 

'" L..- '" L..- (il:) _ [Cmn - Abmn]Amn - 0 (52) 

where 
Figure 15: The 1st mode with normalized frequency 0 

C~~) = Vr[EmiEkn + EimEnkJ + 2(1 - vHHimHkn, Dmn = 1, for mn of ik 

C(ik) b 4 a

3 4 2 aE 1:' + 2(1 )aH H C 1 ~ 'k mn = afi + i)'J'fk + vr iiI'kk - V r ii kk, Vmn =, lor mn = t 

and 

Eim = f3 It ff3i(e)d2J:l~(e)cJ.e, Him = f3 It tif~?) tif!l3{(0cJ.e, fl = f2 = 0,f3 = 4.730 

The above set of linear equations is a typical eigenvalue problem in linear algebra. In this paper, 

we take the Poisson ratio v as 0.3 and solve Equation (52) using the Matlab package and thus get 

nine approximate mode shape functions and corresponding normalized natural frequencies. For the 

special case of square plate, the nine mode shape functions and corresponding normalized natural 

frequencies were computed using Matlab and found to be, 

wi = 0 

w2 = 0 

w; = 0 

w.i = 14.07 

Ws = 19.01 

W6 = 24.62 

wi = 32.69 

Wg = 32.69 

w~ = 66.82 

<Pl(X,y) = 1 

<P2(X, y) = hey) 

<P3(X, y) = hex) 

<P4(X, y) = h(x)h(Y) 

<Ps(x, y) = 0.7071h(y) - 0.7071h(x) 

<P6(X, y) = 0.7069h(y) + 0.7069h(x) + 0.0262h(x)h(y) 

<P7(X, y) = h(x)h(y) 

<Ps(x,y) = h(x)h(Y) 

<P9(X,y) = -0.0185h(y) - 0.0185h(x) + 0.9497h(x)h(y) 

(53) 

where the normalized frequency w· = !!tf-V12P(k-V2) and /j(f.) = ff3j(f.) as appeared in the 

appendix. Figure 15 to Figure 23 are the 3-D approximate modeshape functions of square plate. 

175 
Figure 16: The 2nd mode with normalized frequency 0 

Figure 17: The 3rd mode with normalized frequency 0 

176 
Figure 18: The 4th mode with normalized frequency 14.07 

Figure 19: The 5th mode with normalized frequency 19.81 

177 
Figure 20: The 6th mode with normalized frequency 24.62 

Figure 21: The 7th mode with normalized frequency 36.29 

178 
Figure 22: The 8th mode with normalized frequency 36.29 

Figure 23: The 9th mode with normalized frequency 66.82 

179 
180 

References 

[1] Slocum, A., Precision Machine Design, Draft, 1989. 

[2] Binnig, G., and Rohrer, H., "Scanning Tunneling Microscopy," Helvetica Physica Acta, 

Vol. 55, 1982, pp. 726-735. 

[3] Harris, c. M and Crede, C. E., Shock and Vibration Handbook, McGraw-Hill Book Company, 

New York 1976. 

[4] Sandercock, J. R., "A Dynamic Antivibration System," Proceedings of First International 

Conference of Vibration control in Optics and Metrology, February 1987, London, England, 

pp. 157-165. 

[5] Newport Catalog in, "Vibration Isolation System," CA, 1990. 

[6] Hughes, P. C. and Skelton, R. E., "Controllability and Observability of Linear Matrix-SecondOrder Systems," Journal of Applied Mechanics, Vol. 47, June 1980, pp. 415-420. 

[7] Yang, B. and Mote, C. D. Jr., "Controllability and Observability of Distributed Gyroscopic 

Systems," Journal of Dynamic Systems, Measurement, and Control, Vol. 113, March 1991, 

pp.11-17. 

[8] Park, J-H and Asada, H., "Design and Control of Minimum-Phase Flexible Arms with Torque 

Transmission Mechanisms," IEEE International Conference on Robotics and Automation, 

May 1990, pp. 1790-1795. 

[9J Bennighof, J. K. and Meirovitch, L., "Active Vibration of a Distributed System With Moving 

Support," Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, 1988, 

pp. 246-253. 

[10] Timoshenko, S., Theory of Plates and Shells, McGraw-Hall Book Company, Inc., New York 

and London, 1940. 

[11] Soedel, W., Vibrations of Shells and Plates, Marcel Dekker, Inc. New York and Basel, 1982. 

[12] Chen, C-T, Linear System Theory and Design, Holt, Rinehart and Winston, 1984. 

[13] Timoshenko, S. and Young, D. H., Vibration Problems in Engineering, New York, 

Van Nostrand, 1975. 

[14] Ogata, K., Modern Control Engineering, Prentice-Hall Inc. 1990. 

[15] Balas, M. J., "Feedback Control of Flexible Systems," IEEE Trans. Automatic Control, 

Vol. AC-23, Aug. 1978, pp. 674-679. 

[16] Wonham, W., Multivariable Control, Springer, 1974. 

[17] Young, D., "Vibration of Rectangular Plates By the Ritz Method," Journal of Applied 

Mechanics, 17, 1950, pp. 448-453. 

Bibliography 

[1] Hisatani, M., Inami, S., Ohtsuka, T. and Fujita, M, "Design and Testing of a Flexible RotorMagnetic Bearing System," Proceedings of the Second International Symposium on Magnetic: 

Bearings, July 1990, Tokyo, Japan, pp. 131-138. 

[2] McCallum, D. C., "Dynamic Modelling and Analysis of a Magnetically Suspended Flexible 

Rotor," NASA Conference in Aerospace Applications of Magnetic Suspension Technology, 

September 1990, pp. 499-538. 

[3] Meirovitch, L., Analytical Methods in Vibrations, The Macmillan Co., New York, 1967. 
N92-27731 

STABILITY AND PERFORMANCE OF NOTCH FILTER CONTROL FOR 

UNBALANCE RESPONSE 

C. R. Knospe 

Department of Mechanical and Aerospace Engineering 

U ni versi ty of Virginia 

Charlottesville, Virginia 22901 USA 

May 28,1991 

181 
ABSTRACT 

Many current applications of magnetic bearings for rotating machinery employ 

notch filters in the feedback control loop to reduce the synchronous forces transmitted 

through the bearings. In this paper, the capabilities and limitations of notch filter control 

are investigated. First, a rigid rotor is examined with some classical root locus 

techniques. Notch filter control is shown to result in conditional stability whenever 

complete synchronous attenuation is required. Next, a nondimensional parametric 

symmetric flexible three mass rotor model is constructed. An examination of this model 

for several test cases illustrates the limited attenuation possible with notch filters at and 

near the system critical speeds when the bearing damping is low. The notch filter's 

alteration of the feedback loop is shown to cause stability problems which limits 

performance. Poor transient response may also result. A high speed compressor is then 

examined as a candidate for notch filter control. A collocated 22 mass station model with 

lead-lag control is used. The analysis confirms the reduction in stability robustness that 

can occur with notch filter control. The author concludes that other methods of 

synchronous vibration control yield greater performance without compromising stability. 

NOMENCLATURE 

c derivative feedback coefficient 

c

r 

rotor damping 

C nondimensional bearing damping, c/ c 

r 

e

u 

unbalance eccentricity 

F b bearing force 

F u unbalance force 

g notch gain 

H feedback transfer function 

k proportional feedback coefficient 

kb open loop magnetic bearing stiffness 

keq equivalent bearing stiffness 

Keq nondimensional equivalent bearing stiffness, keq/ks 

ks shaft stiffness 

PRECEDING PAGE BLANK NOT FILMED 183 
184 

j 

m 

mb 

md 

M 

N 

p 

Pe 

Po 

s 

W 

Z 

Zl 

Z2 

(J 

cp 

() 

¢ 

(d 

(0 

(r 

Wo 

W 

FI 

rotor mass 

bearing rotor mass 

disk rotor mass 

mass ratio, 2mb/md 

notch filter transfer function 

characteristic polynomial 

even part of characteristic polynomial 

odd part of characteristic polynomial 

complex frequency variable 

notch width 

rotor posi tion 

complex bearing displacement, Zl = Xl + j Y 1 

complex midspan displacement, Z2 = X2 + j Y 2 

angle from PD zero to notch zero 

angle from notch pole to notch zero 

angle from notch pole to notch zero 

angle of arrival of locus 

notch pole damping 

notch zero damping 

rigid bearing shaft damping, cr/2~ ksmd 

operating speed, notch center frequency 

nondimensional operating speed, wo/ wr 

rigid bearings critical speed, ~ ks/md 

nondimensional complex frequency, s/ wr 

INTRODUCTION 

In the last decade, active magnetic bearings for rotating machinery have moved 

from a promising concept to industrial application. Magnetic bearings have been installed 

in a variety of machines including pumps and compressors [1,2]. They have been 

employed successfully in several large rotating machinery applications including over 25 

thousand hours of operation on a natural gas pipeline compressor r2]. While these initial 

experiences with industrial application of magnetic bearings have been encouraging, 

problems with their installation have been noted. Often, installation of current design of 

magnetic bearings requires several weeks of "tuning" of the controller [2]. Undoubtedly, 

as digital control becomes more widespread for magnetic bearings, this time will be 

shortened. However, the authors believe that the fundamental factor in the long 

controller installation time is the amount of tuning required to achieve stability and 

acceptable performance. Better analysis of the rotor dynamic and control issues of a 

particular application before installation should greatly reduce on-site tuning. 

One area that the authors believe has undergone insufficient analysis is the use of 

notch filters. Many current applications of magnetic bearings have a notch filter in the 
control feedback loop to suppress rotor synchronous response [3]. The notch frequency is 

placed at the operating speed and causes the bearings effective stiffness and damping at 

this speed to be greatly reduced. In principle, the bearings exert little harmonic force 

upon the rotor and the rotor spins about its inertial axis. Thus, a greatly reduced 

harmonic force is transmitted to the foundation. However, since the stiffness and 

damping of the bearings at the rotational speed is very small, the orbits at the bearings 

may become quite large. The notch filter technique is often referred to as "automatic 

balancing". This name may be misleading since the reduced bearing stiffness and 

damping are not analogous to conventional rotor balancing techniques. In conventional 

rotor balancing, correction weights are added to the shaft so as to reduce the residual 

unbalance. These weights produce forces which rotate with the shaft counteracting the 

forces due to the shafts unbalance distribution. Conventional balancing does not change 

the bearing properties. Thus, conventional balancing does not affect system stability or 

transient response. Notch filtering changes both these since it alters the bearing 

properties. With the notch filter, the unbalance distribution about the geometric axis is 

unaltered; however, the rotor spins about its inertial axis. In theory, the motion of the 

shaft is not transmitted to the foundation because of the very low stiffness and damping. 

Since notch filters achieve synchronous attenuation through altering the magnetic 

bearing feedback loop, stability becomes an important issue. In practice, the stability 

issue has a profound impact upon the efficacy of notch filters as a solution to the 

unbalance response problem. This result has been reported by Beatty [4] for single mass 

flexible rotors with massless bearings. For the same reason, a notch filter controlled 

system may also have poor transient response. 

The authors emphasize, however, that it is not necessary to use feedback 

modification to achieve unbalance response attenuation. Because the synchronous 

response is highly correlated, it can be reduced through an open loop (feedforward) 

scheme without altering the system transient response or stability. This method has 

been employed by many researchers [5,6,7,8]. Recently, the authors have demonstrated 

reductions in transmitted synchronous vibration of 42 dB (over one hundred fold) on an 

experimental rotor rig [9]. It is interesting to note that, to the authors' knowledge, open 

loop controllers are currently not in use on any commercial machines. The promise of 

these controllers will not be discussed further in this paper as the focus remains the 

examination of notch filter controllers which are widely employed in commercial 

machines. 

In this paper, the stability and performance of notch filter control systems is 

examined. In Section II, a rigid rotor model is used to introduce the stability and 

performance issues of notch filter controllers. Section III examines an extended 

symmetric three mass rotor model and solves for a nondimensionalized characteristic 

equation and bearing response. In Section IV, the analysis' results are presented and the 

stability and performance of notch filter controllers is discussed. Section V examines the 

robustness of a 22 mass station model of a high speed compressor with notch filters in the 

feedback loop. Section VI closes with conclusions. 

II. RIGID ROTOR ANALYSIS 

A rigid rotor system with magnetic bearings is discussed here to introduce the 

instability that can be produced by notch filters in the feedback loop. A rigid rotor in 

magnetic bearings without stabilizing feedback may be described by a mass, m, attached 

to a negative spring [10], kb < 0, with a transfer function between bearing force, F b' and 

rotor position, Z 

185 
186 

z~ 1 FJ;TSJ = ms2 + kb (1) 

A block diagram representation is shown in Figure 1. This system has poles at ± ~ -kb/m 

and is unstable since one pole is in the right half of the complex plane. The system may 

be stabilized using proportional- derivative (PD) control 

F (s) 

~ == H(s) = cs + k (2) 

resulting in a stable closed loop system transfer function between unbalance force, F , u 

and rotor position 

~ 1 FJSJ = ms2 + cs + keq (3) 

where k = kb + k, if c and k are positive. As illustrated in Figure 2, a root locus 

eq eq 

diagram for the system, the PD control places a zero on the real axis in the left half of the 

complex plane at -kj c. Whether this zero is to the right or left of the pole at - f -kb/m, 

the system will be stabilized provided k > -kb. The bearing of the closed loop system 

will have equivalent stiffness keq and damping c. 

The transfer function for a simple notch filter centered at the operating speed w

o

' 

characterized by its gain, g, and its width, W, is 

S2 + 2 (owos + W 2 

N(s) = S2 

0 

+ 2 (dwos + w 2 

0 

(4) 

(0 

g=~ W = 2(dwo (5) 

where (0 and (d are the damping of the notch filter zeros and poles respectively. The 

notch gain g is the gain of a signal at frequency Wo as it passes through the notch .. The 

notch depth, D, D = 1 - g ,specifies the amount of signal rejected at woo Note that if 

the notch gain is zero then a signal at Wo is completely removed by the filter. If the notch 

gain is one then the signal is completely passed. The notch width is the width of the 

frequency band where attenuation is greater than -3dB when the notch depth is one [4]. 

Figure 3 shows the magnitude plot of notch filters of various depths and widths. 

A notch filter may be placed in the magnetic bearing feedback loop in essentially 

two fashions: (1) directly in serial with the PD control, and (2) in serial with PD control 

after the plant has been compensated for its negative bearing stiffness. In the first case, 

the controller transfer function is 
F (s) ~ == H(s) = (cs + k) N(s) (6) 

and in the second case 

F (s) ~ == H(s) = -kb + (cs + keq) N(s) (7) 

In the first case, if the notch has a gain 

then the system will have a negative stiffness to vibrations at Wo and will therefore be 

unstable. In the second case, the notch gain would have to be negative to produce an 

effective negative stiffness at frequency woo Since it is simpler for explanation and no 

generality is lost, only the second case will be examined in this paper. 

When the notch gain is zero, the bearings have no synchronous stiffness or 

damping and no synchronous vibration is transmitted to the foundation. In practice, 

however, kb cannot be known precisely and one cannot cancel it exactly using feedback. 

It is likely that the bearings after this compensation would have some equivalent stiffness. 

This would limit the ability of the notch filter to attenuate the transmitted vibration. 

Thus, the assumption that kb can be precisely canceled will yield the ideal performance 

for the notch filter. This ideal case is examined here since the problems associated with 

notch filters, as will be shown, are serious enough that even their idealized performance 

will discourage their continued use. 

After feedback compensation for the negative bearing stiffness, the plant (rotor 

plus stabilizing stiffness -kb) has the transfer function 

(8) 

and the notch filter feedback controller has the transfer function 

H(s) = (keq 

+ cs) N(s) (9) 

The plant has two poles at the origin of the complex plane while the controller has poles 

at 

and zeros at 

_ keg 

c ( 2 

o 

If the notch gain is zero ((0 = 0) then the complex zeros of GH are on the imaginary axis. 

If the notch width is 20% of Wo ((d = 0.1), a possible pole-zero structure and root locus 

is shown in Figure 4. Note that two closed loop poles are in the right half complex plane 

187 
188 

and the system is unstable. Even though the poles of the notch filter are placed near the 

zeros, the loci stray into the right half plane. 

Interestingly, the conditional stability of zero notch gain controllers can be 

examined through the classical root locus technique of the angle of arrival. The angle of 

arrival is the angle in the complex plane at which a locus approaches an open loop zero. 

Evans [9] first established that the sum of the angles from the open loop poles of the 

system to a point on a locus minus the sum of the angles from the open loop zeros to the 

same point must be 1800 . From this, it is easy to calculate the angle of arrival of a locus 

at a zero. For the example, the loci must approach the imaginary zeros from the left to 

ensure unconditional stability. Thus, their angles of arrival must be between 900 and 

2700 . Given that the notch is thin ((d < < 1), this yields a condition for stability of these 

roots in terms of the angle from the PD zero on the negative real axis to the open loop 

imaginary zero, (3: 

Clearly, this condition is only satisfied when the zero on the real axis is in the right half 

plane. Thus, for a given ratio of equivalent stiffness to damping (which would be chosen 

by the designer for transient response since this determines the log decrement) the closed 

loop system with notch filter will go unstable as the stiffness is increased. 

Indeed, it is easy to show that conditional stability of this kind will always result if 

the notch gain is zero for any notch width. Figure 5 illustrates the argument. Kote that 

for any notch filter of the form Eqn. (4), the poles and zeros lie along a semi-circle of 

radius w in the left half plane. From geometry, the angle from any possible notch pole o 

circumscribing the two undamped zeros is right (Le. <p + e = 900 ). The angles from the 

open loop poles to a point on the locus as it arrives at the notch zero are <p, e, 900 , and 

900 . The angles from the open loop zeros to the point are 1/J, (3, and 900 where 1/J, the 

angle of arrival, must satisfy 

for unconditional stability. The angle of arrival condition 

with 

and 

<p + e = 900 , yields 

-1/J=(3 

This establishes that conditional stability will always occur if the PD control zero is 

placed on the negative real axis (Le., damping and stiffness are positive). Conditional 

stability can only be eliminated by having a notch gain greater than zero. However, as 

the notch is made more shallow, the attenuation of the transmitted synchronous vibration 

is reduced. 
This conditional stability is not surprising since the notch filter introduces phase 

lag at frequencies below the center frequency. Thus, the feedback controller may not 

have phase lead at the rotor natural frequencies, resulting in instability. 

III. FLEXIBLE ROTOR MODEL 

A symmetric three mass rotor model with flexible shaft and notch filter controller 

is examined in this section. The model to be used, shown in Figure 6, is described by the 

Laplace domain dynamical equations 

[mbs2 + i ks + kb + H(s)] ZI (s) = [i ks

] Z2(s) 

[mds2 + crs + ks

] Z2(s) = [ks

] ZI (s) + F u(s) 

(10) 

where mb is the rotor bearing mass, md is the rotor disk mass, c

r is the rotor damping, ks 

is the shaft stiffness, ZI (s) is the complex displacement at the bearing, Z2(s) is the 

complex displacement at midspan, H(s) is the controller transfer function, and F u(s) is 

the unbalance force which is assumed to act at the midspan. The feedback controller 

transfer function is given by 

H(s) = -kb + (cs + keq) N(s) (11) 

where N( s) is the notch filter transfer function defined in Eqn. (4). The characteristic 

equation for this system is given by 

(12) 

With the nondimensional quantities w , ( , M, C, K ,and W defined in the 

r r eq 

nomenclature, the characteristic polynomial, Eqn. (12), becomes 

o = [i M .,\2 + i][.,\2 + 2(r"\ + 1][.,\2 + 2(dW"\ + ZJ2] 

+[2C(r"\ + KeqH.,\2 + 2(r"\ + 1][.,\2 + 2(ow"\ + w2] 

-i [.,\2 + 2(dW"\ + w2] 

(13) 

where .,\ is the nondimensional complex frequency, .,\ = s/w

r

. This is a sixth order 

polynomial in .,\ which defines the closed loop poles of rotor--<:ontroller system, 

(14) 

where the coefficients are defined by 

P6 = M/2 

189 
190 

P5 = M(dw + M(r + 2(rC 

P4 = ~ MW2 + 2M(/dw + ~ (M+l) + 4(r(oCw + 4(/C + Keq 

P3 = M (rW2 + (M + 1) (dw + (r + 2(rC W2 + 2(rC + 2(rKeq 

+ 2(4(/ C + Keq) (0 W (15) 

P2 = ~ (M + 1) w2 + 2 (r(dw + (4(/ C + Keq) W2 

+ 4(C + Keq) (r(o W + Keq 

PI = (r W2 + 2(V + Keq) (r W2 + 2 Keq (0 w 

Po = Keq W2 

The unbalance force transmitted through the bearings to the foundation is, in terms of 

the nondimensionalized parameters, 

(16) 

Using the coefficients of the characteristic polynomial, an efficient procedure may be 

employed for finding the largest stabilizing notch depth as a function of the 

nondimensionalized parameters (0' (r' V, Keq, wand M. 

For a system to be stable, the roots of its characteristic polynomial must all lie in 

the left half of the complex plane. Polynomials satisfying this condition are called 

Hurwitz [11,12]. A method for determining the lowest possible notch gain for a stable 

rotor system is to continually check a Hurwitz stability condition as (0 is decreased 

starting with (0 equal to (d (no notch filter). When the notch filter is absent from the 

feedback loop, the rotor system will be stable if C and Keq are positive. As the notch is 

made deeper for a given bearing (V, K

eq), the closed loop poles will move continuously in 

the complex plane. When the notch becomes of sufficient depth, a complex pole will 

enter the right half plane. On a Nyquist plot, this will appear as a clockwise encirclement 

of the critical point, as discussed in Beatty [4]. As the notch becomes deeper, the 

encirclement will remain. Thus, the range of notch gains between zero and one is divided 

into a stable and an unstable interval. 

IV. SIMPLE MODEL RESULTS 

In this section, the degree of attenuation of synchronous transmitted force 

obtainable with a notch filter controller is examined. This is done to explore the limits of 

notch filters and not to suggest an actual method of implementation. Thus, while we 

show the attenuation possible over an entire speed range, we are not suggesting that this 

is in practice desirable or implementable. 

Given the nondimensional parameters for the rotor (M, ( ), the control (C, K , r eq 
(d)' and the operating speed (w), the notch of greatest possible depth ((0) that may be 

employed while preserving system stability may be found by repeatedly checking 

stability. From the notch depth so determined, the magnitude of synchronous bearing 

force can be calculated using Eqn. (16). This is the minimum transmitted force due to 

unbalance that can be obtained using a notch filter in the feedback loop. (It is easy to 

demonstrate that maximizing notch depth minimizes transmitted force.) In cases with 

non-zero notch gain, the system has only marginal stability. In this case, a pair of poles 

lies along the imaginary axis. Thus, any transient to this system will cause it to 'ring' at 

this frequency. The only way to amend this undesirable behavior is to reduce the notch 

depth and thus the synchronous attenuation obtained. Note that in practice the degree of 

synchronous response attenuation indicated in this analysis cannot be obtained; any 

implemented feedback controller must have some stability margin. 

The analysis was conducted for a three disk magnetic bearing rotor rig used at the 

University of Virginia. This rig has been used in various research projects and is well 

characterized [10,13,14]. The nominal values of the nondimensional parameters are 

M = 1.466 

C = 10.5 

(d = 0.10 

(r = 0.0625 

Keq = 0.906 

(Width = 20% wo) 

Figure 7 shows the theoretical non-dimensional transmitted synchronous force (without 

notch filtering) as a function of nondimensional operating speed wand nondimensional 

bearing damping C. Note the two separate critical speeds at low damping. The limit 

imposed by stability to the attenuation of this synchronous transmitted force are now 

examined. 

In Figure 8 the minimum notch gain that may be employed while maintaining 

stability is shown as a function of operating speed and damping. A very deep notch can 

be obtained above the first critical speed if a high degree of bearing damping is employed. 

However, if the bearing damping is less than five times the rotor damping, a notch in the 

region of the second critical cannot be 20 dB deep (gain of 0.1). To achieve this depth at 

the first critical, the bearing damping must be approximately twenty times the rotor 

damping. Unfortunately, the synchronous vibration problem is greatest at the critical 

frequencies where the notch must be the shallowest to maintain stability. In design of PD 

control for magnetic bearings, the damping is chosen to yield good transient performance 

and robustness to unmodeled destabilizing forces. It is not desirable to set the bearing 

damping so as to permit the use of a notch filter. 

Figure 9 shows the minimum synchronous bearing force that can be achieved wHh 

a notch filter controller at each operating speed as a function of bearing damping. The 

notch employed at each operating speed and damping is the deepest that may be used 

with system stability maintained. As Figure 8 suggests, the attenuation of notch filter 

control when the bearing damping is light is poor near the rotor criticals, approximately 6 

dB as can be seen in comparing Figures 7 and 9. When the nondimensional rotor 

damping is above 10, 20 dB (factor of 10) attenuation can be obtained at any operating 

speed. 

Figure 10 shows the nondimensional bearing force (without notch) for the same 

three mass rotor model as before except that the bearing masses have been reduced to one 

quarter the midspan disk mass (M = 0.5). Thus, this model acts more like a single mass 

c-3 

191 
192 

rotor. Note that the second critical speed is significantly higher. Figure 11 shows the 

minimum stabilizing notch gain as a function of the nondimensional rotational frequency 

and damping. Note that the range of operating speeds at low damping near the second 

critical speed requiring shallow notch filters is much broader than with the first rotor 

examined (Figure 8). Interestingly, the maximum transmitted force with the notch filter, 

Figure 12, does not occur at the same frequency as the second critical (without notch) or 

where the notch is the shallowest. While this seems counter-intuitive, the introduction of 

the notch filter alters the location of the closed loop poles in the complex plane. As 

discussed by Dorf [15], the synchronous response of a system is inversely proportional to 

the distance of the poles from the synchronous frequency on the imaginary axis. Thus, 

the maximum synchronous response of a synchronous notch system will not occur at the 

critical frequency of the system without notch since the closed loop pole locations have 

been altered by the introduction of the notch. 

The author wishes to emphasize that the performance indicated here is ideal since 

it has been assumed that the unstable bearing stiffness can be precisely canceled through 

feedback and that notch filter controller-rotor system can operate without any stability 

margin. It should also be pointed out that the notch controller-rotor systems represented 

that are marginally stable possess a pole on the imaginary axis. Therefore, any 

disturbance acting at this asynchronous frequency will result in very large dispIacements. 

v. ROBUSTNESS ANALYSIS 

We now examine a more realistic rotor model to gauge the effect of notch filters on 

magnetic bearing system robustness. The 'rotor' employed for this analysis is a 22 mass 

station model of a high speed test rig constructed at the University of Virginia to 

simulate an aircraft compressor [16]. The designed operating speed range of this machine 

is 30,000 to 70,000 rpm. The model employs collocated sensors and actuators and local 

lead-lag control. The negative bearing stiffness is assumed to have been compensated. 

The magnetic bearings and the sensors are assumed to have infinite bandwidth" 

Gyroscopic terms are not included in the model. These assumptions were made so that 

the results are easier to analyze. We may fairly attribute changes in robustness with the 

introduction of notch filters to the notch filters themselves and not to the notch filters' 

interaction with other destabilizing mechanisms (e.g. non-collocation). The rotor with 

bearing locations is shown in Figure 13. 

The structured singular value method is used to analyze the magnetic bearing 

system robustness with notch filters. Multiplicative uncertainty elements (~1' ~2) are 

placed in the feedback path as shown in Figure 14. These uncertainties are complex 

numbers and therefore represent some gain and phase change to the signals in the 

feedback loop. A notch filter operating speed is fixed and the structured singular values 

of this plant (rotor, phase lead control, notch filters) with respect to the multiplicative 

uncertainty is computed [17]. The structured singular value is the inverse of the size of 

the smallest complex uncertainty matrix ~ = diag (~1' ~2) which destabilizes the 

system. Thus, the structured singular value can be thought of as the inverse of the 

gain/phase margin at each frequency. Large structured singular values in a frequency 

range indicates poor stability robustness to unmodeled dynamics in this frequency band. 

In this analysis, the maximum structured singular values over frequency is found 

for the rotor system with and without notch filters. This serves as our robustness 

measure. We examine this measure as a function of the center frequency of the notch 

filter. Robustness is therefore examined as a function of notch filter/rotor operating 

speed much as in Section IV. 
In the first analysis, a narrow notch with a notch gain of 0.1 is used. Figure 15 

shows the maximum structured singular value as a function of notch center frequency. 

Also shown is the maximum structured singular value for the system without notch 

filters. Note that the maximum structured singular value ("mu") is highest in the region 

of the rotors critical speeds without notches (first critical: 5530 rpm; second: 10910 rpm; 

third: 22350 rpm; fourth 55800 rpm). Thus, if a notch filter with 20 dB attenuation were 

used on this rig near one of these speeds, the system would be much more prone to 

destabilization due to uncertainties in each feedback loop. The use of notch filters in this 

operating speed range will make the rotor system much more sensitive to components in 

the feedback loop (sensors, filters, amplifiers, and actuators). This may help to explain 

the difficulties experienced in "tuning" magnetic bearing systems. 

The maximum structured singular value can be converted to either gain margin or 

phase margin specifications. These margins are guaranteed margins; that is the system 

will be stable for at least the amount of variation specified by the margin. Because the 

system we are examining is a resonant system (which is always stabilized by collocated 

phase-lead control), closed loop stability is much more sensitive to phase changes. Thus, 

it is reasonable to expect that the actual multivariable phase margin is not much greater 

than the guaranteed phase margin specified by the maximum structured singular value. 

Figure 16 shows the guaranteed phase margin as a function of notch center frequency. 

Note that without notch filters, the system has 41· phase margin. However, with a notch 

filter included, the phase margin drops considerably, especially near critical speeds. It 

should be noted that most control systems are designed to have phase margins greater 

than 20·. In the author's opinion, a healthy phase margin is necessary for a properly 

running magnetic bearing system. 

This analysis was also carried out with a notch filter with 40 dB depth. The 

maximum structured singular value as a function of notch center frequency for this case is 

shown in Figure 17. Below approximately the third critical speed the rotor is unstable 

(without any multiplicative uncertain). As the notch center frequency is increased, the 

system becomes less sensitive to phase/gain changes in the feedback loops. Figure 18 

shows the corresponding guaranteed phase margin of the system with and without notch 

filters as a function of notch center frequency. Note that at no frequency in the rotors 

operating speed range will the system with notch filters have a phase margin of 20· . 

193 
194 

VI. CONCLUSIONS 

Analysis of synchronous notch filter controllers for unbalance response attenuation 

of magnetically suspended rotors demonstrates that the introduction of a notch filter into 

the feedback loop has a profound affect on system stability and robustness. It was shown 

that for a rigid rotor complete attenuation was impossible without conditional stability. 

For flexible rotors, notch depth was restricted by instability near the critical speeds. If 

the bearing damping is low, transmitted force attenuation is small near the critical speed. 

When set for a given operating speed, asynchronous disturbances can cause large 

displacements since the notch filter controlled rotor may be marginally stable. This is an 

important consideration for practical rotor systems which have subharmonic excitations 

due to cross coupled effects such as seals. Structured singular value analysis was used to 

show the reduced robustness that may occur when notch filters are introduced into the 

feedback loop. This analysis examined the robustness with respect to the simultaneous 

inependent gain/phase changes in each loop. Notch filter controllers may also have poor 

robustness to changes in the rotor (for example, thermal induced changes in Young's 

modulus) and destabilizing fluid forces which are not representable by this structure. 

Due to these problems with notch filter controllers, the author strongly 

recommends that magnetic bearing users employ open loop (feedforward) control 

strategies for synchronous vibration reduction. These controllers have been demonstrated 

by many researchers to yield superior vibration attenuation with no stability problems. 
[1] 

[2] 

[3] 

[4] 

[5] 

[6] 

[7] 

[8] 

[9] 

[10] 

[11] 

[12] 

[13] 

REFERENCES 

Imlach, J., Humphris, R., Blair, B., Allaire, P., and Lewis, D., "Testing of a 

Magnetic Bearing Equipped Canned Motor Pump for Installation in the Field," 

2nd International Symposium on Magnetic Bearings, Tokyo, Japan, July 12-14, 

1990, pp. 39-45. 

Foster, E., Kulle, V., and Peterson, R., "The Application of Active Magnetic 

Bearings to a Natural Gas Pipeline Compressor," ASME Paper 86-GT-1, 

presented at International Gas Turbine Conference and Exhibit, Dusseldorf, West 

Germany, June 8-12, 1986. 

Haberman, H. and Brunet, M., "The Active Magnetic Bearing Enables Optimum 

Damping of Flexible Rotors," ASME Paper 84-GT-117, 1984. 

Beatty, R., "Notch Filter Control of Magnetic Bearings to Improve Rotor 

Synchronous Response", Master's Thesis, MIT, May 1988. 

Burrows, C.R., Sahinkaya, N., Traxler, A., and G. Schweitzer, "Design and 

Application of a Magnetic Bearing for Vibration Control and Stabilization of a 

Flexible Rotor," Proceedings of the First International Symposium on Magnetic 

Bearings, ETH Zurich, Switzerland, June 6-8, Springer-Verlag, 1988. 

Higuchi, T., Mizuno, T., and Tsukamoto, M., "Digital Control System for 

Matnetic Bearings with Automatic Balancing," Proceedings of the 2nd 

International Symposium on Magnetic Bearings, Tokyo, Japan, July 12-14, 1990. 

Kanemimtsu, Y., Ohsawa, M., and Watnabe, K., "Real Time Balancing of a 

Flexible Rotor Supported by Magnetic Bearings," Proceedings of the 2nd 

International Symposium on Magnetic Bearings, Tokyo, Japan, JUly 12-14, 1990. 

Nonami, K., and Kawamata, S., "Feedforward Control to Unbalance Force 

Cancellation for Flexible Rotor Systems," Proceedings of the International 

Symposium on Advanced Computers for Dynamics and Design (ACD&D), 

Tsuchiura, Japan, Sept. 6-8, 1989. 

Knospe, C.R., Humphris, R.R., and Sundaram, S., "Flexible Rotor Balancing 

using Magnetic Bearings," Proceeding of the Conference on Recent Advances in 

Active Control of Sound and Vibration, Blacksburg, VA., April 15-17, 1991. 

Techomics Publishing, Lancaster, PA, pp. 420-429, 1991. 

Humphris, R., Allaire, P., Lewis, D., and Barrett, 1., "Diagnostic and Control 

Features with Magnetic Bearings," Proc. of the 24th Intersociety Energy 

Conversion Engineering Conference, Washington, D.C., August 6-11, 1989, pp. 

1491-1498. 

Evans, W., Control-System Dynamics, McGraw-Hill, New York, 1954, pp. 

96-121. 

Bhattacharyya, S. P., Robust Stabilization Against Structured Perturbations, 

Lecture Notes in Control and Information Sciences, Vol. 99, Springer Verlag, 

Berlin, 1987, pp. 14-22. 

Humphris, R., Kelm, R., Lewis, D., and Allaire, P., "Effect of Control Algorithms 

on Magnetic Journal Bearing Properties," Journal of Engineering for Gas Turbines 

and Power, Vol. 108, Oct. 1986, pp. 624-632. 

195 
196 

[14] 

[15] 

[16] 

[17] 

Williams, R., Keith, F., and Allaire, P., "Digital Control of Active Magnetic 

Bearings," IEEE Transactions on Industrial Electronics, Vol. 37, No.1, February 

1990, pp. 19-27. 

Dorf, R., Modern Control Systems, Addison-Wesley, Reading, MA, 1967, pg. 190. 

Maslen, E., Allaire, P., Scott, M., and Herman, P., "Magnetic Bearing Design for 

a High Speed Rotor," 

Doyle, J.C., "Analysis of Feedback Systems with Structural Uncertaintie..')", lEE 

Proceedings, Part D., Volume 129, No.6, pp. 242-250, Nov. 1982. 
G(s) 

1 Z(s) 

+ 

c s+k 

H(s) 

Figure 1: Block diagram of rigid rotor system in magnetic bearings 

3 cc 111 closed loop poles II 

9 \ 2 

s 

/' 

./ 

1 

I 

e 

-1 "-

"'--

-2 ~- ~------~/ 

-3 

-5 -'f -3 -2 -1 a 1 

Real s 

Figure 2: Root locus for PD control of a rigid rotor 

197 
0 

CQ -5 

'0 

C .;; 

0 -10 

-\~-l 

100 

t:IO 0 II) 

'0 

~ 

! -l00r Q.,. 

-2~_1 

... 

a 

9 

s 

198 

3 

2 

1 

0 

-1 

-2 

-3 

-s 

Figure 4: 

\( 

1oo 

Frequency (rad/sec) 

f\-

~ 

tOO 

Frequency (rad/sec) 

Figure 3: Notch filter magnitude plots 

closed loop poles 

I 

Root locus for notch filter-PD control of a rigid rotor 

((0 = 0, (d = 0.1) 

-

-

101 

101 
Imag 

S-Plane 

Figure 5: Locus angle for arrival condition ((0 = 0, (d < 1) 

CENTER MASS 

1 Z2 

BEARING MASS ks ks BEARING MASS 

2 md 2 lz mb SHAFT mb 1 

kb 

r ~ 

H(s) ~k JuCr 

H(s) b ~ ~ 

I I 

Figure 6: Symmetric three mass rotor model 

199 
200 

, ·0 

0.0 

Figure 7: Nondimensional transmitted synchronous force at each nondimensional 

operating speed as a function of nondimensional bearing damping 

(M = 1.466, (d = 0.1) 

Figure 8: Minimum notch gain at each nondimensional operating speed as a 

function of nondimensional bearing damping (M = 1.466, (d = 0.1) 
Figure 9: With notch filter control: Nondimensional transmitted synchronous 

force at each nondimensional operating speed as a function of 

nondimensional bearing damping (M = 1.466, (d 0.1) 

C> 

Figure 10: Nondimensional transmitted synchronous force at each nondimensional 

operating speed as a function of nondimensional bearing damping 

(M 0.5, (d 0.1) 

201 
202 

Figure 11: Minimum notch gain at each nondimensional operating speed as a 

function of nondimensional bearing damping (M = 0.5, (d = 0.1) 

Figure 12: With notch filter control: Nondimensional transmitted synchronous 

force at each nondimensional operating speed as a function of 

nondimensional bearing damping (M = 0.5, (d = 0.1) 
BEARING JOURNAL BEARING JOURNAL 

Figure 13: High speed rotor for model aircraft compressor 

ROTOR 

I AI L 

I I 

\, 

I L 

I Az,J 

UNCERTAINTY 

PHASE 

LEAD 

J 1 

I I 

J I 

I J 

NOTCH 

FILTERS 

.J 1 

I I 

J 

I JFigure 14: Uncertainty elements in feedback path 

203 
204 

102~1 ----------------r---------~----~----~--~--~--~-~~ 

~ 1 

;-

t 

fI 

! 

~ 

WITH NOTCH 

I JV\ I ! \ I 

J 

I 

-i 

I 

J 

~ l 

J 

i I \\~ I "1 

:~ '~--l 

t

---------------------------------------------------------------------------------------------------------------- -------- i 

WITHOUT i 1oo ' , , !! !: 

1~ 1~ 

OPERATING SPEED (RPM) 

Figure 15: Maximum structured singular value with and without notch filters as a 

function of operating speed (notch gain = 0.1) 

45~1 --------------------------~----~----_r--~--~--~-~~ 

~ _ _ _______ ___ _ __ _ _ _ __ ___ _ __ ____ __ ______ __ __ _ _______ ___ ____________ ___________ __________ __ ____ ____ ____ ___ _ __ __ ___________ 1 40: WITHOUT ! j 

I 

35~ 

30~ 

I 

I 

25 f20l I 

I 

I 

15~ ! 

I 

10~ 

! 

,~ 

/ WITH NOTCH 

,I 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

~! I 

i 

I 

I 

~ 

--t I 

1 

j 

! 

I 

J 

---I ! 

i 

1~-:-4 _____________ ----"--__ -'---~_~____'_ __ _____J i 

105 

OPERATING SPEED (RPM) 

Figure 16: Guaranteed Phase margin with and without notch filters as a function of 

operating speed (notch gain = 0.1) 
r--

! 

r 

:J 

~ 101~ 

~ ~ ~ f--

I 

r--

WITH NOTeB 

I 

~ ~ 

: WITHOUT L ___ --- - ______________ - - - -- - _____________ -- --- --- - ---- -- - --- - ---- ------- -----_ ------ --- ------ -- ____ ------- -- ___________ _ 

i IOoLI ________________ ~ ________ ~ ____ ~ ____ ~ __ ~ __ ~ ____ ~~ 

104 

OPERATING SPEED (RPM) 

Figure 17: Maximum Structural singular value with and without notch filters as a 

function of operating speed (notch gain = 0.01) 

45~i --------------------------------~----~--~--~--~~~ 

i I 40 r------------------------------------------------------------------------------- ------------- ------ ---------- ------ --- -- --' 

r WITHOUT. ; 

0 35 

@ 

0 30 

z 

- 25 Co:j 1 

~ I 

~ 20~ 1 

~ I 

~ 15'~ 

I = I 

Il.. 1O~ 

1 

I 

I 

1 

1 

5~ I 

I 1 

i 

1 lb4 

OPERATING SPEED (RPM) 

Figure 18: Guaranteed Phase Martin with and without notch filters as a function of 

operating speed (notch gain = 0.01) 

1 

I 

205 
Session 4 

MICRO GRAVITY AND VIBRATION ISOLATION 1 

Chairman - Mike Scott 

NASA Langley Research Center 

PRECEDING PAGE BLANK NOT FllM!D 207 
N92-27732 

A. Six Degree-of-Freedom Magnetic Bearing for 

NIicrogravity Vibration Isolation * 

A. Peter Allan and Carl R. Knospe 

Department of Mechanical and Aerospace Engineering 

University of Virginia 

August 20, 1991 

PRECEDING PAGE BLANK NOT FILMED 209 
1 Introduction 

The authors have previously presented a conceptual design for a coarse-fine actuator pair and discussed 

its efficacy in the microgravity vibration isolation application[1]. The coarse stage comprises a Stewart 

platform [2] which is mounted in a spacecraft and isolates low frequency, high amplitude vibration s. The 

fine stage is a novel magnetic bearing mounted on the Stewart platform (between t he legs for compactness) 

and levitates the experiment to isolate all frequencies at low amplitudes. The combination is illustra ted in 

Figure 1. 

Figure 1: Coarse-Fine Actuator Pair 

This paper will present a survey of published 6 DOF levitation designs and discuss a novel magnetic 

bearing in terms of design, predicted performance, and control issues. 

'Supported in part by the NASA Lewis Research Center and the Commonwealth of Virginia 's Ce llter for IlIlIovat.ive 

Technology. 

PRECEDING PAGE BLANK NOT FiLrv'r£D 

211 
2 Survey of Published Designs 

Several designs for 6 DOF levitation are discussed in the literature. A comparison of the specifications for 

these designs is given in Table 1. 

Group Trans. Rot. 

Honeywell ±5 mm ±1.6° 

N. Wales ±5mm < ±.2° 

NASA ±4 mm ±30 C 

SatCon ±10 mm ±80 C 

IBM ±5 mm ±4° 

Toshiba ±2mm ±1.5° 

a Requirement, not limitation 

blncludes experiment package 

CEstimated by authors 

Force Envelope Weight 

43 N 27x34x.50 cm 36 kg 

.04 N a 100x100x100 cm b ? 

445 N 30x30x 1.5 cm C ? 

4N 40x40x12 cm C 4.9 kg 

32 N 2.5x2.5x15 cm C ? 

20 N C 25x25x20 cm 8 kg 

Table 1: Comparison of Published Designs 

Actuator Sensor 

Mag. Brng. Eddy & Flux 

Lorentz Capacitive 

Mag. Brng. Eddy 

Lorentz Eddy 

Lorentz Optical 

Mag. Brng. Eddy 

Four designs specifically for microgravity isolation have been published. Honeywell [3J has a well developed system called FEAMIS with which they have demonstrated impressive isolation performance. The 

system is designed for the Space Shuttle experiment configuration. The University College of North Wales 

[4] also has a well developed system designed for the European Space Agency experiment configuration. 

NASA [5J and SatCon [6J both have laboratory levitation systems. 

Two levitation designs were developed for different applications, but they are mentioned here because 

they are similar and could be easily adapted to the isolation application. IBM [7J has a laboratory levitated 

robot "wrist" which enhances robot accuracy and performance. Toshiba [8J has a satellite antenna pointing 

system which is fully developed. Both devices have demonstrated positional accuracies on the order of 1 Jim. 

Isolation of vibrations with large amplitudes - typically occurring at low frequencies - requires a 

large translational range. SatCon's system has the largest range, but there is a significant tradeoff with the 

device's force capability. A coarse-fine approach would allow both a large range, provided by the coarse 

stage, and a high force capability, since the levitation gaps are small. There is no available data on the 

rotational range requirements of the application. Isolation with an umbilical disturbance requires a high 

force capability as is offered by the systems from Honeywell, NASA, IBM, and Toshiba. Space and weight 

should be minimized in any spacecraft. Sateon, IBM, and Toshiba's systems offfer advantages in envelope 

space and weight. 

The choice of the actuator technology between Lorentz force and magnetic bearings has no definitive 

advantage. Lorentz actuators offer linearity, simplicity, and compactness. Magnetic bearings offer higher 

force capability and lower power consumption, particularly if gaps are minimized. 

Four position sensor technologies offer promising performance. Eddy current position probes are simple 

and robust, but bulky and heavy for large gaps. Capacitive sensors are simple and light weight, but can 

be noisy in unconstrained environments. Optical lateral effect photo-diodes are compact and quiet, but 

they require substantial supporting electronics. Hall effect flux sensors can be used with magnetic bearing 

designs both to linearize the control problem, and to measure position. 

3 Design 

The magnetic bearing proposed has two parts: a stator which is a.tta.ched to the spacecraft, and a surrounding "flotor" to which the experiment is attached. 

212 
The stator is illustrated in Figure 2. It has twelve pole pieces and coils arranged around the surface 

of a cube. The cube and pole pieces are ferromagnetic. Each pair of pole pieces and the region of the 

cube to which they are attached comprise a typical "horseshoe" electromagnet causing an attractive force 

toward the nearby flotor. Magnetic flux through the center of the cube will cause an imbalance in the flux 

levels of a pair of pole pieces, resulting in a net torque on the flotor. Differential Hall effect sensors will be 

located in the cube side of each pole piece to measure the local flux. AU electrical connections will be to 

the stator. 

Figure 2: Stator and Typical Coil 

The flotor is illustrated in Figure 3. Three ferromagnetic bands are rigidly attached to each other, but 

form independent flux paths. The bands are thicker in the region near the pole pieces to avoid saturation. 

Flux which passes through the center of the cube is returned through the remaining portion of the bands. 

Four mounting posts will attach to corners of the cube, and pass through clearances in the flotor. These 

posts could carry cooling fluid to be circulated through the stator if it is required. 

Design equations relating force and moments to the coil currents will be derived below referring to 

Figure 4. The figure shows a schematic slice through the stator and flotor with appropriate nomenclature 

and sign convention information. It should be noted that a complete model comprises three such systems, 

but they are identical and orthogonal, so only one will be analyzed. 

The relationship between coil currents (il •... , i 4 ) and the force and moment generated in one slice 

of the stator (Fy, Mz ) can be derived from Maxwell's Equations. The first Maxwell equation (1), which 

relates magnetic field intensity (H) around a closed path to the electric current density (J) through that 

path, is discretized and applied to closed loops drawn through the slice. N is the number of turns in each 

coil, and Gi are the air gap lengths which are dependent on the stator's position relative to the flotor. 

The iron flux paths are ignored because their reluctance is low relative to that of the air gaps. Many such 

equations can be written (2), but only three are independent. 

(1) 

213 
Figure 3: Flotor 

HtGt - H2G2 N (it - i 2 ) 

-H3G3 + H4 G4 N (-i3 + i4 ) 

-HtGt - H4 G4 N(-it -i4) (2) 

-H2G2 - H3G3 N(-i2- i 3) 

The second Maxwell equation (3), which ensures conservation of ma.gnetic induction (B), is used to 

obtain a fourth independent equation (4). 

~ ·B = 0 (3) 

(4) 

We can assume linear magnetization in the air gaps (5), where flo is the permeability of free space, to 

obtain a relation between magnetic induction in the gaps and coil currents (6). 

214 
Figure 4: Schematic Cross Section of Magnetic Bearing 

i = 1, ... ,4 (5) 

{ 

Bl 

Bz 

B3 } - G1GZG3 + G1GZG4 

N~ + G1G3G4 + GZG3G4 

B4 

(6) 

GZG3 + GZG4 -G3G4 GZG4 GZG3 +G3G4 

-G3G4 

G1G3 + G1G4 G1G4 G1G3 +G3G4 

GZG4 G1G4 

G1GZ + G1G4 -G1GZ +GZG4 Pl 

GZG3 G1G3 -G1GZ 

G1GZ + G1G3 

+G2G3 

The four gaps are geometrically related to the offset of the sta.tor with respect to the fiotor by the 

relations (7) which assume small angles. 

G1 = Go - y - s() 

Gz = Go - y + s() 

G3 = Go + y - s() 

G4 = Go + y + s() 

Go is the air ga.p length with the stator centered in the fiotor. 

( 7) 

215 
The magnetic energy stored in the magnetic bearing (wm ) is found from (8) where Ag is the area of 

the pole faces. 

~JooB.JjdV 

~:o (B~Gt + B~G2 + B5G3 + B~G4) 

The force and moment on the stator are found from the relations (9) and (10). 

F: _ oWm 

y - oy 

AI = oWm 

zoO 

(8) 

(9) 

(10) 

After considerable algebraic manipulation, and introduction (without loss of generality) of the linear 

current transformations (11) we obtain the force and moment relations sought (12) and (13). 

)1 = i1 + i2 + i3 + i4 

h = il - i2 + i3 - i4 

13 = it - i2 - i3 + i4 

M _ AgN2SllO (GOj2 + Osjt + y13) (G6jt + GoOsh + Osy13 - y2jd 

z - 4Go (G6 _ 02s2 _ y2)2 

(11) 

(12) 

(13) 

The current j2 is analogous to the bias current in a conventional bidirectional thrust bearing and 

could be fixed at a constant value - nominally half of the maximum current. The force generated is 

predominantly driven by 13 and the moment by it. The system is unstable (negative stiffness) in both 

translation and rotation. The currents it, ... , i4 can be found by a pseudo-inverse technique from jt, h, 13. 

Closed form analytic inverses to (12) and (13) have been found for a known position. 

4 Predicted Performance 

The equations of the previous section were used to predict the performance of a specific design. The design 

has a center cube of 2 in. on a side, pole faces of 1 x .5 in., and pole length of 2 in. Maximum current 

is determined by allowing a coil current density of .5000 amp/in2 which is known to be conservative from 

previous designs. The gap in the centered position was chosen to be .125 in. plus an allowance of .030 in. 

for inclusion of flux sensors and a protective layer on the inside of the bands. The resulting specifications 

for the design are presented in Table 2. The .53 N force is a continuous worst case, with the stator moved 

away from the flotor in the direction of the force. The continuous force capability in the centered position 

is 175 N. Intermittent force capability is limited only by the current capability of the amplifiers, and the 

saturation limit of the magnetic material used. Using Vanadium Permadur with this design, saturation 

would occur at about 1000 N. Of the 4 .. 5 kg weight, the flotor comprises only 1.2 kg. 

216 
Trans. Envelope 

±3.2 mm 15x15x15 em 

Table 2: SpE'cification of UVA Design 

When compared with the designs presented in Table 1, the UVA design has several advantages. The 

envelope is substantially smaller than any of the previous designs, while the performance is similar. In 

addition to saving space, this compactness allows the flotor to be naturally rigid, and thus avoids control 

problems with structural dynamics. The design is quite dense in comparison with the others, but it is 

lighter than the lightest for which data were available. 

5 Control 

A regulator has been designed to reject the disturbances caused by tht:' umbilical connection to the experiment. A schematic is shown in Figure .5. Nonlinearities in the magnetic bearing are eliminated by using 

flux feedback in a minor loop [3]. Six acceleromE'ters mounted on the flotor produce a generalized acceleration signal which is fed back through a linear controller. More details on the controller are available in [9]. 

The desired control force is processed through an inverse magnetic circuit model to obtain a desired flux 

signal. This model could be either a digital algE'braic model, or an appropriately trained neural network. 

Magnetic Bearing 

Trans- i 1 B Magnetic 1 F Plant 

~ I I Perrneance Coils ~r-+ Circuits Dynamics Amplifiers 1 1 

1 1 ~ Umbilical 

X 

1 _____ - ______ 1 Disturban ce 

Aux Hall X (X-D) 

- Control I+- Sensors I+- Noise 

(PO) 

Noise -+ Accelerometers Relative B.! Inverse Fd Linear Position Mag. i+- Clct. .......... Controller Sensors Model (H2) 

Noise 

Figure 5: Control Schematic 

A relative position sensor has not been chosE'n but the optical scheme used in IBM's design is a strong 

candidate. Alternatively, the current and flux signals could be processed to infer position [10]. The purpose 

of the relative position signal is only to prev('nt collision with the walls, so accuracy demands are relatively 

low. 

217 
6 Conclusion 

A design for a novel magnetic bearing, proposed as the fine stage of a coarse-fine actuator for microgravity 

vibration isolation, has been presented. The bearing is novel in that it uses a geometry that has just 

three independent flux path systems. This contrasts the twelve flux path systems (six bidirectional thrust 

bearings) used in conventional designs. The novel design results in compactness, light weight and high performance, when compared with the published designs. A control system is proposed to reject disturbances 

caused by an umbilical connection to the experiment. 

Future work will focus on building a laboratory version of the bearing and control system. 

References 

[IJ A. Peter Allan and Carl R. Knospe. A six degree-of-freedom actuator design for microgravity vibration isolation. In International Workshop on Vibration Isolation Technology for Microgravity Science 

Applications, Cleveland, Ohio, April 23-25, 1991. NASA Lewis Research Center. 

[2J D. Stewart. A platform with six degrees of freedom. Proceedings of the Institute of Mechanical 

Engineers, 180( 1 ):371-386, 1965. 

[3] Terry S. Allen, Douglas D. Havenhill, and Kevin D. Kral. FEAMTS: A magnetically suspended isolation system for space-based materials processing. In Annual AAS Guidance and Control Conference, 

Keystone, Colorado, February 1-5, 1986. Rocky Mountain Section, American Astronautical Society. 

[4J D. 1. Jones, A. R. Owens, and R. G. Owen. A microgravity isolation mount. Acta Astronautica, 

15(6/7):441-448,1987. 

[5J Carlos M. Grodsinsky. Development and approach to low-frequency microgravity isolation systems. 

Technical Paper 2984, NASA, August 1990. 

[6J Ralph Fenn and Bruce Johnson. A six degre(' of freedom Lorentz force vibration isolator with nonlinear 

controller. In International W07'kshop on Fibration Isolation Tf'chn%gy for Microgravity Science 

Applications, Cleveland, Ohio, April 23-25, 1991. NASA Lewis R('search Center. 

[7J Ralph L. Hollis, S. E. Salcudean, and A. Peter Allan. A six degree-of-freedom magnetically levitated 

variable compliance fine-motion wrist: Design, modeling and control. IEEE Transactions on Robotics 

and Automation, 7(3):320-332,1991. 

[8J Kenichi Takahara, Tamane Ozawa, Hiroshi Takahashi, Shitta Shingu, Toshiro Ohashi, and Hitoshi 

Sugiura. Development of a magnetically suspended, tetrahedron-shaped antenna pointing system. 

In 22nd Aerospace Mechanisms Symposium, Hampton, VA, May 4-6, 1988. NASA Langley Research 

Center. 

[9J R. D. Hampton and Carl R. Knospe. Extended H2 synthesis for multiple-degree-of-freedom controllers. 

In International Symposium on Magnetic Sw:pen8ion Technology, Hampton, VA, August 19-23, 1991. 

NASA Langley Research Center. 

[10J D. Zlatnik and A. Traxler. Cost-effective impl('mentation of active magnetic bearings. In 2nd International Symposium on Magnetic Bearing8, Tokyo, Japan, July 12-14, 1990. Institute of Industrial 

Science, University of Tokyo. 

218 
· . 

N92-27733 

A SIX OEGREE-OF-FREEDOM LORENTZ FORCE VIBRATION ISOLATOR 

WITH NONLINEAR CONTROLLER 

INTERNATIONAL SYMPOSIUM ON 

MAGNETIC SUSPENSION TECHNOLOGY 

NASA LANGLEY RESEARCH CENTER 

August 19-23, 1991 

Ralph C. Fenn 

SatCon Technology Corporation 

12 Emily Street 

Cambridge, MA 02139 

(617) 661-0540 

The other major contributors to this project were Michael Gerver, physicist, and Bruce 

Johnson, Dynamic Systems and Controls Division Leader at SatCon. The project was sponsored 

by NASA Marshall Space Flight Center. 

219 
This paper presents the results of a Phase II Small Business Innovation Research program 

sponsored by NASA Marshall Space Flight Center. Technology is developed for isolating 

acceleration sensitive "microgravity" experiments from structural vibrations of a spacecraft, such as 

Space Station. Two hardware articles were constructed, a six degree of freedom Lorentz force 

isolator, and a one degree of freedom low acceleration testbed capable of tests at typical 

experiment accelerations. 

PRESENTATION OVERVIEW 

o Microgravity experiment isolation requirements 

o Six degree of freedom suspension specifications 

o SatCon six degree of freedom Lorentz force isolator 

Prototype space based system 

- Design 

- Hardware 

- Test results 

o SatCon single degree of freedom testbed 

Low acceleration precision test facility 

- Design 

- Hardware 

- Test results 

o Nonlinear control 

Simulations 

Test results 

PRECEDING PAGE BLANK NOT FILM!:D 221 
The need for isolation of microgravity experiments has been established recently based on 

Spacelab measurements and modeling of experiment requirements. Low frequency accelerations, 

caused by air drag and gravity gradients, small and fall below experiment acceleration limits. High 

frequency vibrations, caused by rotating machinery, require isolation, but simple mechanical 

isolators are adequate. The difficult vibrations at moderate frequencies, caused by crew motion, 

require a combination of large stroke and relatively low crossover frequency that is best provided 

by active suspensions. Isolation above approximately 0.04 Hz is required. 

222 

EXPERIMENT REQUIREMENTS VS THE ENVIRONMENT 

-2 Spoc.lab & Meosurements 01 0 

-4 

General laboratory Space 

-6 Volume in U.S, Lob Module 

Rotating 

Crew Motion Machinery '- ,. II 

-5 -4 -3 -2 -1 o 2 

Log Frequency (Hz) 

J 

CHARACTERISTIC 

FREQUENCY RANGES 

o LOW FREQUENCIES 

DON'T REQUIRE 

ISOLATION 

o HIGH FREQUENCIES (10-

100Hz) REQUIRE 

ISOLATION BUT EASY 

MECHANICAL 

SUSPENSIONS 

o MIDDLE FREQUENCIES 

(0.04-10Hz) HARDEST; 

CREW MOTION 

- LOW CROSSOVER 

- LARGE STROKE 

o INTERSECTION OF 

ENVIRONMENT AND 

REQUIREMENT PLOTS AT 

.04 Hz 
The precious plot shows the acceleration environment and limits. Given the 0.04 Hz 

maximum base following bandwidth from the previous plot, the required suspension stroke can be 

determined. This figure shows that a peak-to-peak actuator displacement of 2 cm is required for 

desired isolation. 

VIBRATION AMPLITUDE MEASUREMENTS AND LIMITS 

0 SOLID LINE IS THE 2 

General Lab. Acceleration Limits VIBRATION POSITION 

:§: Attitude + / AMPLITUDE LIMIT 

5 0 Control 

~ g- O ±1 em STROKE IS is -2 + Crew Soorino 

g REQUIRED FOR a. 

I ISOLATION DOWN TO -" g 

a. -4 a 00 Spocelob 0.04 Hz 

§ o 00 00 

0 0 0 

a 0 

-6 o 0 

-5 -4 -J -2 -1 0 2 

Log Frequency (HZ) 

223 
Both attractive and Lorentz force actuators were considered for this application. Because 

of the large stroke requirement, the typical mass penalty of Lorentz force actuators did not exist. 

Many other advantages of Lorentz force actuation are beneficial in this application as listed below. 

224 

THE ADVANTAGES OF LORENTZ FORCE ACTUATORS 

(FORCE ex CURRENT TIMES FLUX DENSITY) 

o OPEN-LOOP STABILITY (FACILITATES NON-LINEAR CONTROLLERS) 

o INHERENT ZERO GRAVITY ISOLATION AT ZERO CURRENT 

o CAN ISOLATE TO LOWER FREQUENCIES THAN FERRO-ATTRACTIVE ACTUATORS 

o MECHANICAL SIMPLICITY FACILITATING SIX DOF DESIGNS 

o EASY INTEGRATION WITH STANDARD ELECTRONICS 

o EQUIVALENT MASS PER UNIT FORCE WITH ATTRACTIVE ACTUATORS DUE TO 

LARGE STROKE 

o SATURATION DOES NOT LIMIT FORCE LIKE ATTRACTIVE ACTUATORS 
The previous figures showed how the stroke, base following bandwidth, actuator bandwidth 

and force requirements were formulated, as summarized here. 

ISOLATOR FUNCTIONAL REQUIREMENTS 

o STROKE (X, Y, AND Z) 

o MAXIMUM BASE-FOLLOWING FREQUENCY 

(MAXIMIZE "FREE FLYING") 

o MINIMUM ACTUATOR BANDWIDTH 

(COUNTERBALANCE DIRECT FORCES) 

o FORCE FOR 500 KG EXPERIMENT 

±1 em 

4 X 10-2 Hz 

1 N 

225 
A prototype six degree of freedom (DOF) isolator was constructed that had the 

characteristics listed below. The width and depth were scaled approximately to typical orbiter 

locker size. Weight was reduced to some degree by aluminum construction, but further reductions 

are possible. The prototype force capability was sized for very large 500 kg experiments. This 

capacity could be reduced, giving a substantial mass savings. 

226 

SIX DOF ISOLATOR DESIGN 

FORCE 

DIMENSIONS: 

STROKE 

WIDTH AND DEPTH 

HEIGHT AT CENTER 

WEIGHT: 

SUSPENDED PLATFORM 

BASE STRUCTURE 

TOTAL 

ISOLATOR POWER: 

1 N Z AXIS 

1 N X OR Y AXIS 

(EXPER CG 15 CM UP) 

OPEN·LOOP ACTUATOR BW: 

4 N (EXCEEDS REQUIREMENTS) 

±1 CM 

45 CM 

8CM 

5.0 KG 

4.5 KG 

9.5 KG 

1W 

4W 

> 100 HZ 
The prototype suspension shown below has four actuators, supplying eight forces, and eight 

position sensors. Each of the four isolator sides is identical, which provides symmetry and reduces 

controller complexity. Four Lorentz force actuators in the center of each side produce vertical and 

tangential forces. Two mounting plates are provided, one for the experiment on top, and the 

second for Space Station attachment below. Eddy current position sensors measure the vertical and 

tangential position at each corner. 

SATCON SIX OOF MAGNETIC SUSPENSION 

VERTICAL POSITION SENSOR II OF .1 

SENSOR TARGET DISK 

TANGENTIAL 

POSITION 

SENSOR 

II OF .1 

227 
The actuator shown below has two permanent magnets that produce flux in the central air 

gap, where the coils cross. The flux returns through the four posts at the corners of the mounting 

plates. ilL" shaped coil mounts comprised of separate horizontal and vertical coils are laced through 

the gap. The return current returns outside the gap. The force constant is 1 Newton per ampere 

and the coil resistance is 9 ohms. Force capacity depends entirely on the duty cycle because the 

actuators are heat limited. 

228 

ONE OF THE SIX DOF ISOLATOR ACTUATORS 

MOUNTING 

PLATE 

MAGNETIC 

FLUX 

PERMANENT 

MAGNET 

COIL SUPPORT 

CURRENT 

PATH 

11 OF 2) LORENTZ 

FORCE 
This top view of the isolator shows the upper mounting plate surrounded by the position 

sensors and circular targets, and the actuators on the center of each side. 

THE COMPLETED SIX-DOF ISOLATOR 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

229 
A photograph of one of the actuators is shown below. The crossing point of the coils IS 

visible in the center of the gap, between the permanent magnets. One of the aluminum foil eddy 

current sensor targets is also shown. 

AN ACTUATOR INSTALLED ON THE SIX-DOF ISOLATOR 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

230 
These plots show experimental data for initial condition responses of roll of the suspended 

platform. A long, soft spring was used to unload the gravity force and give a nominally centered 

coil position within the gap. The top two plots are concurrent traces of the x axis and y axis roll 

motions (cf> and tIr). The second plot shows that the roll axes are decoupled by the controller. Good 

damping characteristics are also exhibited. 

INITIAL CONDITION RESPONSE OF ROTATIONAL AXES 

(a) phi 

rad Lin 188~iv 

~~!:II-[!--lii-i~II'~-I;111 -398.44" -- .seconds -- 597.66" phi ang/ 

(b) psi 

rad Lin tHen/Div 

~~:li:l~i!-:~--i~I--!~l_;I-11 -398 44" -- seconds -- 597.66" . psi angl 

231 
The second article of hardware constructed is a one degree of freedom testbed to simulate 

on orbit accelerations and test controllers. The figure below shows an integrated Lorentz force 

motor / air slide on the left, which produces expected Space Station accelerations. On the right 

is another air slide supported by two air boxes, which simulates the floating experiment mass. The 

relative position of the "experiment" stage and the "Space Station" stage is controlled to maximize 

isolation in one DOF while preventing "bottoming out" of the central isolation actuator. This 

apparatus is useful for testing nonlinear controllers and determining the effect of signal noise levels 

throughout the control system. 

232 

ONE DEGREE OF FREEDOM TESTBED 

"SPACE STATION" STAGE 

ACCELEROMETER 

AIR SLIDE BOX 

INPUT ACTUATOR 

COIL 

EDDY CURRENT POSITION SENSOR 

"EXPERIMENT" STAGE 

f-------------140cm ---------------t 

PRECISION LOW ACCELERATION TEST FACILITY MICROGRAVITY LEVEL 

ACCELERATIONS 

] 
The single digit microgravity background accelerations were produced using noncontacting 

actuators, sensors and mechanical suspensions where possible. The only connection to the sensitive 

Space Station stage are several thirty four gage wires carrying the accelerometer power and signals. 

ONE DOF TESTBED 

o INPUT STAGE SIMULATES SPACE STATION VIBRATIONS. 

o EXPERIMENT STAGE IS ISOLATED BY LINEAR ACTUATOR IN CENTER. 

o EACH STAGE HAS POSITION AND ACCELERATION FEEDBACK. 

o SIMULATE TYPICAL SPACE ACCELERATIONS AND SIGNAL LEVELS: 

IMP. FOR NONLINEAR CONTROL TESTS, SENSOR AND ACTUATOR TESTS. 

o NONCONTACTING HARDWARE: 

- AIR SLIDES: ACCURATE SPACE STATION ACCELERATION REPLICATION 

W/O STICTION AND SENSITIVE ISOLATION EVALUATION 

- NONCONTACTING POSITION SENSORS 

- NONCONTACTING INPUT MOTOR AND ISOLATION ACTUATOR 

- AIR LINES ON NONMOVING PART 

- ONLY ACCELEROMETER LEADS CONNECT TO EXPERIMENT 

o VERY STIFF STRUCTURE 

233 
This figure shows the one DOF testbed mounted on the granite surface plate. The 

accelerometers mounted on top of each stage are visible. One of the two 0.12 J..I.ffi resolution 

differential micrometers is shown on the right. 

ONE DOF TESTBED 

ORIGINAL PAGE 

BLACK AND WHITE OGRAP~ 

234 
The integrated Lorentz force motor / air slide is shown below. An eight inch long 

permanent magnet lies on each side of the central air slide. Flux crosses the gap and returns 

through the airslide and backiron holding the magnets. A coil passes through the gap and encircles 

the air slide. The Lorentz force on the coil, which is mounted on the air slide, creates the desired 

Space Station accelerations. 

LORENTZ FORCE INPUT MOTOR AND INSTRUMENTATION 

235 
The figures below show experimental data from the one DOF testbed with the desired 0.04 

Hz crossover linear controller. The step response shows the desired low friction characteristics that 

facilitate controller testing using expected on orbit parameters. The frequency response of the 

system on the lower plot shows crossover to be somewhat higher than the design value of 0.04 Hz. 

This may be due to unmodeled viscous damping in the air slide. 

STEP RESPONSE OF THE 0.04 Hz BANDWIDTH POSITION CONTROL 

TRANSFER FUNCTION OF 0.04 Hz BANDWIDTH POSITION CONTROL 

Uolts/uolt / Log 

u:~::IIIDlI~I~I~~1 1011 -- Hertz -- 5 DSP ExAcclDSP HrAcc 

236 
Nonlinear controllers offer many advantages over linear designs. In this application no 

weight is given to the location of the coil in the gap, as long as the coil does not hit the stops. An 

ideal controller would not apply forces to the suspended platform carrying the experiment unless 

the suspension was likely to bottom out. This actuator nonlinearity suggests a nonlinear controller 

that has a gain that is position dependent. When the suspension is centered, the controller should 

"turn off' and not apply undesirable forces. The gain should increase when infrequent 

environmental accelerations are very large so that the experiment must be forced to follow the 

spacecraft. Such a controller can allow an experiment to free fly at all frequencies, given limits to 

the position amplitude of the vibrations. 

NONLINEAR CONTROLLER ADVANTAGES 

o ALL ACTUATORS HAVE SATURATION NONLINEARITY 

o A LINEAR CONTROLLER APPLIES EXCESSIVE FORCES 

o A NONLINEAR CONTROLLER CAN FREE FLY AT ALL FREQUENCIES (AT SMALL 

AMPLITUDES) 

o THE SUSPENSION COULD BE STIFFENED BY GAIN SCHEDULING ANTICIPATING 

LARGE BASE MOTIONS 

o ADVANCED CONTROLLERS COULD MINIMIZE A COST FUNCTION OF STROKE 

AND FORCE USING A STOCHASTIC MODEL OF EXPERIMENT SENSITIVITY AND 

THE ENVIRONMENT 

237 
This figure showing D3 mission data illustrates the advantage of a variable gain controller. 

The vast majority of time has quiescent acceleration levels that are orders of magnitude lower than 

the peak values. These typical low levels are shown at the left of the plots here. During the great 

majority of the time that the experiments run, there are no large accelerations requiring isolator 

action. However, if a linear suspension controller is used, every small but finite motion will 

produce a proportional and unwanted experiment acceleration. These low level but frequent 

controller induced accelerations may cause the majority of experiment damage, rather than the 

much more infrequent large accelerations. 

238 

LARGE VIBRATION DYNAMIC RANGE BUT LOW 

AVERAGE VALUE 

10 mg.----------------------. 

-10 mg~--------------------~ 10 mg 

IIPT Y f--~ ...... ~tlI!n.:fll\'f 

- 1 0 mg f-----------;-rn.-----:c---nr;r.r 10 mg 

-10 mg '----------""-
A controller having the desired "dead zone" characteristic without limit cycling behavior is 

the cubic error controller shown below. The only alteration to a linear position controller is the 

addition of one operation that cubes the position error before it enters the linear compensator. 

This cube operation approximates a dead zone but is smoother. 

CONTROL SYSTEM EXAMPLE WITH CUBIC 

NONLINEARITY 

NONLINEAR 

GAP 

COMPENSATOR 

GAP TARGET 

(TYPICALLY =0) 

INERTIAL 

ACCELERA nON 

TARGET (=0) 

COIL GAP 

POSITION 

LINEAR GAP 

COMPENSATOR 

+ 

+ 

MAGNETIC 

ACTUATOR 

8-: E 

ACTUATOR ACTUATOR 

CURRENT FORCE 

UMBILICAL 

AND 

INTERNAL 

FORCES 

SPACE STATION 

INERTIAL MOTION 

ISOLATED 

MASS 

INERTIAL 

POSITION 

ISOLA TED MASS 

INERITAL 

ACCLERA TION 

239 
The block diagram on the previous page shows how both position control and acceleration 

control are used to isolate base vibrations and reject direct forces. The actuator gap position 

control has a very low bandwidth of 0.04, as developed in the first viewgraphs from environmental 

accelerations and experiment requirements. The acceleration loop should have a bandwidth of 100 

Hz to counterbalance the major directly applied forces. The one degree of freedom testbed has 

position and acceleration control while the six DOF isolator as constructed has only position 

feedback, but could be easily modified to add acceleration control. Describing function analysis can 

be used to model the cubic nonlinearity as 3/4 (amplitudef This shows explicitly that the loop 

gain is reduced dramatically for small excursions. The gain during one DOF cubic controller tests 

was chosen to provide just slightly more force at maximum stroke than the linear design. 

240 

A CUBIC GAP ERROR NONLINEAR CONTROLLER 

o GAP LOOP IS LOW PASS (0.04 HZ) BASE FOLLOWING. 

o ACCELERATION LOOP IS BANDPASS REGULATOR 

(TARGET = 0) REJECTS DIRECT FORCES. 

o THE NONLINEAR CONTROLLER REDUCES UNNEEDED FORCES DURING LOW 

AMPLITUDE MOTIONS. 

o THE NONLINEAR GAIN GIVES THE SAME LOOP GAIN AT MAXIMUM DISTUBBANCE 

AMPLITUDE (AND THE SAME BANDWIDTH). 

o THE DESCRIBING FUNCTION ALLOWS LINEAR ANALYSIS WHEN THE INPUT 

FUNDAMENTAL PREDOMINATES. 

o THE DESCRIBING FUNCTION OF (A*SIN(WT))3IS 3/4 A2. 

o THE GAP LOOP GAIN BECOMES PROPORTIONAL TO THE ERROR2. 

o A STOCHASTIC DESCRIBING FUNCTION FOR (RANDOM)3 IS 3*0-2

. USE FOR GAIN 

SELECTION FOR STOCHASTIC NONLINEAR CONTROLLER. 
The force for small fractions of the maximum displacement is greatly reduced by the 

nonlinear controller. For the gains shown here, the ability of the two controller designs to 

absorb large accelerations is nearly identical. The nonlinear controller applies larger forces at 

large, but infrequent, disturbances than the linear design. In this way, the lack of action at small 

displacements is compensated for. 

CUBIC ERROR CONTROLLER FORCE vs DISPLACEMENT 

~ a 

~ 0 

Z 

~ 

U.l 

U 

co: 

[t 

0.5 

0 

-0.5 

-1 

CUBIC ERROR CONTROLLER FORCE vs DISPLACEMENT 

" 

,,/// 

NONLINEAR CONTROLLER 

Gain = 1.5 • error"2 • K 

,

,/ LINEAR CONTROLLER 

Gain =K 

-1.5 L: _-'-_...L-_'--.........J._--'-_--'-_-'--_..L..----...JL..----....J 

-1 -0.8 -0.6 -0.4 -0.2 o 0.2 0.4 0.6 0.8 

DISPLACEMENT (em) 

NO FORCE IS APPLIED FOR SMALL DISPLACEMENTS 

241 
The continuous plots here show the predicted linear response and the predicted nonlinear 

response using describing functions. Nonlinear simulation data points are also plotted. It shows 

that the describing function discussed above approximates very closely the nonlinear response of 

the system. The plot shows the desirable behavior of reduced base following bandwidth for small 

position disturbances. Low bandwidth gives better isolation and less experiment damage. 

~ 'c 

0' 

0 

'" 0' 

.3 

242 

10- 4 

10-0 

CONTROL SYSTEM EXAMPLE WITH NONLINEAR 

SIMULATION DATA 

_ Linear Design - 0.04 Hz BW 

____ Predicted Nonlinear - 0.1 em Amp. 

o Nonlinear Simulations - 0.1 em Amp. 

1) 

2) 

3) 

4) 

COMPARES EXPERIMENT 

ACCELERATIONS FOR 

10% FULL-SCALE BASE 

MOTION 

CUBIC NONLINEARITY IS 

AN ADJUSTABLE GAIN -

DOWN BY A FACTOR OF 

90 

ISOLATION FREQUENCY 

REDUCED BY A FACTOR 

OF 17 

10-3 10-2 10-' 100 10' 

NONLINEAR 

CONTROLLER 

PRODUCES LOWER 

EXPERIMENT 

ACCELERATIONS IF 

BASE RMS VIBRATION IS 

MUCH SMALLER TUAN 

PEAK VALUES 

Log Frequency (radians/sec) 
This time plot shows how the nonlinear controller essentially "turns off' when the coils are 

within 15% of the centered position. Because this application has no penalty for small steady state 

position errors, this behavior is preferable because of the lower forces applied to the experiment 

by the controller. 

CUBIC ERROR AND LINEAR INITIAL CONDITION RESPONSES 

0.9 

O.B 

0.7 

E 

~ 0.6 

e .., 

E 0.5 8 

c 

a. 0.4 a 

15 

) 0.3 

0.2 

0.1 

0 

0 10 20 30 40 50 60 70 

Time (seconds) 

MEASURED DATA FROM SINGLE-DEGREE-OF-FREEDOM TESTBED 

243 
The paper shows that microgravity isolation will be required on Space Station, and that 

current technology can satisfy this need. Lorentz force actuation with nonlinear controls is a good 

match to the requirements of this application. 

244 

SUMMARY 

o MICROGRAVITY ISOLATORS ARE REQUIRED. 

o 0.04 HZ ISOLATION AND ±1 CM STROKE ARE REQUIRED. 

o BOTH BASE ISOLATION AND DIRECT FORCE REJECTION ARE DESIRABLIE. 

o LORENTZ FORCE ACTUATORS ARE WELL SUITED FOR THIS APPLICATION. 

o A NEW TWO DEGREE OF FREEDOM ACTUATOR WAS DESIGNED. 

o A SIX DEGREE OF FREEDOM SUSPENSION WAS DESIGNED, CONSTRUCTED AND 

TESTED. 

o NONLINEAR POSITION CONTROLLERS CAN REDUCE EXPERIMENT 

ACCELERATIONS. 

o A ONE DOF MICROGRAVITY ACCELERATION TESTBED WAS BUILT. 

INVESTIGATE ACCELERATION DISTURBANCES PRODUCED BY 

CONNECTIONS TO THE EXPERIMENT: 

- POWER 

- SIGNAL 

- COOLING 
Session 5 

SUPERCONDUCTIVITY 1 . 

Chairman - Jim Downer 

SatCon Technology Corporation 

24S 
N92-27734 

Recent Progress Towards Developing a High Field, High-Tc 

Superconducting Magnet for Magnetic Suspension 

and Balance Systems. 

L. Pierre de Rochemont, Carlton E. Oakes, Michael R. Squillante 

Radiation Monitoring Devices, Inc. 

44 Hunt Street 

Watertown, MA 02172 

Hong.Min Duan, Allen M. Hermann 

Center for Applied Superconductivity 

University of Colorado, Boulder 

Boulder, CO 80303 

Robert J. Andrews 

Rome Laboratory 

Solid State Sciences Directorate 

Hanscom AFB, MA 01731 

Roger B. Poeppel 

Materials and Components Technology Division 

Argonne National Laboratory 

9700 South Cass Avenue 

Argonne, IL 60439·4838 

Victor A. Maroni 

Chemical Technology Division 

Argonne National Laboratory 

9700 South Cass Avenue 

Argonne, IL 60439·4838 

Ingrid A. Carlberg and Warren C. Kelliher 

Engineering Laboratory 

NASA Langley Research Center 

Hampton, VA 23665·5225 

PRECEDING PAGE BLANK NOT FII..M!:D 

247 
I. INTRODUCTION. 

The initial discovery of the high-Tc superconducting ceramics in 1986 [BednolZ and Milller], 

rapidly followed by the subsequent development of compositional families which exhibited zero 

resistance transition temperatures at 90 K [Wu], 125 K [Hennall1l], and recently as high as 132 K 

[Hongbao et al., ChalldracllOod et al.], heralded predictions for major breakthroughs in mankind's 

technical mastery of the universe. Images of high-speed magnetically levitated trains racing across 

the continent or inexpensive electricity transported thousands of miles over resistanceless power 

lines littered the pseudo scientific literature to popularize these new observations. As had been 

the case when the first type-I low-Tc superconductors were identified in 1911 [Onnes], a more 

thorough investigation of the intrinsic properties of these materials fostered sobering attitudes 

within the technical and engineering communities as practical limitations to the application of this 

technology were identified. 

In the 50 years succeeding the discovery of superconductivity, the physical foundations upon 

which an understanding of the onset and preservation of the resistanceless conductive state were 

constructed. This arduous research path led to the commercialization of superconductors for 

applications as diverse as low field magnetometry, high field magnetism, and charged particle 

acceleration throughout the 1960's, -70's, and -80's. Although superconductors remain a modest 

industry by global business standards, their reliability and unique performance capabilities in 

medical and extremely high-cost experimental physics apparatus has demonstrated feasibility for 

their integration into complex systems where down time spells disaster. 

There is a clear need for the development of the high-T c superconductors. Relieving the 

constraint of systems operation at liquid helium cryogenic temperatures makes the application of 

superconducting devices more broadly possible on the basis of overall system cost and simplicity. 

At present, NASA has identified interest in applying high-Tc superconducting magnets to the 

following aerospace technology applications: vibrational isolation, high accuracy pointing, and 

magnetic suspension in wind tunnel testing. The most challenging system requirements for these 

application orientations will be found in the suspension and balance systems used in conjunction 

with cyrogenic wind tunnels. Levitation is required in this test apparatus to remove aerodynamic 

interference caused by a mechanical support under conditions of dynamic or unsteady testing. 

Superconducting magnets for this application will have to be capable of maintaining DC fields on 

the order of 6 - 8 Tesla, in addition to an overlapping large amplitude ac sinewave field at 5 Hz, 

superposed by higher frequency (50 Hz to 60 Hz) 0.1 % maximum field strength signals which are 

critical to system control. 

This paper will briefly review superconducting magnet and high-Tc superconducting oxide 

ceramic materials technology to identify areas of fundamental impasse to the fabrication of 

components and devices that tap what are believed to be the true potential of these new 

materials. Fortunately a great knowledge base on the subject of superconductivity and 

superconductive devices has already been acquired through the development of low-Tc 

superconductor components. However, the high-Tc ceramics pose problems in fundamentally 

different areas which have to be solved. We will map out an experimental plan designed to 

research process technologies which, if suitably implemented, should allow us to overcome many 

of these deficiencies. We will conclude with an assessment of where and on what regimes 

magnetic system designers should focus their attention to advance the practical development of 

systems based on these new materials. 

II. FUNDAMENTAL CONSIDERATIONS TO THE DESIGN OF SUPERCONDUCTING MAGNETS. 

The superconductive state is a thermodynamic phase of material systems susceptible to 

"delicate" and complex internal electronic interactions. The phase space mapped out by the 

superconducting state is defined through the following parameters of state: temperature, T, 

magnetic field, H, and current density, J. Critical values for each of these parameters mark the 

transition of the material from its superconducting phase to its normal resistive phase. The 

critical values for each of these state parameters are dependent upon the thermodynamic 

weighting of the other state variables through a system of Lagrangian constraints. That is, the 

highest critical load that can be sustained by this thermodynamic phase, be it thermal, magnetic, 

or electrical, is obtained through the application of minimal stress on the other two state variables. 

PRECEDING PA~ BLANK NOT FILMED 249 
Zero electrical resistance can be maintained at the highest temperatures in the absence of any 

applied or generated magnetic field, and through the passage of minimal current densities. The 

superconductive phase will persist under the weight of high magnetic fields at the coldest 

temperatures and with minimal current densities, and so on and so forth. While both 

temperature, T, and magnetic field, H, are fundamental thermodynamic s~ate variables defined by 

the internal dynamics and energies intrinsic to a specific materials system, critical current 

densities, Jo are far more susceptible to influences extrinsic to the material system and can 

generally be increased through improved materials processing. 

The objective in designing and constructing a high field superconducting magnet is 

essentially to run the gambit. It is necessary to construct a superconductive surface topology 

which allows the material system to sustain its thermodynamic phase through the application of 

maximal stress on at least two, and many times all three of the state parameters. Figure 1 shows a 

topological design using a tape/ribbon conductor. The tape is constructed to have a surface 

coverage of superconducting materia1. As diagrammed, the poles of the magnet will be subject to 

considerable thermodynamic stress. Maximum magnetic load will be fundamentally limited by the 

effects of strain produced in this "stress node" of the magnet. Magnetic field densities in the 

superconductor will be greatest in those regions where the radial field lines loop back down 

through the core of the magnet. A high current will induce a strong magnetic field. The ultimate 

field density in the core of the magnet is proportional to the current passing through the coil and 

defined by a shape factor which relates the surface current paths to the induced field strength. 

The generation of these fields which penetrate through the superconductor, will in turn pinch-off 

the critical current densities passing through the conductor at these stress points in the coil, and, 

as a result, start limiting the maximum field. 

H Field 

Superconducting Currents 

Figure 1. Magnetic coil based on a ribbon composite-conductor design. The high-Tc 

superconducting ceramic is either embedded as a sheet within the ribbon, or is 

applied as a surface coverage to the structure. 

It is therefore necessary for the superconductor to be magnetically hardened at the poles. 

When magnetic flux bundles, tluxoids, penetrate the superconductor they wi11 interact with the 

supercurrents through Lorentz forces. Greater fluxoid densities, wi11 activate the frequency of 

these interactions. This interaction will deflect the supercurrents from their intended path and 

exert an equal and opposite force upon the fluxoid. (See Figure 2). Fluxoids win move in 

response to this force, and if they drift through the material they will dissipate their energy into 

the superconductor. Their energy is ultimately converted to heat, which in turn applies greater 

250 
stress to this thermodynamic phase of the material. However, if the fluxoids are pinned by 

potentials greater than the interaction energy of the Lorentz forces, their movement will be 

prevented and less heat is dissipated into the system. 

(a) 

Unpinned 

Fluxoid 

Penetrating FJuxoid 

/ 

/ 

/ 

Pinning Center /I 

/ 

2e' 

(b) 

FJuxoid Pinned 

bva defect 

Figure 2. Lorentz force interaction between a penetrating fluxoid and supercurrents 

within the conductor (a). Fluxoids can be pinned within the superconductor to 

prevent heat generation by defects having physical dimensions smaller than the 

coherence lengths of the superconducting Cooper pair (b). 

The conducting surface topology given in Figure 1 is attractive in researching these new 

materials for a number of reasons. It allows the entire superconductor to be bathed completely in 

the thermal reservoir, thereby effecting more uniform control over the thermal load applied to, or 

generated within, the superconductor. If continuous ribbons of tape are used, this design reduces 

the potential need for spliced joints between segments of the coil. Spliced joints electrically connect 

superconducting segments of tape through the application of normal conductor material. They 

would certainly be needed if edge wound ribbon conductor coils are considered. When high 

currents are applied to these joints they can also generate heat sufficient to drive normal state 

transitions and quench the superconducting state along the entire coil. 

Implicit to the successful design of a high-Tc superconducting magnet is the design of the 

conductor ribbon. A composite structure to these conductors is required. (See Figure 3). First, 

the superconductor needs to be intimately contacted to a metal1ic substrate material. This metal 

must have a high thermal conductivity so heat generated within the material can be quickly 

transported out of the superconducting medium. This thermal shunt is necessary to reduce the 

occurrence of normal state transitions and to avoid generating conditions which could precipitate 

a quenched coil. Secondly, the metal enveloping the superconductor must also be an excellent 

electrical conductor. In the event the coil does quench an electrical shunt is needed to drain the 

current in the system. 

In addition to anticipating problems related to quenching the superconductor coil, the 

ribbon design must also anticipate the enormous pressures under which it is likely to be subject 

when incorporated into the design of a high field magnet. Differences in the field densities across 

a coil as it generates strong magnetic fields can exert enormous mechanical stress on the coil. 

Fields of 6 Tesla are known to exert mechanical pressures upon coils on the order of 140 atm, 

which is equivalent to pressures contained within gas cylinders. Magnetic fields approaching 

10 Tesla can generate pressures equivalent to 520 atm, which approaches the yield strength of 

annealed copper. Therefore, it is imperative that a strong mechanical superstructure be 

251 
embedded within the ribbon. This can be accomplished by having a stainless steel base. Stainless 

steel has electrical and thermal properties which are not sufficient to accommodate shunt 

characteristics required in the structure. Finally, this entire structure should be encapsulated by a 

good electrical insulator to avoid high voltage arc discharges between various windings within the 

coil, or the coil and its confinement chamber. 

Electrical Insulator 

Electrical and Thermal Shunt 

Tape Cross-Section 

Superconductor 

Stainless Steel 

Superstructure for 

Mechanical 

Reinforcement 

Figure 3. Schematic design of the superconducting ribbon to be applIed to the 

construction of a high field magnet. 

III. FUNDAMENTAL PROPERTIES OF TilE HIGH-Tc CERAMIC OXIDE SUPERCONDUCTORS. 

The challenge presented to the materials engineer trying to overcome the natural difficulties 

posed by these materials systems is formidable. The difficulties involved can be appreciated by 

examining the "compositional windows" over which high-Tc superconductivity is observed to occur 

in these ceramics. High-Tc superconductivity is now known to occur in a number of ceramic 

materials systems with the perovskite crystal structure. Current understanding of the high-Tc 

ceramic oxides has been developed upon the observation that the superconducting compositions 

in these material systems are located over a compositional domain between adjacent 

semiconducting (insulating) and metallic manifestations of these complex metal oxides [Kitazawa, 

1990]. (See Figure 4). 

1. ELECTRONIC STRUCTURE OF THE CERAMIC SUPERCONDUCTORS. 

The current focus in the scientific literature mainly emphasizes that the evolution of 

superconductivity, which is nestled in the vicinity of a semiconductor-to-metal compositional 

transition, is triggered by high-level carrier doping in a semiconductor (insulator) which has a 

nonconventional energy gap at the half-filled position of its conduction band. The energy gap 

involved in these systems has its origin in strongly correlated multi-body interactions: charge 

density waves (CDW) in the barium bismuthates (BaBi03) or electronic correlation in the case of 

the cuprates. 

The electronic properties of the superconducting cuprates are fundamentally characterized 

by a two-dimensional network of covalent Cu-O bonds which form a Cu02 square lattice in the 

a-b (basal) plane of the perovskite crystal structure. Cu-O bonding along the c-axis is believed to 

be ionic and electrical conduction is essentially two-dimensional along the a-b plane and can be 

modeled by assuming a pile of alternating ultra-thin metallic and insulating layers. (See Figure 5). 

The chemistry within the ionic layer controls the amount of charge carriers transferred into the 

superconducting sheets, which in turn, influences whether or not the superconductive phase will 

252 
form and at what temperature it occurs if it does [Cava et al., Jorgensen]. As a result, these layers 

have come to be known as "electronic doping" regions. (See Figure 5). 

Sflin Gl,!ss 

Domam 

I 

I 

tII-~ --·MilIed" Phase ---I.~----- Metallic Conductor --_ 

Hole Doping in X-V-MoO Molt Insulator 

Figure 4. Compositional dependence on the electrical phase of high-Tc superconducting 

ceramic cuprates. 

Electronic "Doping" 

Reservoirs 

''Active'' Superconducting 

Planes 

Figure s. Electronic structure of the high-Tc superconducting cuprates. 

The transfer probability from a metallic plane to the adjacent one across the intervening 

insulating layer(s) seems to be a very sensiti:ve function of the nature of the ionic layer. As a result 

of these structural features, superconducting parameters in the cup rates are highly dependent 

upon interlayer coupling, and are consequently anisotropic. A fundamental consideration to 

making these systems work in high field magnet applications will be to maintain specific 

253 
crystallographic orientations vis-a-vis the applied magnetic field and the superconducting current 

path. This requires the entire ceramic to have a "textured" quality. That is, its c-axis must be 

oriented relative to the metallic substrate surface on a macroscopic scale. 

Tc in these materials can depend sharply on composition, and the emergence of 

superconductivity is observed to be in a compositional domain located between insulating 

(semiconducting) and metallic manifestations of these material systems. The unit cell structures 

for these materials is indeed quite complex. Figure 6 shows the unit cells for 6 of the 

superconducting phases which have been identified for the Tl-Ba-Ca-Cu-O superconducting 

system. The most interesting phases have the most complex structures. The primary task goal in 

manufacturing a single phase tape will be to replicate one of these atomic structures throughout a 

surface layer 20-50 p,m thick, 1 cm wide, and 10-100 m long. 

o TI 

• Co 

o 80 

• Cu • 0 

1021 1122 1223 

2021. 

2122 

2223 

Figure 6. Six of the superconducting phases identified in the Tl-Ba-Ca-Cu-O system. 

While depositing the proper stoichiometry in the film or coating is a necessary prerequisite, 

it will not assure the formation of the desired phase. During synthesis these materials have to be 

processed over wide temperature ranges. Over different thermal regimes various phases of the 

material will have stronger tendencies to form. For instance, if the 2223 stoichiometry is 

deposited but the material is processed at temperatures which favor the formation of the lower Tc 

2021 phase, the material will phase separate into this phase and an equal stoichiometric blend of 

barium and copper oxides which can be insulating. As a general rule, it appears that the more 

interesting compositions have the narrowest synthesis windows to form phase stabilized solids and 

are the most difficult to form. Consequently, once phase separation has been initiated the 

coatings will have poor electrical properties and be of little use to fabricating a magnet. 

2. INTRINSIC MAGNETIC PROPERTIES OF TilE HIGH-Tc CERAMICS. 

The truly magnificent property of these materials is their magnetic hardness. While actual 

values for the upper critical magnetic fields for these materials is still not yet known, for many of 

the different systems they are believed to be on the order of many hundreds, if not more than a 

thousand, of Tesla for many of the different compositional families [Kang et al., Larbelestier]. 

Current impediments towards achieving an accurate appraisal for these properties has involved 

many complex issues related to defects. Defects in these materials can be both beneficial and 

detrimental to their ultimate performance. When point defects are arrayed into a structured 

lattice dramatic increases in transition temperature, upper critical field, and, most significantly, 

critical current density can be achieved. However, larger defects located in the path of the 

254 
superconducting currents can severely degrade their capacity to carry supercurrents as well as 

their performance in magnetic fields. 

3. EXTRINSIC MAGNETIC PROPERTIES OF TilE HIGH-Tc CERAMICS. 

Many of the same "tricks" used to develop high quality low-Tc superconductors, such as the 

deliberate generation of defects to serve as flux pinning centers, can be adapted to the high-Tc 

superconducting ceramics. Flux pinning centers improve critical current densities by preventing 

the free motion of penetrating fluxoids, which dissipate their kinetic energies into the system 

through Lorentz force interactions with the supercurrents. Although this approach can be 

applied to high-Tc conductors, it must be done on a significantly different physical scale. The 

coherence length (~)--(nominally defined as the maximal separation of two electrons in a Cooper 

pair, beyond which they split and revert back to normally resistive charge conductors )--is 

anisotropic in the cuprates and are orders qf magnitude shorter in the high-Tc materials. Typiq,l 

values are found to be on the order of 2-4 A for ~ parallel to the perovskite c-axis and ~= 16-30 A 

along the a-b plane. This compares unfavorably to coherence lengths of up to a couple microns 

for some of the low-Tc materials [Doss]. 

Deliberately induced defects will only serve as flux-pinning centers if they have a spatial 

extent less than the coherence length of the Cooper pair, (see Figure 2), otherwise they will 

stimulate pair transitions to the normal state. Flux pinning point defects can be generated in 

these films using high-energy particle irradiations. This treatment will form defects by slightly 

perturbing the location of an ion from its equilibrium position in the lattice. It can raise the 

critical current density in films from 10-') to 107 Ncm2 [Venturini et. ai., van Dover, et ai., 1989, 

1990]. Unfortunately, these techniques are only useful in samples exhibiting good texture, for 

instance, single crystals or high quality epitaxial films. A materials synthesis process, like spray 

pyrolysis, capable of producing large area films will produce inherently polycrystalline films which 

could conceivably be dominated by weak link intergranular connections. The ultimate success of 

any large area deposition process will be strongly influenced by its ability to control the 

orientation of these individual grain granules. 

1 2 

Grain Boundary 

Figure 7. Superconducting-Insulating-Superconducting (SIS) junctions at the boundaries 

betwe~n grains limit critical current densities in c-axis aligned polycrystalline 

ceramIcs. 

255 
In view of the strong anisotropy and poor conductivity of the cuprate superconductors in 

directions parallel to the perovskite c-axis, a necessary, but not sufficient requirement, will be to 

orient all the individual grains with their c-axes perpendicular to the current paths in the 

conductor, i.e., in the plane of the substrate. It has been shown that the relative orientation of the 

basal (a-b) planes in c-axis aligned bicrystals can greatly influence the critical current densities 

transported across the grain boundary [Dimas et al., 1988]. Grain boundaries in which the c-axes 

are perfectly aligned but have the orientation of their basal planes skewed by a screw rotation of 

more than 10° behave as Josephson junctions and will have relatively low and highly magnetic 

field dependent critical current densities. (See Figure 7). This occurrence can greatly inhibit the 

performance of the superconductor in magnetic applications. 

The formation of these superconductor-insulator-superconductor (SIS) junctions is believed 

to be the result of structural disorder at the grain boundary which occurs as a natural consequence 

of the need to accommodate the lattice mismatch at the boundary plane [Dimas et al., 1990]. One 

would expect that this region of insulating structural disorder to be on the order of lO's of 

angstroms, and that tunneling current densities through these effective Josephson junctions will 

depend directly on the degree of coupling between the superconducting regions. Polycrystalline 

films loaded with these superconductor-insulator-superconductor (SIS) junctions will have 

relatively low and highly magnetic field dependent critical current densities which cannot be 

improved through the generation of radiation induced defects. This occurrence can greatly inhibit 

the performance of the superconductor in high field magnet applications. 

Consequently, the suitability of using high-Tc superconducting ceramics in high field magnet 

applications will likely depend upon the selection of a materials system based on a number of 

intrinsic properties. As a result of the sensitivity of these grain boundaries to magnetic fields, 

intrinsic parameters other than transition temperature will likely playa more determinant role in 

selecting the materials systems for a high field magnetic component. Since charge transport 

through the insulator is a tunneling process, higher critical current densities across the grain 

boundary are likely to be obtained using a materials system exhibiting longer coherence lengths. 

If one of the electrons in a Cooper pair has tunneled through the barrier, but its coherence length 

is long enough to remain bound to the other electron in the superconducting paired state across 

the insulating region, the probability for supercurrent transport across the junction is greatly 

enhanced. (See Figure 8). In general, coherence lengths seem to follow an inverse relationship to 

the Tc of the material. 

256 

Superconductor Normal Conductor / 

Insulator 

-.... -

e 

I 

L Coherence length j 

Superconductor 

Figure 8. Tunneling of a paired electron state through an insulating barrier. 
4. CHEMICAL SENSITMTIES OF HIGH-Tc SUPERCONDUCTING CERAMICS. 

All of the high-Tc superconducting ceramics are known to participate in thermodynamically 

unstable reactions with carbon dioxide (C02) and water (H20) [Sleight]. They generally have 

favorable chemical reactivities with oxygen. As a result of the unstable reactions, a finished film 

with a nice sharp high-Tc transition will degrade over time as lower Tc knees grow into the 

transition region, and insulating regions metamorphose within the grain boundaries to pinch-off 

critical current densities (Jc)' Water is known to attack the Y-Ba-Cu-O superconductor by 

preferentially dissolving barium, so the use of organic solvents is now preferred in solution bulk 

processes [Trolier et al.]. However, the use of organic solvents will increase the likelihood that 

CO2 remains trapped in the lattice and corrodes the lattice through other reaction paths. CO2 is 

created in the lattice during the initial firing of these organic laden ceramic formulations. 

It has recently been confirmed that the presence of either H20 or CO2 will deteriorate 

critical current densities in these films by altering the surface properties of individual grains, 

thereby degrading current transport across their boundaries. The formation of BaC03, insulating 

Y 2BaCuOs, Y 203' and CuO have been observed to occur at various temperatures and pressures 

as the Y-Ba-Cu-O ceramic oxides react with CO2 which evolves during firing [Poeppel et al., 

1990a]. However, substantial improvements in lc and thermodynamic phase stabilization can be 

achieved if CO2 is efficiently removed from the lattice. It has been confirmed that the kinetics of 

CO2 removal from these ceramics is strongly influenced by the partial pressure of CO2 gas over 

the solid. Low-pressure high oxygen (02) flow rate treatments or low pressure annealing in ozone 

(03) have produced large, multilayer Y-Ba-Cu-O coils with acceptable critical current densities 

[Poeppel et al., 1990a, 1990b]. 

IV. CHEMICAL SPRAY PYROLYSIS AND CERAMIC MATERIALS PROCESSING. 

This research program will focus on adapting chemical spray pyrolysis to the manufacture of 

superconducting ribbons. Spray pyrolysis is a process where soluble precursor salts are dissolved 

in a solution which is then sprayed on to a hot surface. The cationic salts then precipitate out of 

solution and react together to form a coating of the desired compound, as the solvent, used to 

transport the reactants to the substrate, is evaporated from the surface. The high-Tc 

superconductors comprise a fairly complex materials system, not yet fully understood, and have 

very unique chemical properties (sensitivities) which must be respected if good quality films are to 

be produced. The entire synthesis process is composed of three basic steps: deposition, 

calcination, (where the precursor by-products are broken down and driven out of the film), and 

sintering, (where the stoichiometric mix is annealed to drive local atomic displacements to form a 

stabilized superconductive phase). 

1. Strategies Towards Achieving Stoichiometric Control at the Molecular Level. 

As is evident upon inspecting the electronic-structure properties of the high-Tc 

superconducting crystal structure, any bulk process capable of producing good quality films or 

coating must exert stoichiometric control at the molecular level. Although solution processes are 

attractive for the homogeneous mixing they can provide, not all of the precursor salts exhibit good 

or similar solubility in the solvent. Therefore, the likelihood for single species agglomerations to 

form as the salts precipitate out of solution and into the films near the hot substrate surface is 

real. 

In the first phase of this development we countered the possibility for single phase 

agglomeration by preparing stoichiometric solutions which used an organic (glycerol) as a 

chemical binder. The objective was to find ways to ''gel'' all the different precursors together 

though an organic chain(s). This approach greatly enhanced the chemical uniformity of the 

sprayed films, as determined by backscattered scanning electron microscopy. On the basis of 

thermal analysis it appears as though we are forming derivatized salt complexes. Figure 9 shows 

individual thermogravimetric (TGA) spectra of the various precursors used in our process. TGA 

measures the percentage weight changes in a compound residue versus temperature and allows 

the experimentalist to determine at which temperature regimes the material is likely to outgas and 

to infer what chemical decomposition species are forming on the basis of molar percentage weight 

changes. 

As is clearly evident in the figure the decomposition spectra is seen to change from the 

257 
~ 

til 

QC 

--·, ... OJI~'-'''. --. It' aD:"'I" QIf ~rl.&oa.'llG 

'--'::':'~CA-cit;' --.~-. -

1 

.... ~~\·:'·Xlt:'arl".","\.L_, .... , ... 1- .. ., 1aJ:.! .... UI : __ .. itT Clonun .... 'nMo"i 

~.----====------

5 e., 

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'\! 

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i I 

e r.1 ~ 

1 ; i: 

I, 

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iA.a----II::.- ~:":':II J~. 

a.< .. I_CII!..I~Ia.I"_ 

......... I'"t •• t .. t.CC/4 ... 

"ill:; Sic..» ,;:.» rill.i 

'...,.... ....... 10 

• t 

t I- ZL .. , • 

--+ 

• "tir"Iii1i'--liia 

I 

- ·'-.tL" -,i~,t:!."'-na::ii-'1I12 

., 

-·,t~~·--LiiQ.""t' 

:... .. J_I:!.,lftlCOII.H- '.,. __ 0 

.._., '.'" LO"_ ... '-..... ILm .. o,_re..c 

\ I 

\ I 

i r 1 \ ; \ , Jii 

Ii 

~ . 

t: i:.:: I::'~ £:.:: i:.:: I~:'= L:.: .::..::; ... :;..: .::.: 't';..: 

c .... J .... :I.;~: .. r_ :-=! .. ~.~.t=:)J~'~ ;'::~:I 

:;:" 

'-!-i .... 10.'131 .. :1_1"" .... a ',l .. :T.!I«! OELTA SE,;>IES re"7 ~,;;c ...... "..;, .• _ ........ , """~ eFt.. r.of Sf"t?/£s rcr.7 I.; .. _.~ .:-7"":,-: 5_=::';:=-S t:;·- I_-_...-CI'I: .... _-'·~ 

CU2(OH)3 - (NO)3 

-_ .. "j l::2 .~ I~"'·-i~-~,g 

11-=-":'7.-1.';)(111""" CI' 'I.L_ 

s .. , 

~ 

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........ , ..... I.ot/.". .... :. , ..... ,. .. C'1_tIOAG "II .. ~ 

-'-'-', \ 

\ 

\ 

i 

\ 

&iG.m , _____ t.,,1I: .:1.1IIIl oc 

DELTA SERIES TCA7 

212 Ba-Ca-Cu-(N03)2 in H20 only 

Ca(N03)2 Ba(N03)2 

1_ ·-:12 ¥,".:rc '" If :r::l·lJO: , ___ as:gp:ur!If"·U",L,,"1 .• , 

: ( .... '\ 1-" ,..-

;\8,,: '\ /' '"" i ~ ! i'---- \ \) ~~, ~\!~ , I 

, . 

• ii:=' '1"':" :{:1: II':.:" ~:.= "1:%.21 • ,o',.:" .:,.~ .t~= t:'!1.= ;:: .... ,t o.r. .. :_::!t.IIC I,DIoII ":"~.1.J".O 

"'_\ .. ~ ...... SoD ,,_ ... 

~~;.~\o I."'" DI,..t;.oD :=:":;~ S.:::f' .... FS ,-;'':-

212 Ba-Ca-Cu-(N03)2 in H20 with 

20% Glycerol Binder by volume 

Figure 9. Thermal decomposition spectra of residues dried from aqueous salt solutions containing Ba(N03h, 

Ca(N03h, Cu(N03h, only, and solution mixtures of the three salts with and without an organic binder. 
single species cases. In aqueous solution both Ba(N03h and Ca(N03h appear to have an affinity 

for each other and complex together. This is verified through the loss of their individual spectra, 

and by percentage weight changes which indicate that they are decomposing simultaneously. 

However, the Cu(N03h aqueous salt derivative decomposes independently in .the case of 

aqueous only, and aqueous/20%-ethanol by volume solutions. When the glycerol IS added the 

spectra for the Cu(N03h aqueous salt derivative is observed to shift to higher temperatures as 

the Ca(N03)2/Ba(N03h complex shifts to lower temperatures. 

Our objective in performing this work is to identify the conditions which derivatize all of the 

salts into a "single complex" which decomposes simultaneously at an intermediate temperature. 

This eventuality would allow all of the metal oxide components in superconductor to form 

together and to be located physically close to one another to facilitate the sintering process. 

Figure 10 shows the R-T curve for films prepared in the first phase of the research effort. In 

this instance Ba-Ca-Cu-O precursor films were spray pyrolyzed using a nitrate salt aqueous 

solution which contained 20% glycerol as a chemical binder. Tl20 3 was diffused into the film to 

form the superconducting TI-Ba-Ca-Cu-O phase. While these results represent, to our 

knowledge, the highest zero resistance temperatures for films prepared using this process, the 

films were phase unstable. Over time lower-Tc knees grew into the transition to zero resistance. 

We attribute this phase instability to the likely presence of water and COb formed in the material 

during processing, which are naturally abundant as a result of our aqueous/organic solution 

chemistry. 

8' 

-..J' 

OJ 

u 

c: 

co 

t; 

'r;; 

OJ 

~ 

10 

8 

6 

4 

2 

a 

0 

111.5 K o 

SO 100 150 200 250 300 

Temperature (K) 

Figure 10. R-T curve of a film prepared by spray pyrolyzing Ba-Ca-Cu-O and diffusing 

Tl20 3 to form superconducting Tl-Ba-Ca-Cu-O. 

A current objective of our work is to reduce the amount of water used in the process. While 

investigating other nonaqueous solvents we have found that formamide, (H3CCN), is an excellent 

solvent for non-transition metal salt precursors. It should be noted that extreme care must be 

exercised when mixing Cu(N03h with organics. The redox active copper atom can catalyze the 

formation of some very explosive compounds. However, these reaction pathways appear to be 

shunted when the less reactive salts are mixed into the organic prior to the introduction of 

Cu(N03h· 

2. CALCINATION--FORMING THE SUPERCONDUCTING CERAMIC. 

The sprayed films are not initially superconducting. Solution stoichiometries could be 

maintained in the precipitated surface residue by spraying at surface temperatures which did not 

259 
pyrolyze the salt compounds into their respective oxides, even though these films had been dried 

of most of their solvents. Once the appropriate stoichiometry had been deposited on to the 

surface it could then be converted into its oxide form through calcination. 

Over the course of the next year this development will focus on how gas pressure and 

atmosphere flow rates can be optimized during the calcination process to efficiently remove CO2 

from the lattice. It has been confirmed that the kinetics of CO2 removal from these ceramics is 

strongly influenced by the partial pressure of CO2 gas over the solid. Low-pressure high oxygen 

(02) flow rate treatments or low pressure annealing in ozone (03) have froduced large, 

multilayer Y-Ba-Cu-O coils with acceptable critical current densities [PoeppeZ et a., 1990a, 1990b]. 

Once optimal solution chemistries have been identified, studies into the calcination process 

will be performed at Argonne National Laboratories, Argonne, IL. ANL, through the 

Superconductivity Pilot Center Program, will examine outgassing products during the thermal 

conversion processing step to determine optimal gas atmosphere and pressure parameters for this 

stage of the process. This work will involve ill situ diffuse reflectance infrared Fourier transform 

(DRIFT) spectroscopic and gas chromatographic investigations to probe the chemical 

transformations that take place when the spray pyrolyzed high-Tc superconducting ceramic 

formulations are calcined and converted to superconducting films and coatings. The dried 

salt-complex residues obtained from the spray pyrolysis process will be placed in a controlled 

environment DRIFT cell (CEDC), (see Figure 11), and the thermal treatment schedule will be 

monitored by recording the infrared spectra of the solid residue and the gases evolving from the 

residue. The outgassing species will also be monitored downstream of the DRIFT cell using 

on-line gas chromatography. Thermal treatment parameters, such as heating rate and gas 

atmosphere, will be varied in a systematic manner designed to optimize product properties. The 

useable range of the DRIFT technique is normally limited to ~5500 C and total pressures near 

atmospheric; hO'\,ever, ANL will attempt (on a best effort basis) to perform DRIFT studies of the 

thermal treatment proce~s under reduced pressure conditions. 

O-RING SEAL 

WINDOW 

SAMPLE CUP 

CHAMBER 

THERMOCOUPLE 

SAMPLE POST 

COOLANT (OUT) 

GAS 

ENTRANCE PO 

CENTIMETERS 

I I I I I I I I 

o 2345678 

COMPRESSION NUT 

WINDOW 

SCREEN 

HEA T ING ELEMENT 

COOLANT CHAMBER 

O-RING SEAL 

COOLANT (IN) 

Figure 11. Schematic of the Argonne National Laboratory, DRIFT cell to be used to 

study the calcination process of the high-Tc superconducting ceramics. 

3. TEXTURING TIlE CERAMIC. 

Films prepared via solution processes are inherently porous and in fact need to have a 

spongy texture in order to allow the outgassed products a pathway to efficiently escape the lattice. 

260 
It is therefore necessary to densify the film after calcining. This can be accomplished by cold 

pressing the ceramic under pressures which densify the film to roughly 10% of its initial thickness. 

This process is essential to obtaining good c-axis alignment and texture in these ceramics. (See 

Figure 12). Texture can be loosely defined as c-axis alignment and excellent grain boundary 

alignment. 

Cold press 

Remelt 

Figure 12. Densification and melt processing leads to films with improved texture. 

Once the films have been pressed they should be subject to partial remelt. The purpose of 

this remelt is to locally rearrange atomic configurations into a phase-stabilized superconducting 

crystalline phase. A key objective to this aspect of the process is to improve supercurrent 

transport across the grain boundary. 

V. FLUX PINNING IN HIGH-Tc SUPERCONDUCTORS 

The generation of flux pinning centers is a critical aspect of high-Tc superconducting magnet 

technology. Flux pinning centers are deliberately induced defects embedded within the 

superconductor which have physical dimensions shorter than the coherence length(s) of 

superconducting Cooper pairs. If they were to have dimensions larger than the coherence length 

they would induce transitions to the normal state. Fluxoids pinned at a defect center will be 

prevented from dissipating their kinetic energy through the generation of heat in the system. A 

difficulty of working with the high-Tc ceramics is that their coherence lengths are very short. 

However, flux pinning centers can be introduced in these systems using ionizing radiation to 

randomly introduce point defects throughout the medium. 

Researchers at Oak Ridge National Laboratory, Oak Ridge, TN, have recently shown that 

high energy, heavy-ion (Z=30) irradiations can increase intragranular critical current densities to 

magnitudes of 108 Ncm2 in 5-10 Tesla fields [Christian]. The orientation of the incident 

irradiation must be aligned parallel to the orientation of the penetrating magnetic flux lines. This 

irradiation is capable of producing a line (or lattice) of correlated point defects in the crystal 

roughly 3 to 5 microns in length. (See Figure 13). This kind of flux pinning can be likened to a 

seamstress' hem. A hem made with a greater number of stitches is more resistant to tearing than 

one made with a single stitch. Analogously, a fluxoid pinned by a single point defect will be more 

responsive to stress imposed by Lorentz forces than a fluxoid pinned along a line of defects. 

Increases in the flux pinning potentials appear to be independent upon the crystallographic 

orientation and are solely dependent on the relative orientation of the line defect to the orientation of penetrating lines of flux. 

261 
While this technology represents some major breakthrough, both in terms of assessing the 

quality of these new materials and focusing attention on how strong a role correlated forces play 

in these systems, they may not be useful at all in films lacking any kind of texture. The 

susceptibility of polycrystalline films to magnetic fields at grain boundaries is a far greater 

problem which does not appear to be remedied through the generation of defects with improved 

flux pinning potentials. 

Supen:ond.aor 

-';""-com:Io'cd nlll rlftnlnc cenlers 

. . 

pettet"'ill, 

nuoicl 

rclion 

Figure 13. Heavy-ions accelerated to high energy leave a trail of point defects within the 

crystal along their bombardment path. Enhanced flux pinning will result when the 

penetrating flux lines are oriented parallel to this defect string. 

VI. COMMENTS ON TilE SELECTION OF WHICH MATERIALS SYSTEMS 

At present there are a number of different compositions in the perovskite crystal family 

which exhibit high-Tc superconductivity. Each family has been observed to have intrinsic 

properties unique to its compositional domain. Some are observed to have higher transition 

temperatures, others have lower anisotropy, and yet others, those with the lower T c's have longer 

coherence lengths. Table I lists these various properties for some of the more well known and 

technologically important oxide superconductors. All of these factors come into play when 

considering the practical design and construction of a high field, high-T c magnet. There is not one 

single property which can be used to evaluate the relative merits of one materials system over 

another. The timing of the development of a magnetic coil using various materials systems should 

immediately take into account the volume of data available on materials processing. Delivery of a 

coil or component can be severely hampered in cases were insufficient data is available of the 

temperature-compositional phase relationships and chemical sensitivities of the materials system. 

Most significantly, more pragmatic development may result if the current focus of development 

were to shift from transition temperature and more towards coherence lengths and relative 

isotropy as the alluring intrinsic properties. 

VII. COMMENTS ON WHERE TO Focus SYSTEM DESIGNS TO TAKE ADVANTAGE OF THESE 

MATERIALS. 

Even though the high-Tc superconductors may still be many years from widespread 

application in systems the engineering community should start taking a good look now on how to 

take advantage of these systems. At this stage, and perhaps on into the future, the concept of 

liquid nitrogen-cooled high field superconducting magnets does not appear relevant to any of the 

materials systems under study. Figure 14 shows data collected by researchers at Oak Ridge 

262 
Table 1 

Material System Tc(K) Coherence Length (A) Known Synthesis Properties 

Isotropic 

(Ba,K)Bi03 20-30 43 Difficult, (Hygroscopic) 

YBaZCu30x 60-90 31 Most well Known 

TI/NCu/O 90-120 16-30 Toxic, Not Well Known 

(Nd,Ce )zCu04+x 22-30 70 Not Well Known 

Bi-Sr-Pb-Ca-Cu-O 88-110 30-40 Relatively Well Known 

Bi-Sr -Sb-Ca-Cu-O 90-132 Unknown 

Most Antisotropic 

263 
National Laboratory and the General Electric Research Laboratory, Schnecteddy, NY, on the 

magnetic dependence of c-axis oriented TI-Ba-Ca-Cu-O films prepared by diffusing T120 3 in 

spray pyrolyzed Ba-Ca-Cu-O. It is clear that even though this system has one of the highest Tc 

superconducting phases, and on the basis of its single crystal properties is one of the hardest 

magnetic materials of this new class of crystals, it is not capable of sustaining a magnetic load until 

it is cooled to lower temperature. This plot does not describe the upper critical fields which this 

material system can sustain, rather it diagrams the irreversibility field conditions provoked by 

defect structures which are extrinsic to the material system itself. 

106 

.. 

E 10 5 4.2K u 20K ;c 

- 40K 

C 

CD 

.. 10· .. 

::I 

0 

iii 

~ 103 

a:: 

0 

10 2 

.01 .1 10 

Field (Tesla) 

Figure 14. Critical current density versus magnetic load in c-axis aligned polycrystalline 

TI-Ba-Ca-Cu-O films. (After Tkaczyk et a\.) 

Similar behavior has been observed in the Bi-Sr-Pb-Ca-Cu-O family of oxide 

superconductors which also have Tc's greater than 100 K. This family of superconductor is 

generally considered to be the most anisotropic. The anisotropy of these materials is a matter of 

serious concern to high field magnet design engineers. However, again at lower temperature the 

anisotropy of this system appears to be lifted and the relative orientation of the crystal vis-a.-vis the 

application of thermodynamic stress on the system is less of a problem. (See Figure 15). 

The points at which these recently discovered materials really come into their own is in the 

niche of low temperature, very high field applications. By low temperature we include 

temperatures up to 25-30 K. Figure 16 compares the magnetic load performance of 

Bi-Sr-Ca-Cu-O (BiSCCO) superconductors to niobium-titanium (Nb-Ti) and niobium-tin (Nb3Sn) 

at 77 K and 4.2 K. Even though the low-Tc superconductors do not operate at liquid nitrogen 

temperatures, critical current densities in this high-Tc superconductor drop very rapidly with 

increasing load. However, at liquid helium temperatures the BiSCCO systems can sustain 105 

Ncm2 critical current densities to fields well beyond the operating potential of the conventional 

superconductors. This mapping should define the design parameters for systems which take 

advantage of the advances in technology which can be exploited by these new materials systems. 

As it is now possible to purchase cryostats capable of reaching = 10 K at reasonable cost, the 

attraction of the high-Tc superconducting ceramics should not emphasize liquid nitrogen 

operation as much as high magnetic load capability. ' 

264 
105 

~ 

~.. t5K 

1':~:::~:: 10 \ .5K 

,55K 8lc-axls 

10 2 \ 65K 

nK 

Magnetic Field 8(T) 

~ 42K 105 -o-oa ~ ., ~ a-o--o-a 

·i".~ 

~ 10' 35K ,\5K 8 1/ c .. xls 

102 \ 

, 45K 

10' 55K 

02468 

Magnetic Field 8(T) 

w .. 

0.01 '--'---'----''"----.J 

o 2 4 6 8 

Magnetic Field 8(T) 

Figure 15. Temperature dependence of the critical current density anisotropy factor for 

textured 2212 BiSCCO tape [After Kumakura et ai.]. 

- 106 

t\j 

E 

~ Q. 4.2K E 

as 

-

~ + 

in BSCCO z 

w 

0 

Iz 77 K ·w 

a: 

a: 

::l 

u 

....J 

<: 

u 

I- BSCCO 

c: 103 U 

0 5 10 15 20 25 

MAGNETIC FIELD (tesla) 

Figure 16. Critical current density versus magnetic load in BiSCCO wires. [After 

Larbalestier] 

265 
References: 

Bednorz, J.G., Muller, KA., Z. Phys. B64, 189 (1986). 

Cava, R.J., Hewat, A.W., Hewat, E.A., Batlogg, B., Marezio, M., Rabe, KM., Krajewsji, J.J., Peck, 

W.F., Jr., and, Rupp, L.W., Jr., Physica C 165, 419 (1990). 

Chandrachood, M.R, Mulla, I.S., and Sinha, A.P.B., Appl. Phys. Lett. 55(14), 1472 (1989). 

Christian, David, Oak Ridge National Laboratory, Oak Ridge, TN, Private communication, July 

15, 1991. 

Dimos (1988), D., Chaudhari, P., Mannhart, J., LeGoues, F.K, Phys. Rev. Lett. 61(2), 219 (1988). 

Dimos (1990), D., Chaudhari, P., Mannhart, Phys. Rev. B 41(7), 4038 (1990). 

Doss, J.D., "Engineer's Guide 10 Higlz-Temperature Superconductivity", John Wiley & Sons, New 

York, 1989. 

Hermann, A.M., and Sheng, Z.Z., "The High High- Tc Tl-Ba-Ca-Cu-O Superconducting System", 

presented at the SERI Thin Film Conference, Solar Energy Research Institute, Boulder, 

CO, November, 1988. 

Hongbao, L., Liezhao, C, Ling, Z., Zhiqiang, M., Oxian, L.X., Zhidong, Y., Bai, X., Xianglei, M., 

Guien, Z., Yaozhong, R., Zhaojia, C, and Yuheng, A., Solid State Commun. 69, 867 (1989). 

Jorgensen, J.D., "Defects and Superconductivity in the Copper Oxides", Physics Today 44(6), 34 

(1991). 

Kitazawa, A., "Electronic Structures of Oxide SupercunductorsDeve!opment of Concepts", in Earlier 

and Recent Aspects of Superconductivity, J.G. Bednorz and KA. Muller, (eds.), Springer 

Series in Solid-State Sciences 90, Springer-Verlag, New York, 1990, p. 45 - 65. 

Kumakura, H., Togano, K., Maeda, Kase, J., and Morimoto, T., Appl. Phys. Leu. 58(24), 2830 

(1991). 

Larbalestier, D., "Critical Currents and MAgnet Applications of High-Tc Superconductors", 

Physics Today, 44(6), 74 (1991). 

Onnes, H.K, "The resistance of pure mercury at helium temperatures", Comm. Leiden. 120b (28 

April 1911). 

Poeppel (1990a), R.B., et aI., "Fabrication Advances for Improved Perfonnance of Long Lengths of 

High-Temperature Superconducling Wire alld Tape", Proc. 1990 Appl. Superconductivity 

Conf., Snowmass Village, CO, Sept. 24-28, (1990). To be published in IEEE Trans. Magn., 

vol. 27 (March 1991). 

Poeppel (1990b), R.B., et aI., ''Atmo!>,plzere COlllrol During Preparation of YBa2Cu307-x Magnetic 

Windings", Proc. 3rd Intnatl. Symp. on Superconductivity, Sendai, Miyagi Prefecture, Japan, 

Nov. 6-9, 1990. 

Sleight (1991), A.W., "Compmisoll uf Higlz-Tc Superconducting Compounds: Implications for 

Applications", paper B1.1, Industrial and Competitiveness Consortia, Materials in 

Washington Forum, Washington D.C, February 28 to March 1, 1991, (sponsored by the 

Materials Research Society, Pittsburgh, PA). 

Tkaczyk, J.E., et aI., 1990 Fall Meeting of the Mater. Res. Soc., Boston, MA. 

Trolier, S.E., et aI., Am. Ceram. Soc. Bull. 76, 759 (1988). 

van Dover (1989), R.B., Gyorgy, E.M., Schnee meyer, L.F., Mitchell, J.W., Rao, KV., Puzniak, R., 

and Waszczak, J.V., Nature 342, 55 (1989). 

van Dover (1990), RB., Gyorgy, E.M., White, A.E., Schneemeyer, L.F., Felder, R.J., and 

Waszczak, J.V., Appl. Phys. Lett. 56(26), 2681 (1990). 

Venturini, E.L., Barbour, J.C, Ginley, D.S., Baughman, RJ., and Morosin, B., Appl. Phys. Lett. 

56(24), 2456 (1990). 

Wu, M.K, Ashburn, J.R., Torng, C.J., Hor, P.H., Meng, R.L., Gao, L., Huang, Z.J., Wang, Y.Q., 

and Chu, CW., Phys. Rev. Lett. 58, 908 (1987). 

266 
N92-27735 

LEVITATION OF YBa2Cu307-x SUPERCONDUCTOR IN A VARIABLE 

MAGNETIC FIELD 

Alexander N. Terentiev and Anatoliy A. Kuznetsov 

Institute of Chemical Physics Academy of Sciences of the USSR, 

117977 Moscow USSR 

267 
SUMMARY 

The influence of both a linear alternating and rotational magnetic field component on the 

levitation behavior of a YBa2Cua07 -x superconductor was examined. The transition from a plastic 

regime of levitation to an elastic one, induced by an alternating field component, was observed. 

An elastic regime in contrast to a plastic one is characterized by the unique position of stable 

levitation and field frequency dependence of relaxation time to this position. It was concluded that 

vibrations of a magnet levitated above the superconductor can induce a transition from a plastic 

regime of levitation to an elastic one. It was found that a rotational magnetic field component 

induces rotation of a levitated superconductor. Rotational frictional motion of flux lines is likely 

to be an origin of torque developed. A prototype of a motor based on a levitated superconductor 

rotor is proposed. 

INTRODUCTION 

The discovery of high Tc superconductivity stimulated a study of passive levitation phenomenon 

in a system consisting of a permanent magnet and high Tc superconductor. This levitation phenomenon is of great importance for passive contactless magnetic bearings. High Tc superconductors 

are type 2 superconductors exhibiting low values of the first critical field. These specific features of 

the new superconductors result in the fact that in magnetic bearings a high Tc superconductor is in 

the mixed state and a magnetic field penetrates inside the superconductor in the form of flux lines. 

Flux lines do not freely exist in a superconductor body but are pinned by lattice inhomogeneities. 

Strong pinning leads to hysteresis of the magnetization curve. Hysteresis of the magnetization curve 

due to the pinning of flux lines is the origin of two unusual levitation effects. The first effect is the 

possibility of stable suspension of the superconductor below a permanent magnet, first discovered 

with an YBa2Cua07-x sample doped with silver oxide (ref. 1). This effect is the consequence of 

large magnetic hysteresis leading to a positive superconductor magnetization after the external field 

decreased. The second effect is friction in levitated superconductors resulting in a continuous range 

of stable levitation positions and orientations (ref. 2). 

ELASTIC LEVITATION 

Another class of unusual magnetomechanical levitation effects was discovered by applying a 

variable magnetic field component to a superconductor levitated above the permanent magnet. A 

schematic diagram of the experiment is represented in fig. 1. The superconducting specimen was 

levitated above the ring-shaped permanent magnet, magnetized along the axis. In order to create 

an alternating field component at the sample position, an electric coil was placed inside the magnet 

so that the coil axis coincided with the magnet axis. The permanent magnet containing the coil was 

placed at the bottom of the bath with liquid nitrogen. In the case of superconductor levitation in the 

P::tECED!NG P.~;:tE BLANK NOT FiLM!:D 269 
static magnetic field of the permanent magnet so-called dry magnetic friction is observed. There is a 

continuous range of levitation positions. After the displacement of the sample along Z-axis from the 

initial levitation position the new position is also stable for levitation. There is no visible mechanical 

relaxation to the original position. This is the rigid or plastic type of levitation described in (ref. 2). 

The superconductor levitated in this regime is similar to the load on an inclined plane rested due to 

friction. When alternating current is applied to the coil, a new levitation behavior appears. In this 

case a unique position of stable levitation having height ho is observed. If the initial position of 

levitation is beyond ho , the superconductor is forced to float up off the magnet. If it is higher than 

ho the superconducter is forced to float down. Therefore the superconductor displacement from 

the equilibrium position generates a restoring force and the sample returns to the original position. 

In this regime a levitated superconductor is similar to a spring-suspended weight. Therefore a 

variable magnetic field induces the transition from a plastic type of levitation to an elastic one, 

characterized by a single position of stable levitation. Switching off the alternating field component 

leads to the inverse transition from an elastic levitation to a plastic one. It was found that the time 

of relaxation to the unique position of levitation in the elastic levitation regime depends strongly 

on the variable field frequency. The experiment was the following. The superconductor levitated 

in a variable magnetic field was displaced by means of non-magnetic pincers 2 mm down from the 

equilibrium position; then the superconductor was liberated from pincers and the time of relaxation 

to the original position was measured. The results are represented in fig. 2. One can subdivide the 

field frequency dependence of the relaxation time in two parts. In the low frequency range (0-100 

Hz) the relaxation time decreases with increasing field frequency. In the high frequency range, 

(100-5000 Hz) the relaxation time is constant. Let's consider the structure of the hysteresis loop 

of a high Tc superconductor. Due to the irreversibility, magnetization of the superconductor is not 

a simple function of the external field. Consequently, the mechanical force in the inhomogeneous 

magnetic field depends not only on the field intensity but also on the magnetic history of the 

sample. The hysteresis loop of the superconductor consists of two curves (fig. 3): the upper-curve 

m + (H) corresponds to increasing the magnetic field and the down-curve m - (H) corresponds 

to decreasing the magnetic field. The existence of two different curves is a consequence of the 

irreversible part of magnetization of superconductors with pinning. According to the Bean critical 

state theory (ref. 3) these curves correspond to the different directions of the critical current inside 

the superconductor. From this it is obvious that increasing the external magnetic field by a value 

exceeding 2Hp, where Hp is the field value resulting in the penetration of the magnetic field to 

the center of the superconductor, leads to the transition of sample magnetization from the m - (H) 

curve to the m + (H) curve if initial magnetization is related to the m - (H) curve. Decreasing the 

field to the same value leads to the inverse transition. These transitions between the curves form 

the minor loop. Due to hysteresis the superconductor magnetization can exhibit any value ranging 

from m+ to m- under a given field intensity. Hysteresis of magnetization leads to the hysteresis 

of repulsive force acting on a superconductor so that repulsive force can exhibit any value from r+ 

to r- under a given levitation height. The appearance of a unique position of levitation in the 

elastic regime is clearly seen when the amplitude of the alternating component is large enough to 

induce the cycle transitions between the m+ (H) and m-(H) curves of the hysteresis loop. The 

magnetization value of the superconductor in this case is the following: 

(1) 

where f is field frequency. One can see from (1) that after applying an alternating field the 

average value of magnetization equals to the reversible magnetization value (m+ + m-)/2 having no 

hysteresis. This means that the origin of the continuous range of levitation points disappeared and 

only the unique point of levitation occurs. However in the experiment the elastic regime of levitation 

is observed when the amplitude of an alternating field is low compared to the Hp parameter. Elastic 

levitation is likely to occur even when the alternating field is low compared to the Hp parameter and 

270 
the flux lines motion is induced only in the thin surface layer of superconducting grains. Thus the 

microscopic origin of the transition from the plastic type of levitation to the elastic one is the flux 

lines motion induced by the variable field. In the elastic regime the levitation height is determined 

by the reversible magnetization of superconductor (m+ + m-)/2 see (1). This conclusion is of 

importance because the reversible magnetization is low compared to the irreversible one in high 

quality oxide superconductors. This means that the load capacity in the elastic regime of levitation 

is less than that in the plastic regime. In order to explain the field frequency dependence of 

relaxation time in elastic regime of levitation consider the evolution of the point representing the 

state of the superconductor in the plane repulsive force - levitation height plane (r-h plane) see fig. 

4. Consider for simplicity that the alternating component has the form of rectangular pulses and 

the inhomogeneity of the alternating field may be neglected compared to the one of the static field. 

In this case the magnetic moment of a superconductor will oscillate and the representing point will 

be displaced instantaneously vertically up or vertically down after each change of the sign of an 

alternating component. This means that the value of repulsive force, acting on the superconductor, 

changes without any change in the levitation height. Let's suppose that the field frequency is rather 

low so that after each change of the sign of alternating field the superconductor occupies the new 

equilibrium position which we called the local equilibrium point. Therefore the point representing 

the state of the superconductor reaches the line r=mg after each change of the alternating field sign. 

In the elastic regime the global equilibrium height ho is determined as the crosspoint of the lines 

r=mg and (r+ + r-)/2. Displacement of the superconductor from the global equilibrium point 

ho induces the relaxation motion of a superconductor. During this motion alternating field pulses 

having different signs displace the operating point in the different directions along the line r=mg 

(see fig. 4). But the contributions of the pulses of different signs are not equivalent because when the 

operating point is in the local equilibrium the distance between the lines r+ and r=mg is not equal 

to the one between r- and r=mg lines. Due to these differences in the contributions of impulses of 

opposite signs the operating point is displaced towards the global equilibrium point ho until reaching 

it. When the superconductor occupies the global equilibrium point the contribution of the impulses 

with opposite signs becomes equivalent and the superconductor oscillates near this point without 

the resulting displacement. From this consideration one can conclude that at low frequencies each 

cycle of the alternating field induces the particular displacement of a superconductor. If in order for 

the superconductor to reach the global equilibrium, N cycles is required, the relaxation time will be 

equal to N If. One can see that the relaxation time is inversely proportional to the field frequency 

in the low frequency regime, so that at zero frequency the relaxation time is infinite. This means 

the transition to the plastic regime of levitation in a static field. Therefore the considerations of 

the relaxation process of a superconductor in a variable magnetic field presented here explain the 

increase of time relaxation observed in the experiment in the low frequency range. 

Now let's consider the vibrations of the magnet levitated above the superconductor. The 

levitated magnet generates an inhomogeneous magnetic field in the surrounding space. Due to 

the field inhomogeneity a vibrational motion of the magnet induces a change of the magnetic field 

value near the magnet. Therefore the vibrating magnet generates a variable field component in 

surrounding space. Since the superconductor providing the levitation is placed in the vicinity of the 

magnet, the variable magnetic field affects it. The variable magnetic field forces the flux lines to 

move inside the superconductor and as a consequence induces the transition from the plastic regime 

of levitation to the elastic one. Therefore the transition from the plastic regime of levitation to 

the elastic one may be induced when the permanent magnet levitated above the superconductor is 

forced to vibrate relative to the superconductor. This conclusion is of great importance because in 

using such a bearing, for instance in aerospace applications, variations in load, attitude and speed 

occur. These disturbances will induce vibration of the levitated magnet, and as a consequence, 

change the levitation height and decrease the load capacity of the bearing. It should be noted that 

the inverse situation occurs when a superconductor levitated above a magnet is forced to vibrate 

271 
relative to a rested magnet and is physically equivalent to the one considered above. Thus all 

the conclusions made in the case of the magnet levitated above the superconductor are true for a 

superconductor levitated above a magnet. 

ROTATION OF LEVITATED SUPERCONDUCTOR 

The second interesting effect is rotation of a levitated YBCO superconductor due to a rotational 

magnetic field. For the rotation experiment, two ceramic samples YBa2Cu307-x (YBCO) and 

YBa2Cu307-x-Ag20 (YBCO-Ag) prepared by means of ordinary ceramic technology were used. 

The first sample was a ring shape with these dimensions: outer diameter 7 mm, inner diameter 4 

mm, thickness 2 mm. The second sample was a parallelepiped shape with dimensions 5.5*1.0*1.0 

mm3. A ring-shaped permanent magnet (SmCo5) magnetized along the z-axis was the source of 

the inhomogeneous field. The Z-axis coincided with the magnet symmetry axis. The magnet had 

dimensions of 34 mm outer diameter, 10 mm inner diameter and 5 mm thickness. The experiment 

was carried out with the apparatus illustrated in fig. 5. A glass tube containing the superconductor 

was attached to the vacuum main. This tube was placed inside the Dewar with liquid nitrogen. 

The special external platform containing the ring-shaped magnet and four air coils provided the 

levitation of the magnet and creation of the rotational field component. An infrared beam passed 

through the tube and provided the registration of the rotation by infrared detector. The output 

of the detector was connected to the rotating-mirror oscillograph. An AC generator connected to 

the two equivalent power amplifiers was used to supply the current through the coils to create the 

rotational field. 

At low rotational magnetic fields, rotation of the levitated superconductor was not observed. As 

the field intensity was increased, torsion oscillations of the superconductor appeared. When the 

rotational magnetic field intensity exceeded the critical value, the levitated superconductor began 

to rotate in the XY plane. In all of the experiments the superconductor rotated in the direction 

of field rotation. It was found that the rotation frequency increases with the increase of rotating 

field intensity until the rotation frequency achieves a certain value of about 10 Hz. Then the 

rotating frequency stops increasing and the further growing of the rotational field intensity causes 

considerable superconductor oscillations in the XY plane. The subsequent increase of rotating 

field intensity causes the rotation to be unstable. In this regime chaotic-like radial oscillations 

were observed. Active deceleration of the rotational superconductor (YBCO sample) and the 

subsequent active acceleration by the rotational field (10 Oe 50 Hz) is represented in fig. 6. One 

can see the rotational field develops considerable torque acting on the levitated superconductor. 

Superconductors' spin rate decay vs time in a static field is represented in fig. 7. Here we see 

a clear straight line decay. Note that the sample doped with silver oxide exhibits considerably 

stronger friction torque compared to the undoped sample. The torque acting on a levitated 

superconductor in a rotating magnetic field can arise from 1) diamagnetic geometric form effects, 

2) rigid sample magnetization due to trapped flux lines, 3) anisotropy of type 2 superconductor, 

leading to transverse magnetization of the Abrikosov lattice, or 4) frictional rotational motion of 

flux lines induced by the rotating magnetic field. In cases 1) - 3) only synchronous rotation of 

the superconductor can occur. Only in case 4), when frictional rotational motion of flux lines 

drives the rotation of the superconductor, the rotational frequency of the superconductor may be 

less than the external field frequency and be independent of it. In this case the flux lines rotate 

with a frequency equal to the field frequency. Moving vortices develop a frictional torque which 

acts on the superconducting body inducing rotation. However, the rotational frequency of the 

specimen is controlled by external friction (in our case magnetic friction) and may be substantially 

less than the field frequency. In all our experiments the superconductor rotational frequency was 

272 
less (substantially) than field frequency. From this we concluded that frictional rotational motion 

of flux lines inside the superconductor is an origin of superconductor rotation. 

While a superconductor is rotating around a center of a homogeneously magnetized ring, no 

changes of the magnetic field in a superconductor occur. Consequently no flux lines motion occurs 

in the superconductor. Real magnets, however, have some magnetization inhomogeneity leading to 

the existence of the asymmetry of a magnetic field with respect to their vertical axis. In that case 

during rotation the magnetic field in the specimen does not remain constant causing the flux lines 

motion. As a result a magnet friction torque occurs (ref. 4). Moving over an atomic lattice, flux lines 

are acted upon by two different microscopic forces (ref. 5): 1) The pinning force, which does not 

depend on the motion speed of a flux line and is analogous to the dry friction force, 2) The viscous 

force, which is directly proportional to the flux line speed. The superconductor rotational rate decay 

is observed to be linear (see fig. 7); i.e. the friction torque does not depend upon the rotational 

frequency. This conforms with the data obtained by F. Moon et al. (ref. 4) in the experiments 

with the high frequency rotation of the magnet levitated above the superconductor. Thus, it may 

be concluded that the pinning force acting upon moving flux lines is the origin of the macroscopic 

rotational torque developed by the rotational magnetic field. The magnitude of the viscous force 

is negligible. It should be noted that different superconducting samples exhibit different friction 

torque during free rotation (see fig. 7). One can see that friction torque increases as pinning force 

decreases. The magnitude of angular acceleration of the levitated superconductor in the case of 

active acceleration of the superconductor by the rotational field is directly proportional to the 

torque acting on the superconductor. Similar to that case the magnitude of angular deceleration 

of the freely rotating superconductor is proportional to the magnetic friction torque. By using the 

slopes of this dependency (see fig. 6,7) we calculated that rotational field torque / friction 

torque =40 for YBCO sample and rotational magnetic field 10 Oe, 50 Hz. This conclusion is of 

great importance because it means that magnetic friction in levitated superconductors is not the 

factor restricting the rotational speed and in principle one can reach considerably higher speed 

magnitude. The instability of the rotating superconductor in a horizontal plane is likely to be the 

origin of low rotation rate. It was observed that the maximal rotation frequency of the levitated 

superconductor is approximately equal to the radial resonance frequency of the superconductor. 

Therefore, one can suppose that low frequency natural resonance restricts the rotational frequency. 

The apparatus represented in fig. 5 may be considered as the prototype of a new motor based on 

a superconductor levitated rotor. We called this type of motor a superconductor hysteresis motor 

because the rotational field develops the torque acting on the superconductor due to the pinning 

of flux lines. Pinning of flux lines leads to the hysteresis of superconductor magnetization and the 

occurrence of a non-zero angle between the vector of magnetization and the vector of a rotational 

field. The occurrence of this angle results in the development of torque acting on a superconductor. 

This method of torque generation qualitatively differs from that used in the ordinary motor based 

on a magnet levitated above a superconductor as a rotor (ref. 6). In a magnet levitated motor 

there is an additional small magnet connected with the main magnet providing the levitation. The 

small magnet is acted upon by the rotational field to induce rotation. In contrast, in hysteresis, 

the superconductor motor rotational field acts on the levitated superconductor rotor immediately. 

Another important feature of the hysteresis motor is independence of the torque generated upon 

the relation between the superconductor rotation frequency and field frequency. It is required only 

that field frequency exceed the rotation frequency. This property makes initiation of rotor rotation 

effortless. 

273 
CONCLUSIONS 

Influence of both linear alternating and rotational magnetic field components on a levitation 

behavior of YBa2Cu307 -x superconductor was examined. The transition from a plastic regime of 

levitation to an elastic one, induced by an alternating field component was discovered. In contrast 

to plastic levitation, elastic levitation is characterized by a unique position of levitation and field 

frequency dependence of relaxation to the equilibrium position after disturbance. The elastic type of 

levitation exhibits low load capacity compared to the plastic one. It was concluded that vibrations 

of a magnet levitated above the superconductor can induce the transition from plastic levitation 

to an elastic one. 

The rotational field component causes the levitated superconductor to rotate. Rotational 

frictional motion of flux lines is likely to be an origin of the torque developed. Frictional torque 

developed during rotation of the superconductor is low compared to the torque developed by 

the rotational field. Instability of the rotating superconductor in a horizontal plane restricts the 

maximal rotational frequency. A new type of motor based on the superconductor levitated rotor 

was proposed. 

REFERENCES 

1. Shapira, Y., C. Y. Huang, E. J. McNiff, Jr., P. N. Peters, B. B. Schwartz, M. K. Wu: 

Magnetization and magnet suspension of YBa2Cu30x-AgO ceramic superconductors. J. Mag. 

& Mag. Materials., vol. 78, 1989, pp. 19-30. 

2. Brandt, E. H.,: Friction in levitated superconductors. Appl. Phys. Lett., vol. 53, no. 16, 1988, 

pp. 1554-1556. 

3. Bean, C. P.,: Magnetization of hard superconductors. Phys. Rev. Lett., vol. 8, no. 6, 1962, 

pp. 250-253. 

4. Moon, F. C., and Chang, P.-Z.,: High-speed rotation of magnets on high Tc superconducting 

bearing. Appl. Phys. Lett., vol. 56, no. 4, 1990, pp. 397-399. 

5. Matsushita, T.,: Electromagnetic phenomena and hysteresis losses in superconductors. 

Cryogenics., vol. 30, 1990, pp. 314-323. 

6. Weinberger, B. R., Lynds, L., Hull, J. R.: Magnetic bearings using high-temperature superconductors: some practical considerations. Supercond. Sci. Technol., vol. 3 1990, pp. 381-388. 

274 
-

LEVITATION POINTS 

,-------c::==J 

~L c=J --~---~ 

RING-SHAPED MAGNET 

o 

...l 

\OJ 

1i: 

TIME 

u 1 ________ _ 

1= 

\OJ 

Z 

" < 

,; 

TIME 

1. Apparatus for levitation experiment in the variable 

magnetic field 

Vl 

t:.i 

~ 

1.5 

E= 

z 1.0 e 

o 

-

Eo-

< 

>< 

< ..J 0.5 ~ 

CI:: 

e 

e 

___ e_e_ e_e_ 

50 100 150 200 250 3()0 

FIELD FREQUENCY, liz 

2. Field frequency dependence of the relaxation time of 

the superconductor to the unique position of stable 

levitation in elastic levitation regime. 

275 
276 

Ul 

> 

O.9~ I 

1 

~ 

e- __ 

e._e--e, ~ /e -e, .. '" , ' -e_-e ~ 06: e ' --e-_e-.. "' . ~ I: e / .. I ,i " / ~ J el ' I 

- -I I, , .e 

Q) 03-1 I i { e-.. _e--e~ 

" 

,~ f . ~ • '/ ,.-e-- _ 

= 

!I I 

_ ____________ ~--~'L-_Te~------------ .s 0- /e / ~ ~ ~ I 

~ ~ e- e f'Of-03-i _e_e--.-e-- I 

... . ; . : " ~ -J I '. Q) J/ 1/ = ~ ,r eJl-0.6 --, -e-e-____ ,e, ~ ~ e--e_ _~. ~ 1 -e-e--e 

I -0.9l'---L __ ~' ! 1 I 

'-0.5 -0.3 -0.1 0 0.1 0.3 

I 

0.5 

Applied field ( kOe) 

3. Hysteresis loop of YBCO superconductor used in the 

levitation experiment. T=77K. 

r 

GLOBAL EQUILIBRIUM 

POINT 

LOCAL EQUILIBRIUM 

POINTS 

LEVITATION HEIGHT 

mg 

4. Relaxation of superconductor to the unique position of 

levitation in elastic levitation regime. Alternating 

field has the form of rectangular pulses. 
SUPERCONDUCTOR 

\ 

--

~\ 

~ 

INFRARED 

DETECTOR 

INFRARED TOP VIEW Y 

t BEAM 

LlOUID 

NITROGEN 

MAGNET 

-. -~ ~ /' 

SUPERCONDUCTOR 

5. Apparatus for rotation experiment. 

I Qr-----------------------------------------------------------, 

a 

• .. A 

.. 

.. .. • .. 

.. • .. 

9~----~----_.------~~----------~r_------------------r_----~ eta 119 12 14 16 'I 

TIME, S 

6. Active deceleration and acceleration of rotating 

superconductor induced by rotational magnetic field 

(50 Hz, 100e). 

X 

277 
278 

4r-----------------------------------------------------------~ 

N 3 

--

• - WEAK PINNING SAMPLE 

• - STRONG PINNING SAMPLE 

• 

• 

• 

• 

TIME, S 

7. Superconductor rotation frequency decay in static 

magnetic field. 
N92-27736 

Hybrid Superconducting Magnetic Bearing (HSMB) For High Load Devices 

C. K. McMichael(a) , K. B. Ma, M. A. Lamb(b) , M. W. Lin(c) , L. Chow, 

R. L. Meng, P. H. Hor, and W. K. Chu 

Texas Center for Superconductivity at the University of Houston (TCSUH) 

(a) C. K. McMichael is an undergraduate fellow from the University of Houston. 

(b) M. A. Lamb is an undergraduate fellow from the University of Houston. 

(c) M. W. Lin is an undergraduate fellow from the California Institute of Technology. 

279 
SUMMARY 

Lifting capacities greater than 41 N/cm2 (60 psi) at 77 K have been 

achieved with a new type of levitation (hybrid) using a combination of 

permanent magnets and high quality melt-textured YIBa2Cu307-5 (YBCO). 

The key concept of the hybrid superconducting magnetic bearing (HSMB) is 

the use of strong magnetic repulsion and attraction from permanent 

magnets for high levitation or suspension forces in conjunction with a 

superconductor's flux pinning characteristics to counteract the inherent 

instabilities in a system consisting of magnets only. To illustrate this 

concept, radial and axial forces between magnet/superconductor, 

magnet/magnet, and magnet/superconductor/ magnet, were measured 

and compared for the thrust bearing configurations. 

INTRODUCTION 

The objectives of developing a more viable high temperature 

superconductor (HTS) bearing are to achieve higher stiffness and higher 

load lifting capacity while maintaining high vibration damping and low 

rotational dissipation at a temperature of 77 K. The origin of the 

inefficiency in previous systems utilizing active magnetic suspension, such 

as electrical feed back controls or complex pneumatic gas bearing systems, 

lies in their continuous energy consumption. Superconductors in their 

present-day bulk form are good candidates for simple superconducting 

magnetic bearing (SMB) devices [1, 2, 3] such as a levitated magnet over a 

disk ofYBCO. However, this simple type of bearing arrangement yields 

limited levitation, limited suspension, and low magnetic stiffness. This is 

due to the finite rotor magnetic field and the finite Jc of the 

superconducting stator. In view of the fact that zero field cooling (ZFC) 

results in force creep (gap creep) [4] and low radial stiffness for such 

magnetic bearings, field cooled conditions (FC) should be addressed. In 

addition, it is impractical to cool the bearing elements (superconductors) 

before assembling the bearing device (magnetic rotor). Under FC 

conditions, a negligible static levitation force occurs when no extemalload 

is applied in any direction. In contrast, a much higher magnetic stiffness 

for radial displacement is found in FC as compared to ZFC conditions. 

PRECEDING PAGE BLANK NOT filMED 

281 
282 

In this report, a simple approach to improve upon the limitations of the 

5MBs is presented. Higher levitation, suspension, and stiffness forces are 

needed to implement 5MBs into a wider range of applications. This is 

achievable in a passive magnetic bearing system composed of strong 

permanent magnets with a design that alleviates the inherent instability as 

stated in Earnshaw's theorem [5]. The HSMB design overcomes the 

magnet/magnet instability by using high quality continuously processed 

melt-textured YBCO material [6] placed between the rotor and stator 

magnets. This design allows for greater stiffness values and maintains a 

much higher static load-lifting capacity compared to 

magnet/superconductor bearings. 

HTS 

FC 

ZFC 

5MB 

HSMB 

Tc 

J c 

YBCO 

ABBREVIATIONS 

high temperature superconductor 

field cooled 

zero field cooled 

superconducting magnetic bearing 

hybrid superconducting magnetic bearing 

critical temperature 

critical current density 

y lBa2Cua07-o 

EXPERIMENTAL 

A dipole permanent magnet (1.27 cm length, 0.95 cm diameter, 0.426 T 

surface field) used in a rotor was attached to a static force measurement 

system [7] incorporating an elastic beam with strain gauges. This 

cantilever beam was fixed to a motorized stage controlled by a computer. A 

stationary cold stage held fixed on an optical table was used with liquid 

nitrogen (77K) to cool the superconductor and, when needed, an opposing 

permanent magnet. The collected data was converted into static forces and 

force hystereses versus displacement, for both radial and axial movement 

with the thrust bearing configuration. 

For comparison between ZFC and FC conditions, the axial force creep 

and the radial stiffness between the rotor magnet and a YBCO disk (0.47 cm 
thick, 2.23 mm diameter) was measured and the results are displayed in 

Figs. 1 and 2, respectively. 

4.9ir---~~-~~-~-~--~-

4.7 

_ 4.6 ~ 

2. 

o ZFC HTS 

• FC HTS 

2.1p!-~----~-----~":"'-----I 

1 00 200 300 400 500 600 700 800 900 1000 

Elapsed Time (s) 

Fig. 1 Force creep - force between magnet and HTS as a function of time 

under ZFC and FC conditions. 

3r---~--------------------~ 

2.5 

2 

1.5 

-.5 

-1 

-1.5 

-20 2 

o ZFC HTS 

• FC HTS 

Displacement 

4 6 8 10 

X- Xo (mm) 

Fig. 2 Radial hysteresis loops - change of force from the initial setup value 

(different for FC and ZFC cases) as magnet is displaced across an HTS disk, 

as a function of the displacement from the initial point. 

283 
284 

Radial and axial force hysteresis measurements were also taken from the 

same YBCO disk starting at a fixed distance of 0.25 mm from the surface of 

the rotor magnet. These results are shown in Figs. 3-5. 

2.25:r----------~--------r 

2 

1.75 

1. 

~1.2 

Lf 

I 

u.. .75 

.5 

.2 

o Hybrid 

• 

.4 .6 .8 

X-Xo (mm) 

Displacement 

~T ~+ 

1.2 

Fig. 3 Axial hysteresis loops - change of force from the initial setup value 

(different for Fe HTS and hybrid cases) as the magnet is pressed onto the 

HTS disk, as a function of the displacement from the initial point. 

1.4r--~--~------~-------t 

1. 

.8 

~ .6 

Lf 

~ .4 

Displacement 

.-

Displacement • --- n<F-""-,f-7;r-..~--- 0 Hybrid --11 

• Fe HIS _HIS. 

-.40 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 2 

X-Xo (mm) 

Fig. 4 Radial hysteresis loops - change of force from the initial setup value 

(different for Fe HTS and hybrid cases) as the magnet is displaced across 

the HTS disk, as a function of the displacement from the initial point near 

the center. 
A pennanent magnet (0.95 cm diameter, 1.27 cm length, 0.416 T surface 

field) was fixed at the bottom of the apparatus as a stator with polarity 

attracting the rotor magnet. At 77 K, measurements (Fig. 6) were taken of 

the negative shear stiffness (N/mm) and correlated directly to the repulsion 

force. 

2.5 

2 

z 

--; 1. l.J.... 

I 

l.J.... 

2 

o Hybrid 

• Fe HTS 

4 6 8 10 

X-Xo (mm) 

Fig. 5 Radial force versus displacement with minor hysteresis loops -

change of force from the initial setup value (different for Fe HTS and hybrid 

cases) as the magnet is displaced across the HTS disk, as a function of the 

displacement from the initial point near the center. 

1.0t------~----~----~ 

E 

E .8 ~ en 

en 

<l> 

c: .6 :::: 

C75 

<l> 

> .4 ~ C) 

<l> 

z 

.2 

00 2 4 6 8 10 12 

Repulsive Axial Force (N) 

Fig. 6 Stability versus thrust for the stator magnet - the negative stiffness in 

the radial direction is used as a measure of the instability that has to be 

overcome if the stator magnet is to provide a given amount of thrust. 

285 
286 

Then the rotor magnet was held fixed over a superconductor placed on top 

of the stator magnet to form a prototype HSMB (magnet / superconductor / 

magnet) non-rotating setup. Radial and axial force hysteresis 

measurements were made for this HSMB setup with a 6 mm gap between 

both magnets and compared with the corresponding results for the Fe 5MB 

in Figs. 3-5. 

RESULTS AND DISCUSSION 

It is known that the force between a magnet and an HTS disk is much 

smaller under FC conditions than under ZFC conditions. This is no longer 

a disadvantage for FC conditions, since our central idea is to use magnets 

to provide the thrust force, with the HTS providing the required 

stabilization. For example, our FC 5MB provided practically zero lifting 

force, while the HSMB can provide up to 8.88 N. What we have shown in 

Fig. 1 is that the force creep under similar load is almost the same for both 

ZFC and FC conditions. The time scale in which the creep occurs is also 

similar. In 10 minutes, the magnetIHTS force decreased by 5.3% of its 

initial value for ZFC conditions, whereas, the decrease was only 4.8% for 

FC conditions. Since forces required for stabilization purposes can be 

expected to be smaller than that of the main thrust, this translates into an 

advantage for the FC case. This is further supported by our measurements 

of the retaining force against a displacement in the radial direction, as 

shown in Fig. 2. The stiffness that comes from FC conditions is bigger, and 

so is the maximum force that can be sustained before it yields. 

Since we would have to supply the required thrust using additional 

magnets, the next question concerns whether the presence of this extra 

magnet would annul these advantages of higher stability. To investigate 

this, we have put a magnet below the HTS disk and measured changes of 

the forces as the rotor magnet above the HTS disk is displaced in the axial 

and radial directions. The negative stiffness (instability) in the radial 

direction due to this additional stator magnet is plotted as a function of the 

thrust that it can provide at various gap distances in Fig. 6. This instability 

is the inherent instability if we used the magnets only. This is to be 

overcome by placing the HTS disk in between the two magnets. We have 

definitely shown that this can be accomplished in Figs. 4 and 5. The effects 
of the stator magnet are not apparent until displacements as large as a 

significant fraction of a millimeter from the original position are reached. 

Although there is no instability to be overcome in the axial direction, we 

have also included measurements in this direction in Fig~ 6, to show the 

final stiffness that can be achieved in the magnetisuperconductor/magnet 

system. This axial stiffness is similar to that of the magnet/magnet system 

with the same gap distance between magnets, but is definitely inferior to 

the magnet/magnet system that has the same gap as the top 

magnetisuperconductor pair in our hybrid system. 

In conclusion, we have shown that the HSMB allows us to increase the 

thrust over that which can be provided by 5MBs. The stiffness that can be 

achieved is similar to magnetimagnet systems with the same 

magnet/magnet gap distance. Thus, higher stiffnesses can be attained if 

we decrease this gap, but then the thickness of the intervening HTS disk 

would be decreased accordingly. The radial stability would be 

compromised. An optimum HTS thickness would have to be determined. 

REFERENCES 

1. F. C. Moon and P.-Z Chang, Appl. Phys. Lett. 56, 397 (1990). 

2. B. R. Weinberger, L. Lynds, and J. R. Hull, Supercond. Sci. Technol. 3, 

381 (1990). 

3. C. K. McMichael, K. B. Ma, M. W. Lin, M. A. Lamb, R. L. Meng, Y. Y. 

Xue, P. H. Hor, and W. K. Chu, to be published in Appl. Phys. Lett. 

4. F. C. Moon and J. R. Hull, 25th IECEC 3, 425 (1990). 

5. S. Earnshaw, "On the Nature of the Molecular Forces which Regulate 

the Constitution of the Luminferous Ether," Trans. Camb. Phil. Soc. 7, 

pp. 97-112, (1842). 

6. R. L. Meng, C. Kinalidis, Y. Y. Sun, L. Gao, Y. K. Tao, P. H. Hor and C. 

W. Chu, Nature 345, 326 (1990). 

7. F. C. Moon, M. M. Yanoviak, and R. Ware, Appl. Phys. Lett. 52,1534 

(1988). 

287 
N92-27737 

CHARACTERIZATION 

OF 

SUPERCONDUCTING MAGNETIC BEARINGS 

( Dynamic stiffness and damping coefficient in axial direction ) 

Ryoichi Takahata, Hirochika Ueyama 

Koyo Seiko Co., Ltd. 

24-1 Kokubuhiganjo, Kashiwara, Osaka 582, Japan 

Tsutom Yotsuya 

Osaka Prefectural Industrial Technology Research Institute 

2-1-53 Enokojima, Nishi-ku, Osaka 550, Japan 

PRECEDING PAGE BLANK NOT FILMED 289 
ABSTRACT 

High-Tc superconductor as a stator and permanent magnets for a rotor were assembled into a 

superconducting magnetic bearing. The dynamic stiffness and the damping coefficient of the 

supercpnducting magnetic bearing in axial direction were measured. The dynamic stiffness depended on 

an axial gap between superconductor and permanent magnet. The superconducting magnetic bearings 

are advantageous for a passive bearing, because they have a vibration damping effect that a permanent 

magnet bearing does not have. The tendency of its vibration damping coefficient indicated an increase 

as the resonant frequency increased. 

INTRODUCTION 

Since a high-Tc superconductor was discovered, many efforts have been made on developing a 

superconducting magnetic bearing (SMB) (ref.1). The 5MB has been appreciated by several factors, 

levitation pressure, dynamic stiffness (ref.2), damping coefficient, and the rotational speed (ref.3). 

Recently a melt process on bulk YBa2Cu30x has been improved (ref.4) and a levitation pressure 

has also become large.'" The 5MB has been able to support a rotor weighing about 1 kg, rotating 

at a speed of 5,000rpm. t 

One of the purpose of this work is to examine the dynamic stiffness and the damping coefficient 

of 5MB in axial direction. They are very significant for bearing design. 

EXPERIMENT 

Construction of 5MB 

A superconducting magnetic bearing can be assembled by using high-Tc superconductor as a 

stator and permanent magnets for a rotor. The superconductor used in this test was a bulk YBa2Cu30x 

prepared by quench and melt growth (QMG) process. The diameter of the bulk was 43mm and 12mm 

in thickness, and was made by Nippon Steel Corporation. The rotor had 4 permanent magnets (Nd-FeB, Sumitomo Special Metal Co., Ltd.). The surface flux density of the magnets was 0.45T. Each of the 

permanent magnets has 20mm in diameter and 4mm in thickness. 

* K.Miyamoto and K.Sawano et al. :"Quench and Melt Growth (QMG) Processed Superconducting Materials 

t for Levitation and Magnetic Flux Trapping", Submitted to Proc. ISS'90 (1990) in Sendai, Japan 

R.Takahata, H.Ueyama and T.Yotsuya: "Load Carrying Capacity of Super conducting Magnetic 

Bearings", Submitted to Proc. The International Symposium on Application of Electromagnetic Force:; 

(1991) in Sendai, Japan· 

PRECEDING PAGE BLANK NOT FILMED 

291 
-z 

-

X 

LL 

Q) 

v 

.... 

0 

LL 

v 

',t:i 

Q) 

s::: 

tn 

CO 

:E 

10 

5 

0 

-5 

-10 

o 

N 

S 

• I YBCO I 

123 

Axial Gap, Z (mm) 

Fig.1 Static stiffness of 5MB 

4 

The maximum carrying load capacity of the tested bearing was 5 kg in axial direction and the 

levitation pressure was 3.4N/cm2, Its value was measured by means of road cell, when the magnet 

approached the surface of bulk YBa2Cu30x cooled down to liquid nitrogen temperature. 

The static stiffness of tested bearing was 9N/mm as shown in Fig.1. It was also measured by 

means of road cell when the magnets were moved slowly in axial direction after the bulk YBa2Cu30X 

was cooled down by liquid nitrogen at 2mm axial gap between magnet and superconductor. 

Test equipment 

The apparatus shown in Fig.2 was constructed to measure the vibration damping and t.he 

dynamic stiffness of 5MB in axial direction. A shaft having permanent magnets on its lower side was 

located vertically above the bulk YBa2Cu30x. The shaft was able to be supported with no mechanical 

contact by active magnetic bearings in radial direction and by 5MB in axial direction. To decrease the 

damping effect brought about by eddy current, conducting materials were located as far from permanent 

magnets as possible. The total mass of the shaft was 1.118 kg. 

292 

FFT 

Analyzer 

I I '--"""--fl Active . Magnetic 

Bearing 

Liquid 

Nitrogen 

Fig.2 Dynamic stiffness measuring apparatus 
_ 0.5 

E 

E 0 

-

+J 

~ -0.5 

E 0.5 

Q) 

v 

CO 

0. 0 VI 

o 

-0.5 

(a) 5MB 

(b) PMB 

j~NwmMNWWJVWV ~--------------------~ o 2.0 

Time (sec.) 

Fig.3 Vibration of shaft in axial direction; 

(a) in the case of 8MB, (b) in the case of PMB 

Test Procedure 

The shaft was supported by active magnetic bearings in radial direction and fixed at initial gap 

Zo in axial direction; then the bulk YBa2Cu30x was cooled down to about 17K by liquid nitrogen. 

After above field cooling, the shaft was released and supported with no mechanical contact. At that 

time an axial gap of 8MB decreased to Z<Zo. That is the equilibrium position. 

RESULT AND DISCUSSION 

8MB model in one degree of freedom 

A vibration of the shaft in axial direction was measured by gap sensor when an external impulse 

force Fz acted on the shaft that was supported by 8MB. It is shown in Fig.3(a). Fig.3(b) shows a 

vibration of the shaft supported by a permanent magnet bearing (PMB) by the same procedure. The 

vibration damping of 8MB was larger than that of PMB using repulsive forces of permanent magnets. 

Therefore an 8MB model in one degree of freedom can be shown in Fig.4(b). The motion of this model 

can also be described by equation (1). 

mz + cz + kz = Fz (1) 

In this equation m IS the mass of shaft, k is the spring constant and c is the damping coefficient 

respectively. 

(a) 5MB model 

c 

(b) One degree 

of freedom 

Fig.4 8MB model in 1 degree of freedom 

293 
-

E 105 

--Z 

-

~ 104 

CI 

0 

..J 

~ 103 VI 

VI 

OJ 

s:: 

- 102 -',p 

VI 

0.1 1 10 100 

Frequency, Log f (Hz) 

Fig.5 Dynamic stiffness vs vibration frequency (simulation) 

The dynamic stiffness K of axial displacement for external force Fz can be also described by 

equation (2). 

I K I = V ( k - mw 2 ) 2 + w 2 c 2 (2) 

where w is the angular velocity. Arbitrary values (k=1.6, 3.7, 5.4,11.5,14.2, 20.0X103N/m, c=O.I, 

1.0, 10.0Ns/m) in equation (2) are simulated and the results are shown in Fig.5. The minimum value 

of dynamic stiffness appears at resonant frequency Wo that depends upon only spring constant k 

(wo = vklm). And that minimum value is decided by the damping coefficient c. So it is possible to 

estimate the damping coefficient by means of measuring dynamic stiffness. 

Measured spring constant, k 

When the shaft was struck by an impulse hammer in axial direction, the axial vibration of it was 

measured at several gaps of Z. The values of Z of 5MB were 0.8, 1.3, 1.9 mm which corresponded to 

the initial gap Zo = 2.0, 3.0, 4.0mm respectively. Z did not change after the hammering 

Spring constant of axial direction is able to be given by equation (3) 

k = 4n2 • m . fo 2 (3) 

where fo is the resonant frequency. 

The value of spring constant k calculated from equation (3) using the measured fo is shown in 

Fig.6. The spring constant increased as the axial gap decreased. The value of spring constant was 

15,000N/m at Z= Imm. 

Measured damping coefficient, Cs 

It is also possible to estimate damping coefficient Cs from the decreasing characteristics of 

vibration amplitude. Damping coefficient Cs can be described by equation (4). 

Cs = 2m·p (4) 

where p is a natural logarithm of damping ratio per second in vibration amplitude. 

Measured damping coefficient, Cs is shown in Fig.7. Damping coefficient Cs also increased as an 

axial gap decreased. 

294 
E 30 

-

Z 

", 

o 

... 

X 

_ 20 -

~ 

..... 

r::: 

ro t; 10 -

r::: 

o 

u 

O'l 

I 

-

-

r::: o L-______ ~I ________ ~I ______ ~ 

o 2 3 

Axial Gap, Z (mm) 

-E -

VI 

Z 

-

..... 

r::: 

(I) 

'0 

:E 

(I) 

o 

u 

O'l 

r::: 

c.. 

E 

ro 

o 

6 r-------,--------,-------. 

4 

2 

o L-______ ~ ______ ~ ______ ~ 

o 1 2 3 

Axial Gap , Z (mm) 

Fig.S Change in spring constant with axial gap Fig.? Change in damping coefficient with axial gap 

But in this test equipment. Cs included the intrinsic damping coefficient Ci in addition to the 

damping coefficient C(SMB) due to 8MB was caused by eddy current loss and air resistance in a vibration 

of the shaft. It was clear that the vibration of the shaft supported by the permanent magnet 

bearing, not having a damping factor, had actually a little damping as shown in Fig.3(b). The damping 

coefficient C(SMB) is given by equation (5). 

C(SMB) Cs - Ci (5) 

Measured dynamic stiffness, K(w) 

We also measured dynamic stiffness K(w) of 8MB directly by means of FFT analyzer and 

frequency changeable external force Fz{w) acting on the shaft with no mechanical contact. That force 

was attractive force generated by an electromagnet and swept sine-wave excitation current l(w). 

The dynamic stiffness can be measured as the transfer function from the external force Fz«(,» to 

the displacement Z(w) of the shaft as shown in equation (6). 

K(w) = Fz(w) I Z(w) (6) 

0.1 10 100 

Frequency I Log f {Hz} 

Fig.8 Dynamic stiffness vs vibration frequency in the 8MB and PMB 

295 
The measured dynamic stiffness of 5MB and PMB are shown in Fig.8. The damping coefficient of 

PMB was constant independently of frequency by judging from the minimum value of dynamic stiffness 

in comparison with Fig.5. Its value of damping coefficient was 0.6Ns/m and seemed to indicate the 

value of Ci' while the values of Cs were 1.0, 1.3, 1.9 Ns/m at resonant frequency fo = 16.0, 17.75, 

21.0Hz respectively, so C(SMB) were calculated from equation (5), C(SMB)=0.4,0.7,1.3(Ns/m). The value of 

C(SMB) seems to increase as the resonant frequency fo increased. 

These values of Cs in this test are a little smaller than the damping coefficients cs, measured by 

hammering, shown in Fig.7, because here K(w) was measured by taking I(w) instead of Fz(w) in 

equation (6). As I(w) is swept sine-wave excitation current, the actual Fz(w) acting on the shaft in this 

test is proportional to I(w)2 and is larger than I(w) for vibration at resonant point so that the 

measured dynamic stiffness appearing in Fig.8 seems to be a little smaller than actual dynamic 

stiffness. Therefore we think it is necessary to linearize I(w) for Fz(w) in the next step. 

Bearing design 

Measured damping coefficients of 5MB were smaller at least by one order of magnitude than that 

of active magnetic bearings. It is very important for bearing design to improve the damping coefficient. 

This damping factor of 5MB seemed to be dependent on hysteresis loop shown in fig.I. Therefore an 

improvement of YBa2Cu30x materials with a larger hysteresis loop and stiffness than that is expected for 

one of the ways to develop a practical 5MB. If the material improvement is i.mpossible, it will be 

necessary to add another damping mechanism for 5MB to be used in a cryogenic environment. 

CONCLUSIONS 

Dynamic characteristics of the superconducting magnetic bearing, using high-Tc superconductor 

as a stator and a permanent magnet for a rotor, in axial direction were measured. 

(1) Dynamic stiffness and damping coefficient of 5MB were dependent on an axial gap. 

(2) 5MB had a damping factor that had never been vbserved on PMB. 

(3) Damping coefficients of 5MB increased as the resonant frequency increased. These values were 

smaller at least by one order of magnitude than that of the active magnetic bearing. 

It is very significant for bearing design to clarify the dynamic stiffness and damping coefficient 

of 5MB. Accordingly the test equipment will be more improved to measure those factors exactly. 

ACKNOWLEDGMENTS 

The authors wish to thank Dr.K.Sawano and Mr.K.Miyamoto of Nippon Steel Corporation for 

supplying bulk YBa2Cu30x in this test. 

REFERENCE 

1. F.C.Moon and P.-Z.Chang: AppJ. Phys. Lett. 56 (4), 397 (1990) 

2. F.C.Moon, K-C.Weng, and P-Z.Chang: J. AppJ. Phys. 66(11) (1989), 5643 

3. R.Takahata and T.Yotsuya: IEEE Trans. on magn., 27 (2), 2423 (1991) 

4. M.Morita, K.Miyamoto, and K.Sawano et al. : Physica C 172 (1990), 383 

296 
Session 6 

BEARINGS 2 

Chainnan - Claude Keckler 

NASA Langley Research Center 

297 
N92-27738 

FEASIBILITY OF MAGNETIC BEARINGS FOR ADVANCED GAS TURBINE ENGINES· 

David Hibner. Senior Project Engineer 

United Technologies Corporation. Pratt & Whitney 

East Hartford. Connecticut 06108 

Lewis Rosado. Project Engineer 

Wright Laboratory 

Wright-Patterson AFB. Ohio 45433 

PRECEDING PAGE BLANK NOT FllMfD 

299 
ABSTRACf 

The application of active magnetic bearings to advanced gas turbine engines will provide a product with major 

improvements compared to current oil lubricated bearing designs. A re-thinking of the engine rotating and static 

structure design is necessary and will provide the designer with significantly more freedom to meet the demanding 

goals of improved performance, increased durability, higher reliability, and increased thrust-to-weight ratio via engine 

weight reduction. The product specific technology necessary for this high speed, high temperature. dynamically 

complex application has been defined. The resulting benefits from this innovative approach to aircraft engine rotor 

support and the complementary engine changes and improvements have been assessed. 

INTRODUCfION 

The aircraft gas turbine engine represents the most challenging application of active magnetic bearings. It is the 

most technologically advanced, high speed rotating machinery operational in the world today. Compared to all other 

turbomachinery, the gas turbine engine demonstrates higher levels and larger cyclic variations of stress and 

temperature primarily because of the stringent requirements for thrust/weight, fuel consumption, reliability, and 

durability. Rolling element bearings, both ball and roller, have always been used for turbojet and turbofan gas turbine 

engine main shafts because of their long service life. high load capacity, tolerance to oil contamination, and their 

survivability to short-term loss of oil. A change from this fundamental and proven technology will only result if 

significant benefits of a better technology can be demonstrated and if the limits of rolling element bearings are 

reached. 

Studies made by Pratt & Whitney and the U. S. Air Force have shown the feasibility of using main shaft active 

magnetic bearings as a replacement for oil lubricated rolling element bearings in advanced military aircraft engines. 

The studies have also shown that Significant benefits including weight reduction, improved performance, improved 

durability, reduced external vibration, and unlimited bearing life are possible. Technology readiness by the turn of the 

century can be achieved by maturing existing technology. Magnetic bearing technology has advanced significantly in the 

past 25 years, particularly in recent years with digital controls, highe~ power density, and more power-efficient designs. 

Magnetic bearings have been applied successfully to over 100 large ground-based turbomachines such as natural gas 

compressors, turbo expanders, and gas, steam, and water turbines. This equipment is in operation worldwide and has 

demonstrated high reliability, improved performance, durability, and unexcelled vibration control with many years and 

hundreds of thousands of hours of successful operation. Large ground-based turbomachinery, among the 1500 + pieces 

of rotating equipment with magnetic bearings operating today, are cited because of their similarity to gas turbine 

engines. While these machines with S2M or MBI magnetic bearings compare well with gas turbine engines in size, 

weight, power, speed, thrust and radial loads, and general operation, there are major differences in gas turbine engine 

operating temperatures, dynamic loads, and other factors unique to flight conditions. It is these unique requirements 

that need to be addressed during the next ten years. 

*Magnetic Bearing Feasibility and Development, Wright Laboratory Contract F33615-87-C-2701. 

PRE~OING PAGE BLANK NOT F1LM!:D 301 
The need for an improved bearing for gas turbine engines has evolved from future fighter aircraft requirements of 

increased thrust-to-weight ratio over the best engines available today. A 100% increase in this important engine 

parameter must be achieved while increasing fuel efficiency in order to increase range, improve engine component 

durability, and reduce life-cycle cost. To achieve these goals, the Air Force has embarked on a major long-range 

initiative. The Integrated High Performance Thrbine Engine Technology (IHPTET) Initiative is aimed at developing 

the technology necessary to meet future weapon system propulsion requirements. Aggressive propulsion system goals 

have been jointly established by the Air Force and Pratt & Whitney and have set the focus of the engine component 

technology initiatives. Conceptual far-term engine designs have been initiated to determine the overall engine cycle 

flow path geometry and technology features that are needed to satisfy the above goals. These studies have indicated 

that the resulting rotor speeds will be significantly increased over the current st~te-of-the-art designs. Consequently, 

unconventional main shaft support systems, such as magnetic bearings that are able to operate at higher speeds and 

temperatures, become very desirable. In addition, magnetic bearings have better damping characteristics than squeeze 

film dampers to control shaft dynamics and reduce engine vibration. 

Advanced engine designs which are being studied under the IHPTET Initiative will require advancements in rolling 

element bearing technology that may not be possible within the required time frame. Rolling element bearings used in 

current production engines are operating at speeds up to 2.4 million DN (DN = shaft diameter in mm x shaft rpm). 

With the recent development of a high fracture tough bearing material (MSO NiL), it is now feasible to operate rolling 

element bearings at speeds up to 3.0 million DN. 'The advanced engine designs being studied under the IHPTET 

Initiative will require the bearings to operate well above 3.0 million DN and at temperatures that exceed the bearing 

material capability (hot hardness) and the liquid lubricant thermal stability. Bearing compartment seal durability will 

be adversely affected by a high temperature environment, and higher engine speeds will produce higher seal sliding 

velocities and cause seal wear problems. Blade tip and labyrinth seal designs will have to be improved to control 

operating clearances. In addition, these engines will require bearings that have superior fatigue life and better 

damping characteristics. Magnetic bearings have the potential for meeting these requirements since they do not 

require a liquid lubricant and there is no physical contact between the rotor and the mount structure. Consequently, 

there is no wear mechanism to limit operational life. 

Contained herein are the results of the Air Force sponsored magnetic bearing feasibility program. It includes, in 

addition to the potential benefits of gas turbine engines with active magnetic bearings, the results of a literature search 

which was conducted to define the state of the art, a feasibility study wherein advanced magnetic bearings were 

designed for an advanced military aircraft engine, and a technology requirement assessment which defined the 

technology necessary to further enhance the application of magnetic bearing rotor support systems for Air Force 

propulsion needs. 

POTENTIAL BENEFITS OF GAS TURBINE ENGINES WITH ACTIVE MAGNETIC BEARINGS 

The active magnetic bearing represents an innovative approach to aircraft engine rotor support with the potential to 

provide significant benefits not possible with rolling element bearings. An engine with a full complement of radial and 

thrust magnetic bearings combined with electrical accessories would add a new dimension to the design of aircraft gas 

turbine engines. This magnetic bearing engine would incorporate many electrical components, some of which are 

necessary because of the elimination of a mechanical power takeoff, i.e., the tower shaft and the accessory gearbox. 

An integral, main shaft starter/generator and electric fuel pumps for both main and augmentor supplies are required. 

Other components such as electric vane and nozzle actuators become attractive for this "mostly" electric engine. The 

successful application of magnetic bearings would result in future engines with the following features: 

• Reduced engine weight 

• Elimination of oil and hydraulic systems 

• Improved fire/safety survivability 

• Simplified, less costly bearing compartment seals 

302 
• Elimination of the tower shaft 

• Elimination of the accessory gearbox 

• Higher rotor speed potential 

• Reduced blade tip and seal clearances 

• Reduced rotor-to-case deflections due to aircraft maneuvers 

• Reduced secondary airflow for cooling and thrust balance 

• Reduced bearing power consumption 

• Superior engine vibration response control 

• System health monitoring 

• Virtually unlimited bearing life. 

These features would reduce the propulsion system fuel consumption and maintenance requirements, and increase 

thrust-to-weight and reliability, thus providing greater aircraft capability with lower life cycle cost. The improvements 

in reliability, durability, and vibration control are exemplified by the dramatic Change in the engine external 

components relative to a conventional engine of today, as is shown in Figures 1 and 2. The incorporation of magnetic 

bearings and other electrical components will produce an engine with significantly less plumbing and mechanical 

structure which is susceptible to vibration and fatigue failure. The elimination of a majority of the failure-prone 

hardware alone will provide a greater than 2:1 improvement in reliability. With the anticipated superior vibration 

control of magnetic bearings, the durability of the remaining structure (e.g., fuel and bleed air lines) will be 

significantly improved. Improvements in maintainability of the external engine structure are readily apparent primarily 

because of the resulting simplicity. The remaining components only include the engine and magnetic bearing 

electronic control system, electric fuel pumps and associated delivery systems, electric actuators, and the air bleed and 

service systems. 

Increased Thrust-to-Weight Ratio 

Among the most fundamental means to increase engine specific thrust and, therefore, thrust-to-weight is to 

increase the speed of the rotating components in the engine. Since the aerodynamic work interactions of the 

turbomachinery within the engine are proportional to the square of the tip speed of the blading, increased rotational 

speed has a dramatic effect on the performance of an engine. The stress levels in the blading material also increase 

with the square of the tip speed, thereby requiring improved materials with increased working stress levels and reduced 

densities. The current operating speed capability of rolling element bearings used in today's engines could be increased 

to values of 3.0 million DN if improvements in lubrication technology and the materials used in the elements, races, 

and cages are realized. While progress in rolling element bearing technology will continue, active magnetic bearing 

systems have already demonstrated DN values of more than 4.5 million, a significantly higher level. The limitation of 

operating speed and DN of a magnetic bearing is dependent upon centrifugal stresses generated in the materials used 

for rotor construction, and does not involve the frictional heating and fatigue limits associated with rolling element 

bearings. Considering recently demonstrated developments in magnetic bearing technology, step increases in rotor 

speed and gas turbine engine performance are believed to be achievable within the time frame consistent with IHPTET 

Initiative goals. Thus, higher speed, longer life turbine engines are achievable with active magnetic bearings. 

303 
304 

IOOZ1\.E 

ACTu.'ClIO 

vIEw rRO", BOTTOM 

Figure 1. Conventional Engine External Components 
EHGJNE ArT 

( ... GI ... E 'ORWARD 

VIFW f.""ROM BOTTO'" 

VARIABLE 

VAHE 

A(; TUATOR 

Figure 2. Magnetic Bearing Engine External Components 

Design and Aerodynamic Advantages 

The higher DN capability of magnetic bearings will increase the allowable bearing-limited speed for a shaft of a 

given size, or permit larger shafting for a specific operational speed, thus increasing shaft stiffness and providing more 

design freedom. Since magnetic bearings do not require lubrication, the overall engine design could be quite different. 

No oil tank, supply or scavenge pumps, oil piping or coolers would be required. Weight savings and additional design 

freedoms could accrue. Bearing compartment temperature limits related to lubricants could be raised significantly 

since magnetic bearings can be made to operate in temperature environments exceeding lOOO°F if magnetic material 

and insulation research continue to extend the temperature range of the most promising materials. Further design 

advantages in the use of magnetic bearings for aircraft gas turbine engines are possible by electronically varying the 

stiffness and damping of each bearing. The rotor could be made to rotate about the inertial axis rather than the 

305 
geometric axis, and thereby reduce the structural vibration caused by rotor imbalance. The axial position of the rotor 

could also be controlled by the magnetic thrust bearing. With more sophisticated digital controller algorithms, it will 

be possible to improve performance by closing blade tip and seal clearances in a manner similar to currently employed 

thermal methods, but more efficiently. 

Operational Impact 

Magnetic bearings in a high performance turbine engine will provide important operational benefits. The 

elimination of lubrication oil in an all-magnetic bearing engine has logistic and supply advantages, and eliminates the 

need for filters and the possibility of contamination. It also eliminates oil servicing and sampling. Bearing life is 

essentially unlimited, and higher temperature operation is possible. Energy losses associated with the friction and the 

lubrication systems in rolling or sliding element bearings are eliminated; the electrical power required for magnetic 

bearing operation is relatively small. Signals for system diagnostics already exist in the electronic control of the 

magnetic bearing. Both the radial and axial bearing control sensors may be used not only for VIbration and position 

control, but also for monitoring imbalance level. As rotor imbalance increases due to erosion or foreign object 

damage, the levels can be monitored to prevent set limits from being exceeded. SignalS proportional to bearing current 

can be used as measures of bearing load. Using these data, the net axial thrust load on the rotor can be determined. 

With magnetiC bearings, improvements in engine health monitoring will be possible. 

LITERATURE SURVEY OF MAGNETIC BEARING TECHNOLOGY (1988) 

A literature survey, which identified and defined the current state of the art relative to design, analysis, 

manufacture, operability and use of magnetic bearings, focused on bearing load capacity, damping characteristics, 

electronic control systems, power requirements, and size and weight of both the bearing and the control system. Of 

prime importance was determining future development trends in digital control technology, high saturation flux 

magnetic materials, high temperature insulation materials, and high strength rotor lamination materials. The literature 

survey showed three types of magnetic bearings: passive, active, and hybrid concepts. Passive magnetic bearings employ 

high-energy permanent magnets configured either for repulsion or attraction. Because of their low load capacity and 

lack of damping, these bearings were not considered suitable for aircraft engine applications. Active magnetic bearings 

of the "attractive force" type are the dominant design in most commercial installations. They employ closed-loop 

analog control systems. Hybrid magnetic bearings use both permanent magnets and electro magnets wherein the 

permanent magnets generate the static (bias) force and the electro magnets generate the dynamic force. Negative 

features of hybrid bearings are low stiffness and the need for larger air gaps to control permanent magnet related 

stabilities. However, because of the lower power consumption requirements, imaginative hybrid design configurations 

could have the potential to enhance significantly the application of these bearings for aircraft engine applications 

(Ref. 1). Because the current design philosophy of commercially operating active magnetic bearing systems is dictated 

by land-based applications, size and weight considerations do not playa primary role. These magnetic bearings and 

analog control systems are bulky and heavy and are not suitable for aircraft engine applications. The literature survey 

has, however, revealed that advanced magnetic materials, such as Supermendur, and coil current densities similar to 

those presently achieved in aircraft electric power generators can be used to design magnetic bearings with significant 

size and weight reductions necessary for aircraft engine applications. Order of magnitude reductions in control system 

size and weight are also achievable by replacing the analog controls with digital controls. Miniaturized digital controls 

with adaptive algorithms, which are necessary for the dynamically complex gas turbine engine, can be developed. 

These developments in control technology have the potential to provide weight and size reductions of the electric 

generators, heat exchangers, power amplifiers, and even the magnetic bearing structure. Key development areas, 

which are critical for the advancement of magnetic bearing technology for aircraft engines, include: magnetic bearing 

control technology, high saturation flux magnetic materials, high temperature insulation materials, and high strength 

rotor lamination materials. Major conclusions on each of these areas are discussed below. 

Magnetic Bearing Control Technology for Aircraft Gas Turbine Engines 

Most magnetic bearing controllers use analog circuits which have inherent size, weight, and versatility 

disadvantages. Digital controllers, however, have the potential to overcome many of the drawbacks associated with 
analog controllers and, therefore, will be more suitable for aircraft engine applications. Significant development effort 

would, however, be required before a miniaturized digital control system can be produced. The previously 

uncompetitive weight and size of magnetic bearing systems, compared with rolling element bearing systems, has 

precluded their application to rotor support in aircraft turbine engines. This literature survey showed that the basic 

technology now exists for implementing an aircraft magnetic bearing system with weight and size competitive with 

conventional bearings. Significant reductions in the magnetic bearing design loads result from using a microprocessor 

implementation of a model follower control strategy having disturbance estimation and eccentricity offset capabilities 

(Ref. 2). By forcing the rotor geometric center to orbit around its mass center during operation at any speed (including 

shaft critical speeds) and with a limited degree of imbalance (including blade loss), the magnetic bearing need only be 

designed to withstand aircraft maneuver loads. These loads are a small fraction of the rotor imbalance loads that must 

be reacted. The reduced loads made possible by this new control technology would permit significant reductions in 

weight and size of the magnetic bearings, their control circuitry, power amplifiers, and the generators needed to power 

them. The application of magnetic bearing systems to support the rotors of aircraft turbine engines should result in 

more predictable rotor damping, nearly zero dynamic force transmitted to the support structure, elimination of most 

in-flight shut-downs (IFSDs) caused by high engine vibration, and improved engine reliability (dual channel electronics 

with no single point failure). 

High Saturation Flux Magnetic Materials 

Iron-cobalt materials like Vanadium Permendur and Supermendur have immediate applications for significant size 

and weight reductions in active and hybrid magnetic bearings. Magnetic saturation flux densities of 2.4 teslas appear 

possible (Refs. 3-5). Thus, with small air gaps (10 mils), large weight reductions appear practical. Optimization design 

analyses will be necessary to determine achievable weight and size reductions, and development will be necessary to 

improve heat treatment procedures for optimal magnetic and mechanical properties. 

High Temperature Insulation Materials 

State-of-the-art high temperature winding insulation materials are ceramics, polyimides, polyesters, silicones and 

epoxy Novolac. While ceramics have up to 2000°C maximum useful temperature, the other high temperature 

insulation materials have maximum useful temperatures between 250°C and 315°C. Cracking problems in the ceramic 

and epoxy encapsulants may be handled using special curing schemes and fillers including glass microspheres. Vacuum 

pressure impregnation can eliminate cracking problems but provides less mechanical and chemical protection for the 

windings. Numerous IEEE and ASTM standard test procedures for electric rotating machine insulation may be used 

to evaluate high temperature insulation systems for active magnetic bearings. When operating requirements are 

specified, appropriate insulation can be selected and developed to provide the required life for aircraft engine 

environmental conditions. 

High Strength Rotor Lamination Materials 

Iron-cobalt-vanadium-nickel and specially heat treated iron-cobalt-vanadium alloys appear to be very attractive 

high speed rotor lamination materials. Flux densities of 2 teslas at 50 to 100 oersteds and yield strengths of 100,000 psi 

have been reported (Ref. 6). A commercially available iron-cobalt-vanadium-nickel alloy is Rotelloy, but the 

properties of Rotelloy are not well documented. Reported values of mechanical and magnetic properties were not 

referenced to any standard test procedures. Currently available alloys appear to be adequate for high DN rotor 

applications, but it will be necessary to document the heat treatment procedures and the reported mechanical and 

magnetic. properties. 

ENGINE AND MISSION SELECTION FOR THE FEASIBILITY STUDY 

Under an Air Force sponsored program, Pratt & Whitney conducted configuration definition and long-range 

planning studies to define required propulsion system technologies for future weapon systems. The study involved 

extensive Pratt & Whitney and airframer coordination to meet the IHPTET goals of doubling current propulsion 

system capability. Representative advanced engine preliminary designs capable of meeting the IHPTET goals, and 

307 
realistic missions for these engines were selected. Mechanical component operating conditions were also predicted. A 

far-term advanced engine, which had been optimized for a Mach 3.0 Interceptor Aircraft, was selected for the 

magnetic bearing feasibility study. The magnetic bearing system requirements in terms of bearing loads, bearing 

compartment size, operating temperature, bearing stiffness and damping, and shaft diameter and rotational speeds 

were predicted. These design requirements were dictated by the selected mission profile. This engine was selected for 

the magnetic bearing feasibility study because the bearing compartment temperatures and bearing loads were much 

higher than other engines, thereby dictating an advanced level of magnetic bearing technology to meet these stringent 

requirements. 

The far-term engine conventional bearing design incorporated five main shaft bearings, one of which was an 

intershaft roller bearing. Because it appears not to be technically feasible to incorporate an intershaft magnetic 

bearing, a modification to the engine bearing arrangement was made. The bearing was changed from intershaft to a 

conventional case supported radial bearing. This is the arrangement for which the operating conditions were predicted. 

Specifically, the bearing damping and stiffness, maximum load, maximum operating temperatures, and bearing 

compartment constraints were used for the design of magnetic bearings for advanced IHPTET engines. 

FEASIBILITY STUDY 

The purpose of the feasibility study was to apply the knowledge gained from the literature survey and determine if 

magnetic bearings could be designed under the conditions and within the constraints imposed by the selected engine 

and mission. The literature survey provided the current level of technology and offered insight into possible 

advancements in required technology areas such as digital controls, high temperature winding wire insulation, high 

strength rotor lamination materials, and high saturation flux magnetic materials. The selected far-term engine 

(Figure 3), which had the requirement of meeting IHPI'ET goals, was a particularly challenging target because of very 

high rotor speed, high bearing compartment operating temperatures, and high rotor thrust. In addition, space was at a 

premium for both the bearing compartments and the externally mounted digital electronic control. By applying 

state-of-the-art technology, it was concluded that a practical design which would meet advanced military aircraft 

engine requirements could not be achieved. Significant modifications including excessive cooling air requirements, the 

inclusion of thrust balance air, changes to the rotor construction, and the placement of generators on both rotors were 

necessary. This resulted in a very uncompetitive design compared to rolling element systems. An 

all-barriers-removed design could meet the advanced engine requirements and could be achieved by developing 

existing basic technology. Technology programs are essential to develop flight worthy digital controls, reliable auxiliary 

bearings, high power density starter/generators, high flux density magnetic materials, high temperature position 

sensors, and durable wire insulation. It is concluded that, with a firm commitment to the technology, the application of 

active magnetic bearings to military aircraft engines could be demonstrated within a time frame consistent with the 

objectives of the IHPTET Initiative. 

State-of-the-Art Magnetic Bearing Design 

The state-of-the-art design of magnetic bearings for the far-term engine was based on the philosophy that the 

bearings and the integral starter generator could be built using existing technology. It was concluded that the design 

would not fit into the limited bearing compartment space and environment without compromising performance, weight, 

and engine configuration. This was based upon limitations in material properties, insulation capabilities, and the 

analog control systems which are well known today. The integral starter/generator also did not fit into the available 

space forward of the No.2 bearing, thereby requiring an additional generator to be placed on the low rotor. The 

analog controller was also found to be excessively large and heavy. Table I presents a summary of the state-of-the-art 

magnetic bearing design dimensions. The state-of-the-art bearing dimensions as designed with the full thrust and 

radial load requirements were considerably beyond the bearing compartment envelopes. A reduction in the thrust 

bearings capabilities was necessary to fit the envelope and resulted in a compromise in the engine thrust balance 

system. Full rotor thrust could not be taken by the thrust bearings but needed to be offset by conventional thrust 

balancing which imposed a performance penalty. Minor modifications were also required in the rotating and static 

structure to accommodate these large bearings. The saturation flux density level of the materials used in this 

state-of-the-art design was based on proven technology. Levels of 1.5 teslas to 1.7 teslas were assumed and are 

considered entirely feasible based on experience at these levels in other electro magnetic equipment. 

308 
Figure 3. Conventional Bearing Engine Design 

". ,..-'! ~--"-L 

Figure 4. State-of-the-Art Magnetic Bearing Engine Design 

309 
TABLE I. STATE-OF-THE-ART AND ALL-BARRIERS-REMOVED DESIGN DIMENSION SUMMARY 

Available Available State-of-the-Art A11-Barriers-Removed 

Bearing Axial Length OD Length 00 Length 00 

Number (inches) (inches) (inches) (inches) (inches) (inches) 

Radial/thrust No.1, 4.0 10.0 5.18 9.8 3.58 9.8 

low rotor 

Radial No.4, 3.5 7.75 3.18 7.7 1.41 7.7 

low rotor 

Radial/thrust No.2, 3.0 11.0 7.26 10.4 4.66 10.4 

high rotor (4.5) (10.0) 

Radial No.3, 3.5 9.5 4.25 10.1 1.95 10.1 

high rotor 

The environmental temperatures in the bearing compartments (860°F, 145O°F) are considered very severe with 

today's proven insulation technology. While there are published data on ceramic impregnants capable of withstanding 

these temperatures, their use in this type of application is not proven. To keep the risk to a reasonable level, proven 

epoxy encapsulants were used in the state-of-the-art design. This required the use of cooling air to keep the bearing 

compartments under 4OQ°F, a temperature comparable to conventional bearing compartments. Cooling air to 

accomplish this requires an external cooling system since ambient air can be as high as 64Q°F during parts of the 

assumed mission. A 20 mil and 15 mil radial air gap for the thrust and radial bearings, respectively, were used for the 

state-of-the-art design. Reduction of this gap would allow a size reduction in the bearings but would increase the 

likelihood of contacting the auxiliary bearings during aircraft maneuvers. With the current proven flux density 

capability, the 20 mil and 15 mil gaps provided a lower risk design. Nickel plated copper wire was assumed for the 

state-of-the-art design. This plating prevents oxidation of the copper and has been proven in a 550°F environment. 

The analog electronic controller for the state-of-the-art bearing design would see temperatures in excess of 640°F 

if it were placed on the side of the engine without a means to cool it. An analog controller would require cooling air to 

create the environment currently seen by engine fuel control systems. A volume estimate of the analog controller and 

power switching electronics would be approximately 2.5 cubic feet. This 2 to 1 size reduction of current production 

controllers would be accomplished by high density packaging. However, a system this large would present a severe 

performance penalty if mounted on the engine within the nacelle. To minimize this performance penalty and that 

associated with cooling air requirements, it was assumed to be airframe mounted. 

The auxiliary bearings, which are necessary for preventing magnetic bearing contact during high but temporary axial 

and radial loads, were designed to provide limited life during conditions such as surge, high aircraft maneuvers, or hard 

landings. The clearance between the shaft and the auxiliary bearing was set at one-half the magnetic bearing clearance 

enabling the auxiliary bearing to support the excessive load without damaging the magnetic bearing. Under conditions 

of prolonged heavy loading, bearing life would be severely compromised if they were not oil lubricated. The auxiliary 

bearings designed for the state-of-the-art magnetic bearing engine would have a life measured in minutes. This 

requires an engine shutdown if loads exceed the magnetic bearing support capability as would be expected during a 

significant blade failure. The state-of-the-art magnetic bearing engine cross section (Figure 4) shows two types of 

auxiliary bearings which are considered necessary for intermittent overload and safe shutdown. The sleeve bearings, 

consisting of dissimilar materials with high lubricity (e.g., carbon and silicon nitride), are designed to contact first and 

react the momentary high loading. The two solid lubricated ball bearings would provide the thrust and radial support 

during shutdown after a failure. 

With the elimination of the oiling system, the tower shaft and external gearbox were also removed. This results in a 

cleaner flow path and requires the mechanically driven externals to be electrical. Starting the engine must be 

accomplished with a high rotor mounted integral starter/generator. Considering the temperature and space constraints 

imposed by the far-term engine and the selected mission, a single permanent magnet starter/generator could not be 

designed for the power requirements of the aircraft (250 KVA) using state-of-the-art technology. The alternative was 

310 
to place a starter/generator on the high rotor and place a second generator on the low rotor forward of the No.1 

bearing in the nose cone. This also required an additional support structure at the inlet and added significant weight 

and complexity to the engine. 

Design Technology Shortfalls 

The application of state-of-the-art magnetic bearing technology to the far-term engine did not provide a practical 

design that would meet all the requirements .of this advanced aircraft engine. Significant modifications to the 

configuration were necessary and severe performance and weight penalties were anticipated. As a result of the 

state-of-the-art configuration study, technology shortfalls were identified in the magnetic bearing, the associated 

controls, the starter/generator, and the auxiliary bearings. Specifically, the shortfalls were a direct result of high 

environmental temperature, load and power requirements, size and weight constraints, and life requirements. Each of 

the items is addressed below in order to provide an understanding of the deficiencies and the development necessary to 

overcome these technology shortfalls. 

Magnetic Bearings. The primary problems associated with the magnetic bearing are size, weight and temperature 

capability. Load capacity was achieved in the state-of-the-art design by increasing the size and, therefore, the weight. 

Load capacity measured in terms of unit volume or unit weight must be increased significantly for magnetic bearings to 

become practical. Significant improvements in soft magnetic materials for both the stator and the rotor lamination 

materials to increase the flux density are essential. The bearing compartment environmental temperature for the 

state-of-the-art design was assumed to be maintained below 400°F primarily because of the lack of durable, high 

temperature wire insulation materials. Development in this area is also required and appears to be feasible at 

temperatures approaching the magnetic material Curie point. 

Controller. With state-of-the-art technology, the controller (analog design) is significantly heavy and too large to 

be mounted within the nacelle. Miniaturized digital control systems with expanded control capability are essential for 

advanced aircraft engine designs. Integration of this control system with the engine electronic fuel control will offer 

additional benefits. 

Starter/Generator. The space and temperature constraints imposed by the far-term engine required the 

incorporation of a homopolar generator into the state-of-the-art design. This design would be capable of ope-rating in 

the engine environment but only half as efficient in size and weight as a permanent magnet design; thus, the engine 

required an additional generator on the low rotor. The weight and performance penalties associated with this 

approach were expected to be unacceptable. A high temperature, high efficiency starter/generator must be developed. 

Advanced materials and insulation capabilities required for the magnetic bearing could also be used in the 

starter/generator. 

Auxiliary Bearings. The state-of-the-art auxiliary bearing limitation was primarily low life. There is a need for a 

fail-safe backup bearing to allow, in addition to intermittent heavy loading, engine operation during failure of the 

magnetic bearing system. The goal of sufficient life to enable the pilot to return to base requires extensive 

development of a solid lubricant bearing capable of operating at temperature levels approaching 1500°F. 

All-Barriers-Removed Magnetic Bearing Design 

The all-barriers-removed design of magnetic bearings for the far-term engine was based upon the philosophy that 

the bearings and integral starter/generator could be built within a time frame consistent with the objectives of the 

IHPTET Initiative by developing basic technology which exists today. It does not, for example, depend upon 

unexpected breakthroughs such as high temperature super-conductivity or the development of specialized magnetic 

materials which have Curie temperatures much greater than available tOday. Development in the areas cited above or 

in related fields is currently in progress; what is required is the extension or redirection of these efforts toward the 

specific needs of active magnetic bearings in the gas turbine engine application. Table I presents a summary of the 

all-barriers-removed magnetic bearing design dimensions. 

The all-barriers-removed bearing designs were successfully incorporated into the far-term engine (Figure 5). The 

forward bearings (Nos. 1 and 2) were designed to operate at the maximum environmental temperature of 860°F and 

311 
handle the full radial and thrust load without thrust balance air. The rear bearings (Nos. 3 and 4) were designed to 

operate at a maximum temperature of 145O°F in order to keep below the Curie temperature of the magnetic materials. 

Cooling air was required for the No.3 bearing location where surrounding environmental temperatures exceed 3500°F. 

The required load capacity of these advanced bearings was achieved by assuming saturation flux densities of 2.4 teslas. 

Further increases in load capacity were achieved with air gap reductions to 10 mils radial, approximately half the gap of 

the state-of-the-art design. With advanced, adaptive digital controls, full dynamic control and stability with this small 

clearance should be achievable. 

With the magnetic bearings operating at temperatures of 145O°F, ceramic insulation is necessary. The development 

of ceramic impregnation and encapsulation techniques need to be developed to guarantee the life requirements of 

these bearings. At high temperatures, the copper wire would experience a significant increase in electrical resistivity 

causing increased power consumption due to higher I2R losses. It is, therefore, desirable to keep the resistivity as low 

as possible either through the use of high thermal insulation, compact cooling systems, or a change of material (e.g., 

silver). Silver wire has been assumed for the high temperature bearing locations in the all-barriers-removed design. A 

miniaturized digital controller was assumed for the all-barriers-removed design. The development of a flight worthy 

reliable controller one-fifth to one-tenth the size assumed in the state-of-the-art design appears to be technically 

possible. This is based on experience obtained from engine control system designs. With a volume of 0.5 to 0.25 cubic 

feet, placement on the engine with cooling schemes used today for the engine digital electronic controller will make 

the magnetic bearing system very attractive from a weight and performance standpoint. The auxiliary bearings for the 

all-barriers-removed design, as shown in Figure 5, appear to be essentially the same as the state-of-the-art design. 

The difference lies in their temperature and life capability. Development in this important area is critical to the 

success of the active magnetic bearing and the schemes shown are only representative of a concept requiring extensive 

development. The starter/generator shown on the all-barriers-removed design is a permanent magnet design with the 

full capability to supply all aircraft required power. This 250 KVA system, which resides in a 640°F environment, 

would require development but is considered achievable within the IHPTET time frame. 

Technology Readiness Development 

In order to achieve technology readiness within the IHPTET time frame, development in seven key areas is 

required. 

(1) Digital Controls and Control Algorithms 

Commercially available active magnetic bearings employ analog controllers. Since these active magnetic bearings 

are for ground-based applications with minimal space and weight constraints, the analog controllers have not been 

optimized and are large and heavy. To meet the requirements of the advanced aircraft engine bearings, the controller 

must be engine mountable, compact, lightweight, and very reliable in addition to being adaptive and integrable with the 

associated engine/flight systems. These conditions determine a dictated digital control system design not available as a 

commercial unit. The payoffs of using digital controllers include size and weight reductions and the benefits of 

combining digital active magnetic bearing controllers with digital electronic engine controllers. The digital active 

magnetic bearing controller will lead to improved reliability without increase in size through the incorporation of 

redundancies in the hardware and software. Digital controllers will make it possible to take advantage of "modem" 

control methodologies like digital filters for replacing lead compensation networks. Finally, digital controls can employ 

unusual control algorithms to improve system performance and not be limited to traditional control approaches like 

proportional-integral-derivative circuits. Considerable development work will be necessary to provide a fault-tolerant, 

miniaturized military quality digital active magnetic bearing controller capable of surviving the stringent engine load 

and temperature environment. 

312 
; (L __ 

-"~---- -.- .. ----.~ 

Figure 5. All-Barriers-Removed Magnetic Bearing Engine Design 

313 
(2) Magnetic Bearing Power Electronics 

The size and weight of present, commercially available electronic power amplifiers for magnetic bearings are 

unsuitable for use in advanced aircraft engines. To fully utilize the superior capabilities of an active magnetic bearing 

system as compared to the rolling element bearings, power amplifier package weight and volume must be reduced by at 

least an order of magnitude. No commercially available power amplifier can presently operate in the 640°F ambient 

and 20 G vibration environment required for the targeted engine application. Lightweight, high power density, fault 

tolerant power electronics with sufficient gain and bandwidth to meet the acceleration rates commensurate with high 

shaft speeds and engine G loads must be developed. It must be engine mounted and be capable of surviving the high 

load and temperature environment. 

(3) High Strength. High Flux Magnetic Materials 

Advanced aircraft engines will require bearings to operate above 3.0 million ON and to require minimum space. 

Active magnetic bearings have the potential to exceed these requirements. Active magnetic bearings for advanced 

engine applications require magnetic materials with high saturation flux densities to provide the highest performance 

while occupying minimum space. Additionally, the rotor lamination magnetic materials must have mechanical yield 

strengths between 30,000 and 70,000 psi for ON values between 3 and 5 million mm-rpm. Therefore, there is a need to 

develop heat treatment procedures to produce rotor magnetic materials with yield strengths of 70,000 psi and higher 

and magnetic saturation flux densities of 2.0 teslas and higher. High mechanical strength, high saturation flux magnetic 

materials (i.e., Vanadium Permendur and Vanadium Permendur/Nickel) must be optimized to maximize these 

properties and minimize alternating current losses. Heat treatment procedures need to be developed to provide 

consistent quality material which meets the required specifications. 

(4) High Temperature Winding Insulation 

Electrical windings for magnetic bearings require impregnation systems for supplementary electrical insulation, 

mechanical support against vibrations and chemical protection. For engine temperatures (550°F to 1500°F), ceramic 

impregnation appears to be a promising candidate. High temperature (up to 1500°F) insulation materials for the 

bearing electrical windings, capable of withstanding a vibratory and changing thermal environment without degrading, 

are required for magnetic bearing engines. 

(5) Improved Rotor Position Sensors 

A key magnetic bearing component requiring reexamination is the position sensor used as the feedback element. 

The concept and the design of the position sensor used in magnetic bearing controls need to be reexamined in the light 

of the unique requirements for the advanced engines and in light of new understanding on the requirements for 

magnetic bearing sensors. Present commercially available sensors for magnetic bearings were designed for 

ground-based applications with minimal space restrictions but with major limitations on cost. For the aircraft engine 

applications, the size of the sensors needs to be reduced significantly because the radial bearing sensor represents 

about 20 percent of the bearing/sensor length. Thus, there is a need for sensor size reduction without sacrifices in 

reliability or accuracy. The proof of the new design concept verification of the sensor designs would also be required 

under the severe conditions imposed by advanced engine applications. Additionally, the availability of extensive control 

capabilities through digital controls and adaptive control methodologies calls for a re-thinking of sensor concepts and 

possibly a replacement of the sensor feedback with electronically synthesized feedback signals. The development of 

new or improved position or velocity sensors with significant improvements in accuracy and capable of operating in the 

high speed, high temperature engine environment is necessary. They must be space efficient and potentially capable of 

measuring relative rotor position at the center of the bearing applied force. 

(6) Integral Electric Starter/Generator 

This study has produced size, weight, and power requirements for an advanced engine generator. The generator 

was mounted on the high speed engine rotor with the overall size envelope being l1-inch 00, 4.8-inch 10, and 6-inch 

length. The power requirements were 247 KVA continuous (including 40 KVA isolated windings for engine functions), 

371 KVA 5-minute rating, and a 467 KVA lO-second rating. Additionally, the minimum ambient air temperature for 

314 
the subject aircraft was projected to be about 640 0 P which is quite stringent as compared to currently available 

generator winding temperature capabilities. Existing aircraft electric power generators utilize a wound rotor design 

with rotating rectifiers. Because these rectifiers cannot be used in the 640 0 P environment anticipated for the targeted 

engine application, and rotor cooling below this temperature is not feasible, new generator technology must be 

developed. In addition to providing electric power for aircraft services and dual, fully capable isolated windings for 

engine requirements, the generator will be operated as an electric motor and used to start the engine. If the full 

potential of active magnetic bearings is to be realized, a main shaft starter/generator must replace the engine tower 

shaft, gearbox, 'and associated mechanical drive systems. Improvement on existing high speed motor and generator 

technology to meet the engine/aircraft needs and to operate reliably in the high temperature engine environment is 

necessary. 

(7) Auxiliary Support Bearings 

Advanced fail-safe auxiliary bearing technology has been identified as a critical need. In an aircraft engine 

configuration wherein the primary support for the main shaft rotor is provided by an active magnetic bearing system, 

the auxiliary bearings would serve as a fail-safe support mechanism. The unlevitated rotor will be statically supported 

by the auxiliary bearings. In the event of a power failure in the magnetic bearing control circuit or during excessive 

bearing loading caused by the accidental loss of a turbine blade or severe aircraft maneuvers, the auxiliary bearings 

must be capable of withstanding these high loads to prevent contact between the magnetic bearing rotor and stator. 

The auxiliary bearings, under these high loading conditions, must have sufficient life to enable the pilot to fly the 

aircraft safely to the nearest airbase. Auxiliary bearings must also be capable of withstanding magnetic bearing 

overloads for a limited time period in the high temperature bearing compartment. Silicon nitride ball bearings (steel 

races) have shown promise at very high DN levels but at room temperature. The development of non-liquid lubricated 

sleeve bearings could significantly reduce the high weight associated with the rolling element bearing design. 

PARAMETRIC ANALYSIS 

The IHPTET engine designed with all-barriers-removed magnetic bearings formed the basis for studies which 

ascertained the benefits for an advanced military aircraft engine. Parametric analyses were conducted using 

state-of-the-art design/analysis tools. The parametric analyses showed that the incorporation of magnetic bearings 

into a far-term IHPTET military engine could provide a 16% engine weight savings when compared with a current 

technology IHPTET base type conventional bearing engine. This more-electric engine would be oil free and have an 

integrated full authority digital electronic control and magnetic bearing control system. This weight savings could 

provide improvements in aircraft takeoff gross weight (TOGW) and mission range. A 5.6% weight savings was 

calculated in comparison with a far-term engine with high temperature, liquid lubricated conventional mount rolling 

element bearings and many of the other projected "electric" engine improvements. This weight savings is considered 

to be a very high payoff for advanced engine technology for IHPTET. 

The incorporation of magnetic bearings into a far-term military engine would provide other major benefits which 

are known to be positive, but are difficult to quantify. These include reliability, durability, maintainability, vibration 

control, fire safety, reduced heat rejection, and cost. The improvements in reliability, durability, and vibration control 

are exemplified by the dramatic change in the engine external components relative to a conventional engine of today. 

The incorporation of magnetic bearings and other associated more-electric components would produce an engine with 

significantly less plumbing and mechanical structure which is susceptible to vibration fatigue failure. The elimination 

of a majority of tbe failure-prone hardware alone will provide a greater than 2:1 improvement in reliability. With the 

anticipated superior vibration control of magnetic bearings, the durability of the remaining structure (e.g., fuel and air 

lines) would be significantly improved. Improvements in maintainability of the engine external structure is readily 

apparent primarily because of simplicity. Remaining components only include the full electronic control system, 

electric fuel pump and associated delivery systems, electric actuators, and the air bleed and service systems. 

The elimination of oil and hydraulic fluids would greatly improve the fire safety of the aircraft. The total impact of 

this benefit has not been assessed. Heat generation within the bearing and power section of the control system has 

also not been assessed in detail, but in comparison with rolling element bearings, reductions of more than 5:1 are 

expected. This is particularly important for high Mach number aircraft which utilize fuel/oil coolers and air/oil heat 

315 
exchangers at the expense of range and fuel bum. The issue of system cost was not addressed in this study, but if the 

historical trends in changeovers from mechanical to electronic systems are an indication, lower cost is anticipated. 

Within the scope of this program, the search for penalties associated with the implementation of magnetic bearings 

into an advanced military engine did not surface anything significant. A magnetic bearing engine would be dramatically 

different than today's engines, and before full-scale engine development can be initiated, technology shortfalls must be 

addressed to achieve technology readiness within the IHPTET time frame. Much of this development represents a 

maturing of known technology and does not require significant breakthroughs. However, technology development 

must be pursued to reduce the risk to a level commensurate with the time frame associated with 21st century engine 

development. The payoff potential of magnetic bearing engines is significant and achievable. 

CONCLUSIONS 

Active magnetic bearings as replacements for conventional oil lubricated rolling element bearings in advanced 

military aircraft engines is feasible for 21st century applications. The engine feasibility study descnbed herein provided 

invaluable insight into active magnetic bearings for advanced military engines. It is concluded that the application is 

practical and the required technologies could be matured to achieve technology readiness by the tum of the century. 

Many benefits have been defined and, in particular, have shown that significant weight savings are possible, increased 

reliability and durability are achievable, and higher levels of overall engine performance could result. The successful 

application of this concept would result in engines with no lubrication system, higher rotor speeds, reduced blade tip 

and seal clearances, reduced cooling and thrust balance air, reduced system weight, and enhanced rotor dynamic 

control. These features would, in tum, enhance propulsion system fuel consumption, thrust-to-weight ratio, 

maintenance, and reliability, thus providing greater aircraft capability with lower life cycle cost. 

ACKNOWLEDGEMENTS 

The authors acknowledge the diligent efforts of John Miner, Prem Bansal, Carol Shurick, Allan Carlson, and 

Paul Wawrzonek of Pratt & Whitney; and Messrs. Howard Moses, Donatus Ohanehi, Frank Pinckney, John Connelly, 

and David Bourke of MBI. 

REFERENCES 

1. Meeks, C. and V. Spencer, "Development of a Compact, Light Weight Magnetic Bearing," ASME Paper 

9O-GT -240, presented at the Gas Turbine and Aeroengine Congress and Exposition, Brussels, Belgium, June 

11-14,1990. 

2. Reinig, K. D. and Desrochers, A. A., "Disturbance Accommodating Controllers for Rotating Mechanical 

Systems," ASME Transactions, Journal of Dynamic Systems, Measurement, and Control, Vol. 108, No.1, March 

1986, pp. 24-31. 

3. Chen, Chih-Wen, Magnetism and Metallurgy of Soft Magnetic Materials, Dover Publications, Inc., New York, 

1986, pp. 390-397. 

4. Cullity, B. D., Introduction to Magnetic Materials, Addison-Wesley Publishing Company, Reading, 

Massachusetts, 1972, "Special Alloys," pp. 525-531. 

5. Metals Handbook, Ninth Edition, American Society for Metals, 1980, "Magnetically Soft Materials," pp. 

597-614. 

6. Major, R. v., Martin, M. C. and Branson, M. w., "The Development of Cobalt-Iron Soft Magnetic Alloys with 

Improved Mechanical Properties for Use in Electrical Generators," Second Conference on Advances in 

Magnetic Materials and Their Applications, lEE, September 1-3, 1976, pp. 53-56. 

316 
N92-27739 

Low Power Magnetic Bearing Design 

For High Speed Rotating Machinery 

P. E. Allaire, E. H. Maslen, 

and R. R. Humphris, 

Department of Mechanical and Aerospace Engineering 

University of Virginia 

Charlottesville, VA 22901 

C. K. Sortore 

Aura Systems, Inc. 

EI Segundo, CA 90245 

P. A. Studer 

Magnetic Concepts 

Silver Springs, MD 20901 

317 
SUMMARY 

Magnetic suspension technology has advanced to the point of being able to offer a 

number of advantages to a variety of applications in the rotating machinery and aerospace 

fields. One strong advantage of magnetic bearings over conventional bearings is the decrease in 

power consumption. The use of permanent magnets, along with electromagnets, is one 

appealing option which can further reduce the power consumption of the bearing. 

The design and construction of a set of permanent magnet biased, actively controlled 

magnetic bearings for a flexible rotor is presented. Both permanent magnets and 

electromagnets are used in a configuration which effectively provides the necessary fluxes in the 

appropriate air gaps, while simultaneously keeping the undesirable destabilizing forces to a 

minimum. The design includes two radial bearings and a thrust bearing. 

The theoretical development behind the design is briefly discussed. Experimental 

performance results for a set of operating prototype bearings is presented. The results include 

measurements of load capacity, bearing stiffness and damping and the dynamic response of the 

rotor. With few exceptions, the experimental measurements matched very well with the 

predicted performance. The power consumption of these bearings was found to be significantly 

reduced from that for a comparable set of all electromagnetic bearings. 

PRECEDING PAGE BLANK NOT FILMED 319 
INTRODUCTION 

Magnetic bearings have a number of strong advantages. One most obvious advantage is 

their non~ontacting, virtually friction-free characteristics. Entire lubrication systems and the 

need for mechanical oil seals, which add to friction losses and instabilities associated with cross 

coupled bearing coefficients, can be eliminated by using these types of bearings. The life 

expectancy of a magnetic bearing, in many cases, can be much higher than that of a conventional 

bearing. Due to the non~ontacting nature of the bearings, mechanical parts do not wear out. 

This can obviously increase system reliability and decrease costly repairs and necessary 

maintenance which interrupt profitable machine operation. If designed properly, a magnetic 

bearing can perform under much harsher conditions and environments for extended periods of time 

which would not be possible with other types of bearings. One further advantage of the 

frictionless characteristic of these bearings is that of power loss. The power consumption of a 

conventional fluid-film bearing is in many cases much more than for a magnetic bearing. 

Power loss reductions of one order of magnitude or more can be expected when a machine is 

converted from using conventional bearings to magnetic bearings. 

A variety of work has been accomplished on a number of different applications and aspects 

of magnetic bearings. An extensive amount of research has been performed by a number of 

university and industry researchers on the development of magnetic bearings in an· industrial 

canned motor pump [1]. A number of other successful industrial applications of magnetic bearings has been reported by Weise [21. Burrows et. al. [3] presents the development and application of a 

magnetic bearing specifically designed for the vibration control of a flexible rotor. Keith, et. al. 

[4] successfully developed a PC-based digital controller for magnetic bearings. Continuing 

research is being performed in the areas of digital and adaptive controls for magnetic bearings. In 

researching the use of permanent magnets in combination with electromagnets, of particular 

interest are two patents credited to Philip Studer [5, 6]. These patents contain a number of 

features, primarily dealing with permanent magnets, which have useful application to the bearings 

discussed in this paper. Wilson and Stu~er [7] have also applied the permanent magnet bias 

concept to a linear motion bearing. Ohkami et. al. [8] have performed some interesting 

comparison studies of magnetic bearings of various configurations which use permanent magnets. 

Another paper by Tsuchiya et. al. [9] studies and comments on the stability of a high speed rotor 

which is suspended in magnetic bearings biased with permanent magnets. Meeks [10] has also 

performed a comparison of the various magnetic bearing design approaches and concludes that the 

combining of actively controlled electromagnets with permanent magnets results in a superior 

magnetic bearing in terms of size, weight and power consumption. The rare earth permanent 

magnets of today, in particular Sm-Co and Nd-Fe-Bo magnets, offer very high performance 

characteristics in terms of magnetic strength, energy product and thermal qualities. The magnet 

designer is able to concentrate a very large amount of magnetic energy in a small package, making 

more efficient use of available space. 

The design concept for the permanent magnet biased magnetic bearing design discussed in 

this paper is a variation on research and development reported by Studer [5, 6]. The following 

two sections give a brief description of how the bearings conceptually operate. 

Radial MagnetiC Bearing Description 

A diagram of a permanent magnet biased radial magnetic bearing is shown in Figure 1. This 

bearing is designed to operate at one end of the rotor and control radial forces only. Four axially 

magnetized arc segment magnets are positioned circumferentially adjacent to the stator. The bias 

flux generated by the permanent magnets passes down the laminated stator pole leg, through the 

working air gap, axially along the shaft, then returns to the permanent magnet via . 

320 
a radial bias pole piece. The active control flux generated by the coils also passes down the stator 

pole leg and through the working air gap. The return path for the active flux is then 

circumferentially around the stator, as shown in Figure 1. This design requires only four poles and 

four coils, unlike an all electromagnetic design which generally requires eight. In addition, since 

the coils for each bearing axis are connected in series, the bearing control system requires only five 

current amplifier channels, which is half as many as required of the all electromagnetic bearing. 

Combination Radial/Thrust Magnetic Bearing Description 

A schematic of this bearing design, revealing the various magnetic paths, is shown in 

Figure 2. This bearing combines control of both radial and thrust forces. The radial portion of 

the bearing is identical to that which was described in the previous section. The thrust control 

however, is implemented by a unique magnetic flux configuration. The permanent magnet bias 

flux passing along the shaft splits equally between the two thrust poles before returning to the 

permanent magnet. A single active coil produces a magnetic flux, in the shape of a toroid, which 

symmetrically adds or subtracts to the bias flux in the working air gaps between the thrust disk 

and thrust poles. 

Design Concept 

The bearings designed for this project are different from all electromagnetic bearing designs 

in that they employ both permanent magnets and electromagnets. Permanent magnets generate 

the bias flux in the working air gaps and electromagnets are used to modulate this flux. 

The purpose of establishing a bias flux in the working air gaps is to linearize the governing 

force equation of the magnetic actuator. The bias flux is a nominal flux density about which the 

control flux is varied. If a bias flux of zero is used, (only one opposing actuator is operated at a 

time,) then the force generated by the actuator on the rotor follows a quadratic force law, i.e., the 

force will be proportional to the square of the flux density in the air gaps. Consequently, the force 

slew rate will be zero when the rotor is in the nominal balanced position and the transient 

response will be adversely effected. If, however, the bearing fluxes are modulated about a 

non-zero bias flux, (with opposing actuators symmetrically perturbed,) it is easily shown that the 

force becomes linearly related to the control flux. The following section demonstrates this 

important relation. 

Force Relationships 

The force generated in an air gap of area Ag and length g by a magnetic actuator can be 

expressed by the direct relation 

F =...LrB )2A 2J.LO \ g G (1) 

where Bg is the flux density in the air gap and J.Lo is the permeability of free space. If only a single 

axis of the bearing is considered, then the net force acting on the shaft will be the difference of the 

two opposite acting actuator forces. Assuming the areas of the two opposing air gaps are the 

same, the force acting on the shaft by the magnetic bearing can be expressed as 

(2) 

321 
The flux density in the air gaps is being supplied by two sources, i.e., the permanent 

magnet and the coil. In order to properly provide differential control, the fluxes in the two gaps 

are symmetrically perturbed so that the flux in one gap is increased while the flux in the opposite 

gap is decreased by the same amount. This implies that 

(3,4) 

where Bpm is the flux density generated by' the permanent magnet and Be is the flux density 

generated by the coil. Substituting Eqs. l3, 4) into Eq. (2), expanding and simplifying, the force 

acting on the shaft can now be expressed as 

F =~B BA shaft /-LO pm c g (5) 

By expressing the equation for the force on the shaft in this form, it is interesting to note that the 

force is not only proportional to the bias level, Bpm, but it is also linearized with respect to the 

control flux, Be. . 

Open Loop Stiffness and Actuator Gain 

The force generated by the bearing in the horizontal direction, F x, can be accurately 

approximated by the truncated Taylor series expansion in the following way: 

F ~ F J + OFj x + O~_j ic 

x x x = 0 Ox x = 0 'Oi x = 0 

i=O i=O ci=O 

c c c 

If tne magnetic circuit is balanced, then the first term in Eq. (6) is equal to zero and 

F = K x + K.i 

x x 1 C 

where x represents the rotor displacement and ie represents the control current in the 

electromagnetic coil. The parameters Kx and Ki are defined as 

(6) 

(7) 

of of 

K = ~j 0 and K. = ~j 0 ·(8,9) x uX x = 1 ul X = 

i=O ci=O 

c c 

The quantity Kx is referred to as the open loop stiffness and represents the change in the 

horizontal force due to horizontal displacement. The open loop stiffness is always negative which 

implies that the bearing is unstable in the open loop control configuration. Unlike a actual spring 

with a positive stiffness, a positive dispacement of the rotor toward the magnet will increase the 

attractive force. The quantity Ki represents the actuator gain of the bearing. It represents 

changes in the horizontal force due to control current, ie. Equivalent expressions exist for the 

components of the vertical force expression. Expressions for the open loop stiffness and the 

actuator gain are determined by performing the appropriate differentiation of the force expression. 

These expressions take on the form 

322 
(10) 

and 

(11) 

where Land H represent the length and demagnetization force, respectively, of the permanent 

magnet and N is the number of turns in the electromagnetic coil. 

Control System Description 

The control elements of this system are those components which detect the motion of the 

shaft, determine the required control force and generate a coil current required by the magnetic 

bearing to generate this force. The magnetic bearing system consists of four distinct components: 

the magnetic actuator, the displacement sensors and associated conditioning circuits, the analog 

PID controller and the power amplifier. 

The actual magnetic bearing mainly consists of the electromagnetic coils, iron pole pieces, 

rotor and permanent magnets. The signal conditioning component consists of the eddy current 

induction displacement sensors, signal amplification and coordinate transformation circuits. The 

analog controller primarily consists of three separate components. The components take the form 

of proportional (P), integral (I) and derivative (D) compensation networks. These three parallel 

stages are added together through a summing amplifier to produce the output of the analog 

controller. The last component in the control loop is the power amplifier. The amplifier, upon 

request of the controller, supplies the required current to magnetic coils to produce the necessary 

fluxes in the bearing. 

The dynamics of the bearing-rotor system can be combined with the operating 

characteristics of the control electronics to form a closed-loop control system. This control 

system is shown in a simplified block diagram form in Figure 3. The displacement sensor 

characteristics, analog controller and amplifier make up the relatively complex transfer function of 

the feedback controller, Gc(s). The feedback controller relates the rotor position to the actuator 

current. The closed-loop transfer function for this magnetic bearing system, as determined from 

this block diagram, is given by 

~ 1 

FJSJ = ms

2 + K + K.Gc(s) x 1 

(12) 

where m is the mass of the rotor supported by the bearing. 

Prototype Bearing Construction 

The four-pole radial bearing stators, as shown in the diagrams of Figures 1 and 2, were 

designed to be identical for both bearings. The stators and rotors were constructed of 3% 

silicon-iron lamination material which had a thickness of 0.007 inches. Each laminated 

component consists of approximately 100 laminations. The laminations were glued together using 

a two part activator/resin adhesive and the shape was machined by wire EDM (electric discharge 

machining.) The bearing stators have an outside diameter of approximately 3.0 inches and an 

323 
axial length of approximately 0.7 inches. The outside diameter of the laminated rotor is 

approximately 1.5 inches. The thrust bearing components were machined from soft magnet iron. 

The high energy permanent magnets, made out of a geodymium-Iron-Boron alloy, have a 

maximum energy product of 30 MG-Oe. The bearings support a shaft weighing approximately 

3.7 Ibm. 

Load Capacity 

Measurements of the maximum load applied to the shaft, before falling out of support, are 

plotted as a function of proportional controller gain, Kp , in Figure 4. The force in this test was 

applied by hanging weights on the shaft. A pulley system was constructed in such a way that the 

force could be applied in the desired direction. The force in the plots represents forces applied 

along the bearing axes. 

The variation of the maximum load at lower proportional gains is actually a measure of the 

stability threshold of the system. It is noted in Eq. t 8) that the open loop stiffness, Kx is defined 

at a nominal operating point, i.e., rotor position and control current equal to zero. However, as 

the bearing is loaded with a static force, the steady state current begins to increase. It can be 

shown analytically that Kx is a function of the operating point of the control current. That is, as 

the control current current increases, Kx also increases. Increasing proportional gain has the effect 

of compensating for this increase in Kx and consequently increasing the stability of the system. 

The measurements made at higher proportional gains represent a more accurate measure of 

the actual load capacity of the bearing. Enough stability is provided so that magnetic saturation 

is reached in the bearing pole structures. The maximum predicted loads in the plots of Figure 4 

are calculated at the point of magnetic saturation. 

Equivalent Bearing Stiffness and Damping 

Measurements of the equivalent stiffness of the bearings are shown in Figure 5. This simple 

measurement was performed by applying a constant force, ~F , and noting the displacement, ~x , 

of the shaft (controller integrators turned off.) The stiffness then is given simply by Keq= 

~F / ~x. A linear regression was performed on the measured data, which resulted in very good 

correlation, as can be observed in the plots. It is noted that the proportional gain has a direct 

effect on the stiffness of the bearings, as has been previously demonstrated by Humphris, et. al. 

[11]. 

Relative damping in the bearings was investigated from a white noise frequency response 

analysis of the bearing and rotor. The analysis was performed by injecting noise, composed of all 

frequencies of interest, into one axis of the turbine-end radial bearing, and performing a FFT 

(Fast Fourier Transform) analysis on the vibration response of that axis. This linear frequency 

response, composed of 100 averages, is shown in Figure 6. The derivative controller gain, Kr was 

varied through a range of values as noted in the plot. As expected, the derivative gain had a 

direct effect on the damping in the bearings [11]. The first large spike represents the first two 

modes of shaft vibration. They are very close together in frequency and essentially 

indistinguishable. The frequency of the second spike is the third mode of vibration and the third 

small spike at approximately 60,000 cpm is the fourth mode. It is noted that the variation of the 

derivative gain strongly effects the first two modes, has a small effect on the third mode and 

virtually no influence on the vibration amplitude of the fourth mode. 

324 
Critical Speeds and Rotor Response 

The damped synchronous critical speeds of the flexible shaft supported by these bearings 

can be approximately determined from the white noise frequency response plots of Figure 6. 

These values, however, represent the zero speed natural frequencies, and the gyroscopic stiffening 

effects of any attached disks would not be included. Since the natural frequency is given by Wn = 

.JKTID, where k is the shaft stiffness and m in the modal mass of the rotor, it is of course expected 

that the observed critical speeds, when the shaft was spinning, would be higher. 

Plots showing the vibration magnitude and phase for the shaft speeds that were obtained is 

included in Figure 7. Amplitude information was taken directly from the magnetic bearing 

sensors and a key-phase sensor was used to provide the phase information. According to the 

maximum vibration amplitudes observed in Figure 7, the first vibration mode is observed to occur 

at approximately 10,000 rpm and the second at approximately 13,000 rpm. 

Power Consumption 

Finally, a number of power consumption measurements were made. Measurements of the 

power were taken with a wattmeter for a number of cases. This meter is used with the 

assumption that the measured voltage and current being supplied to the control electronics is 

sinusoidal in nature. In addition, it is realized that it represents a somewhat gross measurement 

as it includes all the inefficiencies of the various electronic components. Table 1 summarizes the 

results. The non~ssential electronic diagnostic components of the bearing system were observed 

to consume only about 7 watts. These measurements represent a significant improvement over 

the 500 watts of approximate total power consumed by a comparable current biased all 

electromagnetic bearing design. 

CONCLUSIONS 

The brief theory which was presented in this paper established the basic electromagnetic 

and mechanical relationships necessary to develop a set of permanent magnet biased magnetic 

bearings. The design involved both radial and thrust bearings. The availability of newer 

rare-earth high energy permanent magnets made it possible to effectively provide the necessary 

bias fluxes in the bearing. 

The bearings and rotor were successfully constructed and operated. A number of tests and 

experiments were performed on the bearing-rotor system. The tests consisted of load capacity, 

stiffness and damping measurements. The results proved to be very positive in that the 

theoretical predictions and the observed performance matched reasonably well, giving credibility 

to the models which were used to perform the analysis. Of particular interest for this study was 

the measured power consumption of the bearings. It clearly demonstrates that the use of 

permanent magnets can improve the operating efficiency of an active magnetic bearing. 

It was successfully observed and demonstrated that these bearings have strong potential for 

future use as efficient, reliable bearings. However, further research and development is required in 

the areas of controls, magnetic materials and actuator design before it is possible to install them 

into a useful industrial application. 

325 
REFERENCES 

1. Allaire P.; Imlach, J.; McDonald, J.; Humphris, R.; Lewis, D.; Banerjee, B.; Blair, B.; Clayton, 

J.; Flack, R.: "Design, Construction and Test of Magnetic Bearings in an Industrial Canned 

Motor Pump," Pump Users Symposium, Texas A & M, Houston, TX, May 1989. 

2. Weise, D. A.: "Present Industrial Applications of Active Magnetic Bearings," Presented at the 

22nd Intersociety Energy Conversion Engineering Conference, Philadelphia, Pennsylvania, August 

1987. 

3. Burrows, C. R., Sahinkaya, N.; Traxler, A.; and Schweitzer, G.: "Design and Application of a 

Magnetic Bearing for Vibration Control and Stabilization of a Flexible Rotor," Proceedings of the 

First International Magnetic Bearings Symposium, ETH Zurich, Switzerland, June 1988. 

4. Keith F. J., Williams, R. D.; Allaire, P. E.; and Schafer, R. M.: "Digital Control of Magnetic 

Bearings Supporting a Multimass Flexible Rotor," Presented at the Magnetic Suspension 

Technology Workshop, Hampton, Virginia, February 1988. 

5. Studer. P. A.: NASA, Magnetic Bearing, Patent 3865442, Patent Application 100637, February 

1975. 

6. Studer, P. A.: NASA, Linear Magnetic Bearing, Patent 4387935, Patent Application 214361, 

December 1980. 

7. Wilson, M.; and Studer, P. A.: "Linear Magnetic Bearings," Presented at the International 

Workshop on Rare Earth-Cobalt Magnets and Their Applications, Roanoake, Virginia, June 

1981. 

8. Ohkami, Y., Okamato, 0.; Kida, T.; Murakami, C.; Nakajima, A.; Hagihara, S.; and Yabuuchi, 

K.: "A Comparison Study of Various Types of Magnetic Bearings Utilizing Permanent Magnets," 

Presented at the International Workshop on Rare Earth-Cobalt Permanent Magnets and Their 

Applications, Roanoake, Virginia, June 1981. 

9. Tsuchiya, K; Inoue, M.; Nakajima, A.; Ohkami, Y.; and Murakami, C.: "On Stability of 

Magnetically Suspended Rotor at High Rotational Speed,." Presented at the Aerospace Sciences 

Meeting, Reno, Nevada, January 1989. 

10. Meeks, C.: "Trends in Magnetic Bearing Design," Paper presented at Naval Sea Systems 

Command Magnetic Bearing Forum, Washington, D. C., July 1989. 

11. Humphris, R. R.; KeIrn, R. D.; Lewis, D. W.; and Allaire, P. E.: "Effect of Control Algorithms 

on Magnetic Journal Bearing Properties," Journal of Engineering for Gas Turbines and Power, 

Vol. 108, October 1986. 

326 
BIAS POLE 

PIECE 

PERMANENT MAGNET 

STATOR 

COIL 

ROTOR 

5HAfT 

PERMANENT MAGNET FLUX --- --

ACTIVE CONTROL fLUX ~ 

Figure 1 - Permanent Magnet Biased Radial Magnetic Bearing Flux Paths 

·PERMANENT MAGNET 

THRUST COIL 

STATOR 

RADIAL COIL 

THRUST DISKROTOR 

THRUS T POL ES -----.-'r-t---. SHAfT 

Permanent Magnet Flux - - - - ~ 

Active Control Flux 

Figure 2 - Permanent Magnet Biased Radial/Thrust Magnetic Bearing Flux Paths 

327 
static 

load 

(lbO 

x(s) 

+ 

Figure 3 - Closed-Loop Magnetic Bearing Control System 

50~~~R~ad~jal~Be~um~'-g----' -~--~Truru=--s~t~B~e-um~'-g----' 

40 

--------r---------

redicted --' 

30 

20 P~c..r:'!. ~ --------

10 

O~--r-----~----~~ ~--r-----T-----~~ 

8000 

3 s 7 3 s 7 

proportional gain, Kp proportional gain, Kp 

Figure 4 - Maximum Load Capacity 

Radial Bearing Thrust Bearing " 

" --_..1-" " 

" • 

. al 6000 eqwv ent 

measUIQI - "II! 

,,~ 

stiffness 

Keq 4000 

(lbf/in) 

2000 

o 

3 s 7 9 3 s 7 9 

proportional gain, K p proportional gain, Kp 

Figure 5 - Equivalent Bearing Stiffness 

328 
0.02 

Kr =4 

O.Q1S 

magnitude Kr =6 

0.Q1 

0.005 

O~---r--~~~--------~~~==~ 

o 10000 30000 50000 70000 

excitation frequency (cpm) 

Figure 6 - Measured White Noise Linear Frequency Response 

180 

90 

phase turbine·end 

(degrees) 

0 

-90 

-180 

2 

l..5 thrust-end 

vibration 

amplitude 

(mils) I 

O.S 

0 

0 SOOO 10000 ISOOO 20000 2S000 

rotor speed (rpm) 

Figure 7 - Rotor Runup Response 

329 
N92-27740 

PROGRESS OF MAGNETIC SUSPENSION SYSTEMS 

AND MAGNETIC BEARINGS IN THE USSR 

Kuzin A.V. 

Moscow Aviation Technological Institute 

SUMMARY 

This paper traces the development and progress of magnetic suspension systems and magnetic 

bearings in the USSR. The paper describes magnetic bearings for turbomachines, magnetic suspension 

systems for vibration isolation, some special measuring devices, wind tunnels and other applications. 

The design, principles of operation and dynamic characteristics of the systems are presented. 

",.' . 

PRECEDING PAGE BLANK NOT FllM!:D 331 
INTRODUCTION 

Due to increase of range, speed and operation life of moving objects, gain in accuracy of instruments 

and machines and growth of rotational speeds of their individual elements, the problem of improving 

the quality of bearing assemblies and suspensions becomes ever more acute. 

Modem bearings should meet the following requirements: they must have capacity for long-duration 

and stable operation in any environment at low and high speeds, should have moments close to zero, 

and must consume a small quantity of energy; they should be easily producible and not too expensive. 

Quite a number of different bearings and suspensions, to one degree or another, satisfy some of the 

above-mentioned requirements. 

These problems find their most exhaustive solution in electromagnetic suspensions (EMS) in which 

the weight of a suspended body and loads acting on it are counterbalanced by the magnetic field strength. 

Free levitation of bodies in an electromagnetic field ensures functioning of suspensions at super-high 

speeds bringing about extremely small disturbing moments. The service life of EMS is detennined 

mainly by the operation life of electronic equipment whose failure-free perfonnance may last for dozens 

of years. Absence of contact, wear, noise and vibrations, ability to function in vacuum and corrosive 

mediums, wide temperature range, and low energy demand offer conditions for provision of high 

accuracy and operating longevity of instruments and devices incorporating EMS and make EMS ever 

more perspective. 

Theoretical studies in the field of noncontact electromagnetic suspension began (approximately) in 

1839 when English scientist Earnshaw proved that a static system of bodies which repel one another 

or have an attraction for each other, with a force inversely proportional to the square of the distance 

between them, is unstable (ref. 1). 

Exactly one century later (in 1939) Brounbeck corroborated this inference, except that in his opinion 

stable spatial suspension of bodies in stationary magnetic and electric fields is possible but refers only to 

bodies having relative magnetic penneability or relative dielectric pennittivity less than a unit (ref. 2). 

Arkadiev V.K. was the first Russian scientist who demonstrated electromagnetic suspension. He 

suspended a penn anent magnet measuring 4 x 4 x 10 mm and weighing about 1.2 g in the space above 

the concave surface of a superconductive metallic disk whose diameter was 40 mm and was immersed 

in a vessel filled with liquid helium (ref. 3). Ponizovsky V.M. (Penn State University) (ref. 4) was 

one of the first Russian scientists who put into practice magnetic suspension with an external control 

system. Following American scientist J. Beams (ref. 5) in 1957 he built up an EMS set for suspension 

of steel balls whose diameters were from 2 to 5 mm. The balls were rotated in a vacuum by means of 

PRECEDING PAGE BLANK NO. FILMfD 333 
a rotating magnetic field with the aim of conducting strength tests of steel balls and various coatings. 

Ponizovsky V.M. has been engaged in research work in the field of EMS for more than 20 years. One 

of his essential achievements manifested itself in double magnetic suspension of ferromagnetic rotors 

which is described in his work (ref. 6) and one version of which is presented on fig. 1. 1;2 - suspended 

rotors; 3,4 - servo systems of control of currents in solenoid 7 containing movable magnetic core 9 and 

damper 10, and in solenoid 11 containing core 12; 5,6 - rotors position inductive pickups. 

The double magnetic suspension may be used for studying stability of motion of a liquid between 

two spheres rotating at different angular velocity and for studying stability of fluid film on the surface 

of a rotating sphere. 

During the last two decades the main achievements in the field of magnetic suspension have been 

connected with creation of new precision measuring instruments of control systems and navigation of 

moving objects, high-speed turbomachines and electric machines using magnetic bearings, effective 

vibration isolation systems incorporating EMS and EMS intended for windtunnel studies. 

EMS OF GYROSCOPIC INSTRUMENTS 

Cardinal improvement of accuracy of gyroscopic devices can be attained through replacement of 

conventional suspensins by noncontact suspensions. 

Many works are devoted to the discovery of stability conditions of a solid body (a gyroscope, rotor 

in particular) in noncontact suspension. Such interest in this problem is connected with the principal 

nature of stability of a solid body in noncontact suspension. 

Passive noncontact suspensions in which the stability of the equilibrium position of a solid body is 

ensured by the special choice of parameters of resonant circuits that were studied rather minutely. 

In their book (ref. 7) the scientists of the Moscow Technical College (MTC) discuss the questions 

of theory and application of instrument EMS. They generalize the principles of construction of EMS, 

analyse main alternative schemes and designs, offer methods of study and the designing of power, 

dynamic and moment characteristics. Figs. 2 and 3 present designs of two-axle octapole and three-axle 

magnetoresonant suspensions used in gyroscopic instruments of the moment and attitude sensors type, 

the floated integrating gyroscope type, and the gyroscopic accelerometer type. 

Quite a number of works are devoted to analysis of noncontact suspensions incorporating servo 

systems changing the field of forces of a suspension depending upon position of the body (refs. 8-16). 

334 
For twenty years the scientists of the Scientific Research Institute of Applied Mathematics and 

Cybernetics affiliated with the Gorky State University have been studying and designing nonbearing 

assemblies for measuring instruments. 

Fig. 4 presents a functional diagram of the magnetic suspension which is employed by gyrocompass 

(refs. 9, 10). In this instrument the sensing element consists of a nonmagnetic rod, the upper part of 

which accommodates ferromagnetic sphere 1 and the lower part carries hydrochamber 2 with a fast 

moving rotor, 3 - body position pickup; 4 - controller; and 5 - electromagnet. In the mock-up of this 

suspension a body whose mass was 1-1.5 kg was suspended, being attached to a ferromagnetic sphere 

whose mass was 70-120 g. 

Fig. 5 presents a functional diagram of the magnetic suspension used in torque magnetometer 

(ref. 11) in which ferromagnetic sphere 3, whose mass is 20-200 g, and which is tested for anisotropic 

properties, is suspended in the field of two coaxial electromagnets 1, 2; 4 - body position pickup; and 

5 - controller. 

Fig. 6 presents a functional diagram of the instrument in which magnetic suspension is used 

for noncontact suspension of sensing element 1, whose mass is 0.5-1.5 kg, by attaching it to two 

ferromagnetic spheres 2, 3 in the field of two coaxial electromagnets 4, 5 (ref. 17). 

A peculiarity of the regulation processes in electromagnetic suspension devices is the natural 

instability of the suspended object. Existence of limitations for value of control voltage on windings 

of electromagnets leads to limited domain of the object's stability in space and to limited range of 

permissible external disturbances. Domain of states of stability in space is one of the most important 

characteristics of systems having a naturally unstable object of control which determines optimization 

for synthesis of control algorithms (ref. 12). In papers (refs. 13-17) the authors synthesize control 

algorithms for magnetic suspension systems presented on figs. 4, 5,6 in accordance with the criterion 

of maximum domain of stability of the object which is suspended in space, make analysis of different 

systems of control with allowance for non-linearity of characteristics of power amplifier, and discuss 

rigidity dependences and values of permissible external disturbances induced by system parameters. 

Fig. 7 shows a block diagram of a magnetic suspension optimum control system; the diagram is 

reduced to dimensionless form (ref. 17), where 1 - transfer frunction of the object being suspended; 2 -

electromagnet; 3 - power amplifier; 4 - transfer function of optimum controller; 5 - link of electromagnet 

X3 current negative feedback; X4 displacement of the object; T - ratio of electromagnet time constant 

to selected scale of time coinciding with the object time constant; and p - differentiation statement. 

Stability of a rotor in electromagnetic suspension with allowance for sluggishness of its circuits is 

analysed in a paper (ref. 18) in which the authors discovered the condition of damping of nutation 

335 
oscillations of the rotor. In ref. 19 the author discusses nonlinear reasonances occurring with combined 

radial, axial and angular oscillations at different frequencies, where energy transfer between motions of 

a gyroscope rotor takes place. 

Noncoincidence of the rotor shape of a noncontact gyroscope with a sphere provokes occurrence of 

moment relative to the centre of the mass of the rotor and therefore induces gyroscope drifts. Calculation 

of moment of forces applied to an ellipsoidal rotor in electromagnetic suspension is demonstrated in 

ref. 20. The moment of forces applied to a rotor whose shape differs little from spherical fonn is 

calculated in refs. 21-23. 

The questions of gyroscope dynamics with noncontact suspensions arranged on a vibrating mounting 

are discussed in refs. 24-26. 

Increase of mass and dimensions of structural elements of magnetic suspensions and application of 

resilient suspension for attachment of a useful load to the suspended body necessitate consideration 

of the resilient properties of a structure when designing suspension stabilization systems. Usage of 

a regulator synthesized without allowance for these properties may lead to diminution of domain of 

attraction, i.e., a region of absolute stability of the equilibrium state in the phase space of variables 

of the system which is always limited due to instability of the object of regulation and limitedness of 

control, and even to loss of stability of the equilibrium state. In ref. 27 the author, assuming that 

the powercharacteristicsof an electromagnet are linear, synthesizes the control algorithm of the system 

of stabilization (of magnetic suspension) with allowance for resilient properties of its construction, 

providing maximum domain of attraction and absolute stability of the equilibrium state. The author 

discusses a three-mass model of magnetic suspension which takes into account the elasticity of the 

bearing and suspended body (fig. 8). A characteristic feature of the controller providing maximum 

domain of attraction and absolute stability in the discussed case when only clearance and current are 

measured, necessitates introducing additional correction of sensor signals which occurs when second 

order active filters tuned to the particular frequencies of elastic vibrations of the bearing and suspended 

body are used. 

In ref. 28 the author gives quantitative estimates of pennissible application of the simplest magnetic 

suspension regulator which does not allow for elasticity of mounting in a two-mass model. 

The application of gyroscopes to noncontact suspensions is not limited by navigation and control 

of moving objects. Such gyroscopes are used in delicate physical experiments, in particular, for 

measurement of the effects of the general theory of relativity onboard a satellite which is free from drift. 

In this case it is necessary to measure gyroscope drift equal to 7 seconds of arc a year. Such exceptional 

accuracy requires taking account of extremely small moments acting on the gyroscope. In particular, 

336 
when analysing motion of the rotor it is necessary to take into account the oscillations of atoms inside 

the body of the gyroscope, i.e., to determine the so called heat barrier to gyroscope accuracy. Refs. 29 

and 30 are devoted to solving this problem. 

Ref. 31 is devoted to determining the principal vector and principal moment of forces acting on a 

confined superconductive body in a magnetostatic field. 

The approximate calculation procedure of the power characteristics for suspension of a cryogenic 

gyroscope which allows us to obtain final formulae for forces and rigidity of suspension in a case when 

supporting coils of unspecified form are used, is suggested in ref. 32. 

SYSTEMS OF MAGNETIC SUSPENSION IN FINAL·CONTROL DEVICES 

DESIGNED FOR ORIENTATION OF SPACE VEmCLES (SV) 

Nowadays there is widespread application of magnetic suspension, i.e., inertia engine-flywheels 

allowing stabilization and changes of angular position in space without use of a propulsive mass which 

is always limited onboard satellites and is replenished with difficulty. Space Vehicles (SV) move in 

the conditions of space where damping is absent. 

The basis of an electromechanical orientation control system consists of rotating the inertia massflywheel. 

When the engine rotates the flywheel, then, according to the law of conservation of momentum the 

SV should rotate in the opposite direction at an angular velocity as low as the moment of inertia of 

the flywheel is in comparison with the moment of inertia of the SV. The main disadvantages of the 

systems with inertia flywheels are limited operation life and aptitude to enter saturation mode. The 

first disadvantage is explained by the presence of friction parts in bearings, and the second drawback 

is referred to maximum permissible rotational speed. These considerations have induced designers of 

inertia flywheels to give paramount importance to the questions of increasing the operation life and 

rotational speed accompanied by reduction of energy consumption, mass and dimensions of the system. 

Since the mass of the flywheel is in reverse relationship to rotational speed, there is a tendency to 

choose maximum possible speed of rotation. 

Operation life of ordinary bearings is a function of the number of revolutions, and as in all phenomena 

connected with friction, it is characterized by wide scatter of the value of mean-time-between failures 

and value of moments of friction. Here selection of proper lubrication is of great importance. Usage 

of liquid or gas lubrication in cosmos conditions requires construction of hermetic casing, the mass of 

which may constitute a considerable part of the system's total mass. 

337 
There is potential for application of magnetic bearings in the gyroscopes and flywheels of space 

vehicles' attitude control systems. About twenty five years ago a group of specialists with the Allunion Scientific Research Institute of Electromechanics (ASRIE, Moscow) under the leadership of 

academician Sheremetievsky N.N. began research woIks on an EMS problem for orientation of space 

vehicles. The result was the creation of an original spherical electromotor-flywheel for the orientation 

system of orbital station "Salut-S" and powered gyroscopes which are successfully used in the orientation 

system installed in orbital station "Mir" (refs. 33, 34, 3S). 

Fig. 9 displays an actuator device of the attitude control system where 1 - a support-free spherical 

rotor-flywheel of a three-axle electromotor acts as three flywheels simultaneously. The system of 

electromagnetic suspension incorporating electromagnets 2 through 7 creates an electromagnetic field 

which solely holds the flywheel in support-free state at the centre of the stator body of three collectorfree electromotors: 8, 9, and 10. The spherical flywheel has a number of advantages in comparison 

with conventional flywheels fitted along three axes: it allows control of angular motion of SV about 

three axes simultaneously, it is not connected with the body gyroscopically, and it has lesser mass and 

dimensions. 

The main parameters of a spherical electromotor-flywheel (ref. 36) are mass - 230 kg; rotor diameter -

0.64 m; rotation speed - 800 r.p.m.; maximum kinetic moment - 200 Nms; control moment - 3 Nm. 

Further development of endeavors in this direction will be creation of an electromagnetic bearing for 

high-speed powered gyroscopes. Main parameters are mass of gyroscope - 160 kg; rotor diameter - 0.4 

m; rotation speed - 10000 r.p.m; kinetic moment - 1000 Nms; control moment-200 Nm;and precession 

angle - unlimited. 

The system of automatic protection of EMS has been worked out in the ASRIE and was used for 

protection of a number of big-size rotor mechanisms with magnetic suspension of the rotor, such as an 

electro-gas blowing system for gas-cooling nuclear reactor "EG-90/1.2S" (p=lS00 kW, n=3ooo r.p.m.; 

Mr=lS00 kg), turbo-compressor for gas main "GPA-C-16"(P=16000 kW, n=S300 r.p.m.; Mr=1200 kg), 

diametral fan "DV" (P=l00 kW, n=3000 r.p.m.; Mr=300 kg) (ref. 37). 

EMS may be successfully used as a ball support of the dynamic stand designed for physical modelling 

of different flight conditions of SV under space conditions. The dynamic stand is a movable platform 

which accommodates tested equipment including power units imparting angular motion. Suspension of 

the dynamic stand platform should provide three rotary degrees of freedom and absence of resistance 

to angular motion, i.e., real conditions in which a space vehicle operates. Nowadays the dynamic 

stand platform is suspended mainly with the aid of spherical gasdynamic bearings having significant 

disturbing moments. Application of an electromagnetic bearing in the dynamic stand allows it to have 

338 
disturbing moment which is far smaller than in the case when gasdynamic bearings are used. In the 

Moscow Aviation Institute specialists from the Electrical Engineering Department have designed and 

constructed a magnetic bearing for the dynamic stand which at a suspending mass of 1000 kg has 

adverse friction moment not exceeding 0.3 g.cm at lateral rigidity of 6000 N/m; i.e., its performance 

satisfies the requirements specified for dynamic stands of SV (refs. 38-40). 

MAGNETIC SUSPENSION FOR TURBOMACIllNES 

Modem level development of engineering puts forward more and more contradictory requirements 

for bearings of rotor machines, which in a number of cases are practically unrealisable if we use existing 

rolling-contact bearings and plain bearings. First of all there is a substantial increase in rotational speed 

and operation in extreme conditions; second, there is a reduction of noise and vibrations, a gain in 

accuracy of rotation, an increase in operation life, and a decrease of mass dimensions and losses from 

friction. Magnetic bearings with an external control system are regarded as an alternative to existing 

rolling-contact bearings and plain bearings. Owing to the absence of mechanical contact there is no 

necessity for lubrication. The bearings can operate in a vacuum or in corrosive mediums as well as 

over a wide range of temperatures; there are no friction problems of wear, or noise; these bearings 

allow development of maximum rotational speeds, and it is worth mentioning that the operation life of 

magnetic bearings does not depend on rotational speed; it is determined only by the operation life of 

the control system that may amount to several dozen years. The control system ensures high accuracy 

of rotation (tenth fractions of micron), high rigidity at static loads (2000 N/ILm), active damping of 

oscillations, low requirements to accuracy of balancing and assembly of rotor, easy control of static 

and dynamic rigidities. 

The research works package of the Pskov Branch of the Leningrad Polytechnical Institute scientific 

group is devoted to creation of magnetic bearings for a high-speed grinding electrospindle (refs. 41-45). 

Super-high-speed grinding allows us to raise labour productivity, increase operation life of tools and 

ensure higher quality of the work surface. Fig. 10 displays the block diagram of a designed experimental 

model of a high-speed electrospindle with active magnetic bearings (AMB). The model was designed on 

the basis of a production-type grinding electro spindle 3W-120/0.4 (120000 r.p.m.; 0.4 kW) by means of 

substitution of active magnetic bearings for ball bearings. The driving part of the spindle consists of an 

induction motor having stator 6 and squirrel-cage rotor 12. Radial AMB consists of trunnion 13 fitted on 

shaft 1, the core of stator 3 with windings 4 and inductive pickup 5 of radial translations of the trunnion. 

The stator core is stacked sheets of electrical-sheet steel and has eight poles. Axial AMB consists of 

two ring electromagnets, 7 and 9, ferromagnetic disk 8 fitted on the shaft, and inductive pickup 10 of 

axial translations of the rotor. When suspension is switched off, or in emergencies, the rotor rests on 

emergency bearings 2 and 11 with bronzegraphite inserts. Fig. 11 shows the block diagram of a radial 

magnetic bearing coordinate Y optimum regulator ensuring minimum integral square error of regulation 

339 
in the presence of limitation of the maximum value of the integral square manipulated variable in 

transient processes in the absence of disturbances. KI, K2, TI, T2, T3, T4, Ts - synthesized parameters of 

the regulator; liv, Viv, - variable components of signals; lie, Vic - direct components of signal; f3 = l2dhe 

(ref. 44). 

The production test results of the electrospindle model with AMB in operations of high-speed 

grinding prove the high efficiency of AMB. 

There is potential for AMB application in metal-cutting machine tools where usage of super-speed 

cutting regimes allows considerable decrease in wear of tools and improves accuracy of the work 

surface. The results of research work relating to development of the high-speed spindle of a metalcutting machine tool using magnetic bearings which is carried out in the Experimental Science Research 

Metal-cutting Machine Tools Institute, Moscow are presented in refs. 46-49. 

Today there is an actual problem, i.e., the problem of AMB application in cooling life-support system 

turbines of flying vehicles where for development of maximum efficiency, rotational speed of the rotor 

should amount to 150000-180000 r.p.m. Research work relating to this theme was carried out in the 

Moscow Aviation Institute and the results of the work are presented in refs. 50-53. 

MAGNETIC SUSPENSION OF NONCONTACT ELECTRIC MOTORS 

Beginning in 1970 a scientific group of the Electric machines department of the Moscow Energetics 

Institute has been engaged in development and study of magnetic suspension of high-speed rotors of 

high-frequency electric motors with the aim of increasing their operational life. Such studies were 

needed because with the increase of rotational speed, operation life of rolling -contact bearings dwindles 

sharply to several hundred hours. Air-gas-cushion (aerostatic and aerodynamic) bearings are rather 

difficult to manufacture and, as a rule, for their normal operation they need an air compressor and 

air purifiers to clean air from moisture and dust. The scientific group suggested a design of magnetic 

suspension of a high-speed rotor in a rotating magnetic field (ref. 54), which has two functions 

simultaneously: it provides magnetic suspension forces of the rotor and creates electromagnetic moment 

of rotation as in an ordinary electric motor. 

In accordance with this principle scientists have developed magnetic suspension of a disk-type rotor 

of a front electric motor (fig. 12) and of a cylindrical rotor of an electric motor (fig. 13) (ref. 55). On 

fig. 12 two stators (1 and 2) flank two-core disk-type rotors (3 and 4) of the face motor. Its active parts 

are connected by means of a hollow non-magnetic bush (5) inside which shaft (6) is rigidly secured. 

The rotor represents a bobbin designed to take up yarn. During starting and/or stoppage the rotor rests 

on safety bronze rings (7) and safety ball bearings (8) whose outer races do not contact the stator 

during magnetic stabilization of rotor position. The mass of the rotor is I kg. Fig. 13 displays a block 

340 
diagram of a combined magnetic suspension of a one-core rotor of a longitudinal axis autoregulation 

motor: 1, 2 - upper permanent magnets; 3, 4 - lower penn anent magnets; 5 - electromagnet; 6 - rotor 

position inductive pickup; 7 - core of stator with winding; 8 - rotor; and 9 - shaft: 

The suggested suspension of the rotor in a rotating magnetic working field with an autoregulation 

resonance circuit has the following advantages: economical operation, simplicity of design and 

suspension regulation scheme, absence of complicated control servo systems and special structural 

assemblies for rotor magnetic suspension. Feasibility of magnetic suspension of a rotor in a working 

rotating field was experimentally substantiated in 1973. 

VIBRATION ISOLATION DEVICES WITH MAGNETIC SUSPENSION 

In many cases the EMS may help essentially to solve the problem of vibration isolation of objects 

exposed to dynamic or kinematic vibrational and impact actions. At present mechanical elastic couplings 

prevail in vibration isolation engineering. When mechanical couplings are objectionable and therefore 

are replaced by electromagnetic suspension, in many cases it becomes necessary to provide effective 

protection of a suspended object against vibrations. High efficiency of EMS vibration isolation 

devices may be secured through implementation of wide potentialities of fonnation of desired dynamic 

suspension characteristics by the selection of proper algorithms to regulate voltages and currents of 

windings of power electromagnets in accordance with the characteristics of motion of the suspended 

object and mounting. Not many papers (refs. 56-61) are devoted to studies of EMS vibration isolation 

properties and to the development of vibration isolation devices incorporating EMS. 

In ref. 56 the authors analyse types, characteristics and perspectives of application of magnetic 

vibration isolators. 

In ref. 61 the author discusses vibration isolation properties of EMS devices of different designs. 

He has established dependences of these properties on parameters and transfer functions of stabilization 

circuits. 

A group of scientists from the Scientific Research Institute of Applied Mathematics and Cybernetics 

has developed vibration-isolated magnetic suspension of a body with a ferromagnetic disk. Refs. 57-59 

contain a description of the design and a functional diagram of the system of automatic regulation of 

magnetic suspension of a body which is suspended in a magnetic field by means of a ferromagnetic 

disk attached to it; diameter of the disk is 300 mm and clearance between the disk and electromagnet 

is 5 mm. Experimenters suspended a body, mass 10 kg, with watt consumption being 100 W. The 

frequency of body oscillations in the horizontal plane was 0.25-1 herz. Fig. 14 presents a diagrammatic 

representation of the suspension: A - front view; B - top view; 1 - electromagnets; 2 - first channel 

341 
pickup coil; 3 - coils of pickups of the second and third channels; 4 - suspending body; and 5 -

conductive disk. 

The functional diagram of the suspension control system is shown on fig. 15; it consists of three 

channels: channel 1 - body vertical stabilization and two identical channels 2, 3 - stabilization of the 

body according to angle of inclination and stabilization of the body in accordance with displacements 

in directions going via opposite electromagnets !l M • Each channel has its own inductive pickup .D.. 

Signals of pickups 11 are transduced by amplifying-and-converting links Y n into voltages of direct 

current, the value and polarity of which are determined by values and directions of displacements of 

the body along corresponding coordinates. To ensure stability channels 2 and 3 are supplemented with 

forcing links <P and channel 1 is provided with correcting feedback OC responding to the sum of 

currents of B 11 ., Y M - power amplifiers. T - links time constants; p - differentiation statement. 

The suspension, if recommended for application in vibration isolation of instruments when mounting, 

is exposed to horizontal oscillations. 

Present-day main features of gravimetric measurements consist of stringent requirements as to their 

accuracy. This is attributed to the fact that changes of gravitational force are small and from the pole 

to the equator they do not exeed 0.5%. The biggest anomalies do not exceed 0.05% of the value of 

free-fall acceleration. Urgency is attached to the problem of measuring gravitational force on a moving 

base (ship, aircraft, etc.). The specifics of a moving base assume that measurements are made against 

the background of inertia interferences, the value of which are considerably higher than variations of 

free-fall acceleration. One of the main methods of eliminating the influence of inertia interferences is 

suppression of the interferences by means of vibration isolation devices. On the strength of equivalence 

of gravitational and inertia forces it is principally impossible to derive a desired signal from gravimeter 

readings, i.e. to segregate free-fall acceleration from disturbing accelerations. For separation of inertia 

acceleration and free-fall acceleration scientists exploit their differing characteristics. Accelerations of 

motion change with relatively high frequency, whereas free-fall acceleration changes slowly. Using 

this phenomenon we may apply frequency filtering of the disturbances. 

Vibration isolation of a ballistic gravimeter using an interferrometric method of measurements may 

be effected by installing an auxiliary comer reflector on the vibration damper which has the capacity 

for filtering low frequencies. 

The Kharkov Scientific Research Metrology Institute, in cooperation with the Moscow Aviation 

Institute, has developed a vibration isolation device in which, for construction of the vibration damper, 

the initiators suggested the use of a solenoid magnetic suspension effecting the elastic coupling of the 

isolated object with the vibrating base and possessing a significant extent of tractive characteristic and 

342 
zone of stable equilibriwn in the absence of an external system of regulation (ref. 60). Fig. 16 displays 

a diagram of a ballistic gravimeter, showing 1 - accelerometer; 2 - vibration damper; 3 - regulator; 

4 - auxiliary comer reflector; 5 - interferometer; 6 - ballistic unit; 7 - test body; 8 - electromagnetic 

centering system; 9 - laser; and 10 - photodetector. The accelerometer senses disturbed motion of the 

isolated object and reacts accordingly; from the accelerometer output the signal, via the filter of upper 

frequencies, enters the input of the correcting circuit which produces the law of control of feedback 

force action regulating the position of the movable part of the vibration damper. The regulator is a 

proportionally-integrally-differential regulator. The regulator incotpOrates an accelerometer in which 

elastic coupling of the inertia element with the body is effected with the aid of a magnetic support 

with a resonant circuit. For damping of motion of the inertia element all mechanical coupling is 

filled with oil. The accelerometer has small weight and dimensions. The developed vibration damper 

incorporates a combined system of electromagnetic centering with resonant circuits and additional 

active electromagnetic damping which ensures horizontal stabilization of the movable part of the 

vibration damper, having a weight of 200 g and an initial clearance of 0.15 mm at accelerations 

equal to 0.1 g. Design of the device also allows angular stabilization, the factor which is rather 

important for interferential methods of measurements. An experimental test of the vibration damper in 

conjunction with the ballistic gravimeter has shown that the vibration damper eliminates the effect of 

inertia interferences, thus permitting improvement of accuracy of determination of free-fall acceleration 

under real test conditions by 2.5-7 times. 

SYSTEMS OF MAGNETIC SUSPENSION FOR WIND TUNNELS 

Absolute absence of mechanical contacts with the suspended object (test model) allows us to solve 

the principal problems of aerodynamics which cannot be solved by conventional means: measurement 

of aerodynamic loads acting on the model without the effect of mechanical supporting devices, wake 

studies, study of base pressure, etc.; these opportunities stimulate growing interest to EMS engineering 

(ref. 62). 

At present there are two systems of electromagnetic suspension for wind tunnels in the USSR. One 

was constructed in 1983 as a result of a collaboration between the Moscow Aviation Institute and 

the Central Aero-Hydrodynamic Institute and was intended for studies of models with six degrees of 

freedom in a subsonic wind tunnel, the working part of which measured 400 mm x 600 mm (ref. 63). 

The second system was created in the Moscow Aviation Institute in 1989; it is designed for laboratory 

investigations and for the development of magnetic suspension technology. The suspension has six 

degrees of freedom and its working part measures 300 mm x 400 mm. Fig. 17 displays a model 

suspended in the suspension system of the Moscow Aviation Institute (ref. 64). 

343 
Both systems comprise seven electromagnets which are arranged as shown on fig. 18. 

The optical system for determination of model position is based on usage of photodiode regions. 

Rays of light of special form cross the model as shown on fig. 19. Position of the model can be 

calculated by measuring the position of the model shadow on the surfaces of the detectors. The original 

design of the sensitive system (ref. 65) ensures determination of vertical and horizontal displacements 

of the model in one optical channel (fig. 20). 

Both systems of electromagnetic suspension have analog control systems. Their design adopted 

control algorithms which provide maximum domain of stability of the suspended object in the presence 

of limitations of control actions (refs. 66, 67). Model roll stabilization is effected by passive means. 

All electromagnets have copper windings with natural cooling and are provided with bipolar 

transistorized power sources. In the process of calibration, known values of static forces and moments 

are applied to the model and position of the model and currents of electromagnets are measured. 

Aerodynamic loads are computed by means of a digital minicomputer on the basis of established 

empirical dependences between currents of electromagnets, position of the model and external loads 

(ref. 68). 

The current research efforts are directed at realization of the following technical problems: 

1. Tests of models at high angles of attack, dynamic tests; 

2. Development of a digital control system; 

3. Perfection of means and methods of measurements. 

MAGNETICALLY LEVITATED TRAINS 

Nowadays there exists an essential problem - to create a new principal means of ground transport, 

the characteristics of which would be as follows: unlimited speed of movement, high economy index, 

absence of pollution and a minimum of noise emission. The solution of this problem is connected with 

high-speed ground transport (HSGT) using magnetic levitation. 

Since 1976 the USSR has been addressing the problem of HSGT. Up to 1980 general areas 

and geographical directions of HSGT introduction were defined. Models of various systems were 

constructed and tested, such as linear engines and magnetic suspension systems as well as their feeding 

and control parts, and general normal and alarm breaking power supply systems. Also, there were 

elaborations of technical assignments for experimental carriages of 40 tons weight and for prototypes 

with electromagnetic suspension EMS added with one-side linear asynchronous engine OLAE and 

344 
with electrodynamic suspension system EDS added with linear synchronous engine LSE. Experimental 

HSOT-system "HE-Ol" was created in the city of Novocherkassk. The system "HE-Ol" has L-way 

with pennitted loading of 10 tons, air gap is 0.02-0.025 m, EMS, the number of electromagnets is at 

four each; the lifting force of the electromagnetic system is 29.4 kN; the side force - 14.72 kN. 

The prototype for HSOT in Ramenskoye city has a track of 600 metres in length for motion testing. 

In 1979 the first in the USSR with a carriage of 10 tons weight on constant magnets was tested at a 

distance of 120 metres. 

From 1980 on that prototype and the main parts of new devices of HSOT were tested. In 1985 an 

experimental carriage of 14 tons weight with EMS was created. In 1986 complex testing began on a 

prototype route, and a speed of 30 km per hour was reached. 

The main technical characteristics of the USSR's HSOT systems which are working out in the USSR 

are given in table 1 (refs. 69, 70). Here "Soyus-E" is HSOT-train with EMS and OLAE, "Soyus-D" is 

HSOT -train with EDS and LSE. 

CONCLUSION 

The presented article reflects the main technical applications and the main directions of development 

of magnetic suspension systems and magnetic bearings but it does not pretend to completely cover the 

discussed problem. The analysed advantages of magnetic suspension systems and ever more increasing 

requirements to bearing assemblies of instruments, mechanisms and machines promote wider and wider 

introduction of noncontact systems of magnetic suspension. 

The author expresses his gratitude to Dr. R. A. Kilgore (NASA Langley) and to the Organizing 

Committee of ISMST for their support and for giving us the opportunity to present this work to the 

Symposium. 

345 
Table 1. 

r----------------------------------------.-----------------------------------------, 

Parameters 

Size, m 

- width 

- height 

Number of carriages in train 

Carriage mass, tons 

Max i mum speed, km pe~"' hour· 

Number of passengers in train 

ar·mcha i 1"'S 

Working period of time in a 

d-:3.Y, hours 

Duration of stand, min 

Passenger passing ability in a 

day, passenger-km 

Acceleration when starting, 

m • pel"' sq • sec· 

Slowing down when braking, 

m • pel' sq • sec. : - 1 -_ "'rna I 

alarm 

Traction power, roW 

346 

Parameters'Value for 

HE - 01 

4-12 

1.77 

1.48 

1 

..,. 

--' 

50 

2 

Soyus-E 

'-Ie £..J 

3. E. 

4 .-:. .... 

up to 10 

40 

400 

870 

18 

r-;. ._' 

5.48 

up to 1 

up to 1 

up to :; 

50 

I HSGT-systemsl I 

SOYT.ls-D 

'-.e: 

~ __ f 

4 .-: . . ... 

up to 10 

40 

400 

870 

18 

..., ._' 

up to 1.5 

up to 1 

up to ..,. 

I ._' 

50 I 

J 
8 

7 

,~ Sr==----' 

~1 

Fig. 1 

Double magnetic suspension 

x 

Fig. 4 

EMS for gyrocompass 

T 

Fig. 2 

Two-axle magnetoresonant suspension 

y 

x 

Fig. 3 

Three-axle magnetoresonant suspension 

x 

x 

Fig. 5 Fig. 6 

EMS for torque magnetometer 

347 
348 

3 2 

$ 1 

~ -,;-rp rp 1 X3 -1 

u -- p2 -1 - Tp+1 -rp 

5 

-1 

U 

4 

T+l I (p+l) Xl - ,... 

, 

Fig. 7 Block diagram of EMS optimal control system 

z 

y Fig. 8 Three-mass model of EMS 

z 

x 

Fig. 9 An actuator device of the attitude control system for 

orientation of space vehicles 

• 
3 

Fig. 10 

Block diagram of high-speed electro spindle 

Fig. 11 

Block diagram of a radial magnetic bearing coordinate 

Y optimum regulator 

A - A 

349 
350 

Fig. 12 

EMS of disk-type rotor of front electric 

motor 

Fig. 13 

1 

~ 

2 

9 

-----8 

7 

4 

5 

6 

EMS of cylindrical rotor of electric motor 
Fig. 14 

Vibration isolation 

EMS of body with 

ferromagnetic disk 

A) Front view 

B) Top view 

5 

_l+Tp cp K(p)-l + liP 

T:::50HC, TrlHc 

A) 

2 

8) 

-K 

1------------+--+----1 0 C K (p) = Tp+ 1 1-----( 

'----' K=-sl 0, T~l OI1C 

KaHan 3 

cp 

Fig. 15 

Functional diagram of the suspension control system 

351 
Fig. 16 Vibration isolation of a ballistic gravimeter 

Fig. 17 Model suspended in suspension system of the MAr 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

352 
1--

1 

1 

1 

6 

y 

2 

7 

\ 

I 

/ 

" 5 / ---

3 

Fig. 18 EMS for wind tunnel 

y 

Dl 

ZI Y 

4,5 

Fig. 19 Position sensing system 

Dl 

D2 

Fig. 20 Signal processing 

6,7 

y 

2,3 

353 
REFERENCES 

1. Earnshaw S. On the Nature of the Molecular Forces - Transactions of Cambridge Philips Society -

1842 - v.7. 

2. Brounbeck W. Freischuebende Korperin Electrischen und Magnetischen Feld. - Ztschr. f. Physik. 

- 1939 - Bd 112 - H.7, 8. 

3. Arkadiev V.K. A Floating Magnet. - Nature - 1947 - v.160. 

4. Ponizovsky V.M. Induction of Large Centrifugal Fields II -Instruments and Technique of Experiment 

(ITE). - 1957 - No.7 - pp. 69-72. 

5. Beans J.W., Joung J.J., Moore J.W., Journal of Applied Physics - 1946 - v.17. 

6. Ponizovsky V.M. Double Magnetic Suspension of Ferromagnetic Rotors II ITE - 1976 - No.1 -

pp. 181-183. 

7. Osokin Y.A., Gerdy V.N., Maikov K.A., Stankevitch H.H. Theory and Application of Electromagnetic Suspensions - Moscow (M.): Machine Building. 1980 - 288 p. 

8. Vyshkov Y.D., Ivanov B.I. Magnetic Bearings in Automatics - M.: Energy - 1978 - 160 p. 

9. Voronkov V.S., Pozdeev O.D., Sandalov V.M. On Dynamics of Magnetic Suspension II Transactions 

of Colleges, Electromechanics - 1974 - No. 10 - pp. 1082-1089. 

10. Ganiev R.F., Vorobiev V.M., Liuty A.I. Resonance Oscillations of Gyroscopic Systems - Kiev: 

Scientific Thought - 1979 - 186 p. 

11. Denisov G.G., Posdeev O.D., Khimin Y.A. On Rotary Hysteresis in Variable Magnetic Fields /I 

Transactions of Colleges, Physics - 1978 - No.5 - pp. 64-67. 

12. Stepaniants G.A., Tararoschenko N.S. On Structure of Laws of Control Providing Absolute Stability 

of Control Systems with Unstable Object II Reports of Academy of Sciences of the USSR. - 1970 -

No.4 - pp. 774-776. 

13. Voronkov V.S., Posdeev O.D. Effect of High Frequency Disturbances on Operation of Magnetic 

Suspension II Transactions of Colleges, Electromechanics - 1979 - No.9 - pp. 945-950. 

14. Voronkov V.S., Pozdeev O.D. Optimization of System of Stabilization of Magnetic Suspension II 

Transactions of Colleges, Instrument Engineering - 1979 - No.9 - pp. 53-57. 

354 
15. Voronkov V.S., Pozdeev 0.0. Investigation of Systems of Stabilization of Magnetic Bearing II 

Transactions of USSR Academy of Sciences, Magnetics of Rigid Body (MRB) - 1980 - No.4 -

pp.30-39. 

16. Voronkov V.S. Synthesis of System of Stabilization of Magnetic Suspension and Experimental 

Investigation of its Dynamics 1/ Transactions of Colleges, Instrument Engineering - No.8 - pp. 32-37. 

17. Voronkov V.S. Synthesis and Analysis of Systems of Stabilization of Magnetic Suspension: Author's 

Essay of Dissertation of Candidate of Technical Sciences - M. - 1982. 

18. Sorin V.M. Stability of Rotor in Electromagnetic Suspension with Allowance for Sluggishness of its 

Circuits 1/ Works of Leningrad Poly technical Institute (LPI) - 1969 - No.307 - pp. 46-53. 

19. Sorin V.M. Sone Types of Vibrations of Rotor in Electromagnetic Suspension II Works of LPI -

1982 - No.386 - pp. 94-98. 

20. Sorin V.M. Moments Acting on Non-spherical Body in Electromagnetic Suspension II Engineering 

Journal, MRB - 1968 - No.2 - pp. 31-39. 

21. Martynenko Y.G. Drifts of Electrostatic Gyroscope Provoked by Non-sphericity of Rotor II Transactions of USSR Academy of Sciences, MRB - 1970 - No.1 - pp. 10-18. 

22. Urman Y.M. Moment of Forces Provoked by Rotor Non-sphericity in Cryogenic Suspension II 

Transactions of Colleges, Instrument Engineering - 1974 - No.ll - pp. 87-92. 

23. Urman Y.M. Drifting moments provoked by rotor nonsphericity in suspension having axial symmetric 

field II Transactions of USSR Academy of Sciences, MIT - 1973 - No.1 - pp. 24-31. 

24. Martynenko Y.G., Savchenko T.A. Resonance Motions of Gyroscope with Noncontact Suspension 

on Vibrating Base II Transactins of USSR Academy of Sciences, MRB - 1977 - No.6 - pp. 16-23. 

25. Savchenko T.A. Stability of Motion of Gyroscope with Noncontact Suspension at Angular Vibrations 

of the Base II Transactions of USSR Academy of Sciences, MRB - 1979 - No.3 - pp. 7-14. 

26. Savchenko T.A. Resonance Motions of Gryoscope with Noncontact Suspension in the Presence of 

Two-component Vibration of the Base 1/ Transactions of USSR Academy of Science, MRB - 1980 -

No.6 - pp. 9-16. 

27. Voronkov V.S., Pozdeev 0.0. Synthesis of System of Stablilization of Magnetic Suspension with 

Allowance for Elasticity of Elements of its Construction 1/ Transactions of Colleges, Instrument 

Engineering - 1987 - No.2 - pp. 61-65. 

355 
28. Voronkov V.S. Analysis of Dynamics of System of Stabilization of Elastic Base Magnetic Suspension 

/I Transactions of Colleges, Instrument Engineering - 1988 - No.7 - pp. 41-45. 

29. Ishlinsky A.Y., Zhuravlev V.F., K1imov D.M. Heat Barrier of Accuracy of Gyroscopes Having 

Noncontact Suspension /I Present-day Problems of Mathematics and Mechanics and Appendices -

M.: Moscow Physicotechnical Institute - 1983 - pp. 21-28. 

30. Kobrin A.I., Martynenko Y.G. Effects of Heat Oscillations of Crystal Lattice on Accuracy of 

Gyroscope in Noncontact Suspension II Moscow Energetics Institute (MEl) works. - 1983 - No.14 -

pp. 10-15. 

31. Ryabov A.B. Determination of Main Vector and Main Moment of Forces Acting on Superconductive 

Body in Magnetic Field II Transactions of USSR Academy of Sciences, MRB - 1969 - No.6 -

pp.34-37. 

32. Zhuravlev V.F., Rudenko V.M. Refering to Analysis of Power Characteristics of Suspension of 

Cryogenic Gyroscope II Transactions of USSR Academy of Sciences, MRB - 1983 - No.1 - pp. 9-15. 

33. Sheremetievsky N.N. Problems of Construction of Flywheel-motor (spherical type) for Control of 

Position of Space Object II Report to World Electrotechnical Congress - 1977 - p. 15. 

34. Veinberg D.M., Vereschagin V.P., Danilov-Nitusov N.N., Sheremetievsky N.N. Systems of Magnetic 

Suspension in Executive Organs of Control of Orientation of Space Vehicles II Transactions of USSR 

Academy of Science, MRB - 1981 - No.3 - pp. 152-157. 

35. Sheremetievsky N.N., Veinberg D.M., Vereshchagin V.P., Danilov-Nitusov N.N. Powered Gyroscope with Electromagnetic Bearings for the Orientation System of Orbital Stations /I Transactions 

of USSR Academy of Sciences, Space Researches - 1983 - Vol. 21 - No.1 - pp. 10-16. 

36. Sheremetievsky N.N. Electromechanics and Peace Cosmos II Electrotechnics - 1987 - No.6 - pp. 

10-16. 

37. Sheremetievsky N.N. Magnetic Suspension of Rotors of the Electric Machines and Mechanisms /I 

Works of ASRIE - 1989 - Vol. 89. 

38. Vyshkov Y.D., Zheltov V.P., Korobkov V.P. Identification of Power Characteristics of Electromagnets of Dynamic Stands II Works of Moscow Aviation Institute - 1974 - No.305 - pp. 74-78. 

39. Vyshkov Y.D., Korobkov V.P. Moment of Electromagnetic Friction in Spherical Rotor Magnetic 

Suspension System. - In book: Automatization of Technological Processes in Different Branches of 

National Economy - Kuibishev - 1975 - pp. 279-280. 

356 
40. Vyshkov Y.D., Ivanov V.I., Korobkov V.P. Investigation of Braking Moments Acting on Spherical 

Rotor in Electromagnetic Suspension - In book: Present-day Methods and Means of Balancing of 

Machines and Instruments - Yaroslavl - 1976 - pp. 6-7. 

41. Zhuravlev Y.N. Electromagnetic Forces in Conical Radial 1brust Electromagnetic Bearing II 

Electricity - 1982 - No.ll - pp. 61-63. 

42. Zhuravlev Y.N., Vetlitsin A.M., Kbmylko N.V. Experimental Investigation of Electromagnetic 

Bearings for High-speed Rotors II Machines and Tools - 1982 - No.5 - pp. 13-14. 

43. Zhuravlev Y.N. Synthesis of Linear Optimum System of Control of Magnetic Suspension of Rigid 

Rotor II Science of Machines - No.4 - 1987 - pp. 49-56. 

44. Zhuravlev Y.N., Kbmylko N.V. Dynamic Optimization of Linear System of Control of Active 

Magnetic Bearing II Transactions of Colleges, Electromechanics - No.12 - 1987 - pp. 74-82. 

45. Zhuravlev Y.N. Control of Dynamics of Flexible Rotor in Active Magnetic Bearings II Transactions 

of Colleges, Instrument Engineering - 1988 - No.6 - pp. 7-12. 

46. Averianov OJ., Betin V.N., Eisenshtock OJ. System of Control of Electromagnetic Bearings of 

Spindle II Machines and Tools - 1985 - No.ll - pp. 19-20. 

47. Vasiliev A.V., Betin V.N., Eisenshtock OJ. Eletromagnetic Bearings with External Automatic 

Stabilization II Machines and Tools - 1985 - No.9 - pp. 16-18. 

48. Betin V.N., Eisenshtock OJ. Dynamic of Radial Motion Spindle on Magnetic Bearings II Machines 

and Tools - 1988 - No.5 - pp. 20-22. 

49. Vasiliev A.V., Eisenshtock OJ. Calculation of Parameters of Electromagnetic Bearings II Machines 

and Tools - 1989 - No.2 - pp. 16-19. 

50. Shleenkin L.A. Radial Electromagnetic Suspension of High-speed Rotors II Electromechanical. 

Electromagnetic and Electronic Devices of Systems of Electrical Equipment of Flying Vehicles 

- M.: Moscow Aviation Institute - 1984 - pp. 44-47. 

51. Shleenkin L.A. Synthesis of System of Stabilization of Active Magnetic Bearing - In book: Electronic 

Devices of Systems of Electrical Equipment of Flying Vehicles - M.: Moscow Aviation Institute -

1985 - pp. 42-46. 

52. Bushuev V.A., Kuznetsov V.V., Shleenkin L.A. Radial Magnetic Bearings of Electrospindels - In 

book: Electric Drive and Automatization in Machine Building - M.: All-union Correspondencecourse Machine Building Institute - 1985. 

357 
53. Shleenkin L.A. Multichannel System of Stabilization of High-speed Rotor - In book: On-board 

Converters of Systems of Electrical Equipment of Flying Vehicles - M.: Moscow Aviation Institute -

1986 - pp. 13-18. 

54. Sharov V.S., Galkin V.1. Gyromotor with Magnetic Suspension of Ferromagnetic Rotor /I Works of 

MEl - 1974 - No.187 - pp. 128-131. 

55. Sharov V.S. Features of Design of Magnetic Suspension of Rotors of High-speed Electromotors -

M.: MEl - 1982 - p. 85. 

56. Piatin Y.M., Taisov V.N. Magnetic Vibration Isolators. Types, Characteristics and Perspectives of 

Application // Works of MADI - 1978 - No.139 - pp. 90-92. 

57. Vorobjev V.M., Vorobjev-Obukhov A.V., Dmitriev A.Y., Pozdeev O.D. Magnetic Suspension of 

Body with Ferromagnetic Disk /I ITE - 1976 - No.5 - pp. 245-247. 

58. Vorobjev V.M., Vorobjev-Obukhov A.V., Pozdeev O.D. Vibration Isolated Electromagnetic Suspension - In book: Vibration Isolation of Man-operator and Vibrations in Machines - M.: Science -

1977 - pp. 57-61. 

59. Vorobjev-Obukhov A.V. Investigation of Stability of Magnetic Suspension with Ferromagnetic Disk 

/I Transactions of Colleges, Electromechanics - 1978 - No.12 - pp. 1300-1305. 

60. Shurubkin V.D. Investigation and Development of Ballistic Gravimeter Magnetic Suspension 

Vibration Damper, (the Gravimeter is Designed for Detennination of Absolute Values of Free 

Fall Acceleration on a Movable Base): Author's Essay of Dessertation of Candidate of Technical 

Sciences - M.: Moscow Aviation Institute - 1981. 

61. Vyshkov Y.D. Vibration Isolation Properties of Electromagntic Suspension Devices 1/ Transactions 

of Colleges, Instrument Engineering - 1985 - No.9 - pp. 49-54. 

62. Beliaev L.B., Shlnnanov P.M. Magnetic Suspension of Models in Wind Tunnels /I Reviews of 

Central Aero-Hydrodynamic Institute - 1979 - No.557 - p. 58. 

63. Vyshkov Y.D., Kovalnogov S.A., Usachov V.N., Shapovalov G.K. Magnetic Suspension and Balance 

System for Low-speed Wind Tunnel /I Scientific Notes of Central Aero-Hyrodynamic Institute -

1986 - No.4 - pp. 94-97. 

64. Kuzin A.V. Magnetic Suspension System for Aerodynamic Researches /I Instruments and Technique 

of Experiment - 1990 - No.4 - pp. 

358 
65. Kuzin A.V. Photoelectrical Sensors ofthe Magnetic Suspension Systems II Transactions of Colleges, 

Instrument Engineering - 1990 - No.4 - pp. 63-67. 

66. Kuzin A.V., Vyshkov Y.D. Optimization of Control in Multicomponental System of Electromagnetic 

Suspension II Transactions of Colleges, Instrument Engineering - 1987 - No.ll - pp. 44-49. 

67. Kuzin A.V. Synthesis of the Magnetic Suspension Stabilization System for the Models in Wind 

Tunnel II Transactions of Colleges, Electromechanics - 1990 - No.5 - pp. 48-57. 

68. Vyshkov Y.D., Kuzin A.V., Usachov V.N. Force Measurement Using Electromagnetic Suspension 

of Boaded Object. Paper presented at the 2nd Conference, Force Measurements. Modem Methods 

and Means - Novosibirsk - 1986 - pp. 43-44. 

69. Bocharov V.1. High-Speed Ground Transport with Linear Drive and Magnetic Suspension II M.: 

Transport - 1985 - 279 p. 

70. Bocharov V.I. Transport with Superconductive Magnets II Rostov-na-Donu: University of Rostov -

1988 - 152 p. 

359 
Session 7 

SENSORS AND CONTROLS 2 

Chairman - Monique Gaffney 

SatCon Technology Corporation 

PRECEDING PAGE BLANK NOT F!LMfD 361 
N92-27741 

EXTENDED H2 SYNTHESIS 

FOR MULTIPLE DEGREE-OF-FREEDOM CONTROLLERS 

R. David Hampton 

Carl R. Knospe 

Center for Innovative Technology 

University of Virginia 

August 16, 1991 

PRECEDING PAGfi: BLANK NOT F!LMfD 

363 
SUMMARY 

H2 synthesis te~hniques are developed for a general multiple-input-multiple-output 

(MIMO) ~ystem subject to both stochastic and deterministic disturbances. The H2 ~ynthesIs. IS ~xtended by incorporati?n of anticipated disturbance power-spectral-density mform~tIOn mto .the controller-desIg? process, as well as by frequency weightings of g.eneral~zed coordI!lates and control mputs. The methodology is applied to a simple 

~mgle:-mput-multIpl~utput. (S~MO) ~roblem, analogous to the type of vibration 

IsolatIOn problem antIcIpated m mlcrogravlty research experiments. 

INTRODUCTION 

The vibration environment onboard current and planned manned orbiters requires 

isolation for microgravity science experiments. The disturbance frequencies are sufficiently 

low, and the attenuation requirements sufficiently great, so as to preclude a solely passive 

isolation system (ref. 1). 

Since the disturbances to be attenuated are three-dimensional (ref 2, p.2), the 

isolation actuator must be capable of acting over six degrees of freedom. The requisite 

multiple-degree-of-freedom (MDOF) controller is much more difficult to design than a 

single-degree-of-freedom (SDOF) controller, because the isolation system has many 

inputs (actuator forces) and outputs (measured displacements and accelerations). 

Multiple-input-multiple-output (MIMO) designs can be very susceptible to unmodeled 

cross-coupling between channels of input or output (ref. 3), a problem not encountered in 

SDOF design. The control forces used must therefore be properly coordinated if the 

controller's performance is to be sufficiently insensitive to unmodeled dynamics (Le., 

robust). The design of a robust MIMO control system requires the iterative use of 

synthesis and analysis tools, the former for controller design and the latter for system 

performance and stability evaluation (ref. 4). 

A particular vibration isolation problem may involve different kinds of undesirable 

outputs, such as excessive absolute accelerations and unacceptable relative displacements. 

Some of these undesired outputs may be more important than others, and the degree of 

undesirability may vary with direction or frequency. For example, rattlespace constraints 

may be highly directional. Or a crystal-growth experiment may be particularly sensitive 

to accelerations at certain frequencies (ref. 2, p. 7) or in certain directions. One of the 

365 
goals, then, must be to design a controller capable of minimizing selected plant outputs as 

dictated by these considerations. 

Plant outputs, however, cannot be minimized apart from consideration of the 

associated control costs, because any active control both consumes power and releases heat. 

Since both of these costs are of concern in a space environment, the control effort used 

should not be excessive. And at higher frequencies control effort should also be minimized 

in order to limit controller bandwidth for the sake of robustness concerns (ref. 5, p. 218). 

This paper describes a design procedure, known as extended H2 synthesis (ref. 5, p. 

267), for developing active isolation system controllers. A single-input-multiple--output 

design problem is then addressed using the presented procedure. 

BASIC PROBLEM AND SOLUTION 

Problem Statement 

We will use Linear Quadratic Gaussian (LQG) theory to design the MDOF 

controller. This theory has been extensively studied and ussed. LQG is chosen as a 

synthesis procedure since the quadratic performance index relates well to 

root-mean-square statistics and power spectral density. 

When linearized, the differential equations of motion of the plant can be 

representable in state-space form by the first order system of equations 

i: = AK + B!! + Edid + Es~ y = CK + D!! 

~ = Y + Mn 

where K is the state vector, y is the output vector, ~ is the measurement vector, u is the 

control vector, id is a known or measurable disturbance vector, and ~ and n are processand sensor noise respectively. We begin by making a series of reasonable mathematical 

assumptions. Assume that not all states are accessible, so that rank C ~ dim K. Let the 

initial conditions on the state vector be K (0) = Ko; let Ko, ~, n, and id be independent and 

bounded; let Ko be Gaussian (ref. 6, p. 272); and let n and ~ be zero-mean white 

Gaussian, with cov[~(t),~( T)] = Vtb(t-T) and cov[n(t), n( T)] = V3b(t-T) (ref. 6, p. 272). 

Assume that {A,B} and {A,Es Vttj2} are stabilizable, where Vt = Vttj2 Vttj2* (the 

asterisk here means "conjugate transpose"); and that {C,A} is detectable (ref. 5, p. 226). 

Let Vt and V3 be positive semidefinite (PSD) and positive definite (PD), respectively. 

We choose a performance index of the form 

(2) 

where Wt is PSD and W3 is PD (ref. 6; pp. 272,276). "(511 is the expected-value operator, 

needed since the system is excited stochastically by Ws. The cost rate functional form 

366 
(with II lim {") is used to allow both for the white noise disturbance Ws and for the 

T ----+00 

non-dwindling disturbance fd. 

If Z(t) is defined by Z(t)= {~(T), a ~ T ~ t}; and if 11(t) = ~[t,Z(t),fd] defines the set 

of admissible controls (ref. 6, p. 272), where ~ is a vector operator that is linear in terms of 

its arguments; the basic problem objective is to find an admissible control function 11*(t) 

which minimizes J with respect to the set of admissible control functions 11(t). [The 

asterisk here indicates optimality, in the sense defined by Eqn. (2).] 

Problem Decomposition 

The basic problem, as stated in Eqns. (1) and (2), can be decomposed into two 

parallel subproblems, one stochastic and the other deterministic. Suppose that ~ = ~s + ~d, where ~s is the portion of the system response due to disturbance ~, and where ~d is 

the portion of the response due to fd. Let Ys, Yd, ~s, ~d, Zs, Zd, 11s, and 11d be 

correspondingly defined. 

Then J = lim Tl JT {6([~I + ~I][Wl W2]{~S ++ ~d})} dt 

T--1OO a s d WI W !!.s !!.d 2 3 

(3a) 

can be reduced to J = Js + Jd, where 

Js = lim Tl J T {6 ([~I + !!.I] [W 

1 

W2] {~uS})} dt 

T --100 aSs WI W _s 

2 3 

(3b) 

and 1 T( [WIW2]) J d = lim T J [~I + !!. I ] {~d} d t 

T --100 Odd WI W !!.d 2 3 

(3c) 

The problem is now separable into a stochastic- and a deterministic subproblem, each of 

which has an analytical solution. The two subproblems are stated, and their solutions 

presented (without development) below. 

Statement: 

Given: 

Stochastic Subproblem and Solution 

~S = A ~s + B !!.s + Es w s 

Ys = C ~s + D!!.s (rank C ~ dim ~s) 

~s = Ys + M!!. 

{A,B} is stabilizable, {C,A 1 is detectable 

~s(O) = ~so is Gaussian with zero mean 

(4a) 

(4b) 

(4c) 

367 
368 

~so, ws, and!! are independent and bounded 

such that cov~s(t), Ws(T)] = V1b(t-T) 

and cov[Q(t),!!( T)] = V3b(t-T) 

where V 1 is PSD and V 3 is PD 

Js = lim+-{6' fT j[5~][W1W2l{~S})dt} T-+oo 0 \ W' W !!s 

2 3 

where \"11 is PSD and W 3 is PD 

~s(t) = {~s(T), 0 ~ T ~ t}, !!s(t) = ~s[t,~s(t)] 

defines the set of admissible controls 

(4d) 

(4e) 

( 4f) 

(4g) 

Find: An admissible control function !!s*(t) which minimizes Js with respect 

to the admissible control functions !!s( t) 

Solution (See ref. 6, pp. 272-277; and ref. 7, ch. 11): 

!!s* (t) = -K ~s(t) (5a) 

Statement: 

Given: 

where ~s is an estimate of ~s using a Luenberger observer (ref. 7, pp. 

288-289) having observer gain matrix L 

K = Wi1 (B'P + W2') (5b) 

P is the unique PD solution to 

PA + A'P - (PB + W2) Wi1(PB + W2)' + W1 = 0 (5c) 

L = QC' (M V3 M,)-l (5d) 

Q is the unique PD solution to 

AQ + QA' - QC' (M V3M,)-lCQ + Es V1 E~ = 0 (5e) 

P exists if {A,B} is stabilizable and {C,A} is detectable 

or if the system is asymptotically stable 

Q exists if {A, Es Vl1j2} is stabilizable and {C,A} is detectable 

or if the system is asymptotically stable 

Deterministic Subproblem and Solution 

~d = A Kd + B !!d + Ed fd 

Yd = C ~d + D !!d (rank C ~ dim ~d) 

~d = Yd 

{A,B} is stabilizable, {C,A} is detectable 

~d(O) = ~dO 

(6a) 

(6b) 

(6c) 
~dO and fd are independent and bounded 

Jd = 1 i m T1 f T (~d!!d [W1 W2] {~d}) dt 

T-too 0 W2 W3 !!d 

(6d) 

where W1 is PSD and W3 is PD 

~d = {~d( T), 0 ~ T ~ t}, !!d(t) = ~d[t, Zd(t), fd] (6e) 

defines the set of admissible controls 

Find: An admissible control function !!d*(t) which minimizes Jd with respect to the 

set of admissible control functions !!d(t) 

Solution (refs. 8; 9; and 10, pp. 156-157): 

!!d* (t) = -K ~d - Wi1 B' f~ exp[-A'(t-T)] PEd fd(T) dT 

where K = Wi1 (B'P + W2) 

P is the unique PD solution to 

-1 

PA + A'P ~ (PB + W2) W 3 (PB + W2)' + W1 = 0 

P exists if {A,B} is stabilizable and {C,A} is detectable 

or if the system is asymptotically stable 

Combined Solution to Basic Problem 

(7a) 

(7b) 

(7c) 

When rank C < dim 2fd, an estimate Kd of 2fd must be used in the feedback. If one uses 

an asymptotic (i.e., Luenberger) observer, with gains L chosen to give an optimal solution 

to the stochastic subproblem, he can then combine the stochastic and deterministic 

subproblem solutions so as to use the same observer and regulator. This allows the optimal 

solution (feedback portion) to be realized physically. If such a choice is made, 

!!*(t) = u~(t) +!!~(t) = -K ~(t) _Wi1 B'f~ exp[-A'(t-T)] PEd fd(T)dT (8a) 

where ~ is an estimate of ~ using a Luenberger observer 

having observer gain matrix L 

K = Wi1 (B'P + W2') 

L = QC'(M V3 M,)-l 

P ,Q, and A are as defined previously 

(8b) 

(8c) 

If fs and!!. are correlated by 6 [fs(t), !!.(T)] = V2D(t-T), then the above solution has the 

modification (ref. 7, pp. 414--417) that 

L = (QC' + Es V2)(M V3M,)-1 (8d) 

where Q is the unique PD solution to 

AQ + QA' - QC'(M V3M,)-lCQ + Es\71E~ = 0 (8e) 

369 
PROBLEM EXTENSIONS 

Frequency Weighting 

(Sf) 

(Sg) 

Suppose now that it is desired to frequency weight the states ~ and the control!!. in 

the cost rate functional, so that the weightings vary with frequency (ref. 11). Let ~ be 

considered to be the input to a filter 1I1(s) of which 1~ is the output, and let 1I1(s) have a 

state-space representation defined by {A1,B1,Cl,Dd [i.e., 1I1(s) = C1(sI-A1)-IB1+ Dd. 

Then 

i1 = A1 ~1 + B1 ~ 

1~ = C1 ~1 + D1 ~ 

(9a) 

(9b) 

expresses 1~ in terms of ~, employing pseudostates ~1. Similarly, if!!. is considered to be the 

input to a filter if"3(S) of which 1!!. is the output, and if if"3(S) has a state-space 

representation defined by {A2,B2,C2,D2}, 1!!. can be expressed in terms of !!., employing 

pseudostates ~2: 

i2 = A2 ~2 + B2 !!. (lOa) 

1!!. = C2 ~2 + D2!!.2 (lOb) 

Suppose now that these frequency-weighted states (1~) and controls (ill) are further 

weighted by constant weighting matrices W1 and W2, respectively. The resulting state 

equations and performance index are as follows: 

where 

370 

~ = 1A x + 1B !!. + 1Ed!d + 1Es Ws 

y = 1C ~ + D !!. 

~=y+M!! 

1J = 6{1 im +- fT([~, !!.'1[lW11W2]{N}) dt} 

T-Ioo 0 1W21W3 -

(lIa) 

(lIb) 

(lIc) 

(lId) 

(lIe) 

(11f) 
'B ~ [g,] 

IC = [C 0 0] 

IW2 = [ g 1 

C2'W3D2 

1W 3 = [D2W 3D2] 

o 

o 

o 

Disturbance Accommodation 

(l1g) 

(l1h) 

(l1i) 

(l1j) 

(11k) 

(111) 

(11m) 

Suppose further that the stochastic disturbance is not Ws but !s, where !s is a 

stochastically modeled disturbance with power spectral density 

Sf(W) = S * f1/2 (jW)Sfl/2 (jw). Defining Hf(jW) by Sfl/2(jW) V1

1/ 2, one can consider Is to be 

the output of a filter Hf(S) excited by zero-mean white Gaussian noise Ws (ref. 12) with 

power VI (Le., covb!s(t), Ws(T)] = VI 8(t-T). 

In state-space form, 

such that 

k = As £.. + Ws 

!s = Cs(sI - As)-l 

( ) ( As)-l Hf s = Cs sI 

(12a) 

(12b) 

(12c) 

Incorporating these new pseudostates (~) into the state equations and performance index 

371 
yields • A 

~ = 2A ~ + 2B !!. + 2Ed!d + 2Es ws 

r = 2C ~ + D !!. 

~=r+M!! 

2J = 6 [1 im f JT(~, !!.,][l

W1

IW2]{!}) dt] 

T-loo 0 lW~ lW 3 !!. 

- where ~ = {r} 

A 0 0 Es Cs 

2A = BI Al 0 0 

0 0 A2 0 

0 0 0 As 

'B = r ~,l 2C = [C 0 0 0] 

'Ed r ~dl 

'Es [~ 1 

D~WIDI D~WICI 

2W1 = C~WIDI C~WICI 

0 0 

0 0 

372 

0 0 

0 0 

C~W3C2 0 

0 0 

(13a) 

(13b) 

(13c) 

(13d) 

(13e) 

(13f) 

(13g) 

(13h) 

(13j) 

(13k) 
2W2 = 

o 

o 

o 

The solution to this problem has been given previously. 

SYNTHESIS MODEL 

(13m) 

(13n) 

The model given at the close of the previous section is the model from which the 

controller is synthesized. The synthesis involves the determination of observer gains Land 

regulator feedback gains K. Preview gains KFF can also be determined, if desired, to 

approximate the Duhamel integral term of the optimal control. One approach to 

determining these preview gains has been presented in reference 9. Further study of the 

determination and use of these gains is needed. 

ANALYSIS MODEL 

Once the controller has been selected, it must be connected to the actual plant and 

the resulting "analysis model" used to evaluate closed-loop-system performance and 

stability. For constant gain matrices K, L, and KFF the open loop transfer function from 

Y to UFB [=-K ~ is 

,JJL 2A-2BK-L2C L cnu y (s) = 1-----+---4 

-FBw here the form 

-K 

[~J~ 

[ClD] 

o 

(14a) 

indicates C(sI - A)-1 B + D. The closed loop transfer functions, respectively, from Fd and 

Fs to X, are 

A - BK Ed+BKFF 

dfL F (S) = I-L_C_2_A_-_2_B_K_-L_2_C-+_2 B_K_F_F----j 

X _d I 0 0 

A -BK 

and ~L F (s) = LC 2A-2BK-L2C 2BKFF - -s 

I o o 

(14b) 

(14c) 

373 
The return ratio matrices (ref. 4) at the Y(s) and U(s) nodes, respectively, for D == 

0, are 

A2_BK-L2C 0 L 

L2(S) = -BK A 0 (15a) 

0 -C 0 

2A--2BK-L2C LC 0 

Ll(S) = 0 A B (15b) 

K 0 0 

The corresponding return difference matrices and inverse return difference matrices (ref. 4) 

are as follows: 

2A--2BK-L2C 0 L 

I + L2(S) = -BK A 0 (15c) 

0 -C I 

2A--2BK-L2C LC 0 

I + Ll(S) = 0 A B (15d) 

K 0 I 

I + L21(s) = I + [K(sI - 2A + 2B K + L2C)-1L]-1[C(sI - A)-lB]-l (15e) 

1+ Ll1(s) = I + [C(sI - A)-lB]-l[K(sI - 2A + 2B K + L2C)-1L]-1 (15f) 

The singular values of these matrices can be used to evaluate system noise and disturbance 

attenuation, stability margins, and sensitivity (ref. 4). Iterative application of the 

synthesis- and analysis models can be used to produce the desired controller. 

EXAMPLE PROBLEM 

Suppose one wishes to develop a controller to isolate a space experiment of mass m 

and position x(t), from a unidirectional acceleration disturbance a(t). Assume that a wall 

having position d(t) acts on m through an umbilical with stiffness k and damping c. (See 

figure 1). Suppose further that rattlespace constraints require the transmissibility to be 

unity below 10-3 Hz, and that it is desired to attenuate the disturbance by at least two 

orders of magnitude between 0.05 and 10 Hz. Let a linear actuator, applying a force that 

varies with control current i, be connected between the wall and the experiment in parallel 

with the umbilical. 

For this problem, it is desirable at low frequencies to penalize the relative 

displacement of the experiment heavily, so that the experiment "tracks" the wall. At 

intermediate frequencies, however, the absolute acceleration of the experiment should be 

heavily penalized to accomplish the desired disturbance rejection. The state space model, 

374 
then, should have relative position x-d and absolute acceleration x as states, allowing them 

to be frequency-weighted in the performance index. 

The system equation of motion is .. ' , ..' 'k' c A IX 

X = -k(x-d)-c(x-d) - lXi, where k = -, c = -, and IX = -

m m m 

In state-space form, the equations can be written as 

where Xi(t) = x(t) - d(t) 

X2(t) = x(t) - o(t) 

X3(S) = (S~~h) S2X(S), Wh high, 

so that X3(t)~ x(t) for W«Wh 

Frequency-weighting the states so that 

:~:~:~} = r~% ~ ~s 1 {~:~:~} IX3(S) 0 1 (S+W~hS+W2) X3(S) 

(16a) 

(16b) 

(16c) 

(16d) 

(16e) 

(17a) 

(where Wi < W2) results in a performance index that penalizes Xl more highly at low 

frequencies and X3 more highly at intermediate frequencies. If the control is 

frequency-weighted so that 

IU(S) = ( ~4S ) U(s) [W4<Wh] , (17b) s W4 

at higher frequencies the control will be more heavily penalized. This is desirable both for 

the sake of robustness and since X3 approximates x only at frequencies sufficiently below 

Who Finally, let the input acceleration be considered to come from zero-mean Gaussian 

white noise filtered through +w f . 

S Wf 

375 
The resultant state equations are as indicated on page 8, where 

Assume that 

C1 = 0 0 0 

[

WJ 0 01 

o W2 0 

D1 = 0 1 0 

[

0 0 01 

and 

000 

A2 = -W4 

B2 = 1 

C2 = -w2 

4 

D2 = W4 

As =-we 

Bs = 1 

Cs = we 

Ds = 0 

cov ws(t), W2( Tl] = 1 ~ (t - T) 

cov n1(t), n1(T) = 0.001 s(t- T) 

cov n2(t), n2( T) = 0.001 Set - ,). 

(18a) 

(18b) 

(18c) 

(18d) 

Since A1 has a zero [lstl column, 2A will have a corresponding zero [4th] column. To make 

the frequency-weighted' system PC,2A} observable, obtain J (x-d) dt as a measured state 

(Le., the first pseudostate, Zl1) and modify 2C accordingly. Let the measurement noise 

associated with Zl1 be n3, such that 

Gain matrix W1 can be varied to "tune" the optimal control to give the most 

satisfactory results. The transmissiblity between a(t) and x(t) is given in figure 2. The 

control uses feedback (and observer) gains obtained from system parameters and 

weightings as indicated on the figure. Note that the low-frequency transmissibility is 

unity, as desired, and that for intermediate frequencies the transmissibility rolls off with a 

slope of -1. 

376 
If a different frequency-weighting of X3 is used, it is to be anticipated that the 

transmissibility curve will change as well. 

W2 S 

For lX3(S) = (S+Wl )2(S+W2J2 X3(S) (19) 

the resultant selected transmissibility curve is given in figure 3. The low-frequency 

transmissibility again, is unity; but now for the intermediate frequencies the 

transmissibility rolls off with a slope of -2, as expected. Adding another pole at Wi and at 

W2 to the X3(S) frequency weighting would further improve the intermediate-frequency 

roll-off. The present controller, however, meets the design specifications. 

If state frequency-weightings of lX1(S) = S~~3 Xl(S) (20a) 

w2 s 

and lX3(S) = (S+Wl )2(S+W2P X3(S) (20b) 

are used, the results (figure 4) are similar to those given previously in figure 3. Note that 

with this latter choice of frequency weighting however, (Le., without anylirigid body poles"), 

the frequency-weighted system PC,2A J is observable, without augmenting the actual plant 

output y as was previously necessary. Consequently this is the preferred control. 

DISCUSSION 

H2 synthesis, as the example problem indicates, provides a highly versatile 

loop-shaping tool. It is especially useful in controller development for SIMO and MIMO 

systems, where classical loop-shaping methods are most lacking. Once the designer has 

expressed the system equations in terms of states for which he has an intuitive feel, and of 

measurable outputs, the design process becomes relatively easy. He frequency weights (Le., 

filters) the states and control inputs according to his engineering experience and intuition, 

to indicate the relative importance of each as a function of frequency. Then he weights 

these frequency-weighted states and controls relatLre to each other. The H2 synthesis 

methodology automatically provides him with a set of regulator and observer gains that are 

optimal with respect to the chosen weightings, given a quadratic performance index. 

Known aspects of the input disturbances and sensor noise can be incorporated into the 

design as well. Singular value checks provide the ability to evaluate system robustness. 

With a few iterations, the skillful engineer can complete his design. Excellent computer 

software packages already exist to assist in the task. 

The frequency weighting tells the H2 synthesis machinery how much "cost" to place 

on a state or control input at any frequency, relative to its cost at other frequencies. If, for 

example, absolute acceleration is undesirable only in a particular frequency range, that is 

where it should be most heavily weighted. The subsequent weighting of the 

frequency-weighted states and control inputs tell the synthesis machinery how much cost 

to place on each frequency-weighted state or control relative to the others. 

377 
In the example problem changing the relative weighting between absolute 

acceleration and relative displacement caused the frequency range of unit transmissibility 

to vary. An increase in the sharpness of the bandpass filter, used in the acceleration 

frequency weighting, resulted in a corresponding increase in the rate of gain roll-off. 

Increasing the weighting of relative velocity added damping to the system, as expected; and 

adjusting the acceleration bandpass filter's lower pole location allowed fine tuning of the 

unit transmissibility upper frequency limit. Use of a high-pass filter for control weighting 

produced a control which responds favorably (Le., minimally) at higher frequencies, where 

the plant models typically are invalid. 

CONCLUDING REMARKS 

The extended H2 synthesis method has been developed and applied to a 

one-dimensional microgravity vibration isolation problem, for which it seems particularly 

well-suited. Research continues toward the application of H2 synthesis to the full 

six-degree-of-freedom isolation problem. 

378 
A 

B 

c 

C 

D 

E 

f 

H 

~s) 

i 

I 

j 

J 

K 

L 

m 

M 

n 

o 

P 

Q 

s 

S(s) 

t 

11 

V 

w 

W,ir 

()( 

()( 

"8 

6 

-' 

w 

Capi talization 

CL 

cov 

FF 

MDOF 

MIMO 

OL 

PD 

PSD 

SDOF 

SIMO 

SYMBOLS AND ABBREVIATIONS 

Alphabetical Symbols 

System dynamic matrix 

System control input matrix 

Umbilical damping 

Systems State output matrix 

Control transmission matrix 

System disturbance input matrix 

Disturbance vector 

Stochastic-disturbance input filter 

Transfer function matrix 

Control current 

Identy matrix 

Square root of -1 

Performance index 

Control feedback gain matrix 

Observer gain matrix 

Experiment mass 

Sensor noise input matrix 

Sensor noise vector 

Zero matrix 

Algebraic Riccati Equation solution for regulator feedback gains 

Algebraic Riccati Equation solution for observer gains 

Laplace variable 

Stochastic-disturbance power-spectral-density matrix 

Time 

Control vector 

Covariance matrix 

White-noise disturbance vector 

Weighting matrix 

Actuator proportionality constant 

Admissible-control function 

Dirac delta function 

Expected-value operator 

Disturbance-accommodation pseudostates 

Circular frequency 

Laplace transform, indicated by context 

Closed loop 

Covariance 

Abbreviations 

Feedforward (preview) gain 

Multiple--degree-of-freedom 

Multiple-input-multiple-output 

Open loop 

Positive definite 

Positive semidefinite 

Single--degree-of-freedom 

Single-input-multiple-output 

379 
post subscript 0 

post subscript 1 

post subscript 2 

post subscript 3 

postsubscript d 

postsubscript f 

postsubscript s 

post superscript 1/2 

post superscript ' 

postsuperscript -1 

post superscript * 

underline 

overbar -

overhat ~ 

overtilde N 

presuperscript 1 

presuperscript 2 

Subscripts, Superscripts, and Diacritical Marks 

Value at time t=O 

With A,B,C,D,e: related to state-frequency weighting 

state-space description 

With L: return ratio matrix at control node 

With V: process noise covariance 

With w,W,'If": state (or pseudostate) weightings, applied 

subsequent to any frequency weighting 

With A,B,C,D,e: related to state-frequency-weighting 

state-space description 

With L: return ratio matrix at output node. 

With V,W: cross-weightings 

With V: measurement noise covariance 

With W, 'If": control weightings 

Related to deterministic disturbance 

Related to filter for stochastic disturbance 

Related to stochastic disturbance 

Square root or spectral factorization 

Transpose 

Inverse 

Optimum or conjugate transpose 

Vector 

With A: closed loop system dynamic matrix 

With x: augmented with frequency-weighting 

pseudostates _ 

Augmented with frequency-weighting- and 

disturbance-accommodation pseudostates 

Estimated or associated with cross-correlation 

With ~,X,!!, or U: frequency-weighted 

With other symbols: related to system augmented by 

frequency weighting 

Related to system augmented by frequency-weighting 

and disturbance-accommodation 

ACKNOWLEDGEMENTS 

This work was supported in part by the NASA Lewis Research Center and by the 

Center for Innovative Technology of the Commonwealth of Virginia. 

380 
REFERENCES 

1. Grodsinsky, C.M.; and Brown, G.V.: "Non-intrusive Inertial Vibration Isolation 

Technology for Microgravity Space Experiments." NASA TM-201386, January 

1990. 

2. Nelson, E.S.: "An Examination of Anticipated g-Jitter on Space Station and Its 

Effects on Materials Processes." NASA TM-103775, April 1991. 

3. Knospe, C.R.; Hampton, R.D., and Allaire, P.E.: "Control Issues of Microgravity 

Vibration Isolation." Acta Astronautica, accepted for publication. 

4. Safonov, M.G.; Laub, A.J.; and Hartmann, G.L.: "Feedback Properties of 

Multivariable Systems: The Role and Use of the Return Difference Matrix." 

IEEE Trans. on Automatic Controls, Vol. AC-26, No.1, February 1981, pp. 

47-65. 

5. Maciejowski, J.M.: Multivariable Feedback Design. Addison-Wesley Publishing 

Company, Inc., Wokingham, England, 1989. 

6. Sage, A.P.; and White, C.C., III: Optimum Systems Control, 2nd ed. Prentice Hall, 

Inc., Englewood Cliffs, New Jersey, 1977. 

7. Friedland, B.: Control System Design: An Introduction to State-Space Methods. 

McGraw-Hill, Inc., New York, 1986. 

8. Salukvadze, M.E.: "Analytic Design of Regulators (Constant Disturbances)." 

Translated in Automation and Remote Control, Vol. 22, No. 10, October 1961, 

pp. 1147-1155. Originally published in Avtomatika i Telemakhanika, Vol. 22, 

No. 10, February 1961, pp. 1279-1287. 

9. Hampton, R.D.; Knospe, C.R.; Allaire, P.E.; Lewis, D.W.; and Grodsinsky, C.M.: 

"An Optimal Control Law for Microgravity Vibration Isolation." Workshop on 

Aerospace Applications of Magnetic Suspension Technology, September 25-27, 

1990, NASA Conference Publication 10066, Part 2, March 1991, pp. 447-476. 

10. Bryson, A.E., Jr.; and Ho, Yu-Chi: Applied Optimal Control. Hemisphere 

Publishing Corporation, Washington, D.C., 1975. 

11. Gupta, N.K.: "Frequency Shaped Cost Functionals: Extension of Linear - Quadratic-Gaussian Design Methods." AlA A Journal of Guidance and Control, 

November/December 1980, pp. 529-535. 

12. Johnson, C.D.: "Further Study of the Linear Regulator with Disturbances - The 

Case of Vector Disturbances Satisfying a Linear Differential Equation." IEEE 

Trans. on Automatic Control (Short Papers), Vol. AC-15, April 1970, pp. 

222-228. 

381 
::: 

~ 

lJ 

382 

Plate 

Shakr[' 

m 75 Ibm 

k 1.544 lbf/ft 

c 0 lbf-sec/ft 

cc 2 lbf/amp 

k 

c 

m 

x(t) 

FIGURE 1: Example-Problem Model 

TRANSMISSIBILITY PLOT # 1 

10' ---------------------,------~----

10° 

I ()' 

10 2 

I () 1 

I(} 4 

1 ()~ 

10(' 

1 () 7 

m 

k 

c = a 

wI = 

W = I 

75 Ibm 

1. 544 lbf/ft 

o lbf-sec/ft 

2 Ibf/amp 

0.003 Hz 

diag (0.001, 

W2 = 10 Hz 

w J = 0.01 Hz 

w+ = 10 Hz 

wf = 10 Hz 

wit = 1000 Hz 

40, 15000) 

", 

I ORL-__ ------' ___ ~_,__--------'------'-------'-----'------~ 

10 ~ 104 HP 10 2 10-' lO' lO2 10' 

Frequency (Hz) 

FIGURE 2: Transmissibility Plot for 1st Control Weighting 
.5 

cO 

<.J 

.5 

:1:l 

<.J 

TRANSMISSIBILITY PLOT #2 

IOI 

10" 

10' 

I02 

I0 1 _ 

I ()-4 m 75 Ibm wa = 10 Hz 

k 1.544 lbf/ft w J = 0.01 Hz 

10 5 -

c = 0 lbf-sec/ft w+= 10 Hz 

01 2 lbf/amp wf = 10 Hz 

IO-1l -

w, = 0.075 Hz w h = 1000 Hz 

W = diag (0.01, 2600, 107 ) I 

10 7 

10 5 

____ L ________ .1. ________ ...1...-__________ ..l.. ________ ---1----_______ .~ ________ ~ __ _ 

10 4 10 3 lO2 10- 1 100 IO' 102 

Frequency (Hz) 

FIGURE 3: Transmissibility Plot for 2nd Control Weighting 

TRANSMISSIBILITY PLOT #3 

1 0" r···· ........ ··~··· .. ··t ... ~ ... -.... - .... ---.. - ',. '1 1• 

t. 

10-' \, t. 

10 2 

10 3 

104 -

10-5 

10-6 

10 7 

10-5 

m = 75 Ibm 

, 

+ 

11-., 

k 1.544 Ibf/ft 

c = 0 lbf-sec/ft 

CIt = 2 Ibf/amp 

w, = 0.075 Hz 

W = diag (0.01, 

" 

W1 = 10 Hz 

Wg = 0.01 Hz w. = 10 Hz 

wf = 10 Hz 

wh = 1000 Hz 

2600, 107 ) 

, ______ ----1... _______ ----1.-______ L--______ ..1..........-- _____ •• 

I04 I03 10 2 ]()I 10° 

Frequency (Hz) 

102 

FIGURE 4: Transmissibility Plot for 3rd Control Weighting 

101 

10\ 

383 
Experimental Results in Nonlinear Compensation 

of a 

One Degree-of-Freedom Magnetic Suspension 

David 1. Trumper, James C. Sanders, Tiep H. Nguyen, and Michael A. Queen 

Dept. of Electrical Engineering 

Univ. of N. Carolina at Charlotte 

Charlotte, NC 28223 

PRECEOING PAGe: BLANK NOr FILMED 385 
1 Introduction 

Nonlinear control techniques are of increasing interest in magnetic bearing applications. A 

one-degree-of-freedom magnetic suspension system has been constructed to serve as a test 

system for nonlinear control. The objective of this effort is to build an accurate model for the 

nonlinear suspension dynamics and to show the advantages of compensating for these 

nonlinearities by using a nonlinear controller. The results obtained with a nonlinear controller 

are experimentally demonstrated as superior to those obtained with a linear controller. 

Specifically, a controller which contains a force-control block yields transient responses which 

are largely independent of the operating point air gap. 

A block diagram for the suspension system is shown in Figure 1. As shown in the figure, 

a one inch steel ball is suspended below a 3500-turn solenoid wound on a one inch steel core. 

The solenoid is driven by a hysteretic switching current drive. The ball position is sensed using 

a photo diode array illuminated by an array of infrared LEDs. The system is controlled by a 

PC-based algorithm and data acquisition system. Within the control algorithm, corrections 

are made for sensor nonlinearities and for the solenoid nonlinear force characteristics. 

Theory for feedback linearization is presented in [1-4]. The application of linearization to 

magnetic suspension systems has been discussed in [5-10]. The results presented herein are an 

experimental investigation of ideas presented in [10]. Here, feedback linearizing 

transformations are demonstrated for second-order and third-order models of a 

one-degree-of-freedom magnetic suspension. Simulated responses are presented, but no 

experimental results are given. This is due to two shortcomings. First, the optical sensor used 

in [10] is not sufficiently stable to allow accurate position measurements which are required to 

linearize the suspension. Second, the force measurement scheme consists of a balance beam 

which allows only static force measurements. These deficiencies have been rectified in the 

present effort, allowing the presentation of experimental results verifying the advantages of 

using nonlinear compensation for magnetic suspensions. 

In the following sections the design of the position sensor, switching power amplifier, 

force measurement fixture, and nonlinear controller are presented, along with experimental 

results for the power amplifier, force measurements, and suspension dynamics. 

PRECEOING PAGE BLANK NOT FtLMED 387 
2 Position Sensor 

The position sensor works by arranging for the suspended ball to cast a shadow on a 

16-element linear photodiode array. The array is illuminated by a vertical linear array of four 

infrared light emitting diodes. In order to reduce interference from external optical sources, 

the photodiode array is covered by a piece of red plastic taken from a display bezel, and 

shielded with a closed-ended tube, in which end a slit has been cut of width sufficient to 

admit the LED illumination but block most other external light. 

In initial work, the individual photodiode currents were used to study the uniformity of 

illumination, but in operation, all sixteen currents are summed together at the virtual ground 

input of a transresistance amplifier. The vertical spacing of the LEDs was adjusted to achieve 

the minimum nonuniformity, but a significant amount remains. Because of this, the sensor 

output is not purely linear with ball position. 

This uniformity is measured by making use of a test fixture which is depicted in Figure 2. 

Here a test ball is glued into an adapter ring which connects it with a piezoelectric load cell 

which is itself mounted on an adapter ring which is epoxied onto the anvil of a differential 

thread micrometer. With this fixture, the ball can be vertically translated with a resolution of 

better than 10 {lm. Simultaneously, the force acting on the ball can be measured via the load 

cell. Because the piezoelectric load cell is very stiff, the combined system has a resonant 

frequency of about 5 kHz, which allows the load cell output to be interpreted as measuring 

applied force for all frequencies of interest. Force measurements are described in more detail 

in Section 4. Here, the test fixture was used to set a known air gap, and thereby calibrate the 

position sensor. Because the ball enters the beam from below, the test fixture does not 

interfere with the optical path when performing this calibration. 

Measurements of the uncorrected sensor output indicate a deviation from the best-fit 

straight line of about ±1 mm. Samples of the measured data are stored in a table in the 

control computer, and used to linearly interpolate position, in order to remove this deviation. 

The controller samples the sensor voltage and updates the control law output at a 1 kHz rate. 

At each sample, the data table is used to interpolate position by using a bisection algorithm. 

This corrected position is fed to the lead compensation block and thus to the rest of the loop. 

Following this correction, the sensor corrected output shows deviations from a best-fit 

straight line of about ±O.l mm. The largest remaining error term is due to instability of the 

LED intensity, primarily with respect to temperature. This instability limits the accuracy of 

the data table used for interpolation. In future implementations, it would be advantageous to 

design a sensor in which absolute intensity is not of first-order importance to the 

measurement. One approach would be to use a lateral effect photocell, in which the location 

of the illumination rather than its intensity is the important parameter. In any case, the 

sensor linearity is satisfactory for the current purposes. 

3 Power Amplifier 

A schematic for the solenoid current drive is shown in Figure 3. The power amplifier is of the 

388 
Setpoint 

Computer 

LED 

EMitters 

Current 

Drive 

Transresistance 

Amplifier 

Coil 

4 Element[-----

IR Emitter - -

Array 

Figure 1: Control loop block diagram. 

SolenOid 

16 Element 

Photodiode 

Array 

Pole IR TranSMissive Filter 

F ace ~----r---,----.-_ ...1_"':>"'-_-1 __ ~_ 

Shade 

MicroMeter 

Figure 2: Micrometer and load cell fixture. 

16 Detector 

Array 

389 
Ref in 0 to -10 » 0 - 1. 5A 

4. 7k 

Rl 821 120 

R2 R3 

~ 1 821 Ul R5 1 k COM R6 1'--" R8 

oOl~L - 7 

GE 03 2 LM7, 

A114B 

Cl l ~ 4 ' 1M 

R14 68k 68k 3 M 2.2k Dl ::';= R7 R4 R9 Rll (... 20V 

100 uF ....I- lOBg f

T zener 

C6 -=~ 

II 

C2 

cc" 

01u~ "l 22 L1 Rl0 

(1'"'''' 01 

2N3792 

---.L 02 

-40 

C3 l 03 6. 8u 

D I RF530 rf' D2 10k VDy 750 10V R12 

R13 zener 

Figure 3: Current drive schematic. 

390 
hysteretic type. A comparison of this type of converter to sample/hold and minimum pulse 

width converters is given in [11]. The operation of the amplifier is described as follows. 

The coil voltage is controlled by transistor Q3 acting as a switch. When Q3 is on, 40 volts 

is applied to the coil, thereby increasing the coil current. When Q3 is off, the coil current 

freewheels through the flyback diode D3 , ther~by decreasing the coil current. The switching of 

Q3 is controlled by comparator UI through the common base transistor QI which provides 

level shifting, and the gate-network D2-R13 which limits the gate voltage to 10 volts when QI 

is on and provides a turn-off path when QI is off. 

Comparator UI switches on and off based upon the difference between the reference level 

as scaled by the input network RI -R4 and the actual current level as measured by sense 

resistor R5 • The switching has a hysteretic component determined by the feedback network 

R9 , R14 , and C5. Components R14 and C5 are included to eliminate a burst of oscillation 

which occurred on the comparator switching transients and which resulted in undue heating 

of the power FET Q3. The 14,-CI low pass filter serves to attenuate spikes due to stray 

inductance in R5 and feedthrough capacitance in the solenoid coil LI . Without this filter, the 

supply oscillates at about 1 MHz. 

A goal of this design is to operate with only a single external power supply. Thus 

transistor Q2 and its bias network are used to supply -20 volts to the low side of comparator 

UI . Through resistors R7 and R4 this -20 volt supply is used to offset the comparator input 

voltages to within the allowable common mode range of the comparator. Resistors R7 and R4 

are adjusted relative to the values in the rest of the input network in order to reject changes 

in the -20 volt supply level. This prevents transients on the -20 volt supply from disturbing 

the switching thresholds. One additional consequence of the chosen topology is that the 

reference voltage must go negative to set an increase in the coil current. 

The solenoid consists of 3500 turns of #22 wire, with a room temperature resistance of 

RL = 28 Ohms. This resistance rises to about RL = 33 Ohms at the typical operating 

temperature (iL = 0.6A). If the solenoid is alternately switched between 0 and 40 Volts, the 

resulting current waveform has an exponential time constant of about 60 msec, implying a 

low-frequency coil inductance of about 2 H. However, based upon measurements at the 10 

kHz supply mid-point operating frequency, the coil demonstrates a high-frequency 

incremental inductance of 200 mHo This value is used in the analysis which follows. 

In operation, the coil current will oscillate between a low-threshold current II and 

high-threshold current 12 , This oscillation will take the form of an asymmetric triangle wave, 

with II and 12 set by the reference voltage and the amount of comparator hysteresis. 

Neglecting the flyback diode voltage drop, the cycle time T for this oscillation is given by 

(1) 

where T = Ld(R5 + RL), and IF = 40/(R5 + RL) is the full scale current which results if the 

switch QI remains closed. For the design values, 

II = -0.1488Vref - 5.605 x 10-3 (2) 

391 
and 

12 = -0.1488v,.ef - 9.766 x 10- 4 (3) 

There is thus 12 - 11 ~ 4.6 rnA of switching ripple, and the current remains within about 

2.3 rnA of the setpoint for all inputs which do not exceed the current slew rate limit imposed 

by the finite supply voltages. This latter limitation has a significant impact on closed-loop 

operation as discussed in Section 5. 

The switching frequency is given by liT. Using the results from (1)-(3), the switching 

frequency as a function of average current (11 + 12 )/2 is calculated and compared to the 

measured frequency in Figure 4. Note that the frequency is zero at both zero and full-scale 

currents, and peaks at about the mid-scale current. The measured frequency was recorded as 

the current was increased from zero to full scale, and closely matches the calculated frequency. 

However the actual frequency exhibits significant hysteresis dependent upon the time history 

of supply current. This effect is due to the magnetic hysteresis in the solenoid core, and can 

be as large as 2 kHz at the maximum frequency point. 

4 Force Measurements 

The electromagnet force as a function of position and current is measured with the load cell 

and micrometer fixture which was used to calibrate the optical sensor. With the micrometer 

at a fixed position, the electromagnet current is cycled from zero to full scale and then back 

to zero, with a triangular time dependence. Over multiple cycles, the load cell amplifier 

output is measured at about 200 points within each cycle and averaged at each point over the 

multiple cycles. The form of the resulting data is shown in Figure 5. 

The force curves exhibit significant hysteresis, which is due to using cold-rolled steel as 

the core material. In future designs, a magnetically-softer material should be used. Also note 

that the hysteresis curves have essentially constant width in current, independent of air gap. 

This is explained by the fact that the ball is only weakly coupled to the core and thus the core 

flux is largely independent of ball position. 

The measured force rises as the square of current for low currents, as would be predicted 

by a first order field analysis, and then rises less strongly at higher currents, due to saturation 

in the core. In the low-current region (i < O.4A), the force is well modeled by 

. 2 F-C( Z ) 

- x + 0.0025 (4) 

where F is the electromagnet force in Newtons, i is the coil current in amps, x is the air gap 

in meters, and C = 6.5 X 10-4 Nm2 I A2. Note that the actual air gap plus 2.5 mm is used in 

this law. This accounts for the fact that the force does not become infinite at zero air gap. 

Beyond 0.4 Amps, saturation becomes significant, and a more complex model is required. 

The force curves exhibit significant hysteresis, which is due to using cold-rolled steel as 

the core material. In future designs, a magnetically-softer material should be used. Also note 

that the hysteresis curves have essentially constant width in current, independent of air gap. 

392 
'N' 

g 

j 

...... 

~ ~ u 

~ 

§ 

.£ 

14000 

12000 

10000 

SOOO 

6000 

4000 

2000 

0 

0 

,/,/'" 

/ 

1//' me"""'" 

l 

i// 

0.2 0.4 

.----' ,&------.q. ••• " •• 

0.6 O.S 

Current (Amperes) 

. . , 

, 

, 

, 

\\ 

''Ii\. , 

Figure 4: Switching frequency as a function of current. 

Force versus current at 3, 5, S, and 15 mm 

, 

, 

, 

. , 

, 

1.2 

9r-------.-------.--------r-------.------~--~--_. 

S 

7 

6 

5 

4 

3 

2 

1 

0 

0 0.2 0.4 

..... ::::. 

0.6 O.S 

current (Amperes) 

.. : ..... .. : ..... 

;;,''' .... Smm 

1.2 

Figure 5: Uncompensated electromagnet force as a function of current at air gaps of 3, 5, 8, 

and 15 mm. 

393 
This is explained by the fact that the ball is only weakly coupled to the core and thus the core 

flux is largely independent of ball position. 

However, this model is not developed in the i-F plane, since for the present purpose of 

nonlinear compensation what is required is a function which, given the air gap x and a desired 

force Fd , yields the current in Amperes necessary to realize this force. At low forces relative to 

the air gap, this function is found by inverting (4), and thus increases linearly with air gap 

and as the square root of desired force. At higher forces, the current must grow more strongly 

with desired force. A reasonable fit to the data has been empirically found to be 

[F; ( ( %-0.002 ) ) 2 2 is = (x + 0.0025)V C + 0.0195e o:oii6 - 2.5(x - 0.01) Fd + 400(x - 0.002) Fd (5) 

This function fits the data well over the operating range of the suspension. 

The quality of the fit achieved by (5) is determined experimentally by writing a test 

program which cyclically ramps the desired force up and down while measuring the actual 

force with the load cell fixture. The results of this experiment are shown in Figure 6. The 

four traces shown in the figure are for air gaps of 3, 5, 8, and 15 mm; these traces essentially 

overlay, showing the success of the compensation (5). There is however, an error of about 10% 

in the gain, and the force drops off slightly from a straight line at high current and the 

smaller air gaps. The source of the gain error has not yet been adequately identified, as the 

data has only recently been acquired. However, hysteresis represents the most significant error 

term, particularly at small air gaps, where the force hysteresis magnitude approaches the 

weight of the ball. As mentioned above, this error term can best be addressed by using a 

magnetically-softer core material. 

The results of the above force modeling are used to design the nonlinear compensator, 

which is described in the next section. 

5 Nonlinear vs. Linear Control 

A block diagram for the nonlinear compensation control loop is shown in Figure 7. The blocks 

labelled Sensor Compensator, Lead Compensator, Gain, and Nonlinear Compensator are 

implemented in floating point arithmetic within the control computer, which is an 

80386/80387-based system with a processor clock frequency of 20 MHz. The AID and D I A 

converters both have 12-bit resolution, and reside on a circuit card within the computer. The 

current drive, electromagnet, and sensor have been described in detail above. The mass of the 

ball M = 0.06 kg times the acceleration of gravity 9 is equal to approximately 0.6 Newtons. 

This force sums with the electromagnet force as the input to the block labelled 1 1M S2 which 

has air gap x as its output. 

All the blocks within the control computer algorithm are updated at a 1 kHz rate. The 

Nonlinear Compensation block implements (5) appropriately scaled for the 12-bit D I A 

converter, c:.nd for the algorithm air gap representation in millimeters. The anticipated gravity 

load of 0.6 N is added to the error signal to give Fd = Fe + 0.6 which is input to the Nonlinear 

Compensation block as the force to be maintained on the ball. Adding the gravity load at this 

394 
Actual vs desired force at 3, 5, 8, 15 rnm 

8r-----r-----r-----r-----r-----r-----r-----r-----r----. 

7 

6 

5 

4 

3 

2 

1 2 3 4 5 6 7 8 9 

Desired force (Newtons) 

Figure 6: Compensated electromagnet force as a function of desired force at air gaps of 3, 5, 8, 

and 15 mm. 

Nonlinear 

Compensation 

Lead 

Compensator 

Sensor 

Compensator 

Compensated 

Position 

Mg=O.6N 

Magnet 

Figure 7: Nonlinear compensated control loop block diagram. 

x 

395 
point greatly reduces the static error in suspension, since the loop uses only lead 

compensation and thus is of type o. The reference signal is subtraded from the output of the 

lead compensator to yield the force error Fe. The loop lead compensation is placed in the 

feedback path in order to reduce the amplitude of the transient under step inputs as 

compared with placing the lead compensator in the forward path. The lead compensator has 

a zero at z = 0.94, a pole at z = 0, and a DC gain of unity. 

The linear loop uses the same lead compensation singularity locations, but differs from 

the nonlinear loop in that the nonlinear compensation operation is replaced by a constant 

gain. Additionally, it is not possible to add a constant force offset term in the linear case. The 

error under Type 0 linear compensation has been found to reach 4-5 mm at the largest air 

gaps. Thus, in the linear compensation, the reference input is manually reset to achieve a 

desired air gap. All results are reported herein in terms of actual air gap. 

A comparison of the loop performance under linear and nonlinear compensation is made 

as follows. At an air gap of 14.6 mm, both the linear and nonlinear compensator gains are 

adjusted to achieve essentially identical step responses with approximately 26 msec rise time. 

Then these gains are left unchanged as the air gap is set to 8.4 mm, 5.7 mm, and 3.7 mm. 

The resulting transients for the nonlinear and linear compensated systems are shown in 

Figure 8. In each of the figures, the top trace represents the compensated air gap as output 

by the Sensor Compensation block, with a sensitivity of 0.1 mm per division. Thus the steps 

shown represent a change in position of approximately 0.25 mm. The lower trace in each 

figure is the coil current as measured by a hall effect probe. This trace is AC coupled, and has 

a sensitivity of 50 mA per division. 

As shown in the figures, the nonlinear compensated loop maintains a nearly constant step 

response as the air gap is reduced by about a factor of four, whereas the linear compensated 

loop performance deteriorates significantly. One measure of this change is the asymmetry 

between the positive going and negative going transients. Since the top trace represents the 

air gap which increases as the ball moves away from the pole face, the positive-going transient 

is associated with the ball moving away from the pole face, and likewise the negative-going 

transient is associated with the ball moving toward the pole face. 

Another measure is the variation in rise and fall times as indicated on each trace. The 

rise and fall times for the nonlinear compensation loop remain symmetric at approximately 

25 msec for all responses except at 3.7 mm where a small amount of asymmetry is visible, and 

the rise time increases slightly to about 29 msec. By comparison, the rise and fall times for 

the linear compensation loop change dramatically and exhibit significant asymmetry, as 

shown in the figure. The associated current traces also show significant asymmetry under the 

linear compensator, but remain symmetric under the nonlinear compensator. Note that as the 

air gap is reduced, the magnitude of the current transient decreases, since the incremental 

current-to-force gain of the electromagnet increases at smaller air gaps. 

The transients shown in Figure 8 are the result of averaging 32 traces. This was done to 

eliminate a baseline limit-cycle noise of approximately 50 mY. The magnitude and dominant 

frequency of this noise depend strongly upon the controller gain, lead-zero location, and 

operating point air gap. The cause of this limit cycle has not yet been thoroughly 

396 
RISE .. 27.1 ... . 

FALL 27.1 .. . 

RISE" 25.S .... 

FALL .. 25.9,.. 

gap=14.6mm 

RIse.. 25.S .... RISE · 24.1"'1 

FALL" IB.3"'1 FALL · 24.S .... 

{\ 

l \, ---I 

1 " J'-'--- ", \ , 

\ , 

U ~ 

\ I --:: 

\~ 

gap=S.4mm 

J-,,~~ , J., f \,J-..____. -1, 

+ 

RISE .. 50.4 .... RISE" 24 .3 .... F~LL . 25." .... Fi\L.L" 23.51'11 

1<' X 

J \ 

V gap=5.7mm 

T ::--V".-.....-... ,,/ 

, 

' , 

RISE .. 52.' ... , i I RISE · 29,S"'1 

FALL . IIi.5 ... 

~"""'-'- - '" 

,.,... 

~ ...... ,,,.""''\j\vv .. ."..,..-~v~ 

gap=3.7mm 

i FALL · 28.2 ... I I I, ,/"',,-~- +-\c T 

I - ± \ 

i \ i 

I \ 

~ ~ / \ - V ~ ~ 

Figure 8: Step responses of linear and nonlinear compensated loops at air gaps of 14.6, 8.4, 

5.7, and 3.7 mm (top to bottom). Left column shows response with linear compensator. Right 

column shows response with nonlinear compensator. In both columns, the top trace is incremental air gap, 0.1 mm/div, and the bottom trace is coil current, 50 mA/div. The time base 

is 100 msec/div for all traces. 

397 
investigated; however it is believed to be due to the finite quantization levels of the 12-bit 

converter used in these experiments. This is physically reasonable, since for the ±10 volt 

range of the converter, the least significant bit represents about 5 mY, and thus the limit 

cycle entails a total span of about 10 least significant bits. For an open-loop unstable system 

such as this suspension, some amount of limit cycling is inevitable in the presence of 

amplitude quantization. A describing-function analysis of the quantized loop and simulation 

experiments are planned to verify quantization as the cause of this behavior. 

Another destabilizing effect, which can be observed if the current trace is examined in 

detail, is voltage saturation of the current drive. The current drive operates from a unipolar 

40 volt supply. Thus, especially at small air gaps when the current required for suspension is 

small, the maximum negative slew rate is highly constrained. This slew rate limiting becomes 

significant when the ball is stepped towards the pole face. Initially, current is increased to 

draw the ball toward the pole face, but then must be rapidly decreased to stop the ball at its 

new closer position. If the current cannot be rapidly decreased, the ball strongly overshoots. 

This effect contributes significantly to the asymmetric transients observed for the linear 

compensator in Figure 8, and also can degrade the stability of the nonlinear compensated 

loop if the gain is increased much above the value used in Figure 8. In the describing function 

sense, the lagging current which occurs in saturation adds negative phase shift which degrades 

the loop stability. 

At small air gaps, the current source voltage saturation can lead to loss of control as 

shown in Figure 9. Here, the linearly compensated system is operating at a gain higher than 

that shown in Figure 8, but still within the short-term stability boundary. However, once 

every few minutes, stability is lost. The trace shown in this figure captures that process. The 

transient is negative-going, and thus toward the pole face. As the transient is initiated, the 

current is increased to draw the ball upward, and then enters voltage saturation in which the 

current source power FET is shut off for approximately 30 msec, during which time the trace 

takes the form of a decaying exponential, since the coil voltage is constant and equal to zero 

minus the flyback diode voltage drop. In the second and later transients, the current actually 

does reach zero. By this process, the ball diverges from suspension. 

To avoid this effect, it is clear that the current source must be modified to be capable of 

applying bipolar voltages to the coil. This can be accomplished within the framework of the 

present hysteretic design by replacing the single power FET with an H-bridge driver. These 

are available from a number of manufacturers in integrated form. 

6 Conclusions and suggestions for further work 

The experimental results presented herein demonstrate the effectiveness of using nonlinear 

compensation for variable reluctance magnetic suspensions. Several improvements are 

suggested within the text. The most significant of these is to adopt a current source which 

has a bipolar voltage capability, so as to avoid the current slew-rate saturation which has 

been shown to destabilize the loop under certain conditions. The quantization-driven limit 

cycles which were observed require more investigation; it is likely that a higher-resolution 

398 
{ 

'. ! V' 

Figure 9: Loss of suspension due to current source voltage saturation. Trace 1 is position at 

0.05 mm/div, and trace 2 is current at 20 mA/div. The time base is 20 msec/div. 

399 
converter would reduce the magnitude of these cycles. The core should be replaced with a 

lower-hysteresis material in order to improve the accuracy of the force correction. At very 

small air gaps « 1 mm), this remanent magnetization is sufficient to lift the ball, and control 

is lost. Also, the pole face should made somewhat conical, in order to more strongly center 

the ball. At very small air gaps, the ball was observed to pull out to the corner of the pole 

face where the field is more concentrated. Finally, the optical sensor stability could be 

improved, perhaps by using a lateral effect photo-sensor. 

7 References 

[1] Slotine, J. E., and Li, W., Applied Nonlinear Control, Prentice-Hall, 1991 

[2] Spong, M., and Vidyasagar, M., Robot Dynamics and Control, Wiley, 1989, pp. 259-283. 

[3] Su, R., "On the linear equivalents of nonlinear systems," Systems and Control Letters, 

vol. 2, No.1, pp. 48-52, July, 1982. 

[4] Hunt, L.R., Su, R., and Meyer, G., "Global Transformations of Nonlinear Systems," IEEE 

Transactions on Automatic Control, Vol. AC-28, No.1, Jan., 1983. 

[5] Jayawant, B.V., Hodkinson, R.L., Wheeler, A.R., and Whorlow, R.J., "Transducers and 

Their Influence in the Design of Magnetically Suspended Vehicles," LE.E. Conf. on Control 

Aspects of New Forms of Guided Land Transport, LE.E. Publication No. 117, Aug., 1974, 

pp. 200-206. 

[6] Jayawant, B.V., Sinha, P.K., Wheeler, A.R., and Whorlow, R.J., "Development of I-ton 

Magnetically Suspended Vehicle Using Controlled D.C. Electromagnets," Proc. I.E.E., 

Vol. 123, No.9, Sept., 1976. 

[7] Groom, N.J., and Waldeck, G.C., "Magnetic Suspension System for a Laboratory Model 

Annular Momentum Control Device," AIAA Paper No. 79-1755, 1979. 

[8] Traxler, A., Meyer, F., and Murbach, H., "Fast Digital Control of a Magnetic Bearing 

with a Microprocessor," International Kongress Mikroelektronik, Munich, Nov 13-15, 1984, pp 

94-102. 

[9] Trumper, D.L., "Magnetic Suspension Techniques for Precision Motion Control," Ph.D. 

Thesis, Dept. of Elec. Eng. and Compo Sci., M.LT., Camb., Mass., Sept., 1990. 

[10] Trumper, D.L., "Nonlinear Compensation Techniques for Magnetic Suspension Systems," 

NASA Workshop on Aerospace Applications of Magnetic Suspension Technology, Hampton, 

VA, Sept. 25-27, 1990. 

[11] Keith, F. J., et al. , "Switching Amplifier Design for Magnetic Bearings," Proceedings of 

the Second International Symposium on Magnetic Bearings, Tokyo, Japan, July 12-14, 1990, 

pp. 211-218. 

400 
N92-27743 

CONTROL CONCEPTS 

FOR 

ACTIVE MAGNETIC BEARINGS 

R. SIEGWARTl,2, D. VISCHERl, R. LARSONNEUR1.2, 

R. HERZOGl, A. TRAXLER2, H. BLEULERl, G. SCHWEITZERl 

1 Mechatronics Lab, Swiss Federal Institute of Technology (ETH), 8092 ZUrich, Switzerland 

2 MECOS Traxler AG, CH-8400 Winterthur, Switzerland 

401 
Active Magnetic Bearings (AMB) are becoming increasingly significant for various industrial applications. 

Examples are turbo-compressors, centrifuges, high-speed milling and grinding spindles, vibration 

isolation, linear guides, magnetically levitated trains, vacuum and space applications. Thanks to the rapid 

progress and drastic cost reduction in power- and micro-electronics, the number of AMB applications is 

growing very fast. 

Industrial use of AMBs leads to new requirements for AMB-actuators, sensor systems and rotor dynamics. 

Especially desirable are new and better control concepts to meet demands such as low cost AMB, high 

stiffness, high performance, high robustness, high damping up to several kHz, vibration isolation, forcefree rotation and unbalance cancellation. 

This paper surveys various control concepts for active magnetic bearings and discusses their advantages 

and disadvantages. Theoretical and experimental results are presented. 

1. INTRODUCTION 

Basics and feasibility of Active Magnetic Bearings (AMBs) were first shown by Beams, Young and Moore 

in 1946 [Beams et al. 46]. Considerable progress has been made since, though the basic principle is still the 

same. 

This basic principle gives no general information on how the displacement is measured, how the controller 

is designed or how the AMB-actuator (electromagnetic coil) is controlled. 

Up to now, most AMB-systems made use of current amplifiers to drive the electromagnetic coils and 

mainly analog PD I PID controllers were applied. 

For todays and tomorrows demanding AMB-applications, new control concepts for the actuator and the 

main controller have to be taken into consideration. 

The AMB controller design can be divided into two levels. The first level involves the choice of the input 

and output variables of the AMB-actuator. This can be denoted as the "actuator control 

configuration". The following rough classification can be made: 

- current control 

- voltage control 

- flux measurement and flux density control 

- "self-sensing" control (operation without displacement sensor) 

The second level is concerned with the "main controller" itself, i.e. the relation between measured 

signals and actuator input signals. Design approaches for the main controller are: 

- PD, PID (root locus) 

- LQR, LQG, pole placement (observer based) 

- direct low order controller design (SPOC-D, chapter 4.3) 

- Hoo and other frequency-domain methods 

403 

PRECEDING PAGE BLANK NOT FtlM!:D 
Furthennore, a so called ''feedforward controller" can be added to the standard feedback loop. This subject 

is not addressed in this paper. 

Prior to the choice of the actuator control configuration and the controller layout, the AMB-engineer should 

carefully analyze and optimize the configuration of the plant (rotor). The configuration of the plant is 

basically given through the observability, the controllability, the structural dynamics and the AMB-actuator 

design [Keith et. aI90], [Siegwart et al. 90]. These aspects are not addressed in this paper. 

Starting with the general model of the AMB-actuator (section 2), different actuator control configurations 

are outlined (section 3). The principles of current, voltage, flux-density and self-sensing control are 

described, and their advantages and disadvantages are discussed. 

Section 4 gives a general overview on the design specifications of the main controller and the different 

controller layout approaches. PDIPID controllers are widely used low order controllers for applications 

where perfonnance requirements are not very demanding. For high perfonnance requirements, observer 

based LQRlLQG regulators are well suited. However, there is still a computational on-line burden because 

of high order and full coupling in the MIMO case. To close the gap, a tool for direct low order controller 

design (SPOC-D, chapter 4.3) is shown. Demanding applications, e.g. high perfonnance control of flexible 

shafts, lead to sophisticated control specifications, mostly in frequency domain. This is the motivation for 

HOO control (chapter 4.4). 

Some of the new concepts for actuator control configurations and main AMB controller design discussed in 

this paper are already used at the Swiss Federal Institute of Technology (ETH) and by the Swiss AMB 

system manufacturer MECOS Traxler AG. Theoretical and experimental results are presented in section 5. 

2. THE BASIC AMB.EQUATIONS 

coil! 

(positive side) (negative side) 

Figure 1: Notations for a two-sided actuator with one mechanical degree of 

freedom, rotor displacement x . A displacement to the left is defined positive, for 

x=O the air gaps are Xo. More symbols are listed in table 1 on the next page. 

The basic AMB equations are obtained from Maxwell's laws [Breinl 80], [Traxler 85], [Vischer 88]. The 

derivations are not shown here. Neglecting secondary effects such as copper resistance, stray fields and 

saturation, and assuming that the complete energy of the magnetic field is concentrated within the active air 

gap, we get the following well-known equations for an AMB: 

According to figure 1 and to the notation in table 1 we find an electromagnetic force F 

proportional to the square of the current i in the coil divided by the air gap. The force can also be 

described by the flux density B. 

2 ':"2 

F = N AJ.lo '+ = ~B 2 

+ 4 ( )2 + Xo - x J.lo 

2 ':"'2 

F = N AJ.lo '- = ~B 2 

- 4 (xo + X)2 J.lo (2.1) 

The relation for the voltage u in the coil can be found as 

404 
(2.2) 

Usually AMB actuators are operated around a constant operating point. The operating point is defined 

through the following nominal values: 

. B - N/1o io -0 xo' 10, 0 - ---, Un - 2 Xo 

Around the operating point the relations for the AMB actuator can be linearized for x « Xo and i « iO: 

F = Lo i; + Lo i; x + Lo!:JLi =~B2 + 2A B B + 2 22 2 + 0 0+ Xo Xo Xo /10 /10 

F = Lo i; _ Lo i; x + Lo!:JLi = ~ B2 + 2A B B 

- 2 Xo 2 x; 2 Xo - /10 0 /10 0 - (2.3) 

u+ =~(Lo~X+Loi+J=NA~B+ dt Xo dt 

u_ = ~(-!:JL4x + 4i-J = NA~B_ dt Xo dt (2.4) 

By arranging the AMB in axially opposed pairs of coils (figure 1), as it is usually done, the linearized force 

F and voltage u result in 

F=F -F + -

(2.5) 

u -u 

u= + -

2 ---

_ Xo d [21 L1)-x+ i; 2' io (i+ - t)] _ Xo d F &.1)- --- ---

2io dt x~ Xo 2 2io dt (2.6) 

(2.7) 

u = NAi.(B+ - B_) = NAi. B 

dt 2 dt (2.8) 

Substituting force and voltage in equation (2.5) and (2.6) by the corresponding quantities in equation (2.7) 

and (2.8), displacement X from the nominal position can be described as a function of B, i and u. 

2 x; xo. x=-_·_·B--·, 

X=_·-· 1 Xo J d xo· U t--·, 

Lo io io 

(2.9) 

(2.10) 

Applying equation (2.9), the displacement signal x can therefore be directly calculated from the flux density 

B, measured for instance by a hall-effect sensor, and the current in coil i (chapter 5.1, [Zlatnik & Traxler 

90]). Similarly, one could derive the displacement through current i and the integration of voltage u. From 

405 
control theory, however, it is known that the output of an integrator is not observable by its input. Thus it is 

not possible to reconstruct the air gap of a magnetic bearing by directly using equation (2.10). 

Nevertheless, it will be shown later (chapter 3.5) that, by closing the loop with the mechanical model, it 

becomes possible to stabilize the AMB-system by the measurements of u and i only. 

Operating point 

Xo Nominal airgap 

~ : Nominal current 

Bo =!!!!.:...1:.: Nominal flux density 

2 Jr. 

Variables (functions of time) 

F: ;E. 

B+ ; k 

"+ ; "-

i+ = ~ +( 

L = io+ i_ 

Electromagnetic force 

Flux density 

Voltage 

Currents in the coils 

(corresponding relations 

for F. B and u) 

Table 1: Notations 

Basic bearing constants: 

N : Number of windings 

A : Iron cross-sectional area 

(/10 = 1.257 .1O~ Vs I Am : permeability of air) 

Secondary bearing constants: 

N2A La = 2x~Q : Inductance at x = const.= 0 

Ie.; =2LaJ..: Force-current factor 

Xo 

k. = kj..i2.. Force-displacement factor 

Xo 

3. AMB-ACTUATOR CONTROL CONFIGURATION 

An AMB-actuator usually consists of a pair of coils (fig. 1) and two power amplifiers. The actuator control 

configuration determines how the AMB-actuator is controlled. Starting with a general state space model of 

an AMB-system, the basic ideas of current, flux-density, voltage and self-sensing control are derived and 

discussed in this section. 

State-Space Model 

u+ 

u -

J i+ 

J 

Figure 2: Linearized state-space model for one mechanical degree of freedom and 

Mo coils according to figure 1. The Mo currents 0+, L),in each coil of the bearing, 

rotor velocity i and displacement x are selected as state variables. 

x 

x 

The complete state-space model for the AMB system includes at least two mechanical states (velocity and 

displacement). In addition, each electromagnet contributes one state variable to the model. In the case of 

two-sided actuators (fig. 1), two state variables, for example the currents in the coils, are necessary for each 

mechanical degree of freedom to completely describe the behavior of the open loop system. 

Figure 2 and 3 show the state-space model of an AMB actuator acting on a general mechanical system. For 

simplicity we assume in chapter 3, that the mechanical system is an unbound mass m with one degree of 

freedom x. According to Newton's law we get the following differential equation: 

mX=F (3.1) 

(For a rigid body rotor, m would stand for an equivalent rotor mass effective at the actuator.) 

406 
The MIMO-system (Multiple Input Multiple Output) shown in figure 2 is observable from the current 

measurements i+, L alone. Using the voltage inputs u+, u-, it is also controllable. This means that the 

measurement of the rotor displacement x is not needed for control. 

This has been demonstrated in practical setups by Vi scher and in several student projects at ETH [Jordil & 

Volery 90], [Colloti & Kucera 91]. A patent [Vi scher, Traxler & Bleuler 88] has been applied for. 

A simpler state space model is found choosing B+ and R as state variables rather then i+ and i- (fig. 3). 

J 

I-----~X 

Mq +Dq+ Kq = F X 

Figure 3: Linearized state-space model for one mechanical degree offreedom and 

two coils according to figure 1. The two flux densities (B +, B -,) in each coil of the 

bearing, rotor velocity i and displacement x are selected as state variables. 

3.1 Voltage Control 

The state space models shown in figure 2 and 3 can now be used to design a bearing control with voltage 

instead of current as input variable. This will be called "voltage control". Voltage control has been 

investigated thoroughly by many authors [Ulbrich & Anton 84], often in the context of magnetically 

levitated vehicles (e.g. [Jayawant 81], [BreinI80]). 

~ ................................... 11 

J : F _1 i J i J , 4> ® .... ] 

: _t. ~-----------------------~-----~ l + 

2 

x 

4a) 

I--__ ~i++( 

2 

4b) 

Figure 4: Transformed state-space model for the system offigure 2 with a single 

mass model of the mechanical system. This choice of state variables produces two 

decoupled subsystems, figure 4a (with states x, i and F) and figure 4b with the 

single state variable (i+ + () / 2. Figure 4b shows that the body movement only 

depends on the difference between the two input voltages u+ and U., whereas the 

sum o/the currents i++i. is only afunction of the sum u++u .. 

407 
The system of figure 2 is observable if at least two of the three outputs (i+, L and x) are available to the 

controller. The following two cases, both of which have some advantages for AMB applications, will be 

examined further: 

• voltage control combined with three measurements (i+, L, and x) 

• voltage control combined with the current measurements only ("self sensing" bearing) 

The system of figure 3 is observable if x and either B+ or B- are available to the controller. 

One way to control the above systems is to implement a Luenberger observer and a state feedback 

controller. The full state-feedback matrix has 8 coefficients (2 inputs, 4 states). Some additional control 

parameters are used for the Luenberger observer. Such controllers were built and tested at ETH. 

As we deal only with a single mechanical degree of freedom, we seek to simplify this controller. It is 

possible to describe the plant (fig. 2 and 3) as a set of two SISO-systems (Single Input Single Output), as 

shown in fig. 4. If the four values (i+ + L) 12, x, iand F [Gottzein & Cramer 77] or [Gottzein et al. 77]) 

are used as state variables instead of i+, i., x and i , the MIMO-system can be replaced by a 3rd order and 

a first order SISO-system. The transfer function of the first subsystem (fig. 4a) is 

2io 1 x=--"3u 

xom s (3.2) 

which is a simple triple integrator. The transfer function of the second subsystem (fig. 4b) is 

i+ ;'- = ~ ;(u+ ;u_ ) 

(3.3) 

which is a first order system independent of the rotor movement. 

Thus, a controller for the voltage-controlled bearing consists of two independent sub-controllers according 

to the two subsystems of figure 4. For the subsystem in figure 4b a_simple proportional controller is 

suitable. Since its main function is to keep the premagnetization current (i+ + C)12 at a nominal value iO ,we 

like to refer to it as "operating point controller". 

The extension to a full order system with multiple mechanical degrees of freedom is straightforward. As 

seen before, each pair of opposing electromagnets is separated into two subsystems. The subsystem of 

figure 4b remains independent of the mechanical system. 

The influence from one mechanical degree of freedom to another acts just like an additional force input 

at the corresponding summation points in figures 2 or 3. Decentralization, i.e. the implementation of local 

feedback based on a complete model, is feasible in most practical cases [Bleuler 84], with the obvious 

implications on the model order used for analysis. With such a layout approach, the on-line computing 

power requirements grow only proportional to the number of control channels. 

In many cases, it is even possible to simplify one step further and to base control layout itself on a 

decentralized model, which brings us back to the simple models described in this chapter. 

3.3 Current Control 

i - d eSlT 'ed~ _ 

u 

MIMO 

(Figure 2) 

Figure 5: AMB-system with current controlled actuator 

408 

1-------1~~ X 
Strictly speaking, the tenn "current-controlled bearing" designates a special voltage-controlled bearing 

consisting of two current controllers as inner loops and a position control as outer loop. Because magnet 

current in reality is a state variable, the dynamics of the inner control loop is usually neglected for treatment 

of the outer loop with current as plant-input. 

The inner control loops keep the two currents at their desired values, which is possible as long as the 

voltages are not saturated and the assumption of infinite inner loop gains Kp is legitimate. The transfer 

characteristic is given by equation (2.5) as 

i -i and i =i => F=kx+k.(i+-t)=kx+k.i + -+ - S I 2 S I desired - desired (3.4 ) 

Equation (3.4) shows that the current controlled bearing can be interpreted as a ''force-source'', which is not 

entirely perfect due to the undesirable term (ks x) corresponding to a spring with a negative stiffness ks. 

This negative stiffness tenn only turns up in the context of current control. 

3.4 Flux Density Control 

Quite similar to the current control, the flux density measurements can also be used to directly control the 

flux densities B+ and R in the air-gaps to desired values by means of two inner loops, as shown in figure 

6. 

B+desired~ 

B 

-desired ~ -

MIMO 

(Figure 3) 

I------I .. ~ X 

Figure 6: AMB-system withflux density controlled actuator 

The behavior of the flux density controlled bearing is then given by equation 2.7. 

B+ = B+ and B = B_ => F = 2NA~(B+ - B_) = 2NA~B desired - desired X 2 x 

o 0 (3.5) 

The advantages of this actuator control configuration is that it yields an almost perfect ''force-source'' 

without the negative bearing stiffness associated with the current control. Furthennore the relation between 

force and flux density is linear, as opposed to current control and voltage control, where the assumed 

equations are only valid around the operating point and some other specific locations in the work space. 

As we could see in equation (2.9), the displacement x can be calculated from the flux density and the 

current in the coil. This type of indirect displacement measurement is excellently suited for large air gaps 

(chapter 5.1). 

3.5 Comparison of Actuator Control Configurations 

Current control has the advantage that the two states associated with the two magnetic coils can be neglected 

under certain conditions (see chapter 3.3). It makes the design of the main controller a little easier (e.g. PD 

control is feasible). 

When voltage control is employed, only one of the two states is taken care of by an inner actuator loop, 

whereas the second state has to be considered in the layout of the main controller. 

Voltage controlled AMBs, however, have the advantages that the open loop system has no negative 

stiffness ks (highly instable open loop system). It is known from control theory, that a highly instable open 

409 
loop system is very sensitive to time lag and noise in the measurement. Detailed description can be found in 

[Vischer 88]. Future comparison involving other criteria is shown in figure 7. 

Criteria Voltage Current Flux 

Control Control Control 

Sensitivity to Timelag in <). • .0.- the Measurement 

,sensItIvity to NOIse III the .0.- • <). Measurement 

Copper Resistance liliiii ~~ 0. 

Stray Field .. ~~ <} 

Saturation of Iron 4Q. .. (). 

Validity of Linearization lila • .0 

G Advantage _ Minor Disadvantage" Disadvantage 

Figure 7: Comparison of actuator control configurations 

Flux density control: Force-source (eq. 2.2) 

Current Control: "Force-source" & negative stiffness (eq. 2.5) 

Voltage control: "Force derivative source" if the the rotor is approximated by one mass (eq 2.7 and 2.8) 

3.5 Self-Sensing AMB 

The transfer function (3.8) from input u=(u+-uJ/2 to output i=(i+-iJ/2 nicely shows the operating principle 

and the feasibility of the self-sensing bearing. 

(3.8) 

Both transfer functions (3.3) & (3.8) are of full order; therefore it can be deduced that the voltage controlled 

AMB-plant is observable and controllable from the measurements of the current (i+-L) and i only. 

Figure 8 shows the corresponding simple state-space model. 

u-..... ~ i 

Figure 8: Transformed state-space model of the SISO-plant of figure 4 for selfsensing operation. (State variables: i=(i}-i2)12, i and x) This system together with 

the subsystem offigure 4b can be used to design a simple linear controller for the 

self-sensing bearing. 

It can be shown, that the simplest linear main controller for the self-sensing bearing is 

bzsz +bls+bo • 

u= I 

lZts + ao 

410 

(3.9) 
4. DESIGN OF THE MAIN CONTROLLER 

The controller is generally a part of a mechatronic (electro-mechanical) system. It feeds back some sensed 

signals of the system to the actuators of the system. Thus, the controller is involved with the whole system 

and can never be regarded isolated. The system design starts with the design of the plant and the design and 

placement of the sensors and actuators, called control configuration. Next, an appropriate model of the 

system has to be derived and control layout specifications have to be defined. Thereby, the modelling and 

the control design cannot be treated as separate problems [Skelton 89]. After the controller layout, the 

controller has to be implemented and tested. 

Thus, the main controller layout is only a part of the whole AMB-system design and has to be done in tight 

cooperation with rotor design, sensor and actuator design and placement, modelling and implementation. 

The good controller layout leads only to good performance if the system configuration (actuator, sensor, 

mechanical structure etc.) is optimized. 

AMB-systems can usually be modelled as quite linear systems, even if the AMB-actuator is not absolutely 

linear. A suspended flexible structure can lead to a high order model. We therefore assume, that the plant, 

P, and the controller, C, are linear and time-invariant (LTI). 

~------------------------p 

w=~J-f---- u 

Xb 

Xi =z 

xl 

y 

u : controller output 

1] : noise 4--n--...,n---., ... -J X b : bearing displacement 

F;x : excitation force 

Fu : unbalance force 

controller i..---C 

Figure 9: Block scheme of a typical AMB-system 

xi: displacements of interest 

x; : non-measured state variables 

Y : sensor signal (displacement, 

flux, current ... ) 

T : sampling time 

Figure 9 shows a general AMB system, where GA(S) is the transfer matrix of the AMB-actuator, GR(S) that 

of the rotor plant (suspended body) and GF(S) that of the sensor and signal filtering. The transfer matrices 

GA(S), GR(S) and GF(S) describe the AMB-plant P. C(z) is the transfer matrix of the controller C which has 

to be designed. The controller C is assumed to be time discrete. 

The inputs to the plant are divided into two vector signals: 

- The actuator input vector u, consisting of those inputs to the plant which can be manipulated by the 

controller. 

- The exogenous input vector W, consisting of all other input quantities such as noise, excitation forces, 

etc. 

The output of the plant consists of two vector signals: 

411 
- The measured output vector y, consisting of those measured signals which are accessible to the 

controller. 

- The regulated output vector z, consisting of all outputs of interest such as actuator input, rotor 

displacements, measured and non measured state variables. 

This notation of the plant includes more details about the AMB system than is common in 

classical control [Boyd et al. 90]. The exogenous inputs and regulated variables contain each 

signal subiect to constraints or specification, whether it is measured or not. 

Some general examples of specifications for AMB-systems can be found in the next paragraph. 

4. 1 Specifications for the Controller Layout 

The controller layout of an AMB system is always restricted by different specifications. The specifications 

have to be defined by the AMB-engineer and include e.g. physical aspects of the plant and specifications on 

the system performance. Common examples are: 

closed loop stability 

maximum stiffness over a given frequency band [Herzog & Bleuler 90] 

limitation of the amplifier's bandwith [Keith et al. 90], [Siegwart & Traxler 90] 

noise rejection, noise filtering 

force free rotation around the inertial axis [Higuchi et al 90] 

damping to cross critical speed 

vibration rejection 

robustness (changes in the plant, modelling errors, nonlinearities) 

The constraints and specifications often define upper and lower bounds for the input-output behavior of the 

AMB-system shown in figure 9. 

Control specifications of an AMB-system --------, 

k" • H 

x,F. -"F - x. 

ox 

, ~ 

I 

{1Hz 

• H 0" 

=.!! 11 ~ 

I 

flHz 

u 1f\J\ • H =- of, F 

0 

f. 21. flHz 

I 

u 

• HoF • =-F 

OJ< ~ flHz 

• High robustness versus changes .1 P in the plant P 

Figure 10: An example/or the specifications given/or an AMB system. 

Possible specifications of input-output transfer function of AMB-systems are shown in figure 10. 

Unfortunately, the different specifications often are in opposition to each other. It is up to the talented 

control engineer to find an acceptable compromise. After defining the bounds of the controller layout, 

different design tools help to find an optimal solution to the control problem. 

412 
4.2 On Different Controller Design Approaches 

Modern AMB controllers will almost certainly make use of digital control with its well-known advantages 

such as large flexibility in controller structure changes during machine installation or easy implementation of 

additional controller features ("feedforward" control, automatic adaptation to changing plant parameters, 

machine monitoring etc.). 

In the process of controller design, the control engineer has either to find a control law that meet the design 

specifications (chapter 4.1) or determine that none exists. If there is no controller meeting the specifications, 

the control engineer has to change the specifications and/or the system configuration. Thus, a good 

controller design tool should allow an account of all design specifications of the given design problem and 

consider the specific control configuration of the system. 

Specific control features of AMB systems are: 

- only very few system states, most often the displacements at the coils, are measured. 

::::) observer based controller (LQG, LQR, H2, Hoo) 

- the controller often has to be of much lower order than an adequate plant model 

::::) direct low order controller design (PD, PID, SPOC-D) 

- many control specifications have to be considered (see chapter 4.1) 

::::) Hoo, 'convex optimization' of the class of all stabilizing controller, SPOC-D 

Many different control approaches for linear and time-invariant (L TI) are available and it is up to the control 

engineer to choose the most appropriate to solve his control problem. Some of them, namely the PD, PID, 

LQG, LQR and the more advanced direct low order controller design (SPOC-D) and HOO methods are 

discussed in the following. 

PD, PID controller layout 

PD and PID controllers are the most common and most used controllers. The basic idea is to use a feedback 

similarly to 'a mechanical spring and damper'. The big advantages are, that they are easy to understand and 

easy to implement (even in analog technique). In many applications they are fairly robust due to the positive 

real transfer function of a PD controller. However, with PD and PID the controller has always to be 

decentralized for MIMO-systems. Only very few specifications can be met by PD / PID controllers and 

closed-loop stability can not be guaranteed. PD / PID is a predefined low order approach which does 

usually not account for high demanding specifications of high order plants. 

Observer Based High Order Controller 

As stated before, a typical property of many practical AMB systems is the fact that only very few system 

states, most often the displacements at the AMB-coils, are measured. This is the case especially with 

flexible rotors, where the order of an appropriate plant model is much higher than the number of sensor 

signals available. The well-known consequence is: 

A high order observer-based state feedback must be implemented including the full 

dynamics of the plant. Stability and good performance of the nominal closed-loop system 

may then be achieved by an appropriate controller design method such as the well-known 

L R and L methods inear uadratic Riccati res . Linear uadratic Gaussian . 

One crucial drawback of this controller design approach, however, is that this high order control scheme 

will require a considerable amount of computation time for the estimation of the non-measured state 

variables and for the calculation of the corresponding controller output signals. The consequence is either 

the need of a sophisticated and expensive multi-processor or the acceptance of low sampling rates whenever 

single-processor implementations are used. 

413 
Hence, low order discrete-time dynamic output control schemes must be sought in order to simplify the 

control task. The most general approaches for such a low order controller are summarized in figure 12: 

Controller Reduction and Practical Aspects of Low Order Controller Implementation: 

According to figure 11 the three basic ways to achieve a practically implementable discrete-time controller 

are: 

- model reduction prior to the controller design 

- controller reduction after controller design 

- direct low order controller design 

Model 

Reduction 

LQG or Hoo Design 

(high order level) 

LQG or Hoo Design 

(low order level) 

Controller 

Reduction 

Figure 11: Basic principles of low order controller design (figure from (Anderson 

& Liu 89]) 

Many among the first two mentioned reduction techniques can be denoted as so called "open-loop" 

reduction methods. This means that stability of the resulting closed-loop system is not an intrinsic property 

of the reduction process. A practical example, well-known to any AMB control engineer, is that high 

frequency bending eigenmodes will often turn out to be unstable when reduced order controllers or 

controllers relying on reduced models are used. 

Both listed approaches of a practical implementation of reduced AMB controllers are quite ineffective: On 

the one hand, "tuning" is a time-intensive and therefore expensive job, and obtained results can hardly be 

transferred to any other type of machine. On the other hand, notch-filtering of bending eigenmodes has a 

drastically deteriorating impact on the overall controller performance, since the necessary controller phase 

lead is degraded even in the rigid body (i.e. low frequency) range. Thus, the use of notch-filters makes the 

following controller tuning a necessary task, and, roughly spoken, renders the preceding LQR or LQG 

controller layout often very unqualified. 

Another, more sophisticated way is to account for the neglected plant dynamic in the controller 

design specifications. Such specifications can be included in Hoo and 'convex optimization' of 

the class of all stabilizing controller. 

This approach seems very promising, especially because all neglected plant dynamic of the real physical 

plant, not only of an appropriate model, can be included in the control specifications. 

Direct Design of Low Order Dynamic Compensators: 

A promising and most practical solution to the problem of obtaining low order controllers for high order 

plants is the direct low order controller design: [Bernstein & Hyland 84], [Larsonneur 90]: 

414 
Order and structure of the discrete-time controller for the nominal high order (i.e. not 

reduced) plant model are predefined prior to the controller layout (structurally constrained 

controller). This predefinition is made according to practical needs such as physical 

considerations complexity constraints, decentralization, symmetry etc. 

This approach is, in fact, very common in AMB applications where, quite often, discrete-time low order 

approximations of traditional continuous-time P(I)D control schemes are implemented. The most simple 

discrete-time PD approximations are the following ones (controller output u, measured plant output y, 

sampling time T, time event k, proportional respective differential control coefficients P and D): 

uj(k) = (p + ~)yj(k) - ~ Yj(k -1) 

(4.1) 

( 3D} 4D D u.(k) = P + - .(k) - -y.(k - 1) + -y.(k - 2) 

• 2T' 2T' 2T • (4.2) 

Such P(I)D controller schemes exactly match above direct design definition: the controller order (e.g. 1st or 

2nd order) and a decentralized structure (sensor signal Yi is fed back on actuator input Ui only) are 

predefined prior to the controller layout (determination of P resp. D). The control parameters P and D can 

then be obtained by numerical simulations or, again, by on-site "tuning" of the AMB system. 

In many cases, no set of control parameters (P ,D) can be found stabilizing both low frequency rigid body 

and higher frequency bending eigenmodes. More sophisticated approaches for direct low order controller 

design, namely the so called SPOC-D approach, are therefore required (see next paragraph). 

4.3 Structure-Predefined Optimal Control for Discrete Systems (SPOC-D) 

Lately, a direct low order controller design method for discrete-time systems named SPOC-D (StructurePredefined Optimal Control for Discrete Systems) has been developed at the Swiss Federal Institute of 

Technology (ETH). This method has a strongly practical orientation. Similar to the LQR/LQG design 

methods, SPOC-D uses a quadratic performance criterion to be optimized, accounting for a high order plant 

model as well as for the controller dynamics. The fundamental difference to these classical methods, 

however, is that the controller order and structure are not a result of the controller design process, as it is 

the case for LQRlLQG or familiar methods, where high order plants generally lead to high order controllers 

(see figure 11). The SPOC-D method combines the advantages of a system optimization including the full 

plant dynamics on the one hand and possibly simple low order dynamic compensator schemes on the other 

hand and, thus, closes the gap between the classical LQR/LQG or pole placement methods and the more 

practical and less sophisticated P(I)D approaches. 

The main features of SPOC-D can be summarized as follows: 

- discrete-time controller order and structure are freely predefinable according to practical 

needs (low or high order, fully coupled or completely decentralized, etc.) 

- determination of an optimal set of control parameters by minimizing a quadratic 

performance criterion involving both, the full plant and the controller dynamics 

- analytical description of the performance criterion (by Lyapunov equations) and 

corresponding vector gradient allowing for an efficient numerical optimization process 

- consideration of additional linear or nonlinear control specifications in order to achieve 

specific controller properties of practical importance (stiffness, noise reduction at high 

frequencies, band pass filtering, symmetries, etc.) 

A detailed description of the SPOC-D method is not presented in this paper but can be found in [Larsonneur 

90]. However, controller layout results for a high speed AMB milling spindle are presented in chapter 5.3. 

415 
4.4 Hoo: A MiniMax Approach to Control 

Cultural Remarks and Motivation for Hoo Control 

An intuitively most appealing motivation for HOO control is supplied by its differential game analogy [Doyle 

et al. 89]: consider a plant with two inputs. These two inputs which are also called players are set up in 

opposition. The first player u(t) (that's you in fact !) is the control input generated by the controller (your 

strategy). The second player w(t) (your adversary) is an exogenous input signal which could represent 

some disturbance. Of course, this exogenous input signal is a priori unknown to you; the only available 

signal for the controller input is the measured plant output y(t). Your objective is to minimize the "worst 

case" disturbance, that is to minimize the disturbance which causes the maximal "damage" (in terms of 

energy) to the plant output z(t). This "minimax" optimization problem characterizes HOO control. Note that 

figure 9 in section 4 exactly matches the situation described above. 

Practical Aspects of Designing and Implementing Hoo Controllers 

The off-line effort for computing HOO controllers has been drastically reduced recently by the "state space 

approach" in [Doyle et al. 89], where the resulting controller is basically given in terms of two algebraic 

Riccati equations. HOO software packages are already available [Matlab], and algorithms are being improved 

and standardized. These advances have a common desirable consequence: the Hoo approach is nowadays 

available to a broader section of the control community. However, there is still a computational on-line 

burden because standard HOO designed MIMO (multiple input multiple output) controllers are fully coupled, 

and their order is roughly the same as the order of the plant. That is why there remains a strong need to 

keep up with the latest developments in special purpose controller architectures, in modern "closed-loop" 

controller reduction schemes [Anderson & Liu 89], [Mustafa & Glover 91], and in decentralized control 

[Wu 90]. 

Experimental implementations of Hoo designed controllers for AMB systems (especially for high 

performance AMB milling spindles) will be effectuated soon at our institute. The AMB milling spindle is a 

particularly challenging application example of HOO control since the cutting forces of the milling process 

appear as a highly unpredictable exogenous input which may cause intolerable vibrations of the milling tool. 

Some theoretical considerations to this problem were carried out in [Herzog & Bleuler 90]. In [Matsumura 

et al. 90] experimental results based on the Hoo "mixed sensitivity" approach were shown. A theoretical 

example is shown in chapter 5.4. 

5. THEORETICAL AND EXPERIMENTAL RESULTS 

5.1 Displacement Sensing by Flux Density Measurement 

The laboratory prototype crystal-growth system shown on figure 13 makes use of equation (2.9) for the 

displacement measurement [Zlatnik & Traxler 90]. The flux density measurement together with a current 

measurement is used for the displacement sensing. The lack of a special displacement sensor is specially 

useful for large air-gaps, lower costs and encapsulated rotor systems. A liquid phase epitaxy centrifuge in a 

similar arrangement and with a totally encapsulated rotor, is currently installed at MECOS Traxler AG. The 

temperature at the front end of the rotor goes up to 800· Celsius. 

5.2 Self-sensing AMB Systems 

One way to build a self-sensing bearing is to design a Luenberger observer for the voltage controlled 

system of 4th order according to figure 4. The observer can be tuned by comparing the estimated air gap 

with the measurement of a position sensor. A state feedback can then be implemented and self-sensing 

operation is achieved by switching position feedback from the measured signal to the estimated one. This 

was implemented in [Jordil & Volery 90] on a signal processor with a sampling time of 120 Jls. 

416 
ORIGINAL PAGE 

BLACK AND WH ITE PHOTOGRAPh 

°4-~ __ ~ __ L-~ __ ~~l f 

o 100 l aO ems] 

Figure 12a: Demonstration model of the self sensing bearing with one controlled 

degree of freedom. The Box on the right contains power amplifier, power supply 

and controller. 

Figure 12b: Measurement of impact response (hammer) of position signal of a 

self-sensing AMB. The air gap of the bearing is 0.7 mm, rotor mass is 8 kg, 

bearing diameter is 78 mm, bias current is 0.5 A and maximum force is over lOON. 

The static behavior is satisfactory, similar to the current controlled bearing. The 

dynamic response is still not exciting, and has to be improved. 

An analog realization of a self-sensing bearing was successfully completed as a student project [Colloti & 

Kucera 91]. The controller makes use of the separation shown in figure 4. The complete circuit needs very 

few electronic components. A good robustness of the bearing was achieved. 

The measurement result of figure 12 shows the system response to an impact force, a blow with a hammer 

on the rotor. Maximum rotor displacement of this measurement was about 0.3 mm which is almost 

maximum rotor clearance in the auxiliary bearing and about 50% of the total air gap in the bearing magnet. 

Further technical data of this system is given in the figure caption 

417 
ORiG1NP .. L PP,0t: 

BLACK AND WH TE PHOTOGRAPH 

Figure 13 Laboratory set-up of a crystal-growth system with displacement 

sensing by flux and current measurement. 

5.3 Optimal Control of a Stiff AMB System using the SPOC-D Method 

The example in this chapter is from an actually realized system, a high performance AMB milling spindle, 

controlled by a single digital signal processor (DSP) [Siegwart et al. 90]. It illustrates the large variety of 

con!Tol goals offered by the SPOC-D method. 

The procedure to obtain an appropriate controller fulfilling the desired requirements can be summarized as 

follows (see details in [Larsonneur 90]): 

1. Step: Predefinition of discrete-time controller structure and order according to the practical feasibility. 

For the milling spindle example, two decentralized dynamic compensators, each of 4th order, 

have been chosen (sampling frequency 10kHz). This yields the following IIR (J nfinite Impulse 

Response) controller transfer function in the z-domain: 

(

z) = u(z) = do + d1z1 + d2 z2 + d3z3 + d4z-4 

g () 1 -1 - 2 - 3 -4 Y z +c1z +c2 z +c3z +c4 z 

G( z) = [gl (z) 0] o g2(Z) (4.3) 

Note that this controller predefinition uses two decentralized 4th order controllers g(z) for a 

plant of total order 14 (including sensor and anti-aliasing filter state variables), and involves 

only 18 control coefficients, whereas a full state observer for this plant would require 56 control 

coefficients and corresponding multiplications. 

2. Step: Introduction of additional control specifications in order to achieve requirements of important 

practical relevance. Here, the static bearing stiffness (without integrator feedback), suppression 

of rotation-synchronous AMB force components (analogous to notch-filters) and noise 

suppression at high frequencies are introduced as parameter constraints. This results in an 

interdependence of the control parameters. For the given case, four control coefficients of each 

dynamic compensator will be dependent on the other five. 

418 

Note that the conditions of bearing stiffness, unbalance and noise suppression or other 

parameter constraints are directly introduced into the controller design process before 
optimization and not achieved by any specific choice of weighting matrices during the controller 

optimization process. 

3. Step: Determination of the independent and dependent control parameters by numerical minimizing a 

quadratic performance criterion (which includes the parameter constraint equations). Efficient 

numerical minimizing procedures can be used since vector gradients are formulated analytically. 

The resulting controller transfer function of this optimization process for the AMB milling spindle is shown 

in the following figure: 

controller: hase 2oo.-------------.--.-.~.-,,-.-,,---.~.-.-.-.-., 

· ....... . t •••••••• 

1()4 !;;;;:;;;#Wi~&;;i;;;:;;:;;:;i 'iii;;;;;:;;;~;i; iii; 

10

3 

~ ~ ~ ~ ~:~ ~ ~~ ~ n ~:~:T~:~ ~ ~ ~ ~ j ~ ~ ~]~:~ ::~ i ~1 j j ~ ~ ~ ~ T~~ -j~ ~ ~ 

101 102 103 104 

-100 ..... : ... : .. :. -:- > -:~;:. :d' 'oo:"d-;;":'; .:.:-:-:-~- -1-' '.: -.; .: .. :- -:.:- ~ .. · ....... flgl y ..... ··e ashe .... . 

: : : : : :1::: ran$e: : I: : : ~: >ang~ I: : ::: · . . -200 L..-~' ~. ----..,;,.~--.--.--. -' .~.~. '-' ---' --' ~''''':''-----l 

101 103 

frequency [Hz] frequency [Hz] 

Figure 14: Transfer functions of the SPOC-D optimized decentralized discretetime controller (4th order) at rear andfront AMB of the high speed milling spindle. 

The conditions of static bearing stiffness (J), unbalance force suppression (2) and 

noise suppression (3) are introduced by control parameter constraints. 

As can be seen from above results the SPOC-D optimized decentralized low order controller perfectly 

accounts for the the desired spindle requirements: high stiffness, unbalance and noise suppression and large 

"damping" (positive controller phase lead) in the low frequency rigid body range as well as in the higher 

frequency bending eigenmode range. This is made possible by optimally using the design freedom offered 

by low order dynamic compensators in a most practical and straightforward way, instead of "tuning" 

otherwise obtained controllers so that they match the desired requirements. 

5.4 Stiff AMB Control: HOO versus PD 

Comparing different controller layout methods is not an easy task. Clearly, any comparison must be made 

with respect to a common performance index. There is an erroneous and prejudiced opinion stating that PD 

controllers are mostly "nearly optimal" in "some" sense, and that modem control theory only allows small 

"performance improvements" at the expense of extremely high sophistication. Our illustrative example here 

proves the contrary. 

Consider the controlled AMB system in figure 15. The two mass oscillator P stands for a simple 

electromagnetically supported flexible shaft. The system is assumed to be subjected to an unknown 

disturbance force w(t) acting on the bottom mass mI' Let z(t) denote the displacement of ml caused by 

w(t), and let T(s) be the frequency-domain compliance: z(s) = T(s) w(s). Let the objective of controller 

C(s) be to stabilize P(s) and to maintain the magnitude of dynamic compliance ITOm)1 uniformly below a 

given bound a, i.e. IT(im)1 < a for all frequencies m. The main feature of this example is that the 

disturbance and actuator forces are not acting on the same mass. This implies the following drawback for 

PD control C(s) = - (p + d s): neither low nor high (p, d) gains are appropriate for very stiff control, i.e. 

for a small value of a. Note that high (p, d) gains lead to a rigid top mass m2, whereas the bottom mass ml 

is nearly undamped, which produces a high resonance peak of dynamic compliance IT(im)1. 

Obviously, "optimal" (p, d) tuning leads to investigating maxm ITOm)1 as a function of (p, d), see figure 

16. It can be concluded from this example that PD controllers may give poor performance results especially 

419 
if the actuator and disturbance forces are not acting on the same place. Now, what is the answer of HOO to 

all this? In [Herzog & Bleuler 90] we derived the following result: 

For the above example, there exist stabilizing controllers C(s) enabling an arbitrarily low 

com Hance ak bound a> O. 

Of course, a low value of a implies high controller authority. Actually there is a trade-off between several 

requirements. This trade-off reasoning is absolutely fundamental to control engineering. PD control 

disguises this fact since high (p, d) gains do not necessarily lead to high performance. The freedom offered 

by PD tuning is only a tiny little subset of the freedom offered by the set of all stabilizing controllers. 

However, if the performance specifications are not very demanding, the reduced freedom of PD controllers 

is mostly sufficient. 

420 

displacement 

y(t) 

controller 

C 

control force u(t) 

m2 

plant 

p 

Figure 15: Control problem and objective 

3 contour plot of peak compliance 

2.8 

2.6 

~ 2.4 C 

.~ 

~ 2.2 ..... 

g 

u 2 i 1.8 ~ 

1.6 

1.4 

1.7>.4 0.5 0.6 0.7 0.8 0.9 

spring coefficient p 

1.1 

~ 

1 

u 

Control objective: 

~+-------..... frequency (0 

.2 

Figure 16: Contour plot/or the/ollowing peak level values: {3, 2.75, 2.5}. The 

cross marks the optimum (p, d) tuning POpl:::: 0.7444, dofJ :::: 2.0478. The 

corresponding (p, d)-optimal peak compliance is about maxw/T(im)j :::: 2.3438. 

Parameter values o/plant P: m1 =m2 =c = 1. 
6 • CONCLUSION AND OUTLOOK 

Various control configurations of AMB-actuators have been presented. Voltage and flux density control are 

promising for many applications, advantages are clearly indicated by theory. Extended experimental 

comparisons remain to be done. 

A self-sensing AMB has been presented in theory and realization, i.e. an AMB using no sensing hardware 

in the bearing [Bleuler & Vischer 91]. Self-sensing AMB are a promising solution for low cost applications 

or applications where conventional sensing hardware is expensive. 

The control layout is regarded as a key point of AMB system design. However, a good control layout alone 

cannot guarantee a good system behavior when the "conditioning" of the control plant is bad. 

New approaches to control design as they have been outlined in this paper have many advantages compared 

to the widely used PD and PID control. With new control design tools such as direct low order controller 

design [Larsonneur 90] , HOO or 'convex optimization' over the set of all stabilizing controllers [Boyd et al. 

90], controller specifications can be met, which are not achievable by PD/pID or even by LQGILQR 

approaches. Some examples show the advantages of the new design techniques. 

A successful control layout, especially for high performance systems, is still a very challenging engineering 

problem. There are thousands of problems to be solved. New AMB-systems, with better control 

configurations have to be designed, better sensor and actuator hardware has to be developed and new 

control design methods have to be investigated. To improve the performance of AMB systems it is essential 

that the whole system is treated as a mechatronic product where all parts are interdependent. Not the isolated 

design of AMB components, but smart integration of all parts into the overall system will result in 

successful products. 

7 • REFERENCES 

[Anderson & Liu 89] Anderson B.D.O and Liu Y.: Controller Reduction: Concepts and Approaches, IEEE 

Transactions on Automatic Control, Vol. 34, No.8, pp. 802-812, 1989 

[Beams et al. 46] Beams J.W., Young J.L. and lW. Moore: The Production of High Centrifugal fields, 

Journ. of App!. Physics, Vol 17, pp 886-890, 1946 

[Bernstein & Hyland 84] Bernstein D.S. and D.C. Hyland: The Optimal Projection Equations for FixedOrder Dynamic Compensation, IEEE Trans. AC, Vol. 29, No. 11, 1984 

[Bleuler 84] Bleuler H: Decentralized Control of Magnetic Bearing Systems, Doctor thesis no 7573, ETH 

ZUrich 84 

[Bleuler & Vi scher 91] Bleuler H., Vischer D.: Magnetic Bearing Systems with Minimal Hardware 

Requirement, ROMAG '91 Magnetic Bearing & Dry Gas Seals, Int. Conf., Alexandria Va., March 91 

[Boyd et al. 90] Boyd S., Barratt C. and S. Norman: Linear Controller Design: Limits of Performance Via 

Convex Optimization, Proceedings of the IEEE, Vol. 78, March 1990. 

[Breinl 80] Breinl W.: Entwurf eines unempfindlichen Tragregelsystems flir ein Magnetschwebefahrzeug. 

Fortschrittbericht der VDI-Zeitschriften, Reihe 8, Nr. 34, MUnchen, 1980. 

[Colloti & Kucera 91] Colloti A. and L. Kucera: Low Cost Magnetic Bearings, Semesterarbeit IfR 1991. 

[Doyle et al. 89] Doyle J.C., Glover K., Khargonekar P.P., and B. A. Francis: State Space Solutions to 

Standard H2 and HOO Control Problems, IEEE Trans. AC, Aug. 1989, Vol. 34, No.8, p. 831-847. 

[Gottzein & Cramer 77] Gottzein E. and W. Cramer: Critical Evaluation of Multivariable Control 

Techniques based on MAGLEV Vehicle Design. IFAC Symposium on Multivariable Technological 

Systems, Canada, July 1977. 

421 
[Gottzein et aI. 77] Gottzein E., Miller L. and R Meisinger: Magnetic Suspension Control System for High 

Speed Ground Transportation Vehicles. World Electrical Congress, Moscow, June 1977. 

[Herzog & Bleuler 90] Herzog Rand H. Bleuler: Stiff AMB Control using an HOO Approach, 2nd Int. 

Symp. on Magnetic Bearings, Tokyo 1990 

[Higuchi et al. 90] Higuchi T., Mizuno T. and M. Tsukamoto: Digital Control System for Magnetic 

Bearings with Automatic Balancing, 2nd Int. Symp. on Magnetic Bearings, Tokyo 1990 

[Jayawant 81] Jayawant B.V.: Electromagnetic Levitation and Suspension Techniques, London, Arnold, 

1981 

[Jordil & Volery 90] Jordil P. and F. Volery: Regulation d'un palier magnetique sans senseur de position, 

Student's diploma project, Feb. 1990, Inst. for Robotics, ETH ZUrich 

[Keith et al. 90] Keith F.J., Maslen E.H., Humphris R.R, and RD. Williams: Switching Amplifier 

Design for Magnetic Beaarings, 2nd Int. Symp. on Magnetic Bearings, Tokyo 1990 

[Larsonneur 90] Larsonneur R: Design and Control of Active Magnetic Bearing Systems for High Speed 

Rotation, Doctoral Thesis No. 9140, ETH ZUrich, 1990 

[Matlab] Chiang RY. and M.G. Safonov: User's Guide of the Robust Control MATLAB Toolbox, The 

Mathworks Inc., Natick, MA 01760 

[Matsumura et aI. 90] Matsumura F., Fujita M. and M. Shimizu: HOO Robust Control Design for a Magnetic 

Suspension System, 2nd Int. Symp. on Magnetic Bearings, Tokyo 1990 

[Mustafa & Glover 91] Mustafa D. and K. Glover: Controller Reduction by ROO Balanced Truncation, 

IEEE Trans. AC, June 1991, Vol. 36, No.6, p. 668-682. 

[Siegwart & Traxler 90] Siegwart R. and A Traxler: Performance and Limits of AMB-Actuators lllustrated 

on an Electromagnetically Suspended Milling Spindle, Proc. 25th Intersociety Energy Conversion 

Engineering Conference. Nevada, August 1990 

[Siegwart et al. 90] Siegwart R, Larsonneur Rand A. Traxler: Design and Performance of a High Speed 

Milling Spindle in Digitally Controlled Active Magnetic Bearings, 2nd Int. Symp. on Magnetic Bearings, 

Tokyo 1990 

[Skelton 89] Skelton R.E.: Model Error Concepts in Control Design, Int. J. Control, Vol. 49, No.5, 1989 

[Traxler 85] Vischer D.: Eigenschaften und Auslegung von berUhrungsfreien elektromagnetischen Lagern, 

Doctor Thesis No. 7851, ETH ZUrich, 1985 

[Ulbrich & Anton 84] Ulbrich H. and E. Anton: Theory and Application of Magnetic Bearings with 

Integrated Displacement and Velocity Sensors, The Inst. of Mech. Eng., C299/84, Cambridge 1984 

[Vischer 88] Vischer D.: Sensorlose und spannungsgesteuerte Magnetlager, Doctor Thesis No. 8665, ETH 

ZUrich, 1988 

[Vischer, Traxler & Bleuler 88] Vischer D., Traxler A, Bleuler H.: "Magnetlager", patent No. 678090, 

22.11.88, Switzerland 

[Wu 90] WU Q.: An Application of Hoo Theory to Decentralized Robust Control, thesis ETH Zurich, No. 

9116 

[Zlatnik & Traxler 90] Zlatnik D. and A Traxler: Cost-Effective Implementation of AMB, 2nd Int. Symp. 

on Magnetic bearings, Tokyo, 1990 

422 
N92-27744 

CON!PTJTER A.IDED DESIGN OF DIGITAL CONTROLLER 

FOR RADIAL ACTIVE J\;IAGNETIC BEARINGS * 

Zhong CAIt Zupei SHE~·r:- Zulling ZHA)l"U+ Hongbin ZHAO':' 

.l.Lab. of :\fcchat.ronics and Control. Department. of Engineering Physics. 

Tsing-hua University, Beijing-, P.R. China 

:j:Beijing Institute of Printing, Beijing. P.R. China 

423 
Abstract 

A five degrees of freedom Actiw :\fagnetir B('ar· 

ings (.-L\fB) system is developed in Tsinghua 

Univ('rsity. which is controlled by digital con· 

trollers. 

The model of the radial A~fB system is lin· 

('ariud and the state equation is derived. Based 

on the state variables feedback theory, digital 

controllers are designed. The performance of the 

controllers are evaluated according to experimen· 

tal results. 

The Computer Aided Design (CAD) method is 

used to design controllers for magnetic bearings. 

The controllers are implemented with a digital 

signal processing (DSP) system. The control al· 

gorithms are realized with real·time programs. It 

is very easy to change the controller by changing 

or modifying the programs. 

In order to identify the dynamic parameters of 

the controlled magnetic bearings system. a spe· 

cial experiment was carried out. Also, the on· 

line Recursive Least Squares (RLS) parameter 

identiHcation method is studied. It can be real· 

ized with the digital controllers. On·line paramo 

eters identification is essential for the realization 

of adaptive controller. 

Introduction 

A magnetic bearings system with electromag· 

np.t.ir at,t,radivp. f'orrp. iR an inhp.rp.nt,ly opp.n.loop 

unstable system. The uncontrolled magnetic 

force provides a negative stiffness to the magnetic 

·Supported by the NlI.tional Natural Science Foundation of China 

hp.arings sysT,p.m, i.P.., whp.n rohp. gap hp.t.\\"Pp.n rot,or 

and bearing is reduced. the magnetic force 'Will 

be increased. In this case, compensation to such 

a system is necessary. The j\J.\JB controllers can 

eliminate the negative stiffness and provide pos· 

itive stiffness and damping to the . ..\...\fB system. 

Therefore. the performance of the controllers is 

a decisive factor to the performance of the .-\..\lli 

system. Many papers have described design of 

the control system. [1, 2, 3, 4J 

In order to design a practical A..o.vfB controller. 

which is easy to implement and has relatively 

good performance. some control algorithms are 

studied on a computer system. 

Design of digital controllers can be divided into 

several steps. Firstly. the discrete model and 

state equation of the system are obtaint'd accord· 

ing to the original system. Secondly. a controller 

is designed with the CA.D method according to 

the st'lected control algorithm. Thirdly, the de· 

signed controller can be simulated with computer 

before implemented as a real·time control program. Lastly, the coefficients of the control pro· 

~ams are tuned to reduce the effects of devia· 

tions of the system model. And, if necessary. the 

system modelismodified, and:the controller'is reo 

designed. 

In our magnetic bearings system, the rotor has 

five degrees of freedom need to control, one axial 

degree of freedom and four radial degrees of free· 

dom. Generally, the a:cial A.lVIB system can be 

considered as a single degree of freedom system. 

i.e. it is uncoupled with the radial A..."\-fB system. 

In our early work, digital and analog controllers 

for axial MID had been studied. [51 

The axial A .. \ffi controllers are Single· Input 

PRECEDING PAGE BLANK NOT FtlM£D 425 
A x B 

y 

F ig'llI~ 1: S(,nl(,Ulr~ of Radial ~Iag,n('t.ic Bearings 

Single-Output (SISO) controllers, which can be 

a.nalyzed and designed with the classical control 

theory. However, it is difficult to design the 

Multi-Input ~lulti.01]tput (~l~fO I controller'!. 

a:s u:seJ foc a raJial.-L'v1B :SYtjlelH. wil.h Ole da:s:si· 

cal control theory. 

III th.b paper. WI" Cucu:s our ~Ludy o'iI the radial 

. -\'~fB controllers with the state variables feed· 

back theory. 

Radial Bearings System 

Figure 1 shows the schematic structure of ra· 

dial magnetic bearings used in our e.lperiment. 

The horizontal rotor is supported by two radial 

magnetic bearings, A and B. Each bearing con· 

troIs- two motion directions of rotor. :r and y, in 

t.h~ n x~d CartE'sian coordinat.E's. ThE' origin of 

the- coordina.tes. 0 is at the ma.ss (',-"fiter of t,he rotor. The electromagnetic force of each direction 

is produced by two opposite magnets. The mag· 

nets in !J direction provide- an additional force 

.to support the weight of the rotor. 

In actual magnetic bearings, the relation· 

ship between magnetic (or..:e and control current 

and rotor position are nonlin~ar. Howl'"er. when 

th~ rotor position is near the reference posit,ion, 

till' relatj"II~h.ip can be liut'arizeJ a~: 

426 

where. 

kp-position stiffm·ss 

hi-current stiffness 

x-displacement from reference position 

i-control current 

( 1) 

The total current in magnets can be divided 

into ('ontrol current and bias current. Th(' bias 

current makes the ma.gnets work in the linear 

range of magnetizing curve. [6] 

Taking state variables vector as. 

control variables vector as. 

The sta.te equation of the magnetic bearings 

system is. 

x= AX+BU 

where. state matrix . 

A=( 

0 0 T 

1 0 

0 0 0 [ 

L 0 0 -.\i 

0 L ;.''yi 0 

c:ont.rol mat.rh. 

/ 0 0 \ 

B=!:!. 0 0 

~ kp L 0 

0 L 

The 2 x 2 submatriies 0, I are zero and identity matri'(cs, respectively, and. 

1+~ J" 

1 _ mi,-i, 

-" 

1 _ mi._I, ) J" 

i l 

1+~ "'11 I 
Generally, J ,,/ J.r -< 1. when the rotor rotates 

at the low speed, 9ubmatrix M can be con:iidered 

as zero matri."{, Le., the gyroscopic effects can bt' 

omitted. 

The rotor positions in each direction are measured by four eddy·current displacement sensors 

mounted near radial bearings. In the linear range 

of the sensors, the outputs of sensors, which are 

produced by analog circuits, are DC voltages 

proportional to the displacement of the rotor in 

each dir{'ction. W h{'n the rotor is at reference 

position:'! in bearings, all the outputs of the sensors are zero. Therefore, the output equation of 

the magnetic bearings system is, 

y=cx 

where, 

output matrix. 

C=(I 000)" o I 0 0 

Design of Control System 

The CAD method is used to design digital optimal state variables feedback. control system. [7] 

For a continuous time systt'm, the performance 

index to be minimized is, 

J = 10'.:0 [XT (i)QX{t) + UT (l)RU(l) Jul 

where, Q and R are the state weighting matrix 

and control wt'ighting matm, respectively. 

Givl'!n sampling pp.riod T, t.h P. st.ate MIlIat.ion 

can be discreti-l;ed as, 

X(k) = FX(k - 1) + GU(k - 1) 

where, F and G are the discrete state matrix and 

control matrix, respectively. 

And the performance index can be discretized 

as. 

00 

j = I:[XT (k)QIX(k) + 2XT (k)QsU(k) 

};==o 

1.5 -------------~----- I 

1.0 

I 1000 100 1 

h

' /' I 

1 

-I 

0 

>-

'-.-

I :' ftc) /' 1 

-. 

...,J 

-->-

1/ / I 

,//1 q=O.l I I I 

J // I I 1 I 

0.5 <I I I 1 I 1r-----------------

~ 1 I I I 

I I 

100 200 30G .wo 

tiT 

Fjgllr~ '2: Simniat,ion Result.s of St.ep R~sponsp 

where, Ql, Q: and QJ are the discrete state 

weighting matri"'{, control weighting matrix a.nd 

cross weighting matri~, respectively. 

Given the continuous state equation, weighting matrixes Q and R. and sampling period T. 

a computer program is available to compute the 

opt.imal st;!.t.e varia.bil~s f~p.nha.dt gain mat.rix K 

for digital controller. The choices of weighting 

matrixes Q and R have decisive effects to the 

dynamics of, a. magnetic bearings system. 

We choose the matrixes. 

Q = diag(q,q,q,q,O,O,O!O), 

R = I 

where, q > 0 and I is a. .. x 4 identity match. 

These choices mean that only the squares of displacements and coniroi currents are weighted in 

the performance index J. 

The simulation of step response of the magnetic bearings system controlled by controllers 

with different values of q are shown in Figure 2_ 

The simulation results shows that a big q corresponds fast response of the system. 

Identification of System Parameters 

The optimal state variables feedback. control 

theory is very suitable for designing . ..\.i"m control 

427 
B 

F'igur(' 3: Paramet('rs Identilication Experimen" 

tal System 

'5Y'5tem from th(' givj>n sy'5tem moq('l. However. 

if the parameters of the system are not accurate 

. enough, the designed control system will not be 

optimal or even make controlled system unstable. 

Because t.he A ... \,fB '5Y'5t.em i8 open-loop unst.able ami uuulinear. i:luwe impurLanL paraweLeri:l uf 

system. such as position stiffness kl' and current 

stiffness k;, are strongly dependent on- operating 

point of A}.tffi system. It is difficult to measure 

the system parameters accurately from an openloop system. However, when a simple controller, 

like PO controller. can suspend the rotor stably, 

the parameters can be measured from the closeloop system. 

Figure 3 shows a schematic experimental syst,p.m. Thp. horizont.al rot.or, wit.h rot.at.ion spp.p.d 

o = 0, is suspended stably. Setting this working state as the operating point of the magnetic 

bearings system, the reference position of rotor 

in bearhlgs, the C~"1'ents in bearing coils can 

be measured and the bearing forces can also be 

dp.ddp.d ar.r.ording t.o t.hp. st,rnc:t.llrp. of magnp.t.ir. 

bearings and the rotor. 

When a small weight ml is loaded to the rotor, it will have small displacements from the 

reference position. The displacements of rotor 

and the currents in bearings can be measured directly. The changes of bearing forces can also be 

428 

decided. Changing the weight to m2(m2::F md. 

another set of data. can be obtained in the same 

way. According to the linear assumption. bt'aring forces are expressed as Eq. (1). Therefore, a 

set of ~quation8 is obtained. Consequently. the 

kp and I:; can be obtained by solving thest' equations . 

. -\nother close·loop measurt'ment method. 

called Recursive Least Squares (RLS) parameters identifica.tion method. is also studied. This 

method can be realized on-line with a digital controller and the difference equations of an .~\lli system can be obtained directly. 

Consider a single degree of freedom rotor! the 

motion equation, 

mx = kpz + kji 

can be transformed to a difference equation, 

where, 

a2 =-1 

k T'! 

al =2+ -pm 

1 •. 1'2 

b _ It, ~ 1---

m 

d = 2 - delay number of sampling period 

." (Ie) - random noise at sampling time Ie T 

T - sampling period 

The predicted system output is, 

(2) 

(3) 

i.(k) - ol~(k - 1) - ~(k - 2) + ,31i(k - d) + '1 (k 

= -x(k - 2) + yT (k - 1)9(k - 1) + l1(k) 

where, the input and output vector, 

Y(k - 1) = [z(k - 1), i(k - d)Jf 

predicted parameters vector, 

From the control inputs i and system outputs 

z, at kth sampling period, the predicted system 

parameters are,. 
B(k) = B(k - 1) + N(k)[.r(k) - x(k)] 

where. x(k) is the rotor displacement measured 

at kTth time. 

And the matrix 

/._ _ P(k - I)V(k - 1) 

N( .) - 1 + V7'(k - I)P(k - IlV(k -1) 

the positive definite covariance matrh 

P[kj = 1- N[kjV'l'[k - IjP[k - 1] 

The initial iteration values are, 

P(O) = aI, a = 5 ..... 104 

8(0) = 0 

The simulation results oC RLS parameters 

identification with a PO controller are shown in 

Fig-ure -l. The predicted system parameters con· 

verge to the real system parameters stably. i.e., 

From the identified parameters at. /31 and 

Eq. (2) and (3), the parameters kp • hi can be 

c:ompnt.f!ri. 

It is the advantage of the on-line parameters 

identificat.ion t.hat the difference equat.ion of t.he 

~Ylltelll ill obtaiued ilirecLly, aud accordiug to the 

difference equation an on· line control output can 

be calculated. Based on this idea. the adaptive 

controller can be designed. 

Implementation of Digital Control 

System 

As we know, the radial A.\fB system has 8 

state variables and 4 control variables. The feed· 

back gain matrbt is a 4 X 8 matri.~. When the 

optimal control algorithm is directly realized in 

a real· time program, at least 32 multiplications 

and additions have to be done within an inter· 

rupt period. And, counting in the calculation 

of observing state variablesl the control program 

will be very large. 

In our test· rig, a TMS32010 l)SP system 

was used to implement the control algorithm. 

1.0 

0.5 

r 

3,.=2.1 

b 1=O.0077 

0.0 4-jh-I-r.,..,.,..."-nrrrr',, TITlllllllllnlrrl rl rl II II III I

o 10 t/T 20 30 

Figure 4: Simulation of On· line Parameters Identification with PO Digital Controller 

TS1S32010 can do a multiplication or addition 

in a 200ns instruction cycle. However, the limi· 

tation of in· chip data RAi\1 makes it difficult to 

run the optimal control program. which needs 

many data R. \...\f Cor controller coefficients. To 

simplify the structure of the control system. a de-

~entralized controller is used. which is obtained 

by simply omitting all the coupling elements in 

the optimal feedback gain matrix. 

For oW' wagnetic bearingll ~Y::ltew, at low roo 

tation speed of rotor. the coupling elements in 

optimal feedback gain matrix K arc very small 

compared with the uncoupling elements. There· 

fore, it is believable that this simplification will 

not cause large degradation of system performance compared with the optimal central con· 

trol. Figure 5 shows the step response of radial 

magnetic bearings controlled by the decentral· 

ized controller and the optimal central controller. 

And this result has also been verified in some 

other papers. [8] 

To obtain velocity of the rotor. which can not 

be measured directly, the digital differentiators 

are used. A modified differentiators algorithm 

is. 

ud(k) = ~[z(k)+3z(k-l)-.3z(k-2)-xrk-3)J 

429 
1.5 - - - - - - - - - - - - - - - - - - -

I Decentral 

I I 

~I I 

--~-----~--- ______ I 1/ I Central 

1.0 

/ I 

I! I 

1/ I 

J! I 

~--------~--------- J I 

--.. 

,.;, 

--- :>< 

0.5 

{ q=lOO 

o 100 200 

tiT 

Figure ·5: Comparsion of Central and Decentral· 

ized Controllers 

where, 

l'-sampling period 

x(k)-input displacement at sampling time kT 

This algorithm can reduce the effects of input 

noise to system performance, 

The block diagram of control system is shown 

in ~'igure 6, The digital control system consists 

of displacement sensors, sWitching power ampli· 

liers, DSP system and a host computer. The 

control program can be loaded to the memory of 

the DSP. The structure and parameters of the 

controllers can be changed easily in the memory. 

The Howchart of the real·time control program 

is shown in ~'igure 7. In this digital system, only 

one AID converter and one D IA converter are 

used. Four input and output ports are switched 

by two multiplexers. This simplification is economic use of hardware, but increases the time of in· 

terrupt service program. 

Experimental Results 

According to the designed controller. the feed· 

back parameters are tuned. The step responses 

of the radial magnetic bearings with different 

feedback parameters are measured. In fact, when 

the velocities of the rotor are obtained by dif· 

ferentiators, the decentralized radial A .. Ivrn con430 

8-1 

llUX 

12bit TlIS 

320 

DSP 

PC 

L...-____ -----JJ I 

~I 

1-8 

JroX 

~'igure 6: Block Diagram of Control System 

Main Program 

~'igure 7: Howchart of the Real·time Control 

Program 
1.2 lV=O.5mm 

Tl1 <T}a<7}3 

7}---Damping 

,.0 +r-r-"'-"""'"-,""-T.,..."...."-,.,.,,rrrrTT..,-.,....,-roTTl 

0.0 100.0 200.0 300.0 

t (n:ls) 

FigllTl~ R; St,pp Rpsponsp of t,hp. Rania! .-\\'fR System 

troller can also be considered as four PD controllers. From the view of PD connoner. changing of gains of proportional and differential paths 

means changing of stiffness and damping of system. Figure 8 shows a set of step responses 

curves with different damping 'I and same stiffness. 

Conclusions 

Computer Aided Design method is very suitable for the design of radial magnetic bearings 

~nnt,rnl 'Iv'It.pm. Thp np<;ilTllPn rnnt.rnJlpT ~"n - ----- -- .'" - - -_. ---- -- --0--- - - ----- ---- - .. _-

be simulated with the simulation program before ,implemented as a practical AJ.\1B controller. 

And, the effects of controller coefficients to the 

system perfonnance can be revealed by simulation. For example, increasing of position weights 

in'ii-perfonnanceindexwill increase the speed of 

system response. With the CAD method, the 

development cycle of Mill controller is shorter,_ 

The experimental results show that the simple decentralized state variables feedback digital controllers also have relatively good performance. This control system has simple structure 

and is easy to implement in a digital control system. 

W hen the static rotor is suspended stably, 

the close-loop measurement can be carried out 

to identify the system parameters. The online parameters identification is an advanced parameters identification method. Based on this 

method, an adaptive controller can be realized. 

References 

1. HumphrislLH.. Allaire.P.t: .. 04t:tfect of Control Algorithms on magnetic J ouma! Bearing 

properties", J.t:ng. Gas. Turb. Pow., vol. 108 

pp.624 (1986) 

2. Kcith.F .J ... Vv·illiams.R.D ... "illairc. P.E .. 

"Digita.l Control of \fagnetic Bearings Supporting a '\-lultimass Flexible Rotor", Tribology 

Trans., vo1.33, no.3, pp.307·314, (1990) 

3. Hisatani~f., Inoue.Y .. \litsui,J .. "'Development oC Digitally Controlled :\iagnetic Bear· 

ings", Bulletin of JSME, vo1.29, no.247. pp.2U220, (1986) 

4. Youce!-Toumi,K., -A Digital Time Delay 

Controller for Active '\-lagnetic Bearings"'. 2nd 

Inter. SYlllp. on \1agnetic Bearings, pp.l·j. 

(1990) 

5. Cai,Z., Zhang,Z~f., Zhao.H.B., "Performance of the Active Magnetic Dearings". Proc. 

of the 2nd Intern. Symp. on \fa~etic Bearing, 

Tokyo, Japan, pp.251-255 (1990) 

6. Cai,Z., Zhao,H.B., et aI, '"Design of Digital Active Magnetic Hearings Controllers", 2nd 

Symp. on Modem Design Methodology, Wuxi, 

China, (1990) 

7.. Sun, Z.Q., et al, "Computer Aided Design 

uf Contrul System", Tsinghua University Press, 

(1988) 

8. Bleuler ,H. "Decentralized Control of Magnetic Rotor Bearing Systems" Ph.D. Dissertation, ETH, Switzerland, (1984) 

431 
Session 8 

MICROGRAVITY AND VIBRATION ISOLATION 2 

Chairman - Ralph Fenn 

SatCon Technology Corporation 

PRECEDING PAGE BLANK NOT FtLM'ED 

433 
N92-27745 

A MICROGRA VITY VIBRATION ISOLATION RIG 

Bibhuti B. Banerjee 

Carl R. Knospe 

Paul E. Allaire 

Center for Magnetic BearingsjROMAC 

University of Virginia 

Charlottesville, VA 22903 USA 

PRECEDING PAGE SLANt< NOT FtLMED 

435 
1. ABSTRACT 

It is well-known that the spacecraft environment deviates from a state of 

zero gravity due to various random as well as repetitive sources. Science 

experiments that require a microgravity environment must therefore be isolated 

from these disturbances. Active control of noncontact magnetic actuators enables 

such isolation. A one-degree-of-freedom test rig has been constructed to 

demonstrate the isolation capability achievable using magnetic actuators. A 

cylindrical mass on noncontacting electromagnetic supports simulates a 

microgravity experiment on board an orbiter. Disturbances generated by an 

electrodynamic shaker are transmitted to the mass via air dashpots representing 

umbilicals. A compact Lorentz actuator has been designed to provide attenuation of 

this disturbance. 

2. INTRODUCTION 

Space exploration was initiated for the investigation of space itself, ranging 

from the planetary system to the limits of the universe. Resulting benefits of this 

effort include satellite communications and earth observation and imaging systems. 

The scope of space exploration widened in the early eighties with the development 

of the space shuttle - a system capable of transporting a large cargo to a low earth 

orbit, and recovering the payloarl or frequently servicing it in space. A parallel 

development was the gradual change in the role of man in space, starting with the 

primarily technical function of a pilot and evolving into a more active involvement 

encompassing interactive work and scientific experimentation in space. 

Space-based laboratories like the Skylab and the Spacelab were flown to utilize the 

"vanishingly low" gravitational forces available for extended periods of time. The 

results, however, were mixed at best, and disappointing in certain cases. This can 

be explained in part by the fact that the environment aboard the spacecrafts 

deviates considerably from the ideal of zero gravity due to disturbances produced by 

plachinery and people on board, thruster fire, and other factors. 

The incentives for performing science experiments in space include the 

investigation of phenomena that are influenced by gravity on earth, the 

development of novel materials and the improvement of processes like crystal 

This work was supported in part by the NASA Lewis Research Center and the 

Center for Innovative Technology of the Commonwealth of Virginia. 

PRECEDING PAGE BLANK NOT FtlMED 437 
438 

growth [1]. In theory, a freely orbiting spacecraft offers a state of zero gravity to 

objects inside it, since the gravitational force is balanced by the centrifugal force [2]. 

However, in practice, there are various residual forces that disturb the environment. 

Attempts to estimate these residual forces have been made in the past few 

years [3-101. The orbital microgravity environment can be divided into three 

classes, as detailed in Table 1. Quasi-steady accelerations are generated by three 

sources - gravity gradient, aerodynamic drag and rotational acceleration. Any 

point of an orbiting structure that is at a distance from the structure's center of 

mass experiences a gravitational field that is different from that at the spacecraft 

center of mass. Aerodynamic drag due to the earth's atmosphere represents the 

absolute lower limit of the achievable background microgravity level, if the effect of 

light pressure is neglected. Finally, in order to keep the same vertical orientation on 

the space station with respect to the earth, the station must maintain a constant 

pitch rate about its center of mass. This creates a centripetal force that results in a 

rotational acceleration. 

Orbital thruster fire and the steady-state operation of machinery like fans 

and pumps on board a spacecraft are among the sources of periodic accelerations, 

which occur at known frequencies. Impulsive disturbances like crew push-off and 

the start-up and shut-down of machinery create non-periodic accelerations. The 

irregular, unpredictable nature of these accelerations complicates attempts at 

isolation. 

Theoretical acceleration requirements for various processes and experimental 

conditions have been investigated l3,7,11]. The common feature of curves depicting 

the frequency-dependent requirements is that, for a given process, the acceleration 

threshold is lowest from steady-state to about (0.01 - 0.1) Hz, depending upon the 

type of experiment. The acceptable acceleration then increases linearly with 

increasing frequency, up to (1 - 10) Hz. Subsequently, it increases as the square of 

the frequency. The acceleration tolerance also typically scales inversely with the 

volume that characterizes the process. The slopes and breakpoints result from 

fundamental aspects of a process, and the shape of the curve can be considered to be 

characteristic of a family of experiments. The acceleration level thresholds range 

from an extreme level of (10-7 - 10-8) go for some material science and fluid science 

experiments, to only 10-.3 go for the majority of biology and biotechnology 

experiments. 

A comparison of the microgravity requirements with the actual environment 

available on the spacecraft indicates the need for vibration isolation. Moreover, the 

frequency range of interest spans several decades, thus requiring the use of multiple 

strategies for isolation. 

For the high frequency range, passive isolators can serve adequately. Since 

these are relatively simple and cheap, they can be placed at each interface between a 

disturbance source and the space station. It should be noted that the sensitivity of 

various categories of experiments to high frequency disturbances is also 

comparatively low. 

In the quasi-static frequency range, the extremely low stiffness and large 

motion required make attempts at isolation very difficult. Rattlespace constraints 

prohibit the occurrence of such large relative motions between the payload and the 

spacecraft. This imposes a fundamental limitation upon vibration isolation. 

Consequently, efforts at minimizing the input disturbances, like reducing the surface 

area presented to the atmosphere so as to reduce atmospheric drag and locating 
payloads as close to the spacecraft's center of mass as possible, are necessary. 

Owens and Jones have also suggested the possibility of canceling such disturbances 

by continuous thruster control of the whole spacecraft [11]. 

At intermediate frequencies - approximately between 0.01 Hz and 1 Hz -

no passive isolation scheme can be effective due to the displacements and isolation 

levels required. Only active vibration isolation at the payload-spacecraft interface 

allows the synthesis of the desired isolator properties and the adjustment of these 

properties using a control loop. 

The actuator used to implement an active control scheme in the 

intermediate frequency range should ideally be noncontacting. The ideas of 

acoustic, electrostatic and electromagnetic (Lorentz force) levitation have been 

considered in the context of containerless processing of materials in a low gravity 

environment [12-15]. The first two techniques are limited to small objects. Lorentz 

forces are utilized by placing an electrically conductive sample within a suitably 

designed coil excited by a radio frequency current. Currents induced in the sample 

interact with the magnetic field of the coil to produce forces that tend to move the 

sample away from regions of high magnetic flux density. These currents also tend 

to heat the sample, which is often utilized to melt it. However, the inability to 

control this heating effect independently of the coil current required for levitation is 

a limitation of this technique. Some unwanted stirring of a melt by the induced 

currents also occurs. 

Noncontact magnetic actuators, utilizing electromagnets or permanent 

magnets, appear to be the best solution for vibration isolation in the intermediate 

frequency range [16]. These actuators produce relatively large forces and can be 

applied to the isolation of a variety of science experiments. An active magnetic 

isolation system can be "tuned" by simply changing control law gains to 

accommodate changes in the payload or the expected disturbance environment, or 

to produce improved performance once in orbit. Such experiments need only be 

enclosed in a container, and can have umbilicals connecting them to the spacecraft. 

A Long Action Magnetic Actuator (LAMA) has been proposed for this 

purpose f17]. This is a magnetic thrust bearing modified to accommodate longer 

strokes than those found in typical industrial applications. The pole-faces are 

inclined at an acute angle to the axis of motion, instead of being perpendicular to it. 

Detailed studies of magnetic thrust bearing design and use have been made [18-20]. 

The LAMA would be suitable for those intermediate frequencies that require 

motions not exceeding about a hundred miles. Since the forces called for are of the 

order of a few pounds at most, such actuators can be quite compact, the size being 

primarily determined by the stroke required. 

A single-axis magnetic actuator similar to a magnetic thrust bearing has 

been described in [21]. The authors compared various sensing options to close the 

actuator control loop - gap and current sensing, force sensing and flux sensing. In 

their experiment, the authors achieved force linearization using flux feedback. Due 

to shaker and accelerometer limitations, the lowest recorded frequency of their 

measured data was 5 Hz. A subsequent paper described a similar isolation system 

extended to six degrees-of-freedom, called the Fluids Experiment Apparatus 

Magnetic Isolation System (FEAMIS) [22]. 

An interesting dual-mode approach to vibration isolation of large payloads 

over long displacements has been discussed in [23]. It was intended to provide the 

high performance active isolation of noncontact magnetic suspension technology 

without the limitations on articulation imposed by the small air gaps used in such 

439 
440 

systems. In such a tandem system, a "coarse" motion actuator was controlled as a 

followup actuator, always attempting to keep the gap displacement for the magnetic 

actuator within its design limits. The magnetic actuator functioned as a "fine" 

motion actuator, ignoring the presence of the other, coarse actuator. The 

performance requirements on the coarse actuator were not very stringent, since the 

imperfections of its motions would be attenuated by the fine actuator. 

The operation of microgravity science experiments is likely to require the use 

of an umbilical. An example is a plastic tube formed into a helical shape and 

carrying a coolant. Acceleration control to reject disturbances caused by the 

compliance of the umbilical has been theoretically investigated [24]. The umbilical 

was assumed to have stiffness, but not damping. The microgravity quality 

deteriorated with increasing umbilical stiffness, as expected. Acceleration control 

improved disturbance rejection greatly when compared to position~nly control, but 

there was a price to be paid in the form of a more complicated control system. An 

active umbilical control strategy, in which the extension of the umbilical is 

minimized by making one end track the other, was also analyzed. It was found to 

be effective in principle and comparable in performance to the acceleration control 

loop technique. 

3. EXPERIMENTAL RIG 

An experimental rig to demonstrate vibration isolation down to microgravity 

levels in one degre~f-freedom has been constructed, and is shown in Figures 1 and 

2. An innovative long stroke Lorentz actuator, described in detail in the next 

section, will be used to implement the isolation scheme. 

An electrodynamic shaker with a long, peak-to-peak stroke of 6.25 inches 

represents the space platform. The shaker is mounted, via aluminum plates, on a 

concrete block resting on the laboratory floor. The shaker can generate sinusoidal, 

random or impulse waveforms at frequencies down to DC, thus simulating the 

disturbances typically produced on a space station that require active isolation. 

The umbilicals connecting a science experiment to the space platform are 

expected to be flexible hoses and wires. These will be modeled by air dashpots with 

adjustable stiffness and damping coefficients. This type of dashpot has been 

evaluated at NASA Lewis in a single~egr~f-freedom mass-spring~amper 

system in a fixed-fixed mounting configuration [2.5]. The test indicated the 

possibility of a nonlinear stiffness/damping mechanism in these air dashpots. The 

vibration isolation rig has been designed so that different kinds of umbilicals may be 

employed, including actual hoses used for fluid transfer. This is important, since 

very little work has been done to date on vibration isolation to microgravity levels 

in the presence of an actual physical connection between the experiment and the 

space platform. 

The long stroke Lorentz actuator, in parallel to the umbilical(s), connects the 

shaker armature to the mass representing a microgravity science experiment in 

space. This mass is a solid steel cylinder weighing 75 pounds, which is a typical 

weight for such an experiment. The cylinder is horizontally suspended in space by 

the magnetic forces generated by a noncontact electromagnetic support system. 

Similar to radial magnetic bearings, the support system consists of two eight-pole 

structures, mounted on a concrete base, at the two ends of the cylindrical mass. 

This concrete base is massive compared to the "experiment" mass, and rests on the 

same laboratory floor as the separate concrete block on which the shaker is 
mounted. Eddy current probes sense the radial position of the cylinder and 

complete the feedback loop supplying current to the electromagnets. When the 

electromagnetic support system is turned off, the cylinder rests on a pair of 

touchdown pedestals made of delrin. 

The axial acceleration of the cylinder will be sensed off a sensory plate 

mounted at its free end, using a very low frequency accelerometer with a maximum 

resolution of 1 j.lg. Provision has been made for the use of other types of 

accelerometers, and the sensing of other states of the system, like position. The 

accelerometer signal will be fed to a feedback control circuit that determines the 

current required in the electromagnetic actuator to isolate the cylinder from the 

disturbances generated by the shaker. A control strategy for such an isolation 

system with multiple degrees~f-freedom is discussed in [26]. 

The background vibration levels on the concrete base on which the cylinder 

is mounted have been measured over twenty-four-hour periods, in both the 

horizontal and the vertical directions. These vibrations are of the order of milli-g's, 

the quietest period occurring from late in the night to early in the morning. 

Operating at this time will yield the highest degree of reproducibility in our results. 

Figures 3 and 4 show the frequency spectrum of the background acceleration in the 

horizontal and vertical directions. The vertical vibration shows acceleration 

components corresponding to natural frequencies of the mounting plate. The 

horizontal vibration has significant content at 45 Hz. The authors believe this is a 

floor mode. 

4. THE LONG-STROKE LORENTZ ACTUATOR 

A compact long-stroke Lorentz Actuator has been designed, built and tested 

in the laboratory. An intermediate version of the design was presented at the 

Workshop on Aerospace Applications of Magnetic Suspension Technology at NASA 

Langley in September, 1990 [27]. The final design described here incorporates many 

of the same features, but is much more linear with coil position. This was 

accomplished through modification of the flux distribution. 

A schematic of the typical Lorentz Actuator, along with the terminology 

used, is shown in Figure 5. The current carrying coil moves in and out along the 

core. A strong permanent magnet in the shell maintains a constant magnetic flux in 

the cylindrical air gap across the pole faces, irrespective of the current in the coil 

(within design limits). The Lorentz force generated, therefore, can be linearly 

varied with coil current [28]. 

The requirements for the laboratory prototype were fixed at a total stroke of 

two inches and enough force capability to isolate a mass of 75 lbs. connected by an 

umbilical (air dashpot) to a source generating very low frequency vibrations. Force 

linearity with position and with current were also required. Moreover, in view of 

the ultimate goal of deployment in space, such a device had to be compact and 

lightweight. Low power consumption and low heat generation during operation 

were also important. 

A computer program was written to implement a simple design algorithm for 

a Lorentz Actuator. The steps of this algorithm are presented in Figure 6. 

Using a permanent magnet material with a very high maximum energy 

product of 35 MGOe (mega-Gauss-Oersted) [29] resulted in a design that required 

441 
442 

a ring magnet of 3.20 in. outer diameter. The magnet manufacturer, however, could 

make such a magnet in one piece only if its outer diameter were less than 2 in.; 

making a ring magnet with a 3.20 in. outer diameter would have required the costly 

assembly of multiple segments, with an escalation of costs. 

The possibility of designing a Lorentz Actuator satisfying all the 

requirements, with the outer diameter of the magnet being additionally constrained 

to less than 2 in., was therefore explored. The significant parameter in this context 

is the gap ratio, defined as the ratio of the shell-to---core air gap to the 

pole-face-to---core air gap. Conventional designs use ratios of 5: 1 or higher in order 

to minimize leakage of magnetic flux from the shell to the core. Figures produced 

by the design program suggested that the design requirements could be met, along 

with the additional constraint, if the rule of thumb of using a gap ratio of 5: 1 or 

more were drastically violated. Apparently, flux leakage, which the computer 

program did not take into account, would result in the failure of such a design. It 

was then hypothesized that this would not necessarily be the case if the core of the 

actuator were saturated during normal operation. The permeability of a saturated 

ferromagnetic material approaches that of air, and so most of the leakage that 

would have occurred, with such a low gap ratio (less than 2: 1) and an unsaturated 

core, would be prevented. 

A good way of verifying this hypothesis, without actually building such an 

actuator, is the use of finite element analysis. A commercially available magnetic 

finite element analysis package, MAGGIE, with a nonlinear modeling capability, 

was chosen. It also allowed us to take leakage and fringing into account, and 

different materials and geometries could be "tested" with relative ease. 

A number of designs incorporating various features, were analyzed using the 

finite element analysis package. The finite element model was generated so as to 

achieve as much accuracy as possible, within hardware limitations. The mesh 

consists predominantly of quad elements. Infinite air elements, used earlier, were 

found to cause severe restrictions on mesh fineness. A mesh with only about 

100 elements could be used. An air thickness of an inch on three sides of the 

axisymmetric model was specified instead. This was determined to be as accurate 

as having infinite air elements on all three sides for a model of this size, while a 

relatively fine mesh with about 400 elements could be used without encountering 

core memory limitations. Moreover, the finest mesh allowed by the configuration of 

our 386-based personal computer was used for the analysis. 

Position linearity was improved, relative to the intermediate design, by 

increasing the length of the magnet, imparting a lip to it by reducing the shell outer 

diameter, and reducing the core diameter. The gap ratio resulting from the last 

change mentioned above is still only 1.47: 1 - much smaller than a typically 

specified value of 5:1. The use of such an unconventionally low gap ratio enabled 

the design of a compact and lightweight actuator. Use of a large ratio would also 

have required a large diameter magnet that could not be made in one piece, thus 

increasing costs. The decrease in flux, and therefore force, caused by the increase in 

the length of the magnet was compensated, to some extent, by a reduction in the 

inner diameter of the magnet and a doubling of the pole piece thickness. Figure 7 

shows the design. The overall length of the actuator is 4 in., while the outer 

diameter is only 1.95 in .. 
The salient features of the final design of the compact Lorentz Actuator are 

described below: 

• Long Stroke - The requirement of two inches of total stroke is satisfied. 

• Position Linearity - Over the whole two inches of stroke, the actuator exhibits a 

high degree of linearity. For a constant coil current, this means that the actuator 

force is the same irrespective of the axial position of the coil, within the stroke 

bounds. Figures 8 and 9 depict this relationship for positive and negative coil 

currents respectively. Note that flux leakage has been reduced to almost zero over 

the shell-to-core gap to achieve this. The maximum flux density across the 

shell-to-core gap is only about 7% of the maximum flux density across the 

pole-face gap. 

• Current Linearity - This requires that the average flux density in the effective 

air gap remain constant with variations in the coil current between the upper and 

the lower limits. This is indeed the case, resulting in force vs. current linearity, 

Figure 10. 

• Force - A maximum force of 1.25 lbs is produced by this actuator, which is 

sufficient for our needs. This peak force requires a coil current of 2.5 A. 

• Weight - At 2.28 lb., this actuator is only a tenth of a pound heavier than the 

previous design. 

• Current Density - A value of 1000 A/sq. in. in continuous use ensures cool 

operation. For peak loads, a fivefold increase in current density is possible. 

• Materials - The magnet is made of neodymium iron boron, which has a very 

high maximum energy density product of 35 MGOe. Selection of such a material 

helped make the design compact. The high permeability circuit material is a 48% 

nickel-iron alloy that saturates at 1.5 kG. The B-H curve for this material, 

provided by the manufacturer, was input to MAGGIE as a table of a large number 

of points on the curve. This was necessary because a nonlinear material 

characteristic was being modeled. 

The design specifications of the Lorentz Actuator are detailed in Table 2. 

This actuator was built and tested in our laboratory. Figure 11 compares the 

measured magnetic flux density in the radial direction along the shell-to-core and 

pole-face-to-core gaps with the values predicted by finite element analysis, for no 

current in the coil. The measured peak value is lower, but is spread over a wider 

axial distance. There is good agreement, especially over most of the shell-to-core 

gap, where near-zero values of flux density are crucial to achieve force versus 

position linearity. The actual actuator force is plotted against position for a number 

of values of coil current in Figure 12. The measured values of force are greater, in 

each case, than the predicted values since most of the small amount of leakage flux 

across the shell-to-core gap was neglected in calculating the predicted forces. 

Moreover, since the coil does see slightly greater total flux as it moves into the 

actuator, because of the small amounts of leakage, the forces measured increase 

somewhat with such motion. However, for low values of current and for coil 

positions that do not place it very near the closed end of the actuator, the actual 

forces deviate by less than 10% from the predicted values. 

443 
444 

5. CONCLUSION 

The rig designed to demonstrate vibration isolation to microgravity levels in 

one-dimension has been built and assembled. Measurements of the background 

acceleration levels have also been made, and the quietest period for operation has 

been determined. A compact, long stroke Lorentz actuator has also been designed, 

built, and tested. Its performance has been shown to match that predicted by finite 

element analysis very well. Microgravity isolation experiments will be conducted in 

the very near future. 
6. REFERENCES 

1. Feuerbacher, B., "Introduction," Chapter 1, Materials Sciences in Space, Ed. 

B. Feuerbacher, et al., Springer-Verlag, Berlin, 1986. 

2. Hamacher, H., "Simulation of Weightlessness," Chapter 3, Materials Sciences 

in Space, Ed. B. Feuerbacher, et al., Springer-Verlag, Berlin, 1986. 

3. Teledyne Brown Engineering, "Low Acceleration Characterization of Space 

Station Environment," Report No. SP858-MSFC-2928, Oct. 1985. 

4. Chase, T.L., "Report on Micro-g Measurements for Space Shuttle 

Experiments," NASA Lewis Research Center, Dec. 1985. 

5. Teledyne Brown Engineering, Abstracts, Workshop on Measurement and 

Characterization of the Acceleration Environment on Board the Space 

Station. Guntersville, Alabama, Aug. 11-14, 1986. 

6. Hamacher, H., R. Jilg and U. Merbold, "Analysis of Microgravity 

Measurements Performed During Dl," 6th European Symposium on 

"Materials Sciences under Microgravity Conditions." Bordeaux, Dec. 2-5, 

1986. 

7. Booz, Allen & Hamilton, "Overview of Space Station Microgravity 

Requirements," report presented to Dr. J .-D. Bartoe, Chief Scientist, Office 

of Space Station, July 14, 1989. 

8. McDonnell Douglas Corporation "Space Station Definition and Preliminary 

Design," WP-D2, DR-D2, Book 22, Section 8 (Loads and Structural 

Dynamics), Dec. 1985. 

9. Ramachandran, N., and C.A. Winter, "The Effects of g-Jitter and Surface 

Tension Induced Convection on Float Zones," 28th Aerospace Sciences 

Meeting, AIAA, Reno, Nevada, Jan. 8-11, 1990. 

10. Armentrout, R.W., "Two-Body Dynamic simulation of Space Station 

Exercise Treadmill Including Startup Transient Effects," Memo No. 

A96-J749-STN-M-RW A-900006, Jan. 10, 1990. 

11. Owen, R.G., and D.l. Jones, "Columbus Applications Study (\-VP. 

1.1)," Technical Note No. BTN-DOl, University College of North Wales, 

School of Electronic Engineering Science, Bangor, Gwynedd, Sep. 1988. 

12. Naumann, R.J. and D.D. Elleman, "Containerless Processing Technology," 

Chapter 12, Materials Sciences in Space, Ed. B. Feuerbacher, et al., 

Springer-Verlag, Berlin, 1986. 

13. Hendricks, C.D., "Levitation, Coating, and Transport of Particulate 

Materials," Materials Processing in the Reduced Gravitv Environment of 

Space, Ed. G.E. Rindone, et al., vol. 9, pp. 59, Elsevier Science Publishing 

Co., Amsterdam, 1982. 

14. Rhim, W.-K., M. Collender, M.T. Hyson, W.T. Sims and D.D. Elleman, 

"Development of Electrostatic Positioner for Space Materials, Processing," 

Rev. Sci. Instrum., vol. 56, no. 2, p. 307, 1985. 

445 
446 

15. Frost, R.T. and C.W. Chang, "Theory and Applications of Electromagnetic 

Levitation," Materials Processing in the Reduced Gravity Environment of 

Space, Ed. G.E. Rindone, et al., vol. 9, pp. 71, Elsevier Science Publishing 

Co., Amsterdam, 1983. 

16. Grodsinsky, C.M. and G.V. Brown, "Nonintrusive Inertial Vibration 

Isolation Technology for Microgravity Space Experiments," submitted for 

publication to Journal of Spacecraft and Rockets, AIAA, Jan. 1990. 

17. Allaire, P.E., M.A. Scott and B.B. Banerjee, "Magnetic Actuators for 

Microgravity Space Isolation," Workshop on Vibration Isolation Technology 

for Microgravity Science Experiments," NASA Lewis, Cleveland, Ohip, Sep. 

28-29, 1988. 

18. Banerjee, B.B., "Analysis and Design of Magnetic Thrust Bearings," M.S. 

Thesis, Univ. of Virginia, Charlottesville, May 1988. 

19. Allaire, P.E., A. Mikula, B.B. Banerjee, D.W. Lewis and J. Imlach, "Design 

and Test of a Magnetic Thrust Bearing," Journal of the Franklin Institute, 

vol. 326, no. 6, pp. 831-847, 1989. 

20. Allaire, P.E., J. Imlach, J.P. McDonald, R.R. Humphris, D.W. Lewis, B.B. 

Banerjee, B.J. Blair, J. Claydon and R.D. Flack, "Design, Construction and 

Test of Magnetic Bearings in an Industrial Canned Motor Pump," Proc. of 

the Sixth International Pump Users Symposium, Texas A&M Univ., College 

Station, Nov. 1988. 

21. Havenhill, D.D. and K.D. Kral, "Payload Isolation Using Magnetic 

Suspension," AAS 8.5-D14, Annual AAS Guidance and Control Conference, 

Keystone, Colorado, Feb. 2--6, 1985. 

22. Allen, T.S., D.D. Havenhill and K.D. Kral, "FEAMIS: A Magnetically 

Suspended Isolation System for Space-Based Materials Processing," AAS 

86-D17, Annual AAS Guidance and Control Conference, Keystone, Colorado, 

Feb. 1-.5, 1986. 

23. Hamilton, B.J., J.H. Andrus and D.R. Carter, "Pointing Mount with Active 

Vibration Isolation for Large Payloads," AAS 87-D33, Annual AAS 

Guidance and Control Conference, Keystone, Colorado, Jan. 31 - Feb. 4, 

1987. 

24. Jones, D.L, A.R. Owens, R.G. Owen and G. Roberts, "Microgravity 

Isolation Mount: Design Report," Technical Note No. BTN-D09, University 

College of North Wales, School of Electronic Engineering Science, Bangor, 

Gwynedd, Sep. 1989. 

2.5. Sutliff, T., "Vibration Isolation: Airpot (Dashpot) Damping 

Evaluation," PIR No. 89-9, NASA, Lewis, Cleveland, Ohio, 1989. 

26. Hampton, R.D. and C.R. Knospe, "Extended H2 Synthesis for 

Multiple-Degree-of-Freedom Controllers," International Symposium on 

Magnetic Suspension Technology, NASA CP-3152, 1992. 
27. Banerjee, B.B., P .E. Allaire and C.R. Knospe, "Vibration Isolation of 

Science Experiments in Space - Design of a Laboratory Test Setup," 

Workshop on Aerospace Applications of Magnetic Suspension Technology, 

NASA CP-lO066 Part 2, Paper 26, March 1991. 

28. Carlson, A.B., D.G. Gisser and F.K. Manasse, "Magnetics and 

Electromechanics," Chapter 17, Electrical Engineering: Concepts and 

Applications, Addison-Wesley Publishing Company, Reading Massachusetts, 

1989. 

29. McCaig, M. and A.G. Clegg, Permanent Magnets in Theory and Practice, 

John Wiley & Sons, New York, 1987. 

447 
448 

Table 1: Typical Disturbance Environment on a Spacecraft 

QUASI-STEADY ACCELERATIQNS 

1e-7 g (0 to 1e-3) Hz Aerodynamic Drag 

1e-8 g (0 to 1e-3) Hz light Pressure 

1e-7 9 (0 to 1e-3) Hz Gravity Gradient 

PERIQDIC ACCELERATIONS 

le-2 9 9 Hz Thruster Fire 

(Orbital) 

le-3 9 (5 to 20) Hz Crew Motion 

le-4 9 17 Hz Ku Band Antenna 

NON-PERIQDIC ACCELERATIONS 

le-4 9 1 Hz Thruster Fire 

(Attitudinal) 

1e-4 g 1 Hz Crew Push-Off 

Table 2: Design Specifications for the Lorentz Actuator 

LQRENTZ ACTUATOR FINAL DESIGN 

Total length 

Magnet outer diameter 

Magnet inner diameter 

Magnet length 

Shell outer diameter 

Pole-piece thickness 

Core diameter 

Air gap 

Shell-to-core gap 

Gap ratio 

Coil length 

Coil wire diameter 

Number of turns 

Number of layers 

Maximum coil current 

Air gap flux density 

Max. force generated 

Actuator wt. (no coil) 

3.87 in 

• 1.95 in 

1.25 in 

2.77 in 

• 1.68 in 

0.80 in 

0.75 in 

• 0.17 in 

• 0.25 in 

· 1.47 : 1 

• 4.00 in 

• 26.67 mils 

• 600 turns 

• 4 layers 

• 2.5 A 

• 0.145 T 

• 1.25 Ibf 

• 2.28 Ibf 
Steel Plate Magnetic Supports 

-:::::: :::: ::: :::: ::: :::::: :::::: ~hpO.f :::::::::- :::::::::::::: --:--::: -:'£)(pe;<:;:Ment:--: ::::::::::: ::----: ::--:::::: :::: 

\ / (Mass) 

Shaker Lorentz 

'; ~ Sensor~ ::::::::: ::::: :::::: :::::::::::: :A:c:f;:o'dt 6i<:: ::::::::: --::: :ccc::c ::: ::::: Cott or :: ::::::::: : :c ::::::::: ::::::: :::: :::::: 

/ 

Concrete Base Touchdown Pedestals 

Fig. 1: Design Drawing of the Experiment Rig 

ORiG!NAL PP,GE 

BLACK AND WHITE PHOTOGRAI-'H 

Fig. 2: The Experiment Rig Partially Assembled 

449 
111f\1l r---,------.---,-----,-------,---,---,---- -r------,-----, 

" hori7 . fft " <> 

<> 

8 

<> 

100 

<> <> <> 

]0 L-_~ __ ~ __ ~ __ ~ _ _ L__~ __ -L __ ~ __ ~_~ 

o so 100 ] SO 200 7.~0 

Freq (H z ) 

300 3S0 400 4 SO 500 

Fig. 3: Background Vibration in the Laboratory Horizontal 

I nll/\ ,------,----.-----,---.,----,---r----,---,-----,----, 

" vert . f fL " <> 

<> 

<> 

<> 

100 :1: 

]n ~-~--~--~- ~-~~-~--~--~--~-~ 

II 100 1 ')0 200 2S0 300 3sn 100 1 SO 

f"rf'q (Hz) 

Fig. 4: Background Vibration in the Laboratory Vertical 

450 
Lorentz Actuator 

Permanent Magnet Shell 

. ~:tf~ 

:":'?~

,;' 

-C:!". 

--

- .' Pole-pIece ,.'%,< 0-

....-.,. ... ~ -' 

,; .. 

~%'t; .:?S~ -.?: 

Coil 

Open 

End 

~.:R 

_ JiJii~~~jj,i.::;J; 

Axis of Symmetry 

Closed 

End 

Fig. 5: Schematic of a Lorentz Actuator 

451 
452 

LORENTZ ACTUATOR : DESIGN EQUATIONS 

1. Assume permanent magnet operating point for maximum 

energy product: (-H1, B1). 

2. Compute magnet flux, fm • B 1 • Am. 

3. Compute circuit flux, fc • H 1 • Lm / R, where R is 

the circuit reluctance. 

4. Compare fm and fc. 

5. Adjust operating point until fm • fc • f, the actual 

operating point. (When saturated, f • saturation 

flux in saturated segment of circui1.) 

6. Calculate air gap flux density, Bg • f / Ag. 

7. Compute force capability, F • i • I • Bg, where i is 

the actuator current and I is the total length of 

coil wire in the air gap. 

8. Change actuator geometry or circuit / magnet 

material until desired force level is achieved. 

Fig. 6: A Simple Algorithm for Designing a Lorentz Actuator 

Fig. 7: The Compact, Long - Stroke Lorentz Actuator 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH . 
Compact Lorentz Actuator - Force 

Coil Currents Positive (as Shown) 

Force (lbf) 1.6 -----

1.4 -

1.2 

1 

0.8 -

0.6 

0.4 

0.2 

o-----------------&o--------------~o 

* ~( * 

O~--------------~D----------------~O 

)( 

o -----~- J ___ ~ __ .l ______ L ___________ L-_____ - --

o 0.5 1 1.5 2 2.5 

Coil Distance from Closed End (inches) 

Fig. 8: Force vs. Position (for Positive Coil Currents) 

453 
454 

Compact Lorentz Actuator - Force 

Coil Currents Negative (as Shown) 

Force (-ve) (lbt) 1.6--~----·--------- --- --------------_. -------

1.4 

1.2 

1 

0.8 

0.6 

0.4 . 

0.2 

o----------------~o~--------------~o 

II f1 [I 

)( 

o _________ .......l. ___ .. ---.-----. L_. ________ ~I _____ ~ _ _L ---_____ _ 

o 0.5 1 1.5 2 

Coil Distance from Closed End (inches) 

l-~_- 2~6~-_~_~ 2.~A-_-+-~_~.~-~--~ ~-1.~ ~-------- --O~5 -A I 

2.5 

Fig. 9: Force vs. Position (for Negative Coil Currents) 
Compact Lorentz Actuator - Force 

Legend Indicates Coil Position 

Force (lbf) 

1.5 

1 -

0.5 

o --~-~-~------_M'__--~----~------.----------

-0.5 

-1 

-1.5--~---- ____ L ______ L_~~L_. ___ ..1 ______ l~ ___ ~___._l __ - -- L ---

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 

Current in Coil (A) 

E -t-- Out --*-- Mid --B-- -] In 

---------------------

Fig. 10: Force vs. Current (for Three Different Coil 

Positions) 

455 
0.3 

0.25 

0.2 

~ 

~ 

-~ 0.15 

c 

~ 

"'" ] 0.1 u. 

-;;; 

.;( 

< 

0.05 

0 

-0.05 

0 0.5 

Compact Lorentz Actuator Field Density 

. 0. ~ooo 

1.5 2 2.5 3 3.5 

Position (in.) 

o 

o 

Measured 0 

Predicted -

o 

o 

o~ .. 000 

4 4.5 5 

Fig. 11 : Comparison of 

Values (for 

Actual Flux 

No Current 

Density with 

in the Coil) 

Predicted 

456 

Compact Lorentz Actuator Force 

o 0 

o 0 o 0 0 0 

o 

<> + + + + + + + + + + + + + 

0.5 + 

o 0 0 0 0 0 0 0 0 0 0 0 0 

o 

o ........... . 

x 

x x x x x x x x x x x x x 

l> 

... '" l> '" A l> '" l> A '" '" A l> 

- -I 

- - - - - - - - - - -

0.5 1.5 2 2.5 3 

Coil Position (in.) 

<> 

+ <> 

+ o o 

1.5 Amp 0 

1.0Amp + 

0.5 Amp 0 

-0.5 Amp x 

-1.0 Amp A 

-1.5 Amp - Predicted -

o + 

o 

·····~···t················ 

x x 

-

-

A 

-

3.5 4 4.5 

Fig. 12: Comparison of Actual Force vs. Position 

Characteristics with Analytical Predictions 
N92-27746 

VIBRATION DAMPING OF ELASTIC WAVES IN ELECTRICALLY CONDUCTING 

MEDIA SUBJECTED TO HIGH MAGNETIC FIELDS 

T. G. Horwath 

TG&C Associates, Inc. 

One Cessna Lane 

Falmouth, Virginia 22405 

21 August 1991 

457 
Abstract: 

The propagation of vibrational energy in bulk, torsional, 

and flexural modes, in electrically conducting media can 

undergo strong attenuation if subjected to high magnetic 

fields in certain spatial arrangements. The reasons for this 

are induced Eddy currents which are generated by the volume 

elements of the media moving transversally to the magnetic 

field at acoustic velocities. In magnetic fields achievable 

with superconductors, the non-conservative (dissipative) 

forces are comparable to the elastic and inertial forces for 

most metal~. Strong dissipation of vibrational energy in the 

form of heat takes place as a result. A simplified theory is 

presented based on engineering representations of 

electrodynamics, attenuation values for representative 

metals are calculated, and problems encountered in 

formulating a generalized theory based on electrodynamics of 

moving media are discussed. General applications as well as 

applications specific to maglev are discussed. 

Introduction: 

The interconnection of elastic and electromagnetic phenomena in 

media capable of supporting both, have with a few exceptions been 

only curiosities so far. Few applications have been developed so 

far, mainly because of the relative minuteness of the effects. 

The special cases of acoustic propagation and vibration in the 

presence of steady state magnetic fields, magneto-acoustics, 

however, did receive some attention and have been investigated on 

a few occasions. 

In 1968, LILLEY and CARMICHAEL1 at the University of Western 

Ontario, Canada, conducted laboratory experiments with standing 

elastic waves in a metal bar subjected to a magnetic field. The 

PRECEDING PAGE BLANK NOT FILMED 

459 
investigators reported slight damping effects which depended on 

the magnitude as well as the gradient of the field. 

Later, in 1985, LEE2 at the Stanford University Department of 

Mechanical Engineering analyzed electromagnetic damping together 

with thermoelastic damping of structures. Strong dependence on 

structural and geometrical configurations was found, as one would 

expect. 

The major shortcoming in exploiting magneto-acoustic phenomena 

for practical applications was due to the limit of magnetic field 

strength which could be produced by practical means. This was 

exacerbated by the fact that the effects have a second order 

dependence on field strength, as will be shown later. There is 

always the possibility, of course, of using conventional (low 

temperature) superconducting technology to generate the required 

fields. The complexity of the cryogenic support systems and the 

cost of such systems could be justified only in the rarest of 

circumstances. 

Recent advances in the technology of high temperature 

superconductors, will render magneto-acoustic effects much more 

relevant in the future. This was first recognized by HORWATH3 in 

a paper presented to the 119th meeting of the Acoustical Society 

in May 1990. Magnetic fields of several Tesla and possibly tens 

of Tesla will soon be achievable with such high temperature 

superconducting materials at a low cryogenic overhead. Such 

materials have the further advantage of much higher critical 

fields and currents. Their only limitation at present is 

relatively low current densities. 

In the high magnetic fields achievable with superconductors the 

non-conservative or dissipative forces in electrically conducting 

elastic media will become comparable to the elastic and inertial 

forces. As a result of this it will be possible to achieve 

significant direct dissipation of acoustic energy in metals, for 

instance, for both bulk waves and flexural waves. This will 

provide means for damping on a scale difficult to achieve before, 

and thus open new regimes for applications. 

First order estimates of the damping effects will be presented in 

the following. The attenuation lengths of longitudinal waves in 

bulk materials subjected to high magnetic fields will be 

calculated. This will be followed by a similar determination of 

the transversal impedance component in electrically conducting 

plates, which are subjected to high magnetic fields. Only very 

simple special cases will be discussed, aimed mainly at 

introducing the concept. 

460 
Propagation of Longitudinal Waves in Bulk Material: 

x 

B 

p,V -..,... ... .L....::""'------~~"r_---....;::=_r-... z 

dz 

y 

Figure 1 

Figure 1 depicts a section of an electrically conducting slab, 

which is penetrated by a homogeneous magnetic field B, at normal 

incidence. A pressure disturbance, periodic or aperiodic, is 

applied at one end and propagates along the z-axis, through the 

magnetic field region, causing motion of the slab material at 

acoustic velocities. This produces a voltage in the y-direction 

in the volume element 4xoyodz 

E = -d~/dt = -2yoBv ( 1 ) 

which in turn gives rise to a current in the same volume. 

I = E/R = -2axoBvdz ( 2 ) 

It is tacitly assumed here, for simplicity, that the current path 

is closed through the fringe regions outside the magnetic field 

with essentially zero resistance. The current flowing in this 

volume element of the slab experiences a Lorentz Force, which is 

counteracting the driving disturbance. 

(3 ) 

461 
From this the pressure is obtained as 

dp = dF/dA = dF/4xoyo = -ovB2dz (4 ) 

For elastic wave propagation in bulk material the pressure is 

related to the velocity by 

v = p/(c5E)1/2 

where c5 is the density and E the bulk modulus of the 

Using this relationship the differential equation is 

from equation (4) 

dp/p = -aB2dz/c5c 

The attenuation length thus follows as 

Za b = (c5E) 1 / 2 / aB2 

(5 ) 

material. 

obtained 

(6 ) 

( 7 ) 

The attenuation is a function of the usual material parameters, 

such as density, sound velocity, and electrical conductivity, as 

expected, and has an inverse square dependence on the magnetic 

field. 

Table 1 below presents the attenuation length calculated by the 

above methodology for different metals subjected to a magnetic 

field of 10 Tesla. 

462 
Material 

Aluminum 

Copper 

Steel 

ATTENUATION LENGTH FOR BULK WAVES 

IN VARIOUS METALS 

( Magnetic Field = 10 Tesla ) 

Electrical 

Conductivity 

[Ohn( 1 m- 1 ] 

3.77 X 10' 

5.85 X 10' 

Density 

2690 

8930 

7650 

Table 1 

Bulk 

Modulus 

[Nm- 2 ] 

7.18 X 1010 

1.23 X 1011 

2.12 X 10 1 1 

Propagation of Torsional (Shear) Waves: 

T 

B F---.... z 

dz 

T 

Figure 2 

Attenuation 

Length 

[m] 

3.68 X 10- 3 

5.67 X 10. 3 

6.48 X 10- 2 

The calculations proceed in a similar fashion as in the above 

case. Figure 2 shows a section of an electrically conducting rod 

which is penetrated by an axial magnetic field B. A torque 

disturbance is applied to the rod at one end and propagates along 

463 
the longitudinal axis, producing a radial voltage in the annular 

volume element of the rod section 2nrdrdz 

E = -d~/dt = -Brwdr (8 ) 

The current in this volume element is 

I = E/R = -2nawBdz (9 ) 

The Lorentz force acting on this current element generates a 

counter torque, which per unit cross sectional area is 

dT = -owB2 dz (10) 

For torsional waves propagation this torque per unit area is 

related to the angular velocity by 

w = T / ( c5G ) 1 / 2 

where G is the shear modulus of the 

relationship together with equation 

equation follows 

material. 

(10) the 

(11) 

Using this 

differential 

(12) 

which yields the attenuation length for torsional waves 

Za t = (c5G) 1 / 2 / aB2 (13) 

464 
Again, as expected, the attenuation is a function of the same 

material parameters as above, and is inversely proportional to 

the square of the magnetic field. 

Table 2 lists attenuation lengths for torsional waves in 

different metals in a field of 10 Tesla. 

Material 

Aluminum 

Copper 

Steel 

ATTENUATION LENGTH FOR TORSIONAL WAVES 

IN VARIOUS METALS 

( Magnetic Field = 10 Tesla ) 

Electrical 

Conductivity 

[Ohm- 1 m- 1 ] 

3.77 X 107 

5.85 X 107 

6.21 X 10' 

Density 

2690 

8930 

7650 

Table 2 

Shear 

Modulus 

[Nm- 2 ] 

2.69 X 1010 

4.55 X 1010 

7.95 X 1011 

Transversal Damping Impedance in Plates: 

Attenuation 

Length 

[m] 

2.25 X 10- 3 

3.44 X 10- 3 

3.97 X 10- 2 

Flexural waves are more difficult to treat in this context 

because of their highly dispersive nature, which precludes the 

use of a simple relationship between pressure and velocity. A 

somewhat different approach is taken therefore, calculating a 

damping impedance rather than an attenuation length. 

465 
x 

B, grad B 

p,v 

Figure 3 

Figure 3 depicts a section of an electrically conducting plate 

is now subjected to an inhomogeneous magnetic field B, with a 

strong gradient grad B. Both field and gradient are perpendicular 

to the plate. It is further assumed that the field region is 

contained within a circle of the radius Ra. A pressure 

disturbance is applied from the opposite side of the plate, 

causing the plate material to move in the direction of the field 

gradient, with an acoustic velocity typical for a flexural 

vibration mode. Circular currents are induced in annular elements 

of the material with the volume 4nrxodr as a result of the 

changing magnetic flux caused by this motion. 

The voltage induced is obtained from Faraday's Law of Induction 

as 

E = -d~/dt = -JJ dB/dx dx/dt dA (14) 

or 

E = J J v. grad. B dA (15) 

The current element is obtained from Ohm's Law as 

466 
dI = Eaxodr/rrr (16) 

performing the integration in (15) and sUbstituting the result 

into this the current element becomes 

dI = arxodrvxgradxB (17) 

which allows determination of the Lorentz force element 

dF = 2 rrrdIl3y • (18) 

and by sUbstituting (17) into (18) and integrating, the total 

Lorentz force acting on the circular region is obtained as 

F = I2anx. r' v. B, • grad. B dr (19) 

which becomes 

F 2/3 orrx,. R. 3 V" I3y z grad. B (20) 

Finally, considering that the pressure p = F/A, and the 

transversal damping impedance Zt = p/v, the latter becomes 

Zt = 2 13 axo R .. By • gradx B (21 ) 

This transversal damping impedance is again a function of 

electrical conductivity, thickness of the plate, radius of the 

field region, and is proportional to the product of the magnetic 

field and its gradient. 

467 
468 

Table 3 below presents the transversal damping impedances for 

the same materials. Assumed is a thickness of the plate of one 

centimeter, an active area of one square meter, and a magnetic 

field of 10 Tesla with a gradient of 10 Tesla per meter. For 

these conditions the damping impedances for metals are very high. 

TRANSVERSAL IMPEDANCE 

FOR VARIOUS METALS 

( Area = 1m2, Thickness 

Field = 10 T, Gradient 

Electrical 

Material Conductivity 

[Ohm- 1 m- 1 ] 

Aluminum 3.77 x 10' 

Copper 5.85 x 10' 

Steel 6.21 x 106 

Table 3 

= 10- 2 m, 

= 10Tm- 1 ) 

Attempts to Formulate a Generalized Theory: 

Transversal 

Impedance 

[Nm- 3 sec] 

7.09 X 106 

1.10 X 10' 

1.17 X 106 

The above considerations were based on very el7ment~ry 

electromagnetic theory, and furthermore made use of eng1neer1ng 

representations applied to very simple, special cases. It would 

be desirable to have a more rigorous and generalized theory, 

describing all possible interactions between electromagnetic 

fields and sound fields in electrically conducting media. In the 

attempt to construct such a theory it became immediately 

apparent, however, that it will be very complicated at best, if 

not entirely impossible to develop. The reasons for this are the 

following: 

(1) The theory would have to be based on the Electrodynamics of 

Moving Media, or Relativistic Electrodynamics. The Maxwell 
Equations, which are the cornerstone of most electrodynamic 

phenomena, do not apply in this case. They have no provision for 

moving media, and are hence not compatible with the description 

of the Lorentz Force, which is, the result of a moving conductor. 

Relativistic Electrodynamics have much more complicated 

formulations than the Maxwell Equations. 

(2) Electrodynamics, relativistic or not, in general deals with 

time variant, non-stationary phenomena, and therefore by 

necessity is represented in time domain. Acoustic and elastic 

phenomena, on the other hand, because of their stationary nature 

are better described in the spectral domain. This lack of very 

basic compatibility is another shortcoming. 

For the above reasons it is believed that investigations of even 

slightly more complicated geometries than discussed above will 

have to resort to numerical methods, based on engineering 

formulations of electromagnetic principles. Such approaches are 

useful and effective, but in the view of the author do not 

provide the same degree of insight in a general sense, and are 

also not as elegant from a physicists point of view. 

General Applications: 

Very interesting application possibilities will become practical 

when high magnetic fields generated with high temperature 

superconductors become routinely available. A few of such 

possibilities are outlined in the following: 

(1) Vibration Isolation: The most obvious is, of course, 

vibration isolation. Because of the short attenuation length in 

metals, it will be possible to dissipate energy directly in 

vibration mounts such as springs. This will mlnlmlze both 

transmitted vibrations to the foundation, as well as the buildup 

of vibrational amplitudes at the source. The vibrational energy 

will, of course, be dissipated as heat in the regions subjected 

to the magnetic field, and provisions for heat removal will be 

required. 

(2) Selective Mode Damping: In the most general case, the 

dissipation of acoustic energy will be anisotropic, depending on 

the relative orientations of the magnetic and acoustic vector 

variables. This characteristic can be exploited for the selective 

damping of vibration and propagation modes, and also for the 

suppression or enhancement of mode conversions. 

(3) Anechoic Structures: The impedance figures for plates 

indicate that it may be possible to match the characteristic 

impedance of water. Under such conditions, plates and other 

structures submerged in water may be rendered anechoic. 

(4) Suppressed Radiation: The same is true for vibrating plates 

radiating acoustic energy. It would be possible to change the 

impedance of such plates either locally, or globally, to suppress 
selected radiating modes, or possibly even vibration in its 

entirety. 

(5) Structural Hardening: Finally, it is foreseen that the 

response of plates to impinging transient pressure waves, such as 

shock waves, for example, could be altered significantly, 

providing much greater stiffness and resistance to such 

phenomena. 

Specific Applications to Magnetic Suspension: 

The utilization of the phenomena discussed to various magnetic 

suspension applications can result in considerable synergies 

particularly when very high magnetic fields are involved. 

Substantial damping forces can be obtained for various magnetic 

suspension applications if design configurations are chosen which 

enhance the discussed effects. 

One inc:easi~gly important system concept based on magnetic suspens~on ~s the magnetically levitated train, or maglev. 

Maglevs are subjected to vibrations induced by irregularities of 

the tracks, by fluctuations of the magnetic propulsion and 

levitation forces, and by various transient aerodynamic phenomena 

such as wind gusts, entry and exit of tunnels, and other passing 

maglev trains. The vibrations induced by these various sources 

will have to be attenuated in the interest of ride quality. 

Attenuation has to be accomplished mainly by the suspension, may 

it be the primary suspension (levitation), the secondary, or a 

combination of the two. Electromagnetic vibration damping is a 

natural choice for maglevs because of the high magnetic fields 

used for levitation. 

The values for damping impedances of plates presented in Table 2 

are comparable to the stiffnesses of electrodynamic (EDS) maglev 

suspensions. This type of maglev system also utilizes 

superconducting magnets for primary levitation. The magnetic 

fields are of sufficient magnitUde to allow the construction of 

simple and efficient electrodynamic vibration isolators using the 

same superconducting magnets which provide the primary 

levitation. 

Conclusions: 

It is envisioned that this area of magneto-acoustic interactions 

will play an important role in vibration damping in the future, 

leading to many interesting and important applications, including 

the ones outlined above. Practical means for generating the 

necessary magnetic fields are being developed at a rapid pace, 

since the discovery of high temperature superconducting 

materials. The fields of acoustics and structural vibrations will 

undoubtedly benefit from these developments, which are driven by 

a vast commercial potential encompassing all fields of electrical 

technologies. 

470 
References: 

(1) Lilley, F. E. and Carmichael, C. M. 

Can J Earth Sciences Vol.5, Pt.1 p 825-9 (1968) 

(2) Lee, u. 

AlAA Journal Vol.23, p 1783-90 (1985) 

(3) Horwath, T. G. Paper No. JJ-4 presented at the 

119-th Meeting of the Acoustical Society of America (1990) 

471 
N92-27747 

Coarse-Fine Residual Gravity Cancellation System with 

Magnetic Levitation 

S.E. Salcudean 

Department of Electrical Engineering, University of British Columbia 

2356 Main Mall, Vancouver, B.C., Canada, V6T iW5 

H. Davis, C. T. Chen, D.E. Goertz 

Department of Physics, University of British Columbia 

6224 Agricultural Road, Vancouver, B.C., Canada, V6T iZl 

B.V. Tryggvason 

Canadian Astronaut Program, Canadian Space Agency 

Rockliffe Base, Ottawa, Ont., Canada, KiA iAi 

PRECEDING PAGE BLANK NOT FILMED 473 
Abstract 

Aircraft flights along parabolic trajectories have been proposed and executed in order to achieve 

low-cost, near free-fall conditions of moderate duration (e.g. NASA KC-135 flights). This paper 

describes a six degrees-of-freedom experiment isolation system designed to cancel out residual 

accelerations due to mechanical vibrations and errors in aircraft trajectory. The isolation system 

consists of a fine-motion magnetic levitator whose stator is transported by a conventional 

coarse-motion stage. The levitator uses wide-gap voice-coil actuators and has the dual purpose of 

isolating the experiment platform from aircraft vibrations and actively cancelling residual 

accelerations through feedback control. The coarse-motion stage tracks the levitated platform in 

order to keep the levitator's coils centered within their matching magnetic gaps. Aspects of 

system design, an analysis of the proposed control strategy and simulation results are presented. 

Feasibility experiments are also discussed. 

I. Introduction 

A number of scientific experiments require zero-gravity conditions. As an alternative to 

outer-space experiments and drop-towers, aircraft flights along parabolic trajectories have been 

proposed and executed in order to achieve low-cost, near free-fall conditions of moderate duration. 

Due to the deviation of the aircraft flight trajectory from a perfect parabola and due to 

mechanical vibrations, equipment that is solidly attached to the aircraft is still subject to small, 

unwanted, forces. At low frequencies, these forces are due to deviations in aircraft trajectory, 

while at high frequencies, these forces are due mainly to mechanical vibrations. 

In order to deal with the problem of residual forces, large motion isolation mounts (LMIMs) have 

been proposed in joint studies between the Engineering Physics Department at the University of 

British Columbia (UBC) and the Canadian Astronaut Program [1, 2, 3]. The proposed 

approaches would allow low-friction, 3 DOF motion of an experimental setup (on an x - y gantry 

with additional z motion) within a specified, encaged volume within the aircraft. Low-friction 

motion of the experimental platform with respect to the aircraft frame can be achieved by using 

air or magnetic bearings along each degree of freedom, thus isolating the experimental platform 

from the body of the aircraft. Such a large motion isolation mount would enable a closer 

approximation to free-fall (indeed, limited only by friction, vibrations and drag) than what can 

be obtained when the experimental platform is solidly connected to the aircraft. 

Because an object free-floating in the aircraft could exceed its travel limit in a very short period 

of time which depends on the aircraft acceleration history and the release conditions, a number of 

experiments have been performed on a one-dimensional (z-axis) LMIM in the KC-135 to 

determine the time of free-fall before the limit of travel is exceeded [1, 2, 3]. The system has also 

been modelled to give statistical results with reasonable accuracy. From the instant of release at 

the start of the zero-g parabola, a 5 second free-float period can be obtained for approximately 

50% of the attempts. The range of free-float times is from 1 second to 13 seconds. With optimum 

release conditions the free-float period can be extended to about 8 seconds with 50% assurance. 

475 

PRECEDING PAGE BLANK NOT FtLMfD 
Motion isolation reduced accelerations transmitted from the aircraft to the object to under 5 mg 

during the free-fall period and much of that value was due to instrumentation noise. 

Active gravity cancellation has also been proposed and can be achieved by using linear motors to 

actuate one or several degrees of freedom [3]. 

In this paper, it is proposed that the platform carrying the zero-gravity experiment be completely 

isolated from the aircraft frame, by making use of active magnetic levitation. The approach is 

similar to the one proposed in [4, 5] for the design and control of a magnetically levitated 

(maglev) robot wrist for fine compliant motion. Although active magnetic levitation of the 

experiment platform would reduce high frequency disturbances due to aircraft frame vibrations, 

it would provide too little motion range to allow for the larger, low frequency deviations from 

free-fall due to aircraft trajectory errors. Therefore, this paper proposes a coarse-fine residual 

gravity cancellation system using magnetic levitation for small, high frequency motion isolation, 

combined with a coarse positioning system for low frequency motion isolation. 

Coarse-fine motion systems have been proposed, analyzed and used before for increasing speed 

and dexterity in manufacturing tasks [6, 7, 8, 5]. In [5], a coarse-fine redundant manipulator 

using a maglev wrist was proposed. The work presented in this paper differs from what was 

previously reported in several ways. First, the specific problem of active zero-g control through 

acceleration feedback is considered and analyzed. Second, 6 DOF coarse-fine motion coordination 

schemes are proposed, analysed and simulated with realistic assumptions on the performance of 

the coarse and fine motion stages. Finally, 6 DOF tracking of a levitated platform by a 

coarse-motion stage is experimentally demonstrated for the first time. 

This paper is organized as follows: In Section II, the new coarse-fine vibration isolation system 

for micro-gravity experiments is proposed and some overall design ideas are presented. In Section 

III, the coarse-fine motion system is modelled. Control and coordination algorithms are also 

proposed and analysed. These involve acceleration feedback and the use of coarse and fine sensors 

for tracking of the free-falling experiment platform. In Section IV, motion simulation results are 

presented under realistic design assumptions and using measured acceleration data from NASA 

KC-135 parabolic flights. In Section V, the experimental setup used to demonstrate the 

feasibility of the proposed system is described and the experiments performed to date are 

summarized. Both simulations and experiments demonstrate that a coarse-fine motion isolation 

system with magnetic levitation is feasible. 

II. Coarse-Fine Isolation Mount Design 

There are several possible approaches to isolating the experiment platform from the aircraft 

carrying it. The simplest solution is just to allow the platform to float inside the aircraft, while 

tracking it with a coarse motion stage and latching it at the end of the free-fall parabola or 

whenever necessary. However, there are several good reasons to consider an active vibration 

isolation system. These include the ability to cancel disturbances on the experiment platform, 

such as pulling forces by data collection and power wires, inadvertent touching of the experiment 

by an operator or motion caused by reaction forces due to the experiment itself. Also, as shown 

476 
Flotor 

} Fine motion stage 

.ss } 

,L Coarse motion stage 

{ 0 A I 'sA} 

Aircraft floor 

Figure 1: Overview of the proposed coarse-fine vibration isolation system. 

in [1, 2, 3], the duration of free-fall of a package inside an aircraft executing a parabolic flight is 

strongly dependent on how it is released. An active isolation system would allow a controlled zero 

acceleration release at a desired instant and at a specific location in the airplane. Finally, an 

active large motion isolation system would allow the exertion of small centering forces on the 

experiment platform, in effect trading acceleration levels for experiment duration. This ability 

would gain in importance if the aircraft acceleration levels on parabolic flights could be decreased 

through better sensing and control. 

Active vibration isolation solutions that involve direct mechanical linkages and that would also 

allow some controlled exertion of forces would be difficult to design and implement, simply 

because the actuator exerting the force would also transmit unwanted vibrations. Thus,some 

active levitation method is desirable because it would allow low cutoff frequency low-pass filtering 

of the actuation forces. Such active levitation methods could involve magnetic-bearing type of 

actuators with iron in the magnetic gap or voice-coil type of actuators (or Lorentz actuators) 

with conductors in the magnetic gap, the latter having several advantages, some of which are the 

need for just a single actuator for bi-directional motion along each degree of freedom, the 

linearity of applied force with command current, the better force characteristic with large 

magnetic gaps and the simplicity of design. 

The vibration isolation system proposed in this paper would use large-gap voice-coil actuators. 

The system overview is given in Figure 1 . The concept follows closely [4, 5]. A coarse motion 

stage, attached to the aircraft body, can impart fast, controlled, 3-DOF (or more) motion to the 

stator of a levitator. For simplicity, the coarse-motion stage shown in Figure 1 is a cartesian 

477 
FIotor 

Magnets (4) 

Stator 

+ 

Flat copper coil 

Figure 2: The schematic of the magnetic actuator used for the levitator. 

robot of the gantry type equipped with a spherical wrist, but there is considerable freedom in 

choosing its structure. 

In keeping with the terminology proposed in [5], the levitated experiment platform will be 

referred to as the flotor. The levitator's Rotor is actuated by at least six moving coil or "voice 

coil" actuators, shown in Figure 2. 

Each actuator has a magnetic assembly, attached to the Rotor and a matching coil, attached to 

the stator. Each coil fits within the gap of the magnetic circuit created by its matching magnetic 

assembly, allowing only a limited motion range or workspace (of the order of ±20 - 30mm) of the 

Rotor with respect to the Rotor. Although the Rotor is not physically attached to the stator 

(except, perhaps, for wires carrying signals and power) controlled Lorentz forces can be imparted 

to the platform by controlling the currents through the coils attached to the stator. Six linearly 

independent wrench vectors (6-vectors with three force and three torque components) can be 

generated with almost any location and orientation of the actuators. Indeed, with a suitably 

chosen geometry, 6 DOF motion along six degrees of freedom can be achieved without excessive 

coil currents [5]. 

With the best of current technology, it would be very difficult, if not impossible, for the 

levitator's voice coil motors to produce enough force to support the entire weight of the Rotor 

under normal gravity conditions. Thus, a latch mechanism is necessary to fix the Rotor under 

normal (or higher than normal) gravitational accelerations. 

The position and orientation of the Rotor with respect to the stator can be obtained by an optical 

sensor similar to the ones presented in [9, 4, 5] and others. An example is given in Figure 3. 

478 
o LED#l 

LED #2 

D--

PSD#2 

LED #3 PSD#l 

Figure 3: Optical sensing system for the levitator. 

Three narrow beam light-emitting diodes are attached to the platform. They project intersecting, 

orthogonal beams of light on the surfaces of three orthogonal, two-dimensional, lateral-effect 

position sensing diodes (PSDs) [10] attached to the stator. A simple kinematic calculation 

(intersection of three spheres) can be used to generate the position and orientation of the Rotor 

with respect to the stator by using the three sets of two-dimensional light spot coordinates sensed 

by the PSDs. The position sensing system described in Figure 3 has a limited range of motion 

that can be enlarged by using commercially available PSD cameras. 

The performance of the coarse-fine isolation system will depend on the flight characteristics of the 

KC-135 aircraft. The aircraft translational acceleration levels axes are primarily stochastic during 

the free-fall part of the flight parabola which lasts somewhat less than 20 seconds. Typical 

acceleration levels are presented in [11], where it is shown that acceleration peaks perpendicular 

to the aircraft Roor can exceed 50 mg for brief instants and can have an RMS value of 20 mg. 

Acceleration in the plane of the aircraft Roor have much lower peak amplitudes. Thus, the coarse 

tracker will be expected to generate accelerations of up to 50 mg to follow the Rotor in free-fall. 

The distance which the coarse tracker must travel is limited by the internal space in the KC-135 

aircraft and is typically less than 1.5 m in the vertical direction when allowance is made for a real 

experimental package and installation facilities. 

III. Modelling and Control 

The following coordinate systems are defined and shown in Figure 4: 

479 
Inertial z/ 

Frame 

{ 01'1} 

Airplane 

trajectory 

near parabola) 

Figure 4: The coordinate systems describing the motion isolation system. 

• {o A, QA}, attached to the aircraft frame at the nominal center of the coarse motion stage 

workspace. 

• {os, Qs}, attached to the levitator's stator. 

• {OF, QF}, attached to the Botor's center of mass and aligned about its principal axes of 

symmetry. When the Bot or is in its nominal position, the Botor and stator coordinate 

systems coincide. 

• an inertial system {O[, I}, whose origin coincides with with OA at the start of the free-fall 

parabola. The identity matrix I is chosen as illustrated in Figure 4, with the z-axis being 

aligned with the gravitational force, and the initial aircraft velocity lying in the yz-plane. 

(g = [00 - 9.81]Y). 

All vectors and matrices expressed in the inertial system will be shown in bold letters. 

We assume that the Botor (and the experimental platform it carries) can be accurately modelled 

by a rigid body having mass m and inertia matrix J with respect to its center of mass in the 

inertial coordinate system. In Botor coordinates, the Botor's inertia matrix becomes 

J = QFTJQF. Let a and a = Q~a, wand w = Q~w denote the Botor's acceleration and angular 

velocity in inertial and, respectively, Botor coordinates, let f denote the force acting on the Botor, 

and let T denote the torque acting at the Botor's center of mass. 

It is well known that the Botor's rotational motion is described by the following differential 

equations: 

where, for any vector v = [VI V2 V3]Y 

480 

(1) 
(2) 

In flotor frame, the equations of motion of the flotor are simply Newton's law and Euler's equation: 

rna = rng + j + h Jw + w x Jw = T + Td , (3) 

where WI = QFW, f = QFj, g = QFg, T = QFT, and fd = QFh and T = QFTd are disturbance 

forces and torques (from eddy-current coupling between flotor and stator, flow of air, dragging 

power wires, etc). 

The coarse-motion stage should have at least three, but preferably six, degrees of freedom. It is 

assumed that the coarse-motion has a closed-loop controller that servoes the stator's position and 

orientation with respect to the aircraft frame, i.e., that the coordinates Ar AS of Os - OA in QA 

frame (os - 0 A = QA Ar AS) and Qs -1 QA = QsT QA are available and controllable. A reasonable 

assumption on the behaviour of the the stator position under feedback control is that of a second 

order system with limits on velocity and acceleration: 

(4) 

II A;: AS 11< amax (5) 

II Ar AS II < Vmax (6) 

where Wo determines the cutoff frequency at which the stator can no longer track the command 

input Ar ASd and the damping coefficient ( determines the overshoot of the response. In the above 

equations, the characteristic frequency, damping ratio and acceleration and velocity bounds are 

the same for each axis, but these can be selected to match a particular coarse-motion stage, once 

it will be selected. In case the coarse-motion stage has more than 3 DOF, similar assumptions can 

be made on the stator orientation servo by using some appropriate orientation parametrization. 

It will be assumed that the disturbance forces exerted on the stator in reaction to forces applied 

by the levitator, as well as the effects of the aircraft motion, have negligible effects on the 

coarse-stage motion. If this is not the case, a detailed stability analysis of the coupled motion of 

the coarse and fine systems should be done along the lines of the work presented in [8]. During 

the free-fall part of the flight, the acceleration levels do not exceed 50 mg [11], so even with a 

heavy experiment platform (300 lb or so), the forces required to completely stop the platform 

motion are quite small. 

Because of the limited motion range of the flotor with respect to the stator, the flotor will quickly 

exceed its motion range, even with small deviations of the aircraft trajectory from an ideal 

parabola. Therefore, during the free-fall part of the aircraft flight, the commanded stator position 

should coincide with the flotor position, i.e., Ar ASd = Ar AF, where OF - 0A = QA Ar AF. The 

481 
L--______ ----j Accelerometer 

a =a-g A 

a 

Figure 5: Control loop for the flotor acceleration feedback. 

coordinates Ar AF can be obtained from the combined measurement of the stator with respect to 

the aircraft (through the conventional sensors of the coarse-motion stage) and that of the flotor 

with respect to the stator (through the levitator's optical sensor). 

III.a. Flotor Acceleration Feedback 

It will be assumed that accelerometers are used to measure the acceleration a of OF with respect 

to an inertial frame. Since accelerometers are attached to the flotor, the flotor frame coordinates 

a of the flotor acceleration are available. 

Once the flotor can be released, the resultant f of its actuators' action is some compensated 

function of the acceleration error, as shown in Figure 5. In terms of Laplace transforms, 

](s) = c(s)(ar(s) - a(s)). (7) 

where c(s), a(s) and ar(s) are the Laplace transforms of the feedback compensator, the flotor 

acceleration and the required acceleration, respectively. Due to the simplicity of the flotor 

dynamics (single rigid mass) in Figure 5, any proper, stable, real-rational transfer function can be 

obtained from the desired acceleration ar to the actual acceleration a of the flotor (of course, 

there will be limits on achievable performance due to plant uncertainty, actuator saturation, etc.). 

Choosing a first order stable transfer function leads to a compensator c( s) that is simply an 

integrator, i.e. velocity feedback: 

(8) 

which leads to 

.!. s 1..s A 

a(s) = ~ar(s) + --k 9 + ~h(s). s+~ s+~ s+~ 

(9) 

Usually, a is measured by a proof-mass accelerometer providing a signal aA = a - 9 (thus zero in 

free fall). In terms of this signal, the above equation becomes 

(10) 

482 
Clearly, for reasonably high gain k, the acceleration of the fiotor and platform does indeed track 

the desired acceleration ar and rejects the disturbance force !d. Usually, ar = g, leading to 

aA(s) ~ 0, although, as it will be seen later, this may not always be the best approach. 

The angular acceleration of the fiotor can be controlled in a similar way, , i. e., by using angular 

velocity feedback. The fiotor angular acceleration can be regulated to zero by the control law 

T = -kwJw, with some positive gain kw. Indeed, consider the Lyapunov function V = ~wT Jw. 

Along the trajectories described by the Euler equation in (3) (with rd = 0), we have that 

. 1 

V = "2 [WT(T -w x Jw) + (r -w X Jw?w] =wTr = -kwwTJw < o. (11) 

Thus the signal 6 = -w x J w is bounded and decreases to zero. By taking the Laplace transform 

of Euler's equation and letting aw = W, we obtain that 

A S -1 A 

aw ( s) = k J 6 ( s ), 

s + w 

(12) 

so the angular acceleration of the fiotor should be kept small at low frequencies. 

Before moving on, a comment on the nature of the disturbances acting on the fiotor (or 

experimental platform) and on means of rejecting them is in order. On one hand, disturbance 

forces can be both unknown and very difficult to measure, e.g. forces due to an experiment 

operator touching the fiotor. The only hope of attenuating these disturbances is through 

accelerometer feedback. On the other hand, some unpredictable disturbances can be easily 

measured, e.g. the forces and torques applied to the fiotor by an umbilical carrying signals and 

power. These disturbances can be rejected to a large extent through feed-forward through the 

flotor's actuating coils, while accelerometer feedback is still in effect. 

Umbilical disturbances can be measured by means of standard strain-gauge force-torque sensors 

or through other, more sophisticated, techniques. Even magnetic levitation can be used, with the 

same proof-mass principle used in some accelerometers. For example, the umbilical can be 

attached to the fiotor through an intermediate levitated proof-mass (i.e., another fiotor), whose 

position and orientation is servoed to that of the experimental platform. By monitoring the 

forces needed to keep the proof-mass in place (e.g., by monitoring the coil currents of Lorentz 

actuators, if the proof-mass uses Lorentz levitation), one obtains the forces and torques exerted 

by the umbilical. 

III.b. Acceleration Feedback with Centering Motion 

Although, ideally, the desired fiotor acceleration ar is zero, in practice, even the coarse motion 

platform will "run out of space" because of errors in the aircraft trajectory. Instead of letting the 

platform reach its motion limit (with associated high acceleration due to hard mechanical 

contact), it may be instead desirable to provide low-level "drift" accelerations that tend to bring 

the fiotor to the nominal center of the coarse motion platform. We will assume that this 

nominal center coincides with the aircraft reference frame origin 0A. There are a couple of ways 

in which a centering drift motion can be obtained. First, one can modify the control action (8) by 

483 
adding a proportional derivative term in the flotor offset rFA = QFT(OA - OF) with respect to the 

aircraft frame: 

where kp and kv are positive and small. The coordinates rFA of OA - OF in flotor frame are 

obtained from the coarse-stage and levitator's sensors. 

With k = 0 in the above (to see what the effect of this centering force is), applying this PD 

controller to Newton's equation in (3) (expressed in inertial coordinates) leads to 

(13) 

(14) 

Therefore, in inertial coordinates, the equation of motion of the flotor coordinate system origin 

with respect to the aircraft frame becomes 

d

2 kv d kp ) kv ( ) 1 

-(OF - OA) + --(OF - OA) + -(OF - OA = -w X OF - OA + -fd, dt 2 m dt m m m 

(15) 

where we made use of the fact that 

(16) 

and 

(17) 

(note that errors in aircraft trajectories are included in fd). 

The angular acceleration w of the levitator's flotor should be small, even without angular 

acceleration servoing, because the aircraft rotates relatively slowly during the parabolic flight. 

Therefore, the error OF - OA of equation (15) should be small. In addition, due to the 

orthogonality of w x (OA - OF) to the centering force ~(OF - OA) acting on the flotor, it should be 

possible to use a Lyapunov argument to show that, in the absence of disturbance forces fd and 

assuming that w is bounded, OF - OA converges to zero. 

Therefore, by using only local information (i.e., no inertial reference) the flotor can be made to 

track the aircraft center. Note that, in order to insure low accelerations, the constants kp and kv 

should be made as small as possible. 

As a second way to achieve a centering force on the flotor, note that the desired acceleration ar of 

(8) can be set according to a PD law similar to (13), i.e., 

(18) 

If the acceleration controller works well, a should track ar - 9 closely (see equation (10)), so, in 

effect, (13) will be quite well approximated. Of course, for such an approach to work, the 

484 
acceleration gain of (8) should lead to a substantially faster time constant than the time 

constants associated with (18). 

It is also possible to make the gains kp and kv depend on how close the platform is to the aircraft 

walls - the larger OF - OA, the larger kp and kv. In particular, a moderately large workspace 

without drift can be implemented by setting these gains to zero within a certain radius 

IloF - oA11 < r. 

A corrective term for drift in the orientation of the platform can also be devised. In particular, if 

the coarse-motion stage is only a 3-DOF system, as the airplane goes through a parabola, the 

levitator's stator will change orientation with it. Therefore, in spite of being free to move in 

translation, the flotor orientation must track that of the stator. Tracking could be achieved by 

using a control scheme based on the vector part of the Euler quaternion, as done in [5]. The 

rotation matrix Q AF = QAT QF of the fiotor with respect to the aircraft is represented by the 

Euler quaternion [,80 ,8TjT as 

QAF = exp(¢> sx) = 1+ 2,80,8 X +2(,8X)2 (19) 

where p = [,8o,8T]T = [cos(¢>/2)sin(¢>/2)sTV, and sand ¢> are the normalized axis (lIsll = 1) and, 

respectively, the angle of the rotation matrix QAF. This parametrization has several advantages, 

the most important one being the explicit representation of the axis of rotation. 

It can be shown [12] that after linearization (approximate or by exact cancellation of the 

dynamics, as in computed torque control), for rotation angles less than 180 degrees, the fiotor's 

rotational dynamics is given by 

i3 = ~J-IT 2 

Similarly to (13), a PD term can be added to the fiotor torque in such a way as to bring the 

orientation of the fiotor towards some central orientation aligned with the aircraft: 

(20) 

(21) 

where the orientation vector ,8 that corresponds to ,80 ~ 0 can be obtained from (19) and is given 

by 

1 T 

,8x = 2(1 Q)l (QAF - QAF ), + tr AF 2 

(22) 

where trQAF denotes the trace of QAF. 

It is clear that, when the platform acceleration is not measured, there can be no acceleration 

error correction for the platform. This is probably no serious drawback, because the platform is 

in near free-fall condition (except for some interaction with the coarse motion stage through eddy 

current damping and very little air drag). The coarse-motion stage can still be used to track the 

platform and the moving coil actuators can still be used to center the fiotor. However, some of 

the control over the acceleration levels exercised on the fiotor is lost. 

485 
Airplane Z-Acceleration wrt Plane 

0.4 ,-------,------,-----, 

0.3 . . .................. ! ...................•.•• : .................... . 

0.2 

0.1 

o 

-0.1 

-0.2 .... ............ ...... ....... .............. . 

-0.3 

(Data supplied by CSA) -0.4 L--__ ---L ___ ---L-__ ----' 

o 5 10 15 

Time (s) 

e 

'-' 

§ 

.... 

.... .... CIl 

g; 

Flotor Position wrt Plane 

2.----.----.----. 

1 .... 

------

-1 ..... . 

-2 

-3 N.().~m~rjIlg.t:llc:>ti.()~ ..... : . . . . 

- : x-axis -- : y-axis 

+ : z-axis 

-4L-----'-----'-------' 

o 5 10 15 

Time (s) 

Figure 6: The position of the platform with respect to the airplane with a given disturbance in the 

z-axis of the airplane. 

IV. Simulation Setup and Results 

The motion of the system described in Section I, with the control laws described in Section II, 

was simulated using the software packages PRO-MATLABTM and SIMULABTM, by The 

Math Works. The complete simulation was performed by describing the equations of motion of 

every component of the system i.e., the flotor dynamics, the stator dynamics, and the aircraft 

kinematics, in the inertial coordinate system {O[, I}. The control algorithms presented in Section 

II were applied in local coordinates as described, i.e., the flotor control algorithms were expressed 

in flotor coordinates, the coarse-motion stage dynamics were expressed in aircraft coordinates and 

the aircraft kinematics were expressed in inertial coordinates. 

Acceleration data obtained on NASA KC-135 parabolic flights [11] were used to drive the aircraft 

kinematics. Although there was no measured data available on the orientation of the KC-135 

during flight, the initial aircraft orientation at the start of the parabola and the final orientation 

at the end of free-fall are fairly well known. These show that the aircraft undergoes a change in 

pitch angle of about -60 degrees and is rolling to the right roughly 20 degrees during the free-fall 

486 
2 r--_-=Fl-=o::::.;t:..::o:.::.rrP..::o:::s~itI::.:· o::..:.n=-wrt..:..:..:.;;:..:P:...;I:::an=e_---, 

-2 ..................... _ ............ . 

- : x-axis: -- : y-axis : 

_4L-~~~L-~~~~~~~ + : z-axis: No cente:· motion 

o 5 10 15 

Time (s) 

Stator Velocit 0.4 .----=..::=~==~=;.~:.:.:L.:::.L---, 

f\ (wn Airplan~) 

.J. ... t ........... : ...................... l .......... . t t: : + . 

--~~l-.~.r.- : . .L. ............... . -~-------

0.2 

o ~ 

~ -0.2 ~ 

> -0.4 

: x-axis -axis: + : z-axis -0.6 "------"-------'----'-""---'-'------..:.--'---------''--' 

o 5 10 15 

Time (s) 

0.02 

e 

';;' 0 

~ -0.02 

o 

-0.04 

: x-axis -axis: +: z-axis -0.06 '------'----"~---'------' 

..... 

~ 

o 5 10 15 

Time (s) 

f+ 

+ + 0.2 + .. +..... .. ~ ............... : + 

+ + 

o 

~ ~ -0.2 

i..-: y-axis 

+ : z-axis -0.4 '----'----'-------'----"-------'--'------' 

o 5 10 15 

Time (s) 

Figure 7: Flotor-stator tracking errors and stator velocity and acceleration. 

parabola. In all the simulations performed, it was assumed that this rotation occurs at a constant 

angular rate, about the fixed Euler eigenaxis of rotation between the initial and final orientations. 

Some typical results are displayed in Figures 6, 7, 8 and 9. Unless otherwise specified, airplane 

coordinates are used. 

Figure 6 shows the acceleration data and the flotor position. Figure 7 shows the tracking errors in 

x, y, z. As expected, the coarse-motion stage tracking error along the z-axis is substantially 

larger than for the x and y axis. With fairly stringent performance limitations on the coarse 

motion stage (2 Hz bandwidth, 5 m/s/s max. acceleration, 1 m/s max. velocity), typical tracking 

errors are about ±10 mm in the y-axis, ±30 mm in the x-axis and ±40 mm in the z axis. These 

errors are reduced drastically as the bandwidth of the tracking platform is increased. It is fairly 

simple to design a wide-gap levitator that matches these workspace requirements. For example, 

the stator could be shaped as a rectangular shell with flat coils (as shown in Figure 2) embedded 

in its walls. The matching fiotor would have a large face available for an experiment platform, 

and would have a substantial travel in the z axis, while maintaining relatively small magnetic 

gaps for the actuators. The optical sensor shown in Figure 3 could be employed with minor 

487 
§ 

..... 

~ o 

(§ 

xlO-3 Flotor Orientation 

O~--~,. ___ ~~~~~----~ 

, 

, 

, 

:" .. - ,,~ , . , 

~1 ........... / ............................................. . , 

, 

, 

, 

, 

, 

I 

I 

I 

-2·-{··· , 

, 

I 

, 

, 

, 

, 

, 

-3 I ·r············· I I 

I I I, I, I, 

I I 

I, 

-4 '; ............... . I, 

II 

II 

II 

" " " " -5 " . 

- : K-axis -- : y-axis 

+ ::z-axis 

-6~----~L-----~------~ 

o 5 lO 15 

Time (s) 

Torque on the Flotor 

1.2,-----,----,-----, 

1 t·····················~·······················:······· .............. -

:- . . 

" ': , 0.8 ~ ..................................... -. ............. - , 

, 

, 

, 

, 

I . 

0.6~ ........ · .......... ·f ................. , .................... -

I 

, 

, 

, 

, 

, 

0.4 r" , 

0.2 

............................ .. .... -

··········· .. ·.:. .. :·x:..riis··-

-- : y-axis 

+ ::z-axis 

O~----------------~ ;-'r 

, I 

" 'i 

-0.2 L-__ ---L. ___ -'--__ ----.J 

o 5 lO 15 

Time (s) 

Figure 8: Orientation error components and torque applied to the fiotor. 

modifications for the large z-axis travel. 

Figure 8 shows the rotation tracking performance (the vector part j3 of the Euler quaternion, as 

defined for equation (19), is displayed) and the torques applied to the fiotor. It can be seen that 

the orientation errors are small and that the torques required to rotate the fiotor are small (the 

fiotor is modelled as a 300 lb cube). 

Figure 9 shows the trade-off between acceleration quality and free-fall duration. Simulation 

results with two sets of centering gains in equation (18) are displayed. It can be seen that as 

these gains are increased, the fiotor moves less with respect to the aircraft. At the same time, the 

acceleration levels on the fiotor increase, as expected. If the required acceleration level for a given 

experiment is known, one can modify the centering acceleration of equation (18) in order to 

optimize experiment duration. Another possible use for centering forces is the avoidance of 

"crashes" into the aircraft walls. 

488 
1 Flotor Position wrt Plane 0.1 Flotor Acceleration 

0.5 

kp=0.05 

kv = 0.05 

-. -. 

e 0 -S 0.05 '-" ........................ E § --~----------- '-" .... kp.:7'.O.05 .. .L . ... .....; 

-0.5 .... ................... ) ..................... Q) rn 

0 kv =0.05 (,) 0 p., ~ -1 " .. :.x...,axis ... : .. 

-- : y-ax~s 

+ : Z-axIS: -1.5 -0.05 

0 5 10 15 0 5 10 15 

Time (s) Time (s) 

0.5 Flotor Position wrt Plane 0.4 Flotor Acceleration 

-. 0.2 \ - : x-a:tis -. ... "' ......................... 

e 0 -S t -- : y-ax~s 

'-" E t+ : z-runs 

c:: -+, . -+, 

0 '-" 0 -.-.~.~.-.-.-.++. •. ~.~ . .;..'" ~ ~-

'::l kp~ 0.5 .....; .... Q) t : t . rn -0.5 (,) 0 '\ + : ···kv~·05· .. ··· ~ p., :t : 

-0.2 .. ·V .. ·kp·==-[05 ........ · - : x-axis -- ::y-axis kv ={).5 

-1 + .; z-axis -0.4 

0 5 10 15 0 5 10 15 

Time (s) Time (s) 

Figure 9: Effects of centering control on position and acceleration. 

V. Experimental Setup and Results 

To demonstrate the feasibility of the coarse-fine motion isolation system described in Section I 

and the validity of the control and coarse-fine motion coordination schemes presented in Section 

II, the authors used a Unimation PUMA 500 robot equipped with a magnetically levitated 

fine-motion robot wrist, developed and built in the Electrical Engineering Department at UBC. 

The UBC maglev wrist uses the same design principles applied to the "Magic" wrist described in 

[4, 5] and outlined in Section I of this paper. The weight of its flotor is 0.640 kilograms, its 

motion range is ±4.5 mm and ±7 degrees from the nominal center. Each of the wrist's voice-coil 

actuators produces roughly 2 N / A force per unit current and the power consumption required to 

"fly" the flotor without any additional payload is less than 7 Watts. 

The real-time system employed for the coordinated control of the PUMA robot and the 

levitator's flotor is illustrated in Figure 10. An IBM PC-AT compatible computer hosts a 

Spectrum Inc. digital signal processing (DSP) board using a Texas Instruments Inc. TMSC30 

DSP chip, as well as analog input and output boards linked through a fast, private bus. The PC 

489 
! 

DSP-L 

BU S 

INK 

AID 

i386 

DIA - DSP SOFTWARE 

DEVELOPMENT TOOLS 

- DEBUG MONITOR 

TMSC30 - PUMA-WRIST 

DSP COMMUNICATION 

-MAGLEV PUMA 

WRIST CONTROL 19.2K BAUD BI-DIRECTIONAL LINK CONTROLLER 

PC-AT BUS 

Figure 10: The block diagram of the PUMA-Wrist real-time controller. 

is connected through a 19.2 Kbaud serial link to the PUMA robot controller. 

The floating point DSP board controls the levitator's flotor, computes the stator's position and 

orientation from position and Euler angles information obtained from the robot through the serial 

link, and calculates the updated robot set points (bx, by, bz, roll, pitch, yaw) as a function of 

flotor position. The kinematic calculations required to determine the flotor position with respect 

to the stator are exactly as described in [5]. The flotor controls are updated every 1.5 

milliseconds, with the DSP board running at about 1 MBop. 

The PC is used for DSP software development and for the serial port communications between 

the wrist controller and the robot controller. 

A program written in VAL II handles the serial communications on the PUMA controller side, 

while the robot is in INTERNAL ALTER mode, effectively making it a slave to the wrist's flotor 

motion. The coordination data between the robot and the wrist could only be transmitted every 

56 milliseconds. This could be improved substantially if the PUMA controller could be 

modified. In particular, a Jacobian-based velocity tracking algorithm that does not require the 

on-line solution of the inverse kinematics problem could be implemented. 

Coordinated motion of the Botor and the robot was demonstrated by the authors, with the robot 

following the wrist's flotor position and orientation. Translational tracking with locked 

orientation was also demonstrated. 

Accelerometers were mounted on the flotor, but problems with drift and noise have so far 

prevented successful implementation of acceleration feedback. 

490 
VI. Conclusion 

The authors proposed a coarse-fine large-motion isolation system for residual gravity cancellation 

on parabolic flights. The system would use wide gap magnetic levitation for vibration isolation 

and acceleration servoing of an experimental platform. The proposed isolation mount was 

modelled and control algorithms for acceleration servoing and centering motion were presented. 

The model and the control algorithms were simulated and an experimental coarse-fine system 

using a PUMA robot and maglev wrist was put together in order to demonstrate the system's 

feasibility. 

The proposed gravity cancellation system has several advantages, among which are (i) the ability 

of reducing the dynamic coupling between the aircraft and experimental platform to just eddy 

current coupling, (ii) the ability of using maglev forces to obtain good initial release of the 

experiment platform, (iii) the ability of trading off experiment duration versus quality of the 

free-fall. 

The simulation results and experimental results presented seem to indicate that such a coarse-fine 

approach to vibration isolation is feasible. In particular, the ability of a coarse-motion stage to 

track a levitated platform was demonstrated through both simulations and experiments. The 

only requirement left to demonstrate that the coarse-fine motion isolation system will work as 

proposed is the successful application of acceleration feedback. That work is now in progress. 

Acknowledgements 

The authors wish to thank David Fletcher for machining the maglev wrist used in their 

experiments, Dr. Dale Cherchas for providing space and experimentation time in his lab, and 

Nelson Ho for general help and for writing the symbolic debug monitor for the DSP. The support 

of NSERC and the Canadian Space Agency is gratefully acknowledged. 

References 

[1] A. Adler and J. Bernaldez. Motion isolation mount for microgravity. Technical report, Dept. 

of Physics, University of British Columbia, December 1989. Engineering Physics Project No. 

8918. 

[21 H. Davis. Report on the proposed modifications to the 1-d large motion isolation mount for 

flight tests on the NASA KC-135 aircraft. Technical report, Engineering Physics, University 

of British Columbia, October 1990. (prepared for NRC under contract 31016-0-6022/01-SW). 

491 
[3] H. Davis. Report on the first flights of the large motion isolation mount on the NASA 

KC-135 Aircraft, june 5-9, 1990. Technical report, Engineering Physics, University of British 

Columbia, September 15 1990. (prepared for NRC under contract 31016-0-6022/01-SW). 

[4] R.L. Hollis. Magnetically levitated fine motion robot wrist with programmable compliance, 

October 1989. U.S. Patent number 4,874,998. 

[5] R.L. Hollis, S. Salcudean, and P.A. Allan. A Six Degree-of-Freedom Magnetically Levitated 

Variable Compliance Fine Motion Wrist: Design, Modelling and Control. IEEE Transactions 

on Robotics and Automation, 7(3):320-332, June 1991. 

[6] R. H. Taylor, R. L. Hollis, and M. A. Lavin. Precise manipulation with endpoint sensing. 

IBM J. Res. Develop., 2(4):363-376, July 1985. 

[7] Andre Sharon and David Hardt. Enhancement of robot accuracy using endpoint feedback 

and a macro-micro manipulator system. In American Control Conference proceedings, pages 

1836-1842, San Diego, California, June 6-8 1984. 

[8] S. Salcudean and C. An. On the control of redundant coarse-fine manipulators. In 

Proceedings of the IEEE International Conference on Robotics and Automation, pages 

1843-1840, Scottsdale, Arizona, May l4-18 1989. 

[9] A.E. Brennemann, R.L. Hollis, and R.H. Taylor. General position and orientation sensor for 

fine motions and forces. IBM Technical Disclosure Bulletin, 26(9):4457-4462, February 1984. 

[10] United Detector Technology. Silicon photodetectors catalog. 12525 Chandron Ave., 

Hawthorne, CA 90250. 

[11] B. V. Tryggvason. Acceleration Levels on the KC-135. Technical report, Canadian Space 

Agency, October 1990. Report CSA-CAP.008. 

[12] S. Salcudean. On the control of magnetically levitated robot wrists. In Proceedings of the 

27th IEEE Conference on Decision and Control, pages 186-191, Austin, Texas, December 

1988. 

492 
ATTENDEES 

493 
494 

Alcorn Charles W. Alcorn 

Phone: 804-683-3720 

Old Dominion Unversity 

Dept. of Mechanical Engineering 

N orfolk VA 23529-0247 

Allan A. P. Allan 

Phone:804-~6233 

University of Virginia 

Department of Mech. and Aero. Engrg. 

Charlottesville VA 22903 

Banerjee Bibhuti Banerjee 

Phone:804-~6233 

University of Virginia 

ROMAC Labs, Mech & Aero Engrg. 

Thornton Hall, McCormick Road 

Charlottesville VA 22903 

Batterson James G. Batterson 

Phone: 804-864-4059 

NASA Langley Research Center 

Mail Stop 161 

Hampton VA 23665-5225 

Bichsel J. Bichsel 

Phone: 1-256-51-19 

Eidgenossische Technische Hochschule 

Institut fur Elektrotechnische 

Entwicklungen, ETH ZentrumlETZ F 

CH-8092 Zurich 

SWITZERLAND 

Boehm Josef Boehm 

Phone: 061-745 5000 

University of Salford 

Physics Department, The Crescent 

Salford M5 4WT 

UNITED KINGDOM 

Allaire Paul E. Allaire 

Phone:804-~3292 

University of Virginia 

Mechanical Engineering Department 

Thornton Hall McCormick Road 

Charlottesville VA 22903 

Anderson Willard W. Anderson 

Phone:804-~1718 

NASA Langley Research Center 

Mail Stop 479 

Hampton VA 23665-5225 

Barrett Lloyd Barrett 

Phone: (804) 924-6210 

Univ. of Virginia 

Dept. of Mech. and Aero. 

Engg. 

Charlottesville VA 22903 

Bernhardt Helmut Bernhardt 

Phone: 

Nebenstrasse 2B 

D-W-6330 

Wetzlar 22 

GERMANY 

Boden K Boden 

Phone: 02461-614604 

Kernforschungsanlage Julich GmbH 

Abteilung IGV 

Postfach 1913 

D-5170 Julich 

GERMANY 

Bondarenko Herman A. Bondarenko 

Phone: 06452-4-38-46 

The Sumy Frunze Machine Building 

Science and Production Amalgamation 

G. Kursky Avenue 

Sumy 244609 

U.S.S.R. 
Briggs B. M. Briggs 

Phone: 206-657-3735 

Boeing Aerospace and Electronics 

P. O. Box 3999 

MIS 3C-PC 

Seattle WA 98124 

Britton Thomas C. Britton 

Phone:804-~6619 

Lockheed Engr. & Sciences Co. 

NASA Langley Research Center 

Mail Stop 161 

Hampton VA 23665-5225 

Castleman Bruce W. Castleman 

Phone: 813-539-5708 

Honeywell Inc. 

Mail Station 350-1 

13350 U.S. Highway 19 South 

Clearwater FL 34624-7290 

CqJe David B. Cope 

Phone: 617-890-3200 

Foster-Miller Inc. 

350 Second Avenue 

Building 1 

Waltham MA 02154-1196 

Davis Harold Davis 

Phone: 604-822-2961 

The University of British Columbia 

Department of Physics 

6224 Agricultural Road 

Vancouver, B.C. V6T 1Zl 

CANADA 

Derrickson G. Stephan Derrickson 

Phone: 719-633-8333 

The Spectranetics Corp. 

96 Talamine Court 

Colorado Springs CO 80907 

Britcher Colin P. Britcher 

Ph on e: 804-683-3720 

Old Dominion University 

Dept. of Mech. Engg. 

Norfolk VA 23529-0247 

Burrows Clifford R. Burrows 

Phone: 0225 826935 

University of Bath 

School of Mechanical Engineering 

Claverton Down 

Bath BA2 7AY 

ENGLAND 

Om Wei-Kan Chu 

Phone: 713-743-8250 

Texas Center for Superconductivity 

University of Houston 

4800 Calhoun 

Houston TX 77004-5506 

Daniels Taumi S. Daniels 

Phone:804-~59 

NASA Langley Research Center 

Mail Stop 238 

Hampton VA 23665-5225 

deRochemont L. P. de Rochemont 

Phone: 617-926-1167 

Radiation Monitoring Devices, Inc. 

44 Hunt Street 

Watertown MA 02172 

Dhar Debasish Dhar 

Phone:804-9~3291 

University of Virginia 

ROMAC Labs, Mech & Aero Egnrg 

Thornton Hall, McCormick Road 

Charlottesville VA 22903 

495 
496 

Doederlein Ted A. Doederlein 

Phone: 805-275-5483 

Phillips Laboratory 

OLAC PUSTSS 

Edwards CA 93523-5000 

Dress David Dress 

Phone:~~5126 

NASA Langley Research Center 

Mail Stop 287 

Hampton VA 23665-5225 

Eisenhaure David B. Eisenhaure 

Phone: 617-661-0540 

SatCon Technology Corporation 

12 Emily Street 

Cambridge MA 02139-4507 

Forbes David A. Forbes 

Phone: ~688-7954 

Newport News Shipbuilding 

4101 Washington Avenue 

Dept. E55 

Newport News VA 23607 

Gaffney Monique Gaffney 

Phone: 617-661-0540 

SatCon Technology Corporation 

12 Emily Street 

Cambridge MA 02139 

Gavrilov Victor P. Gavrilov 

Phone: 06452-2-55-80 

Severodonetsk Manuf. Assoc. "AZOT" 

5, Chimikov 

Severodonetsk 349940 

U.S.S.R. 

Downer James R. Downer 

Phone: 617-661-0540, X203 

SatCon Technology Corporation 

12 Emily Street 

Cambridge MA 02142 

DuUm. Jeffrey L. Dutton 

Phone: ~688-3807 

Newport News Shipbuilding 

4101 Washington Avenue 

Dept. E55 

Newport News VA 23607 

Fenn Ralph Fenn 

Phone: 617-661-0540 

SatCon Technology Corporation 

12 Emily Street 

Cambridge MA 02139 

Foumult Jean-Pierre Foucault 

Phone: 14-65-71-160 

ONERA 

29 Avenue De La Division Leclerc 

Chatillon 92320 

FRANCE 

Garbutt Keith S. Garbutt 

Phone: 703595000,X3384 

University of Southampton 

Department of Aeronautics 

Southampton, Hants S09 5NH 

UNITED KINGDOM 

Ghofrani Mehran Ghofrani 

Phone: ~683-3720 

Old Dominion University 

Dept. of Mechanical Engineering 

Norfolk VA 23529-0247 
Girault J. P. Girault 

Phone: 32-21-71-71 

Societe Europeenne de Propulsion 

Div. Propulsion a Liquides et Espace 

B. P. 802 

F-27207 Vernon 

FRANCE 

Goodyer Michael J. Goodyer 

Phone: 703-592374 

The University of Southampton 

Dept. of Aero. and Astro. 

Hampshire 805 5NH 

ENGLAND 

Halbach Klaus Halbach 

Phone: 415-48~5868 

UC Lawrence Berkeley Lab 

MS2-400 

Berkeley CA 94720 

Hawkey Timothy Hawkey 

Phone: 617-661-0540 

SatCon Technology Corp. 

12 Emily Street 

Cambridge MA 02139 

Hibner David H. Hibner 

Phone: 203-565-2238 

Pratt & Whitney 

400 Main Street 

MS 163-09 

East Hartford CT 06108 

Holmberg Neil Holmberg 

Phone: 804-864-6970 

NASA Langley Research Center 

Mail Stop 457 

Hampton VA 23665-5225 

Givan Garry Givan 

Phone: 513-255-1286 

US Air Force 

WL/POSL 

Wright Patterson AFB OH 45433-6563 

Groom Nelson J. Groom 

Phone: 804-864-6613 

NASA Langley Research Center 

Mail Stop 161 

Hampton VA 23665-5225 

Hampton Roy D. Hampton 

Phone:804-~3767 

University of Virginia 

ROMAC Labs, Mech & Aero Engrg 

Thornton Hall, McCormick Road 

Charlottesville VA 22903 

He Jianliang He 

Phone: 708-972-2558 

Argonne National Laboratory 

9700 S. Cass Avenue 

Bldg. 362 

Argonne IL 60439 

Hollis R. L. Hollis 

Phone: 914-945-1653 

IBM 

T. J. Watson Research Center 

P. O. Box 218 

Yorktown Heights NY 10598 

Horwath T. G. Horwath 

Phone: 703-371-3531 

TG&C Associates 

1 Cessna Lane 

Falmouth VA 22405 

497 
498 

Howard John D. Howard 

Phone: 609-921-2792 

VSE International 

127 McCosh Circle 

Princeton NJ 08540 

Jensen Carol Jensen 

Phone: 818-302-9705 

Southern California Edison 

P. O. Box 800/Room 455001 

2244 Walnut Grove Avenue 

Rosemead CA 91770 

Johnson Dexter Johnson 

Phone: 216-433-6046 

NASA Lewis Research Center 

21000 Brookpark Road 

Mail Stop 23-3 

Cleveland OR 44135 

Jordan Thomas L. Jordan 

Phone:~~713 

NASA Langley Research Center 

MS238 

Hampton VA 23665-5225 

Joshi Suresh M. Joshi 

Phone: ~864-6608 

NASA Langley Research Center 

Mail Stop 230 

Hampton VA 23665-5225 

Juengst Carl D. Juengst 

Phone: 206-773-8602 

Boeing Aerospace 

P. O. Box 34113 

Mail Stop 82-24 

Seattle WA 98124-1113 

Ishikawa Hideyuki Ishikawa 

Phone:31~1500 

American Koyo Corp. 

47771 Halyard 

Plymouth MI 48170 

Joffe Benjamin Joffe 

Phone: 818-354-6444 

Jet Propulsion Laboratory 

4800 Oak Grove Drive 

MS251 

Pasadena CA 91109-8099 

Jones Brian R. Jones 

Phone: 415-423-3058 

Lawrence Livermore Nat. Laboratory 

P. O. Box 808 

Livermore CA 94550 

Joshi Prakash B. Joshi 

Phone: 508-689-0003 

Physical Sciences, Inc. 

20 New England Business Center 

Andover MA 01810 

Judd Michael Judd 

Phone: 617-981-7734 

MIT Lincoln Laboratory 

P.O. Box 73 

77 Massachusetts Avenue 

Lexington MA 02173 

Kaplan Nicholas Kaplan 

Phone: 301-628-3481 

AAI Corporation 

5401 Linton Road 

Sykesville MD 21784 
Keckler Claude R. Keckler 

Phone:~~1716 

NASA Langley Research Center 

Mail Stop 479 

Hampton VA 23665-5225 

Kelliher Warren C. Kelliher 

Phone: ~~172 

NASA Langley Research Center 

Mail Stop 416A 

Hampton VA 23665-5225 

Kilgore Robert A. Kilgore 

Phone: ~~5020 

NASA Langley Research Center 

Mail Stop 274 

Hampton VA 23665-5225 

Kneschke Tristan Kneschke 

Phone: 215-542-0700 

LTK Engineering Services 

Two Valley Square, Suite 300 

512 Township Lane Road 

Blue Bell PA 19422 

Knolle Ernst G. Knolle 

Phone: 415-871-9816 

Knolle Magnetrans 

2691 Sean Court 

San Francisco CA 94080 

Kroeger John C. Kroeger 

Phone: 602-561-3175 

Honeywell Satellite Systems 

P. O. Box 52199 

Phoenix AZ 85072-2199 

Keesee John Keesee 

Phone: 

Magnetic Bearings, Inc. 

609 Rock Road 

Radford VA 24141 

Kilgore Allen Kilgore 

Phone:~~5033 

Vigyan, Inc. 

30 Research Dr. 

Hampton VA 23666 

Kipp Ronald W. Kipp 

Phone: 215-824-4887 

Kingsbury, Inc. 

10385 Drummond Road 

Philadelphia PA 19154 

Knight Josiah D. Knight 

Phone: 919-660-5337 

Duke University 

Dept. of Mech. Engrg & MatrI Science 

Durham NC 27706 

Knospe Carl Knospe 

Phone: ~982-2603 

University of Virginia 

Dept. of Mech. & Aero. Engrg 

Thornton Hall, McCormick Road 

Charlottesville VA 22903 

Kuzin Alexander V. Kuzin 

Phone: 095-297-6511 (fax) 

Moscow Aviation-Tech. Institute 

Subfaculty "Microprocessor Systems, 

Electronics, and Electrical Engg." 

Petrovka, 27, Moscow, K31 103737 

U.S.S.R. 

499 
500 

Larsonneur Rene Larsonneur 

Phone: 01-2562539 

Mechatronics Group 

Robotics Institute 

ETH Zurich 

Zurich CH-8092 

SWITZERLAND 

Lewis Pete Lewis 

Phone:~~7238 

NASA Langley Res. Cen. 

MS440 

Hampton VA 23665-5225 

Meeks Crawford R. Meeks 

Phone: 818-886-0250 

AVCON 

19151 Parthenia Street 

Suite G 

Northridge CA 91324 

Melzer Eckhard B. Melzer 

Phone: 551-709-2142 

German Aerospace Research Establishment 

Central Division Windtunnels 

W-3400 

Gottingen 

GERMANY 

~ Mark Motter 

Phone:~~6978 

NASA Langley Research Center 

Mail Stop 442 

Hampton VA 23665-5225 

Nelik Lev Nelik 

Phone: 908-859-7019 

Ingersoll-Rand Company 

Advanced Tech. Research and Dev. 

942 Memorial Parkway 

Phillipsburg NJ 08865 

Lashley Christopher M. Lashley 

Phone: 301-982-2093 

Fare, Inc. 

4716 Pontiac St. Suite 304 

College Park MD 20740 

McMichael Chase K. McMichael 

Phone: 713-743-8262 

Texas Center for Superconductivity 

University of Houston 

4800 Calhoun 

Houston TX 77204-5506 

Meier R. H. Meier 

Phone: 614-392-8382 

Cooper Industries 

105 North Sandusky Street 

Mount Vernon OH 43050 

Morris Michelle L. Morris 

Phone:~~179 

NASA Langley Research Center 

MS416A 

Hampton VA 23665-5225 

Muto Masai Muto 

Phone: 3-5276-6785 

Railway Technical Research Inst. 

Hiei-Kudan-Kita Bldg. 5F, 

4-1-3, Kudan-Kita 

Tokyo 102 

JAPAN 

Neumeyer Charles L. Neumeyer 

Phone: 212-839-1643 

Ebasco Services, Inc. 

2 World Trade Center 

New York NY 10048 
Nguyen Tiep Nguyen 

Phone: 704-547-4371 

Univ. of North Carolina - Charlotte 

Precision Engineering - ARC 

Charlotte NC 28223 

Owen Andrew K. Owen 

Phone: 415-321-5630 

Complere Inc. 

P. O. Box 1697 

Palo Alto CA 94302 

Pang Da-Chen Pang 

Phone: 301-405-5327 

University of Maryland 

Department of Mech. Engg. 

College Park MD 20742 

Petukhova Irina A. Petukhova 

Phone: 06452-9-6193 

Severodonetsk Manuf. Assoc. "AZOT" 

5, Chimikov, 

Severodonetsk 349940 

U.S.S.R. 

Price Douglas B. Price 

Phone:~~6605 

NASA Langley Research Center 

Mail Stop 161 

Hampton VA 23665-5225 

Queen M. A. Queen 

Phone: 704-547-4371 

University of North Carolina 

Precision Engineering - ARC 

Charlotte NC 28223 

Oman Henry Oman 

Phone:2~87S4458 

Boeing Aerospace and Electronics 

19221 Normandy Park Dr., S. W. 

Seattle WA 98166 

Paden Prof. Brad Paden 

Phone: (805) 893-8165 

Univ ofCA 

Dept. of Mech. Engg 

Santa Barbara CA 93106-5070 

Pelrine Dr. Ronald E. Pelrine 

Phone: 415-859-3360 

SRI International 

333 Ravenswood Avenue 

EL137 

Menlo Park CA 94025 

PUoYe,y Tony Poovey 

Phone: 704-547-4371 

Univ. of North Carolina-Charlotte 

Precision Engineering - ARC 

Charlotte NC 28223 

Putman Thomas H. Putman 

Phone: 412-256-1169 

Westinghouse Electric Corp. 

1310 Beulah Road 

Science and Technology Center 

Pittsburgh PA 15235 

Raffi Rhonda C. Raffi 

Phone: 617-661-0541 

SatCon Technology Corporation 

12 Emily Street 

Cambridge MA 02139-4507 

501 
S02 

Roo Dantam K. Rao 

Phone: 518-785-2489 

Mechanical Technology, Inc. 

968 Albany Shaker Road 

Latham NY 12110 

Richey Albert E. Richey 

Phone: 518-456-5456 

Intermagnetics General Corp. 

P.O. Box 566 

Guilderland NY 12084 

Rock Col. J. C. Rock 

Phone: 

Dept. of the Air Force 

6410 McKeon 

San Antonio TX 78218 

Rosado Lewis Rosado 

Phone: 513-255-6519 

US Air Force 

WL/POSL 

Wright Patterson AFB OH 45433-6563 

Sa1cudean S. E. Salcudean 

Phone: 604-822-3243 

University of British Columbia 

Department of Electrical Engineering 

2356 Main Mall 

Vancouver, B. C. V6T-1W5 

CANADA 

SdIott Timothy D. Schott 

Phone: ~864-4715 

NASA Langley Research Center 

Mail Stop 238 

Hampton VA 23665-5225 

Reid John B. Reid 

Phone: (415) 568-1500 

United Magnet Tech. 

1824 Woodsdale Dr. 

Concord CA 94521 

Ritter Jim Ritter 

Phone: 

NASA Langley Res. Ctr. 

MS904 

Hampton VA 23665-5225 

Roland J. P. Roland 

Phone: 1-34-92-27-48 

Aerospatiale 

Route de Vemeuil 78 

Etablissement des Mureaux, BP96 

78133 Les-Mureaux 

FRANCE 

Rothwarf Frederick Rothwarf 

Phone: 703-758-0247 

ATE, Ltd. 

11722 Indian Ridge Road 

Reston VA 22091 

Sanders Clark Sanders 

Phone:7~547~71 

Univ. of North Carolina at Charlotte 

Precision Engineering - ARC 

Charlotte NC 28223 

Srott Michael A Scott 

Phone:~~7 

NASA Langley Research Center 

MS230 

Hampton VA 23665-5225 
Scurlock Ralph G. Scurlock 

Phone: 703-592-046 

The University of Southhampton 

Institute of Cryogenics 

Hampshire S09 5NH 

ENGLAND 

Shmilovich Alex M. Shmilovich 

Phone: 301-309-0230 

Maglev Technology, Inc. 

14160 Saddle River Dr. 

Gaithersburg MD 20878 

Stephens Stuart Stephens 

Phone: 612-544-2721 

Fluidyne Engg. 

5900 Olson Mem. Hwy 

Minneapolis MN 55422 

Takahata Ryoichi Takahata 

Phone: 0729-77-4094 

Koyo Seiko Co., Ltd. 

Research & Development Center 

24-1 Kokubuhiganjyo-cho 

Kashiwara, Osaka 582 

JAPAN 

Tcheng Ping Tcheng 

Phone: 

NASA Langley Res. Cent. 

MS238 

Hampton VA 23665-5225 

Thevenot Wayne Thevenot 

Phone: 202-737-9300 

Maglev USA 

1455 Pennsylvania Ave. 

Washington DC 20024 

Shewfelt Kurt Shewfelt 

Phone: 

Allied Signal Aerosp. 

2525 W. 190th St. 

Dept. 35, MS T53 

Torrance, CA 90509 

Siegwart Roland Y. Siegwart 

Phone: 012563564 

Institute of Robotics 

Mechatronics Group 

ETH Zurich 

Zurich CH-8092 

SWITZERLAND 

StudEr Phillip A. Studer 

Phone: 301-593-7241 

Magnetic Concepts 

10313 Ridgemoor Drive 

Silver Spring MD 20901 

Tanaka Hisashi Tanaka 

Phone: 81-425-73-7205 

Railway Technical Research Institute 

2-8-38 Hikari-cho 

Kokubunji-shi 

Tokyo 

JAPAN 

Terentiev Alexander N. Terentiev 

Phone: 

Institute of Chemical Physics 

U.S.S.R. Academy of Sciences 

117977 Moscow 

U.S.S.R. 

Tozoni Oleg Tozoni 

Phone: 301-309-0230 

Maglev Technology, Inc. 

14160 Saddle River Dr. 

Gaithersburg MD 20878 

503 
504 

Trumper David L. Trumper 

Ph on e: 704-547-4324 

Univ. of North Carolina at Charlotte 

Precision Engineering - ARC 

Room 222 

Charlotte NC 28223 

Unman Prof. Daniel J. Inman 

Phone: (716) 636-2593 

Univ. of Buffalo 

Dept. of Mech and 

Aerosp. Engg. 

Buffalo NY 14260 

Vij Kewal K.Vij 

Phone: 403-250-4792 

NOVA Husky Research Corp. 

2928 - 16th Street N.E. 

Calgary, Alberta T2E 7K7 

CANADA 

Whitestone Robert C. Whitestone 

Phone: 301-267-3458 

David Taylor Research Center 

Code 2712 

Annapolis MD 21402 

Yeh Ting-Jen Yeh 

Phone: 

MIT 

77 Massachusetts Avenue 

Room 35-332 

Cambridge MA 02139 

617-253-2108 

2hao Hong-Bin Zhao 

Phone: 861-2561144-2594 

Tsinghua University 

Dept. of Engg Phys. 

Beijing 100084 

CHINA 

Tryggvason Bjarni Tryggvason 

Phone: 613-993-4106 

Canadian Space Agency 

P. O. Box 7014 

Station V 

Vanier Ontario KIL 8E2 

CANADA 

Vaidya Subhash R. Vaidya 

Phone: 215-758-7355 

Gardner Cryogenics 

2136 City Line Road 

Bethlehem PA 18017 

Wassermann Johann Wassermann 

Phone: VIENNA-58801-5478 

Technical University of Vienna 

Wiedner-Hauptstrasse 8-10 

Vienna A-1040 

AUSTRIA 

Won Dr. Dong-Yeon Won 

Phone: 042-820-2000 

Korea Atomic Energy 

Research Institute 

P. O. Box 7 

Daejun, 305-353 

KOREA 

Youcef-Toumi Kamal Youcef-Toumi 

Phone: 617-253-2216 

Massachusetts Institute of Tech. 

77 Massachusetts Avenue 

Room 35-233 

Cambridge MA 02139 

~dron Millard Zydron 

Phone: 804-688-8693 

Newport News Shipb 

E52B600 

4101 Washington Ave. 

Newport News VA 23607 

Total Number of Attendees 132 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

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1. AGENCY USE ONLY{Leave blan~) 12. REPORT DATE 

May 1992 

13. REPORT TYPE AND DATES COVERED 

Conference Publication 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

International Symposium on Magnetic Suspension Technology 

590-14-11-02 

6. AUTHOR(S) 

Nelson J. Groom and Colin P. Britcher, Editors 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

NASA Langley Research Center REPORT NUMBER 

Hampton, VA 23665-5225 L-17092 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING 

National Aeronautics and Space Administration AGENCY REPORT NUMBER 

Washington, DC 20546-0001 NASA CP-3152, Part 1 

11. SUPPLEMENTARY NOTES 

Nelson J. Groom: Langley Research Center, Hampton, VA; Colin P. Britcher: Old Dominion University 

Research Foundation, Norfolk, VA. 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

U nclassified-U nlimited 

Subject Category 18 

13. ABSTRACT (Maximum 200 words) 

In order to examine the state of technology of all areas of magnetic suspension and to review related recent developments in sensors and controls approaches, superconducting magnet technology, and design/implementation 

practices, a five-day International Symposium on Magnetic Suspension Technology was held at the Langley 

Research Center in Hampton, Virginia, on August 19-23, 1991. 

The symposium included 17 technical sessions in which 55 papers were presented. The technical sessions covered the areas of bearings, sensors and controls, microgravity and vibration isolation, superconductivity, manufacturing applications, wind tunnel magnetic suspension systems, magnetically levitated trains (MAGLEV), 

space applications, and large gap magnetic suspension systems. A list of attendees appears at the end of the 

document. 

14. SUBJECT TERMS 

Magnetic bearings; Magnetic suspension; Large gap magnetic suspension; Small 

gap magnetic suspension; Sensors, Superconducting magnetic suspension systems; 

Control systems 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATIOr. 19. SECURITY CLASSIFICATION 

OF REPORT OF THIS PAGE OF ABSTRACT 

Unclassified Unclassified Unclassified 

N:'N f:J4U·UJ-.lIIU-:J:JUU 

15. NUMBER OF PAGES 

513 

16. PRICE CODE 

A22 

20. LIMITATION 

OF ABSTRACT 

~tand~lr~ . t-orm .. 21'1!( I!.ev .. ~-I!!I) PreSCribed by ANSI Std. Z39-18 

298-102 

NASA-Langley. 1992