NASAContractor Report 1 8 1 7 2 6 

ADVANCED PILOTED AIRCRAFT FLIGHT 

CONTROL SYSTEM DESIGN METHODOLOGY 

VOLUME I: KNOWLEDGE BASE - 

(NASA -CB- 18 17 26 -VOL -1 ) 

AIRCRAFT PLIGHT CONTElOL SYSTEI DESIGN 

METHODOLOGY. VOLUPlli 1 : KbiOWLEDGE BASE Final 

Report [Systems Technology) 285 p CSCL 01C Unclas 

hl)W ANCE D PILOT ED N 8 9- 260 13 

G3/b8 0222709 

Duane T. McRuer and Thomas T. Myers 

Systems Technology, Inc. 

Hawthorne, CA 90250 

Contract No. NASI -1 7987 

October 1988 

I 

ir 

National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton, Virginia 23665-5225 
FOREWORD 

This report presents and illustrates the development of a comprehensive and eclectic methodology for conceptual and preliminary design of 

flight control systems. The methodology is focused on the design stages 

starting with the layout of system requirements and ending when some 

viable competing system architectures (feedback control structures) are 

defined. The approach is centered on the human pilot and the aircraft as 

both the sources of, and the keys to the solution of, many flight control 

problems. The methodology relies heavily on computational procedures 

which are highly interactive with the design engineer. To maximize effectiveness these techniques, as selected and modified to be used together in 

the methodology, form a cadre of computational tools specifically tailored 

for integrated flight control system preliminary design purposes. The 

computer aids are all based on IBM PC compatible machines and most are now 

commercially available. This helps make the methodology as broadly available and useful as possible instead of simply another isolated approach. 

As individual computational programs some of the design aids have 

very great value as system analysis, design and synthesis tools in 

general. Important contributions to one of the programs were made as part 

of this NASA Small Business Innovation Research effort. Other additions 

were inspired by needs of the methodology developments. Systems Technology, Inc., as a Phase I11 SBIR effort, supported this further development 

and the extensive efforts needed to make the programs commercially available. The important, now commercial programs, and their origins, are: 

Program CC. Version 3 -- developed by Peter Thompson, PhD, with later 

STI assistance, for educational, STI in-house, government, and 

industrial use. Several modules were developed under this NASA 

Phase I1 SBIR. 

Program CC. Version Q -- developed as an expansion and extension to 

Version 3 to set an entirely new standard for computer-aided 

control system design. This was supported entirely by STI and 

Peter Thompson, PhD as a Phase I11 effort. 

"LSMP" , Linear Systems Modeling Program - - an expanded and improved 

version of an STI-proprietary program developed over a period of 

many years for larger scale machines, adapted to a PC. The 

final development was also accomplished as an STI-sponsored 

Phase I11 activity. 

Peter Thompson is the author of both versions of Program CC. The forerunners of LSMP have many contributors through the years, although Wade 

Allen and Theodore Rosenthal made the crucial finishing touches during 

the STI-sponsored Phase I11 efforts. 

TR-1228-1-1 i 
A more limited initial software development was also accomplished as 

part of the design methodology. This is "FCX", a pioneering attempt to 

explore the use of expert system techniques, using a commercially available shell program ("LEVEL5") for PCs, for flight control system preliminary design. This was totally supported by the Phase I1 SBIR, and was 

accomplished by Thomas T. Myers assisted by Theodore Rosenthal, and David 

Klyde . 

In developing the design methodology and illustrations represented by 

this report the two named authors were principal contributors. They were 

ably supported on the software developments by the people noted above. 

Peter Thompson also contributed to the methodology in the area of robustness assessment as a coauthor of Supplement 1. To help establish and 

flesh out the design methodology an "expert team" was established early in 

the project. This comprised the first-named author, and two internationally recognized experts -- Dunstan Graham, formerly of Princeton University, to provide a leavening influence on flight control, and John Wykes, 

formerly of Rockwell International, as a leading expert on structural 

dynamics/flight control system interactions. Their aid in formulating 

important questions and their careful review of the methodology played an 

important role in the project. 

The authors have been greatly assisted in their task by many fruitful 

technical exchanges with Mr. Jerrell Elliott, of NASA Langley Research 

Center, who was the NASA Technical Manager for this SBIR. Jerry made many 

constructive technical suggestions. We had other helpful discussions with 

others at Langley, including Richard Hueschen and John McMannus on formulation of rules and expert system implementation, and with Dr. Steven 

Sliwa on functional systems integration. 

As a final note in this foreword it is pertinent to express our 

appreciation to the unknown (to us) people who made it possible for STI to 

undertake this Phase I1 SBIR program. It permitted us to develop a methodology for preliminary design which we use in our consulting efforts with 

industry, to expand our analytical and synthesis computational tools, to 

develop and apply some new and relevant theory, explore and pioneer an 

application of the potentially fruitful new technology of expert systems, 

and has provided some support in developing novel and innovative state of 

the art computer programs. Perhaps most importantly from the standpoint 

of those who originated the SBIR idea, the Phase I and Phase I1 support by 

NASA inspired STI to extend several of the innovations with its own funds 

as a Phase 111 SBIR effort. It is still too early to say whether this 

last phase will have a happy ending, but we're hoping! In the meantime, 

STI is grateful to NASA for the opportunity! 

TR-1228-1-1 ii 
TABLE OF CONTENTS 

VOIIRIE I 

I. INTRODUCTION, APPROACH, AND PRELIMINARIES AND 

OUTLINE OF THE DESIGN METHODOLOGY... ......................... 1 

A. General Background ....................................... 1 

B. Computational Aids ....................................... 3 

C. Preliminaries ............................................ 6 

D. Fundamental Considerations ............................... 7 

E. Summary of Features Needed in Methodology ................ 11 

F. Fundamental Natures of Flight Control Systems 

[Controlled Element, Controller, 

and Their Combinations] .................................. 13 

G. Steps in the Preliminary Design Process .................. 20 

H. Level Detail Available at the End of the FCS 

Architectural Development ................................ 37 

I. Preview of What is to Come ............................... 40 

11. MISSION-BASED REQUIREMENTS FOR LATERAL-DIRECTIONAL 

FCS OF HIGH PERFORMANCE AIRC RAFT............................. 43 

A. Mission-Centered Flying Qualities Requirements ........... 45 

B. Mission-Centered Path and Heading Control Requirements ... 46 

C. Implied Requirements for Coordinated Maneuvers ........... 52 

D. Mission-Based Requirements in the 

Flight Control Design Software ........................... 53 

E. Command and Disturbance Characteristics .................. 54 

111. HIGH PERFORMANCE AIRCRAFT LATERAL-DIRECTIONAL 

CHARACTERISTICS .............................................. 59 

A. Airplane Equations of Motion ............................. 60 

B. Numerical Characteristics for the Example Airplane ....... 62 

C. Literal Approximate Factors for the Airplane 

Characteristics .......................................... 69 

IV. IDENTIFICATION OF CONTROL OF LATERAL-DIRECTIONAL 

CONTROL PROBLEMS.DUE TO THE AIRPLANE ......................... 85 

A. General Path and Heading Control Problems ................ 85 

B. General Roll Control Problems ............................ 91 

C. Pilot Control Problems ................................... 92 

D. Summary of Airplane Dynamic Shortcomings 

and Equalization Needs ................................... 94 

TR-1228-1-1 iii 
TABU OF CONTENTS (CONTINUED) 

Page 

V. PROSPECTUS FOR LATERAL-DIRECTIONAL FLIGHT CONTROL 

SYSTEM ARCHITECTURE .......................................... 97 

A. Equalization Requirements for Control 

Systems in General ....................................... 98 

B. Prospectus for Flight Control System Architecture ........ 100 

C. Prospectus for Augmentation to Alleviate 

Basic Aircraft Dynamic Deficiencies ...................... 104 

VI. PRELIMINARY DESIGN OF CANDIDATE LATERAL-DIRECTIONAL 

FIGHTER FLIGHT CONTROL SYST .................................. 117 

A. Actuation and Sensing .................................... 120 

C. Roll Damper Design ....................................... 127 

D. Bank Angle Control Loop .................................. 134 

B. Yaw Damper Design ........................................ 120 

E. What Next?....... ........................................ 138 

REFERENCES ....................... .................................. R-I 

Note: Supplements have their own pagination. 

SUPPLEMENT 1. LITERAL SINGULAR-VALUE-BASED FLIGHT CONTROL 

SYSTEM DESIGN TECHNIQUES ............................ 1 

Introduction .................................... 1 

Example Problem ................................. 3 

to Input Uncertainties .......................... 5 

Robustness of Stability with Respect 

Motivation for Literal Formulations ............. 13 

Literal Approximations of Open-Loop 

Singular Values ................................. 15 

Literal Formulation of the Robust 

Stability Criterion. ............................ 20 

A Literal Approximation of Structured 

Singular Values ................................. 24 

Summary and Conclusions ......................... 25 

Acknowledgement ................................. 26 

References ...................................... 27 

V 

TR-1228-1-1 iv 
TABLE OF CONTENTS (CONCLUDED) 

Page 

SUPPLEMENT 2. LATERAL FCS REQUIREMENTS-ORIENTED DESIGN 

KNOWLEDGE BASE FOR AN ADVANCED STOL 

FIGHTER IN MISSION PHASE CO ......................... 1 

A. General ......................................... 1 

B. Topic 1 -- Flight Control System Purpose ...... 3 

C. Topic 2 -- Command and Disturbance 

D. Topic 3 -- Unalterable Characteristics 

Characteristics. ................................ 11 

of the Aircraft and Controller .................. 16 

E. Topic 4 -- Pilot-Centered Requirements ........ 22 

References. ......................................... 27 

SUPPLEMENT 3. PILOT-CENTERED REQUIREMENTS AND HUMAN PILOT 

A/FCS INTERACTIONS. ................................. 1 

Body Characteristics ............................ 3 

Pilot Equalization .............................. 30 

A. Effective Vehicle Dynamics and Flying 

Qualities Requirements -- Rigid 

B. Conditions for Acceptable (or Minimum) 

C. Conditions Antithetical to 

D. Minimization of Remnant Excitation of 

E. Minimization of Pilot Effective Aircraft 

Pilot-Induced Oscillations ...................... 32 

Flexible Modes .................................. 33 

System Closed-Loop Excitation of 

Flexible Modes .................................. 34 

F. Reduction of Vibration Feedthrough .............. 35 

References .......................................... 37 

APPENDIX A. THE MULTI-VARIABLE ANALYSIS METHOD .................... A-1 

APPENDIX B. SENSITIVITY VECTORS ................................... B-1 

APPENDIX C. ELEMENTAL SYSTEMS ..................................... C-1 

TR-1228-1-1 V 
LIST OF FIGURES 

Page 

1 . Fundamental Considerations .................................... 8 

2 . Features Needed in Methodology ................................ 11 

3 . Airplane Properties ........................................... 15 

4 . Controller Properties ......................................... 17 

5 . Generalized Flight Control System for Fighter Aircraft 

Including Flexible Modes ["Effective Aircraft. " 

as Seen by the Pilot] ......................................... 18 

6 . Typical Design Phases for Multi-variable Flight 

Control System Synthesis at the Architectural Level ........... 22 

7 . System Preliminary Design Methodology Flow Diagram ............ 23 

8 . Typical Design Phases for Multi-variable Flight Control 

System Synthesis at the Detailed Design Level ................. 24 

9 . First Step in Flight Control Requirements Evolution ........... 25 

10 . Candidate Flight Control System for a 

Highly Unstable Fighter Aircraft .............................. 38 

11 . System Survey Indicating the Infeasibility of Path 

Control with a Pure Gain X + 6, Loop .......................... 49 

12 . Survey of Bare Aircraft Response to Roll Control .............. 86 

13 . Generic Roll Control System for Path Control .................. 88 

14 . 

15 . 

Survey of Response to Roll Command with High Gain 4 + 5, ...... 90 

System Survey of Pure Gain 4 + 6, Closure 

Around Bare Aircraft .......................................... 93 

16 . Elements of the Prospectus .................................... 102 

17 . Some Opportunities for Aircraft Tailoring ..................... 105 

18 . Low Gain Control Prospectus from Sensitivity Vectors .......... 107 

19 . Candidate Lateral FCS Design ................................... 118 

20 . Effect of Washout Variations on the Poles 

in the Yaw Damper Closure ..................................... 122 

TR-1228-1-1 vi 
LIST OF FIGURES (CONCXJDED) 

Page 

21. Effect of Yaw Damper Closure on Denominator .................. 123 

22. Effect of Yaw Damper Closure on Nib,.. . .. ... ...... . . . . . . . . . . . . 124 

23. Effect of Pure Gain Roll Damper Closure 

on Denominator - Yaw Damper Closed ........................... 128 

24. Effect of Roll Damper Closure with Lead-Lag Compensation 

on Denominator - Yaw Damper Closed ........................... 129 

25. Response to 1 deg Aileron Step Yaw 

and Roll Dampers Closed ...................................... 132 

26. Response to 1 deg Rudder Step ................................ 133 

27. Response to a 1 deg Aileron Step, Yaw and Roll 

Dampers Closed, Crossfeed On. ................................ 135 

28. Bank Angle-to-Roll Control Frequency Response ................ 136 

29. Closure of the Bank Angle Control Loop ....................... 137 

30. Bank Angle Response to Bank Angle Command, 

Complete System .............................................. 138 

UST OF TABLES 

Page 

1. Mission Phase-Control Needs Matrix for Advanced Fighter ....... 26 

2. System Architectural Possibilities and Mechanizational 

Side Effects for Superaugmented Aircraft ...................... 39 

3. Compilation of Mission-Centered FCS Design-Crictical 

Requirements .................................................. 47 

4, Requirements Window ........................................... .55 

5. Flight Control System Inputs; Application Point 

and Source (Adapted from Ref. 1) .............................. 57 

6. Lateral Directional Aircraft Equations of Motion .............. 61 

7. Reference Flight Condition .................................... 62 

TR-1228-1-1 vi i 
LIST OF TABLES (CONCIIJDED) 

8 . 

9 . 

10 . 

11 . 

12 . 

13 . 

14 . 

15 . 

16 . 

17 . 

18 . 

19 . 

20 . 

Page 

Summary of Aircraft Alone Characteristics .................... 64 

Aircraft Basic Data .......................................... 65 

Flight and Trim Conditions ................................... 65 

Stability and Control Derivatives ............................ 66 

Characteristic Modes ......................................... 66 

Transfer Function Numerators ................................. 67 

Coupling Numerators .......................................... 68 

Approximate Factors for Lateral-Directional 

Characteristic Function (Stability Axes) ..................... 71 

Literal Approximate Factors-Denominator ...................... 72 

Approximate Factors for Lateral-Directional 

Numerators (Stability Axes) .................................. 77 

Approximate Factors Calculations Spreadsheet Window .......... 79 

Lateral/Directional Essential Feedbacks ...................... 103 

Design Assessment ............................................ 139 

TR-1228-1-1 

c 

viii 
SECTION I 

INTRODUCTION, APPROACH, AND PRELIMINARIES 

AND 

OUTLINE OF THE DESIGN METHODOLOGY 

4 A. GENERAL BACKGROUND 

Our goal in this report is to formulate and illustrate a commehensive methodology to establish feedback architectures for advanced aircraft 

flircht control systems (FCS). Although the analysis and synthesis tools 

in the methodology are useful at all stages of FCS design and development, 

the focus is on the early stages of conceptual and preliminary design. 

This emphasis comes from a recognition that flight control is a major 

player in the new age in aeronautical technology wherein the very early 

integration at a highly dynamic level of many system elements is essential 

to achieve a well-tempered aircraft. At present, control is commonly used 

to redress aerodynamic stability and control deficiencies, and to improve 

overall aircraft performance potential. As Dynamic Systems Integration 

becomes prevalent, control technology increasingly becomes the glue which 

ties together many aeronautical technical disciplines to accomplish highly 

interrelated functions - functions which were hitherto either nonexistent or only marginally associated with one another. Future Flight 

Control Systems will encompass many of the dynamic aspects traditionally 

associated with airframe stability and control, structures (both quasistatic as in maneuver load control; and dynamic as in flexible mode control and gust alleviation), and propulsion. A wide variety of guidance 

features such as automatic fire/flight control and four-dimensional en 

route and terminal navigation, have also acquired a dynamic intimacy with 

FCS. To cope efficiently with this level of dynamic interaction requires 

a design methodology which can: illuminate the many interactions between 

the several subsystems; show the way for configuration tradeoffs between 

aircraft-alone dynamics and automatic controllers; provide data for comparisons between various controller possibilities ; and expose the subtle 

problems inherent in such high degrees of interconnections - all at the 

earliest possible time. 

TR-1228-1-1 1 
The methodology presented is a unified combination of theories, 

emerging computational technologies, empirical data, lore, and practical 

experience -- a mixture of science and art. Considering theory first, we 

should note that many control theories exist, and most have been tried at 

one time or another in illustrative exercises with aircraft dynamics as 

the plant. Yet very few are applied to flight control analysis and synthesis in practice. A useful theory must cope with many complexities, as 

well as often conflicting and incommensurate requirements unique to the 

flight control problem. These include: 

0 accommodation of human pilot 

0 varieties of missions and operating points 

complexity in controlled element dynamics (e.g., 

flexible modes, nonlinear aerodynamics) 

0 complex controllers (e.g., multiloop control 

structures, task-tailored control modes, digital 

components, control effector limits) 

0 multiple function controller elements which have 

both independent and subsidiary status in the 

total FCS (e.g., controllers for stability augmentation which also supply inner loop equalization for guidance loops) 

0 multi-task, multi-desires, qualitative and quantitative requirement statements 

0 a wide cross-section of transient and random 

commands and disturbance functions 

Because of all these complicating factors it is no surprise that many 

theories are found wanting; indeed no single approach is sufficiently 

comprehensive to handle everything, especially when major nonlinear features are present. Nonetheless, a primary thrust in this report is the 

selection and illustration of an eclectic set of theoretical approaches 

for flight control system synthesis and analysis that specifically address 

the features intrinsic to such systems. The techniques adopted are based 

on linear control theory. This is appropriate to the earliest stages of 

preliminary design in that they apply to the small perturbation dynamics 

of the airplane-FCS combination which have to be resolved before more 

L 

TR-1228-1-1 2 
esoteric fundamentally nonlinear phenomena can fruitfully be considered. 

Also, a factor in selecting the techniques to be used is that they should 

be capable of extension in later studies to handle many of the important 

nonlinear phenomena in flight control, e.g., by use of equivalent linearization procedures, such as describing functions. 

B. COMPUTATIONAL AIDS 

To be viable as a design methodology the theories selected must be 

accompanied by appropriate computational aids. In this respect emerging 

concepts and commercially available computer programs from the everexpanding micro-computer technology base have completely changed the possibilities for design. This is especially true for efficient preliminary 

design, which requires a combination of experienced and imaginative engineering to accomplish the system-architect function. Because of the 

interactions with other technlcal disciplines, the complexities of the FCS 

subject itself, the incommensurate and often competitive or conflicting 

criteria and desires, and the unknowns and uncertainties, preliminary 

design has always been an iterative and artistic process. More often than 

not it has also been accomplished by a committee, with unavoidable time 

lags and compromises which can result in less than an optimal overall 

design. For the forthcoming era of more dynamically-integrated elements 

and technologies within the purview of flight control the design engineerarchitect needs a set of computing tools which are not only capable of 

interaction among themselves but, most importantly, are suitable for 

interactive and highly-iterative operations with the engineers involved. 

The selection, development, and appropriate connection of computer programs for this purpose has been a major goal of the project. It was 

intended from the beginning that the computer aiding would be accomplished 

on PC compatible machines, and that the constituent programs would be 

readily available to potential users, At the time this plan was based on 

hope and projections of what might become available during the course of 

the project. 

We have been able to "mechanize the design methodology" using a 

variety of computer tools which are suitable for highly user-interactive 

TR-1228-1-1 3 
activities on PC class machines. The software developments made in this 

project constitute a flight control system design package referred to as 

FCX. This package has two coupled components - a rule-based expert 

system, the "FCX flight control design expert system" and an algorithmic 

computer-aided control system design (CACSD) program, Program CC. The FCX 

flight control design expert system was our first attempt to explore the 

potential of knowledge-based concepts to control system design and specifically to flight control design. The result is a quite limited prototype, but this effort has answered a number of questions about the potential of expert systems for flight control design, their relation to 

existing highly developed algorithmic CACSD software, and specific implementation approaches. Our conclusion is that, while a great deal of work 

must be done, expert system concepts can, should and very likely will make 

a significant contribution to flight control design. 

The FCX rule-base with about 160 rules at this point captures only a 

small portion of the knowledge base contained in this report. However, 

this is enough to answer in the affirmative what we believe is the most 

critical question about this application of expert systems - i.e., can 

knowledge of the physical principles and design concepts of aircraft 

flight control systems be implemented in a useful way. That is, can 

expert systems provide more than just an "intelligent interface" for conventional algorithmic CACSD programs. We are now confident the answer is 

yes and have a prototype with which to carry this effort forward. 

The algorithmic CACSD component which is presently coupled to the FCX 

expert system is STI's Program CC, Version 3. "Program CC" is a control 

system analysis, synthesis, and design package originally developed for 

academic instructional use. It has since been greatly extended to provide 

a comprehensive selection of the many tools and algorithms essential for 

control system theory and practice. These include classical (transfer 

function based) and modern (state space), frequency and time domain, 

single and multiple input/output, continuous and sampled data control 

system analysis and design techniques. Observers, Kalman filters, classical Bode and conventional root locus, pole-placement, singular value and 

structured singular value techniques, etc. are all present. Of particular 

TR-1228-1-1 4 
c 

importance for advanced flight control system design is the coverage of 

several multi-variable analysis/synthesis and robustness assessment procedures, as well as multi-rate digital techniques. 

Most of the modules in Program CC, Version 3, were developed before 

the project began. To provide the additional analysis/synthesis/ 

assessment procedures needed for the design methodology it was supplemented with several modules partly supported by this Phase 2 SBIR and 

partly by Systems Technology, Inc. Program CC, Version 3 is commercially 

available and has found many users in academe, governments, and industry. 

Additional modules and improvements which support the design methodology 

have been added to Version 3 features, along with much other capability, 

to form Program CC, Version 4. The development of Program CC, Version 4 

has been supported by Systems Technology, Inc. and Peter Thompson, PhD, as 

a Phase 3 SBIR effort. Program CC, Version 4 has recently become available.commercially. The FCX expert system was totally developed as part of 

the Phase 2 SBIR effort using the LEVEL5 expert system shell from Information Builders, Inc. Because of the RAM memory requirements of LEVELS, the 

FCX expert system can not yet be coupled to Program CC, Version 4. 

In FCX the programs noted above are supplemented with a spreadsheet 

database element for "SYMPHONY", by Lotus Development Corporation. This 

program is not fundamental to the exercise of the design methodology (the 

three programs above, or their equivalent, a essential). The total computing aid package can be supported on an MS-DOS IBM PC compatible personal computer with 20 MB hard disk and 640K RAM. As individual, commercially viable, programs they exhibit a great number of user friendly 

features, so the expert FCS preliminary design engineer need not be a 

computer expert as well. The FCX flight control system design package, 

expert system and associated programs are discussed in detail in Volume 2. 

One final program needs to be mentioned here - LSMP, STI's Linear 

System Modeling Program. This program has specialized features for modeling complex vehicle systems. It was used in the early work on the 

project, but was not part of the software development. LSMP operates with 

sets of vehicle and control system equations as simultaneous equations in 

which any component block can be as complex as a ratio of two second-order 

TR-1228-1-1 5 
terms. It delivers factored transfer function elements of all kinds - 

denominators, numerators, "coupling numerators, " etc. Thus, vehicle equations of motion, which typically involve second-order terms, are handled 

naturally in the form in which they were originally derived. Control 

system elements are also readily incorporated into the same structure. 

LSMP's outputs include cell displays and matrix listings, transfer function displays, frequency response Bode plots, and single- or multi-trace 

transient response plots. LSMP can provide transfer function files in 

Program CC format. While LSMP's specialized features make it the primary 

vehicle modeling task at STI, Program CC state space modeling capability 

is more than adequate for the present FCX development. 

C. PRELIMINARIES 

While theory and associated computational means are an important 

aspect of the design methodology, the lore, knowledge and experience elements, which guide and govern applications are critical features. This 

material is presented here as summary tables, outlines, recipes, empirical 

data, lists, etc., which encapsulate a great deal of expert knowledge. 

Much of this is presented in topical "knowledge summaries" which are 

attached to the report as "Supplements." The composite of the supplements 

and the report main body elements constitutes a first cut at a "Mark 1 

Knowledge Base" for manned-aircraft flight control. 

The steps in the design methodology are broadly outlined later in 

this introduction. To help put flesh on this general skeleton the steps 

are then illustrated in the next sections by a specific concrete example. 

This will consider a design point for a lateral-directional FCS for a high 

performance fighter. To keep the flow as easy to follow as possible, 

pertinent knowledge base elements, picked out of the supplements and key 

references, are inserted into the example at points where they are most 

re levant. This development constitutes the next five sections of the 

report plus the first supplement. 

In formulating an adequate flight control system design methodology, 

we have considered many things. Many of these appear naturally in their 

own technical context, and will be described in the appropriate technical 

J 

TR-1228-1-1 6 
sections, supplements, and appendices following. Others are intrinsically 

introductory to the subject. These will be presented as separate articles 

in this introduction. The first two topics are philosophical preliminaries which have been considered in laying out the methodology and 

selecting its constituent analysis and computing tools. These are, 

Fundamental Considerations to take into account in 

selecting the design methodology 

What Features 'are Nee ded in the Methodology? 

Because the design methodology is intended for flight control systems as 

contrasted to control systems in general it is pertinent to describe some 

of the peculiar aspects of flight control that require special treatment. 

This is done in an article on 

The Fundamental Natures of Flieht Control Sv stems 

Finally, after these preliminaries describing the idiosyncracies of 

flight control and what special factors need to be accounted for in a 

suitable design methodology, we turn to the subject of the methodology 

itself. This is introduced and outlined in, 

Phases (Stem) in the DeveloDment of a Flieht Control 

Svstem Architecture at the Preliminary Desien - Level 

An immediately following article gives a brief illustration of a longitudinal controller as a typical output from an exercise of the methodology. 

This initial chapter is then concluded with a preview of what $s to 

come in the remaining sections, supplements, and appendices of the report. 

D. FUNDAMENTAL CONSIDERATIONS 

The broad "Fundamental Considerations, It set forth to provide a welldefined philosophical base to underlie our approach to the design methodology, are listed in Fig. 1. The considerations and part of their impact 

on methodology requirements are summarized below. 

TR-1228-1-1 7 
Figure 1. Fundamental Considerations 

1. The Aircraft as the Central Element in Flight Control 

Aircraft as Central Element 

Computational and Presentation Aspects 

Multi-variable Systems 

Mission, Functional Requirements, 

and System Integration 

Human Pilot Interfaces 

Continuous and Discrete Elements 

The primary thesis for the approach adopted here is that AIRCRAFT 

flight control systems have many peculiar features which differentiate 

them from most other control systems - and that these features require 

special treatment in analysis, design, and synthesis. The study of bare 

aircraft dynamics, stability, and control - described by multi degree-offreedom dynamics which are non-linear and time-varying, and characterized 

by parameters which are highly variable and sometimes uncertain - is a 

technical discipline in its own right. The many interactions and connections between aircraft parameters and dynamic behavior treated in this 

discipline serve as starting points for control considerations. In this 

perspective, the aircraft is simultaneously the source of flight control 

problems, and the to their solution. Reflecting this central position 

of the aircraft dynamics in flight control, the control system analysis 

techniques chosen for the design methodology should be specially selected 

TR-1228-1 -I 8 
. 

i 

to focus on the idiosvncracies of air vehicles, and the effective exposure 

of the impact their properties have on flight control system behavior. 

Consistent with this perspective, procedures are desired which have 

direct connections with the aircraft stability and control discipline, 

enhance fundamental physical understanding, help develop insight, and 

provide enlightenment about the many subtleties and mysteries encountered 

in the airplane dynamics and their impact on complex flight control systems. For example, the methodology places heavy stress on the ability to 

relate the airplane’s poles and zeros to their physical origins in terms 

of aerodynamic stability derivatives, preferably in symbolic terms. 

2. Computational and Presentation Aspects 

in Selection of the Methodology 

- Flight control problems are of such high dimensionality and complexity that simply getting viable answers to design questions has in the past 

demanded major computational efforts. Now, however, with modern computers 

calculation no longer poses major difficulties. 

But presentation of results, so they can be easily assimilated and 

understood, remains elusive. Extensive tables of easily computed numerical results can be dreadful hodgepodges without a meaningful graphical 

presentation. In selecting the elements of the design methodology, great 

emphasis is placed on pictorial presentations which permit the ready comprehension of results and illuminate and expose key interactions. Provision of insight and understanding, coupled with easy interpretation, are 

the chief criteria for selecting data presentation formats. For example, 

for insight-provoking visualization the pictorial forms selected include: 

transient responses to appropriate inputs; conventional s-plane root loci; 

and jw Bode frequency responses; unconventional Bode root loci and timevector/sensitivity diagrams. Some of these used to be means to an end - 

graphically computed answers to then difficult analysis/synthesis questions; they now serve a different but still primary role - as pictures 

which DrOVide meaningful Dr esentations of a vast array of numerical 

results. 

TR-1228-1-1 9 
3. Multi-Variable Systems 

Aircraft have many degrees of dynamic freedom so flight control systems are usually multiloop and multi-effector (control point) in nature. 

Because the aircraft dynamics are the central issue in flight control 

system design, novel constraints are imposed on the types of multivariable system analyses which are most useful in the preliminary design 

stage. Most importantly, the methods should be effective in showing the 

way to set up possible system architectures, in illuminating the relative 

benefits and liabilities of competing systems, and in exposing possible 

problems for future detailed examination. For the detailed design phases, 

there may also be a role for techniques which are highly efficient computationally, but which may be more specialized and narrow in scope. 

4. Interrelationships with Mission and Functional 

Requirements and Systems Integration 

Vehicle control in its most general context translates mission 

requirements into mission accomplishment. The mission purposes and tasks 

directly specify part of the FCS architecture and imply other parts. 

Because of this cause-effect relationship, there are very important, 

albeit often subtle, tradeoffs between mission requirements and the control system. These explicit and implicit connections between the overall 

system requirements and the FCS need to be clearly drawn and understood in 

the context of the methodology. 

5. Human Pilot and Flying Qualities Aspects 

A major complication in flight control systems for manned aircraft is 

the presence of the human pilot. The pilot is simultaneously a competitor 

with, or backup for, the automatic control elements for some controller 

functions, and the customer for the beneficial effects of automatic 

control in improving the effective vehicle dynamics. Thus, a major challenge for the methodology is the inclusion of the highly adaptive human 

pilot as a control element and evaluator of the flying qualities of the 

aircraft + flight control system. Further, the analysis procedures should 

TR-1228-1-1 10 
accommodate the compromises associated with dividing assigned functions 

between the human pilot and automatic equipment. 

6. Digital Controllers 

Many modern flight control systems contain digital controllers. Also 

the detailed design phases of flight control system development invariably 

include extensive real-time simulations with actual FCS hardware and/or 

human pilots, wherein the aircraft and other continuous system elements 

are replaced by digital computer surrogates. Consequently, the peculiar 

behavioral features of discrete as well as continuous system elements must 

be accommodated and illuminated in the design methodology. 

E. SUMMARY OF FEATURES NEEDED IN METHODOLOGY 

The fundamental considerations given above describe the broad perspective and underpinnings of our approach. A specification for the 

design methodology requires more detailed considerations in the several 

areas listed in Fig. 1-2. The abbreviated general headings given there 

are elaborated in the following outline "Specification for Methodology 

Features. It 

Capabilities 

Incorporation of the Human Pilot 

Evolution and Traceability of 

Requirements and Trades 

Designer-Centered Desires 

Pigure 2. Features Needed in Methodology 

TR - 12 2 8 - 1 -1 11 
1. Adequate for Present and Future Needs, Wide Range of 

Applications, and Preliminary and Detailed Design. 

a. Serve as the analytical glue which ties together 

other technical disciplines which involve control, e.g., 

(1) vehicle dynamics which incorporate flexible 

modes and nonstationary aerodynamics 

(2) integrated flight/propulsion control 

(3) integrated flight/fire control 

(4) effective vehicle flying qualities 

b. ADDliCable to a wide variety of aircraft - 

airplanes, rotorcraft, heavy-lift airships, aerospace planes, etc. 

c. Techniques appropriate for preliminary and 

detailed design phases. 

(1) broad-gauged insight/system architecture/ 

tradeoff intensive procedures for preliminary design and continuing understanding 

(2) more narrowly constrained, computationally 

efficient, simplified system procedures for 

extensive number crunching in detailed 

design 

2. Control System Analysis Procedure CaDabilities 

a. 

b. 

C. 

d. 

e. 

f. 

TR-1228-1-1 

Multiloop/multi-control point. 

Central importance of air vehicle properties, 

peculiarities, and needs. Maximize use of understanding of special characteristics of aircraft 

as plant. 

Multiple but interrelated FCS system and subsys - 

tem configurations. Mission-phase tailored system dynamics. 

Emphasis on all major vehicle output response 

properties and their degree of harmony. 

Focus on deducing key uncertainties and sensitivities in controlled element parameters. 

Detailed robustness assessment. 

12 
3. 

4. 

5. 

Incorporation of the Human Pilot as an Element in the Overall System 

a. Role allocations between pilot and automatic 

system elements. 

b. Coupling of effective vehicle and pilot models 

for development of pilot-centered requirements on 

the FCS and assessment of pilot-vehicle system 

behavior. Interpretation and implementation of 

flying quality requirements. 

c. Provide tools to interpret pilot behavioral 

data and comments from simulations and 

flight test. 

Clear Cut Evolution and Traceability of Reauirements and 

Tradeoff/Comoromise Possibilities 

a. Mission-dependent direct and implied requirements 

and FCS architectural consequences; 

b. Configuration tradeoffs between airframe and 

flight control. 

Designer-Centered Desires 

a. Easily comprehended pictorial presentations which 

provide maximum physical insight at each step of 

design, reveal and treat implicit requirements, 

help detect conceptual errors, etc. 

b. Good qualitative and quantitative understanding 

of tradeoffs. 

F. FUNDAMENTAL NATURES OF FLIGHT CONTROL SYSTEMS [CONTROLLED 

ELEMENT, CONTROLLER, AND THEIR COMBINATIONS] 

The point has been made as a "Fundamental Consideration" that flight 

control systems for aeronautical vehicles are a peculiar and unique subset 

of all control systems, and demand theories and techniques for synthesis 

and analysis which specifically cater to their peculiar characteristics. 

In tailoring a methodology for flight control analysis/synthesis purposes, 

a logical first step is to identify those features and peculiarities of 

flight control systems and their constituent elements which lead 

specialized needs. The following summary provides some of the unus 

and/or governing characteristics of the aircraft, the controller, 

TR-1228-1-1 13 

t 
their combinations which distinguish a FCS as a system apart from other 

control systems. 

1. Controlled Element - The Airframe 

As an object of control, the airplane is remarkably contrary. It 

includes the properties listed in Fig. 3. 

The major variations in aircraft dynamic characteristics are known in 

form and kind as direct functions of the flight condition defining the 

variables: dynamic pressure (4) , Mach number (M) , angle-of-attack (a), 

weight (W), and sometimes wing sweep, sideslip (B), and effector trim 

positions. To the extent that these variations are known and affect such 

dominant system characteristics as open-loop crossover-region properties, 

they can be "compensated" for by virtue of programmed adjustments in the 

controller (e.g., common airspeed compensation of gains). Sometimes a 

portion of these known or foreseeab'le variations can be considered in the 

design process in the same way as tolerances and unknowns must be; that 

is, as uncertainties with which the system designer must cope. 

Some variations and uncertainties are more important than others. 

This is true even if the absolute values or the percentage of nominal of 

the uncertainties are the same. Whether an uncertainty is important or 

insignificant depends primarily on the poles and zeros of the vehicle 

transfer functions which the uncertainty affects, and on the closed-loop 

system architecture. For example, if variation (including nonlinearity) 

or uncertainty in a particular aerodynamic stability derivative affects 

poles or zeros which occur where the amplitude ratio of one or more of the 

control loops is very large (i.e., well away from a crossover region), 

this variation will be insignificant. (An exception to this rule can 

occur when a zero is in or can, when uncertainties are included, be driven 

nto the right hand plane.) On the other hand, those variations and 

certainties which affect poles and zeros in the crossover regions of the 

lous loops can be critically important to the stability and robustness 

0 !e design. This distinction is extremely important in flight control 

I s, for it places great emphasis upon a detailed knowledge and under- 

; of those aircraft dynamic features which have major impact on the i 

I 14 
COMPLEX DYNAMICS: at a specific equilibrium flight condition, 

six degrees of rigid-body freedom and an indefinite number of 

flexible aeroelastic modes, many potentially subject to control. 

DELIBERATELY UNSTABLE DYNAMICS: particularly on modern craft 

where performance advantages dictate unstable cog. locations and 

reduced size stabilizing structures. 

WIDE RANGE of nominal DYNAIUC CHARACTERISTICS because of: 

-- Extent of total flight envelope 

-- 

FURTHER POTENTIAL EXTENDED RANGE OF DYNAMICS due to UNCERTAINTIES 

because of: 

-- Intangible unknowns in estimation and measurement of aeroNo n 1 i ne a r a e r ody n ami cs 

dynamic characteristics 

Unanticipated additions to the configuration (e.g., new 

stores, appurtenances, unconventional loadings, etc.) 

-- 

-- Manufacturing and maintenance tolerances. 

-- Operational malalignments (egg., asymmetric stores, nonflight-critical damage, etc.). 

LIMITED CONTROL POWER 

Figure 3. Airplane Properties 

TR-1228-1-1 15 
closed-loop dominant modes. Such understanding permits the flight control 

designer to determine for a particular design just what aerodynamic and 

other variations and uncertainties are important, and conversely what 

types of system architectures may be more or less sensitive to particular 

aerodynamic variations and uncertainties. Robustness assessment techniques appropriate for multi-variable systems are particularly valuable in 

improving the designer’s understanding of these matters. 

2. The Controller 

The controller component of a flight control system has many unusual 

characteristics. A summary listing is given in Fig. 4. 

The controller properties noted are in the main similar to those of 

other control systems in kind, although they have marked differences in 

degree. By far the most important of these from the standpoint of a comprehensive methodology are the multi-variable and building’ block natures 

of flight control systems. All of the features of multiple loop control 

presented under the first listed item are common in flight control, and 

the analysis/synthesis techniques must exhibit and provide insight into 

these vehicle/controller interaction Dossibilities. Similarly, the building block character, wherein the outer control loops for one operational 

mode are inner control loops for another, is invariably an important consideration. This is particularly the case with systems which for flight 

safety require a great deal of redundancy, thereby placing a major premium 

on simplicity of mechanization for individual channels. Also, for modern 

superaugmented aircraft, wherein the flight control system is used to 

redress the stability and control imbalances associated with large 

airframe-alone instabilities, the actuator rate and position limits can 

have an importance unparalleled in other control applications. 

3. The Closed-Loop Flight Control System 

The block diagram of Fig. 5 illustrates a generalized flight control 

system for longitudinal control of a high performance fighter aircraft. 

The aircraft dynamics comprise both rigid body and flexible modes excited 

TR-1228-1-1 16 
MULTI-VARIABLE CONTROL, in that control laws are multiloop 

(functions of more than one aircraft output variable) and/or multicontrol point (applied to one or more control effectors). When 

contrasted with single loop flight control systems, multi-variable 

systems exhibit one or more of the following features: 

-- Control is imposed on more than one degree-of-freedom, 

simultaneously and to independent specifications. 

Decoupling of control inputs and/or controlled element output 

variables. 

transfer function relating the primary output variable(s) to 

control input(s). 

Adjustment of the zeros of the effective controlled element 

transfer function relating the primary output variable(s) to 

control input(s). 

transfer functions relating specified output variables to 

disturbance inputs. 

control.) 

Reduction of unwanted disturbances as they reflect to a given 

control effector input (e.g., by complementary filtering of two 

different sensors). 

-- 

-- Adjustment of the poles of the effective Controlled element 

(A feature shared with single loop control.) 

-- 

-- Adjustment of the zeros of certain effective controlled element 

(A feature shared with single loop 

-- 

WELL-KNOWN AND UNDERSTOOD CONTROLLER ELEMENTS. These include: 

-- Controller elements with very small or essentially no 

uncertainties (e.g., many sensors, computational elements, 

etc.). 

present which cannot easily be compensated or neutralized (e.g., 

actuators in which the effective time constant is a known 

function of the trim hinge moment). 

-- Controller elements which have small uncertainties and/or 

introduce small noises (e.g., accelerometers with location and 

orientation uncertainties and vibration pickup; air data probe 

position, scale factor, and gust input errors, etc.). 

-- Controller elements in which known parameter variations are 

RATE- AND POSITION-LIMITED CONTROL EFFECTORS 

CONTINUOUS AND DISCRETE (digital) CONTROL EQUIFMENT for 

equalization, controller parameter compensation, computation, etc. 

WLTI-MODE (building block) CHARACTER: 

-- 

-- 

Controller architecture tailored to a specific mission segment. 

Desired compatibility of ndnimum controller (inner loop) 

operational FCS modes with more extensive (outer loop) 

controller mode possibilities to maximize commonality of 

elements and settings for different operational modes. 

Figure 4. Controller Properties 

TR-1228-i-I 17 
External 

Disturbances, 

rl 

Flexible hdes 1 Genqral ired Coordinates 

ce 

toroosite Feedback 

For Elevator 

Input 

and Observer' 

Eleaents For < 

Elevator 

- 

. rrrn+m; i 

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L 

r 

Elevator 

de 

Elevator E Forward Loop - Equalization - I / :m- 

. Aircraft 

Secondary Dynamics 

Point 

' Attitude, i3 . - 

Pitchino a - 

Velocity 

6, Accol er- ation 

Secondary control 

Control c a7 

- Actuation 

_<VC?Ol 

Equalization, 

Sensor 

control 

Secondary 

Eaual ization I Array + 

Sensor/Equal itation 

Complex 

Figure 5. Generalized Flight Control System for Fighter Aircraft Including 

Flexible Modes ["Effective Aircraft," as Seen by the Pilot] 

by control inputs from the elevator and external disturbances from the 

atmosphere. The vehicle dynamics can also be affected by inputs from 

secondary control points represented here by the control, 6,. As already 

noted above in discussing the nature of the FCS controller, the secondary 

controls can simultaneously serve several potential purposes. The more 

obvious are to use the leading and/or trailing edge wing flaps to exert 

decoupling control, load alleviation, or maneuver enhancement. A conceivable possibility is for damping augmentation for one or more key flexible 

modes for which the elevator is ill-positioned. 

The multi-variable control function which is most often poorly 

appreciated is the modification of the effective aircraft transfer function numerator properties for those transfer functions involving the primary control (here, the elevator). Just as feedbacks in general modify 

the effective vehicle poles, so secondary feedbacks to one control point 

modify the effective vehicle transfer function numerator for another 

TR-1228-1-1 18 
control point. Thus, the secondary control loops provide numerator as 

well as denominator effective vehicle changes to serve as equalization for 

the primary control loop involving the elevator. 

The sensor array block can conceivably include attitude, rate gyro, 

and accelerometer instruments at various locations within the aircraft. 

The signals from these instruments are, of course, functions of both the 

rigid-body and flexible motions. They can be operated upon in various 

ways (e.g., filtered, equalized, combined in observer structures, etc.) to 

provide a composite feedback signal, Ce, for the elevator and other composite feedbacks, C, , for secondary controls. The adjustments of sensor 

locations, signal equalization, weightings of signals, etc., taking place 

in this overall sensor/equalization complex for the composite elevator 

feedback signal, Ce, offer another means of modifying the effective vehicle characteristics. Thus, the effective vehicle as seen for elevator 

inputs is the transfer function, Ce/6e. This is a multiloop transfer 

characteristic since several feedbacks are involved and the subsidiary 

loop through 6, is closed. 

The remaining elements in the feedback control system provide for 

additional forward loop equalization on the composite feedback signal to 

the elevator, and the elevator actuation system dynamics. The controller 

blocks described thus far exert feedback control on the aircraft, thereby 

changing its effective dynamics and acting to suppress the effects of any 

external disturbances. To provide for pilot command inputs, the final 

block of "command input elements" is added to the system. These permit 

additional freedom for adjusting the effective vehicle dynamics as seen 

by the pilot. More often than not for fly-by-wire systems, they consist 

of elementary high-bandwidth low-pass filters, and amplitude shaping on 

the stick signals intended primarily to reduce pilot-induced noise 

(remnant), and to cope with both large and small pilot inputs. Theoretically, however, more elaborate equalization could be used at this input 

end to make up for any residual effective vehicle dynamic deficiencies not 

corrected for or adjusted by the feedback elements. 

In summary, with the generalized flight control system of Fig. 5, we 

have three pathways (the command input elements, sensor/equalization 

TR-1228-1-1 19 
complex, and secondary feedbacks) available for complementary adjustment 

of the effective vehicle dynamics to achieve good flying qualities for 

piloted control. On the other hand, external disturbance suppression, 

ride qualities, and reduction of system sensitivity to parameter variations are adjusted primarily by the combined effects of the sensor/ 

equalization complex feeding composite signals to the elevator and secondary control points. 

While the elevator and secondary control pathways are the means 

generally available for addressing flexible aircraft control, they are not 

equally desirable. The cost, complexity, reliability, and possible aerodynamic performance degradation features associated with the establishment 

of secondary control points, make this approach less desirable especially 

as a potentially multiple-redundant flight crucial item. Also for reasons 

of simplicity, reliability, minimum propagation of pilot-induced noise 

(remnant), etc., the command input elements are ideally pure gains of 

simple low pass filters. Consequently, the major burden for control of 

the aircraft falls on the sensor/equalization complex and forward loop 

equalization elements, and it is only when these are insufficient that the 

flight controls designer will turn to more complex command input elements 

and/or secondary control points. 

G. STEPS IN THE PRELIMINARY DESIGN PROCESS 

Thus far in the introduction we have covered the underlying philosophy and summarized the features desired in the methodology, and have 

described some of the unusual aspects of flight control systems. We turn 

now to an outline of a design methodology constructed to take all of these 

considerations into account. In particular, we will emphasize those steps 

in preliminary design which lead to the flight control system design 

architecture. This is the most important step in synthesis and the 

prelude to any analysis. As used here, system architecture means the FCS 

feedback loops and equalization structures, or in other words, the general 

form of the control laws. The FCS architecture inherently depends on the 

aircraft plus flight control overall requirements - form follows 

TR-1228-1-1 20 
function. There is also the possibility of interaction and tradeoffs 

between the airframe configuration and the FCS - function defines form. 

A typical set of preliminary design phases for multi-variable flight 

control system synthesis from project initiation to the architectural 

level will include the major topics listed in Fig. 6. These are 

described below, in conjunction with the System Preliminary Design Methodology Flow diagram shown in Fig. 7. 

In a complete design process these preliminary design phases are 

succeeded by detail design activities. Some of these are summarized in 

Fig. 8. Although these steps are beyond the scope of this methodology, 

they are mentioned here to indicate where conceptual and preliminary 

design ends in our treatment. 

1. Establish Flight Control System Purpose 

Mission-Specified Purposes -- The purpose of the FCS is derived from 

the purpose of the aircraft which is to accomplish one or more missions. 

Each mission is composed of mission phases consisting of a sequence of 

steady flight conditions (v + 0) transitions between conditions, and 

maneuvers (1 z 0). Together these define the ideal velocity vector time 

history but are not necessarily a complete specification of the vehicle 

attitudes along that trajectory. Some attitude constraints may be 

directly imposed in particular mission phases or maneuvers (e.g., nominal 

pitch attitude in carrier approach/landing, Omax in takeoff rotation, 

/3 0 for many maneuvers). Complete definition of the attitude time 

history over a mission phase requires consideration of what the pilot can 

see (e.g., "situational awareness" factors) and feel, and the number of 

independent control points. If enough control points are available with 

sufficient control power (e.g., the lateral "DFC" modes of the AFTI-F16 

with three control points: aileron, rudder, and ventral canard), a 

nominal trajectory may be satisfied with unusual, if not completely arbitrary, attitudes. Otherwise, the ideal trajectory implies a unique solution for one or more attitude angles (e.g., q5 - tan-l(U0X/g) for - 0 

in a conventional rudder/aileron airplane). The considerations involved 

TR-1228-1-1 21 
(1) Establish Flight Control System Purpose 

(2) Determine Command and Disturbance Characteristics 

(3) Determine Unalterable Properties of the Aircraft 

and Controller Elements 

(4) Pilot-Centered Requirements -- Human Pilot/AFCS 

Interactions 

(5) Establish Overall System Requirements 

(6) Survey of Aircraft Characteristics 

(7) Comparison of Aircraft Characteristics with Requirements 

(8) General Equalization Requirements, and Prospectus for AFCS 

Architecture 

(9) Preliminary Design Analysis of System Possibilities 

(10) Formal Competition Among System Possibilities 

Figure 6, Typical Design Phases for Multi-variable Flight 

Control System Synthesis at the Architectural Level 

TR-1228-1-1 22 
3 

0 

rl 

r.4 

h 

M 

0 

rl 

d 

M 

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v) 

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m 

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(D P' Y 

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a 

3 

P' 

(D 

P, 

Y 

r 

P' 

(D 

Y 

w 

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2 m 

(D 

Ln 

r 
. 

in deciding whether an unusual attitude time history is consistent with 

mission or pilot-centered needs is a topic beyond our current scope. 

Once the attitude characteristics are defined over the mission the 

possible operating point range is established. These may then be considered in company with guidance possibilities to establish feasible operating point profiles. The possibilities include both manual and automatic 

guidance. The fundamental operational requirements of the FCS are thus to 

execute the guidance commands to establish and maintain the desired operating point profiles in the presence of any disturbances. Figure 9 illustrates the process in general. An important feature emphasized there by 

the bi-directional arrows is the possible interplay between the three 

lower blocks. Thus, for example, desirable changes in "Guidance Possibili 

ities" or "Vehicle Operating Point Profiles" may be accommodated by modification in the Mission Phases definitions. There may be many combinations which can satisfy the mission purposes. 

At the conclusion of this design step, a mission-mission phase matrix 

can be constructed which gives a broad overview of what is generally 

involved in the mission phases. The mission phase categories should be 

selected so that the quantities required to define flight control activities are determined once the phase is identified. An example of a mission 

phase matrix for an advanced fighter is shown in Table 1. The mission 

phases are the fundamental constituents of the several vehicle operating 

point profiles and maneuvers which combine together to completely define 

Mission 

Purpose and 

Definition 

Mission 

Phases Operating Point Guidance 171 ~~~~~ L-1 

Possibilities 

I I I I - 

Figure 9. First Step in Flight Control Requirements Evolution 

TR-1228-1-1 25 
c 

w 

u 

3 

3 

2 

k i 

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2 

m 

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& 

PI 

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a 

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. 

TR-1228-1-1 26 
the mission. The descriptive terms for the mission phases are often 

designated by abbreviations (e.g., CL for Climb, CO for air-to-air combat) 

in such military specifications as Ref. 2. Mission phases can be expanded 

as needed to cover novel maneuvers or conditions. 

The command structure indicated in the table provides a qualitative 

guide to control system execution of the mission profile. Thus, flight 

path, 7 (which here is meant to imply both longitudinal and lateral 

flight paths), and speed, U, are general objects of control with three 

levels indicated - "bounded, " "accurate, and "precision. The distinction between accurate and precision is associated with the range of input 

frequencies over which the accuracy is maintained - "precision" control 

requires a higher control bandwidth than "accurate" with both levels 

having similar static accuracies. For an actual aircraft design, these 

qualitative definitions need to be made quantitative very early in the 

preliminary design. Often, however, the qualitative distinctions are 

sufficient to pinpoint critical mission phases/maneuver demands on the 

FCS. These critical conditions and demands are primary drivers for the 

FCS architectural structure. 

Basic Functions 

As described above, the system's specific purposes can be equated 

with the definition of the task(s) it is intended to accomplish in order 

to satisfy the aircraft's various missions. From a functional standpoint 

in accomplishing these processes, the flight control system will ordinarily be expected to perform several basic overall functions, that is to 

provide : 

0 Stability. 

0 Desired responses to specific inputs. 

0 Suppression of the effects of disturbances, 

Modification or elimination of certain crosscomponent variations, and uncertainties. 

coupling effects. 

Most of these basic functions are quantified in specifications, such as 

the military specifications for flying qualities (Ref. 2) and flight 

TR-1228-1-1 27 
control systems (Ref. 3), the Federal Air Regulations, (Ref. 4) etc., and 

in the lore of good (and bad) practice accumulated through the years 

(e.g., Refs. 1, 5, Supplement 2). 

2. Determine Command and Disturbance Characteristics 

The characteristics of the commands and disturbances are largely 

direct consequences of the flight control task(s), and of the environment 

in which that task is to be accomplished. These consequences must be made 

specific by defining the characteristics of a family of representative 

input signals and disturbances. 

As a practical matter, commands and disturbances are not a clearcut 

dichotomy - some commands are contaminated by unwanted parts which drive 

the system in a way indistinguishable from disturbances entering at the 

same point. To be sure that no important forcing or excitation source is 

overlooked, it is pertinent to consider both commands and disturbances as 

"inputs," and then to classify them as to source and nature. A convenient 

set of categories is: 

0 At the Command Point(s) 

-- Desired Inputs (nominal "commands") 

-- Unwanted Inputs (nominal "noise" on 

'I Commands It ) 

0 At various Controller Locations 

-- Internal Disturbances 

0 At locations External to the Controller 

-- Vehicle Induced 

-- Environment 

Ordinarily the entire range of possibilities - from discrete steps 

or impulses to periodic and random processes will be represented in the 

input-disturbances set. This richness of input possibilities is one of 

the predominant features of FCS as contrasted to many other types of 

control systems. 

TR-1228-1-1 28 
3. Determine Properties of the Unalterable 

Aircraft and Controller Elements 

Typically the characteristics of some parts of the system are not 

easily changed by the flight control system designer, at least during a 

given design iteration. Such relatively unalterable elements usually 

include major portions of the aircraft itself, and some actuator and sensor dynamic characteristics. The detailed properties of these system 

components must be determined or estimated at this stage. Particular 

emphasis is placed on: 

Identification of aircraft output variables which 

are candidates as the primary variables to be 

controlled. These primary variables are usually 

a direct consequence of the system purpose, e.g., 

from Table 1 flight path angle. However, other 

output variables such as altitude .or pitch attitude (longitudinally) or heading (directionally) 

may be coupled sufficiently closely with the 

nominal primary variables to serve as 

surrogates. 

0 Identification of aircraft characteristics which 

may be considered adjustable in a tradeoff sense. 

For example, tail size and static margin (as 

trades against control system bandwidth and complexity), number and nature of control effectors 

as trades for operating point options (and margins - as in STOL operations using throttle, 

flaps, and elevators in various ways to trim and 

to establish either STOL or conventional front 

side effective aircraft dynamics - or as trades 

for control system complexity - as in two vs. 

three control point aircraft), etc. Potential 

tradeof fs between aircraft configuration and FCS 

characteristics are major factors in proper overall system integration. 

Establishment of the dynamic modes/characteristics of the unalterable elements which are uncertain and/or highly variable over the range of 

operating conditions. This focuses attention on 

these properties which may require special sensitivity considerations. 

There are invariably a large number of essentially unalterable "standard" elements in the controller and aircraft. These might include power 

supplies, guidance elements, cockpit controls, etc. In most cases these 

elements will be well-defined as to their dynamics and noise properties. 

TR-1228-1-1 29 
4. Pilot-Centered Requirements -- Human Pilot/AFCS Interactions 

In manned aircraft, wherein the pilot is expected to exercise at 

least some controller functions , sometimes the key "unalterable element" 

is the pilot. The interactions between the pilot and the effective 

aircraft are so important and pervasive that they deserve detailed treatment as a separate topic. To avoid interrupting this relatively short 

outline/discussion of requirements and system evolution, this is handled 

with the illustrative example in Section I1 and in a more general vein in 

Supplement 3, which has the above heading as its title. 

5. Establish Overall System Requirements 

From the information and considerations developed above, which are 

often accomplished in parallel during a preliminary design, many of the 

"Givens" for a particular aircraft configuration are established. The 

next step is to draw all this together into statements of overall system 

requirements. 

Some of the requirements can be derived explicitly from the functions 

which must be performed to accomplish the system purposes and mission 

phases. The primary set of these in manned aircraft are affected greatly 

by the presence of the pilot. Somewhat modified versions are of increasing importance in modern advanced aircraft where many of the pilot's controller roles are taken over by automation. Thus, there are in a sense 

two sets of "operational requirements" dictated by the mission - one for 

piloted control and the other for automatic control. An expanded treatment of requirements for an Advanced Fighter is the subject of Supplement 2. 

Besides the "Operational Requirements," other requirements derive 

from the characteristics of the interconnected components, especially the 

unalterable controller and aircraft elements, and from the environment in 

which the entire system operates. These are called "Implied Requirements. '' 

TR-1228-1-1 30 
When integrated and appropriately connected, the requirement sets are 

translated into quantitative specifications which should encompass all of 

the system functions and purposes. They would include: 

0 Command input/primary output static and dynamic 

properties. 

0 Command input/secondary output static and dynamic 

properties. 

0 Primary and secondary responses to disturbances. 

Key sensitivity considerations (unalterable 

element(s) uncertainties, and variabilities 

requiring special attention). 

0 Degree of stability. 

The quantitative requirements may be stated in the time domain as dominant 

mode characteristics, allowable errors, time response boundaries, indicia1 

response measures, etc., or as combinations thereof (such as the Time 

Response Parameter, TRP) and/or such frequency domain specification 

measures as closed-loop system bandwidths; phase, gain, and time delay 

margins; etc. 

6. Survey of Aircraft Characteristics 

In the past many of the aircraft-alone characteristics were often 

good enough to satisfy the piloted control portions of the mission. In 

these cases the key FCS requirements stemmed from a need to correct a few 

deficiencies in aircraft stability and control characteristics. To some 

extent this may still be the case for some mission and flight phases. In 

any event for a particular design iteration, the aircraft-alone properties 

still serve as a primary starting point in the FCS architectural design 

competition. 

An important feature of the aircraft characteristics survey is an 

attempt to relate the airplane’s dynamics characteristics to airplane 

stability and control derivatives. Thus is done by developing literal 

approximate factors for the response parameters which indicate: 

0 sensitivity to uncertainties in airframe parameters (i.e., non-dimensional stability and control derivatives and mass properties) 

TR-1228-1-1 31 
0 variation in airframe parameters over the flight 

envelope - primarily due to p(h), M, a, Uo, 

weight and geometry variations. 

0 possibilities for augmentation from an "equivalent derivative" standpoint 

Because of the third property listed the approximate factors will appear 

later as an element of the prospectus. 

7. Comparison of Aircraft Characteristics with Requirements 

The comparison of aircraft characteristics with requirements has two 

steps. 

a. Preparation of aircraft dynamic descriptive 

information in forms which permit comparisons, 

e.g., characteristic function factors, open-loop 

responses to controls and disturbances, etc. 

b. Identification of problems per the requirements 

(certain "problems" such as unstable modes due to 

relaxed static stability will be known to require 

FCS solution beforehand). 

The comparisons provide a direct indication of the airplane dynamics which 

must be modified by stability augmentation to satisfy pilot desires. They 

also point the way for parallel (inner loop feedbacks) and/or series 

equalizations which support the guidance-centered and/or automatic pilot 

outer-loop closures. 

8. General Equalization Requirements and Prospectus 

for FCS Architecture 

General Eaualization Reauirements 

As a prelude to the development of possible FCS architectures, the 

overall system requirements, operational environment, unalterable element 

characteristics, etc., are viewed as a framework from which to consider 

feedback and equalization requirements. The three major considerations 

are : 

a) The ultimate outer-loop which involves the 

desired output variable or its surrogate, must 

have appropriate equalization to meet the overall 

TR-1228-1-1 32 
system requirements. This ordinarily implies 

that the closed-loop system exhibits: 

Adequate low-frequency steady-state error 

responses. 

Specified closed-loop system dominant mode 

characteristics (for example, bandwidth and 

damping needed for disturbance suppression, 

and for the closed-loop dynamics portion of 

the command/response relationship). 

Specified low-frequency command/response 

relationships (for example, suitable input, 

feedback, and feedforward characteristics to 

achieve desirable values). 

Sufficient phase, gain and delay margins to 

permit robust controllers. 

Noise rejection (smoothing) at frequencies 

at and above control action. 

This equalization can be obtained from either 

series elements operating on the primary variable, or from parallel elements involving the 

feedback of other aircraft output variables, or 

from a combination of both. 

b) Equalization requirements levied by desired 

responses of subsidiary variables to commands and 

disturbances. 

c) Provision of sensitivity constraints and reduction for some selected uncertainhighly variable 

unalterable element modes by driving them into 

specially placed low tolerances, compensation 

zeros. 

ProsDectus for FCS Architecture 

The "Architecture" considered here amounts to the establishment of 

feedbacks, equalization (adjustment of the effective aircraft dynamics as 

seen at a particular command or disturbance entry point), compensation 

(adjustment of particular controller dynamics, usually as a function of 

flight condition), etc. The architectural drawing is characteristically 

a detailed block diagram of the overall system. 

In progressing to topic 8 of the design process sufficient information has become available to consider two types of equalization in detail: 

TR-1228-1-1 33 
a) Series on the primary variable (or its surrogate). 

b) Parallel using controlled element secondary output variables. To establish this part of the 

prospectus, a search is conducted for favorable 

effective aircraft transfer function numerator 

properties. 

While "equalization" including the selection of appropriate feedback 

loops falls conveniently into the two categories (serial and parallel) 

noted above, the actual details of the feedback selection is much more 

involved. The general nature of potentially desirable specific 

feedbacks/controller architectures stems from the organized, but nonetheless artful consideration of the "Elements of the Prospectus" listed in 

Fig. 7. 

The particulars of just what these "Elements of the Prospectus" are 

and how they are actually used in a preliminary design will be illustrated 

in Section V for the advanced aircraft design example. Tables showing the 

literal approximate factors and essential feedbacks summaries (adapted 

from Ref. 1) will be introduced and used on the spot. The multi-variable 

sensitivity vector surveys use the techniques described in Appendix B. 

The multi-variable high gain closure characteristics depend on the effective numerators of the aircraft including coupling numerators. The overall multi-variable analysis technique which covers these aspects is outlined in Appendix A. A catalog of the elemental systems is the subject 

of Appendix C. 

The actual utilization of the elements of the prospectus in the context of the system requirements and other data developed from the previous 

design phases involves a great deal of integrative engineering. The 

entire packet of information and the "rules" based on experience for tying 

it all together and molding the results into feasible system architectures, constitute the knowledge base for an "expert system" for FCS 

design. "FCX", the prototype first generation FCS expert system developed 

to cover some phases of the design methodology, is a first attempt to find 

out how expert system concepts can play a major role in this design phase 

and those immediately before and after. 

TR-1228-1-1 34 
9. Preliminary Design Analysis of System Possibilities 

, 

At the end of these steps the flight control system synthesis will 

hopefully have resulted in one or more feasible FCS block diagrams, which 

show the loop structure and equalization forms. There remains the not 

insignificant task of synthesizing control laws to meet the quantitative 

and qualitative requirements in the presence of all the system disturbances, uncertainties, and variabilities. Because the dynamic requirements 

are not easily cast into terms which can be encapsulated in a comprehensive performance measure, control law synthesis requires iterative operations. This is the case even when the synthesis procedure involves performance indices and optimization processes. In this design methodology 

matters are somewhat simpler in that the control law synthesis proceeds 

within the feedback system architectural constraints already established. 

Thus the fundamental feedbacks and their reasons for being are already 

known -- the synthesis problem at this stage is merely one of finishing 

off. This always includes the determination of gains needed to meet the 

system requirements, and can also involve the introduction of improvements 

via the insertion of equalization and filtering, etc. The analysis,/ 

synthesis procedures and the means to show the system results in terms of 

input-output dynamic characteristics for the several subsystems, the system(s) responses to various commands and disturbances, etc. in the methodology are all provided in Program CC, Versions 3 and 4. 

Results of the analyses are then compared with the system requirements to demonstrate that the synthesis is indeed adequate. When this has 

been established the next step is to determine the airplane and control 

system parameters which govern or limit the design. Typically these are 

the airplane and controller parameters which dominate the system dynamics 

in the various crossover regions for the several control loops, and the 

airplane parameters which serve as sensitivities for atmospheric disturbance inputs. These "governing" parameters are of most concern because the 

design's ability to meet the system requirements will be most sensitive to 

them. Because they exert so much leverage on the adequacy of the design, 

uncertainties in these parameters become major items in design assessments, plans for risk reduction, etc. 

TR-1228-1-1 35 
The final stage of the preliminary design analysis is the assessment 

of the system(s) robustness. Here the focus is on robustness in general 

and robustness with respect to the more uncertain of the governing parameters. Modern robustness assessment techniques are available in Program 

CC, and are used for this part of the design methodology. 

10. Formal Competition Among System Possibilities 

We espouse an FCS design philosophy where "competition" between 

system architectural configurations is an appropriate intermediate goal in 

the synthesis procedure. Just because all of the requirements and desirable features of an FCS cannot be stated in quantitative and commensurate 

terms, judgment and technological subjective considerations inherently 

play a role in establishing the best system architecture; yet these artistic factors can best be applied when a number of system alternatives are 

available as competitive configurations. The competing systems-can be 

compared on a very large number of bases which can be divided into two 

categories: design quantities and qualities. Design quantities include 

the dynamic performance (relative stability, accuracy, speed of response 

or bandwidth, etc.) and the physical characteristics (weight, volume, 

power or energy consumption, etc.). Design qualities include safety, 

operational capability, reliability, maintainability, cost, etc. An 

optimum system is one that has some "best" combination of all these 

features. At this point the design process passes to the detail design 

phases starting with the steps listed in Fig. 8. 

Before ending this introductory summary of the design methodology we 

should recapitulate which design phase the computational aids fit in, as 

follows : 

"LSMP", Linear Systems Modeling Program or Program CC: 

(3) Unalterable Aircraft Properties 

(6) Survey of Aircraft Characteristics 

"Program CC. Versions 3 and 4": 

(7) Comparison of Aircraft Characteristics 

(9) Preliminary Design Analysis 

with Requirements 

TR-1228-1-1 36 
"Program CC. Version 4": 

(9) Robustness Assessment 

"FCX". First Generation Flight Control XDert: 

(7) Comparison of Aircraft Characteristics 

(8) 

(9) 

with Requirements 

Creation of Competing System Possibilities 

Preliminary Design Analysis of System Possibilities 

"FCX" - actually becomes involved in the earlier design phases with "Overall 

System Requirements" and "Survey of Aircraft Characteristics" as well, but 

its principal elements are pertinent to the phases noted. 

H. LEVEL OF DETAIL AVAILABLE AT THE END 

OF THE FCS ARCHITECTURAL DEVELOPMENT 

To provide a concrete example of the result and level of detail 

available at the end of the FCS architectural development, consider a 

system intended to accomplish all the flight control system purposes 

(e.g., stability, desired responses to specified inputs for good flying 

qualities, etc.) for a high performance fighter aircraft designed to be 

flown highly unstable longitudinally with stabilization accomplished by 

the FCS. A typical system architecture resulting at the end of the steps 

described above is shown in Fig. 9a. Another result of such a system 

preliminary design development would be data and criteria combined in a 

data package. Yet a third consequence is exemplified by the alternative 

control laws indicated in Table 2. These alternative control laws may be 

used to accomplish the same general purposes as the system of Fig. 9a. 

They differ in the side effects listed in Table 2. They also differ in 

the kind of sensors and implicitly in their specific advantages/disadvantages for control of flexible modes. Finally, they offer a rich source of 

possibilities for analytical redundancy in multiple-redundant mechanizations. Thus, great strides have been made toward a synthesis solution, 

but considerable analysis and detailed synthesis remains. Further, 

additional attention has to be paid to somewhat more specific criteria 

associated with the peculiarities of a particular flight control system 

design. 

TR-1228-1-1 37 
7 

0 

0 

v) 

c 

QJ 

fl 

0 

.- 

c 

E 

TR-1228-1 -I 

I 

n - 

+ 

v) 

f 

+ 

v) 

+ 

n 

hl 

a 

C 

m 

i) 

0 

Y 

L 

7 

M 

.d 

CT4 
TABLE 2. SYSTEM ARCHITECTURAL POSSIBILITIES AND MECHANIZATIONAL 

SIDE EFFECTS FOR SUPERAUGMENTED AIRCRAFT 

Reduces divergences, but does not get all the way to stability. 

Requires some up-elevator relief in turns; e.g., qe - q - Ro tan Go 

Jq dt, + 6, 

Generally suitable for complete correction of instability. 

Requires up-elevator relief in turns; e.g., qe - q - Ro tan 0, 

Sa, dt, Gwoq + 6, (Gwo - Washout equalization) 

Corrects for instabilit when l/Thl > 0. Can have backside 

< 0s instability and equivalent backside 

< 0) in climbs. 

when accelerometer 

level flt 

is not oriented along stability agis for level flight; further bias in climbs and dives; 

yet another bias with a roll limit cycle. 

plus increment for q feedback in turn entry/exit. 

Requires up-elevator relief in turns; e.g., aZe - aZ - cos 8, sec 0, 

Requires more airspeed compensation than attitude-based systems. 

~/(?B~s + 1)JUq dt, Gwoq + 6, [Pseudo az] 

Generally suitable for complete correction of instability (replaces 

1/Th -based limitations with l/Tel; removes accelerometer bias 

issues). 1 

Requires up-elevator relief in turns. 

Requires more airspeed compensation than attitude-based systems. 

Generally suitable for complete correction of instability. 

Gain changes in turns, with associated Fs/g lightening, etc. 

Requires climb-dive steady-state elevator signal relief. 

0, 4 or a", Gwoq -+ 6, 

Generally suitable for complete correction of instability. 

Gain changes in climbing/diving turns. 

Climb/dive steady-state signal relief. 

Requires up-elevator relief in turn entries/exits, depending on 

specifics of Gwo. 

TR- 1 2 2 8 - 1 -I 39 
The longitudinal system shown in Fig. 10 as an illustration of what 

might be available at the end of the FCS architectural development phase, 

could also be used as the pitch controller for the Advanced Aircraft 

example. Throttle controls appropriate to operation on the backside of 

the power curve would be needed for STOL activities, etc. This system 

could also be cited as an example of the elemental system approach to the 

approximation of dominant modes. In this case, the dominant mode dynamics 

of q/qc are given by the "superaugmented" elemental system in the catalog 

of Appendix C. A complete research study of this type of system, its 

dynamics and flying qualities is given in Refs. 6 and 7. 

I. PREVIEW OF WHAT IS TO COME 

While we have attempted to make the System Design Methodology outlined above and depicted in Fig. 7 as straightforward as possible it is 

intrinsically complicated. Even at the broad-brush level of detail presented there are many interactions which cannot be exposed in a verbal 

summary. And the number of detailed considerations needed in such things 

as the evolution of requirements and the pilot-centered factors can be 

large. Consequently we have attempted in this report to present the mass 

of material involved in the design methodology as clearly as possible. To 

do this the decision was made to provide a fundamental focus on the steps 

in the methodology and many of the details by actually working through an 

illustrative example. The thrust in this text is on simplicity and 

clarity; consequently there are no interruptions to explain the many 

procedural or computational things that might arise, and the illustrative 

steps worked out for the example are indicative rather than comprehensive. 

Some of the more detailed background information is funneled off to supplements. 

The example problem is the design of a lateral-directional FCS for a 

high performance advanced fighter in an interesting and challenging mission phase. When connected with the Design Methodology Flow Diagram of 

Fig. 7 the illustrative problem proceeds as follows: 

Section I1 - "Mission-Based Requirements for Lateral-Directional 

FCS of High Performance Aircraft" 

(1) Flight Control System Purposes 

(2) Command and Disturbance Characteristics 

Includes : 

TR-1228-1-1 40 
(4) Pilot-Centered Requirements 

(5) Overall System Requirements 

Section I11 - "High Performance Aircraft Lateral-Directional 

Character is tics 

(6) Survey of Airplane Characteristics 

Control Problems Due to the Airplane" 

(7) 

Includes : 

Section IV - "Identification of Control of Lateral-Directional 

Includes : 

Comparison of Aircraft Characteristics with 

Requirements 

Section V - "Prospectus for Lateral-Directional Flight Control 

System Architecture" 

Includes : 

(8) General Equalization Requirements and 

Elements of the Prospectus leading to 

Competing System Possibilities 

Section VI - "Preliminary Design of Candidate Lateral-Directional 

Fighter Flight Control System" 

(9) Preliminary Design Analysis 

Supplement 1 - "Literal Singular-Value-Based Flight Control 

Includes : 

System Design Techniques" 

(9) Robustness Assessment 

Includes : 

. 

The developments, discussions, and some details in the design example rely 

on Ref. 1 for background on airplane dynamics, approximate factors, and 

many FCS features and characteristics, and on Refs. 8-10 for computational 

operations using "LSMP" and "Pronram CC. Versio ns 3 and 4". 

One of the major new features in the design methodology is the first 

generation prototype expert system "FCX", which is coupled with "Prozram 

CC. VersLon 3". FCX actually covers parts of several phases within the 

design methodology. It attempts to mechanize in expert system terms many 

of the considerations on which the illustrative design is based. This is 

a novel application of a new technology. To avoid introducing it and all 

its peculiar complexities in the very middle of the example, we have 

worked through the example as if "N" didn't exist. Then, "FCX" is discussed in detail in Volume 2 which includes listings of the 18 FCX knowledge bases as they presently exist. 

As noted above, some topics of the design methodology are too 

involved to be exemplified even sketchily as part of a short and balanced 

TR-1228-1-1 41 
description in working through the example problem. The evolution of 

mission-centered requirements and the consideration of pilot-centered 

requirements are typical examples. These too are handled in greater depth 

in supplements. Supplement 2, "Lateral FCS Requirements-Oriented Design 

Knowledge Base for an Advanced STOL Fighter in Mission Phase CO" contains 

a composite outline/summary of specifications, requirements, considerations, lore, good practices, etc., pertinent to design phases (1) through 

(5). It is a principal support of the briefly stated requirements used in 

Section 11. Similarly, Supplement 3, "Pilot-Centered Requirements and 

Human Pilot FCS Interactions" supports design phases (4), (5), and (9). 

The design example focuses primarily on bringing together the mission 

and pilot-centered requirements, prospectus elements, aircraft dynamic 

deficiencies, etc., and then mixing the batch to emerge with a logical 

preliminary design flight control system architectural structure. In 

achieving this end, certain non-essential simplifications are introduced 

to make the processes easier to follow. The most important of these are 

that the sensor and aircraft flexible mode dynamic properties are 

neglected, and that the controller is continuous. To expand the methodology to flexible mode stabilization issues the reader is referred to Ref. 

11, which considers another preliminary design example where both digital 

control and flexible dynamics are present. (This reference presents a 

continuous system design followed by a discrete controller development. 

The example is preceded by a short discussion of appropriate digital 

system techniques - the w-domain for direct digital design, and the 

hybrid frequency response for system response assessments. Both procedures are illustrated in the design example. the digital design techniques used are part of Program CC, and both the direct digital design 

process and consideration of flexible modes can be considered to be a 

direct follow on to the present report as a part of the design methodology. ) 

The detailed work of the design example is based on several techniques and methods which are not necessarily well-known. Consequently, 

brief summaries are given in appendices. These include: 

0 Appendix A -- Outline of the Multi-variable Analysis Method 

0 Appendix B -- Sensitivity Vectors 

0 Appendix C -- Catalog of Elemental System Characteristics 

TR-1228-1-1 42 
SECTION I1 

MISSION-BASED REQUIREMENTS FOR LATERAL-DIRECTIONAL 

FCS OF HIGH PERFORMANCE AIRCRAFT 

Mission-centered requirements on the flight control system are the 

dynamic form, accuracy, and speed of response which should be exhibited by 

the Aircraft/FCS in order to accomplish the mission. These properties 

need to be translated into quantitatively expressed sets of desired 

command/response relationships (for pilot or guidance system commands) and 

regulation (against disturbances) requirements for each mission phase. 

Mission-centered requirements for control stem primarily from two sources: 

0 Functional 

Control and regulation of the aircraft's: 

Velocitv vector in direction (flight path control) and 

magnitude (speed); 

Attitudes 

-- earth-referenced (pitch, roll, yaw and heading) 

-- air mass-referenced (angle-of-attack, 

aerodynamic sideslip) 

0 pi1 ot Desire% 

Effective vehicle dynamics which enable the pilot to accomplish the mission phases with minimum workload and maximum 

pilot efficiency 

The two sources are intimately related in that a key pilot desire 

and, indeed, the essence of pilot-in-the-loop flying qualities, is for 

effective vehicle dynamics which permit the pilot easily to exert control 

and regulation over the aircraft's velocity vector and attitudes. These 

effective airplane dynamics permit the pilot, when appropriate cues are 

available, to readily accomplish guidance tasks by developing internally 

generated outer-loop "guidance laws". Automatic guidance systems require 

adjustment of the effective airplane dynamics to similar forms which permit simple automatically-generated outer loops and system actions which 

are easily monitored by the pilot. So a duality exists between pilotsupplied and automatic guidance in that what is good for the pilot is also 

good for an automatic system which performs the same kinds of flight 

TR-1228-1-1 43 
operations. Consequently, the form of the inner loops of the FCS can 

ordinarily be shared by the pilot or a set of guidance system outer 

loop(s). The values of particular inner loop control law parameters and 

minor equalization may, however, differ somewhat for piloted and automatic 

control. 

It might be argued on hypothetical grounds that a "better than good" 

automatic system could require fundamentally different inner loops than 

are appropriate for piloted operation in a guidance role. However, pilot 

needs take priority because the pilot is the ultimate monitor, must always 

be able to interrupt and take over from the automatics, and is inherently 

a divided attention controller. Consequently, to assure good pilotvehicle integration, as well as for design and equipment economy, the 

flying qualities-based requirements are a primary basis in specifying the 

feedback control laws which establish the flight control system inner 

loops. 

While the Aircraft/FCS must operate through all mission phases, the 

pilot-vehicle control precision and pilot attentional demands are most 

severe in a limited number of flight operations. Similarly, the requirements on form, accuracy and speed of response for automatically guided 

flight operations are also most severe in only a limited number of mission 

phases. The requirements stemming from the most-demanding mission phases 

therefore become critical design drivers for flight control. Usually the 

design-critical mission phases and associated requirements, as they are 

reflected into FCS feedback control law forms, are substantially the same 

for piloted and automatic control. This follows since, as noted above, it 

scarcely matters whether an automatic system or the pilot is closing the 

outer, guidance loops. (Performance levels associated with automatic and 

manual control may, of course, be different.) 

The development of mission-centered requirements in this section will 

follow the logic presented above. The first article will present those 

based on flying qualities, and the second article follows with path and 

heading control requirements. Numerical values are summarized in the 

third article, creating a "Mission-Centered Requirements Data Base." 

TR-1228-1-1 44 
By their nature most of the mission-centered requirements tend to 

define the dynamic properties of the airplane plus control system, i.e., 

as modal response characteristics, time response parameters, etc. But 

these input/response and stability properties do not exist in a vacuum - 

they are means to convert applied commands to desired outputs in the presence of disturbances. The command inputs and disturbances depend on the 

mission phase, and thus are implicit entries into a mission-oriented set 

of requirements as commands which are to be followed or disturbances which 

are to be regulated against. A tabular form giving a cross section of 

commands and disturbances for the hypothetical advanced fighter is given 

in the final article. Specific entries from this table may serve as candidates for additional requirements leading to system feedback architecture considerations such as the need to provide suitable steady-state 

accuracy in response to a particular input or to regulate a particular 

airplane response variable over a disturbance bandwidth. The commands and 

disturbances may also be used for calculations which exhibit the response 

properties of possible competing systems. 

A. MISSION-CENTERED FLYING QUALITIES REQUIREMENTS 

Many of the flight control design-critical mission phases for an 

advanced fighter are well-defined in flying qualities requirements documents (e.g. MIL-F-8785C, Ref. 2). These include: 

Category A 

-- Rapid Maneuvering, Precision Tracking, 

Precise Flight Path Control 

0 Air-to-Air combat (CO) 

0 Ground Attack (GA) 

Weapon delivery/launch (WD) 

0 Terrain following (TF) 

-- Precision Tracking, Precise Flight Path Control 

0 In-flight refueling (RR) 0 Close formation flying (FF) 

Category C 

-- Terminal flight phases requiring accurate 

flight path control 

0 Approach (PA) 

Landing (L) 

TR-1228-1-1 45 
If the advanced fighter was also a STOL aircraft there are two other 

potentially flight control-critical mission phases that should be added to 

the above, one in each category. In Category A, the CO mission phase 

might be extended to include conditions outside the aerodynamic envelope 

to permit evasive or unusual positioning maneuvers (e.g., supermaneuverability). This would imply that special aerodynamic effectors, 

thrust vector control, or some similar additional effectors be integrated 

into the "normal" Aircraft/FCS set. The additional Category C mission 

phase would be introduced for touchdown, nose-down rotation, and roll out 

control operations on a very narrow (50 ft), short (1500 ft), battle 

damaged runway in the presence of severe crosswinds. 

The numerical requirements for mission-centered lateral-directional 

control quantities for an advanced fighter (Class IV airplane) in Flight 

Phase Category A (CO), "Air-to-air combat" can be culled from the military 

specifications (e.g., Refs. 2 and 3) and conditioned and seasoned by mission and pilot-centered requirements as given, for example, in Supplements 

2 and 3. These are summarized in Table 3. All of the "Effective Denominator Quantities" and many of the "Effective Numerator Quantities" given 

there derive from flying qualities and/or pilot-vehicle integration considerations and thus relate to the aircraft/FCS modes associated with 

stability augmentation. In closed-loop FCS, higher-order modes will be 

present and improved pilot-vehicle system characteristics are possible 

when these minimum specifications are exceeded. Thus, the numerical 

values are to be interpreted as defining lower-order effective modes and 

as minimums for Level 1 flying qualities. 

B. MISSION-CENTERED PATH AND HEADING CONTROL REQUIREMENTS 

Consideration of the FCS designer's charge to "establish desired 

command/response relationships" starts with the bare airplane lateraldirectional control characteristics pertinent to lateral path and heading 

control. Directional control of the velocity vector (i.e., lateral flight 

path, A) and the aircraft x body axis (i.e., azimuth angle, $) is the 

essential ingredient needed for maneuvering, tracking targets, and implementing guidance systems. The following explanation applies generally to 

TR-1228-1-1 46 
TABLE 3. COMPILATION OF MISSION-CENTERED FCS DESIGN-CRITICAL REQUIREMENTS 

Dutch Roll Mode 3.3.1.1 

Undamped Natural Frequency,od > 1 rad/sec Flt Phase Cat A [CO.GA] 

Damping Ratiob > 0.4 Flt Phase Cat A [CO,GA] 

EFFECTIVE NUMERATOR QUANTITY REQUIRE" REFERENCE, COMMENTS 

Roll/Lateral Control1or.u; u; > 0 3.3.2.2 

Positive Effective Dihedral, Li)Ieff Li)].ff O 3.3.6.3 9 3.3.2.5 

Steady Turn Coordination 

__~ _ - -- -- -_- - --- __ --_ --_- 

._ --- - - - - -- _-- - 

Piloted Control @ A 0 poasible 

EFFECTIVE DENOMINATOR QUANTITY 

Coupled Roll-Spiral 

[fSRp OSR] -_ ____ - ___ __ . - - - __ - __ 

Spiral Divergence, Ts 

1/Ts 

--- --I------ ~ /- . . - -. 

REQUIRKMENT REFERENCE COMMENTS. 

3.3.1.4 

Flt Phase Cat A [CO,GA] Not Permitted 

___ - - - __ - _- - - - - - -- -. -___ 

3.3.1.3 

Flt Phaae Cat B 

T > 20 seca 2/1 

Corroaponda tolTs 1>28.8 sacs 

T > 12 sac for Cat A 

2/1 

> -0.0347 

Roll Subsidence, TR 

Piloted Control 

Automatic Control 

BANK ANGLE REGULATION 

Piloted Control 

I I TR < lsec 3.3.1.2 

Flt Phase Cat A 

@ a 0 poa8ibh 3.3.2.5 

B A 0 desirable Implied req't for 

lateral controller 

I.y/el s 0.2 3.1.2.4.2* 

B a 0 desirable 

Pmax < 90°/sec 

Implied req't for 

lateral controller 

W4/Wd A 1 Lateral control purification 

Wd/Wd < 1 next best 

Automatic Control 

STABILITY MARGINS 

Automatic Control 

RT < 3 sec 3.1.2.1* 

Corresponds to Assume: 4m - 45 deg; 

q,4 > 2 rad/sec fCL A 1/2; 

RT A ~/(~w)cL A 3 sec 

fm < 1st f, > 1st 3.1.3.6.1* 

aeroelaatic aeroelastic All closed-loo~ FCS 

I ROLLING MANEWER COORDINATION I 1 

Phase Margin, 4,,, Cain Margin. C, 

45 dog 60 &g 

6dB 8dB G, > 6 dB @ zero airspeed 

'References are to MIL-F-878% (Flying Qualitea of Piloted Airplanes) 

b*en Wil+/Bld > 20 irad/sec)2, the minimum damping rdWd shall be increased 

and * to MIL-F-9490D (Flight Control Systems). 

by Afdud - 0.014 (Wd14/@Id-20) 

TR-1228-1-1 47 
either piloted or automatic control unless otherwise indicated by the 

context. 

Going directly to the path control for a typical airplane, Fig. 11 

indicates that direct proportional control of path with aileron via a pure 

gain controller Yp - Kp is not feasible. This "system survey" shows that 

the free s at the origin, the (slightly divergent) spiral, and the roll 

subsidence combine to form an approximate controlled element transfer 

function, 

A6 s2 (s + l/TR) 

Yc--- 

In the illustration the Dutch roll mode is scarcely involved, being nearly 

cancelled by the quadratic numerator. This is not always the case, but to 

the extent that it is the simplified formulation of the path control problem given here is quite general and would even apply to cases where the 

roll subsidence mode is augmented. It should be stated in passing that 

the spiral and roll subsidence could conceivably be coupled to form a 

"lateral phugoid" (Ref. 1). As noted in Table 3 this is not permitted in 

Class IV aircraft in Mission Phase CO. If present the lateral phugoid 

mode would have to be modified to the uncoupled form (e.g., via inner 

loops) for starters, and then the present arguments would apply. If heading is used as a surrogate for flight path angle the essential characteristics are very similar to Eq. 1. 

Either manual or automatic control of this type of controlled element 

form with only path angle or heading error as a guidance reference 

requires a great deal of very low frequency lead equalization. (The pilot 

can control such difficult controlled elements, but only at the expense of 

the full attention, extremely high workload operations needed to generate 

this very low frequency lead.) 

To provide the lead equalization for a path or heading outer command 

loop closure, theoretically one can develop heading rate or path angle 

rate signals or resort to an efficacious inner loop quantity. For the 

TR-1228-1-1 68 
- u-Root Locus (stable) or 

0000 Complex Bode Root Locus(unstab1e) 

++++Complex Bode Root Locus(stab1e) 

- G( jw) 

---- IG(jw)l Asymptote 

I Closed Loop Roots 

Conventional Root Locus 

4 YpYc (jw) 

Dipole 

Unstable 

Path \ 

Mode 

Bode root locus of 

unstable path mode 

I 

0- -locus 

asymptote 

/ asymptote 

jw - Bode 

L 

0- - Locus 

wd 

+ Bode root 

locus of 

+ dutch roll 

+ dipole 

+ + 

+ + + 

+ 

+ 

+ 

Achieving adequate 

phase margin in the 

path crossover frequency 

region would require 

unacceptably large pilot 

lead equalization 

w(+ %, bliw -Bode and Bode Root Locus 

Figure 11 . System Survey Indicating the Infeasibility 

of Path Control with a Pure Gain X + 6, Loop 

TR-1228-1-1 49 
TR-1228-1-1 

latter an obvious candidate is roll or bank angle. This is further made 

apparent from the steady-turn relationship assuming perfect coordination 

(i.e., pa - p - pg = 0) and insignificant control effector actions. 

Then 

i - 54Lr 

0 

For the dynamics of the path change in a conventional bank-to-turn 

aircraft, the roll subsidence term dominates as the significant 

bandwidth/rise time limitation in orienting the lift vector in order to 

turn. There is, of course, the associated bandwidth/rise time in the 

longitudinal axis to build up the load factor to sustain altitude in the 

turn. The fundamental limits which determine the maximum turn rates and 

path curvatures are seen in this connection. In steady-state, it is set 

, or in a more complex relationship, by the associated induced 

by 'ha, 

drag rise which would lead to critical energy loss in combat maneuvering. 

At the outset of the maneuver the lateral and longitudinal controller 

bandwidths and control powers will govern how rapidly the quasi-steady 

state condition can be achieved. Effective use of the maximum maneuvering 

capability is limited by the human pilot's normal acceleration limits as 

assisted by g suits and other aids. 

Direct side force designs allow the possibility of independent control of all degrees-of-freedom, and different bandwidths can be achieved 

since the roll and normal acceleration dynamics are not involved. However, the lower effective control power of feasible direct side force 

generators (e.g., ventral canards, thrust vectoring) inevitably lead to 

lower maximum turn rates. Thus, if direct side force control is incorporated in a fighter design, it will probably be used as a precision 

"vernier" on top of bank-to-turn maneuvering, and generally be limited to 

specific task-tailoring FCS modes (e.g., wings-level turning adjustments 

in ground attack to avoid introducing "pendulous" errors). Effective use 

of direct side force modes requires careful coordination with conventional 

controls, and is complicated by non-zero lateral acceleration on the 

pilot. We shall not be concerned further with such designs here. 

50 
Besides its fundamental implied requirement as an inner loop for path 

control to provide path mode damping, roll angle control also has a life 

of its own as a bank attitude regulating system. Consequently, the fundamental path control requirement for both the piloted and automatically 

controlled aircraft can be interpreted to include and imply a requirement 

for roll angle control. When this command and regulation control loop has 

been established with high integrity, most of the outer-loop control modes 

imaginable can readily be instrumented. Conversely, without it some are 

very difficult or are not feasible. These outer loops are the primary 

domain of guidance, while from the roll loop inward, the airplane dynamics 

play an increasingly important and dominant role. Consequently, the roll 

control lateral-directional problem is a suitable starting point for the 

FCS architectural design process for both piloted and automatic control. 

The mission-centered response time requirement for automatic roll 

attitude control and regulation given in Table 3 is suitable for a 

fighter automatic-pilot bank angle control. The implied bandwidth, wb4, 

required to achieve the specified response time (RT) is relatively modest 

for very tight integrated fire-flight control. Conseqiently this automatic FCS-based requirement, like many of those based on flying qualities, 

should be considered a minimum. 

Because rolling is centrally involved in path, directional, and 

lateral-directional maneuvers several other requirements which promote 

good roll control characteristics are listed in Table 3. They range from 

restrictions on rolling velocity reversals to conditions which favor pure 

rolling using a single lateral controller. 

There are other requirements which implicitly relate to the ability 

of the Aircraft/FCS to perform the mission. The most pervasive is stability. The stability criteria listed apply to all Aircraft/FCS situations 

in which the loops involve aerodynamics (with GM > 6 dB for zero airspeed). Because most, if not all, of the loops in FCS have some status as 

independent entities (e.g., a yaw-damper may exist on its own as well as 

an inner loop for a roll control mode which, in turn, may be an inner loop 

for path control, etc.) the stability criteria tend to apply for each of 

TR-1228-1-1 51 
the several loops involved. In multiple loop systems the overall system 

is to be stable when each loop is subjected to variations equal to the 

margins given, all other loops being closed with nominal values for the 

control law parameters. 

C. IMPLIED REQUIREMENTS FOR COORDINATED MANEWERS 

The flying qualities and FCS specifications place various explicit 

and implicit limitations on the sideslip responses to pilot or AFCS control actions. For example, Table 3 lists a flying quality requirement 

that sufficient control power and other capability be present to permit 

the pilot to conduct coordinated rolling maneuvers (i.e., /3 z 0 possible). But an explicit requirement for fi A 0 maneuvering is not currently in any general specification per se. 

At first glance this state of specification affairs is somewhat surprising for mission phases CO and GA, because lead pursuit trajectories 

needed for gunnery are ideally zero sideslip for ballistic reasons. Coordinated maneuvering can also minimize target acquisition time. There are, 

however, other factors which need to be weighed, the most important being 

the desired axis about which rolling should occur. When minimum sideslip 

is desired the roll axis should be about the flight path or, in other 

words, about the stability axis. When this incidentally corresponds to 

the reticle axis (and, perhaps the gun line as well) zero sideslip maneuvering can be ideal for gunnery. If not, initial lineup can require the 

development of greater pilot skill and/or more elaborate fire control 

systems to counter various "pendulous effects" on apparent target movements. For instance, a roll axis which is above the sight line causes an 

initial reversed movement of the target when rolling onto a target. Also, 

in aircraft where the pilot is located well above the roll axis, the 

pilot may be subjected to large lateral accelerations when ini.tiating or 

terminating abrupt rolling maneuvers. Inertial coupling considerations 

can also enter which tend to push the preferred roll axis to locations 

which are most favorable in this connection. All of these factors are 

important, and some may lead to specific requirements to task tailor the 

FCS in different ways for different mission phases. 

TR-1228-1-1 52 
While these special circumstances demand attention, in all extreme 

maneuvers of advanced fighters the danger of exceeding the safe flight 

envelope is present. Controllable stalled or even supermaneuvering flight 

well into separated regimes is a desirable attribute for future fighters, 

but rapid departures and structurally unsound maneuvers are not. The 

incidence of uncontrollable flight is significantly reduced by maintaining 

symmetrical loading conditions for both the pilot and the airframe, i.e., 

sideslip very nearly zero. With this background, and recognizing that a 

mature task-tailored control system technology is available for lateral 

control initiated maneuvering tasks, it consequently makes a great deal of 

sense to cut through the jumble of requirements on sideslip by simply 

requiring the basic control system to provide for dynamic coordination 

(B z 0) for all maneuvers commanded by lateral controller action (additional task-tailoring being optional). This would apply for automatic as 

well as manual control, and is entered as an implied requirement in 

Table 3. Capability for generating deliberate sideslip using the rudder 

is, of course, still required. 

D. MISSION-BASED REQUIREMENTS IN THE FLIGHT CONTROL DESIGN SOFTWARE 

The above discussion covers the primary design-critical requirements 

for an example advanced fighter in the air-to-air mission phase (CO). The 

requirements are displayed in tabular form in Table 3. They serve two 

roles: as fundamental guidelines for the FCS design; and as guideposts in 

assessments. The first assessment will be to determine what deficiencies 

are present in the characteristics of the aircraft without any FCS. Then, 

at successive stages in the evolution of the flight control systems 

architecture, further assessments are made until satisfactory design 

closure occurs and a FCS architectural structure is thereby established. 

The requirements and the other knowledge elements for flight control 

design to be discussed in the following sections have been partially 

implemented in a prototype knowledge-based flight control system design 

package called "FCX" which is discussed in Volume 2. Requirements, corresponding to Table 3, appear in two elements of FCX - in a spreadsheet 

database element and in several knowledge bases of the FCX flight control 

TR-1228-1-1 53 
design expert system. The requirements appear in the "REQUIREMENTS" 

window of the spreadsheet applied to the bare aircraft dynamics as shown 

in Table 4. In the FCX expert system the requirements are first particularized for the aircraft and flight condition of interest by the "SPECSET" 

knowledge base. These requirements are then applied to the open-loop 

aircraft dynamics by the "SPECHKOL" knowledge base. An analogous knowledge base called "SPECHK" handles requirement comparisons for loop 

closures in the design process. (Use of distinct SPECHKOL and SPECHK 

knowledge bases is due to limitations in LEVEL 5 grammar, and they could 

be combined in a more sophisticated environment). 

E. COMMAND AND DISTURBANCE CHARACTERISTICS 

The characteristics of the commands are, in the main, direct consequences of the flight control tasks(s) to be performed, while the disturbances depend on the environment in which that task is to be accomplished. 

These consequences must be made specific by defining the characteristics 

of a family of representative input signals and disturbances. 

As a practical matter, commands and disturbances are not a clearcut 

dichotomy - some commands are contaminated by unwanted parts which drive 

the system in a way indistinguishable from disturbances entering at the 

same point. To be sure that no important forcing or excitation source is 

overlooked, it is pertinent to consider both commands and disturbances as 

"inputs," and then to classify them as to source and nature. A convenient 

set of categories is: 

0 At the Command Point(s) 

-- Desired Inputs (nominal "commands") 

-- Unwanted Inputs (nominal "noise on "Commands") 

0 At various Controller Locations 

-_ Internal Disturbances 

0 At locations External to the Controller 

-- Vehicle Induced 

-- Environment 

TR-1228-1-1 54 
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OF FSCR QUALITY 
A chart using these categories to classify the major flight control system 

inputs, which require consideration for an Advanced Fighter is given in 

Table 5. 

Table 5 calls specific attention to the many different forms inputs 

can take. As expected, the entire range of possibilities - from discrete 

steps or impulses to periodic and random processes - is represented. 

The inputs represented in Table 5 pertain to the entire mission. 

Those pertinent to mission phase CO or GA are made specific by an asterisk. A task that starts in preliminary design and continues on unabated 

throughout the entire system development is the chore of quantifying the 

major inputs and disturbances. In the preliminary design phase, it is 

often sufficient to consider nominal and maximum values of the inputs, 

although the entire spectrum of input types must be covered. In later 

design and test phases, the data needs intensify and the effects on the 

system of some inputs need precise definition. A summary of major sources 

for quantitative descriptions of commands and disturbances is given in 

Supplement 2. 

The atmospheric disturbance models are probably the best example of 

model refinement as a function of design phase. At the outset these are 

usually made quite simple in form, but often with outsized (larger than 

nominal or expected) values. Their basic differences across mission phase 

are associated primarily with altitude variations. For more detailed 

design phases, the atmospheric models are ordinarily expanded in detailed 

form, expected and variation values become predominant, and quantitative 

estimates of system performance and behavior may be given in probabilistic 

as well as expected value terms. 

TR-1228-1-1 56 
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SECTION I11 

HIGH PERFORMANCE AIRCRAFT LATERAL-DIRECTIONAL CHARACTERISTICS 

The bases for identification of many potential flight control system 

problems and the inspiration for some solutions derive directly from considering the airplane as an object of control. Although this can be done 

in general terms it is much easier to explain and follow with the aid of a 

concrete example. To this end we have contrived a quantitative mathematical model of an advanced fighter’s lateral-directional characteristics. 

This will be used for numerical work in illustrating the design sequence. 

The study airplane has features which represent some of the more 

troublesome airplane-centered stability and control problems that must be 

corrected by the FCS. It does not, however, indicate the entire range of 

possible difficulties; so from time to time in the discussion other awkward’ or troublesome airplane stability and control considerations will be 

introduced in passing to extend the coverage. For instance, the example 

airplane has a stable Dutch roll mode which might become a divergence and 

subsidence at very high angle-of-attack. Although the numerically defined 

study airplane will not exhibit such conditions, their possible presence 

must be considered as part of the FCS design problem of setting up the 

preliminary FCS architectural possibilities. 

The data bases developed in this section define and explore the airplane as a dynamic entity. To begin, the airplane equations of motion 

for three-degrees-of-freedom lateral-directional control are presented. 

These include transformations between the two types of body-fixed axis 

systems used, with associated transformations between the stability derivatives. The second article presents numerical values for stability derivatives representing the contrived example of an advanced fighter, and 

provides data bases for the characteristic modes, ordinary numerators for 

control inputs, and coupling numerators (Ref. 1). At this point enough 

airplane dynamic data in numerical form is available to start identifying 

some of the airplane deficiencies. This could be accomplished by comparing the airplane’s characteristics data bases with corresponding elements 

in the requirements data base. However, the airplane dynamics are not yet 

TR-1228-1-1 

PRECEDLNG PAGE BkAaK NOT FILMED 

59 
"understood" in that the origins and connections between the fundamental 

stability and control parameters and the example airplane dynamics are not 

well established. 

In order to gain a better appreciation of the physical origins of the 

aircraft properties another data base is developed. This airplane-dynamics interpretative data base is for literal approximate factors. These 

relate the airplane characteristic modes and numerator factors directly to 

combinations of stability derivatives expressed in symbolic form. To the 

extent that numerical values developed from the literal approximate factors are reasonably representative of the actual airplane poles and zeros, 

the connections between the stability derivatives and the poles and zeros 

become direct. One then has explicit symbolic formulae relating the airplane's derivatives to its modes, with the accompanying complete understanding of the origins of the bare airplane's dynamic behavior possibilities. 

The formulas for the literal approximate factors are from Ref. 1, and 

comparisons with data calculated using these factors with the actual airplane characteristics constitute the application data base. When the 

comparisons are very close the understanding is considered complete. If 

not, we supplement these data with a time-vector/phasor data base which 

can provide an excellent graphical representation of modal behavior and 

its connections with the basic forces and moments. For the example 

problem this step is not indicated. 

A. AIRPLANE EQUATIONS OF MOTION 

The lateral-directional equations of motion of the airplane perturbed 

from straight, (wing) level, horizontal flight referred to stability axes 

are given in Table 6 (see Ref. 1). These equations are expressed in terms 

of the rolling and yawing angular velocities p and r about body-fixed X 

and Z axes and the side velocity, v, along the Y axis. The side velocity 

is converted to an inertial sideslip angle @ - v/Uo. The applied accelerations due to the aerodynamic forces depend on the angular rates, the 

aerodynamic sideslip pa = @ - Bg (where Bg is a side velocity gust, air 

mass movement, or asymmetric bias expressed in sideslip terms), and 

TR-1228-1-1 60 
TABLE 6, LATERAL DIRECTIONAL AIRCRAFT EQUATIONS OF MOTION 

rb 

pb 

Perturbation Eauations of Motion (Stability Axesl: 

cos a. sin a. 

-sin a. cos a 

+ N‘r + N’p + I: Nisi 

P 

+ L’r + L’p + I: Li6i 

P 

6i is a generic control surface deflection: 

rudder, side force generator, etc. 

aileron, 

Kinematic Eauations: 

= 4J+B 

a = ;+~r-gfj 0 

Y 

= uoi - gfj 

J?RL-Bodv/Stabilitv Axis Array: 

I r P 

‘b 

0 

4 cos a 

Can be read either 

left to right or down 

Derivative Transformations: 

= L‘ cos a - N’ sin a 

= N‘ cos a + L’ sin a 

B OB 0 

B OB 0 

r 0 P 0 OP 0 

P 0 P 0 r 0 

P 0 P 0 0 r 0 

r 0 P r 0 OP 0 

“;Ib 2 2 = L’ cos a - (N; - L’) sin a cos a - N’ sin a 

= - (Lk + N’) sin a. cos a + N’ sin a 

= N’ cos a - (N; - L‘) sin a cos a - L‘ sin a 

N;Ib = N’ cos a + (N’ + L‘) sin a cos a + L‘ sin a 

2 2 L’ cos a 

2 2 

L;l b 

2 2 

TR-1228-1-1 61 
the aerodynamic and propulsion effectors 6i. The kinematic equations for 

bank angle and azimuth angle rates are also shown. 

Stability axes are desirable for insight and analytical simplicity, 

especially in connection with lateral-directional approximate factors. 

Also, fuselage reference line (FRL) axes are needed to properly account 

for the signals picked up by actual sensors. Thus, rate gyros mounted 

with their sensitive axes along the X and Z FRL axes will measure socalled body axis pb and q,, and the c.g. mounted accelerometers directed 

along the Y axis will pick up the side acceleration, etc. The bank angle, 

4, is a rotation about the X axis, and the bank angle equation given in 

Table 6 is suitable for bank angle as measured by a two degrees-of-freedom gyro with its outer gimbal bearing axis directed along the airplane's 

stability axis. In horizontal flight the X stability axis is horizontal 

in trimmed flight and the bank angle rate 4 is equal to the rolling 

velocity, p, about the X-axis. Notice, however, that the bank angle rate 

4, depends on both the rolling and yawing angular velocity components 

when these are referred to the FRL X and Z axes. Only when the FRL and 

stability axis systems are coincident (i.e., a. = 0) is the bank angle 

rate equal to the rolling velocity, pb - p, and the azimuth angle rate, 

I), equal to the yawing velocity, rb = r. 

B. NUMERICAL CHARACTERISTICS FOR THE EXAMPLE AIRPLANE 

The data needed to define the aircraft for the example are based on 

the flight condition in Table 7. 

TABLE 7. REFERENCE FLIGHT CONDITION 

Straight and level flight at: 

M = 0.6 

Altitude = 35,000 ft 

True speed = 584 fps 

Trim angle-of-attack - 12.4 deg 

Flight path angle = 0 

Load factor - 1 g 

TR-1228-1-1 
The lateral-directional aircraft characteristics including dimensional stability and control derivatives and transfer functions are given 

in Table 8. Due to the moderately high AOA, there are some significant 

differences between fuselage reference line (FRL) and stability axis derivatives. These are reflected in the similarities and differences in the 

transfer function numerators for the two different body axis systems. For 

instance, the characteristic function, A(s), called out as the "Denominator,'' and the transfer functions relating the side acceleration, the sideslip, and the lateral flight path to control effectors are the same for 

both axis systems. On the other hand, the transfer functions relating the 

body rates p and r to control effectors are different. Finally, the 

numerator factors for the roll angle transfer functions are the same for 

both axis systems although the gains differ because they are given by 

Li + tan a, Ni. These similarities and differences need to be accounted 

for later as certain net signals (such as stability axis yaw rate, r) are 

made up of various sensor combinations (such as body axis roll and yaw 

ratio, Pb and rb) . Because the example problem considers only a single 

design point and identical actuator dynamics for all effectors, it is not 

important here to distinguish between control effectiveness sources, so 

they may be considered to be composites derived from aerodynamic and 

thrust vectoring propulsion sources. For the design envelope, however, 

the mix and blending become central issues. 

The information of Tables 7 and 8 appears in the spreadsheet database format in Tables 9 to 14. The database elements include: 

Data Base Element Table breadsheet Window 

AIRCRAFT BASIC DATA 9 

FLIGHT and TRIM CONDITIONS 10 

STABILITY and CONTROL DERIVATIVES 11 

Stability Axes 

Fuselage Reference Line Body Axes 

CHARACTERISTIC MODES 

TRANSFER FUNCTION NUMERATORS 

COUPLING NUMERATORS 

12 

13 

14 

AIRCRAFT 

FLIGHTCOND 

DERIVATIVES 

MODES 

TRANSFERFUNC 

COUPLINGNUM 

TR-1228-1-1 63 
TABLE 8. SUMMARY OF AIRCRAFT ALONE CHARACTERISTICS 

Primed Dimenaional Derivative8 

I STABILITY AXES I FllL BODY AXES 

Y8 Lb Nb ‘6 Lb “a 

L; Nb L; N; Lb Nb L; N: 

yc Lh Nh yL$ 4, N ka 

ye 4 Ni ye Li Ni 

-50.69 -31.31 7.971 -50.69 -32.30 1.060 

0.13435 -0.08792 2.352 -0.5892 -0.3740 -0.04060 2.40 -0.08090 

0.0 6.569 0.3064 0.0 6.350 1.710 

0.01790 6.251 -2.583 0.01790 6.660 

6.56(0.0) (0.1275; 3.081 

0.30M1.761) [-0.733;2.511 

6.5610.127 5; 3. OS] 

(-0.00475) (0.428) (0.0208; 2.841 

6.35(-0.01203) [O. 1332;3.09] 

1.7 lO(O.250) (0.0 1064 ; 2.791 

6.7 3I 0.127 5; 3.081 

6.25(0.0) (2.05) (-2.43) 

-2.58(0.911) [-0.470;0.852] 

6.25(2.05)(-2.43) 

-18. 8NO.O) (0.0280) 

0.0 (0.0) 

68.6(0.0) (-1.802)2. 50) 

0. I175(0.0) (-1.802) (2.50) 

18. ae(o.0280) 

3.20(-2.73) 10.255; 1.3961 

0.00548(0.0) 1-0.0732; 13.771 

68. 61(-1.802) 2.50) 

0.1175(-1.802(2.50) 

6.66(-0.01203)( 1.982) (-2.31) 

-1.180(0.254) [0.0888;2.36] 

6.40( 2.05) (-2.43) 

78(-1 

-0.1175~0.0~(161.2~ 

-0.00548(-0.0732;13.771 

-0.117X 161.2) 

-18.88(0.0)(0.0280) 

-4.15(0.0280) 

66.3(-0.01214)(-1.793)(2.53) 

0.1136(0.0) (-2.2 I) (2.94) 

18.88( 0.0280) 

17.87(0.25 1) (1.912)(-1.9hO) 

0.0306(0.0) [0.0205;5.431 

70. 3(-1.801) (2.50) 

0.1203(-1.801) (2.50) 

02) (2.50) 

-0.1136(-0.01206)(162.9) 

-0.0306(0.250) (132.4) 

-0.1203( 161.2) 

Shorthand notation for eraasfor function tam: 

Cain terw are “COOt-~OCU8” gains. 

(8 + a) - (a); 112 + 2~ga + 41 - (<,%I. 

TR-1228- 1 -I 64 
TABLE 9. AIRCRAFT BASIC DATA 

I tem Symbol Value Units Axes ............................................................ 

Ai rcraf t Type 

Aircraft Class 

Geometry 

Planform Area 

Mean Aerodynamic Chord 

Wing Span 

Thrust Inclination 

Mass Properties 

Weight 

X Center of Gravity 

X Center of Gravity 

Y Center of Gravity 

Z Center of Gravity 

X Moment of Inertia 

Y Moment of Inertia 

Z Moment of Inertia 

XY Product of Inertia 

XZ Product of Inertia 

YZ Product of Inertia 

S 

MAC 

SPAN 

TI NCLNE 

wc 

XCGMAC 

XCG 

YCG 

ZCG 

IXX 

IYY 

IZZ 

IXY 

IXZ 

IYZ 

Advanced Fighter 

IV MIL-F-8785C 

196. 1 f t.'"2 

9.55 ft 

21.94 ft 

-2.76 deg 

16, 300 lbs 

7 %MAC 

0.6685 ft 

(1 ft 

C) f t 

3,679 slug-f t"2 

58,613 slug-f t"2 

59, 541 slug-f t"2 

2,699 slug-ft."'.2 

0 slug-f t'Y 

(3 5 1 IJ g - f t ..". 2 

TABLE 10. FWGHT BND TRIM CONDITIONS 

I tem Symbol Value Units 

F 1 igh t Conti i t ion 

Flight Phase 

Category 

Mach NumberA 1 t i t ude 

True Ai rspeed 

Wing Sweep 

Trim Conditions 

Angle of Attack 

Angle of Sideslip 

Head i ng 

Pitch Attituae 

bank Angle 

Flight Path Angle 

Roll Kate 

Fitch Kate 

Yaw Rate 

Turn Rate 

Normal Load FactotLateral Load Factor 

Axial Load Factor 

CO 

A 

ALT 

VTRUE 

MACH 

AOAo 

EO 

PSI0 

THETA0 

PHI0 

GAMMAo 

PO 

Qo 

RO 

OMEGA0 

no 

nYo 

n :.: o 

-- 

it 

+ps 

deg 

aeg 

9 

body 

body 

body 

body 

body 

body 

body 

body 

body 

body 

TR-12 2 8 - 1 -I 65 
TABLE ir.' STABILITY ANI, CONTROL DERIVATIVES 

Lateral Dimensional Primed Derivatives 

Stability Axes I Body Axes Units 

~~~~~~~~~

Symbol Value I Symbol Va 1 ue 

-50.69 I Ybb -50 69 .f t / sec +. 2 -rad 

VV -0.08679 I Yvb -0 . (38679 5 e c 1 

YB 

LB ' -31.31 Lbb' -32.3 L 

1.06 set.*''-" L

1 

NB 

0.13435 I Lpb' -(> . 374 

-0. (38792 i Npb ' -(I. (:I406 set.''- 1 

LP ' 

1 

NP ' 

Lr ' 2.352 I Lrb' 2.4 

Nr' -0.5892 f Nrb' -ij . tje(j9 sec"- 1 

Yda# (1 I Yda#b (3 1 /sec-rad 

Nda ' 0.3064 I Ndab' 

Ydr# 0.0179 I Ydrltb O.Ol79 1 /sec-rad 

Ldr ' 6.251 I Ldrb' 

Ndr' -2.583 : Ndrb' -1.18 

- 

Sec .*'% - 3 

7.971 NBb' 

s e c e.''. - 

5 e c .' 5 - 

Lda' 6.569 I Ldab' 6.33 s ec -.'*.- L cI 

1.71 ~ec-'''*-2 

6.66 5ec*".-3 .- 

Hoot 

Code 

Delta1 

Del ta2 

Delta3 

Del ta4 

Del ta5 

Del tab 

TABLE 12. CHARACTERISTIC M@DRS 

Psrameter Value 

Type 

rea 1 root -0. (10475 

rea 1 root 0.427 

z (I. 02(:18 

W 2.84 

Bodega i n -(I . 0 1635 

Wsr.''2 

2*Zsr*Wsr 

RLgain 1 

Units 

-------- 

rad /sec 

rad isec 

rad/sec 

-- 

-- 

-- 

Parameter 

Name 

ITS 

I TR 

Zd 

Wd 

,---------- 

deltass 

real complex Config 

poles poles Code 

Numerical factors: L 2 1 

Literal appro:< fac 2 2 1 

-7 

TR-1228-1-1 66 
r( c.1 mmm m;limmm 

TR-1228-1 -I 67 
cn + 

C 

3 

.4 

I r.1 M I I 

68 
The Aircraft Basic Data and Flight and Trim Conditions Data Bases are set 

up for general lateral-directional control situations. Thus the former 

includes provision for product of inertia couplings between the longitudinal and lateral-directional degrees of freedom while the latter contains 

trim conditions for steady-accelerated and/or constant angular velocity 

flight. For the example these are all zero. The "English" notation in 

the Stability Derivative Data Base is plain enough, although the 'b additions are needed to distinguish between FRL body axis and stability axis 

quantities. 

The data elements noted above are incorporated in the FCX flight 

control design expert system as explained in Volume 2. The definition of 

the aircraft including collection of the basic aircraft data is managed 

by the "AIRCRAFT" knowledge base. The aircraft basic data is read from a 

file and the user is queried for actuator and high frequency dynamics 

data. Definition of the flight condition and specification of data which 

is flight condition dependent is managed by the "FLTCOND" knowledge base. 

This includes obtaining stability and control derivatives from file, 

"instantiation" of the bare airframe dynamics model and operation of 

Program CC to obtain the bare airframe dynamics. From this the bare airframe transfer functions are obtained. Assembly of the open-loop aircraft 

dynamics, which include the bare airframe, actuator and effective high 

frequency dynamics, using Program CC is managed by the "ASSESSOL" knowledge base which is consulted by FLTCOND. The "ASSESS" knowledge base 

performs a similar function during the actual FCS design steps. 

C. LITERAL APPROXIMATE FACTORS FOR THE AIRPLANE CHARACTERISTICS 

While the airplane equations of motion describe the balance of forces 

and moments which underlie the airplane's dynamic behavior, the behavior 

itself depends on the natural modes and dynamic scaling of excitations. 

The natural modes are the roots of the characteristic function, while the 

"dynamic scalings" of primary interest are the numerators of the various 

airplane transfer functions for control effector inputs. For lateraldirectional control these are the gains, poles, and zeros of the airplane 

TR-1228-1-1 69 
transfer functions relating bank angle, 4, sideslip, p, and yawing velocity, r, to aileron and rudder. Unfortunately, because of the degree and 

complexity of the characteristic and some numerator polynomial equations, 

connections between the stability derivatives and the transfer function 

poles and zeros can often only be established in numerical terms. Then 

the development of trends between derivatives and poles/zeros can involve 

excessive numerical empiricism, and generalization is, therefore, tedious. 

To counter this, approximate equations have been developed which 

relate the airplane characteristic modes and numerator factors directly to 

combinations of stability derivatives expressed in symbolic form. These 

literal approximate factors allow the analyst to capture the essence of 

pole and zero variation with stability derivatives. Even if the approximations are only qualitatively correct considerable insight is gained 

about the relative importance and influence of particular derivatives on 

the natural modes and dynamic scalings. To the extent that numerical 

values developed from the literal approximate factors are reasonably 

representative of the actual airplane poles and zeros, the connections 

between the stability derivatives and the poles and zeros become direct. 

One then has explicit symbolic formulae relating the airplane's derivatives with its modes, with the accompanying complete understanding of the 

origins of the bare airplane's dynamic behavior possibilities. Further, 

as will be seen later, the approximate factors can also serve to point the 

way for automatic control operations to correct deficiencies in particular 

modes. This article addresses the literal approximate factors for the 

example airplane. 

1. Characteristic Equation Approximate Factors 

Table 15 summarizes the approximate factors for the lateral-directional characteristic function. These are computed below using the stability axis stability derivatives from Table 8. The results are compared 

with the actual modes as also tabulated in Table 8. [Note that in the 

data base structure for the design methodology the derivative data inhabit 

cells in Table 11 while the characteristic modes are present in Table 12. 

TR-1228-1-1 70 
TABLE 15. APPROXIMATE FACTORS FOR LATERAL-DIRECTIONAL 

CHARACTERISTIC FUNCTION (STABILITY AXES) 

FACTORED FORMS 

= s + - (s2 + 2c w s + wz,) dd 

or 

.. 3 3 

(SL + 2TSRWSRS + wL ) SR 

APPROXIMATE FACTORS 

- 1 

TR 

N’ B 

-(Yv + N: + N;)- 2 N, [Ni - ?] 

-L’ + 5 N’ (“i - t] B B 

pB 

L’ 2. 

0 

SR 0 

TR-1228-1-1 71 
TABLE 16. LITE= APPROXIMATE FACTORS 0- DENOMINATOR 

Conf ig: real roll-spiral, complex dutch roll 

ParameterParameter Value Units 

Name Type ------------------------------------ 

ITS9 realpole -(:).00485 rad/sec 

ITk9 realpole 0.427576 rad/sec 

Zd9 

Wd$ omega 2.823295 rad/sec 

zeta 0. (j20201 -- 

Deterrninat ion of LITERAL Pole Configuration 

Omeg a r s B 2 -0. (50207 

Clmeg ad 9 "2 7.9524 

Roll-spiral type 0 real 

Dutch roll type 1 complex 

Pole configuration 1 real roll-spiral, complex dutch roll 

# real poles, LAF 2 

# real poles, calc 2 

Validity check 1 1 VALID 

Lookup Tables 

type code type Confgcode 

0 real 0 4 real roots 

1 complex 1 real roll-spiral, complex dutch roll 

2 complex roll-spiral, real dutch r-011 

0 INVALID 3 2 complex pairs 

1 VALID 4 Undefined 

TR-12 2 8 -li-I 72 
The actual calculation of the approximate factors is accomplished and the 

results stored in Table 16 ("APPROX FACT" spreadsheet window and the comparison with exact factors is a subject of the next section). In the FCX 

flight control expert system (Volume 2), literal approximate factors are 

handled by the "FLTCOND" knowledge base. 

a. Roll Subsidence Mode. (1/T d 

Using the roll mode approximate factor from Table 15: 

- 0.428 rad/sec (vs. 0.427 rad/sec from 

exact numerical factoring) 

This example is somewhat unusual in that the "roll damping" derivative, 

Lf,, in stability axes is destabilizing (Lf, - 0.134 > 0). In FEU body 

axes it is low, but negative (I+ - -0.374 < 0) .* 

Constraint of sideslip (transient coordination) may further degrade 

the roll subsidence mode. This can be verified for the limiting case of 

perfect coordination achieved by a very high gain, B + 6, feedback: 

r4P 4P 6 

*6 6 a ' &a6r 

Nt +G N 

ar +- 

r 

6 

A + G rNB 

B 'r 

0.1175(161.2) 

0.0179(-0.143)(0.356)(144.5) 

(4) 

*Ordinarily both the 

low and moderate angles of 

roll damping derivatives would be negative at 

attack. The loss of roll damping -- as reflected 

in the stability axis derivative is related to the decrease in wing C at 

high a. The effective roll damping increment which creates stabilit+for 

the roll subsidence mode is due to roll-yaw coupling acting through the 

dihedral Lb. 

TR-1228-1-1 73 
b. Dutch Roll Mode. tr~ _. wdl 

The undamped natural frequency, Od, is given by, 

@d 

= 2.82 rad/sec (vs. 2.84 from numerical factoring) (5) 

The damping is, 

(-0.08792 - 32.2/584) - -31.31 -(-0.0868 - 0.5892) - 7.971 

(6) 

- 0.1141 rad/sec 

I, - 0.020 (vs. 0.0208 from numerical factoring) 

The normally (low a) dominant yaw damping from Yv + N; is nearly offset 

by the relatively large Li/Ni term. This is the sideslip coupling term 

which appears in the ~/TR approximate factor, which essentially transfers 

damping from the Dutch roll to the roll subsidence mode. It is, in fact, 

the damping component which makes the roll subsidence stable for this 

flight condition. 

c. SDiral Modes. 1’TSl 

The approximate factor for the spiral is 

1- L5 -I T S TR U 0 [Nb N; - ‘i] 

Using the approximate factor for TR, this becomes 

J -31’32 (-0.5892) - 2.352 1- 

- T S = (0.t28) [%$]I[ 7.97 ] 

= 4.00471 (vs. -0.00475 from numerical factoring) 

(7) 

TR-1228-1-1 74 
For the example airplane the approximate factors for the characteristic function work very well even though the example was not contrived with 

this in mind. Ordinarily the approximations for the natural modes are 

generally representative of trends but could not (and are not intended to) 

serve as an alternative to actually factoring the lateral-directional 

quadratic as this case might indicate. 

When the Table 15 literal approximate factors are seriously deficient 

there is still hope for developing fairly explicit connections between the 

derivatives and the modes. The first step is to examine other, more 

specialized approximate factor formulations, such as those derived from 

simplified equations for the several modes in Ref. 1. If this fails one 

can resort to time-vector diagrams (see, e.g., Ref. 1) to determine the 

most important terms in the equations of motion for each mode. This 

approach examines the eigenvectors and equations of motion for each of the 

characteristic modes of the airplane. To provide a graphical and highly 

insightful presentation, "phasors" for eigenvector ratios are used to 

characterize the relative motions of the airplane's degrees of freedom, 

and each of the airplane's equntions for each characteristic mode are 

represented by time vector diagrams. From these plots the analyst can 

gain a qualitative appreciation of the relative importance of each term in 

the equations of motion for each characteristic mode. Further, the quantitative importance of a particular stab€lity derivative can be seen. 

This leads to an impression of the relative significance of particular 

derivatives and of the most important factors to be viewed as key uncertainties. Finally, the time vector diagrams provide the basis for simplifying the equations of motion, if such simplification is appropriate to 

develop an understanding of a particular point, and for the subsequent 

straightforward development of literal approximate factors. Usually, 

however, the time vectors themselves will permit the analyst to gain 

sufficient appreciation of the physical origins of the aircraft poles in 

terms of fundamental properties. 

TR-1228-1-1 75 
2. Numerator Approximate Factors 

Table 17 lists some of the more important airplane numerator approximate factors for aileron and rudder inputs. Notable for their absence in 

this compilation are approximations for yawing velocity numerators. These 

numerators are cubics which, across a wide variety of aircraft, exhibit 

almost all possible forms. They can be three first orders with one or two 

negative roots, or first order plus quadratic with the possibility that 

either the first order or the quadratic damping have negative signs. 

Because of this wide variety of possibilities there are several literal 

approximate factor possibilities (see, e.g., Refs 1, 12), but because 

these tend to be specialized we have not presented them here. Also not 

presented are coupling numerators because these are usually low-order and 

simple enough in their symbolic form (see Table 6-3, Ref. 1). 

-For illustrative purposes typical examples will be computed below and 

compared with the actual results from factoring the complete transfer 

functions tabulated in Table 8. Just as with the characteristic function 

approximate factors these steps in the design methodology are actually 

accomplished within the data base structure. Thus, the derivative data 

are in cells in Table 11, the exact numerator factors are in Table 13 (via 

the mediation of an analysis program, such as Program CC, to accomplish 

the factoring), and the actual calculation and storage of the approximate 

factors is in Table 18. Finally, the comparison of approximate and exact 

factors is carried out within the data base as an operation in the next 

sect ion. 

a. Roll-Due-to-Lateral Controllex 

The roll numerator for aileron inputs is usually a quadratic dipole 

with an undamped natural frequency which is fairly close to the Dutch roll 

TR-1228-1-1 76 
TABLE 17. APPROXIMATE FACTORS FOR LATERAL-DIRECTIONAL 

NUMERATORS (STABILITY AXES) 

FACTORED FORMS 

4 2 2 N6(s) - A(s +~~‘ws+w) 

a 4 44 4 

B 1 N6 (s) = 

a 

s + -1 1 

T 

B2 

APPROXIMATE FACTORS 

0 

A - -N‘ B 6 a 

Aileron Numerators 

TR-1228-1-1 77 
TABLE 17. (CONCLUDED) 

I FACTORED FORMS 

General : 

a 

N6%) r 

= Aa Y [S - q] [S + q] 

x(s + 25, w s + w2 ) 2 

a 

Y aY Y 

or I 

[. + e-] + e-] 

where a sensor is located x feet 

At the center of rotation: 

APPROXIMATE FACTORS 

A = Y6* 

B r 

Aa = Y6 + x N' 

Y r a 'r 

1 

a 

T 

- 1 I -L 

Ta P 

y2 

U . J 2 or 1 I 0 (Y*N-YN ) a Ax N' 6r B v hr 

a 'r a 

TT 

a 

y3 y4 

Y 

Y, 

1 1. 'r !r, wa or - + - - - 

a 

2 

a Axam; 1 T T 

y3 y4 r 

YY 

Ba Y6 [-N; + Yv - y6 N.] 

r Y r 

-= - 

a 

T 

r y3 y6 

-U (Y N' - Y N') 

'r o r 6r 1. 

Rudder Numerators 

TR-1228-1-1 78 
TABLE 18. APPROXIMATE FACTOR CALCULATIONS 

IN SPREADSHEET WINDOW 

TR-1228-1-1 79 
undamped natural frequency. An appropriate approximate factor in this 

connection is, 

(stability axes) 

a 

"d 

7.97 

- 1.088 (vs. 1.085 from numerical factoring) 

Thus, for the usual positive "lateral stability" associated with positive 

dihedral effect (Lp' < 0) and positive "directional stability" (Np' > 0) 

the W#/Wd > 1 characteristic may be traced to proverse yaw-due-to-lateral 

control effector (N; > 01. 

a 

At higher angles-of-attack, the directional stability as measured by 

Nb will become less stable, even negative. This can cause w$ itself to 

become negative giving rise to a right half plane zero in the roll numerators, which can lead to very serious control difficulties. Although this 

effect is not necessary to consider for the point design example it must 

be borne in mind in considering the final system architecture. 

The damping term of the roll numerator is approximated from 

: -(Yv + N;) + 7 -a L; 

a 

2r4w4 L6 

- -(-0.0868 - 0.5892) + 6.569 0'3064 2.352 - 0.786 

0 - 0.128 (vs. 0.1275 from 0.786 

numerical factoring) '4 .I 2(1.088)(2.82) 

(9) 

Here the yaw damping derivative N+ is more effective than in 'd, as 

it is not offset by the (Lb/Nb)(Ni, - g/Uo) terms. 

TR-1228-1-1 80 
b. SidesliD-Due-to-Rudder 

As a second example of numerator approximate factors, consider the 

sideslip to rudder transfer function. The largest factor is, 

r 

r 

Ni 

yt 

1. -IT 

B3 

- 144.3 (contrasted with 144.5 -2.583 

0.0179 from factoring) 

The other two factors are often quite close together in magnitude. They 

are, accordingly, treated as a sum and product of inverse time constants 

which can then be separately determined with the quadratic formula. Thus, 

L' 

- 1 

r 

T 4 

= -0.13435 + -2.583 

6'251 [4.08792 - z] 

584 

- 0.2118 rad/sec 

1 (6.251)(-0.5892) I -- 

32'2 584 (2.352) [1 - (-2.583)(2.352) 

2 = -0.05106 (rad/sec) 

- 

1 = 0.355; (vs. 0.356 from factoring) T 4 

1 

- I = -0.144; (vs. -0.143 from factoring) T 

B2 

TR-1228-1-1 81 
3. Aircraft Characteristics at Other Flight Conditions 

One of the great advantages of literal approximate factors is their 

ability to explicitly show the effects of changes in flight condition. 

The dimensional derivatives vary directly with density, p, times speed, U, 

or with dynamic pressure, q, so these variations are readily apparent for 

a particular approximate factor. For example, the Dutch roll undamped 

natural frequency, ud, 

so 

The primed dimensional derivative Ni also varies with the dimensionless 

, and with the product of inertia. These quantiand derivatives C 

ties all vary with ang e of attack, and the dimensionless derivatives may 

also vary with Mach number. 

ns 

The flight condition examined here is at 1 g load factor and moderately high angle of attack. Fighters in combat maneuvering will routinely 

operate at much higher load factors. The first-order effect will be an 

increase in angle of attack (AOA) with some generic effects that can be 

anticipated. The dominant effect as AOA increases is a progressive loss 

of (aerodynamic) directional stability. This is reflected in the stability axis NB derivative, which is reduced from a large stable (positive) 

value through zero to negative values. As can be seen from the approximate factors, the dominant effect on the aircraft dynamics is that the 

Dutch roll frequency is reduced, usually with minor effect on the total 

damping, until the mode decomposes into two (low frequency) real roots for 

TR-1228-1-1 82 
N) A 0. As directional stability is further degraded with increasing AOA, 

the two real roots separate with one moving into the right half plane to 

generate an aperiodic divergence. 

As already noted, the complex roll-due-to-aileron zeros undergo a 

similar transformation with increasing AOA. The numerator "undamped 

natural frequency" term o#* ultimately becomes negative with one zero 

moving into the right half plane. This zero then creates a roll reversal 

characteristic in the roll control response. The combination of righthalf-plane zeros with rhp poles creates a very difficult and interesting 

flight control problem. 

TR-1228-1-1 83 
SECTION IV 

IDENTIFICATION OF LATERIAL-DIRECTIONAL CONTROL PROBLEMS 

DUE TO THE AIRPLANE 

At this stage the example aircraft characteristics developed in 

Section I11 can be compared with many of the mission-based requirements 

from Section I1 to define some of the basic aircraft-centered control 

problems. This will be done below, starting with the path and heading 

control problems common to the pilot and automatic flight guidance equipment. Then the flying qualities deficiencies of the bare airplane will be 

examined by comparing the airplane characteristics with the minimum 

requirements. 

A. GENERAL PATH AND HEADING CONTROL PROBLEMS 

By transferring the aircraft characteristics from the data base into 

a controls analysis program (e.g. , Program CC) , the tabular data can be 

given more visual and insightful life as response plots. A survey of the 

aircraft response characteristics to lateral control, 6,, is shown in 

Fig. 12. The survey includes pole-zero plots and jw-Bode diagrams for 

sideslip, bank angle, and the FRL-oriented yawing velocity. The transient 

responses show the same variables plus flight path rate when the airplane 

is excited by an aileron impulse. The key points indicated by the survey 

include : 

0 The very lightly damped dutch roll mode is dominant in the sideslip and FRL rolling velocity 

responses, while it is scarcely perceptible in 

the yaw and path rates and bank angle motions. 

The reasons for these effects are clearly shown 

by the nearly cancelling quadratic pairs in the 

bank angle and yaw rate root and Bode plots. For 

the given input these outputs are practically 

non-observable. 

Conclusion: FRL yaw rate and bank angle feedbacks to aileron are not suitable to correct 

dutch roll difficulties. 

TR-1228-1-1 

PRECEDING PAGE BLAI'X NOT FILMED 

87 85 
ORIGINAL PAGE IS 

OF POOR QUALITY i al 

In 

- 

0 

a 

In 

C 

0 

Q 

In 

c 

L, 

TR-1228-1-1 86 
0 The bank angle and path rate responses are 

closely proportional to one another, and reflect 

primarily the roll subsidence mode. 

Conclusion: Bank angle may be a good surrogate 

for lateral path rate. 

0 The pole/zero separation in the [r4, w+]/[rd, ~d] 

dipole evidenced by wd/wd > 1 and r#/rd > 1 produces the large dutch roll residue in FRL rolling 

velocity (pb) responses to roll controller input. 

Conclusion: FCS designs should be such as to 

effectively decouple the rolling velocity mode 

from dutch roll by reducing the separation of the 

dipole terms. 

0 A closed-loop pure gain bank angle-to-aileron 

control law will have a maximum (neutrally stable) crossover frequency (bandwidth) less than 

wu & 1.25 rad/sec. 

Conclusion: Pure gain bank angle lateral controllers are severely limited in attainable bandwidth by unfavorable W$/Wd > 1. 

The bare airplane dynamic characteristics which affect a bank-to-turn 

design are revealed by considering the path response to command after a 

generic high (but finite) bandwidth roll control system has been established. As indicated in Fig. 13, this shows the potential of high bandwidth FCS in which the inner loop dynamics are dominated by the FCS control law design and airplane control effectiveness (within the control 

power limitations) rather than aerodynamics. The roll response to roll 

commands approach 

where q,d is the roll command bandwidth. 

Over this same bandwidth the roll command will result in a path rate 

response given by the ratio of numerators Nx /N4 . At frequencies lower 6a 6, 

than the smaller of wx and w4, and assuming that the aileron-induced side- 

* & 0, the path response to roll command approaches, '6 a 

force coefficient 

TR-1228-1-1 87 
Rol I 

Command 

------ 

Flight AIRCRAFT 1 

I I Path 

I 

I 

Ba 

IVsa (at high gain G - I I large) 

+- 

N+ 

Figure 13. Generic Roll Control System for Path Control 

a +- - g; w<w w - i 

b4' w4' X 'c N: uO 

a 

This is the steady turn relation already noted in connection with the 

heading control requirements discussion in Section 11. It indicates that 

if the turning maneuver is perfectlv coordinated and a high bandwidth roll 

control system can be implemented, there would be no intrinsic path control problem for bank-to-turn operation beyond the control power issues 

noted previously. 

Next the assumption of perfect coordination is relaxed so that the 

unconstrained sideslip degree-of-freedom is again included. The limiting 

response to roll command (without rudder input) with a generic high gain 

TR-1228-1-1 88 
roll control system 

response is 

f 

4 

- 

(Fig. 13) is summarized in Fig. 14. The path 

N; a 

GN; 

I a +- 

a 

A + GN6 4 4 -+ 

a 

0.388[0.0865, 2.961 

I 6.56[0.1275, 3.081 

As expected, at very low frequencies this approaches 

-+ 0.055 (rad/sec/rad) &- 

4 + *O 

Thus, the steady-state I A/4 I response is again consistent (for 

small 4) with the more general steady coordinated turn relation 

4 + 6, 

At this level of approximation: the closed-loop roll subsidence mode 

(l/Ti) is the governing factor in the roll loop bandwidth ut-,+ and can 

be considered to be large (i.e., roll response is "instantaneous" compared 

with heading change);* the spiral is a pole (kinematic integration) at the 

origin; and the dutch roll mode goes to the roll zero [bd, wd]. The 

effective dutch roll damping ratio of the closed-loop roll control system, 

*The prime on Ti indicates that one loop has been closed and that 

the roll subsidence has been modified thereby from TR to Ti. A prime is 

added for each loop closure which affects a factor present in an openloop dynamic model. 

TR-1228-1-1 C-L 89 
- ais p .. .v 0 

TR-1228-1-1 90 

ORIGINAL PAGE IS 

OF POOR QUALtTY 
would be improved over the bare airframe (Id - 0.021), but would still be 

Level 2 in terms of MIL-C-8785C. However, as revealed by the near absence 

of any dutch roll in the X time history as well as the root and Bode 

plots, the dutch roll residue in X is small due to the typical near cancellation of the q/w4 dipole. The IX/dl Bode plot shows that the q/od 

dipole is minor and favorable such that the path response to roll command 

closely approaches an ideal K/s-like form over an extensive frequency 

range, thereby not limiting any reasonable outer (path) loop crossover. 

Thus, there are no path control problems due to the airplane characteristics gnce an adequate roll control system is achieved. 

While good control of path rate can be achieved with roll control 

alone, it will be seen in the next section (e.g., Fig. 18) that the dutch 

roll cannot be significantly modified with aileron based control action. 

Therefore, at higher frequencies near and including the dutch roll, there 

can be significant sideslip and attendant uncoordination without additional FCS elements. This will cause flying qualities and tracking problems due to sideslip and yawing velocity excitation at the dutch roll. 

B. GENERAL ROU CONTROL PROBLEMS 

To this point, the path and heading problem has been examined without 

consideration of the details of the roll and yaw dynamics. To start, the 

roll response to the control effectors will now be addressed. This provides a preview of the response to the pilot's controllers (stick and 

rudder pedals). The roll response to aileron, assuming perfect coordination (from Table 6 equations with B - 0 and a. - 0 for stability axes) is 

- 4- 

2 

s - L' s - L; (g/uo) 

6 

P 

6.57 

- (+O. 299) (-0.433) 

In this ideal situation, only the roll and spiral modes are present, but 

the spiral, as expected, has become much more unstable. Despite this, 

TR-1228-1-1 91 
bank angle feedback to roll control with lead compensation to offset the 

~/TR lag could provide adequate roll control for either an automatic system or a pilot in continuous control. However, this would not be desirable 

for human pilot operations because the pilot generated lead (TL z TR z 

3.3 secs; from Eq. 14, Supplement 3) would be far too large and the spiral 

is too unstable for unattended operation to be practical. 

Without any sideslip constraints the system survey for the pure gain 

roll controller of Fig. 15 indicates that, while the spiral mode causes 

no control difficulties, the dutch roll dipole limits stable crossover 

frequencies to values below about 1 rad/sec. This stems from the proximity of the dipole to the right half plane, and from the pole-zero order 

( IW,$/Odl > 1) , which results in the phase "dip" at the dipole. 

The attainable response time for a pure gain controller adjusted to 

give a dominant mode of [0.7, 0.31 would be greater than 14 seconds, which 

is far too slow for good roll control. 

C. PILOT CONTROL PROBLEMS 

The basic path and roll control issues treated above are generic, and 

apply to both piloted and automatic control. Because the pilot has workload and attentional limitations as a controller, aircraft flying qualities considerations become central in manual control of effective airplane 

dynamics which are "inner loop" features from the path control standpoint. 

Fortunately, the Section I1 requirements set by flying qualities specifications and pilot-vehicle considerations provide some quantitative guidance on the values of many of the particular aircraft features which have 

already been raised as generic control problems. This permits some of the 

airplane's deficient dynamic properties to be directly identified and 

quantitatively tied down. 

All of the airplane's natural modes fall into this framework. The 

characteristic function (denominator) of Table 8 provides all the necessary information. 

Spiral (s - 0.00475): This is slightly unstable, but with a 

time to double amplitude of 146 sec easily meets the MIL-F-8785C 

TR-1228-1-1 92 
9 6.56 &128,3.08] 

sa (-.0048)(.427)~021,2.84] 

I I I I I 1 I 

-3. -2. -1. 

-U 

a/ Convenfiona/ Roof Locus 

10 

60 

YO 

0.Ol 0.10 w(rad/secl DO 

Wd A I I 

9 4- 

aa 

-inn 

(deg) 

-200 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

- I + 

5 * 1.0 + 

* 0.5 + 

b) ju - Bode and Bode Root Locus 

Figure 15. System Survey of Pure Gain 0 -t 6a Closure 

Around Bare Aircraft 

TR-1228-1 -I 93 
Level 1 requirements for CO (T2 > 12 sec) and also for Category 

B flight (T2 > 20 sec). Further, it is not coupled with the 

roll mode. A slightly unstable spiral mode is not unusual, and 

is only a problem for unattended operation (manual control). If 

outer loop bank angle control is implemented, the spiral will be 

stabilized even at quite low gains. 

Poll s ubs idence (s + 0.427) : The time constant (TR - 2.34 sec) 

is very high and is MIL-F-8785C Level 3 -- a serious deficiency 

for a fighter. It should be no greater than 1 sec to be Level 1 

for the CO mission phase. 

Dutch Roll Mo de [(s2 + 2(0.0208)2.84s + 2.842)]: The frequency 

of this mode is adequate (i.e., greater than 1 rad/sec), but the 

damping ratio is unacceptably low -- almost Level 3. The minimum required is cd 10.4. 

D. SUMMARY OF AIRPLANE DYNAMIC SHORTCOMINGS AND EQUALIZATION NEEDS 

In the discussion above the airplane has been examined as a source of 

problems in path and heading control, bank angle control, and flying qualities. The example airplane characteristics developed in Section I11 have 

been compared with the requirements of Section I1 to expose several major 

shortcomings which will have to be corrected by the flight control system. 

[All of this has been verbalized in the discussion whereas in the design 

methodology the comparisons between requirements and characteristics are 

accomplished within the data base elements -- see Table 41 There are, of 

course, some comparisons which cannot easily be put into quantitative 

terms. Therefore, while it may be somewhat repetitive, the following 

paragraphs will summarize the general equalization requirements which any 

flight control system design will have to satisfy for the example airplane. These will be presented in an order which starts with the effective airplane as presented to the pilot (basically stability augmentation 

or FCS inner loop equalization requirements) and progresses to guidance 

(outer loops) considerations. 

1. Modes to Change to Meet Flying Qualities Requirements 

Dutch roll -- increase damping ratio (to 0.4 or greater) 

Roll mode -- reduce time constant (to 1 second or less) 

TR-1228-1-1 94 
2. Dynamic Coordination for Piloted Inputs to Lateral Controller 

A basic desire for lateral piloted control is to establish a rolling 

velocity response proportional to the pilot's input to the lateral controller which: approximates a first-order system (dominated by the effective roll subsidence mode); is uncontaminated by dutch roll mode effects; 

and is ideally nearly free of transient sideslip. If the flight control 

system employs rolling and yawing velocities and sideslip feedbacks to the 

rudder (or effective directional control effector combinations) and also 

incorporates a crossfeed from the lateral to the directional controller, 

the control law will be, 

'r 6r 

a 

Sr - -Grr - Gp p - GBB - GS Sa 

Then the effective sideslip to lateral controller numerator transfer function will be 

- Nf + Gr NS Br +G " N' + Gir N{ 

a ar P 6a6r ar eff 

The r, p, and B feedbacks are typically used to adjust features other than 

coordination, such as the dutch roll damping and undamped natural frequency, although they may also be useful in enhancing the maneuver coordination. The 6, + 6, crossfeed is usually the last addition made to the 

system, and then only when needed. To achieve ideal perfect coordination 

in rolling maneuvers executed by lateral controller action, the ideal 

crossfeed is, 

Br +GrNg6 6 BP

P ar 

N! + Gr N6 S 6r a ar 

N, B GS - 

a 

br 

This ideal GSr crossfeed is a useful measure of coordination needs even 

when a crossfeed is not physically present in the FCS. It indicates, for 

instance, what the pilot must do with rudder to coordinate rolling maneuvers. Equation 23 is fairly complex expression (a third-order over 

&a 

TR-1228-1-1 95 
third-order in the simplest case), which can vary a great deal with flight 

condition (all of the N's are airplane numerators). However, when attention is paid to coordination as a secondary requirement in selecting the 

Gr and Gp feedbacks, an approximation adequate for excellent coordination 

is usually achieved by nothing more complicated than a lead/lag or lag/ 

lead. 

3. Loops to Improve Effective Numerators 

The roll-to-aileron numerator damping ratio should be increased and 

the separation of the effective [r4, w4]/[rd, wd] dipole should be minimized. No loops are required to improve effective numerators for the 

outer loop variables of path or heading. 

4. Inner Loops to Adjust for Outer Loops 

Control of heading and lateral path angle requires a tight roll loop 

closure. In turn, the roll loop requires inner yaw loops and/or crossfeeds to maintain transient coordination, and to minimize dutch roll artifacts. A rolling velocity to lateral controller loop can act as needed 

roll axis equalization for both piloted and automatic roll control purposes. 

5. Series Compensation 

In all cases, elementary lead/lag or lag/lead type compensation will 

suffice. Series compensation is possibly required in the inner roll (rolling velocity loop), and yaw axis loops (for such things as low-frequency 

washout). For the bank angle automatic control loop, the inner rolling 

velocity closure common to both auto and manual control may be sufficient 

to permit a tight high bandwidth bank angle closure. A lead/lag series 

equalization may be desirable to offset flight conditions where the higher 

frequency airplane, actuator, and sensor lag terms build up. 

TR-1228-1-1 96 
SECTION V 

PROSPECTUS FOR LATERAL-DIRECTIONAL FLIGHT 

CONTROL SYSTEM ARCHITECTURE 

The previous sections have developed the system requirements, 

examined the airplane's dynamic properties, and compared these with the 

requirements. In the comparison several airplane characteristics were 

found wanting. The correction of these inadequacies is a central flight 

control system design problem which must be solved for either manual or 

automatic control. A major leg up on the solution has also been accomplished in that the sources and governing parameters which define the 

airplane-specific control problems have been identified. That is, the 

dynamic characteristics have been related to the airplane's stability and 

control parameters via literal approximate factors. Success with this 

step leads directly to an appreciation for: 

0 possibilities for the adjustment of particular aircraft modes by stability augmentation using an 

"equivalent derivative" approach; 

0 sensitivity to uncertainties in airframe parameters 

(i.e., non-dimensional stability and control derivatives and mass properties); 

0 variation in airframe parameters over the flight 

envelope -- primarily due to p(h), M, a, and Uo variations. 

Correction of the aircraft-centered problems by means of the flight 

control system is a necessary step Fn the flight control design process. 

Unfortunately literal approximate factors do not always work out as well 

as in the example, so supplementary approaches are needed. The description and illustration of these approaches make up part of this section. 

Control system principles are used in the process, but the focus is 

usually on the special features of airplanes as dynamic elements, not as 

general "controlled elements". Correcting the airplane's deficiencies to 

create a superior set of "effective airplane" characteristics is an aspect 

which separates flight control svstem design from control system design in 

general. It stems from the nature of manned airplanes as objects of both 

manual and automatic control. 

TR-1228-1-1 97 
After the airplane's problems have been corrected via control means, 

the other central FCS problem, that of appropriate automatic guidance, can 

be addressed. This is accomplished following general control system 

design principles and procedures and is not as closely dependent on the 

airplane's peculiar dynamics. This follows because the feedbacks needed 

to provide good flying qualities also result in good inner loops for 

outer-loop automatic control. These inner loops provide appropriate 

"parallel equalization" on which to base the guidance loops regardless of 

whether they are mechanized by automatic equipment or formulated internally by the pilot. 

This section treats the initial layout of architectural possibilities 

for the solution of the problems identified previously. The first article' 

describes, in outline form, equalization requirements for control systems 

in general. The second article is also somewhat general in character, but 

is directed specifically to flight control. It describes the elements of 

the flight control system design prospectus. Where possible summary 

tables of prospectus topics are provided. Finally, the third article 

illustrates the application of the prospectus topics to the example airplane. 

A. EQUALIZATION REQUIREMENTS FOR CONTROL SYSTEMS IN GENERAL 

As a prelude to the development of possible FCS architecture, the 

overall system requirements, operational environment, unalterable element 

characteristics, etc., are viewed as a framework from which to consider 

feedback and equalization requirements in general. As noted in the introduction, there are three major considerations: 

1. The ultimate outer-loop which involves the desired output 

variable or its surrogate, must have appropriate equalization to meet the overall system requirements. This implies 

that the closed-loop system exhibit: 

-- Adequate low-frequency steady-state error responses. 

-- Specified closed-loop system dominant mode characteristics (for example, bandwidth and damping needed for 

disturbance suppression, and for the closed-loop 

dynamics portion of the command/response relationship). 

TR-1228-1-1 98 
Specified low-frequency command/response relationships 

(for example, suitable input, feedback, and feedforward characteristics to achieve desirable responses). 

Approximate reduction to crossover model-like (see 

Appendix C or Ref. 1) characteristics in the crossover 

regions with phase, gain and delay margins, and peak 

magnification ratio values sufficient to assure robust 

outer loop control. 

Noise rejection (smoothing) at frequencies at and 

above control action. 

This equalization can be obtained from either series elements operating on the primary variable, or from parallel 

elements involving the feedback of other aircraft output 

variables, or from a combination of both. 

2. Equalization requirements levied by desired responses of 

subsidiary variables to commands and disturbances. 

3. Provision of sensitivity constraints and reduction for some 

selected uncertainhighly variable unalterable element 

modes by driving them into specially placed low tolerances, 

compensation zeros. 

These general points can be made more concrete by connecting them to 

the example airplane FCS. Here the first consideration will refer to the 

bank angle loop, which should follow bank angle commands (from heading or 

path outer-loop guidance elements) with no steady-state error, should 

regulate the airplane's bank angle against lateral-directional disturbances, etc. The equalization needed to permit the bank angle control loop 

to provide rapid responding, well-damped, responses to command can come 

both from the inner loops as parallel equalization, and the outer loop as 

series compensation. The second consideration leads to several inner 

loops which have their own independent roles as lower-level controllers to 

correct airplane deficiencies while incidentally providing parallel 

equalization for the outer loops. The third consideration is a special 

purpose means to substitute low-tolerance poles and zeros for highly variable ones. A partial example of this will be seen in the roll damper 

mechanization for the example problem. 

TR-1228-1-1 99 
B. PROSPECTUS FOR FLIGHT CONTROL SYSTEM ARCHITECTURE 

The "Architecture" to be established here amounts to a control system 

skeleton comprising feedbacks, equalization (adjustment of the effective 

aircraft dynamics as seen at a particular command or disturbance entry 

point), compensation (adjustment of particular controller dynamic properties, usually as a function of flight condition), etc. The architectural 

drawing is characteristically a detailed block diagram of the overall 

sys tem. 

Sufficient information is now available to consider the two general 

types of equalization in detail: 

a) Series on the primary variable (or its surrogate). 

b) Parallel using controlled element secondary output variables. To establish this part of the prospectus, a search 

is conducted for favorable effective aircraft transfer 

function numerator properties. 

For adjustment of the effective aircraft transfer 

functions for the primary variable, examine the 

effects on the primary variable transfer functions of 

infinite gain closures with secondary variable feedbacks. This amounts to examining the ratios of aircraft secondary-to-primary variable and/or couplingto-primary variable numerators. Desirable results 

occur when, for instance, the feedback of a secondary 

variable damps a nuisance mode or provides a region of 

K/s-like character in the primary transfer function 

when it is modified by a secondary variable inner-loop 

closure, etc. 

- For improvement of disturbance responses the effects 

of both primary and potential secondary feedbacks in 

adjusting the disturbance numerators need to be surveyed. 

While "equalization," including the selection of appropriate feedback 

loops, falls conveniently into the two categories (serial and parallel) 

noted above, the actual details of the feedback selection for parallel 

equalization is much more involved. In fact, the development of control 

system possibilities is based on the above factors plus the accumulated 

knowledge of key features of the aircraft as an object of control. The 

general nature of potentially desirable specific feedSacks/controller 

TR-1228-1-1 100 
architectures stems from the organized, but nonetheless artful consideration of the elements of the prospectus listed in Fig. 16. 

The particulars of how these "Elements of the Prospectus" are 

actually used in a preliminary design will be illustrated in the FCS 

design example presented in the next article. Here we will elaborate on 

the elements themselves. The Literal ADD roximate Factors element has 

already been introduced (in Tables 15 and 17). They were used in Section 

I11 to understand the airplane's dynamics and the physical sources of the 

airplane's modes and transfer functions poles and zeros. Table 19 is a 

summary of Lateral-Directional Essential Feedbacks adapted from Ref. 1. 

This table encapsulates a great deal of FCS history in that it contains a 

cross-section of feedbacks which have been successfully demonstrated 

throughout the years. They are "essential" in the sense that the controller function(s) listed in the left hand column require them or reasonable 

surrogates. However, no feedback quantity is. universally applicable to a 

particular function -- all have some problems sometimes. A partial listing is provided in the far right hand column. Finally, the table gives 

first order information about gain adjustments needed as flight condition 

and/or non-dimensional stability parameters change. 

The next two elements of the prospectus are complementary. The 

Multi-variable Sen sitivitv Vector SurvevS provide excellent guidance on 

the low eab effects of the feedback of various airplane output quantities 

on the airplane's natural modes. The underlying details of the multivariable sensitivity vectors are presented in Appendix B. The Eff ective 

Vehicle Characterist ics with Hieh-gain Closures are heavily dependent on 

the effective numerators of the airplane and on the control system structure. The feedback system structure appears implicitly in the guise of 

coupling numerators. The high gain characteristics show what happens to 

some of the modes starting off in the multi-variable sensitivity vector 

survey as the feedback gains become large. The overall vehicle-dynamicscentered multi-variable analysis technique which covers coupling numerators et a1 is outlined in Appendix A. The last prospectus item is Properties of Elemental Systems. These are particularly helpful simplifications 

TR-1228-1-1 101 
0 Literal Approximate Factors of the Aircraft 

-- Indicating the natural stability derivatives 

of the aircraft which affect various modes, 

aircraft numerators, etc. Artificial 

enhancement of these derivatives via automatic control is one way to achieve some 

desired effects (e.g., a Krr -+ 6, feedback 

creates a ANr - KrN6,). 

0 "Essential Feedbacks" Summaries 

-- These are tables, summaries, etc. of what 

various feedbacks are good for. They constitute, in the large, the accumulated experience of past FCS designs, developments, and 

analyses. 

0 Multi-variable Sensitivity Vector Surveys 

-- The examination of the low gain effects of 

imaginable aircraft output motion or kinematic feedbacks on the various aircraft-alone 

modes. 

0 Effective Vehicle Characteristics with High-gain 

Closures 

-- High gain, multi-variable system closures 

result in effective aircraft poles and zeros 

governed by coupling numerators of the aircraft. These reveal the higher gain consequences of the same types of feedbacks examined in the low-gain sensitivity surveys. 

0 Properties of Elemental Systems 

-- Low-order transfer characteristics which 

serve as excellent approximations to dominant 

or nuisance modes of actual systems viewed 

through "windows" focused on local frequency 

regions 

'Figure 16. Elements of the Prospectus 

TR-1228-1-1 102 
ORIGINAL PAGE IS 

OF POOR QUALITY 

- NR 

c N 

d 

r3 

t 

a 

4 0 

.. 

.. . -N n 

a 

a 

- N 

s 

t 

4 

.... 

-NR~ 

.. . . -.a. n t 

- N 

4 

0 

t 

6 

I" 

X 

.. 

-a*\ 

66 

It 

x4 

4 

u) 

t 

P 

-N 

.. 

-& 

d 

0 

TR-1228-1-1 103 
which often provide excellent approximations to dominant modes or, alternatively, frequency domain approximations valid over a limited range of 

frequencies. A catalog of the elemental systems is the subject of Appendix C. 

The actual utilization of the elements of the prospectus in the context of the system requirements and other data developed from the previous 

design phases can involve a good deal of integrative engineering. Taking 

the entire packet of information and tying it all together to mold the 

results into feasible system architectures, constitute the process of 

preliminary FCS design. At the end the flight control system synthesis 

will hopefully have resulted in one or more feasible sets of control laws 

and/or FCS block diagrams which show the loop structure and equalization 

forms. There remains the not insignificant task of adjusting the parameters in the control laws to meet the quantitative and qualitative 

requirements in the presence of all the system disturbances, uncertainties, and variabilities. 

In much of the above discussion, the aircraft has been considered to 

be more or less unalterable or given with the FCS then tailored to correct 

the vehicle’s characteristics. In a true integrated system design, the 

process can also, with some limitations, go the other way. There are 

major opportunities for vehicle tailoring. Some examples are listed in 

Fig. 17. In this approach the aircraft is optimized without regard for 

the stability and control or flying qualities characteristics (except for 

the provision of adequate control power and effector rates) relying on the 

FCS to take care of the deleterious aircraft dynamics which might be left 

over. 

C. PROSPECTUS FOR AUGMENTATION TO ALLEVIATE 

BASIC AIRCRAFT DYNAMIC DEFICIENCIES 

With the basic understanding of the aircraft dynamic problems and 

flight control system requirements established in previous sections the 

elements of the prospectus listed in Fig. 16 can now be applied to each 

issue. Many appropriate Literal ADDroximate Factors have been presented 

TR-1228-1-1 104 
-- Reduced Drag (by adjusting maneuver margin, 

horizontal and vertical tail size, etc.) 

-- Increased L/D (by camber adjustment, or by 

increasing aspect ratio using active control 

for wing-root bending relief, etc.) 

-- Reduced Structural Weight (by gust and maneuver load alleviation) 

-- Reduced Observables (by reduction of tail, 

tail length, etc.) 

. TOTAL SYSTEM RETJABILITY E"cm 

-- Adjusting airframe properties so that minimum 

FCS is adequate for control: [Examples would 

include: the adjustment of aircraft 

roll/aileron effective w /Wd to permit 

permit a simple yaw damper -- good Wr/Wd -- 

as the sole redundant control channel; 

vehicle designs which permit a wide variety 

of stability and control problems to be 

solved using rate gyros alone -- and then 

using skewed gyro packages; appropriate 

adjustment of thrust line inclination to 

provide for good STOL approach 

characteristics, etc.] 

aileron-only control; di i! edral selection to 

0 VEHICLE DESIGN FOB FCS ROBUSTNESS ENIIANCEZIENT AND 

CONTROIS BECONFIGURATION 

-- On multiple-effector aircraft (e.g., flap, 

canard, strake, thrust vector available for 

longitudinal control), aspects similar to the 

above, but with the dimensions of battle 

damage, maintenance foul ups, etc. included. 

Figure 17. Some Opportunities for Aircraft Tailoring 

TR-1228-1-1 105 
in Tables 15 and 17, and need only be referred to as needed. Similarly, 

the Essential Feedbacks Summary exists as Table 19. The prospectus element related to Effective Vehicle Characteristics with High-Gain Closures 

is specific to each candidate system and so is deferred to the detailed 

discussion. 

Only the Multi-variable Sensi tivitv Vector Survevs need to be derived 

to complete the introduction of prospectus topics. For the example airplane, the literal approximate factors in terms of stability axis derivatives work exceedingly well. Consequently, an entire prospectus for the 

improvement via control action of the roll subsidence and dutch roll can 

be accomplished using these relationships, assuming the airplane's motions 

are measured or otherwise estimated in stability axis terms. It is not 

always the case that the approximate factors or the "essential" feedback 

relationships apply as well as in this example. We are also interested in 

other sensible quantities, such as body axis rates and accelerations, for 

which these relationships are more obscure. For this purpose, the multivariable sensitivity vector survey is an important tool. 

X 

Figure 18 shows the gain sensitivity, SK, at low gain (Kx + 0) for 

four potential feedback variables x - pb, rb, p, ) to the two possible 

control points (lateral controller and rudder) . Wih these figures, comparisons can be made of the effects of the candidate feedback amon7 the 

mode%. 

The evolution of potential system feedback possibilities will be 

developed below by examining each airplane deficiency in the context of 

the prospectus elements. This will be done in sequence, starting with the 

roll subsidence mode. 

1. Roll Subsidence Mode -- Low ~/TR 

a. Literal Amroximate Factor for ~/TR (Table 15) 

Augmenting the stability axis Li, roll damping derivative would 

directly improve (increase) ~/TR. 

TR-1228-1-1 106 
3 .- 

cu 

M’ 

n L 

9 1- N 

n 

2f i\ I1 ’\ 

- I\ !\ ‘.c 

cn 

. 

6 u 

ZI 

0 

N 

I’ 

‘f! 

b 

I 

ci? 

TR-I 228-1 -I 107 
b. Essential Feedbacks (Table 19) 

A p + 6, "roll damper" loop will augment Li, 

c. Multi-Variable Sensitivity Vector Survev 

Figure 5-3 indicates that both of the ERL body-axis oriented angular 

velocities as well as sideslip and side acceleration, if used as feedback 

quantities, would have an effect on the roll subsidence. However, only 

Pb -+ 6, can improve (increase) ~/TR without significantly affecting the 

dutch roll and spiral modes (Note the small Pb vectors at the dutch roll 

and spiral modes and the large vector at the roll subsidence). 

d. Effective Characteristics at High Gain 

(D -+ 6,. Gain in Forward Path1 

e 

PC 

-1 

If such a high gain roll damper is used, then the roll angle response 

to lateral controller will tend to a K/s-like form. This is ideal for 

both the pilot and automatic control for regulation of bank angle. High 

gain in this connection means that the roll damper crossover frequency is 

well above that of the outer manual or automatic pilot loop. Note that 

there is no assurance from this high-gain perspective that such high gain 

closures will be stable! 

2. Dutch Roll Mode -- Low Damping Ratio, Td 

a. Essential Feedbacks (Table 19) 

There are three basic feedback candidates for improving dutch roll 

characteristics 

r+S 

r 

TR-1228-1-1 

ay, ay -+ Sr 

108 
. 

For moderate to high AOA flight conditions, the axis about which yaw 

rate is measured becomes very bportant. Stability axis yaw rate is 

generally preferable. The forms involving i3 and ay can be approximated 

by lead/lag equalization on the fl and ay loops, respectively. This equalization is necessary if the dutch roll damping is to be improved. 

b. Literal Amroximate Factor for Cd 

1) 3 -+ Sr loop 

From the approximate factors either a 3 sideslip stability augmenter 

or a stability axis yaw damper, corresponding to augmentation of the stability axis N+ or NB derivatives, will improve the dutch roll damping 

ratio. 

The iy, 9 + 6, feedback can be considered conceptually (i.e., aside 

from mechanizational side effects) as a surrogate for 8, p -+ 6,. This is 

based on the relation 

a 

Y I Yvv + Y6,6, + xa; 

for an 

ometer 

inputs 

accelerometer located at distance Xa from the c.g. If the acceleris properly located (i.e., at the center of percussion for rudder 

see pg. 483, Ref. 1) 

in the frequency regime of interest about the dutch roll mode. At this 

level of approximation the primary distinction between 8, /3 -t 6, and iy, 

ay + 6, is one of gain compensation over the flight envelope (see 

Table 19). 

TR-1228-1-1 109 

~ 
c. Multi-Variable Sensitivity Vector Survey 

Figure 18 shows that only /3 or ay + 6, can affect the dutch roll 

without affecting the roll subsidence and spiral, but they primarily 

affect Wd, not rd. Using 3 or i + 6, (dashed vectors) could improve 

Id with little other effect. An q, + 6, loop could improve rd but with 

significant effects on ~/TR and l/Ts. The increase in ~/TR would be beneficial, but driving the spiral mode far into the left (stable) half plane 

would be undesirable for steady turning. The steady-state turn rate A,, 

when the airplane is banked with an aileron pulse is 

ycg 

0 n 

A* w'T /a' 

+ lims A XR d 

s+O (s + l/Ts) 

Thus, Ass will be non-zero only if l/Ts - 0 (i.e., the spiral is a pure 

kinematic integrator). Otherwise, the turn rate will decay to zero for 

times greater than Ts seconds (assuming a stable spiral). That is, a pure 

gain r + 6, can interfere with a steady-turn unless opposing rudder inputs 

are developed from the system or the pilot. Table 19 indicates that washout equalization is a common solution. 

d. Effective Characteristics at High Gain 

6r 1) B, B + 6, loop (GB (s) is a lead/lag) 

N: + G 6 r(s)N6 4P 

ar B a 

"Is, s + SY A + GR'(s)N: 

. 7.32 I 

0.1175(161.2) 

= 0.0179 (-0.143) (0.355) (144.5) (-0.143)(0.355) 

TR-1228-1-1 110 
. 

&a 

ar 6.57 I-- 

Ni (1/T ) (-0.144)(0.353) 

bb - t] - 0.2118 rad/sec r +- - -L' + 7 

r 

Li 

N6 

- 1 1. 

T T 

81 82 

- 'b 

a 

6 

2 Li N' 

- 1 L; 1 - e] - -0.05106 (rad/sec) 

0 

T T 4 82 r 

I a 'a6,: 

A+KNr 

The fact that these two roots have nearly equal magnitude is due to 

+ 1/TB2], which is due 

Thus, this situation is 

the relatively low value of the damping term [1/T 

in part to the same factors producing low I~/TRI. 

simply another manifestation of the need for increased roll damping. 

81 

2) q, -* 6, loop (FRL body axis yaw rate) 

-18.88(0.0280) 

= -1.180(0.254) [0.0888, 2.361 

TR-1228-1-1 111 
The q, + 6, yaw damper has several undesirable features compared to 

b, B + 6,. First, the dutch roll mode is driven to the complex rudder yaw 

rate zero [rr, Wr] , which is very near to [rd, Wd] , and thus no improvement in the dutch roll damping results. 

This situation is unusual in that ordinarily (low a) Wr << Wd which 

is the key to success for ordinary yaw dampers. From body axis approximate factors given in Ref. 12 

L 

Thus, Wr Will tend to 

decreases with AOA since 

increase with & as in this -case. Further, rr 

1 

L' ) +- Lb Nf - N; p VT sin a 

0 b r 

'b 

A further problem is the significant modification of [r4, u4] to two 

real roots (one of which effectively cancels the spiral pole). Thus, 

there is no dipole-like near-cancellation of the dutch roll mode, and a 

large residue will occur in the roll control response. 

3) rs + 6, loops (stability axis yaw rate) 

The yaw rate numerator is very sensitive to effective yaw rate gyro 

inclination, which can affect the r + 6, situation significantly. (However, it should be noted that bank angle is quite insensitive to axis 

r' Wrl inclination, e.g. N 

approximation can be effectively reduced by inclining the measurement axis 

toward the stability axis. The primary value of this is reduction of wr 

to well below Wd. The alternative may be examined by considering rs + 6, 

based on stability axis yaw rate (rs can be derived from mixing rb and Pb 

as a function of AOA). 

4 .4 

6 s - Ng b). The angle-of-attack in the above [r 

a a 

TR-1228-1-1 112 
I 

4s rs 

N6 6 

ar 

r 

S 

NL 

I 

-18.88(0.0280) 

-2.58(0.911)[-0.470, 0.8521 

L (33) 

This mechanization in the limiting very high gain case appears even worse 

than rb + 6r, because the effective dutch roll mode [e , w ] would be 

rs rs 

unstable. However, at lower realistic gains good dutch roll damping may 

be achieved. This will require detailed analysis in the next section. 

e. Series Eaualization Reauirements 

r + 6, - In the dutch roll frequency region where the yaw damper is 

to have its primary effect, a series compensator should approximate a pure 

gain. However, at lower frequencies the compensator should have an effective washout characteristic to prevent interference with steady turns, 

p + 6, - This loop will require considerable lead (B content) to 

damp the dutch roll. As AOA increases and directional stability is 

reduced increased /3 content in the feedback controller will be increasingly important. 

ay* + 6, - The considerations for this loop are analogous to those 

for /3 + 6,. However, this loop has a peculiar requirement for proper 

location of the accelerometer near the instantaneous center of rotation 

for rudder inputs. The accelerometer will require more extensive adjustment with flight condition than sideslip, and may also be sensitive to 

pickup of local vibrations and structural modes. 

3. Roll Numerator Zero 

The primary FCS design goal for modification of [c4, a41 is to maintain this zero near the [cd, wd] pole. As Id and are improved, the 

significance of the W#/Wd > 1 problem is greatly reduced, and the primary 

need is to maintain the augmented values of e4 and cd close together to 

minimize the dipole residue in the roll response to 6, and inputs. A 

TR-1228-1-1 113 
roll damper will not affect the roll numerator (N’ ‘b - 0), so only feedbacks to the rudder are of interest. From the approximate factor 

6a6a 

I ba 

L; 

- -(Yv + N; - N*) + 7 

a 

*v4 ’ L6 

(34) 

it may be seen 

c+ will be favorable, i.e., comparable to the effect on Id. 

that the incremental effects of the r, B, or ay + 6, on 

Finally, for adjustment of a zero (but not for a pole) for commands 

(but not disturbances) crossfeeds between the control points can be used, 

if necessary. The lateral to directional controller crossfeed, G r, 

described previously is the most likely to be useful for this example. 

6 

6a 

4. Summary of Augmentation Prospectus 

At this point the architectural elements of the FCS suitable for 

manual or automatic control are: 

0 a roll damper 

0 a yaw damper 

0 aileron to rudder crossfeed (possible) 

for B 0 in rapid rolling maneuvers 

0 directional stability enhancement (possibly 

needed to improve coordination and for other 

flight conditions with higher AOA) 

Three competing yaw damper possibilities have been developed, and at 

this point differences in their relative flight condition compensation and 

mechanizational side effects become important. 

While r -+ 6, looks less satisfactory than 5 + 6r, there is a compelling reason not to abandon it because it may be implemented simply in a 

multiple redundant configuration with rate gyro(s). Developing a satisfactory multiple redundant /3 signal is much more difficult. This sensor 

problem can be reduced by approximating /3 + 6, with ay + 6, at the expense 

TR-1228-1-1 114 
of more elaborate gain compensation with flight condition. While accelerometers are common for FCS, their proper location is generally more 

involved than for rate gyros, and they may be more susceptible to flexible 

mode and vibration pickup. This factor alone may mitigate against use of 

an ay with lead to act as a surrogate for ) because of high frequency 

noise amplication. 

The dynamics of the sensors, computational elements, and actuators in 

both the lateral and directional axes are clearly required to have effective bandwidths which are much larger than the roll subsidence ~/TR, and 

dutch roll, Od, breakpoints. 

TR-1228-1-1 115 
SECTION VI 

PRELIMINARY DESIGN OF CANDIDATE 

LATERAL-DIRECTIONAL FIGHTER FLIGHT CONTROL SYSTEM 

In this section one of the candidate FCS concepts is continued to a 

preliminary design level for the example flight condition. Preliminary 

design includes the basic feedback control system architecture (presented 

as system block diagrams), specification of gains and time constants, and 

preliminary identification of key parameters to which the design is sensitive. These issues will all be addressed in this section. 

A formal assessment of sensitivities and robustness is ordinarily 

accomplished as a part of the detailed design, and thus is not treated in 

this section. However, recently developed robustness assessment procedures are sufficiently simple and straightforward to be applied as an 

early preliminary design step. Consequently we have included preliminary 

robustness assessment as part of the design methodology. Because the 

assessment procedures selected depends on relatively new theoretical 

developments and their tie-ins to more familiar concepts, this phase of 

the design methodology needs a more extended and tutorial treatment. We 

have chosen, therefore, to present robustness assessment for the example 

system as a separate topic in a technical paper. This appears as Supplement 1, and immediately follows this section. 

The basic system analyzed here is shown in Fig. 19. It comprises 

three fundamental FCS modes and two provisional enhancements. The fundamental channels are: 

A redundant (rs + 6,) yaw damper which is intended to augment the dutch roll damping characteristics and provide 

favorable adjustment (increase of the damping term) of the 

rolling velocity transfer function quadratic numerator so 

that the dutch roll will be Level 1 when a subsequent rolling velocity loop is closed. This yaw damper is also 

intended to serve as a suitable inner loop for possible 

directional stability augmentation via sideslip feedback 

for high angle-of-attack operations. As the key channel of 

the lateral FCS, this control axis will have the highest 

level of redundancy with at least a double fail-operational 

status. 

TR-1228-1-1 

PRECEDING PAGE BUM NOT FILMED 

117 
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TR-12 28-1 -I 118 
0 A redundant (Pb + Sa) roll damper which, in conjunction 

with the yaw damper, is intended to provide Level 1 flying 

qualities in all conventional lateral control modes. It 

also serves as the key command element for piloted control 

and regulation of roll attitude and lateral maneuvering in 

general, and as an equalizing inner loop for automatic roll 

control. This FCS mode is also multiple redundant in character at a fail-operational level. 

0 The basic lateral automatic FCS control mode (4 + Sa), 

which provides bank angle command and regulation functions 

as an entity in itself, and serves as appropriate inner 

loop equalization for such lower bandwidth guidance 

functions as heading, lateral path, and lateral position 

control. The required redundancy level of the bank angle 

control loop will depend primarily on that of the outerloop functions. For instance, if the fighter is equipped 

with a multiple-redundant mission critical automatic fire 

control system which relies on the bank angle controller as 

a subsidiary loop, then the bank. angle control loop would 

be mechanized at the same level of integrity. On the other 

hand, if the bank angle closure is simply part of a cruise 

or relief autopilot, less redundancy would be required. 

The auxiliary or provisional features are: 

0 Lateral to directional controller crossfeed to improve 

dynamic coordination in lateral controller initiated 

maneuvers. 

0 Directional stability enhancement using sideslip or a 

lateral acceleration surrogate to cope with high angle-ofattack directional stability problems. 

The second provisional feature is not needed for the example aircraft 

flight condition considered, so it is not addressed in detail below. 

Each of the channels involved have an independent status and 

associated independent integrity as FCS operational modes. Because the 

several channels must exist operationally with an integrity consistent 

with a hierarchical control sequence, they will be designed in the appropriate corresponding sequence. Thus, the yaw loop will be closed before 

the rolling velocity loop, etc. However, this design loop closure 

sequence should not be viewed as a single-loop-at-a-time design accomplished without looking ahead to the next steps. For instance, in the yaw 

axis closure an important feature is the adjustment of the rolling 

velocity/aileron numerator [ ri ,ai] to values which will provide both 

TR-1228-1-1 119 
adequate dutch roll damping and near decoupling of the dutch roll from 

aileron-initiated rolling maneuvers after the rolling velocity loop is 

closed. Consequently, both lateral and directional control loops are 

inherently interrelated in the design, requiring either prescience or 

iterative calculations to arrive at a reasonable conclusion. 

A. ACTUATION AND SENSING 

The actuator dynamics, computational and filtering lags, higher frequency aerodynamic and structural mode effects, and sensor dynamics are 

represented as low frequency approximations comprising a first-order lag 

for the actuators' primary amplitude ratio breakpoint, and pure time 

delays for all the other higher frequency effects. This combination is 

the simplest available to describe bandwidth limitations due to phase lags 

from higher order dynamic effects, as is appropriate when the rigid body 

control problems addressed in this example are considered. 

To permit the reader to distinguish the effects of loop closures on 

the actuator modes, the aileron and rudder actuators and pure time delays 

are represented by slightly different numerical values in the system block 

diagram of Fig. 19. 

B. YAW DAMPER DESIGN 

The primary goal of the yaw damper design is to provide a basis for 

adequate dutch roll damping and minimal dutch roll residue in the roll 

command response without unduly interfering with rolling maneuvers and 

steady turns. As described previously, the yaw rate signal must be washed 

out or otherwise cancelled to eliminate top rudder opposition to turns in 

the steady-state. However, to damp the dutch roll, a signal proportional 

to yaw rate is needed at the dutch roll frequency. What is desired in 

terms of equivalent stability derivatives is a frequency sensitive AN,(s) 

which looks like a constant, AN, at ad, and becomes zero at very low frequencies. That is, neglecting actuator and higher frequency dynamics, 

S 

= s + l/Two 

TR-1228-1-1 120 
For the feedback to appear as an incremental yaw damping, ANr(a), at dutch 

roll frequencies demands that the washout breakpoint l/Two, be at least an 

octave below the dutch roll undamped natural frequency. In closer proximity the feedback signal tends to augment the effective yaw axis inertia 

rather than damping. Thus, proper tuning of the washout relative to the 

dutch roll undamped natural frequency is required to achieve the desired 

dutch roll damping augmentation. 

The tradeoffs involved are also indicated on the root loci of 

Fig. 20. This shows the effect on the denominator of the yaw damper 

closure based on stability axis yaw rate with pure gain (Fig. 20a), and 

with washout breakpoints at 6, 3, and 1.5 rad/sec. These correspond to 

approximate (l/Two)/wd ratios of 0, 2, 1, and 0.5, respectively. The 

basic tradeoff is between reducing the washout breakpoint to low frequencies to cause the wd - wr locus to ”bulge” to the left (to maximize the 

attainable dutch roll damping), and maintaining the breakpoint high enough 

to prevent the yaw damper from interfering with steady turns. The washout 

breakpoint was set at 1.5 rad/sec as the maximum value (minimum Two) consistent with the achievement closed-loop damping ratio of ch f 0.4. 

This also illustrates a rule of thumb for yaw damper systems in which the 

airplane’s Wr/fdd ratio is very small. For these systems types, the selection of (l/Two)/wd < 1/2 will typically provide maximum closed-loop dutch 

roll damping ratios near 0.4. 

of a 

Figure 21 shows the system survey for the denominator. It can be 

seen that the maximum attainable dutch roll damping ratio just reaches 

0.4. Thus, even without the roll damper loop closures the MIL-F-8785C 

dutch roll damping requirement for air-to-air combat in the CO mission 

phase could be met with the (l/Two)/wd ratio illustrated here. 

Figure 22 shows the corresponding survey for the effect of the yaw 

damper on the pb/6, numerator to anticipate the roll damper design. The 

wd locus tracks the dutch roll which is ideal for the roll damper development. Thus, the yaw damper gain can be selected to satisfy the dutch roll 

requirements. 

A gain of Kr - -0.8 rad/rad/sec was selected. This essentially maximizes the dutch roll damping, chub, and the roll numerator damping 

TR-1228-1-1 121 
II I L 

Y 

TR-1228-1-1 122 

\ 

3 

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t, 

P, 

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41 

Bare aircraft P -laO 

3t i =0.39 

A 

\ 

E 

Wd 

k wr 

0 

I 

S 

a) Conventional Root Locus Real 5 

High w Rudder 

Channel Pade' 

Frecruen cu radkec 1 6) Bode - Siggie Plot 

Figure 21. Effect of Yaw Damper Closure on Denominator 

TR-1228-1-1 123 
I 61 

N I 

a 

9 

5 

5- 

4- 

3- 

2- 

1- 

- 

I 

- 

- 

c 

rs -----) dr thru Kr%/(s+l15 p -118 

Bare ai rf me i 

1 f = 0.62 \,< 

- 8 

3 

I 

tr - I 

Real s uj Conventiond Root Locus . 

__ 

b) Bode-Siggie Plot Frequenclr (rad/sec) 

Figure 22. Effect of Yaw Damper Closure on NPb 

6a 

TR-1228-1-1 124 
ratio, r$.* As the w$/wa ratio is less than 1, the latter value assures 

that the dutch roll damping ratio after the roll loop closure will be 

greater than that achieved with the yaw damper loop alone if the dutch 

roll root can be driven to [r$,w$]. Even without this closure the 

dutch roll damping ratio of 0.39 with an undamped natural frequency of 

2.1 rad/sec nearly meets the MIL-F-8785C dutch roll damping ratio requirements for air-to-air combat, and exceeds the MIL-F-9490D damping ratio 

minimum of 0.3. 0.6 rad/sec is increased 

over that of the bare airplane, but is still Level 2 for CO. It is, however, Level l for other less stringent flight conditions. 

The roll subsidence mode, l/Ti 

2' 

&a 

All of these features are apparent in the transfer function relating 

bank angle to aileron with the yaw damper loop closed. This is, 

I 6.60[.618,2.25][.857,6.68][.855,39.5] 

(-.00378)(.576)[.392,2.14][.982,6.37][.857,39.0] 

6.80[.618,2.25] - 

(-.00378)(.576)[.392,2.14] 

Notice that at high frequencies that the coupled yaw-axis-actuator, washout mode and the Pade approximations for the still-higher frequency 

effects appear in both the numerator and denominator. The washoutactuator dipole terms have nearly the same natural frequencies, but quite 

different damping ratios, so they do not completely cancel each other. 

Examining Fig. 21 in more detail reveals a 17 dB gain margin with 

respect to driving the dutch roll mode into the right half plane, and a 

similar margin (16 dB) for the coupled washout-rudder actuator mode. For 

the nominal gain, the total open-loop characteristic G(s) is over 10 dB 

below the effective 0 dB line at low frequencies below the dutch roll so 

*The primed notation on these modal parameters indicates the number 

of loop closures that affect the parameter. After three loop closures the 

Dutch roll damping ratio will be Id. 

TR-1228-1-1 125 
the yaw damper will have only a minor effect on steady turns. The phase 

margin above the dutch roll is 85 deg, corresponding to a 0.37 sec delay 

margin. This greatly exceeds the (MIL-F-9490D) phase margin requirements. 

The primary parameters and dynamics to which the yaw damper design is 

sensitive include: 

Gain, K N’ 

6r 

Washout time constant/dutch roll undamped 

natural frequency, (l/Two)/Wd 

Yaw numerator zeros, [cr,wr] 

Steady-state angle-of-attack, [ao] 

The control system gain, Kr, and the washout time constant will have 

essentially zero uncertainty intrinsically, especially with a digital 

controller. The primary sources of uncertainty therefore lie with the 

aerodynamic and propulsion (to the extent thrust vectoring is involved) 

characteristics associated with the loop gain via N‘ , and the dutch 

roll undamped natural frequency. Referring to the approximate factors, 

the primary sources of variation in these terms are the stability derivatives N’ and Nb. The same thing can be said of the yaw numerator zeros 

using the approximate factors in terms of stability axis derivatives. But 

here there is a subtle but major difference because the complex yaw zeros 

are particularly sensitive to the actual angle-of-attack. Indeed the rs 

signal is established by mixing body pb and rb measurements as a function 

of angle-of-attack (e.g., rs - rb cos a. + pb sin ao>. When this feedback 

is mechanized with a measurements it can be very sensitive to AOA measurement error. It is also a potential source of coupling between longitudinal and lateral degrees of freedom, especially for steady rolling 

maneuvers. If the mechanization depends on estimation of a trim a0 additional uncertainties can enter as functions of the maneuver. For example, 

in 360° rolls the angle of attack relating FRL and stability axes may vary 

sufficiently throughout the roll to be noticeable. 

6r 

6r 

TR-1228-1-1 126 
C. ROLL DAMPER DESIGN 

The primary purpose of the roll damper is to reduce the roll mode 

time constant to less than 1.0 sec as required by MIL-F-8785C while further tuning the dutch roll. 

A pure gain pb + 6, closure is shown in Fig. 23. While this might 

produce an acceptable system, it is not ideal because the dutch roll root 

is not driven into the qj zero. Indeed, the increased separation between 

u,$ and "1; will result in a nuisance appearance of the dutch roll mode 

in rolling responses, and hence a lack of dynamic coordination in maneuvers. This can be corrected by inserting lead-lag compensation in the 

roll damper. If the only issue was increasing the dutch roll locus departure angle, the lead-lag could be optimized to produce maximum phase lead 

at the dutch roll. However, there is an additional constraint in that 

placing the lead at too low a frequency will degrade the improvement 

needed for roll mode effective time constant decrease. 

A compromise compensation of 

(0.2s + 1)/(0.04s + 1) 

(37) 

has the duel effects of directing the dutch roll mode towards the [(4,w4] 

numerator, and maintaining a first-order roll subsidence all the way to 

5 rad/sec. This compensation is also an example wherein the uncertainties 

in the roll subsidence are held in closer control by its limiting value at 

Ti + 0.2 second. The features are shown in the suwey of Fig. 24. 

There is a good region of K/s slope in which the pb + 6, loop can be 

closed. For Kp > 0.15 rad/rad/sec, the roll mode requirements are met 

with a very satisfactory dutch roll mode. A nominal gain of 0.3 rad/rad/ 

sec was selected. This gives a 12 dB gain margin on the only mode that 

could be driven unstable -- the aileron actuator coupled with the p-loop 

compensator lag. The only disadvantage of the p-loop compensation is the 

reduction in this gain margin with respect to the Fig. 23 pure gain situation, but the 12 dB gain margin is quite adequate. The phase margin 

near the effective roll mode is 100 deg corresponding to a very high delay 

TR-1228-1-1 127 
6 I 

M 

Y as 

4 

3 

2 

1 

s 

Yaw danper on 

WashoutActuator 

Dipole 

rad 

i,3 radlsec 

L\ Ti 1111l I1 

- - Y - 

a/ Conventional Root Locus 

I is' + 

Real s 

Figure 23. Effect of Pure Gain Roll Damper Closure 

on Denominator - Yaw Damper Closed 

TR-1228-1-1 128 
- Yaw danper on 

I 

M 

Washout-Rudder 1. I 

b) Bode -Siggie Plot Fr e we n cu ( rad/se c 1 

1 C! - 

Figure 24. Effect of Roll Damper Clusure with Lead-Lag 

Compensation on Denominator - Yaw Damper Closed 

g a5- 

P 

h 

a 

e 

S 

Aileron 

Channel 

Podd 

pb ----) da thru Xp(8,2~+1)/(8,04~+1) 

Rudder 

Channel 

Pade' 

TR-1228-1-1 129 
margin of 0.87 sec. This greatly exceeds the MIL-F-9490D phase margin 

requirements. The closed-loop aircraft characteristics to lateral control 

are 

131.4[.618,2.25][.857,6.68](25)[-.866,34.6][- ,* 

(-.0104)(2.11)[.473,2.67][.952,5.61][.534,15.8][.~ . ][.831,52.2] 

(38) 

As far as piloted control is concerned, these effective aircraft 

characteristics are excellent. They feature a roll subsidence time constant of 0.48 sec, a dutch roll damping ratio of 0.47, and an undamped 

dutch roll natural frequency of 2.7 rad/sec. The spiral with T2 - 67 sec 

is more unstable than for the bare airplane, but is still within the Level 

1 requirements. Finally, the roll numerator quadratic comes fairly close 

to the dutch roll quadratic, thereby tending to remove dutch roll effects 

on lateral controller induced maneuvering. 

When these characteristics are examined in conjunction with piloted 

control, the pilot equalization (via Eq. 14 of Supplement 3) will be a 

lead of about 0.5 second to essentially cancel the roll subsidence. This 

is well within the range for excellent ratings near the best end of 

Level 1 if the effective airplane gain (as seen by the pilot) is properly 

set (see, e.g., Refs. 13, 14). 

The most sensitive parameters and dynamics in the roll damper loop 

include : 

Gain, Kp (Li + tan a. Ni) 

Compensation time constants 

Roll mode pole, l/Ti 

As with the yaw loop, the FCS gain and time constants should have 

very low uncertainty, but the overall loop gain will reflect the uncertainty in the roll control effectiveness. The airplane roll mode is 

uncertain as well as low at higher AOA; however, the roll damper has good 

potential for accommodating this uncertainty. The roll damper loop has 

low sensitivity to the dutch roll dipole unless the yaw damper channel is 

off. 

TR-1228-1-1 130 
The time domain characteristics of this combined set of yaw and roll 

damper FCS modes are a final consideration. Time histories of roll rate, 

yaw rate, and sideslip angle for a 1 rad aileron surface command are shown 

in Fig. 25. The roll rate response shows very little dutch roll contamination, and indicates that the roll control response is quite adequate 

without use of an aileron-rudder crossfeed to improve the rolling velocity 

response. The sideslip associated with the lo step aileron input is about 

0.lo until the spiral mode starts to show up significantly. This would 

permit an aileron-only rolling velocity of almost 30 deg/sec without the 

sideslip straying beyond the lo desired requirement. Consequently, an 

aileron to rudder crossfeed may not be essential for this flight condition 

if the pilot can easily coordinate maneuvers with rudder. 

Time responses for 1 degree rudder steps are shown in Fig. 26. These 

are generally well-behaved and, in company with the responses of Fig. 25, 

indicate that classical lateral and directional stability desires are 

generally met. 

Although, as noted above, there is only a weak requirement for an 

aileron-to-rudder crossfeed for this flight condition, it can provide a 

final tuning of the effective airplane dynamics as seen by the pilot. 

The ideal crossfeed 

back to Eq. 23) for the case at hand, 

which makes NB 

6, 

For the example flight condition this 

identically zero will be (referring 

B 

6 

a 

-N 

N; ' 

r 

will be 

(39) 

&r -6.30(.755)(-.917>(2.72)(10.86)[-.863,34.3][.797,34.8~(36.8) 

= (-.0104)(2.11)[ .473,2.671[.952,5.61][ .534,15.82][ .854,39.6][ .831,52.2) 

The ideal crossfeed expression contains non-minimum phase terms which 

cannot be offset by simple cancellation in a practical system. Many of 

the other terms are high frequency in nature and/or tend to offset each 

other. By examining the transient responses of Figs. 25 and 26 it is 

plain that the most prominent mode present in the sideslip response is the 

TR-1228-1-1 131 
4, 

1 I I I 

c 

I I I I 

(deglsec 1 

I I I I I I I 

Time (sec 1 

u/Ro// Rufe 

rb 

(deglsec) 

Time (sec 1 

b/ Yaw Rife 

t 

Figure 25. Response to 1 deg Aileron Step Yaw and Roll Dampers Closed 

TR-1228-1-1 132 
1 

I I I I 

0 

I ! I 

-1 

-2 

pb 

(deglsec) 

-3 F 

c 

I I I I 1 I I I 

0 1 2 3 4 5 -41 

Time (sec) 

u) RON Rate 

c I 

Time (sec) 

b) Yaw Rate 

c) Sides/@ Angle 

Figure 26. Response to 

133 

1 deg Rudder Step 

TR-1228-1-1 
modified dutch roll, with the spiral beginning to have an effect after a 

few seconds. When attention is focused on the frequencies around the 

dutch roll an approximation to the ideal crossfeed becomes, 

-. 373 

(s + 1.5) a 

which corresponds to a low pass filter with a first order rolloff at the 

yaw damper washout frequency. If this last approximation is used as the 

basis for an aileron to rudder crossfeed in the control system the 

response to a 1 deg aileron step will appear as shown in Fig. 27. When 

contrasted with the responses of Fig. 25 the crossfeed is seen to reduce 

transient sideslip to about 1/3 of the level without the crossfeed. 

D. BANK ANGLE CONTROL LOOP 

The bank angle (stability axis 4) frequency response for roll control 

inputs is shown in Fig. 28. This response is K/s-like out to about 3 rad/ 

sec, and will allow a bank angle control loop to be readily closed either 

by the pilot or by the guidance system at frequencies lower than this. 

To the extent that the open-loop characteristics is indeed K/s-like, 

the bank angle regulation requirement of MIL-F-9490D (which specifies that 

the bank angle be returned to 1 deg from a 5 deg offset in 3 sec or less) 

can be interpreted to imply a minimum crossover frequency of 0.54 rad/sec 

for the bank angle control loop. This low crossover frequency is based on 

the response being first-order. As given in Table 3 the specification is 

tightened by taking the 3 seconds as a response time (time to achieve and 

remain within 5% of the final value in response to a step input) and by 

assuming a second-order system. This raises the crossover frequency to 

about 1.4 rad/sec. That either of these interpretations can easily be met 

is seen by examining Fig. 28. The maximum crossover frequency for a pure 

gain bank angle controller is about 2 rad/sec, set by the phase margin 

requirement of 45 deg. 

TR-1228-1-1 134 
pb 

( deg /sec 

4- & 

- 

3- 

- 

2- 

- 

1- / 

- 

8, I I I I I I I I I 

1 

. 

21 

I 

.5 

/ 

/ 

a 

l'I,. jr________ 2 

rb 

(deg /sec 1 

8 1 

b) Yaw Rute 

3 4 5 

Tim 

t 

-,I I I I I I I I I I 

8 1 2 3 4 5 

Tim 

e) Sides/@ Angle 

Figure 27. Response to a 1 deg Aileron Step, Yaw and 

Roll Dampers Closed, Crossfeed On 

TR-1228-1-1 135 
M 

a I h 

Figure 28. Bank Angle-to-Roll Control Frequency Response 

n 20 

i 

A system survey for pure gain 4 + 6, loop is shown in Fig. 29. In 

addition to the specification for response described above, the primary 

consideration is setting the gain to allow adequate relative stability of 

the dutch roll mode, while keeping the complex roll-spiral frequency high 

enough to assure rapid response. A gain of Kd - 0.5 is a good compromise 

which emphasizes roll control bandwidth and rise time. This is at the 

expense of the dutch roll, which just meets the MIL-F-9490D minimum 

damping ratio requirement. At this gain the crossover frequency is 1.3 

rad/sec with a corresponding phase margin of 60 deg, a delay margin of 0.8 

sec, and a gain margin of 13 dB with respect to destabilizing the dutch 

roll. Figure 30 shows the closed-loop bank angle response to a unit step 

bank angle command. The response is within 4 percent of the steady-state 

within 2.5 seconds indicating that the MIL-F-9490D bank angle regulation 

requirements are easily met. 

a 240 -\- 

I e W;i 9 - G(s) * - 

TR-1228-1-1 

L 8% 

136 

128 

e 

d 

-20 

- 

- pk/dal 

Slightly Unstable - ,,,,,,,I .e.. . .. Spiral I, I I. 

B 

. 

-40 ,(,l,l’.’ .’.’ 

- 

-60 

-88 

- 

1 I I I I Ill 

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-248 

I I I11111 I I Illill -368 

.*I .I ,, , , ., I *... .., 1,*.1 II I (I 1.1 ,),) ,(, 

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I I1111: 
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6 I 

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P 

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a 5- 

4- 

3- P 

h x 

-L 

- 

Pure gain Phis -4 da 

MIL-F-9490 D 

- cmjn = 0.3 

- \,66 ," 

2- 

1- 

BJ I 

4 r 

(JJ; 

m I )J, I 

- 

Ti 

1 I I I I 1. 1 I I I 1 I f 

ol Conventiond Roof Locus Real s 

M 

a 

9 

n 

i 

t 

e 

ut I I I 

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d 

B . ................................................. .I I I. 

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-40 :.. 

-60 

-80 

- 4M=6@T - 

I I. 

*. - 1. * I I I I tlll I Ill1111 I I I I IIII 

10'2 10=1 10O 

Frc men cu ( rad/s e c ) b) Bode - Siggie Plof 

Figure 29. Closure of the Bank Angle Control Loop 

TR-1228-1-1 137 
/// // / /// 

112 r & 

---- 

A 

Peak @ 1,833 

> MIL-F-94900 Bank Angle 

: Regulation Requirement 

Roll and Yaw D~MPWS on 

Pure gain Phis ----I da 

Kphi : 03 

I I I I I I I I 1 I 

1 2 3 4 5 

Time (sec) 

Figure 30. Bank Angle Response to Bank Angle 

Command, Complete System 

With the equalization from inner roll and yaw loops, the bank angle 

control loop is relatively insensitive to basic airframe parameters. 

Probably the most critical issue is the sensitivity of the final dutch 

roll damping to the roll loop gain. Uncertainties in the dutch roll 

dipole and to some extent the net high frequency lag are also important in 

insuring adequate dutch roll damping. 

E. WHAT NEXT? 

The tutorial example worked through in this section is sufficiently 

complete to illustrate most of the key stages in the design methodology 

without bogging the reader down in tedious detail. A more comprehensive 

design assessment would examine in depth most of the topics summarized in 

Table 20 (adapted from Ref. 15). The major steps left to finish off a 

preliminary design assessment for the single exemplary flight condition 

are : 

0 Examination of responses to a reasonable cross-section of 

the disturbances represented in Table 4; 

0 Assessment of robustness. 

TR-1228-1-1 138 
. 

-- 

TR-1228-1-1 139 
n 

W 

l-a 

V 

z 

0 

W 

W 

. 

c 

N 

Er; 

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b 

2 

a 

rl 

x 

ti 

a 

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rl 5: 

t? 

rl 

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0 

TR-1228-1-1 140 ORIUNRL PAGE IS 

OF POOR QUALITY 
The first item is a straightforward application of Program CC (or similar 

computer aids) to the three closed-loop systems (yaw damper, yaw damper 

plus roll damper, bank attitude autopilot). The second subject has 

received a good deal of attention in recent years. We have evolved an 

approach to this problem which brings the literal approximate factors idea 

to singular value-based robustness assessment notions and which thereby 

falls very nicely into the FCS design methodology. A tutorial on these 

methods applied to the example problem is given in the form of an AIAA 

technical paper in Supplement 1 to this report. 

In a complete preliminary design three other steps are needed. The 

first is the establishment of competition by developing other architectures to the same level as illustrated here. The second is to examine all 

the competing systems for other critical flight conditions. This permits 

the preliminary establishment of compensation requirements for the controllers in order that they maintain control throughout the total flight 

regime (e.g., see the example compensation requirements in Table 19). 

Then, on the basis of the competitive data developed, the several system 

possibilities are played off against each other taking into account such 

factors as: 

0 Relative differences in performance 

0 Relative differences in sensitivity to uncertainties, 

tolerances, etc., including possibly different governing 

factors 

0 Mechanizational possibilities and their side effects 

(e.g., as illustrated in Table 2) 

0 Economy of equalization and simplicity of compensation 

0 Relative versatility across mission phases, coping with 

stores loading variations, etc. 

0 Inherent reliability and maintainability 

0 Development and life cycle costs 

The result of the competition is a baseline FCS system which will be 

subjected to re-examination in several respects and thoroughly analyzed in 

much more detail. At the outset the airplane, actuator, sensor, etc. 

TR-1228-1-1 141 
dynamics will be made more realistically complex. The airplane’s dynamic 

description will be expanded to account for nonlinear features and the 

lower frequency flexible modes. Some of the important issues brought 

about by the flexible modes are covered in Supplements 2 and 3. The controller itself, if digital, will be modified to take into account the 

sampled data aspects. Reference 11 illustrates this step with an example 

vehicle which includes flexible modes which can, in principle, interact 

with sampling phenomena. 

As the design progresses more and more reliance is placed on more and 

more detailed analyses and simulations -- all in an attempt to forecast 

behavior and anticipate potential problems that may arise. Unfortunately, 

the further along the system development, the more difficult and costly 

become any corrections needed. This places an extreme emphasis on the 

earliest preliminary design phases addressed here as the proper time to 

evolve a system which is solidly based in reality and possesses wellfavored features. 

TR-1228-1-1 142 
REFERENCES 

1. McRuer, Duane T., Irving Ashkenas, and Dunstan Graham, Aircraft Dvnamics and Automatic C ontrol, Princeton University Press, Princeton, N.J., 1973. 

2. "Military Specification -- Flying Qualities of Piloted Airplanes," 

MIL-F-8785C, NOV. 1980. 

3. "Military Specification -- Flight Control Systems Design, Installation and Test of Piloted Aircraft, General Specification For, 

MIL-F-9790D, June 1975. 

4. Federal Aviation Reeulations. P art 25. Airworthiness Standards: 

TransDort Cateeorv AirDhneS, Department of Transportation, 

Federal Aviation Administration, June 1974. 

5. McRuer, Duane T., and Donald E. Johnston, Flight Control Systems 

ProDerties and Problems, Vol. 1, NASA CR-2500, Feb. 1975. 

6. Myers, Thomas T., Duane T. McRuer, and Donald E. Johnston, Flying 

Oual ities and Control SYS tem Alt ernatives for SuDeraumented 

Aircraft, NASA CR-170419, Dec. 1984. 

7. McRuer, Duane T., Donald E. Johnston, and Thomas T. Myers, "A Perspective on Superaugmented Flight Control: Advantages and Problems," J. Guidance. Control. and Dynamics, Vol. 9, No. 5, SeptOct. 1986, pp. 530-540. 

8. Allen, R. Wade, Theodore J. Rosenthal and Raymond E. Magdaleno, LSMP 

User's Guide, Version 2.5, Systems Technology, Inc., Hawthorne, 

CA, 1988. 

9. Thompson, Peter M., Promam CC Version 3 User's Guide, Systems Technology, Inc., Hawthorne, CA, May 1985. 

10. Thompson, Peter M., Program CC Version 4 Tutorial and User's Guide, 

Systems Technology, Inc., Hawthorne, CA, May 1988. 

11. McRuer, Duane T., Richard F. Whitbeck, and Raymond E. Magdelano, 

Methodoloeies for the Direct DiPital Control of Highlv Flexible 

Vehicles, AFWAL-TR-84-3104, Feb. 1985. 

12. Myers, Thomas T., and Donald E. Johnston, Investigation of Potentially Critical Lateral-Directional Flight Conditions for Shuttle 

Orbiter Entrv, Systems Technology, Inc., TR-2143-1, Oct. 1982. 

13. McRuer, Duane T., and Ezra S. Krendel, Mathematical Models of Human 

Pilot Behaviol;, AGARDograph No. 188, Jan. 1974. 

14. McRuer, Duane T., "Pilot Modeling," in Advances in Flying - Qualities, 

AGARD Lecture Series 157, 1988. 

15. Hofmann, L. G., Susan A. Riedel, and Duane T. McRuer, Practical 

Optimal FliFht Control System Design for HelicoDter Aircraft, 

NASA CR 3275, May 1980. 

TR- 122 8 - 1 R- 1 
SUPPLEmNT l* 

SYSTEM DESIGN TECHNIQUESLITERAL SINGULAR-VALUE-BASED FLIGHT CONTROL 

Duane T. McRuer, Thomas T. Myers, and Peter M. Thompson 

Introduction 

Robustness issues for singleinput single-output systems have long been 

understood and appreciated by designers. The objective is to design a controller which is in some sense tolerant and forgiving. Extending these results 

to multi-variable systems has been the focus of a stream of research in recent years. A hallmark of the new approaches has been a renewed emphasis 

on frequency domain techniques, after a period in which these methods had 

often been viewed as mature or even passe. 

The key to extending the frequency domain robustness methods has been 

the generalization of gain using singular values of a matrix [1,2]. Reformulations of this metric, notably using structured singular values [3,4], continues 

to be central to most of the new methods. Most of the work has been done 

in a general context using abstract x = Ax + Bu type linear systems. A 

byproduct of working at this level of abstraction is that the tools ofthe trade 

are largely computer programs implementing very general and sophisticated 

numerical methods. This focus on the computational aspects of the problem 

is a characteristic that multi-variable frequency domain robustness methods 

have in common with earlier time domain and optimal control methods. 

Aircraft flight control system (FCS) design has been an important motivation for new robustness methods. Flight control related work has been 

done in industry, at NASA [5,6], the Air Force [7], and at universities [SI. 

Aircraft manufacturers have also experimented with these methods, but in 

general they are a long way from routine working tools. This is to be expected in the hard-nosed environment of specific aircraft projects, where new 

This supplement treats the robustness assessment for the fighter 

aircraft illustrative design example. As a technical paper it has 

been accepted for publication by the AIAA Journal of Guidance, 

Control, and Dynamics. 

*A11 numbers in this supplement referring to figures, tables, 

equations, and references are for Supplement 1 only. 

-k 

Supplement 1 1 TR-1228-1-1 
theoretical tools have to compete against techniques which have stood the 

test of time on many successful projects. 

An early impediment to the use of singular-valuebased robustness tests 

was the lack of widely available mature software. Commercial packages are 

now available at a reasonable cost, so this is less of an issue. However there are 

more subtle factors at work, generally related to incorporating the thinking 

process and expertise of the flight control designer. General theory is not of 

any great practical interest to the designer faced with a myriad of quantitative 

and qualitative requirements. 

Of more concern is to expose and bound uncertainties in stability derivatives, actuator and sensor dynamics, and other aircraft parameters. To do 

this the designer typically studies single variations using a variety of conventional measures such as gain, phase, and time delay margins, peak amplification ratios, dominant mode characteristics, and so on. 

Coupling several variations to assess overall robustness is where expertise 

and experience are most useful. A designer’s knowledge of the particulars 

of a given airframe is the secret weapon which makes this possible. Multivariable singular-valuebased robustness tests present an opportunity to do 

this traditional job more efficiently and rigorously, but as currently applied 

these tests are strictly numerical, with the result that the designer loses the 

physical insight needed to diagnose a robustness problem. 

Flight control designs in the future will have larger uncertainties in aircraft operating over greatly expanded flight envelopes. Control systems will 

be reconfigurable, perhaps even in real time in the presence of failures or 

I 

Supplement 1 2 TR-1228-1-1 
damage. New robustness procedures offer a solid approach to these problems. The need has never been greater for tying together the existing academic generality with the physical insight of a good designer. This paper 

attempts to improve this relationship; specifically we will: 

0 Connect multi-variable frequency domain singular value methods to 

classical coupling numerator based multi-loop methods [9]. 

0 Develop physical insights between the singular values and aircraft and 

controller dynamics by using literal approximate factors. 

0 Provide a recipe for the identification of the most important aircraft 

and controller parameter uncertainties. 

Example Problem 

Throughout the paper a lateral-directional FCS design for an advanced 

fighter aircraft is used as an example [lo]. A state space model for the aircraft 

is shown in Table 1 (M=0.6, 35,000 ft, 50% fuel). The low frequency effects 

of the rudder and roll control actuators have been modeled as first order lags 

(with poles at 20 and 25 rad/sec, respectively). The unaugmented aircraft 

characteristics were contrived to exhibit several generic problems characteristic of lateral control at moderately high angles-of-attack including: 

0 High roll subsidence time constant (TR = 2.34 sec, MIL-F-87S5C Level 

3) 

0 Low Dutch roll damping ratio (cd = 0.0208, MIL-F-S785C Level 3) 

Supplement 1 3 TK-1228-1-1 
I .. 

x = Ax+Bu 

y = Cx+Du 

P 

.=(>) Y== (7) .=(;) rs 

/3 = side slip (rad) 

pb = body axis roll rate (rad/sec) 

rb = body axis yaw rate (rad/sec) 

q5 = body axis roll angle (rad) 

6, = aileron angle (rad) 

6, = rudder angle (rad) 

T, = stability axis yaw rate (rad/sec) 

-.OS6S 0.215 -.977 0.0539 

-32.3 -.374 2.40 0 

1.06 -.0406 -.0809 0 

0 1 0.220 0 

0 1 0 0 

0 0 0 1 

0 -0.215 0.977 0 

0 0.0179 

6.35 6.66 

1.71 -1.18 

0 0 

0 0 

0 0 

0 0 

Table 1: Lateral-Directional Airframe Model 

Supplement 1 4 TR-1228-1-1 
e Undesirable roll-due-to-aileron control numerator (q/wd > 1, with 

low damping for the complex zero [9]) 

A simple FCS design has been formulated which satisfactorily solves the 

above problems and in addition provides bank angle control. As shown in 

Fig. 1, this system consists of a washed-out stability axis yaw damper (rS + 

&), a body axis roll damper (Pa ba) and an autopilot bank angle command 

and hold loop (4 + &). In traditional designs the feedbacks would be the 

output of three sensors. The inner loop stability augmentation feedbacks 

would be provided by yaw- and roll-rate gyros, with rs being a blended 

combination of 7-6 and pb. The outer loop autopilot would be provided 

by a distinct vertical gyro. Next generation fighters and other aircraft can 

be expected to use integrated inertial reference assemblies in which one set 

of (redundant) gyros provide both attitude and attitude rate information 

through strapdown calculations. 

Robustness of Stability with Respect to Input 

Uncertainties 

An uncertainty model used for the purpose of preliminary flight control design approximates the unmodeled high frequency dynamics of filters, sensors, 

structural modes, notch filters, etc. with effective time delays. These same 

effective delays model sampling delays and actuator rate limits. The low frequency approximations will be adequate if these high frequency dynamics are 

well above the magnitude crossover frequencies that define the bandwidths of 

Supplement 1 5 TR-1228-1-1 
the FCS feedback loops. Thus, in Fig. 1 the rudder and roll control channels 

each contain a nominal effective time delay (0.11 and 0.10 sec respectively). 

From a realistic point of view there are many uncertainties and variations 

which can occur at many points around the FCS loops. Stability derivatives 

should be included in the above list, as well as critical parameters in the 

control system. A complete uncertainty model would account for each source 

in its appropriate location. Here, for concreteness, we consider only the case 

of effective time delays at the inputs to the roll control and rudder. 

The multi-variable uncertainty model is: 

Lump the separate controllers together using the multivariable notation: 

It then follows [1,2] that the closed loop system is robustly stable with respect 

to E,(s) if 

qEm (ju)] < a { I + [KG(jw)]-') for all w (5) 

where 7 and a respectively denote the maximum and minimum singular 

values. 

The final condition (5) is not conservative in the sense that a perturbation 

&(s) is guaranteed to exist which just barely exceeds the frequency domain 

Supplement 1 6 TK-1228-1-1 
v) 

00 

6 

I 

- 

Lo 

+ 

- . 

v) 

Y 

II 

~n 

I= 

II 

L 

1L 

n 

0 

&I 

+ 

m' 

v) 

Y 

11 

-8- 

x 

c-5 - 

+ 

v) 

N 

Y 

d 

m 

d 

d0 

9 

.u 

0 

ON 

N+ 

v) 

v) 

00 

I 

6 

T 

Supplement 1 7 TR-1228-1-1 
.. 

bound and results in closed loop instability. The same condition, however, is 

conservative in the sense that a perturbation Em(s) with a particular structure can violate the frequency domain inequality without causing instability. 

Additional structure has been imposed in (2) on E,(s), namely that (a) the 

uncertainties in the actuator channels are delays and not some other type of 

dynamic element, and (b) there is no cross-coupling of the uncertainties, e.g. 

uncertainty in the roll actuator does not directly lead to uncertainty in the 

rudder position. 

A graphical illustration of the robustness condition (5) is shown in Fig. 2a. 

The perturbation bounds a(,?.?,) are shown for several AT'S, and it is concluded that any combination of effective delays AT, and AT, such that both 

are less than about .1 secs is not destabilizing. It is noted that in the critical 

frequency ranges: 

a[E,(s)] x ATS (6) 

Due to the particular diagonal structure used here it is expected that one 

or both of the effective delays can exceed this bound without destabilizing the 

system. Emerging robustness procedures [3,4] help to alleviate the conservativeness by taking advantage of additional structure on E,,,. The singular 

value test (5) assumes no structure. If a diagonal structure is assumed for 

E,(s), where each diagonal element is the same, then a spectral radius test 

can be used: 

Supplement 1 

E, = (e-'AT - 1) I 

3Em] < e{I + [I'G(jw)]-'} for all w 

8 

(7) 

TR-1228-1-1 
a 20r 

t 

u0 

d 

e 

d 

B 

-20 

-40 

10-I 10 

Secondary ,' Point 

\/ Critical Point 

a) Singular Value Tesf 

10 

Frequency (rad/sec) 

b) Singular Vuhe (E), Specfrul Radius @IJ - und 

Sfrucfured Singular Vulue - @) 

Figure 2. Graphical Robust Stability Tests 

Supplement 1 9 TR-1228-1-1 
.. 

The spectral radius e is defined as the absolute value of the minimum eigenvalue, i.e. e[A] = IA[A]I. (This definition is nonstandard, hence the underline, 

in order to keep the same basic form as the singular value test (5). More 

typically p = Ix[A]l, in which case e[A] = l/p[A-']). 

If a block diagonal structure is assumed for E, then the structured singular value is used. In (2) two 1x1 blocks are defined, which results in the 

following robustness test: 

F[E,] < g{l + [KG(jw)]-'} for all w (8) 

A definition of the structured singular value 2 which suffices in this case is 

[3,41: 

E( A) = a( min D-' AD) e 

10 where D = ( e) 

(9) 

The parameter e minimizes the Frobinius norm of D"AD, where the Frobinius 

norm is the square root of the element magnitudes squared. (This definition is again nonstandard, more typically p[A] = F(minD-'AD) e and 

EM = 1/PL[AI). 

The diagonal scaling e can be given the interpretation of scaling the input 

variable Sr relative to 6,. The singular value test is not invariant to this type 

of scaling, and the innovation of the structured singular value test is to 

minimize over all possible scalings. This definition and interpretation holds 

for the cases of 2 and 3 diagonal blocks, but not for more general block 

. 

structures. 

Supplement 1 10 TR-1228-1-1 
.. 

. 

Graphical applications of the robustness tests (5,7,S) are shown in Fig. 2b. 

For clarity only one uncertainty bound qEm] is shown. The singular value 

test guarantees uncertainties AT up to 0.105 sec in each channel. The spectral 

radius test improves this up to 0.24 sec simultaneously in each channel, but 

nothing formal can be implied from this test for different delays in each 

channel. The structured singular value test guarantees AT up to 0.15 sec in 

each channel. 

To better visualize the conservativeness issue it is useful to compare the 

guaranteed delays from tests (5,7,S) with the actual stability boundaries 

shown in the rudder-aileron time delay parameter plane of Fig. 3. The 

stability boundary is determined by varying the delay (modeled as a 2nd 

order Pade approximation) in the rudder channel, closing the yaw damper 

loop, and then determining the delay margin in the roll loop using an open 

loop Bode plot. Point (A) in Fig. 3 is the nominal condition, and points (B) 

and (C) represent conventional single axis delay margins. The conservativeness of the singular value test has been pointed out in many previous studies 

and is apparent from Fig. 3. Perhaps surprising is that in this example the 

structured singular value test is also conservative. This can be alleviated by 

using a real parameter singular value test [ll] which takes into account the 

fact that AT is a real parameter, but this is beyond the scope of the paper. 

The above discussion has focused on how the additional structure of the 

perturbation can be used to decrease the conservativeness of the robustness 

tests. Questions like this have been raised and for the most part answered 

[3,4] by members of the theoretical community. We do not want to minimize 

Supplement 1 11 TR-1228-1-1 
0.4 

c4 

0 

Q) 

u) 0.3 

6 

v 

L 

b 

0 

0 

-I 

g 0.2 

> 

c 

)r 

0 

Q) 

.- 

- 

n 

3- 

-/// g 

Nominal 

Yaw 

p Channel 

~oundury / 

Delay I Afa = 0.22 sec [ 

0 0. I 0.2 0.3 

Total Delay in Roll Loop, Ta (sed 

Figure 3. Comparison of Stability Boundaries 

in Roll-Yaw Time Delay Parameter Plane 

0.4 

Supplement 1 12 TR-1228-1-1 
the importance of these tests, indeed we want to increase their use, but the 

types of questions asked by researchers are not the ones which designers are 

most likely to ask. For starters, given the simple approximation for F[E,] 

in (6) what is a similar approximation for the other portions of the robustness tests (5,7,8)? What are the low and high frequency approximations? 

What open loop mode creates the critical point around 3 rad/sec? What is 

the mode around 13 rad/sec which is close to becoming critical? What are 

the critical aircraft and controller parameters that determine these critical 

points? Are the stability difficulties cited in the example responsible for the 

critical points? How sensitive are these to changes in the nominal flight control system, and how would matters be changed if the aerodynamics were 

modified? We now turn to an approach to explore these types of questions. 

Motivation for Literal Formulations 

The objective is to develop greater FCS-engineering insight into the new 

frequency domain robustness measures. The approach is to give literal (symbolic) expressions for the singular-value-based tests. This approach involves 

two concepts that have long been used for traditional multi-variable flight 

control design - literal approximate factors and transfer function numerators of higher kinds, also known as coupling numerators [9]. 

Over the years, literal approximate factors have been developed for a wide 

variety of conventional and VSTOL aircraft, rotorcraft, and other vehicles. 

These expressions give approximate relations for transfer function poles and 

zeros literally in terms of stability derivatives. This is best appreciated by 

Supplement 1 13 TR-12 28 -1 -I 
an example such as the lateral-directional example being used here, where 

all of the following derivatives are defined in the stability axes [9]: 

Dutch roll pole: 

Roll-due-to-lateral controller dipole: 

While expressions such as these are often accurate to a few percent for 

numerical calculation, this is not the primary purpose for using literal approximate factors. The real value is in viewing the connections between the 

aircraft poles and zeros and the stability derivatives which are not available 

from a strictly numerical calculation of system eigenvalues. This knowledge, 

in turn, indicates: 

0 the physical origins, nature, vehicle configuration-dependence, and variation with flight condition/configuration of the vehicle poles and zeros; 

0 the physical origins, nature, etc. of the limiting dynamical characteristics (closed loop modes at high gains) corresponding to a particular 

choice of FCS feedback architecture; 

Supplement 1 14 TR- 1 2 28 -1 -I 
0 possible control law components to adjust particular modes or effective 

numerators; 

0 the absolute and relative importance of uncertainties in particular derivat ives . 

Literal Approximations of Open-Loop Singular Values 

With the concepts of literal approximate factors as background, we can now 

discuss the basic approach for developing literal approximations of singular 

values. The open loop case is treated first, which is useful in its own right for 

performance analysis, and which is a starting point for the more complicated 

closed loop case. 

A simplifying change is first made to the aircraft example by assuming 

that q5 and pb are related by the ideal linearized kinematics pb = sd (rather 

than Pb = '4 - fb tanTo). Compute pb by differentiating the 4 measurement, 

which reduces the number of feedback compensators to IC+ and IC, as noted 

in Fig. 1. This change is consistent with the use of an integrated sensor 

package. The open loop combined aircraft controller system is: 

The maximum and minimum singular values of KG are given by 

T=&, e=@ (15) 

Supplement 1 15 TR-1228-1-1 
where and are the maximum and minimum eigenvalues of [II'G]*[II'G], 

and where * denotes the conjugate transpose. The eigenvalues for this type 

of matrix will always be real positive numbers. They are defined using the 

determinant identity: 

I X - - IC]' -a*b - c'd 

-ab* - cd' X - lbl' - Id[' 

= X2 - BX + c = (A - X)(X - A) 

I 

c = XA = lad - bel' 

If the eigenvalues are widely separated (say X > 5X), as is the usual case 

for lateral-directional examples such as this, then the following approximations for the minimum and maximum singular values are very good: 

In the rare cases when the eigenvalues are close together: 

The geometric mean Fa can be exactly computed. In all cases the following 

inequalities are valid: 

The geometric mean is included in this discussion for several reasons: because 

it can be exactly determined, in some cases it approximates the minimum and 

Supplement 1 16 TR-1228-1-1 
maximum singular values, and it can be used as a definition of multi-variable 

bandwidth. 

Literal approximations of the open loop singular values are obtained by 

substituting from (14) into (17) and by using the coupling numerator identity 

191: 

Resulting in: 

Square roots are needed as a final step. Square roots of transfer functions in 

general require non-integer powers of 5, but not so here. The above equations 

are symmetric about the jw axis, and therefore the left-half-plane spectral 

factors can be used for the square roots. 

Figs. 4a and 4b contain Bode plots and transfer functions for the singular value literal approximations. Exact numerical values for 3 and in this 

airplane example are graphically indistinguishable from their literal approximations. As was the case discussed earlier for literal approximate factors, the 

importance of having literal approximations is not numerical, we would be 

just as happy with &lo% accuracy. The importance is directly knowing how 

the singular values depend on the nominal aircraft dynamics. For example, 

the straightline asymptotes in Fig. 4 very clearly indicate the open loop pole 

Supplement 1 17 TR-1228-1 -I 
Frequency (radkec) 

a) Singu/ar Vdues 

141 48 n 

a 

n 

g 

IlSOO(0) (.028)[.820,3.32] 

cu = 

1 20 

t 

d 

U 

c 

0 

d 

B 

-28 

-4Q 

(exact 1 

I- I 

- 

Asymptotes’ I \\ 

(.0048) (.427)(1.5) c.021 , 2.851 (20)(2512 I 

I I 1 I1 Ill1 I 1 I I1 llll -- 

10-I 

6) Geometric Mean 

3 I8 ( I. 5 I )[.547,2.49] [.947,3.64] ( 22.3 ) 

(.0048)(.427)(1.5) [.021,2.85] (20)( 2512 

(approximate) 

(approximate 36.5 (0) (.028)[ .820,3.32] 

KG) * I (1.51)[.547,2.49][.947,3.64] (22.3) 

c 

Figure 4. Literal Approximations for Open Loop 

Singular Values of KC 

Sunnlement 1 18 TR-I 228-1-1 
and zero locations. Several of the breaks are labeled, and it is seen that the 

dominant factors influencing the bandwidth are the yaw damper washout 

time constant Two and the Dutch roll damping ratio (d. Individual poles and 

zeros are labeled below for 5~. Poles and zeros corresponding to the effective 

delays do not appear because they cancel when the left half plane spectral 

factor is computed. 

Coupling zero 

1/T& Lead in K,+ 

11600 (0) (0.02Sl) [0.820,3.32] 1 (0.0048) (0.427) (1.5) [0.021,2.85] (20)(25)2 

-1/Ts 1/Tr 1/Two cd, wd 

Spiral Roll Washout Dutch roll Actuators 

aa = 

- 

- 

Further insight can be gained by concentrating on asymptotes and particular frequency ranges. Take, for example, the low frequency asymptote of 

- 0. Use the following approximations from [9]: (a) the washed out l(,(s) is 

insignificant below 1/TW and (b) generally INfJ << INLI, to obtain: 

Hence it can be seen that the washout time constant T,, and the airframe 

dynamics Nip and Nb all contribute to the slope of e at low frequency. 

The intent of the above discussion has been to show that much can be 

learned about singular values from literal approximations, and that much is 

to be gained by uniting classical and modern multi-variable techniques for 

flight control system analysis and synthesis. For the example given, the actual 

singular values, which can in general only be obtained by assigning numerical 

Supplement 1 19 TR-1228-1-1 
values for all of the parameters the system, are shown to be bounded and/or 

approximated by relatively simple, highly insightful, literal expressions. 

1+-- Nt 

I(, Nf;i or 

Literal Formulation of the Robust Stability 

Criterion 

(28) 

To examine the criterion for robust stability as formulated in (5) we must take 

the additional step of developing literal expressions for the singular values of 

the inverse return difference. The derivation is similar to (14) through (23), 

using I + (KG)-' instead of ICG: 

1x1 - [I + (KG)-l]*[I + (KG)-']I 

= X2 - BX + C = (A - X)(X - A) 

The polynomial coefficients are: 

(29) 

The literal expressions for the max and min singular values follow as before, 

namely that 7 x fi and a M m. 

Supplement 1 20 TR-1228-1-1 
The numerator expression for C is quite interesting - it is precisely the 

coupling numerator expansion for the multi-loop closed loop characteristic 

polynomial [9]. (This is demonstrated here for 2 x 2 systems but is conjectured to hold in general). Hence the closed loop poles are zeros of the literal 

approximation of a. This provides a fundamental connection between classical and modern multi-loop approaches, and allows us to dissect the problem 

in insightful new ways. 

Fig. 5a contains a Bode plot of the literal approximations for 7 and a (only 

e is of interest for robustness analysis, T is included only to show that the 

separation is large). The approximations are graphically indistinguishable 

from exact calculations. The straightline asymptotes included on the plot 

clearly indicate that the robustness weaklink is the dipole [.26,2.S]/[.67,2.6]. 

Improvement can be gained by increasing the .26 damping of the closed loop 

pole. 

Further insight can be gained by examining term-by-term the numerator 

expression for C. It turns out for this example that all of the terms are 

significant, which indicates that open loop airplane modal characteristics 

(roll subsidence and Dutch roll), the system numerators, and the controllers 

all contribute to the robustness of the system. This contrasts with high gain 

systems which are dominated by the controller and numerator characteristics. 

Perhaps surprisingly, the controller actuators and the time delay characteristics are not the limiting robustness feature. If, however, the controllers 

are changed so that the critical low point in the robustness test around 3 

rad/sec is increased, then the secondary critical point seen in Fig. 2 around 

Supplement 1 21 TR-1228-1-1 
Critical Point 

I I I I I I I 1 1 I llll I I Itlll 

H 

a 

9 

n 

i 

t 

d 

e 

d 

B 

U 

- u [I+(KGjl]X 

p [I +(KG)-']% - 

Asymptotes 

(of approximation) 

.0031 [.66,1.7][.26,2.8] [.94,6.0][.53,16][.85,40] [.83,53] 

[.8l, 1.81 [ .67,2.6] [.93 , 9.71 [ .87,33] [ .86,37] 

.O 048 [ .6 6, I .7] [ .2 6,2.8] [ .9 4,6.0] [ .53 , 161 [. 85 401 [ .8 3 ,5 31 

[.81,2.0][.50,2.4][.72,9.9][.86,34][.85,42] 

t \ 

-19 ' 

Solid = Approximation 

Dotted = Exact 

-21 I I I I I 11111 I I I I I I111 I I I I I Ill 

le-' 12 10' 1C 

Frequency (rad/secl 

bl Structured Singuur Vuhe 

! 

Sup p 1 em en t 1 22 TR - 1228- 1 -I 
. 

13 rad/sec would be the limiting factor. Due to its frequency this secondary 

point is a very strong function of the actuators and other high frequency 

dynamics. 

One of the important features of literal approximations is the ability to 

connect the analysis with aircraft configuration characteristics. For example, 

the critical low point in the robustness test occurs around 3 rad/sec, which is 

approximately the natural frequency of the Dutch roll mode. The feedbacks 

have changed the Dutch roll damping t, but not so much the natural frequency wd. The location depends primarily on the directional stability A$, 

and secondarily on the aileron induced yawing Nia and the effective dihederal 

L&. Having thus isolated the key aircraft parameters we can also predict first 

order robustness trends with changes in flight conditions. For example: 

From these relations we can see that the approximate location of the e dip 

is proportional to the square root of dynamic pressure (neglecting Mach and 

aeroelastic variations on the nondimensional derivatives). Another reason 

for isolating key aircraft parameters is that effort can be focused either on 

better identification of these parameters or on desensitizing feedbacks. 

Supplement 1 23 TR-1228-1-1 
.. 

A Literal Approximation of Structured Singular Values 

The same techniques detailed for singular values can be extended to the 

structured singular values. Repeating for clarity: 

k(A) = a(min e D-’AD) (31) 

where A = I+ (KG)-* = (‘ ”> cd 

. In this 2 x 2 case the frequency dependent scaling parameter e can be 

analytically determined: e = Jc/b. It follows in short order that: 

The numerators of a and - p are the same, because C has not changed. 

The denominator of is always smaller, because always 21bcl < jbI2 + IcI2, 

hence as expected 2 a. A transfer function approximation (with integer 

powers of s) is obtained by eliminating 21bc1, which is valid in the aircraft 

example because 21bcl << luI2 + ld12. 

The resulting literal approximation for E, straightline asymptotes, and 

transfer function approximation are shown in Fig. 5b. (If 21bcl is included in 

the literal calculation then straightline and transfer function approximations 

cannot be made but the frequency response is graphically indistinguishable 

Supplement 1 24 TR-1228-1-1 
from the exact calculation). The use of structured singular values means that 

crossfeeds are not allowed in the perturbation. It is concluded from from 

Fig. 5b is that if perturbation crossfeeds are not allowed then the system 

crossfeed numerators Nt and NS', (present respectively in b and c) are of 

reduced importance in determining robustness. This reduced importance is 

seen as a shift of the wed dipole [.26,2.S]/[.67,2.6] to [.26,2.S]/[.50,2.4]. 

The literal analysis is concluded by examining the terms which make up 

B in (2s) and (32). Due to the washout in the yaw damper it is expected 

that the I(, terms a and c are insignificant compared to the K,j terms b and 

d. A numerical test verifies this expectation. In the structured singular value 

expression b is also insignificant, because as seen above 21bcl << lal' + Idl', 

leaving only d as the important term: 

B = lal' + lb12 + lcl' + ldl' 

x lbl' + Id!' (use for E) 

x ldl' = lKrN&/A12 (use for E) (33) 

Eliminating terms like this, while not true in general, often helps identify key 

parameters for a particular problem. 

Summary and Conclusions 

The viewpoint espoused here is that recent advances in frequency domain 

multi-variable robustness techniques, when combined with classical multivariable flight control system design procedures, have much to offer as additional means for the assessment of flight control system designs. An example 

of a lateral-directional flight control system is used to illustrate how regular 

Supplement 1 25 TR-12 2 8-1 -I 
singular value and structured singular values are used to determine robustness measures. The example is then used to illustrate the development of 

various singular-valuebased quantities expressed using literal terms which 

define the aircraft and controller characteristics. The insights and connections exposed in these formulations illuminate the governing and underlying 

features of the system, and give specific emphasis to key and critical robustness issues present in a particular design. 

Acknowledgement 

This work was performed in p,art under Contract NAS1-179S7 with NASA 

Langley Research Center, Ah. Jarrell Elliott, Technical Representative. 

Supplement 1 26 TR-1228-1-1 
References 

. [l] Doyle, J.C. and G. Stein, Multivariable Feedback Design: Concepts for a 

Classical/Modern Synthesis, IEEE Trans. Auto. Control, Vol. AC26, No. 1, Feb. 19S1, pp. 4-16. 

[2] Safonov, M.G., A.J. Laub, and G. Hartmann, Feedback Properties of 

Multivariable Systems: The Role and Use ofthe Return Diflerence Matrix, ibid., pp. 47-65. 

[3] Doyle, J.C. Analysis of Feedback Systems with Structured Uncertainties, 

IEE Proceedings, Vol. 129, Pt. D, No. 6, Nov. 1982. 

[4] Doyle, J.C., Lecture Notes, 1984 ONR/Honeywell Workshop on Advances in Multivariable Control. 

[5] Mukhopadhyay, V., and J.R. Newsom, Application of Matrix Singular 

Value Properties for Evaluating Gain and Phase Margins of iIfultiloop 

Systems, NASA TM-84524, July 1982. 

[SI Newsom J.R. and V. Mukhopadhyay, A Il.iultiloop Robust Controller 

Design Study Using Singular Value Gradients, Journal of Guidance, 

Control & Dynamics, Vol. 8, No. 4, July-Aug. 1985, pp. 514-519. 

[7] Ftidgely, D.B. and S.S. Banda, Introduction to Robust Multivariable Control, AFWAL-TR-85-3102, Feb. 1982. 

[SI Herra-Vaillard, A., J. Paduano, and D. Downing, Sensitivity Analysis of 

Automatic Flight Control Systems Using Singular Value Concepts, AIAA 

Supplement 1 27 TR-1228-1-1 
Paper 85-1899, Proceedings of AIAA Guidance, Navigation and 

Control Conf., Snowmass, Colorado, Aug. 19S5, pp. 342-348. 

[9] McRuer, D.T., I.L. Ashkenas, and D. Graham, Aircraft Dynamics 

and Automatic Control, Princeton University Press, Princeton, N.J., 

1973. 

. 

[lo] Myers, T.T. and D.T. McRuer, Advanced Aircraft Flight Control 

Design Methodology, Phase I, Systems Technology, Inc., TR 1211- 

1, June 19S4. 

[ll] Jones, R.D., Structured Singular Value Analysis f0.r Real Parameter 

Variations, Proceedings of AIAA Guidance, Navigation and 

Control Conf., Monterey, CA, Aug. 1957, pp. 1424-1432. 

Supplement 1 28 TR-1228-14 
. 

LATERAL FCS REQUIREMENTS-ORIENTED DESIGN KNOWLEDGE PE 

FOR AN ADVANCED STOL FIGHTER IN HISSION PHASE CO 

A. GENERAL 

In this supplement we outline a draft knowledge base for the 

requirements aspects of a lateral FCS. To help make matters concrete, 

we will select an advanced STOL fighter as an illustrative design 

example, and then organize specifications, requirements, considerations, 

elaborations/specializations of material, etc., into a composite document. Many of the knowledge base elements will apply generally, 

although the specifics are intended for an advanced STOL fighter in a 

particularly difficult mission phase (air-to-air combat, CO) which exhibits a broad range of features. Because the requirements and considerations for this type of craft in this mission phase are severe, a less 

stringent set will apply for most other aircraft which are less sophisticated and more conventional. Indeed one reason an advanced STOL 

fighter was selected as the example was a desire to maximize the coverage, and thereby permit ready extension by parallel constructions or 

analogy. 

The first level of organization follows the FCS design process 

topics treated previously. These are: 

(1) Flight Control System Purpose 

(2) Command and Disturbance Characteristics 

(3) Unalterable Characteristics of the Aircraft 

and Controller 

(4) Pilot-centered Requirements 

(5) Overall System Requirements 

* References for this supplement appear at the end. 

Supplement 2 1 TR-1228-1-1 
Aircraft Characteristics 

Comparison of Aircraft Characteristics with 

Requirements 

General Equalization Requirements 

and 

Prospectus for FCS Architecture(s) 

Preliminary Design Analysis of System 

Possibilities 

Competition Among Candidate Architecture(s) 

and System(s) 

The ultimate outcomes of this process are: 

0 a FCS system structure or architecture (feedback 

control laws/loops); 

0 the fleshing out of this skeleton as one or more 

suitable system configuration(s); 

0 key sensitivity elements (system parameters/ 

characteristics which are central to the design 

suitability ; 

0 design assessments -- predicted nominal and offnominal properties, design sensitivity, etc. 

This section will focus on the requirements-oriented phases of the 

knowledge base, i.e., ending with step (5) the summary of "Overall 

System Requirements." Although the emphasis here will be on the CO mission phase, many of the items have a high degree of generality for 

highly maneuverable aircraft. Thus, with relatively minor changes and 

additions, these knowledge base summaries for the requirements-oriented 

phases can be used for other aircraft types, or can be extended to other 

critical mission phases. 

In the development below, the first level headings follow directly 

from the general outlines of Design Methodology steps given in Section I 

on each design phase topic. They are further partitioned into subtopics 

in outline form. Elements of the knowledge base are placed where appropriate under the lowest level in the outline. Each knowledge element is 

assigned to one of five categories indicated by [ ] as noted below: 

Supplement 2 2 TR-1228-1-1 
B. 

1. 

[SI - Specification: quantitative constraints on 

specified, measured, or calculated aircraft 

parameters which are formally recognized. 

[R] - Requirement: quantitative or qualitative constraints on design parameters; design criterion. 

[IR] = Implied Requirement: conditions with accompanying qualitative or quantitative requirements 

needed to enable a [SI or [R] to be met (i.e., 

unstated "requirements" implied by a stated 

requirement); corrections or additions necessary to adjust for non-ideal specific conditions once a mechanizational feature (usually 

a sensor) is established ( "requirements" 

needed to fix up or idealize a given control 

system architecture). 

[GP] = Good practice: advice based on past experience. 

[C] - Consideration: an important issue to think 

about in the design process for which it may 

be difficult to make general recommendations. 

TOPIC (1) -- FIJGHT CONTROL SYSTDI PUaPOSE 

Data Base Elements -- Mission and function-oriented specification 

requirements, notably from MIL-F-8785C (Flying Qualities) and MIL-F9490D (Flight Control Systems); possibly taxonomic/anatomical data. 

Knowledge Base Elements -- Cover structure of the Mission, Aircraft 

type, Aircraft/FCS anatomy, Mission-Centered Requirements. 

Aircraft/FCS Taxonomy 

Information Covered -- Classification of aircraft and its purposes 

(mission phases, maneuver complexes) for use in determining applicable 

specifications, and stating other high level requirements and/or considerations which are special and may not otherwise be covered. This 

knowledge base covers lateral flight control for advanced STOL fighters 

with emphasis on the air-to-air combat and other flight phases which 

require precise control in the presence of extreme maneuvering. 

Supplement 2 3 TR-1228-1-1 
[SI Aircraft Type: STOL Fighter (Class IV) 

Mission Phases: Category A, 

-- Air-to-Air Combat (CO) 

-- Ground Attack (GA) 

-- Weapon Delivery/launch (WD) 

[C] STOL landings on hastily prepared runway segments (50' by 1500') will have a major impact 

on the aircraft design. This requires precision directional control just before and after 

touchdown, augmented deceleration, etc. 

[IR] Possible thrust reversal capability; 

directional control capability using 

thrust vectoring. These capabilities 

may also be available for Mission Phase 

(CO) - 

[R,C] Maneuver Complex Key Situations: 

0 Precise tracking in lead pursuit gunnery 

and "wing matchup" in presence of evasive 

target; entire range of usable AOA conditions. 

0 Extremely rapid rolling (up to 250 deg/ 

sec) extremely rapid g onset (slightly 

past "g" suit limits) for evasive maneuvering, acquisition, etc. 

Possible extraordinary maneuvering (e.g., 

supermaneuvering" ) outside of conventional envelope based on aerodynamic control effectors. 

[IR] Precise lateral path control rapid rolling 

with highly constrained sideslip (/3 A 0) in 

the presence of rapid changes in aircraft 

loading. 

[R] Precisely controllable, Departure-free High 

Angle-of-Attack flight: 

[IR] FCS must cope with possible closed-loop 

pilot/vehicle sy tem rolling velocity 

reversal (e. g. , wd 1 0) and directional 

divergence (e.g., Wd < 0) phenomena at 

high AOA. 

9 

Supplement 2 4 TR-1228-1-1 
2. Aircraft/FCS Anatomy 

Information Covered -- The "givens" of the design problem, preliminary or tentative specification of unalterable characteristics of certain aircraft or FCS elements, etc. This knowledge base covers lateral 

flight control issues for multiple effectors (e.g., directional thrust 

vectoring, "aileron" and "rudder" aerodynamic controls) resulting in two 

effectively independent moment application control points producing rolling and yawing moments as primary outputs (side forces are incidentally 

present but not subject to independent side force control capability). 

The operating modes of the FCS comprise both manual and automatic control activities with appropriate consideration for compatibility among 

the modal system elements. 

The fundamental aircraft design has emphasized 

optimization of dynamic maneuvering and cruise 

performance aspects, reduced observables, etc. 

[IR] A variety of stability and control deficiencies are sure to be present, and are 

to be corrected by the flight control 

system. 

[IR] Adequate control power is available. 

Aircraft control system is fly-by-wire with 

pertinent multi-redundant elements. 

FCS is mechanized with digital technology. 

Multi-redundant sensors should be mature technology, simple, highly reliable, exhibit 

repeatable and uniform dynamic and scale characteristics, susceptible to cooperative 

checking/cross checking schemes, etc. (e.g., 

rate gyros and accelerometers display such 

properties, so quad- or tri- plex FCS mechanizations containing such devices will be 

favored by many designers). 

Supplement 2 5 TR-1228-1-1 
.[R] The aircraft/FCS will contain the following 

modes : 

0 Manual Control Only: 

-- Lateral Stability Augmentation 

0 Automatic Control with Manual Interaction: 

-- Bank Angle Control and Regulation 

-- Heading Control and Regulation 

-- Path Control and Regulation for 

several specialized modes such as 

-- Fire Control 

-- Terrain Avoidance 

-- Approach/Landing 

-- Navigation 

[C] The multi-modal aspect of FCS creates 

two hierarchies 

-- The FCS system needed to perform a 

particular function is often an 

essential subsystem for the FCS 

needed for another mode (e.g., the 

lateral stability augmentation system acts as a necessary set of inner 

loops for an automatic bank angle 

control system). 

-- The redundancy levels to support 

fail safe operations, and hence the 

flight critical degree for the several FCS modes are potentially different. 

[IR] The stability augmentation system is to have 

Supplement 2 

-- A high degree of independent integrity 

while simultaneously providing characteristics suitable as inner loop(s) equalization for the outer loop(s). 

6 TR-1228-1-1 
3. Hission-Centered Requirements 

. 

Information Covered -- These requirements include issues that affect 

task performance more than workload and safety, although all three 

aspects may be involved. Additional associated information related to 

workload and safety are covered in "pilot-centered requirements." 

a. Establishment of Trim Conditions 

[R] The aircraft must be able to be trimmed 

throughout the entire aerodynamic flight 

envelope, including accelerated equilibrium 

conditions. 

b. Control Power 

[SI MIL-F-8785C, Para. 3.4.10, Control Margin: 

"Control authority, rate and hinge moment 

capability shall be sufficient to assure 

safety throughout the combined range of all 

attainable angles-of-attack ... and sideslip.. . " 

[SI MIL-F-9490D, Para. 3.2.5.2, Priority: "Essential and flight phase essential flight controls shall be given priority over noncritical controls, and other actuated functions during simultaneous demand operation." 

[R] Sufficient lateral and directional effective 

control power must be available to operate the 

aircraft with aerodynamic control effectors 

throughout the entire aerodynamic envelope, 

and with all control effectors into the 

extended (low speed) and/or (high AOA) flight 

regime(s). In particular, sufficient lateraldirectional control power must be available to 

satisfy: 

[SI Roll Control Effectiveness and Performance -- MIL-F-8785C, Paras. 3.3.4, 

3.3.4.1, 3.3.4.1.1. 

[SI Regulation to wings level, zero sideslip 

flight in all conditions of diving 

flight -- MIL-F-8785C, Para. 3.3.8. 

Supplement 2 7 TR-1228-1-1 
[SI Regulation to straight and level flight 

with asymmetric thrust and/or loadings 

-- MIL-F-8785C, Paras. 3.3.9, 3.3.5.1.1. 

[R] Regulation to straight and level flight 

with all engines out or thrust vectoring 

disabled. 

[SI Avoidance of Inertial Coupling, Regulation to Zero Sideslip in Rolls -- MIL-F8785C, Para. 3.3.2.5. 

[SI Lateral-directional control in 90 deg, 

30 kt Crosswinds -- MIL-F-8785C, Paras. 

3.3.7, 3.3.7.1, and 3.3.7.2. 

[SI Recovery from post-stall departures, 

gyrations, spins. 

c. Lateral-Directional Rigid Body Modes 

i) Spiral mode 

[C] Spiral mode stability -- If manual or 

automatic bank angle control can be 

achieved by a simple proportional bank 

angle (manual or automatic) controller, 

a slightly unstable spiral is generally 

not a critical problem in normal flight. 

Spiral stability can be very desirable 

in IMC; high managerial workload, etc. 

conditions. 

[SI Spiral mode stability - - MIL-F-8785C, 

Para. 3.3.1.3. 

ii) Roll subsidence mode 

[GP] Roll mode characteristic -- the rolling 

velocity response to lateral control 

should approximate a first-order characteristic which is substantially uncoupled from other motions. 

Supplement 2 

[IR] If the flight phase involves significant maneuvering or precise 

tracking, the roll and spiral 

modes should not be coupled as a 

complex mode. 

8 TR-1228-1-1 
. 

1 

[SI Coupled roll-spiral oscillation, 

MIL-F-8785C, Para. 3.3.1.4. 

[SI Roll rate and Bank Angle oscillations, MIL-F-8785C, Paras. 

3.3.2.2, 3.3.2.3. 

[SI Sideslip response to roll control (A/l/k), MIL-F-8785C. Paras. 

3.3.2.4, 3.3.2.4.1. 

[SI Roll mode time constant -- MIL-F-8785C, 

Para. 3.3.1.2. 

iii) Dutch Roll Mode 

[GP] Directional control, characteristic -- 

the sideslip and yawing responses to 

directional control should be proportional to the pilot's command input and 

should approximate a second-order system 

characteristic. Rolling induced by 

sideslipping should be consistent with 

positive effective dihedral (right sideslips require right roll control deflection to keep wings level). 

[SI ilinimum frequency and damping, MIL-F87856, Para. 3.3.1.1. 

[GP] Dutch roll damping -- when the flight 

phase involves significant maneuvering 

or precise tracking augmenting the damping ratio above conventional levels may 

improve performance. 

[C] When a "lateral stability augmenter" exists as a separate operating entity of the FCS, the phase 

margin requirements of MIL-F-9490D 

will apply, and may imply larger 

damping ratios of the effective 

dutch roll mode. 

[SI Magnitude of I4//ll ratio, MIL-F-8785C, 

Para. 3.3.1.1. 

Supplement 2 9 TR-1228-1-1 
[C] If the flight phase involves sfgnificant maneuvering or precise 

tracking, and significant turbulence or buffet is present reducing I4//31 below the MIL-Spec 

Level 1 maximum may improve 

performance. 

iv) Maneuver Coordination 

[GI For rolling maneuvers in response to 

lateral control action (as contrasted to 

rolling maneuvers induced by sideslipping initiated using the rudder), the 

sideslip should be minimized and upelevator corrections should be automatic. . 

Supplement 2 

See "Roll Subsidence Mode" above. 

Turn Coordination, MIL-F-8785C, 

Para. 3.3.2.5. 

Coordination in Steady Banked 

Turns, MIL-F-949OD, Para. 

3.1.2.4.1; Sideslip less than 

2 deg and lateral acceleration 

less than 0.03g. 

Lateral-Acceleration Limits, Rolling , MIL-F-949OD, Para. 

3.1.2.4.1; lateral acceleration at 

the c.g. less than +0.5g for bank 

rates up to the maximum obtainable 

through A/FCS modes (greater than 

90 deg/sec). 

For yawing maneuvers in response 

to directional control action, 

there should be no sideslip reversal in the operational flight 

envelope. 

[SI Rolling in presence of sideslip, MIL-F-8785C, Paras. 

3.3.6.3, 3.3.6.3.2. 

10 TR-1228-1-1 
C. TOPIC (2) -- COBMAND AND DISTUBBANCB CHARACZERISTICS 

Data Base Elements -- Quantitative parameter data for generic command and disturbance models -- e.g., parameters in discrete gust, 

Dryden and/or Von Karman turbulence models, representative sensor 

noise statistics, etc. 

Knowledge Base Elements - - Organized command and disturbance sets ; 

restrictions and qualitative checklists on disturbance/command 

things to consider -- e.g., limitations of Gaussian turbulence 

models, and when this is important. 

1. Cod Inputs and Disturbance Sw 

Information Covered -- Exhaustive listing of the types of commands 

which will be applied by the pilot or automatic control to accomplish 

the mission phases(s), and of the varieties of disturbances which produce effects the FCS may be required to offset or otherwise reduce. 

This knowledge base covers lateral flight control for advanced STOL 

fighters with emphasis on the air-to-air combat, and other flight phases 

which require similar precise control in the presence of extreme maneuver ing . 

[C] Desired Command Deterministic Inputs: 

Steps, Pulses, Doublet Pulses, Cut-off 

Ramps, and Power Series during maneuvers 

[C] Desired Command Random Inputs: 

Generalized step/pulse sequences triggered 

by "random" maneuvering of target 

[C] Unwanted Command Deterministic Inputs: 

. Pilot -- Weber law "errors" in generation of power series inputs 

-- Reversal errors (steps/pulses) 

-- Feedthrough of specific forces 

(including vibratory inputs) 

Supplement 2 11 TR-1228-1-1 
0 FCS -- Slight power series "errors" as 

programmed operating point 

changes or as task-tailored 

control law mode changes 

[C] Unwanted Command Random Inputs: 

0 Pilot -- Remnant (pilot-induced noise) 

0 FCS -- Guidance system internal noise 

Supplement 2 

-- Geometry target noise (scintillation, multi-path, target 

maneuvers of higher order than 

accounted for in the fire control computer, etc.) 

[C] Internal FCS Disturbances: 

0 Unbalanced component biases/drifts 

(includes any steady-state or secular sensor noise components). 

0 Power supply shifts/fluctuations. 

0 Sensor noise. 

-- Random. 

-- Vibratory pickups (periodic and random) . 

-- Flexible mode(s) (inherently involve 

feedback, but signals due to modes 

unimportant in the system feedback 

control performance may be treated as 

a noise injection for steady-state 

performance purposes). 

[C] Vehicle-Induced/Associated External Disturbances 

0 Vehicle Asymmetries (including control 

effector and thrust malalignments, steadystate aeroelastic distortions, etc.) 

0 Stores Release (symmetrical and asymmetrical) 

0 Mechanical shocks 

0 Gun firing 

12 TR-1228-1-1 
0 Unsteady engine(s) thrust (gas ingestion 

from missiles/guns firing, foreign object 

ingestion, extreme sideslip, etc.) 

0 Vibration 

0 Buffeting 

[C] External Environment-Induced Disturbances 

0 Wind -- Steady, Shears 

0 Gusts -- Discrete, Random 

0 Shock/Blast waves 

0 Vortex Encounters 

[IR] Command/Response -- The Aircraft/FCS/Pilot 

System and the Aircraft/FCS System should 

exhibit good, rapid, well-damped command following responses to doublet pulses, pulses, 

steps, and ramps which enter at appropriate 

input points. 

[SI Bank Angle Regulation: plus/minus 

1.0 degree (relative to reference) 

static accuracy achieved and maintained 

within 3 seconds for a 5 degree bank 

attitude offset initial condition, 

MIL-F-9490D, Para. 3.1.2.1. 

[SI A damping ratio of at least 0.3 shall be 

provided for nonstructural A/FCS controlled mode responses, MIL-F-9490D, 

Para. 3.1.2. 

[IR] Disturbance Effect Suppression 

0 Trim -- The FCS must be able to establish 

nonaccelerated trimmed flight conditions 

for all vehicle system asymmetries. 

0 Regulation -- The Aircraf t/FCS' should 

exhibit rapid well-damped returns to trim 

conditions for all temporary discrete 

disturbances. (See e.g., [SI for "Bank 

Angle Regulation" above. ) 

Supplement 2 13 TR-1228-1-1 
2. Comaand/Disturbance Data Base 

Information Covered -- The data base includes quantitative descriptions of commands, external disturbances, and internal disturbances 

including sensor noise. This data base includes information applicable 

to all types of airplanes. 

Major Data Base Sources and Subjects: 

0 MIL-F-8785C. Flying Qualities of Piloted Airplanes, 5 Nov. 1980 (Ref. 1) 

-- Discrete Gust -- Paras. 3.7.1.3 (form), 

3.7.2.3 (length), 3.7.2.4 (magnitude) 

-- Random -- Paras. 3.7.1 (form), 3.7.1.1 

(von Karman form), 3.7.1.2 (Dryden form), 

3.7.2.1 (scale), 3.7.2.2 (intensities) 

-- Random (low altitude) -- Paras. 3.7.3 

et seq 

-- Wind Shear (low altitude) -- Paras. 

3.7.3.2, 3.7.3.3 

-- Carrier Landing Disturbance Model -- 

Paras. 3.7.4 et seq 

0 MIL-F-9490D, Flight Control Systems -- Design, 

Installation and Test of Piloted Aircraft, 

General Specification for 6 June 1975 (Ref. 2) 

-- Discrete Gust -- Paras. 3.1.3.7.2 (form, 

same as MIL-F-8785C), 3.1.3.7.1 (magnitude ) 

-- Random -- Para. 3.1.3.7.1 

-- Landing and Takeoff -- Para. 3.1.3.7.3 

et seq (includes shears) 

-- Transients from Failures - - less than 

+0.5g incremental normal or lateral acceleration at the c.g. or less than +10 deg/ 

sec roll rate (for redundant FCS), 

Para. 3.1.3.3.4 

0 ILS Glideslope Standards, FAA-RD-74-119, 

Vols. I, I1 (STI TR-1043-1, I & II), June 

1975, Oct. 1975 (Ref. 3) 

Supplement 2 14 TR- 1228 - 1 
. 

-- Glideslope Characteristics -- Glideslope 

beam alignment, structure, deviations 

(model and data from 24 sites) 

Automatic Landing Systems, FAA Advisory Circular 20-57A, 12 Jan. 1971 (Ref. 4) 

-- ILS Localizer & Glideslope Characteristics 

-- Steady and Shear Wind Specifications 

-- Wind Model for Approach Simulations 

0 Stochastic Disturbance Data for Flight Control 

System Analysis, ASD-TDR-62-347, Sept. 1962 

(Ref. 5) 

-- Gusts, Winds, Wind Shears -- early data, 

largely superseded 

-- Thrust Irregularities 

-- Acoustical Vibration 

-- Magnetic Field Variations 

0 Compilation and Analysis of Control System 

Command Inputs, AFFDL-TR-65-119, Jan. 1966 

(Ref. 6) 

-- Overflight Interference in ILS Localizer 

-- Approach Coupler Receiver Noise 

-- Terrain Following Profile & Spectra 

0 Terrestrial Environment (Climatic) Criteria 

Guidelines for Use in Aerospace Vehicle Development, NASA TM-82473, 1982 (Ref. 7) 

-- Ground Winds 

-- Inflight Winds 

-- Precipitation (rain, hail, snow) Fog & 

Icing 

-- Atmospheric Pressure and Density 

0 Mathematical Models of Human Pilot Behavior, 

AGARD-AG-188, 1974 (Ref. 8) 

-- Pilot-induced Noise 

Supplement 2 15 TR- 1228 - 1 
D. TOPIC (3) -- UNALTERABLE --STICS 

OF THE AIR- AND CONTROLT.XR 

Data Base Elements -- Some component parameters (e.g., actuator 

dynamics, sensor dynamics, etc.). 

Know1edp;e Base Elements -- Aircraft properties which are nonalterable by virtue of physical limitations or overall design philosophy, especially those which may be particularly important in 

establishing the FCS architecture; uncertain or highly variable aircraft features which should impact the FCS architecture, aircraft 

features which offer tradeoff possibilities, etc. Unalterable control system features may include primary aircraft output variables 

which must be controlled, sensor and actuator non-ideal properties, 

generic sensitivities/uncertainties in control system components, 

etc. 

1. Unalterable Characteristics of the Aircraft 

Information Covered -- Those features of the aircraft which are 

fixed by non-FCS considerations but which may still have a major impact 

on the FCS architecture. The aircraft dynamic properties which are most 

likely to be uncertain, 4 which past experience indicates might have 

substantial effect on the FCS design are also included. Any aircraft 

characteristics which may be susceptible to adjustment in a tradeoff 

sense, and the nature of such tradeoffs between the aircraft and the FCS 

should also be listed. 

[C] The fundamental aircraft design has emphasized 

optimization of dynamic maneuvering and cruise 

performance aspects, reduced observables, etc. 

[IR] A variety of stability and control deficiencies are sure to be present, and are 

to be corrected by the flight control 

sys tem . 

[IR] Manual FCS must cope with such 

possible closed-loop pilot/vehicle 

system problem as rolling velocity 

reversal (e.g. , wd2 < 0) , and 

directional divergence (e. g. , w$ 

< 0) phenomena at high AOA. 

Supplement 2 16 

c -3 

TR-1228-1-1 
[C] Sideslip Sensitivity: 

0 The presence of a plane of aerodynamic 

symmetry creates even-function variations 

of rolling and pitching moments with sideslip. For small perturbations about zero 

sideslip this permits the conventional 

separation of lateral and longitudinal 

equations of motion. At high angles-ofattack this even-function feature tends to 

become sharper, increasing the importance 

of such stability derivatives as Mp2 and 

Na, for small steady or larger sideslip 

perturbations. When this occurs lateral/ 

longitudinal coupling can become very 

troublesome (see, e.g., Ref. 11). 

0 Tendencies for wing-body/tail aerodynamic 

interference effects to change the sign of 

the dihedral effect are most severe as 

sideslip increases. 

There is consequent increased susceptibility 

to lateral/longitudinal couplings, rapid nose 

slice or roll-off departures, wing rock, etc., 

at high angles-of-attack and sideslip. 

[C] Combat suitability may be improved by permitting maneuvers which are outside the normal 

service envelope for aerodynamic control 

effectors, e.g., "supermaneuverability." The 

primary deficiencies will occur for high 

angle-of-attack, and/or non-zero sideslip conditions (such as noted above). 

[IR] The thrust vectoring control must be 

appropriately integrated with the aerodynamic controls to permit such maneuvers. 

[IR] There are powerful incentives for manual 

and automatic FCS , which minimize sideslip excursions in heavy maneuvering 

near the limits of aerodynamic flight. 

[C] The lower frequency aircraft flexible modes 

may potentially be important to the FCS design 

either as bandwidth restricting nuisances or 

as legitimate objects of control. 

Supplement 2 17 TR-1228-1-1 
0 If modes are to be controlled and/or if 

filtering time delays are to be minimized: 

[ IR] Phase stabilization is appropriate 

-- establish favorable flexible 

pole/zero order(s) and desirable 

pole/zero separation by choice and 

location of sensors. This is an 

application of the "sawtooth Bode" 

concept. 

0 If modes are to be ignored: 

[IR] Reduce modal pickup by sensor location; gain stabilize with low pass 

or notch filtering procedures. 

[SI Gain margin > 8 dB for nonstabilized aeroelastic modes, MIL-F9490D, Para. 3.1.3.6.1. 

[C] With a digital FCS, there can be low frequencies generated by the sampling operation, with 

the lowest being the minimum difference 

between a flexible mode frequency and a Sampling frequency. 

[ IR] Flexible and vibratory mode frequencies 

should be compared with the sampling 

frequencies of the controller to assure 

that no potential interaction problem 

exists . 

2. Unalterable Characteristics of the Control Elements 

Information Covered -- The non-ideal aspects of sensors, actuators, 

and other control elements which must be corrected or otherwise taken 

into account in the system design. 

[C] Actuators -- The actuators for the control 

effectors (aerodynamic surfaces and vectoring 

nozzles) can be approximated by first-order 

transfer functions and Pade pure time delays 

as appropriate approximations for the low frequency amplitude ratio and phase characteristics which serve to limit the attainable system bandwidths. (When higher frequency actuator dynamics are important, as in flexible 

mode control or in further calculations, at 

least a third-order actuator transfer characteristic is required). 

Supplement 2 18 TR- 1 2 2 8 - 1 -I 
I- 

* 

[GP] A major nonlinearity in the FCS is actuator rate limiting. This has the firstorder effect of reducing the effective 

time delay by up to T - (actuator amplitude)/2(rate limited velocity) seconds. 

Rate limiting and the consequent reduction of actuator effective bandwidth is 

a primary sensitivity consideration in 

the FCS design. 

[C] Sensor Pickup of Unwanted Signals -- Local 

vibrations and flexible modes (if not to be 

controlled) are important sources of internal 

noise picked up by inertial sensors (e.g., 

rate gyros, accelerometers, position gyros, 

etc.). The pickup is minimized by proper sensor location and signal filtering. 

[IR] Gain stabilize with low-pass or notch 

filtering procedures. 

Supplement 2 

[SI Gain margin > 8 dB for nonstabilized aeroelastic modes, MIL-F9490D. Para. 3.1.3.6.1. 

[IR] With digital controllers, the presence 

of a periodic sensor output signal from 

any source can give rise to frequency 

spectra lines with the lowest frequency 

at the difference between the excitation 

and the sampling frequencies. Antialiasing filtering will often take care 

of this, but some flexible modes may be 

close enough to the lowest sampling 

period to create a low frequency signal 

within the control pass band. 

[ C] Flexible Mode Stabilization (Phase Stabilization) -- The possibility often exists to provide some damping augmentation for particular 

flexible modes by proper location of attitude 

or rate gyros and accelerometers. 

[C] Accelerometers 

0 Pick up local specific forces, so are 

prone to excitation by vibratory and flexible modes. 

19 TR-1228-1-1 
Supplement 2 

0 Location effects relative to a control 

effector which generates both forces and 

moments can have profound effect on the 

signal sensed and on the stability and 

performance of any associated feedback 

loop(s). For lateral acceleration transfer functions, a non-minimum phase zero is 

present in the a/6, transfer function 

when the accelerometer is located aft of 

the center of rotation. (Similar effects 

are present for longitudinal accelerometers. ) 

[IR] Locate accelerometers used in high 

bandwidth loops so as to minimize 

these effects and any vibration 

pickup problems. 

0 The airplane transfer function for longitudinal acceleration has a non-minimum 

phase numerator term when flight is on the 

back side of the thrust required curve (as 

during slow approaches, nearly optimum 

climbs, etc.). 

[IR] Any automatic trim features using an 

accelerometer and integrators should 

be configured so as to avoid closedloop divergences. 

0 The usual acceleration desired for feedback control is incremental, whereas an 

accelerometer picks up the total specific 

force. Suitable adjustments for steadystate biases may be necessary either by 

very low frequency washout or trim like 

cancellation (see, e.g., Table 1-2). 

0 Certain acceleration measurements contain 

even-functions, e.g., 

If a limit cycle is present in the evenfunction (roll axis in the example), there 

will be a net bias from the accelerometer. 

[IR] Integration of such accelerometer 

signals may not be appropriate. 

20 TK-1228-1-1 
[SI Residual Oscillations, 0.02g lateral, peak to peak, MIL-F-9490D, 

Para. 3.1.3.8. 

[C] Sideslip and Angle-of-Attack Sensors -- Sideslip and angle-of-attack are often highly 

desirable feedback quantities. Unfortunately, 

their application is subject to many caveats. 

For high bandwidth aerodynamic sideslip and/or 

angle-of-attack applications, the following 

considerations can be extremely important: 

0 Sensor location effects (position error, 

sensitivity of scale factor and bias to 

local trim conditions of Mach Number, and 

angles-of-attack and sideslip, etc.). 

"Best" aerodynamic locations are often 

conflicting with radars or other installations, so a significant amount of 

calibration/compensation is usually needed 

to offset the location errors. 

0 External environment effects including 

pickup of local flow anomalies, turbulence, etc., icing (both on the ground and 

airborne), aerodynamic heating, damage 

from careless ground handling, etc. 

0 Contamination of desired signal by associated mount dynamics, etc. 

For the above reasons, angle-of-attack and 

sideslip are generally difficult to 

mechanize/install effectively for multiple 

redundant applications. Consequently, surrogates are often used. These include: properly located and compensated normal accelerometers and pitch rate lagged by (Te2 s + 1) 

for angle-of-attack; properly located and compensated side acceleration, inertial sideslip, 

composite signals made up of yawing velocity 

and bank angle, etc., for sideslip. 

[C] None of the surrogate measures are 

directly sensitive to aerodynamic sideslip or AOA. Consequently, they are not 

as suitable as aerodynamic sensors for 

the direct reduction of gust excitation 

sensitivity factors such as L B' 

Supplement 2 21 TR-1228-1-1 
E. TOPIC (4) -- PI=-Cm RIQ-S 

Data Base Elements -- Quantitative specs as in MIL-F-8785C; pilot 

dynamics and modeling data. 

Knowledge Base Elements -- Qualitative pilot needs, check lists of 

good practices, considerations, etc., that are not necessarily hard 

requirements. Existing data on acceptable force/position features 

for fly-by-wire system manipulators and recommended test procedures 

to rule out roll ratchet (e.g., Ref. 9). Note that a very large 

number of the pilot-centered requirements relating to flying qualities have already been covered in this knowledge base under the mission-centered requirements. 

Information Covered -- Pilot-centered requirements including flying 

qualities features are presented in Supplement 4. Also many of the 

flying quality aspects have been summarized in the mission-centered 

knowledge base above. Therefore, the summary below contains only a 

reference listing to details in Supplement 4 and such additional 

flying qualities requirements as are needed. 

1. Unattended Operation 

[C] To minimize the degree of divided attention 

required of the pilot, a bank angle hold (or 

even more elaborate outer loops such as heading hold) modes are indicated for normal operations. 

[IR] Bank angle control is an essential loop 

either for its own sake or as an inner 

loop for heading, lateral position, 

etc.. control. 

[C] When in Category B flight under manual control, the spiral mode should ideally be stable 

or only very slowly diverging. 

[SI Minimum time to double amplitude for the 

spiral is 12 sec for Category A & C 

(includes mission phases CO, GA, WD, PA 

and L), and 20 sec for Category B 

flight, MIL-F-8785B, Para. 3.3.1.3. 

Supplement 2 22 TR-1228-1-1 
2. Lateral Hanetwering 

[R] Dynamic coordination requirements -- The ideal 

aileron -- rudder crossfeed for zero sideslip 

in rolls initiated with the roll controller 

should be consistent with the "pll parameter 

(Ref. 10). 

3. Conditions for Acceptable Pilot Equalization 

[C] The primary piloting lateral control tasks are 

bank angle control, flight path control, target tracking, regulation against gusts, etc. 

[IR] Each of these situations define an 

effective controlled element which 

should.approximate K/s in the region of 

crossover. 

4. Effective TiPe Delay 

[C] The low frequency effect of all the high frequency (above crossover of the pilot/vehicle 

highest bandwidth loop) leads and lags in the 

aircraft/FCS (including actuator, sensor, filter, high frequency aerostructural modes, 

etc.) system can be approximated as a time 

delay. 

[SI For a pilot initiated step control 

input, the response of the aircraft will 

not exhibit a (effective) time delay 

longer than 0.10 sec (for Level 1 flying 

qualities), MIL-F-8785C, Para. 3.5.3. 

5. Conditions Antithetical to Pilot-Induced Oscillations 

[SI There shall be no tendency for sustained or 

uncontrollable lateral-directional oscillations resulting from efforts of the pilot to 

control the airplane, MIL-F-8785C, Para. 

3.3.3. 

6. Minimization of Remuant Excitation of Flexible Modes 

7. Minimization of Pilot/Vehicle Closed-Loop -citation 

of Flexible Modes 

Supplement 2 23 TR-1228-1-1 
8. Reduction of Vibration Feedthrougb 

[C] Items 5-7 above are strongly affected by the 

detailed force and position characteristics of 

the lateral and directional manipulators, and 

of any pilot command equalization filter elements, For modern fly-by-wire systems, the 

manipulator characteristics are not yet 

totally specified. 

[GP] Refer to Ref. 9 for guidance on manipulator force/position characteristics. 

[GP] Experimental check for roll ratchet tendencies with specific forcing function 

as outlined in Ref. 9. 

[GP] Stick filter to attenuate pilot remnant 

for manual roll control: the command 

path should have an effective low pass 

filter characteristic to attenuate pilot 

remnant, and the pass bandwidth should 

generally be below 10 rad/sec. 

F. TOPIC (5) -- OVERALL SYSTEn WUIRBENTS -- 

GENERAL 'I[wpLIED REQUIRBENTS 

Data Base Elements -- Elementary systems (second-order, crossover 

model, quadratic dipole, lead/lag, etc., properties -- Appendix C), 

characteristics, quantitative constraints, summary of likely airplane non-minimum phase zeros. 

Knowledge Base Elements -- General and implied requirements, good 

practices, considerations, pitfalls (e.g., sensor locations, nonminimum phase zeros), quadratic dipole considerations. 

1. System Level Rules of Thumb Which May 

Affect FCS Architectural Considerations 

[GP] Primary Rules of Thumb for Frequency Domain 

Synthesis of High Performance, Low Sensitivity, Feedback Loops. 

0 Provide low frequency equalization appropriate to the steady-state command following requirements. Ordinarily this means 

large amplitude ratios to provide good 

Supplement 2 24 TR-1228-1-1 
command following, insensitivity to uncertainties, and disturbance suppression. In 

other cases it implies very small amplitude ratios (e.g., as with washouts) to 

minimize steady-state bias effects. 

0 In the crossover region, which should 

occur at frequencies greater than those 

contained in the input and/or disturbance 

bandwidths, seek or create (by equalization) a fair stretch of -20 &/decade 

slope for the amplitude ratio; then adjust 

the loop gain so as to put the gain crossover frequency (unit-amplitude ratio) near 

the higher edge of this region while maintaining adequate stability margins. 

0 The "equalization" requirements. can be 

.satisfied by series compensation, introduction of inner loops, adjustment of 

effective aircraft numerators by feedbacks 

to other control effectors, etc. 

[Cl Stability Margins -- Closed-loop systems 

should possess appropriate phase and gain margins consistent with the uncertainties present. 

[SI Phase and Gain Margins in each and every 

closed-loop (with all but the loop being 

examined held at nominal values) over 

the operating envelope shall be: 

0 45 deg and 6 dB (considering all 

aircraft modes in the frequency 

range 0.06 Hz < f, < 1st (uncontrolled) aeroelastic mode) 

0 30 deg and 4.5 dB (fm < 0.06 Hz) 

0 Gain Margin of 6 dB at zero airspeed 

Supplement 2 

[R] Closed-loop system Peak Magnification 

Ratio, % < 4.8 dB (assuming the peaking 

mode is not part of a quadratic dipole 

pair) 

[SI A damping ratio of at least 0.3 shall be 

provided for non-structural AFCS controlled mode responses. MIL-F-9490D, 

Para. 3.1.2 

25 TR-1228-1-1 
All from MIL-F-9490D, Para. 3.1.3.6.1. 

[GP] Quadratic Dipole Pairs -- For manual or automatic closed-loop control with quadratic 

dipole pairs superimposed on a K/s-like characteristic in the crossover region, the ratio 

of the undamped natural frequencies of the 

complex zero and the complex pole should be 

less than unity. (Applicable to roll control 

with aileron, yaw rate control with rudder, 

etc. ) 

[GP] Command Loop Bandwidths -- For a stochastic 

command input contaminated with noise, a 

desirable system bandwidth (outer loop crossover frequency) should approximate the frequency where the command input power is equal 

to the noise power. 

[C] Location of Bending Filters -- Consideration 

should be given to placing structural mode 

filters in the feedback rather than the forward path to minimize the effective time delay 

in response to commands. 

Supplement 2 26 TR-1228-1-1 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

"Military Specification -- Flying Qualities of Piloted Airplanes," 

MIL-F-8785C, NOV. 1980. 

"Flight Control Systems -- Design, Installation and Test of Piloted 

Aircraft, General Specification For," MIL-F-9490D(USAF), 

June 1975. 

Hofmann, Lee Gregor, Warren F. Clement, Dunstan Graham, et al., ILs 

Glide SloDe Standards. Part I: A Review of Flight InsDection 

Standards Affectine Landing Performance and ComDarison With 

Limits Evolved From Svstem Analvsis, FAA-RD-74-119, June 1975. 

Hofmann, Lee Gregor, John J. Shanahan, and Dunstan Graham, ILS Glide . 

SloDe Standards. Part 11: Validation of ProDosed Flight 

InsDection Filter Svstems and ResDonses of Simulated Aircraft on 

COUDhd ADDroacheS, FAA-RD-74-119, 11, Oct. 1975. 

Automatic Landing System (ALS) Federal Aviation Administration Advisory Circular No. 20-57A, Jan. 1971. 

Hart, John E., Lowry A. Adkins, and Larry L. Lacau, Stochastic Disturbance Data for Flight Control Svstem Analvsis, ASD-TDR-62- 

347, Sept. 1962. 

Weir, David H., ComDilation and Analvsis of Flight - Control Svstem 

Command InDuts, AFFDL-TR-65-119, Jan. 1966. 

Turner, Robert E. (Comp.), and C. Kelly Hill (Comp.), Terrestrial 

Environment (Climatic) Criteria Guidelines for Use in AerosDace 

Vehicle DeVelODment, NASA TM-82473, June 1982. 

McRuer, D. T., and E. S. Krendel, Mathematical Models of Human Pilot 

Behavior, AGARDograph No. 188, Jan. 1974. 

Johnston, D. E., and D. T. McRuer, Investivation of Interactions 

Between Limb-ManiDulator Dynamics and Effective Vehicle Roll 

Control Characteristics, NASA CR 3983, May 1986. 

Hoh, Roger H., David G. Mitchell, Irving L. Ashkenas, et al., Proposed MIL Standard and Handbook -- Flving Qualities of Air Vehicles. Volume I: PrODosed MIL Standard. Volume 11: ProDosed 

MIL Handbook, AFWAL-TR-82-3081(1 61 II), Nov. 1982. 

McRuer, Duane T., and Donald E. Johnston, Flight Control Svstems 

ProDerties and Problems, Vol. 1, NASA CR-2500, Feb. 1975. 

Supplement 2 R-1 TR-122U-1-1 
PILOT-CENTWED REQUIREMENTS AND HUMAN 

PILOT A/FCS INTERACTIONS* 

In this supplement the complex but critical issues of pilot-centered 

requirements and flying qualities will be considered. This will not be 

an attempt at an exhaustive treatment of the subject, but will instead 

be a discussion of selected issues bearing on three broad areas: 

0 Integration of pilot-centered requirements into 

the design synthesis. 

0 Conflicts and ambiguities in requirements and 

specifications stemming from the presence of the 

human pilot in the loop. 

0 The problem of maintaining relevant requirements 

in the face of rapid changes in aircraft and 

flight control technology. 

The discussion to follow will treat the six topics of Fig. 1 in the 

sequence shown. 

The development of flight control system technology has been paralleled by the development of flying qualities requirements and specifications, which at any point have ranged from explicitly detailed to 

implicit (or nebulous). In the United States the most formal specifications are the military flying qualities specification, currently MIL-F8785C and the Federal Air Regulations, Ref. 1. These two documents play 

a subtle role in the design of many aircraft -- a role which ranges from 

legal requirement to design guide. Because of this it has been recognized that specifications without a well-documented rationale can be 

quite unsatisfactory. This point has long been recognized by the U.S. 

Air Force, and resulted in the "BIUGs" (Refs. 2 and 3) to support 

MIL-F-8785B and MIL-F-8785C, respectively. Continuing efforts by the 

*All numbers in this supplement referring to figures, tables, equations, and references are for Supplement 2 only. 

Supplement 3 1 TR-1228-1-1 
Effective Vehicle Dynamics and Flying Qualities 

Requirements -- Rigid Body Characteristics 

Conditions for Acceptable Pilot Equalization 

Conditions Antithetical to Pilot-Induced Oscillations 

Minimization of Remnant Excitation of Flexible Modes 

Minimization of Pilot/Effective Aircraft System 

Closed-Loop Excitation of Flexible Modes 

Reduction of Vibration Feedthrough 

~~ ~ 

Figure 1. Pilot-Centered Requirements 

Supplement 3 2 TR-1228-1-1 
. 

. 

Air Force to cast flying qualities requirements in the most suitable 

form for the development of increasingly complex aircraft has lead to 

the proposed MIL Standard and Handbook of Ref. 4. These "background" 

documents provide a link to the vast literature accumulated in years 

ofaircraft flight control system design and research, which are the 

ultimate sources of the pilot-centered requirements. Much of this 

knowledge resides as corporate "group technology" and in the experience 

of skilled designers. 

While the importance of past experience and "lessons learned" is 

undeniable, one of the most difficult challenges that designers of 

advanced aircraft must face is that new technology may invalidate specifications and criteria based on historic designs. The rapid introduction of active control technology into operational aircraft in recent 

years (e.g., the F-16, HIMAT, and Space Shuttle) has made this problem 

particularly acute at present. There is no simple solution for this 

problem -- short of effective research programs over the longer term. 

However, for an aircraft designer faced with an immediate design problem, the most powerful approach will be to take a critical view of all 

specifications and criteria. This requires a solid conceptual understanding of the basis for the requirements, and a set of tools for 

insightful analysis of their implications for advanced designs. 

A. EFFECTIVE VEHICLE DYNAMICS AND FLYING QUALITIES 

REQ-S -- RIGID BODY CHARA~ISTICS 

In this discussion, flying qualities issues may be usefully divided 

into two manual control regimes. 

0 Maneuvering including closed-loop manual 

tracking. 

0 Trim, speed control, and unattended operation. 

These regimes correspond to distinct regions of the effective aircraft 

frequency responses with maneuvering in the higher frequency region, 

while trim, etc., are featured at the lower frequencies. While these 

regimes relate naturally to the frequency domain, time domain specifications are also of interest, particularly for advanced aircraft with high 

order FCS characteristics. Examples of both frequency domain and time 

domain specifications will be discussed in the following. 

Supplement 3 3 TR-1228-1-1 
1. Ungitudinal Hanemvering 

a. Conventional Aircraft 

In this context, conventional aircraft are unaugmented aircraft with 

static stability achieved by aerodynamic means, i.e., with a stable 

static margin. This term can also be reasonably applied to augmented 

aircraft in which the augmentation gains are sufficiently low that the 

dynamic effects may be treated as modifications of naturally occurring 

stability and control derivatives. For conventional aircraft only a 

single longitudinal control point is ordinarily of interest, e.g., an 

elevator. Maneuvering can be treated as constant speed under the short 

period approximation, and thus thrust control is not an issue. Emphasis 

is on pitch attitude control since dynamic fundamentals require path 

control by means of inner loop attitude control. Path naturally follows 

attitude as can be represented by the path to attitude numerator ratio: 

where the "path lag" inverse time constant 1/Td2 is related to the heave 

damping & by 

- 

1. M, - -z,+-zzg Td2 M6 

Equation 1 is generally a reasonable approximation except perhaps for 

atypical configurations (e.g., the Space Shuttle, Refs. 5 and 6) where 

the pilot is well aft of the center of rotation for elevator inputs. 

. 

Supplement 3 4 TR-1228-1-1 
I' 

Historically, the only treatment of path dynamics in the MIL-Spec has 

been a short period requirement based on the control anticipation parameter (CAP) (Ref. 7). There has been some debate over the years as to 

whether this specification form is an adequate treatment of path 

dynamics, or whether an explicit relation to l/Te is needed (Refs. 2 

and 8). In any case for many but certainly not all aircraft, the value 

of l/Teq appears to be sufficiently high relative to the required path 

control bandwidth to justify the traditional specification emphasis on 

pitch attitude control. 

2 

1) Effective 8/hP Frequency Domain Requirements 

Equivalent Vehicle Dynamics 

In recent years the effects of control systems have been partially 

taken into account by defining so-called lower order equivalent system 

(LOES) dynamics. These models approximate the actual aircraft plus control system over a restricted frequency band by a LOES of the classical 

short period form, i.e., 

Here the restricted bandwidth, wl, is usually only implied, but is of 

the order of 10 rad/sec or so. Path/command considerations are not 

explicit in Eq. 3, however, it is recommended (Ref. 4) that in numerical 

fitting for equivalent system parameters, 1/Te2 be fixed consistent with 

Eq. 2. The effective time delay Teff is included to account for all the 

higher frequency (above % ) lags, leads, and pure delays. Time delay 

is a good first approximation since these effects appear primarily as a 

phase angle decrement (A4 A WTeff for w < % ) in the pilot's pitch con- 1 

trol crossover frequency range (1-4 rad/sec). 

1' 

1 

Desirable values of csp and wsp are directly stated in Refs. 3, 9, 

and 10. For transports (Class I11 aircraft), the latest version of the 

military specification (Ref. 9) provides current values. Aircraft which 

Supplement 3 5 TR-1228-1-1 
meet these requirements are very likely to have good flying qualities, 

but several aircraft which do not meet the requirements in all respects 

make up a substantial part of the operational fleet. Because commercial 

transports do not have to meet the military specifications to be 

certified, the aircraft manufacturers have tended to develop their own 

design criteria. These are often based on comparative characteristics 

with other aircraft by the same manufacturer, and are not necessarily 

expressed in equivalent system terms. Consequently, the equivalent 

system values in the military specification (Ref. 9) are primarily useful as design guides for transports. For fighters they are, of course, 

a more solid requirement. 

Effective time delay, Teff, is directly specified in Refs. 3, 9, and 

11. The data base is still growing and there is, as yet, no real 

consensus about allowable values, especially for large aircraft (see 

Table 1 presented later). Further, the usual mix in the Teff between 

time lags and pure time delays has not been thoroughly evaluated. For a 

given Teff near the allowable boundary limits, existing manual control 

theory and recent experiments (Refs. 12 and 13) indicate that a system 

with the Teff largely due to a pure delay will be less desirable than 

one where the Teff is due entirely to time lag components. 

Effective Aircraft 8/6, Bandwidth 

Another approach to defining desirable e/&, properties, particularly 

useful for unconventional dynamics is to specify an effective "airplane 

pitch bandwidth" (e.g., Refs. 3 and 14). This "airplane bandwidth" is 

akin to, but defined differently than that usually used for control systems. It is intended as an effective aircraft dynamic measure, which 

relates to the amount of lead equalization needed from the pilot to 

exert tight closed-loop control. To account for pilot aircraft closedloop control properties, is defined to be the smaller of the frequencies corresponding to a 45 deg phase margin or a 6 dB gain margin. 

The actual specification then becomes, 

Supplement 3 

wt, > Specified Value C 

6 

(4) 

TR-1228-1-1 
The larger qc is the less the pilot lead, 

pilot attentional demand requirements. 

and hence the smaller the 

2) Time Domain Requirements for 

Time domain requirement statements have become more prevalent as 

control system characteristics have become more dominant factors in the 

overall system response. These are often given as inequality constraints or as graphical boundaries. The typical pitch rate response to 

a step pitching velocity command can serve to illustrate most of the 

time domain measures (Fig. 2). The major differences between Figs. 2a 

and 2b are in the initial part of the response and in the underlying 

idealization. Figure 2b shows an indicial response of the particular 

limiting form given, and does not include the effects of high frequency 

actuator and other modes. Figure 2a on the other hand shows a gradual 

initial build up to the maximum velocity, which reflects the higher frequency control system characteristics; further, the remainder of the 

response is not necessarily confined to the Fig. 2b form. Instead other 

dynamics, especially some dipole pairs, may be present in Fig. 2a which 

is intended to represent the actual complete system. At their closest 

juncture, the two figures would be the same except for the high 

frequency lags which affect the initial response. The indicial 

responses shown may be those of the aircraft/flight control system for 

all time, as in a rate command system with very high dc gain, or for a 

short time only as with a conventional short period. In the latter 

case, the phugoid motions will succeed the rapid pitching velocity 

response to its intermediate and temporary quasi steady-state. 

Reference 11 provides recommendations for the rise time (t2 - tl), 

transient peak ratio Aq /Aq and time delay, tl for Supersonic Cruise 1' Research (SCR) aircraft 12 . For Level 1 flying qualities ("Flying qualities clearly adequate to perform the tasks ... under the most arduous set 

'The conditions for applying the Ref. 11 specification are somewhat 

different than indicated in Fig. 2a. In particular the specification 

calls 2 DOF speed constrained equations of motion and pitch response to 

controller force. 

Supplement 3 7 TR-1228-1-1 
-0 

a 

N 

.- - 

L 

0 

z 

-IT Q) 

E I1 .- 

I- I-“ Q) 

.f 

3’ 

e 

- 

Q) 

E 

I- 

.- 

-0 

Q) 

N 

0 

.- - 

E 

z 

L 

0 

N 

Supplement 3 a 

I1 

hl 

al 

Lt 

3 

M 

TR-12 28- 1 -I 

. 
, 

LEVEL 

1 

2 

3 

of environmental conditions likely to be encountered operationally...") 

these are 

8785C SCR (PITCH) LOCKHEED 

0.10 0.12 0.40 

0.20 0.17 0.60 

0.25 0.21 0.70 

( 152.4 (Nonterminal Phases) 

VT 

where VT is in meters/sec. The constants in parenthesis are used when 

VT is expressed in ft/sec. The effective time delay, which can be associated with the Teff described for the frequency domain criteria does 

not, as previously mentioned, yet have consensus values. This is emphasized in Table 1 which gives a cross-section. However, the Lockheed 

recommendations include the direct effect of a lower pilot frequency 

bandwidth associated with very large aircraft. 

TABLE 1. EFFECTIVE TIME DELAY RECOMMENDATIONS 

supp 1 ement 3 9 TR-1228-1-1 
Other time domain criteria appear as boundaries. A typical set for 

rate command/attitude hold systems is shown in Fig. 3a. This criterion 

was established for the space shuttle, and has been noted as in some 

ways inconsistent with other criteria described above (Ref. 15). The 

most important differences are the large initial time delay and the low 

pitch rate overshoot permitted. 

Inserted on Fig. 3 are two other bounding criteria for time response 

to 90 percent of final value and for settling time. These were proposed 

in Ref. 16 and flight validated in Ref. 17 specifically for transports 

with rate command/attitude hold systems. 

Finally, another version of time response boundaries has been proposed for large advanced supersonic aircraft (Ref. 18). A typical 

boundary corresponding to the subsonic boundaries given in Fig. 3a for 

the shuttle is given in Fig. 3b. Comparison of the two boundaries shows 

that much less initial time delay and much greater response overshoot is 

permitted by Fig. 3b. 

In all of the time domain criteria described thus far, there is no 

explicit requirement set on the secondary response/command relationships. Two schemes which do take other responses into explicit account 

are the so-called C criterion, which blends both pitch rate and normal 

acceleration, and the "Time Response Parameter" (TRP) which uses the 

same two quantities. Comparisons made in Ref. 18 indicate that C , in 

its current formulation does not predict good flying characteristics for 

advanced transports as well as Fig. 3b does, so we do not include it 

here. The Time Response Parameter (Refs. 19 and 20) has the form 

* 

* 

The times, td and tc, for 

are defined in Fig. 4 as 

8 and td and TN for the normal acceleration 

are values for the weighting constants Ki. A 

NZ z 

TRP 50.25 has been shown in a number of experiments (e.g., Ref. 20) to 

Supp 1 ement 3 10 TR-1228-1-1 
. 

P m cv 

0 

0 

-m 

0 

a, 

v) 

Y 

-&I E 

I- 

.- 

C 

0 

c 

cn 

a, lx 

B 

m 

a, 

Ll 

3 

M 

.rl 

Lrr 

Supplement 3 11 TR-1228-1-1 
1.0 

v) 

W 

CA 

z 

0 

n 

CA 

W 

(r 

a. 

0.5 c, 

k 

a 

z 

0 

KI = 0.08 

K2 = 0.5 

K3 = 0.3 

K4 = 0.2 

- 4 

CAN BE 

0 PT 1P.1 IZ E D 

t (SEC) 

PJOTE: K4 ONLY REQUIRED FOR S?;IALL TRP VALUES (G 0.23) 

Figure 4. Quantities Involved in the Time Response Parameter 

Supplement 3 12 TR-1228-1-1 
E 

be consistent with pilot ratings of 1-2 on the Cooper-Harper scale. For 

a good aircraft, the most important terms in TRP are the initial cyclic 

parameter (td/tc)g and the K2(td - 0.7) in (TRP)N,. The other terms 

are, in fact, often zero for systems with (TRP) I 0.25, since they are 

included only if the terms in parentheses are positive. 

NZ 

The (TRP). essentially takes care of the primary response to command 

input, whereas the (TRP)N, accounts for the secondary response to command. Accordingly, systems designed to the TRP do consider both good 

primary flying qualities and appropriate motion harmony. The TRP criterion as it now stands was developed for fighter aircraft. 

e 

b. Highly Augmented Aircraft 

There is no clear demarcation between "highly augmented" and more 

conventionally augmented aircraft -- except that the latter are presumed to have basically conventional response characteristics. However, 

the emergence of high reliability, high authority, high gain flight control systems in operational aircraft, particularly with relaxed static 

stability (RSS) (e.g., the Space Shuttle and F-16) has resulted in a 

wider recognition of t1.e need for new requirements and specifications 

with a flight control system orientation as an alternative to fitting 

advanced aircraft characteristics to specifications evolved for conventional aircraft (Refs. 12 and 21). The archetype of these new highly 

augmented aircraft is the "superaugmented" aircraft, which is created by 

application of a high gain pitch rate to elevator (or equivalent) feedback to a RSS airframe (Ref. 12). Superaugmentation has some appealing 

practical features compared to other high gain possibilities (such as an 

angle-of-attack to elevator feedback), and control systems of this 

general type have been applied to several operational RSS aircraft, 

e.g., the Space Shuttle and the X-29. The superaugmentation model is an 

idealization based on an analytical rather than a numerical lower order 

equivalent system representation. Superaugmented aircraft characteristics were discussed in Section 111, but some of their general and unconventional characteristics will be summarized briefly below as a basis 

Supplement 3 13 TR-1228-1-1 
for considering the flying qualities requirements problem for highly 

augmented aircraft. 

0 The airframe characteristics are neutral or 

unstable without augmentation. 

0 The superaugmented characteristic modes are 

unconventional. There is neither a phugoid nor 

true short period mode, instead the aircraft has 

first-order speed and heave modes comparable to a 

neutral airframe and a second-order pure pitch 

mode (uncoupled from heave) which is largely 

defined by FCS parameters. 

0 The pitch response to a pitch rate command is 

given to a first approximation (see Appendix C) 

by : 

where the pitch mode parameters are 

The effective attitude lead l/Tq is generally near 4 which gives q/qc(s) a "K/slike" characteristic. This produces a 

transient pitch response to qc step inputs 

with characteristically low overshoot. 

0 The superaugmented effective time delays tend to 

be large often due to structural mode and other 

FCS filters. 

q is generally much higher than the path to attitude lag 1/Te A -Z, -- this indicates unconventional flying qualities. This characteristic 

appears as an unconventional lag in the 7 (path) 

transient response to q, commands. The lag time 

0 The unconventional effective attitude lead 1/T 

2 

constant is that 

-- approximately 

Supplement 3 

of the -superaugmented heave mode 

To2 sec. 

14 TR-1228-1-1 

a 
0 By varying the prefilter (Gi in Fig. 5) in the 

command path (Sp -+ qc], the superaugmented 

response to the pilot's controller can be modified extensively. The important research question at the moment is selection of the proper Gi 

for a given flight condition and task. 

While superaugmentation is of great current interest, the empirical 

data from which requirements and criteria may be formulated is quite 

limited although relevant research programs are in progress. Data from 

ground and in-flight simulations is available from Refs. 5 and 16. 

These experiments and the Space Shuttle design work have lead to the 

time domain pitch rate response criteria, which were shown previously in 

Fig. 3a. Examination of operational flight experience with the shuttle 

(Refs. 6 and 22, 23) has indicated pilot concerns with path control, 

which were not anticipated in the original (1973) Shuttle flying qualities specification (Ref. 24). The effect is subtle and has been confounded by the issue of unconventional pilot location with respect to 

the center of rotation for elevator commands. 

Current research on this topic will be briefly reviewed here as a 

case example of the problem of using "old specs for new airplanes," and 

to illustrate approaches for critically examining such requirement problems. Figure 5 compares the short-term response to the pilot's pitch 

command of a conventional aircraft (represented by the short period 

approximation), and a superaugmented aircraft with a pure gain Gi (nominally the Shuttle). For purposes of comparison, the short period frequency of the conventional aircraft has been set equal to the pitch mode 

frequency of the superaugmented aircraft wfi. In the pitch attitude 

response, the major distinction between the two aircraft is the location 

of the effective attitude lead -- 1/Td2 in the conventional and 1/T in 

the superaugmented case. The 1/Te2 - wsp separation in the conventional 

aircraft is the source of the large attitude transient overshoot. The 

attitude overshoot is much lower in the superaugmented case since l/Tq 

wfi. Comparing the conventional and superaugmented path (7) responses 

reveals the superaugmented path lag. 

q 

Supplement 3 15 TR-1228-1-1 
8 

15 

I$ 

dB 

#/ 

Superaugmented Heave Superaugmented 

Mode 

dB 

Frequency Response 

{Bode magnitude asymptotes) 

3 

8 

2 

I 

0 

I 

Y 

Conventional 

\ ,- Superaugmented 

4 

0 

0 I 2 3 

Time (sec) 

/mpu/se Response 

Figure 5. Comparison of Short-Term Response to 

Pilot Pitch Command-Convent ional (Short Period) 

vs. Superaugmented Aircraft 

Sup p 1 em en t 3 16 TR-1228-1-1 
From the comparisons of Fig. 5 it might be anticipated that pilots 

of superaugmented aircraft (with Gi essentially a pure gain) would 

observe the more sluggish -y/Sp and downrate its flying qualities. 

However, the problem is more complex because the pilot may be performing 

significant closed-loop tracking. When the pilot closes a reasonably 

high gain inner attitude loop e/#, + 1, and the effective outer loop 

path response -- for both conventional and superaugmented aircraft -- 

approaches 

Thus, if the pilot is performing significant closed-loop tracking, the 

impact of the superaugmented path lag on the pilot's oplnion of flying 

qualities may be significantly reduced (Ref. 12). 

Data with which to examine these effects are quite limited. However, informal pilot comments from the Shuttle astronauts provide some 

insights (Refs. 6 and 22). Astronauts who have commented on the Shuttle's pitch response to control have generally felt that these characteristics are precise and desirable. This is consistent with the expectation that the broad region of %/s - like" slope in the superaugmented 

16/6 I frequency response (Fig. 5 region below 1/T ) would require less 

pilot equalization for attitude control loop closures. There have also 

been, however, comments by the Shuttle crews about unconventional or 

sluggish path response. This has prompted considerable examination of 

the Shuttle pilot location effect, but the anecdotal data are consistent 

with the superaugmentation path lag hypothesis. The important fact is 

that these shuttle flying qualities problems occur in the landing 

flare. In the flare manual closure of a pitch attitude loop is not 

feasible implying that the superaugmented path lag will be "seen" by the 

pilot. As a minimum this can be expected to constrain landing technique 

and probably degrade pilot opinion since altitude control is uniquely 

critical in the flare. 

P q 

Supplement 3 17 TR-1228-1-1 
A formal experiment to test this has not been conducted, although 

some support is available from Ref. 25. This paper reports on a Space 

Shuttle simulation conducted on the NASA-Ames VMS simulator. The operational Shuttle pitch FCS was compared to alternative designs with more 

conventional characteristics (i.e., the effective attitude lead was 

near l/Tf12). Evaluations and pilot ratings were obtained from two 

groups of pilots: 

0 

0 Shuttle pilots 

test pilots with conventional aircraft experience 

Considerable variation in pilot opinion was observed. The study 

conclusions from Ref. 25 were: 

Final Flare and Landing 

A control system that had good flight path control response [i.e., conventional ~/6e] was preferred by pilots with conventional aircraft background, 

The current Shuttle control system, which has 

good attitude control was preferred by the Shuttle pilots who had extensive training with this 

sys tem. 

Steep Glideslope 

No clearcut advantage was seen with either system. There was a general preference for the current shuttle system because of the attitude dropback (overshoot) characteristics. 

These conclusions are consistent with the above hypothesis. 

It should be recalled that the above considerations are for a command path filter, Gi, which is effectively a pure gain. More complex 

filter forms can fundamentally change the effective vehicle response as 

seen by the pilot -- including restoring a more conventional effective 

attitude numerator, and thus creating essentially conventional shortterm flying qualities. Thus, flying qualities requirements for superaugmented aircraft can be expected to focus on what the form of Gi 

should be with the potential for considerable task tailoring. 

An important task-tailoring example is offered by the flare 

maneuver. Consider first a flare maneuver intended to be made up of a 

Supplement 3 18 TR-1228-1-1 
sequence of discrete changes in flight path. These correspond to discrete attitude changes so a pitch rate command/attitude hold system 

would be appropriate. The piloting technique supported by this system 

would include discrete precognitive inputs to modify the pitch angle in 

the appropriate sequence with pursuit behavior to fine tune the attitude. The regulation function of attitude maintenance is largely accomplished by the FCS. This form of landing operation is especially pertinent to carrier approaches with large flight path angles continued to 

touchdown. It is also used on the Shuttle with several steps in the 

flare. 

For the second flare maneuver, consider a spatial exponential as the 

desired trajectory. To accomplish this, the pilot needs to make the 

sink rate proportional to the attitude. This can be done by modulating 

the pitch attitude (as an easily perceived surrogate of sink rate) proportional to altitude. The appropriate flight control system for this 

type of flare would then be attitude command/attitude hold in character. 

This follows the Kc/s-like prescription for the task, i.e., h/Jp A 

Uo8/6p A K/s in the region of pilot-vehicle system crossover. This is 

approximated in conventional aircraft near the minimum of the thrust 

required cunre. It is also supported for some superaugmented aircraft 

by flight data in Ref. 26. 

One final consideration for superaugmented flying qualities is the 

effect of disturbances (both internal FCS noise and atmospheric turbulence) interacting with control power limitations and aircraft structural modes. This interaction has potential for producing control saturation nonlinearities, which can degrade the stability and the dominant 

pitch mode characteristics of superaugmented aircraft because of their 

unconventionally extreme dependence on flight control system parameters 

(Ref. 12). While conventional aircraft are affected by atmospheric turbulence, their dynamics (i.e., the aircraft poles and zeros) are not 

affected. However, for the new class of superaugmented aircraft any 

turbulence induced control saturation will cause changes in the basic 

aircraft dynamics. 

Supplement 3 19 TR-1228-1-1 
c. Direct Force Control Aircraft 

If an additional control effector (independent of the pitch control) 

is added to the aircraft (i.e., direct lift control), the flight control 

system can be mechanized to produce direct force control (DFC). With 

two independent control points available, path and pitch attitude can be 

controlled independently (in the short-term). The most elementary 

implementations of these characteristics are "decoupled modes" such as 

have been flight tested on the CCV and AFT1 F-16 aircraft. The limiting 

characteristics of these modes are summarized in Table 2. In these 

modes the aircraft as seen by the pilot has effectively a single 

degree-of-freedom, and in the normal acceleration or vertical translation modes there is no longer a direct concern with attitude control. 

TABLE 2. LIMITING RESPONSES FOR DFC RESPONSE 

MODES LONGITUDINAL 

Supplement 3 20 TR-1228-1-1 
Thus, the response requirements should deal primarily with the heave or 

path angle response, which would ordinarily be outer loop considerations. Approaches to the handling qualities criteria for direct force 

control aircraft are discussed in Ref. 27. In this work it was found 

that specifications on the "airplane bandwidth" along the lines of those 

discussed earlier, appear to be the most suitable approach. Proposed 

DFC flying qualities specifications are presented which specify bandwidth minimums as a function of task and flying qualities level. 

2. Lateral Maneuvering 

a. Conventional Aircraft 

Since conventional aircraft are ordinarily maneuvered laterally in 

banked turns, an inner bank angle loop is implied to equalize the outer 

lateral path loop. The equalized outer loop dynamics can be examined 

from the X (lateral path of the velocity vector) to bank angle numerator 

ratio : 

* Here, as elsewhere in the report, the following shorthand notation 

for transfer function poles and zeros is used 

(s + a) = (a) 

[s2 + 2cws + "21 - [r, w] 

Supplement 3 21 TR-1228-1-1 
The poles and zeros comprising the second-order wA/wd dipole will generally be close to cancelling since (typically): 

(9) 

cx . I4 

---1 

Further, this dipole will generally be well above the required path control bandwidth frequency so that in the pilot's outer (path) loop crossover frequency region, 

A. gflo 

d S 

- IThus, - if the pilot can achieve good inner loop roll control, the aircraft path response to the pilot's (internal) roll commands will have a 

nearly ideal "K/s-like" characteristic in the crossover region. Thus, 

the primary manual control concern is for roll control, which is 

reflected in the emphasis of conventional flying qualities specifications such as the MIL-Spec. 

The conventional bank angle response to roll control inputs is given 

by 

L= Wd] 

Supplement 3 22 
For an "ideal" aircraft, the Wd/wd dipole should cancel exactly, and the 

spiral root l/Ts should be at the origin. This would eliminate the 

dutch roll residue in roll response to commands, and produce the simple 

"1 DOF" roll response of Eq. 13. 

At this level there is, aside from control power issues, only one flying 

qualities parameter -- the roll subsidence mode time constant TR. Over 

the years considerable flight and simulator studies have established 

upper limits on the roll mode response time TR to achieve acceptable 

transient roll response (Ref. 28). Figure 6 summarizes some of the data 

which has been used to establish upper limits on TR. Criteria from the 

current MIL-Spec are shown in Fig. 7. 

Conventional aircraft do, of course, frequently have dutch roll 

problems. Three different but related approaches have been used for 

dutch roll criteria. 

0 Direct specifications of minimums on dutch roll 

damping and frequency as in Fig. 7b. 

0 Constraints on the dutch roll residues in several 

vehicle response variables, e. g . , the llposc/pav'l 

and "A/3/n" requirements of the MIL-Spec. The 

first of these requirements also attempts to promote wd/wd < 1 to avoid a reduction in dutch roll 

damping as the roll loop is closed by the pilot 

(see Appendix C). These specifications apply to 

rudder fixed dynamics. 

0 Specification of the rudder control by the pilot 

required for coordination (Ref. 4). 

These dutch roll requirements include both frequency domain and time 

domain specification forms. For aircraft such as the Space Shuttle, 

time domain criteria similar to those of Fig. 3, have also been developed for roll control. 

Supplement 3 23 TR-1228-1-1 
Rotinq 

*COOPER 

0 

*: I :4+ 

SCALE 

01 

6!- fl X-14 

-5 i / 

05 10 50 IO 0 500 IC3C TR - 

Figure 6. Ratings vs. Roll Damping -- Flight Test, 

Moving-Base, Fixed-Base with Random Input 

b. Highly Augmented and Unconventional Aircraft 

Specifications for augmented aircraft have been treated using lower 

order equivalent system models comparable to those for longitudinal 

specifications. The lower order equivalent roll response model proposed 

in Ref. 4, Vol. 11, is the transfer function of Eq. 12 with an effective 

time delay element. High gain command augmentation systems (CAS) are 

one class of lateral directional FCS which have had flying qualities 

problems. CAS systems are designed to improve roll control transient 

response by effectively reducing the roll mode time constant TR; however, for unconventionally low values of TR a PI0 phenomenon referred to 

as "roll ratcheting" has been observed. Data from the LATHOS experiment 

(Ref. 29) and experience with roll rate command augmentation systems, 

Supplement 3 

. 
II 

i 

111-L, 111 0.08 

* 

0.10 1 0.4 -1 

a) RECCMNENDED MAXIMUN ROLL-MODE TIME CONSTANT (Seconds ) 

FLIGHT 

PHASE 

CATEGORY 

CLASS 

LEVEL I rT I 2 13 

b) RECOMMENDED MINIMUM DUTCH ROLL FREQUENCY AND DAMPING 

A I 0=19 i 0.35 1 ;:: 1 j I, IV 0.35 

j 11, 111 j 0.19 

B 

i I, 1142, I 

c 1 Iv 1 0.08 1 0.15 1 1.0 i I 

c) SPI!LU STABILITY - RECOMMENDED MIN'fiUM 

TINE TO DOUBLE AMPLITUDE 

* The governing damping requirement is that yielding 

the larger value of Sd, except that a <d of 0.7 is the 

maximum required for Class 111. 

Figure 7. Summary of Lateral/Directional Mode Requirements 

from the MIL-Spec (Reference 9) 

Supplement 3 25 TR- 1 2 2 8 -1 -I 
indicates that roll control problems can occur for particularly low roll 

mode time constants (e.g., less than a third of a second). In general 

these problems appear to be related to lateral stick shaping and sensitivity as affected by the pilot's neuromuscular mode (see Refs. 30, 31). 

The available evidence indicates that the pilot's limb neuromuscular 

system has a resonant peak, which can be "tuned to (an undesirable) 

maximum" by adjusting the effective Tr + r to about 0.1 sec. 

Incorporation of relaxed directional static stability has not become 

a significant design trend as evidenced by the number of fighter aircraft with twin vertical tails. There are, however, potential performance benefits from directional RSS for both fixed wing aircraft and helicopters. Unfortunately, there are some accompanying significant difficulties for lateral FCS design. A dominant phenomenon (Ref. 32) is the 

deterioration of Nf into two real zeros (one potentially in the rhp) as 

directional stability is reduced. A similar phenomenon can occur at 

high angle-of-attack. 

a 

c. Lateral Direct Force Control Aircraft 

With the addition of a third independent lateral-directional control 

effector, direct force control can be achieved. Lateral DFC modes were 

implemented on the CCV and AFT1 F-16, including decoupled modes analogous to those discussed earlier for the longitudinal case (see Table 3). 

The manual control and control power issues for these decoupled modes 

are generally similar to the longitudinal case, but a pilot-centered 

issue specific to the a>. or "wings level turn" mode should be noted in 

contrast to a conventional bank-to-turn aircraft. While sideslip is 

ideally zero for a wings level turn, the side acceleration is not. The 

turn is not coordinated in that the centrifugal force acting on the 

pilot is not balanced by a gravity component as in a conventional banked 

turn. Thus, for combat maneuvering with direct side force control, 

there is a direct impact on pilot support and cockpit controller design. 

Supplement 3 26 TR-1228-1-1 
Direct Side 

Force, or 

Wings Level 

Twn 

( -qy, 

TABLE 3. LIMITING RESPONSES FOR DFC RESPONSE 

MODES LATERAL DIRECTIONAL 

CONS’DIAINTS 

*Prizes denote effective derivatives that account for cross products of 

icertia (see Ref. 27, page 257). 

3. Trim, Speed Control, and Unattended Operation 

Trim, speed control, and unattended operation depend on the longterm dynamics of aircraft and static stability considerations. For 

example, among the most fundamental provisions of the FAR for stability 

and control of Part 25 aircraft are those called out in Sections 25.171 

Supplement 3 27 TR- 12 28- 1-1 
(General) and 25.173 (Static Longitudinal Stability). These in essence 

require that 

"The airplane must be longitudinally ... stable ..." 

"A pull must be required to obtain and maintain 

speeds below the specified trim speed, and a push 

must be required to obtain and maintain speeds above 

the specified trim speed." 

"The airspeed must return to within 10 percent of the 

original trim speed for the climb, approach, and 

landing conditions ... and to within 7.5 percent of the 

original trim speed for the cruising condition ... when 

the control force is slowly released from any speed 

within the range specified ..." 

"The average gradient of the stable slope of the 

stick force vs. speed curve may not be less than 1 lb 

for each 6 kts." 

A strict constructionist reading of the FARs would be that no aperiodic 

divergences are permitted, and that stick force per mile per hour must 

have a stable gradient. For a conventional aircraft (with fully powered 

surface actuators so that stick free and stick fixed characteristics are 

the same) these statements are c0nsister.t (Ref. 21). 

Rate command/attitude hold and superaugmented aircraft with the command filter Gi essentially a pure gain, (e.g., the basic shuttle mechanization) have a longitudinal stick force speed gradient which is zero. 

However, such aircraft can be completely stable, i.e., all of the characteristic modes are well into the left half complex plane. The cause 

of the neutral stick force speed gradient is an effective integrator in 

the command path between the pilot's stick and the elevator command. 

What this means to the pilot is that he may change the trim by pulsing, 

and then releasing the stick to pitch the airplane to a new attitude. 

This is different than for conventional aircraft with parallel trim systems in which the steady-state stick position will change with the trim 

condition. Given this characteristic of rate command/attitude hold systems, the requirements for stick force speed gradient need to be reconsidered. The FAA is examining this issue (Ref. 21) and MIL-F-8785C 

states : 

Supplement 3 28 TR-1228-1-1 
"this requirement for longitudinal static stability 

will be considered satisfied if stability with 

respect to speed is provided through the flight control system, even though the resulting pitch control 

force and deflection gradients may be zero" 

However, aircraft with neutral stick force speed gradients and their 

flying qualities continue to be a subject of controversy, particularly 

in the landing task. As already described, pilot experience and training is at least a part of the issue. Pilots with conventional aircraft 

background on first experience with rate command/attitude hold aircraft 

often comment that it feels unnatural to release back pressure on the 

stick in the landing flare and floating tendencies are a common complaint. There is evidence, however, (Refs. 16, 33) that with experience 

pilots can come to at least accept neutral stick force gradients. 

A recent study of superaugmented aircraft using the TIFS aircraft 

(Ref. 26), has shown that command prefilters, Gi, implemented as washouts can significantly improve pilot opinion in landing. If the washout 

time constant is properly selected, the effective aircraft characteristics will be attitude command/attitude hold, which may be closer than 

rate command/attitude hold to the characteristics of normal aircraft in 

landing approach near the "nose" of the trim 7-V cume (Ref. 12). 

For superaugmented aircraft based on highly unstable airframes, 

(e.g., the X-29 with a 35 percent unstable static margin) the interplay 

of control power, flexible modes, and internal system noise and atmospheric turbulence noted previously can reduce low frequency gain margins, and degrade the stabilization of the basic unstable real airframe 

root. If the low frequency gain margin becomes critical, there is a 

possible tradeoff between increasing the effective control limits 

(reducing the effective nonlinear reduction in q loop gain), and allowing a mildly unstable divergence with a lower bound set on time to double amplitude. This immediately requires grappling with the flying 

qualities issues for mildly unstable aircraft. Conventional aircraft 

can be successful with instabilities (e.g., an unstable spiral is 

permitted by the MIL-Spec requirements of Fig. 8), but there is evidence 

of unfavorable pilot workload associated with even low stable values of 

Supplement 3 29 TR-1228-1-1 
static margin in conventional aircraft. However, to properly consider 

this issue it must be remembered that the flying qualities of RSS 

aircraft with an advanced (e.g., superaugmented) FCS may be 

fundamentally different than for conventional aircraft (Refs. 12 and 

21). 

B. CONDITIONS FOB ACCEPTABLE (OR KlXIMBl) 

PITAIT EQnAtrZATION 

There are several approaches which explicitly emphasize the closedloop piloting features of piloted control. These begin with the notion 

that the dynamics of the pilot and the effective vehicle should combine 

to provide good overall system characteristics with minimum pilot workload and compensation. The Neal-Smith approach (Ref. 34) places constraints on allowable pilot dynamics, low frequency closed-loop droop, 

bandwidth, etc., which are permissible. The criterion works very well 

on small (fighter) aircraft pitch control for which the data were 

obtained, and is always a useful check of a particular control system 

design. 

The second criterion based directly on closed-loop pilot-vehicle 

considerations is based on the so-called crossover model of manual control. An enormous data base, which includes fixed and moving-base simulation, full-scale flight, and other full-scale vehicular control (ranging from automobiles to supertankers) has resulted in the "crossover 

model" law of manual control (e.g., Ref. 31). This states quite simply 

that in the frequency region of pilot-vehicle crossover, the product of 

the open-loop pilot describing function, and the controlled element 

transfer function, Yc, will have the approximate form, 

yP , 

Minimum pilot effort in active closed-loop control is associated with 

little or no lead generation (pilot anticipation) to compensate for the 

dynamic deficiencies of the controlled element. For example, for pitch 

Supplement 3 30 TR-1228-1-1 
attitude control tasks, the crossover law implies that the controlled 

element dynamics in the region of crossover should be approximated by, 

l8/6,(jw)l I K/w i.e., rate ordering, for wbl c w c % 2 (15) 

Meeting this condition means that the pilot can adopt a pure gain proportional control action (with of course the inevitable human delays due 

to perception, central computing, and neuromuscular system lags also 

present for closed-loop control). The upper limit on the crossover 

"region, " wb2, is flexible to insure that no gain margin difficulties 

with higher frequency modes will appear. The lower frequency value, 

wbl, is not necessarily zero frequency -- it is only intended to require 

that IYpYcI >> 1 at law frequencies. While the pilot will compensate 

with lead equalization for first-order lags down to about 1/8 sec to 

make the crossover law hold (Ref. 30), small controlled element time 

lags beyond the crossover do not necessarily detract from the low workload requirement. For instance, a first-order lag of 1/2 sec or less 

(calling for a compensating pilot lead of 1/2 sec) causes only a minor 

pilot rating degradation (Ref. 31). 

The pilot's actions in control are not confined to a proportional 

input/output characteristic; in addition his output contains a broad 

band random noise -- called pilot generated noise or remnant. The remnant is particularly important as a source of excitation of highly resonant modes in the vehicle dynamics. Remnant is increased markedly when 

the pilot must generate lead (Ref. 29). Consequently, the requirement 

of Eq. 15 is consistent with minimizing the pilot equalization dependent 

remnant. 

It is extremely important to emphasize that the controlled element, 

Y,, which is made to approximate Kc/s crossover is very task dependent. 

In the flare, for example, the effective Yc of interest can be h/6 P' 

Supplement 3 31 TR-1228-1-1 
C. CONDITIONS ANTITHETICAL TO 

PIIDT-INDUCED OSCILlATIONS 

A special set of effective vehicle requirements must be considered 

to minimize the possibility of pilot-induced oscillations. As detailed 

in Ref. 35, there are a large number of proximate causes for PIOs. The 

most common by far is the pilot's temporary use of too-high gains in the 

attitude or path control loops in highly stressed, untrained, or unfamiliar circumstances. The "solution" to these PIOs is practice and 

experience with the specific vehicle in the special high stress circumstances. The possibility of PI0 can be alleviated, of course, by providing the desirable types of effective vehicle dynamics already discussed -- but high gain PIOs of the type noted above will still occur 

for some pilots sometimes (currency and practice remain the answer in 

these circumstances). 

The insidious PIOs of major concern are of two kinds and have two 

causes: "synchronous" precognitive behavior and "PI0 syndrome." Synchronous behavior is the capacity of the pilot to lock on to "displayed" 

periodic signals. "Displayed" can in principle mean either through 

motion or visual cueing. When a simple periodic signal such as a sinusoidal or square wave is presented to the pilot to follow, he is capable 

of developing (Ref. 31) an essentially pure gain open-loop block, which 

reproduces an input signal at his manipulator output without appreciable 

lag. This "precognitive behavior" characteristic, when excited by an 

aircraft motion output perceived either visually or proprioceptively, 

can create a short time quasi closed-loop transmission of the oscillation. It has the peculiar effect of raising the PI0 frequency range 

well beyond the pilot's usual control bandwidth. In circumstances which 

are especially favorable to the development of such PIOs, the frequency 

range can be as high as 3 Hz. The circumstances which are "favorable" 

to induce this decidedly unfavorable effect would include a nearly pure 

oscillation uncontaminated by other more random appearing motions. 

Supplement 3 32 TR-1228-1-1 
The PI0 syndrome is present when the effective form of 6/Sp in the 

pilot-vehicle crossover region is given approximately by 

This can occur, When in active control, the pilot will adjust his characteristics as defined by the crossover model (Eq. 14). For the controlled element form of Eq. 16, this 

requires the pilot to generate a low frequency lag. This is often 

described by pilots as a "smoothing low frequency trimming like control 

action." It is an easy to accomplish low workload pilot behavioral pattern in which the pilot often requires only intermittent control action. 

There is seldom any control difficulty as long as the pilot's low frequency lag adaptation is maintained. The trouble arises when an upset 

or other stressful factor such as a system failure occurs. Then in an 

attempt to regain control of the situation, the pilot may regress to a 

pure gain type of proportional control. Under these conditions the 

pilot effective vehicle (with the suddenly changed pilot equalization) 

may temporarily possess too small a gain margin at the high frequency 

mode defined by wn (which will typically be the short period, but could 

conceivably be a flexible mode). 

for instance, when l/Te2 << wsp. 

The solution to the PI0 syndrome is to augment the damping of the 

[r, wn] mode so that > 0.4 or so. This helps to assure adequate gain 

margin under any highly stressed conditions where the pilot may regress 

to a pure gain controller. 

D. KCNIKIZATION OF REMNANT EXCITATION 

OF FLEXIBLE KODES 

The pilot-induced noise can be an important excitation source for 

the lower frequency flexible modes since there can be significant 

Supplement 3 

~~~~ ~ 

33 TR-1228-1-1 
remnant power to about 2 Hz. The effects of remnant excitation are 

minimized in four ways: 

0 reduce requirements for any pilot lead generation 

(by establishing lYcl A K/w in the crossover 

region), thereby reducing the pilot equalization 

dependent remnant source; 

0 provide appropriate manipulator (e.g., control 

column, side stick) force/displacement characteristics; 

0 provide appropriate filtering in the pilot 

Command Input Elements block; 

0 increase the damping of flexible modes which 

reside within the remnant bandwidth. 

These procedures are very much dependent on specific detailed characteristics of the vehicle's primary control system. Reference 34 provides 

exemplary guidance as to the profound effects that can occur under worst 

case circumstances. 

E. IUNII4IZATION OF PIUIT EFFECTIVE AIRCRAFI SYSTR4 

=SED-LOOP EXCITATION OF ELWIBLE MODES 

In the high frequency region of piloted control, e/sP, can be 

approximated by 

As a particular example of the 

control action can drive the 

starting at the wD's toward the 

.'Teffs , 

phenomena described in Appendix C, pilot 

closed-loop pilot-vehicle system roots 

%'s. In the best of circumstances, the 

frequency region over which the pilot can exert effective closed-loop 

control is less than 1 Hz, so the flexible modes which may be involved 

with this type of control difficulty will be very low indeed. For any 

flexible modes in or near the region where pilot control action may have 

an interactive effect, the relative pole zero orders should be properly 

Supplement 3 34 TR-1228-1-1 

, 
adjusted. This closed-loop control condition is different in kind from 

the vibration feedthrough situation described below. 

F. REDUCTION OF VIBRATION FEEDTflRouGEI 

Another component of pilot control action is direct feedthrough of 

lightly damped oscillatory motions within the frequency range. This is 

illustrated for a stiff stick manipulator in Fig. 8. As can be appreciated from these data and Refs. 37 and 38, the amount of the feedthrough can be substantial to frequencies as high as 10 Hz. The phasing 

and amplification of this "biodynamic feedthrough" may be adverse so 

that it tends to destabilize flexible modes, which have undamped natural 

frequencies in this range. 

Figure 8 also shows that pilot response to a vibratory environment 

can excite the resonant modes in the frequency region up to nearly 10 Hz 

simply because the remnant may be increased by the flexible modes 

impinging on the pilot. 

200 I- I 4 

Normalized 

Stick 

output 80 

Variance 60 

(Newtons') 50 

40 

30 'i IO 

Supplement 3 

e 

A 

STIFF STICK 

Tracking Input Correlated A 

I 

20 

10 RMS 

6 =c 

Stick 

Activity 

(N) 4 

2 

Lt 

Pre-I 1.3 2 3 4.5 7 10 "PostI lit I IA I 

Vibration Frequency Exposure 

(Hz) 

Figure 8. Stick Output Variance Components 

for Vibratory Forcing (Reference 36) 

35 TR-1228-1-1 
The primary means to minimize vibration feedthrough and excessive 

remnant include: 

0 use of proper force/displacement loading on the 

manipulator (stiff sticks/columns are a no-no; 

finite breakout forces are needed, etc); 

0 reduce the vibration environment at the pilot 

station by seat design, arm support, etc.; 

0 increase the flexible mode damping and/or reduce 

the modal response for all modes, which have significant amplitudes at the pilot station in the 

0-10 Hz range; 

0 consider the residual excitation (after all the 

above steps have been taken to the extent possible) in the design of the command input elements 

filters; 

Just as with the remnant excitation of the flexible modes, the design 

requirement are vehicle specific -- in this case specific to the flexi: 

ble modes at the pilot station. 

Supplement 3 36 TR-1228-1-1 
c 

1. Federal Aviation Regulations, Part 25, Airworthiness Standards: 

Transport Category Airplanes, Department of Transportation, 

Federal Aviation Administration, June 1974. 

2. Chalk, C. R., T. P. Neal, and T. M. Harris, et al., Background 

Information and User Guide for MIL-F-8785B(ASG), "Military 

Specification - Flying Qu alities of Piloted Airplanes", 

AFFDL-TR-69-72, AUg. 1969. 

3. Moorhouse, David J., and Robert J. Woodcock, Background Information 

and User Guide for MIL-F-8785C, Military Specification -- Flying Qualities of Piloted Airplanes, AFWAL-TR-81-3109, 

July 1982. 

4. Hoh, Roger H., David G. Mitchell, Irving L. Ashkenas, et al., Proposed MIL Standard and Handbook -- Flying Qualities of Air 

Vehicles. Volume I: Proposed MIL Standard. Volume 11: Proposed MIL Handbook, AFWAL-TR-82-3081(1 d II), Nov. 1982. 

5. Weingarten, Norman C., and Charles R. Chalk, In-Flight Investigation of Large Airplane Flying Qualities for Approach and Landing, AFWAL-TR-81-3118, Sept. 1981. 

6. Myers, T. T., D. E. Johnston, and D. T. McRuer, Space Shuttle Flying Qualities and Flight Control System Assessment Study, Phase 

- 11, NASA CR-170406, Dec. 1983. 

7. Bihrle, William, Jr., A Handling Qualities Theory for Precise 

Flight Path Control, AFFDL-TR-65-198, June 1966. 

8. Ashkenas, I. L., "Summary and Interpretation of Recent Longitudinal 

Flying Qualities Results," J. Aircraft, Vol. 8, No. 5, 

May 1971, pp. 324-328. 

9. "Military Specification -- Flying Qualities of Piloted Airplanes," 

MIL-F-8785C, NOV. 1980. 

10. Feather, J. B., "Advanced Supersonic Transport Fixed-Base Simulator 

Evaluations at Landing Approach," Supersonic Cruise Research 

- '79, Part 1, NASA CP-2108, 1980, pp, 269-284. 

11. Chalk, C. R., Calspan Recommendations for SCR Flying Qualities 

Design Criteria, Calspan Rept. 6241-F-5, 1980. 

12. Myers, T. T., D. T. McRuer, and D. E. Johnston, Flying Qualities 

and Control System Alternatives for Superaugmented Aircraft, 

NASA CR-170419, Dec. 1984. 

Supplement 3 37 TR-1228-1-1 
13. Hess, Ronald A., '#The Effects of Time Delays on Systems Subject to 

Manual Control," AIAA Paper No. 82-1523, presented at the AIAA 

Guidance & Control Conference Proceedings, San Diego, CA, 

9-11 Aug. 1982, pp. 165-172. 

14. Hoh, R. H., D. G. Mitchell, and J. Hodgkinson, Bandwidth -- A Criterion for Highly Augmented Airplanes, AGARD CP-333, 19-22 Apr. 

1982. 

15. Myers, T. T., D. E. Johnston, and D. McRuer, Space Shuttle Flying 

Qualities and Flight Control System Assessment Study, NASA 

CR-170391, June 1982. 

16. Mooij, H. A., W. P. DeBoer, and M. F. C. van Gool, Determination of 

Low-Speed Longitudinal Maneuvering Criteria for Transport Aircraft with Advanced Flight Control Systems, NLR TR-79127 U, 

Dec. 1979. 

17. van Gool, M. F. C., Low Speed Handling Qualities of Advanced Transport Aircraft: A Comparison of Ground-Based and In-Flight Simulator Experiments, NLR TR-82041 U, May 1982. 

18. Sudderth, R. W., J. G. Bohn, M. A. Caniff, and G. R. Bennett, 

Development of Longitudinal Handling Qualities Criteria for 

Large Advanced Supersonic Aircraft, NASA CR-137635, Mar. 1975. 

19. Abrams, C., "V/STOL Digital Flight Control System Technology Interfaces, " presented at SAE Guidance and Control Comm. Meeting, 

Oct. 1977. 

20. Abrams, C. R., A Performance Index for Response Evaluation of 

Highly Augmented Military Aircraft. Phase I -- Inner Loop 

Requirements for Command Inputs, NADC-AM-7103, 12 Oct. 1971. 

21. McRuer, Duane, and Thomas T. Myers, Handling Qualities of Aircraft 

with Relaxed Static Stability and Advanced Flight Control Systems. Vol. 11: Ramifications of Flight-Critical HeavilyAugmented Relaxed Static Stability Airplane Characteristics on 

Flying Qualities, DOT/FAA/CT-82-130-2, Sept. 1982. 

22. Myers, T. T., D. E. Johnston, and D. T. McRuer, Space Shuttle Flying Qualities Criteria Assessment, Phase 111, NASA CR-170407, 

Feb. 1984. 

23. Weingarten, Norman C., and Charles R. Chalk, Application of Calspan 

Pitch Rate Control System to the Space Shuttle for Approach and 

Landing, NASA CR-170402, May 1983. 

24. Klinar, W. J., D. W. Gilbert, Clarke T. Hackler, et al., Flying 

Qualities Requirements for the Orbiter Utilizing Closed-Loop, 

Fly-by-Wire Control of Vehicle Response Parameters, NASA Manned 

Spacecraft Ctr. JSC-07151, Dec. 1973. 

Supplement 3 38 TR-1228-1-1 
25. Powers, Bruce G., "Shuttle Low Speed Control System Tests," presented to the Control and Guidance Advisory Subcommittee, 

29 Nov. 1983. 

26. Berthe, C. J., C. R. Chalk, and S. Sarrafian, Pitch Rate Flight 

Control Systems in the Flared Landing Task and Design Criteria 

Development, NASA CR-172491, Oct. 1984. 

27. Hoh, Roger H., Thomas T. Myers, Irving L. Ashkenas, et al., Development of Handling Quality Criteria for Aircraft with Independent Control of Six Degrees-of-Freedom, AFWAL-TR-81-3027, Apr. 

1981. 

28. Ashkenas, I. L., A Study of Conventional Airplane Handling Quali29. Monagan, Stephen J., Rogers E. Smith, and Randall E. Bailey, Lateral FlyinR Qualities of Highly Augmented Fighter Aircraft, 

AFWAL-TR-81-3171, Vols. I and 11, Mar. 1982 

30. Johnston, D. E., and D. T. McRuer, Investigation of Interactions 

Between Limb-Manipulator Dynamics and Effective Vehicle Roll 

Control Characteristics, Systems Technology, Inc., TR-1212-1, 

June 1985. 

31. dcRuer, D. T., and E. S. Krendel, Mathematical Models of Human 

Pilot Behavior, AGARDograph No. 188, Jan. 1974. 

32. Ashkenas, Irving L., and Duane T. McRuer, Competing Flight Control 

Systems for Entry Glider Lateral Control, ASD-TDR-62-699, 

Feb. 1964. 

33. Stapleford, Robert L., Richard H. Klein, and Roger H. Hoh, Handling 

Qualities Criteria for the Space Shuttle Orbiter During the 

Terminal Phase of Flight, NASA CR-2017, Apr. 1972. 

34. Neal, T. P., and R. E. Smith, "An In-Flight Investigation to 

Develop Control System Design Criteria for Fighter Airplanes," 

AFFDL-TR-70-74, June 1970. 

35. Ashkenas, I. L., H. R. Jex, and D. T. McRuer, Pilot Induced Oscillations: Their Cause and Analysis, Systems Technology, Inc., 

TR-239-2, 20 June 1974. 

36. Teper, G. L., H. R. Jex, D. T. McRuer, and W. A. Johnson, A Study 

of Fully-Manual and Augmented-Manual Control Systems for 

Saturn V Booster Using Analytical Pilot Models, NASA CR-1079, 

July 1968. 

Supplement 3 39 TR-1228-1-1 
37. Jex, H. R., and R. E. Magdaleno, "Biomechanical Models for Vibration Feedthrough to Hands and Head for a Semisupine Pilot," 

Aviation, Space and Environ. Med., Vol. 49, No. 1, Jan. 1978, 

pp. 304-316. 

38. Allen, R. W., H. R. Jex, and R. E. Magdaleno, Manual Control Per- * 

formance and Dynamic Response During Sinusoidal Vibration, 

AMRL-TR-73-78, Oct. 1973. 

Supplement 3 40 TR-1228-1-1 
APPENDIX A 

THE MULTI-VARIABLE ANALYSIS KETHOD 

This appendix presents a brief overview of the STI multi-variable 

analysis method developed for the following properties: 

0 A formulation which clearly displays controlledelement-alone and controller-alone characteristics in conventional and well-understood terms. 

0 Analytical operations which can be performed 

using the most efficient analytical and graphical 

procedures of feedback systems analysis so as to 

enhance transfer of skill and intuition from the 

simpler single loop situations. 

0 Sequences and procedures which are highly responsive to physical insights and intuition so as to 

lead to “good” systems with a minimum of iteration. 

0 A presentation of results which is supplementary 

as well as equivalent to the results obtained 

using time responses from computer simulations. 

The presentation here is intended only to give a working understanding to interpret the applications in Section VI. More complete developments are given in Refs. A-1 to A-3. 

A. TRANSFER FUNCTION MATRICES 

A generalized block diagram for a multi-variable (multiloop, multicontrol-point) closed-loop system is shown in Fig. A-1 along with a summary of the open- and closed-loop transfer function matrices for commands and disturbances. The elements of the open-loop command transfer 

function matrix N/A are the familiar transfer functions obtained through 

Cramer’s rule. For example (with m - 3) , 

TR-1228-1 A- 1 
Disturbances 

[71 

- 

- 

Disturbance 

Application 

Matrix 

[El 

Control output 

Variable Plant Control Var i a b I es 

Response [XI 

Feedback 

- -- Matrix 

CGfI [el [AI-' 

Matrix bl - 

- 

- 

- 

con t ro I output 

Variable Plant Control Var i a b I es 

Response [XI 

Feedback 

- -- Matrix 

CGfI [el [AI-' 

Matrix bl - 

- 

C Linearized Laplace transformed equations of motion for plant: 

(matrices of polynomials in s) 

9 Open-loop control input transfer function matrix: (9 is matrix of 

transfer function numerators, A is characteristic polynomial) 

* Control law: 

U = GcSc - GfX 

o Closed-loop output vector: 

x = (a + ~~~1-1 (BG,X, + EII) 

8 Closed-loop transfer function matrices for commands: 

dc adj (A + BGf) BG, -= 

A (A + BGf)-I BG, = det (A + BGf) 

0 Closed-loop transfer function matrices for disturbances: 

adj (A + BGf) E 

det (A + BGf) 

%!I (A + BGf1-l E = -= 

A 

- TR-1228-1 

Figure A-1. General System Matrix Equations 

A-2 
X1 G! 4 

(A-1) 

where the aij and bij's are functions of s. A similar development can 

be made for the open-loop disturbance transfer function matrix A-'E. 

Be COUPLING "ERATORS 

A variety of numerical techniques can be used to directly evaluate 

the open- and closed-loop transfer function matrices for purely computational purposes. The approach to be introduced here is more indirect -- 

but ultimately leads to a powerful, insightful multi-variable procedure 

which has some particular numerical advantages as well. This approach 

is based on literal expansion of the transfer matrices involving generalized transfer function numerators referred to as "coupling numerators" 

or "numerators of higher kinds. " 

The familiar transfer function numerator -- a numerator of the first 

kind -- such as NZ: in Fig. A-2 is constructed according to Cramer's 

rule by replacing the second column in A (corresponding to x2) with the 

first column of B (corresponding to ul) and taking the determinant of 

the resulting matrix of polynomials in S. The first type of coupling 

numerator -- a numerator of the second kind -- extends this algorithm by 

replacing two columns in A with two columns in B before taking the 

determinant. An example is shown in Fig. A-2. 

This coupling numerator is denoted by the symbol on the left and 

defined by the determinant on the right. At the next level, a coupling 

numerator of the third kind would have three columns in A replaced by 

three columns from B (see Fig. A-2). In a similar way numerators up to 

the mth kind can be written for systems of arbitrarily large m. 

TR-1228-1 A- 3 
0 Plant Equations of Motion 

A = 

0 Characteristic Polynomial 

all a12 a13 

a21 a22 a23 

a31 a32 a33 

<: = 

0 Representative Numerator (of the first kind) 

all bll a13 

a21 b21 a23 

a31 b31 a33 

$3x1 = u2u 1 

0 Representative Coupling Numerator (numerator of the second kind) 

bll a12 b12 

b21 a22 b22 

b31 a32 b32 

#3x2x1 = u2u3u 1 

0 Representative Coupling-Coupling Numerator (numerator of the 

third kind) 

bll b13 b12 

b21 b23 b22 

b3l b33 b32 

Figure A-2. Transfer Function Elements (m = 3) 

TR-1228-1 A-4 
Efficient use of the multi-variable method requires knowledge of 

some basic coupling numerator identities. A basic selection for numerators to the third kind are summarized in Fig. A-3. 

= 

Cm CLOSEWLOOP CHARA(XERIST1C POLYNUMIAL 

all + b12<; a12 + bllG:i a13 

a21 + b22c: a22 + b21Gzl a23 

a31 + b32GE: a32 + b31G:i a33 

The procedure for constructing coupling numerators is relatively 

straightforward, but literal expansion of transfer matrices in terms of 

them is quite involved so it is best to start with an example. A multivariable control system that is relatively simple, yet complex enough 

for our present purposes, is shown in the block diagram of Fig. A-4. It 

consists of a controlled element and a controller comprising sensing, 

equalizing, and actuating elements. The plant has three independent 

degrees-of-freedom. It is subject to control inputs applied at two control points and is also disturbed by two external disturbances. 

Together the control variables are functions of a command input and 

feedbacks from two of the three degrees-of-freedom. 

(A-2) 

TR-1228-1 A-5 
If the coupling numerator superscripts are the same or subscripts are 

identical the numerator is identically zero. 

- 

xixi xixk 

Nu1U2 - Nu2u2 

A coupling numerator is not changed by interchange of superscriptsubscript pairs. A coupling numerator is not changed by an even number 

of interchanges of superscripts, subscripts, or both. An odd number of 

interchanges causes a numerator sign change. 

A numerator of the third kind is zero if any two of the outputs or any 

two of the inputs are identical, that is 

Figure A-3. Some Frequently Used Coupling Numerator Identities 

TR-1228-1 A-6 
(Sensing, Actuation 

Controller 

,and Equalization) 1 

-- Gi2 Command Input 

X IC ‘C 

-L 

E 

- 

G”,: 

L 

I Control 

I Input 

Variables 

u2 

I -m 

Disturbances 

u 

TI 72 

Controlled 

Element 

Dynamics 

Output Variables I 

Confro//ed €/emen/ €qua fions of Motion : 

Figure A-4. Example System (m = 3) 

TR-1228-1 A-7 
Expanding in further, albeit tedious, detail, Asys becomes 

+ GE$ 

+ Ggi 

all bll 

a21 b21 

a31 b31 

al 3 

a23 

a3 3 

b12 bll 

b22 b21 

b32 b31 

al 3 

a2 3 

a3 3 

(A-3) 

The complexity of more general forms is more apparent than real. 

The numerators of higher kinds are filled primarily with terms from the 

control application matrix, B, and these elements are usually constants. 

Also both B and the feedback controller matrix Gf are usually sparse 

when contrasted with the plant matrix A. Consequently, numerators 

become simpler in form as they increase in kind order; and many of the 

terms in the expansions are zero because the feedback elements are zero. 

D. CLOSED-LOOP TRANSFER FUNCTION ~RATORS 

While the system characteristic function, Asys, is the denominator 

for all closed-loop transfer functions, regardless of the command or 

disturbance input, the numerator of a closed-loop transfer function will 

depend on the particular command or disturbance. These closed-loop 

numerators can also be developed in terms of open-loop coupling numerators in manner similar to the A development (see Ref. A-2). Thus 

SY S 

TR-1228-1 A-8 
when the closed-loop numerator and denominator are combined to form a 

closed-loop transfer function we have for example: 

X1 

(A-4) 

The term (NE: + GU,j$$i) in Eq. A-4 is referred to as the effective 

numerator of the controlled element with the x2 + u1 loop closed. 

A similar development would yield the transfer function relating the 

response x1 to the disturbance ‘I1 as 

(A-5) 

Here, of course, the disturbance does not go through the block 

Gu2 Therefore, the leading 

numerator term is not multiplied by c2 Note also that 

the term in square brackets is identically zero. 

to get into the doubly closed-loop system. 

in this case. - 1, 

The expansion of A and N in the special case above can be generalized for arbitrary m and p. These developments are rather involved and 

will not be repeated here (see Ref. A-2). However, the general procedure for writing a multi-variable closed-loop transfer function is indicated in Fig. A-5. The expressions of Fig. A-5 may appear to imply an 

enormous number of terms -- this is not the case for most practical 

applications since, by the Fig. A-3 identities, many of the terms are 

zero. However, the secret to the great utility of this approach is that 

practical applications can be made without the user generating the tedious expansions. However, this does require specialized interactive computer programs for computation of coupling numerators. Appreciation of 

this facility requires understanding how the technique is applied in 

practice. This will be illustrated in the next section based on the 

example used above. 

TR-1228-1 A- 9 
The clo.ad-lwp aystem Jennmlnator 1s eqqu4L eo: 

The controlled elemmnt (open-loop p1a.C) 

dcnomlnacor: 

Plus 

The aum of a11 the feedback transfer fimcclons. 

erch mulclpllad by tho approprlace numerator of 

the flrsr klnd. 

_. 

PIUS 

The sum ol ALL the feedback transfer funetlona taken two ac a else. each palr julclplled by 

the ap;)roprlate coupling nuneracor. 

- 

CX' z 

Plus 

Thr sum of a11 che feedbrck cransfer funcrlons 

taken ehree at a time. each crtplec ultlplled 

by the approprlace numrrucor of the third kind. 

- 

me concrolled-element (open-loop plant) 

nunuracor; 

P 

Y 

I 

P 

+ .-" 

brn 

n eL xc 

z L-c cx 

+ 

me ctleeclve clmcd-loop nuwrrcor (of che 

concrolld clemenr) 1s equal to: 

- PlUY 

The sum ot a11 the feedback cranafyr funcrlons. 

each mlclplled by the approprlaca nunerators 

of the second klnd. 

_. 

Plu. 

the sum of all the feedb.3ck cranafer funcrlons 

taken two IC a tine. each comblnaclon ?mlclplled 

by the approprlace nu-racor of che thlrd klnd. 

+ 

NOTES: 

0 1s any xl or llncar conblnAclon of xi's 

0 w 1. any u, or nk 

in genera1 mny terms ulll he zero brcause: 

-- G:; - 0 

-- (cwnlylln*) mlrX.r*cYr I 0. 

Figure A-5. The General Construction of Transfer Functions in 

Terms of Coupling Numerators (Shown Explicitly for m G 3) 

TR-I 228-1 A-1 0 
E.' APPLICATIONS OF TEE METHOD 

1. Elodificatioa of Closed-Loop Poles and 

Zeros with Mdti-variable Feedback 

One of the most fundamental uses of the multi-variable method is in 

understanding how aircraft numerator zeros with respect to one input are 

modified by feedback to another control point. This facility 'lies at 

the heart of the multi-variable synthesis methodology. To illustrate 

consider the x1 response to u2 with only the x2 + u1 loop closed. This 

may be written from the rules of Fig. A-5, since we already have it, by 

setting GE; to zero in the xl/xlc expression of Eq. A-4 above. 

This modified transfer function is 

A + G:;N~: 

(At6) 

One (or more) primes are used as in [X1/U21' and [Nti/Al' above, to 

indicate that one (or more) loops have been closed. 

In the equation above we see that the poles of the effective controlled 

G:~NX,~. 

tered in 

variable 

element have been changed from the roots of A to those of A + 

This is the same kind of change due to feedback as is encounsingle loop feedback problems. The difference in this multisystem is the change in the zeros of the effective controlled 

TQ-1228-1 A-1 1 
Ul x2x1 element numerator from those of 6: to those of + G2NUlu2 . This 

example shows clearly the previously described plant-zero-modification 

property unique to multi-variable control. 

From the standpoint of synthesis this plant dynamics "modification" 

made by the first loop closure, x2 + ul, might be contrived so 

as to compensate or equalize the outer open-loop transfer function, 

GE:[NEi/A]'. Of course, the changes in plant poles and zeros accomplished this way are not independent because the controller transfer 

function GU1 affects both numerator and denominator terms of the effective controlled element transfer function. 

x2 

2. Wmiting Characteristics Approached at High Gain 

Over the frequency range where the x2 + u1 feedback action is really 

dominant, the effective plant transfer function becomes 

(A-7) 

Thus, just as the ordinary ("first kind") numerators of a plant are 

limiting approximations to some of the closed-loop poles in a high-gain 

single loop feedback system, so the coupling ("second kind") numerators 

can play the same role for closed-loop zeros in a multi-variable system. 

Further extensions of this idea are illustrated in Section VI. 

TR-1228-1 A-12 
3. Implications for FCS Synthesis 

The additional design flexibility which comes in multi-variable control from the capability to adjust both the zeros and poles of the 

effective controlled element has many advantages. Perhaps the most significant is the correction of very undesirable plant numerator righthalf -plane zeros. Such non-minimum phase characteristics are sinks 

which draw some closed-loop left-half-plane pole(s) ever closer as loop 

gain is increased. The closed-loop instability incurred as the closedloop poles migrate past the j*axis of imaginaries into the right-halfplane cannot be rectified practically by single loop, or even multiloop 

single control point techniques. (Attempts to cancel a right-half-plane 

zero by introducing a right-half-plane pole in a series compensator can 

be disastrous because of practical system uncertainties and parameter 

variations.) But the introduction of an appropriate output variable fed 

to another control point provides coupling numerator zeros toward which 

the offending plant numerator zeros can be driven by feedback control 

action. 

REPERRNCES FOB APPENDIX A 

A-1. McRuer, D. T., I. L. Ashkenas, and H. R. Pass, Analysis of Multiloop Vehicular Control Systems, ASD-TDR-62-1014, WrightPatterson Air Force Base, OH, Mar. 1964. 

A-2. McRuer, Do, I. Ashkenas, and D. Graham, Aircraft Dynamics and 

Automatic Control. Princeton Universitv Press. 1973. 

A-3. Hofmann, L. G., G. L. Teper, and R. F. Whitbeck, "Application of 

Frequency Domain Multi-variable Control Synthesis Techniques 

to an Illustrative Problem in Jet Engine Control," in Michael 

K. Sain, Joseph L. Peczkowski, and James L. Melsa, eds., 

Alternatives for Linear Multi-variable Control, National Engineering Consortium, Inc., Chicago, IL, 1978, pp. 51-70. 

TR-1228-1 A-1 3 
APPENDIX B 

SENSITIVITY VECTORS 

This appendix presents an outline of the sensitivity methods which 

are an important tool in the "prospectus for control." This development 

is based on Refs. B-1 and B-2. Sensitivity methods provide a means for 

consideration of the effects of open-loop system variations on the 

closed-loop properties. The three measures defined here are called 

tlgain," "(open-loop) pole," and "(open-loop) zero" sensitivities, which 

relate to changes in the position of closed-loop poles due to shifts or 

changes in the open-loop gain, poles, and zeros, respectively. In exact 

terms these sensitivities connect open-loop differential variations with 

closed-loop differential shifts (Refs. B-2 - B-9). They are especially 

useful as a means of assessing the effects of system uncertainties and 

the implications of parameter tolerances on the closed-loop system 

dynamics. The symbols Si, Sij, and Si denote the gain, pole, and zero 

sensitivities, respectively. The subscript and superscript notation 

indicates that a differential increment in the open-loop parameter 

(defined by the subscript) results in a differential increment of the 

ith closed-loop root (denoted in the superscript) which is equal to the 

sensitivity factor times the open-loop parametric variation. 

P j 

Denoting the ith closed-loop root as Xi the sensitivities are 

defined by the relations on the left in Eq. B-1. 

TR -1228-1 B-1 
Note that the gain sensitivity is based on a fractional (percentage) 

change in K, while the pole and zero sensitivities are based on absolute 

shifts of p and z These definitions were adopted here in order to 

provide some simplifications in relationships. 

j j. 

Given the open-loop transfer function G(s), the sensitivities may be 

related to derivatives of G(s) by the expressions on the right in 

Eq. B-1. These relations are developed in Ref. B-1, pg. 177 and lead to 

a means of computing the sensitivities through their relation to the 

modal response ratio Qi of the ith closed-loop root. 

1. Gain Sensitivity 

For simple poles the gain sensitivity is the negative of the modal 

response coefficient as shown in Fig. B-1. The modal response ratio is 

the partial fraction coefficient (residue) of the ith closed-loop pole 

for the weighting function (impulse response). Thus the familiar graphical procedure for evaluation of residues could be used to construct 

Sh as illustrated in Fig. B-2. A valuable geometric interpretation 

of S& as a vector in the complex s-plane can thus be made. Since in 

K is a scalar and the differential change in Xi is along the 

root locus, the Si, vector is tangent to the locus at Xi and points in 

the direction for increasing I KI In modern practice the ideal generation of Sh would be by numerical evaluation of the residue with a computer graphic display of the sensitivity vector in the s-plane. However, a computer generated graphical construction like Fig. B-2 could be 

valuable to the analyst to assess what open-loop poles and zeros dominate the sensitivity. 

axi 

si, = 'm 

2. Pole and Zero Sensitivity 

Pole and zero sensitivities can also be pictured as vectors in the 

complex s-plane. As developed in Fig. B-3 

TF.4 2 2 8- 1 B- 2 
Define Qi(s) as 

When S 

for the (s + qi) mode. 

-qi, Qi(s) becomes simply Qi, the modal response coefficient 

Rearranging, 

Differentiating with respect to s gives 

Evaluating at s = -qi, and noting that G(-qi) = -1, gives 

Qi [w] = -1 

s=-qi 

Therefore, comparing Eq. B-1, 

Figure B-1. Relation of Gain Sensitivity to 

Modal Response Coefficient 

TR- 1 2 2 8- 1 B-3 
Qi 

= -Qi xi + zj 

n 

-c 

j =1 j=1 

Figure 8-2. Graphics Construction of Gain Sensitivity Vector 

T~-1228-1 B -4 
Developed similarly, the pole sensitivity will be 

Figure B-3. Relation of Pole + Zero Sensitivities 

to Gain Sensitivity 

~~1228-1 8- 5 
The magnitude of the pole and zero sensitivities thus amount to divisions of the gain sensitivity by a vector sum of the closed-loop pole 

and the open-loop pole or zero, respectively. A geometric appreciation 

is gained by considering these as vectors in the s-plane, as in 

Fig. B-4. Note that the zero sensitivity vector is in a direction tending to pull the locus more toward the zero, whereas the pole sensitivity 

vector would tend to push the locus away from the pole. 

3. Application of Sensitivity Vectors in 

Control System Synthesis 

The geometric interpretaion of sensitivity is particularly valuable 

in initial consideration of the "prospectus" for control of an element 

such as an aircraft. Since the gain sensitivity vector Si indicates the 

direction and rapidity with which closed-loop poles move with a gain 

change, this display on a conventional root locus can be used to quickly 

assess the potential of a candidate. If the gain along the root locus 

is allowed to approach zero the S$ become vectors indicating the direction and relative rapidity with which the closed-loop roots depart the 

open-loop poles (which may be the closed-loop poles of a previous 

closure) for a candidate closure. Figure B-5a shows a hypothetical 

case. If the loop under consideration is intended to increase I 1/T21 it 

has good potential since the relative effect on the complex root is 

small and increases c1 in any case. However, if the intent was to 

increase C1 with minimal effect on the real pole, this feedback would be 

a poor choice. 

This idea can be extended to produce a quick prospectus survey of 

the relative merits of feeding back xl, x2, or x3 as indicated in 

Fig. B-5b. 

TR- 1 2 28- 1 B-6 

. 
-4 

u) Pole sensitivity 

Xi +pj 

b) Zero Sensitivity 

Figure B-4. Geometric Illustrations of Pole and 

Zero Sensitivity Vectors 

B-7 
U I 

a/ Single Loop 

x2 

b) Mu/ti/oop 

Figurd 3-5. Use of Sensitivity Vectors in 

Hu Lt i loop Control Pros pec t i 

B -8 
REFEBENCES FOB APPENDIX B 

S 

B-1. McRuer, Duane, Irving Ashkenas, and Dunstan Graham, Aircraft 

Dynamics and Automatic Control, Princeton University Press, 

Princeton, NJ, 1973. 

B-2. McRuer, D. T., and R. L. Stapleford, Sensitivity and Modal 

Response for Single Loop and Multiloop Systems, ASD-TDR-62- 

812, Jan. 1963. 

B-3. Mitchell, K., "Estimation of the Effect of a Parameter Change on 

the Roots of Stability Equations ,*I Aeronautical Quarterly, 

Vole I, May 1949. 

B-4. Gates, Jr., 0. B., and C. H. Woodling, A Method for Estimating 

Variations in the Roots of the Lateral-Stability Quartic Due 

to Changes in Mass and Aerodynamic Parameters of an Airplane, 

NACA TN 3134, Jan. 1954. 

B-5. Papoulis, A., "Displacement of the Zeros of the Impedance Z(p) Due 

to Incremental Variations in the Network Elements," Proceedings of the IRE, Vol. 43, 1955. 

B-6. Huang, R. Y., "The Sensitivity of the Poles of Linear Closed-Loop 

Systems," Transactions of the AIEE, Pt. 11, Vol. 77, 1958, 

ppo 182-1860 

B-7. Kuo, F. F., Pole-Zero Sensitivity in Network Functions, University 

of Illinois, Ph.D. Dissertation, 1958. 

B-8. Ur, H., "Root Locus Properties and Sensitivity Relations in Control Systems," Transactions of the IRE, Vol. AC-5, No. 1, Jan. 

1960. 

B-9. Horowitz, I. M., Synthesis of Feedback Systems, New York, Academic 

Press, 1963. 

~~1228-1 B-9 
APPENDIX c 

ELEMENTAL SYSTEMS 

I’ 

. 

Lower order analytical models of high order augmented aircraft can 

be of great value in maintaining insight and defining the key parameters 

in a complex design problem. The two keys to this capability in FCS 

design is a frequency domain view with a focus on the Bode amplitude 

asymptotes and an awareness of the first-order effects of feedback. 

This appendix presents five elemental system models which arise 

naturally in FCS design consideration. As transfer function elements 

these are: 

0 First-order lag in series with an integrator 

1 

G(s) s(Ts + 1) 

0 A second-order factor 

2 

G(s) - [[k) + + 1]*’ 

wn 

0 The crossover model 

0 The superaugmented model (open-loop) 

0 A second-order dipole in series with an integrator 

r - 

TR -1228-1 c-1 
While modern FCS of ten have a large number of poles and zeros, they 

are distributed in special ways characteristic of aircraft problems. 

Specific regions of the frequency response will usually be dominated by 

a few (often one or two) physically understood poles and zeros whose 

effects can be "captured" on the Bode amplitude asymptotes. In consideration of the effects of a feedback loop, the lower order model need 

only be a good approximation in the crossover (IG(j .)I 1) region(s) 

(Ref. C-1, Chapter 9) since: 

and IG(jw)( = O(1) for the crossover region. 

The art of controlling aircraft and other vehicles is then built 

around their basic mechanics, which gives them low pass filter characteristics , and the FCS designer's ability to create integrator-like 

characteristics in the crossover region for the basic (manual or automatic) loops. 

c-2 
1. First-Order Lag in Series with an Integrator 

1 

G(s) s(Ts + 1) 

A typical occurrence of this element is as the simplest (1 DOF) 

representation of bank angle response to roll control. 

c-3 
Phase 

Margin 

(deg) 

90 

80 

70 

60 

50 

40 

30 

20 

IO 

.5 

I 

Tc, Tw, TwCL 

Ill 

I. 

b 

3 \ Reference .------- 

OF 

a) Open -Loop Frequency Responsz and Closed-Loop Bode Root Locus 

b) Error Series 

Figure C-1. First-Order Lag in Series with an Integrator 

TR-1228-1 c-4 
2. Second-Order Factor 

Damping ratio C defines the characteristics: 

I < 1 complex 

 IS^ > 1 real 

TR- 1 228- 1 c-5 
55 

50 

c 

rn 

9 

a 

-0 

1 

45 

Lz 

40 

35~~~ 

! :' . ,, , 

.. , . I ; 135 

11' 

A #O 

.OC5 .o I " .2 .5 I .o 

Is 

1 :i ! 

Second Order Factor 

5- 5- 

Figure C-2. Haximum Amplitude Ratio, ARXu, for Second-Order Factor 

TR-1 228-1 C-6 
I .o 

.8 

.6 

I 

I +J” 

.2 

I \ Second Order Factor ’ 

-=( 

Wn 

[” + 4 

s = jw 

I 

1-2gz 

2 .4 

c- 

.6 .707 .8 

Figure C-3. Frequency at Which mmx Occurs for Second-Order Factor 

TR-1228-1 c-7 
3. The Crossover %del 

One of the most important applications of this model is as a firstorder approximation of manual control. Crossover frequency uc and the 

effective time delay f can be estimated as a function of the first-order 

characteristics of the controlled element (Ref. C-2). 

TR-1228-1 C-8 
u' 

al 

0. 

CnPO 

TR-'I 228-1 c-9 
(rad) (deg) 

__-_ I+lnr/2 - 

run 

___ LWn-: -(erw ____ __ 1 . c . - .8 

8 

90 

80 

70 

-8 60 

.- 50 Y 

2i 40 

2 30 

a 

20 

IO 

0 

I 

L 

C 

-0 

al 

ul 

I I I I I I I I I I 

.I .2 .3 .4 .5 .6 .7 .8 .9 1.0 

Closed-Locp Damping Ratio , 5, 

Figure C-5. Phase Elargin as a Function of 

Closed-Loop Damping Ratio 

Figure C-6. Closed-Loop Undamped Natural Frzquency 

as a Function of Crossover Frequency 

TE12 28-1 c-10 
4. The Superaugnented Hodel 

In the closure of the fundamental pitch rate of a superaugmented 

aircraft the open-loop transfer function has the form (Ref. C-3) 

-KqM6 (s + l/Tq)e-TS 

q€ S2 

The closed-loop response to command is 

-KqM6 (s + l/Tq)emTS -P q' 

qc Is', 41 

1. 

'"h assuming T << 7 = Tq 

TR~ 228-1 c-11 
oo oo Complex Bode Root Locx 

.-, Real Axis Bode 

Root Locus (Siggy) 

/og w - 

-TS 

-K, ME( s + I/Tq )e - 91 

Figure C-7. Superaugmented Dominant Mode Approximation 

5= I 

TR-1228-1 c-12 
4c 

Tr 

R= 

I 

I 1 

tm 

Time - 

Figure C-8. Superaugmented q/q, Transient Response 

~~1228-1 C-13 
\\\\\\ $I- 

-u, I-= c - 

0 

a AI Q1 

E- .- 

3 

.- - 

/- ,' I; 

3 

9 

M 

9 

N 

L 

0 

CQ 

L 

U 

L 

0 

ru 

c 

0 

> 

0 

aJ 

u 

m 

d 

c 

c) 

u 

d 

L 

TR -1228-1 C-1.4 
I 

3.0 

2.5 

I .5 

I .o 

.5 

2.0 

.5 

Rise Time,T, = I/wCa 

1.0 7 .5 

I I I 

4 

I 

.3 

I 

1.0 1.5 2.0 2.5 3.0 3.5 4.0 

High Frequency Gain, wca (~€6') 

Figure C-10. Superaugmented Dominant Mode Characteristics 

in the l/Tq - wCa Parameter Plane 

TR-1228-1 C-15 
5. A Second-Order Dipole In Series with an Integrator 

This characteristic often occurs as the Dutch roll artifact in bank 

angle response to roll control. 

TR-1228-1 

. 

C-16 
t 

0 

1 

b 

*I I1 

el u, 

I1 

'c 

0 

e 

I 

.It 

E 

al 

TR-1228-1 C-17 
BEFWWCES TO APPENDIX C 

C-1. McRuer, Duane, Irving Ashkenas, and Dunstan Graham, Aircraft 

Dynamics and Automatic Control, Princeton University Press, 

Princeton, NJ 1973. 

C-2. McRuer D. T., and E. S. Krendel, "Mathematical Models of Human 

Pilot Behavior," AGARDograph No. 188, Jan. 1974. 

(2-3. Myers, T. T., D. T. McRuer, and D. E. Johnston, Flying Qualities 

and Control Systems Alternatives for Superaugmented Aircraft, 

NASA CR-170419, Dec. 1984. 

TR- 1228 - 1 C-18 
I. Report No. 2. Government Accession NO. 

NASA CR-181726 

4. Title and Subtitle 

Advanced Piloted Aircraft Flight Control System 

Design Methodology 

3. Recipient's Catalog No. 

5. Report Date 

October 1988 

6. Performing Organization Code 

7. Author(s) 

-. Volume 1: Knowledge Base 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 

Systems Technology, Inc. 

13766 South Hawthorne Boulevard 

Hawthorne, CA 90250-7083 

2. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Langley Research Center 

Hampton, VA 23665-5225 

505-66-0 1-02 

11. Contract or Grant No. 

NAS 1- 1 79 8 7 

13. Type of Repon and Period Covered 

Contractor Report 

14. Sponsoring egency Code 

Langley Technical Monitor: Jarrell R. Elliott 

SBIR Phase I1 Final Report 

16. Abstract 

This report presents and illustrates the development of a comprehensive and 

eclectic methodology for conceptual and preliminary design of flight control 

systems. The methodology is focused on the design stages starting with the 

layout of system requirements and ending when some viable competing system 

architectures (feedback control structures) are defined. The approach is 

centered on the human pilot and the aircraft as both the sources of, and the 

keys to the solution of, many flight control problems. 

heavily on computational procedures which are highly interactive with the design 

engineer. To maximize effectiveness, these techniques, as selected and modified 

to be used together in the methodology, form a cadre of computational tools 

specifically tailored for integrated flight control system preliminary design 

purposes. 

most are now commercially available. 

available and useful as possible instead of simply another isolated approach. 

The methodology relies 

The computer aids are all based on IBM PC compatible machines and 

This helps make the methodology as broadly 

2 < I \- %. .$ < 

17. Key Words (Suggested by Author(s)) 18. Distribution Statement 

Artificial intelligence (AI) 

Expert systems . Unclassified - Unlimited 

Flight control sys tem design 

Knowledge-based design Subject Category 08 

Natural lanpuage interface 

19. Security Classif. (of this report) 120. Security Classif. (of this page) 1 21. NO. of pages I 22. Price 

Unclassified I Unclassified I 

NASA FORM 1626 OCT 86