July 2013 

NASA/TM–2013-218026 

Investigation of Control Inceptor Dynamics and 

Effect on Human Subject Performance 

Anthony A. Stanco and Frank M. Cardullo 

State University of New York, Binghamton, New York 

Jacob A. Houck and Richard C. Grube 

Langley Research Center, Hampton, Virginia 

Lon C. Kelly 

Unisys Corporation, Hampton, Virginia 
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA scientific and technical information (STI) 

program plays a key part in helping NASA maintain 

this important role. 

The NASA STI program operates under the 

auspices of the Agency Chief Information Officer. 

It collects, organizes, provides for archiving, and 

disseminates NASA’s STI. The NASA STI 

program provides access to the NASA Aeronautics 

and Space Database and its public interface, the 

NASA Technical Report Server, thus providing one 

of the largest collections of aeronautical and space 

science STI in the world. Results are published in 

both non-NASA channels and by NASA in the 

NASA STI Report Series, which includes the 

following report types: 

TECHNICAL PUBLICATION. Reports of 

completed research or a major significant phase 

of research that present the results of NASA 

Programs and include extensive data or 

theoretical analysis. Includes compilations of 

significant scientific and technical data and 

information deemed to be of continuing 

reference value. NASA counterpart of peerreviewed formal professional papers, but 

having less stringent limitations on manuscript 

length and extent of graphic presentations. 

TECHNICAL MEMORANDUM. Scientific 

and technical findings that are preliminary or of 

specialized interest, e.g., quick release reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis. 

CONTRACTOR REPORT. Scientific and 

technical findings by NASA-sponsored 

contractors and grantees. 

CONFERENCE PUBLICATION. 

Collected papers from scientific and 

technical conferences, symposia, seminars, 

or other meetings sponsored or cosponsored by NASA. 

SPECIAL PUBLICATION. Scientific, 

technical, or historical information from 

NASA programs, projects, and missions, 

often concerned with subjects having 

substantial public interest. 

TECHNICAL TRANSLATION. 

English-language translations of foreign 

scientific and technical material pertinent to 

NASA’s mission.

Specialized services also include organizing 

and publishing research results, distributing 

specialized research announcements and feeds, 

providing information desk and personal search 

support, and enabling data exchange services. 

For more information about the NASA STI 

program, see the following: 

Access the NASA STI program home page 

at http://www.sti.nasa.gov

E-mail your question to help@sti.nasa.gov

Fax your question to the NASA STI 

Information Desk at 443-757-5803 

Phone the NASA STI Information Desk at 

443-757-5802 

Write to: 

 STI Information Desk 

 NASA Center for AeroSpace Information 

 7115 Standard Drive 

 Hanover, MD 21076-1320

 
National Aeronautics and 

Space Administration 

Langley Research Center 

Hampton, Virginia 23681-2199 

 

July 2013 

NASA/TM–2013-218026 

Investigation of Control Inceptor Dynamics and 

Effect on Human Subject Performance 

Anthony A. Stanco and Frank M. Cardullo 

State University of New York, Binghamton, New York 

Jacob A. Houck and Richard C. Grube 

Langley Research Center, Hampton, Virginia 

Lon C. Kelly 

Unisys Corporation, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
i 

 Abstract 

The control inceptor used in a simulated vehicle is an important part of adequately 

representing the dynamics of the simulation. The force feedback sensed by the operator 

through the control inceptor gives the pilot important cues to maintain adequate 

performance. The dynamics of a control inceptor are typically based on a second order 

spring mass damper system with damping, force gradient, breakout force, and natural 

frequency parameters. Changing these parameters can have a great effect on pilot or 

driver control of the vehicle. The neuromuscular system has a very important role in 

controlling the vehicle through the control inceptor. 

Many studies by McRuer ([11],[13],[14]), Aponso ([10],[16]), and Hess 

([4],[5],[6],[7],[8]) have dealt with modeling the neuromuscular system and quantifying 

the effects of a high fidelity control loader as compared to a low fidelity control loader. 

Pilots are adaptive in nature and their control behavior in simulators change based on 

different control loader dynamics. Pilots will change their control behavior to maintain 

tracking bandwidth and minimize tracking error. 

A quasi-transfer of training experiment was performed at the NASA Langley 

Research Center. The study employed a high fidelity control loader and a low fidelity 

control loader. Test subjects trained in both simulations and then were transferred to the 

high fidelity control loader simulation. This is conducted to test the difference between 

training on two different control loader dynamics. The parameters for the high fidelity 

control loader were determined from the literature. The low fidelity control loader 

parameters were found through testing of a simple computer joystick. 
ii 

 A disturbance compensatory task was employed for the quasi transfer of training 

experiments. The compensatory task involved implementing a simple horizon on an out 

the window display. A disturbance consisting of a sum of sinusoids was used. The task 

consisted of the pilot compensating for the disturbance on the roll rate of the aircraft. The 

vehicle dynamics were represented as 1/s and 1/s2

. It is well known that 1/s plant 

dynamics is an easy task, but 1/s2

 plant dynamics is a hard task. The test subject tried to 

maintain level flight throughout the experiment. The test subjects consisted of non-pilots 

to remove any effects of pilot experience. A total of 20 test subjects, 10 placed in a low 

fidelity control inceptor training group and 10 placed in a high fidelity control inceptor 

training group, were used. Each group was trained until they reached a performance 

asymptote, then they were transferred to the high fidelity control inceptor simulation. The 

effect of training on either control inceptor was analyzed. 

 Performance metrics such as RMS tracking error, PSD analysis, and a workload 

analysis were performed to quantify the transfer of training effect on both the high and 

low fidelity control loader simulations. 

Quantitative results of the experiments show that there is no significant difference 

between the high fidelity and low fidelity training groups for 1/s plant dynamics. Both 

their RMS tracking error and PSD results are similar suggesting similar control behavior 

and tracking performance. For 1/s2 plant dynamics there is a greater difference in tracking 

performance and also the PSD. Also, for 1/s2 plant dynamics the test subjects are less 

correlated with the input disturbance function. 
iii 

Contents 

Abstract ........................................................................................................................ i

Contents ...................................................................................................................... iii

List of Tables ................................................................................................................ v

List of Figures ...............................................................................................................vi

Nomenclature ..............................................................................................................ix

Acronyms .....................................................................................................................xi

Chapter 1 - Introduction ............................................................................................... 1

1.1 Introduction.......................................................................................................... 1 

1.2 Objectives and Scope of Research ............................................................................ 3 

1.3 Report Organization ............................................................................................... 4 

Chapter 2 Background .................................................................................................. 5

2.1 Fidelity Assessment................................................................................................ 5 

2.2 Aircraft Control System Dynamics ............................................................................ 6 

2.3 Neuromuscular Models .........................................................................................13 

2.4 Transfer of Training...............................................................................................17 

2.5 Tracking Tasks ......................................................................................................18 

Chapter 3 - Literature Review of Control Force Feedback Dynamics ...............................20

3.1 Introduction.........................................................................................................20 

3.2 Neuromuscular/Pilot system models .......................................................................21 

3.2.1 Precision Model ................................................................................................................................22

3.2.2 Lateral Head Motion Model.............................................................................................................23

3.2.3 Hess Structural Model......................................................................................................................28

3.2.4 Neuromusculoskeletal Model..........................................................................................................30

3.3 Force Feel Research ..............................................................................................32 

Chapter 4 - Design of Transfer of Training Study ...........................................................47

4.1 Introduction.........................................................................................................47 

4.2 Roll Disturbance Compensation Task .......................................................................47 

4.3 Force Feel Parameter Determination .......................................................................50 

4.3.1 High Fidelity Control Loader Parameters........................................................................................50

4.3.2 Low Fidelity Control Loader Parameters ........................................................................................52

4.4 Analysis of Control Loader Parameters.....................................................................56 

4.4.1 Experimentally Obtained High Fidelity Characteristics..................................................................64

4.4.2 Experimentally Obtained Low Fidelity Characteristics ..................................................................70

4.5 Disturbance Input & Performance Metric Tests .........................................................73 
iv 

Chapter 5 - Experimental Setup....................................................................................79

5.1 Introduction.........................................................................................................79 

5.2 Background .........................................................................................................79 

5.3 Implementation of Transfer of Training Study ...........................................................80 

5.3.1 Protocol .............................................................................................................................................81

5.3.2 Test Setup .........................................................................................................................................83

5.3.3 Display Setup ....................................................................................................................................86

5.3.4 Force Feel Parameters Implementation .........................................................................................88

Chapter 6 - Results and Discussion ...............................................................................91

6.1 Introduction.........................................................................................................91 

6.2 Performance Metrics.............................................................................................92 

6.3 PSD Analysis ...................................................................................................... 103 

6.4 Coherence Analysis ............................................................................................. 117 

6.5 Frequency Responses of Test Subjects ................................................................... 119 

6.6 Remnant ........................................................................................................... 130 

Chapter 7 – Conclusions and Future Recommendations .............................................. 131

7.1 Summary........................................................................................................... 131 

7.2 Conclusions ....................................................................................................... 132 

7.3 Future Recommendations .................................................................................... 135 

Appendices................................................................................................................ 137

Appendix A: Control Loader Quasi Transfer of Training Experimental Protocol .................. 137 

Appendix B: Experimental Measured and Calculated Parameters .................................... 141 

Appendix C: Experiment Run Time.............................................................................. 142 

Appendix D: Matlab [21] Code to Calculate Frequency Response .................................... 143 

Appendix E: Experiment Pseudo Code......................................................................... 144 

Appendix F: Experiment Flow Chart ............................................................................ 147 

Appendix G: Mean Square and Variance for High Fidelity and Low Fidelity Training Groups 148 

Appendix H: Peak Power and Frequency for Every Test Subject ...................................... 154 

Appendix I: Average Tracking Error Using More Runs to Train......................................... 156 

Appendix J: Smoothed Periodogram Matlab [21] Code .................................................. 159 

References ................................................................................................................ 162
v 

 List of Tables 

Table 3.2.1 Neuromuscular Subsystems Model Parameter Values ................................23

Table 3.2.2 Lateral Head Motion Parameter Values (Gum, 1973) [2] ............................23

Table 3.3.1 Force Feel Characteristics (Johnston, 1988) [10] ........................................37

Table 3.3.2 Disturbance Sum of Cosines Parameters (Johnston, 1988) [10] ...................37

Table 4.4.1 Control Inceptor Characteristics .................................................................56

Table 4.4.2 Frequency Sweep Input Sinusoid Formulation ............................................59

Table 4.4.3 Acquired High Fidelity Effective Mass with Low Damping Ratio ...............66

Table 4.5.1 Sum of Sines Disturbance Input .................................................................73

Table 4.5.2 Disturbance Input Implemented in MMS Laboratory ..................................75

Table 5.3.1 McFadden Control Loader Parameter Table ...............................................88

Table 5.3.2 Implemented Control Inceptor Characteristics ............................................90

Table 6.2.1 Average Number of Runs to Reach Asymptote ......................................... 101

Table 6.5.1 Disturbance Sum of Sinusoids Parameters ................................................ 123
vi 

 List of Figures 

Figure 2.2.1 Reversible Flight Control System (Takats, 2011) [18] ................................ 7

Figure 2.2.2 Fly-By-Wire Flight Control System (Takats, 2011) [18] ............................. 8

Figure 2.2.3 Position Servo Control Loader Model (Takats, 2011) [18] .........................10

Figure 2.2.4 Analog/Digital Control Loader System (Takats, 2011) [16] .......................11

Figure 2.2.5 Force Servo Control Loader Model (Takats, 2011) [18] .............................12

Figure 2.2.6 McFadden Control Loader Model (McFadden Systems Inc., 1999) [15] .....13

Figure 2.3.1 Lateral Head Motion Block Diagram (Gum, 1973) [2]...............................14

Figure 2.3.2 Neuromuscular Subsystems Model (Magdaleno & McRuer, 1971) [13] .....15

Figure 2.3.3 The Structural Model of the Human operator for Compensatory Tracking 

(Hess, 1985) [8] ..........................................................................................................16

Figure 2.3.4 Neuromusculoskeletal Model (Hosman, 2010) [9] .....................................17

Figure 3.2.1 Antagonistic Muscle Pairs (Magdaleno & McRuer, 1968) [14] ..................21

Figure 3.2.2 Neuromuscular Subsystems Model (Magdaleno & McRuer, 1971) [13] .....23

Figure 3.2.3 Lateral Head Motion Block Diagram (Gum, 1973) [2]...............................23

Figure 3.2.4 Muscle Dynamics Frequency Response ....................................................24

Figure 3.2.5 Muscle Spindle Feedback Frequency Response. ........................................25

Figure 3.2.6 Lateral Head Motion Control Frequency Response ....................................26

Figure 3.2.7 Lateral Head Motion Control Step Response .............................................27

Figure 3.2.8 The Structural Model of the Human operator for Compensatory Tracking 

(Hess, 1985) [8] ..........................................................................................................28

Figure 3.2.9 Revised Structural Model of the Human Operator for Pursuit Tracking 

(Hess, 2000) [4] ..........................................................................................................29

Figure 3.2.10 Neuromusculoskeletal Model (Hosman, 2010) [9] ...................................31

Figure 3.3.1 Lateral Flying Qualities Experimental Set Up (Bailey, 1990) [1] ................32

Figure 3.3.2 Roll Command Gain vs. Roll Mode Time Constant (Bailey, 1990) [1] .......34

Figure 3.3.3 Roll Tracking Task Block Diagram (Johnston, 1988) [10] .........................36

Figure 3.3.4 Effective Controlled Element (Johnston, 1988) [10] ..................................38

Figure 3.3.5 Amplitude Ratio Peak as a Function of Force Gradient Constant (Johnston, 

1988) [10] ...................................................................................................................38

Figure 3.3.6 Task Bandwidth vs. Roll Command Gain (Johnston, 1988) [10] ................39

Figure 3.3.7 Workload vs. the Reciprocal of the Product of Roll Command Gain and 

Task Bandwidth (Johnston, 1988) [10] .........................................................................40

Figure 3.3.8 Cooper Harper Rating vs. Roll Command Gain (Johnston, 1988) [10]........41

Figure 3.3.9 Center-Stick Experimental Setup (Johnston, 1988) [10] .............................42

Figure 3.3.10 Task Tracking Bandwidth as a Function of Feel System Natural Frequency 

(Johnston, 1988) [10] ..................................................................................................43

Figure 3.3.11 Task Tracking Error as a Function of Feel System Natural Frequency 

(Johnston, 1988) [10] ..................................................................................................44

Figure 3.3.12 CHPR as a Function of Feel System Natural Frequency (Johnston, 1988) 

[10].............................................................................................................................45

Figure 4.2.1 Developed Roll Disturbance Compensatory Tracking Task........................48

Figure 4.3.1 Simulated High Fidelity Control Loader Step Response.............................51

Figure 4.3.2 Logitech Computer Joystick Transient Response Obtained from MMS 

Laboratory ..................................................................................................................54
vii 

Figure 4.3.3 Logitech Computer Joystick Transient Response Obtained using Labview 

[20].............................................................................................................................55

Figure 4.4.1 Force Servo Control Loader Model (Takats, 2011) [18] .............................57

Figure 4.4.2 Frequency Sweep Configuration (Takats, 2011) [18] .................................59

Figure 4.4.3 Simulated High Fidelity Frequency Response ...........................................62

Figure 4.4.4 Simulated Low Fidelity Frequency Response ............................................63

Figure 4.4.5 High Fidelity Force vs. Displacement .......................................................64

Figure 4.4.6 High Fidelity Free Release Response with Low Damping Ratio.................65

Figure 4.4.7 Experimental High Fidelity Free Release Response ..................................67

Figure 4.4.8 Experimental High Fidelity Frequency Response with Low Damping Ratio

 ...................................................................................................................................69

Figure 4.4.9 Experimental Low Fidelity Force vs. Displacement ...................................70

Figure 4.4.10 Experimental Low Fidelity Free Release Response..................................71

Figure 4.4.11 Experimental Low Fidelity Frequency Response .....................................72

Figure 4.5.1 Plot of Roll Angle Disturbance ................................................................74

Figure 4.5.2 RMS Tracking Error Obtained from Test within MMS Laboratory ............75

Figure 4.5.3 Slope of RMS Tracking Error Obtained from Test within MMS Laboratory

 ...................................................................................................................................76

Figure 4.5.4 RMS Control Inceptor Deflection Obtained from Test within MMS 

Laboratory ..................................................................................................................77

Figure 4.5.5 Slope of RMS Control Inceptor Deflection Obtained from Test within MMS 

Laboratory ..................................................................................................................78

Figure 5.2.1 Cockpit Motion Facility (NASA LaRC) ....................................................80

Figure 5.3.1 Quasi Transfer of Training Experimental Configuration ............................84

Figure 5.3.2 Out-the-Window Display Setup ................................................................88

Figure 6.2.1 Average Tracking Error for High Fidelity Training Group (1/s Plant 

Dynamics) ..................................................................................................................92

Figure 6.2.2 Average Tracking Error for Low Fidelity Training Group (1/s Plant 

Dynamics) ..................................................................................................................93

Figure 6.2.3 Average Tracking Error Results for Both Training Groups (1/s Plant 

Dynamics) ..................................................................................................................94

Figure 6.2.4 Average Tracking Error Results for High Fidelity Training Group (1/s2 Plant 

Dynamics) ..................................................................................................................95

Figure 6.2.5 Average Tracking Error for Low Fidelity Training Group (1/s2 Plant 

Dynamics) ..................................................................................................................97

Figure 6.2.6 Average Tracking Error Results for Both Training Groups (1/s2 Plant 

Dynamics) ..................................................................................................................97

Figure 6.2.7 Average Tracking Error with Greater Amount of Runs (Test Subject HF001 

1/s Plant Dynamics) ....................................................................................................99

Figure 6.2.8 Average Tracking Error with Greater Amount of Runs (Test Subject LF009 

1/s Plant Dynamics) .................................................................................................. 100

Figure 6.2.9 Average Tracking Error (1/s Plant Dynamics) ......................................... 102

Figure 6.2.10 Average Tracking Error (1/s2 Plant Dynamics) ...................................... 102

Figure 6.3.1 Variance of Roll Stick Deflection 1st Run (High Fidelity Group 1/s Plant 

Dynamics) ................................................................................................................ 104
viii 

Figure 6.3.2 Variance of Roll Stick Deflection 1st Run (Low Fidelity Group 1/s Plant 

Dynamics) ................................................................................................................ 104

Figure 6.3.3 Average Peak Power (1/s Plant Dynamics).............................................. 105

Figure 6.3.4 Average Peak Frequency (1/s Plant Dynamics) ....................................... 106

Figure 6.3.5 Average Peak Power (1/s2 Plant Dynamics) ............................................ 108

Figure 6.3.6 Average Peak Frequency (1/s2 Plant Dynamics) ...................................... 109

Figure 6.3.7 PSD of Disturbance Forcing Function ..................................................... 110

Figure 6.3.8 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

Last Run Training (1/s Plant Dynamics) ..................................................................... 111

Figure 6.3.9 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

First Run Transfer (1/s Plant Dynamics)..................................................................... 111

Figure 6.3.10 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

Last Run Transfer (1/s Plant Dynamics) ..................................................................... 112

Figure 6.3.11 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

Last Run Training (1/s2

 Plant Dynamics).................................................................... 113

Figure 6.3.12 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

First Run Transfer (1/s2

 Plant Dynamics) ................................................................... 113

Figure 6.3.13 Average PSD for High Fidelity and Low Fidelity Training Test Subjects 

Last Run Transfer (1/s2

 Plant Dynamics).................................................................... 114

Figure 6.3.14 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(High Fidelity 1/s Plant Dynamics) ............................................................................ 115

Figure 6.3.15 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(Low Fidelity 1/s Plant Dynamics) ............................................................................. 115

Figure 6.3.16 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(High Fidelity 1/s2 Plant Dynamics) ........................................................................... 116

Figure 6.3.17 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(Low Fidelity 1/s2

 Plant Dynamics)............................................................................ 116

Figure 6.4.1 Coherence between Control Inceptor Deflection and Disturbance Forcing 

Function (1/s Plant Dynamics) ................................................................................... 117

Figure 6.4.2 Coherence between Control Inceptor Deflection and Disturbance Forcing 

Function (1/s2

 Plant Dynamics).................................................................................. 118

Figure 6.5.1 Single Sided Amplitude Spectrum of Disturbance ................................... 123

Figure 6.5.2 Test Subject HF002 Experimental Frequency Response .......................... 124

Figure 6.5.3 Test Subject HF002 Experimental Frequency Response Averaged Over Four 

Runs ......................................................................................................................... 125

Figure 6.5.4 Coherence Between Roll Error and Control Inceptor Deflection for One Run 

(Test Subject HF002) ................................................................................................ 126

Figure 6.5.5 Coherence Between Roll Error and Control Inceptor Deflection Average 

over Four Runs (Test Subject HF002) ........................................................................ 126

Figure 6.5.6 Frequency Response for LTI System (Original Disturbance Forcing 

Function) .................................................................................................................. 128

Figure 6.5.7 Frequency Response for LTI System (Finer Frequency Vector Input) ...... 128

Figure 6.5.8 Frequency Response for LTI System (Chirp Input Signal) ....................... 129

Figure 6.6.1 PSD of Control Inceptor Deflection for Test Subject HF002 .................... 130

Figure 6.6.2 PSD of Control Inceptor Deflection for Test Subject HF005 .................... 131
ix 

 Nomenclature 

Symbol: Definition: Units: 

ω Frequency rad/s 

ζ Damping ratio dimensionless 

τ Time constant seconds 

m or M Mass kg or lb•s2/in 

c, b, or β Damping coefficient lb•s/in

θ Generic Angle degrees 

φ Bank Angle degrees 

k or KFS Force gradient lb/in 

K Generic Gain non-dimensional 

L’Fas Roll Rate Command Gain deg/s2/lb 

P/Fas Roll Sensitivity deg/s/lb 

σe Roll Tracking Error degrees 

σc Manipulator Control Effort (Force or Position) lb or in 

I Inertia kg•m

2

g Gravity m/s2 or ft/s2 

ρ Roll Rate deg/s or rad/s

δac Aileron Deflection Command degrees 

δas Output Lateral Deflection of Control Inceptor inches 

Subscripts Definition 

( )N Relates to Natural Frequency 

( )P Relates to the Pilot 

( )e Relates to Equalization or Effort 

( )sp Relates to the Muscle Spindle 

( )j Relates to the Joint 

( )g Relates to Gravity 

( )h Relates to the Head 

( )m Relates to the Muscle 

( )i Relates to Input 

( )o Relates to Output 

( )NM Relates to Neuromuscular System 

( )FS Relates to the Feel System 

( )C Relates to Control or Manipulator Contact Dynamics of 

a Task 

( )PF Relates to the Proprioceptive Feedback 

( )int Relates to the Limb Dynamics 

( )ms Relates to the Muscle Spindle 

( )gto Relates to the Golgi Tendon 

( )act Relates to Muscle Activation 

( )v Relates to a Velocity 

( )p Relates to a Position 
x 

( )a Relates to an Acceleration 

( )r Relates to a Rate 
xi 

 Acronyms 

CMF Cockpit Motion Facility 

CHPR Cooper Harper Pilot Rating 

CHR Cooper Harper Rating 

CTFT Continuous Time Fourier Transform 

DFT Discrete Fourier Transform 

DTFT Discrete Time Fourier Transform 

EMG Electromyography 

FFT Fast Fourier Transform 

FRF Frequency Response Function 

GFD Generic Flight Deck Simulator 

HFOV Horizontal Field of View 

HQR Handling Qualities Rating 

HUD Head Up Display 

IFD Integration Flight Deck Simulator 

Labview Laboratory Virtual Instrumentation Engineering Workbench 

LATHOS Lateral High Order System 

MMS Man Machine Systems 

PIO Pilot Induced Oscillation 

PO Percent Overshoot 

PSD Power Spectrum Density 

RFD Research Flight Deck Simulator 

RMS Root Mean Square 

SIMES Simulation Evaluation System 

STD Standard Deviation 

STI System Technology Inc. 

USAF United States Air Force 

VFOV Vertical Field of View 
1 

Chapter 1 - Introduction 

1.1 Introduction 

Vehicle simulation is employed to train operators of various vehicles to reach a 

performance level adequate to operate the real-world vehicle. Simulation uses fewer 

resources than the real-world vehicle to train for the same task. With the real-world 

vehicle, the amount of cost and time to perform tasks is not optimal for training 

operators. With a simulation, different environments and tasks can be interchanged 

without losing time and resources. The goal of training is for operators to have good 

transfer of training where operator performance is maintained when transferring to the 

real-world vehicle. Training in simulators helps to train operators efficiently without the 

possibility of accidents. 

Before simulators, operators trained in the real-world vehicles and some small 

number still do. With the introduction of complicated control systems in vehicles today, 

training is necessary in a safe environment before operators enter the real world vehicle. 

This helps prevent accidents during training and helps to train operators to prevent 

accidents from occurring in normal operation of the vehicle. Simulation provides the 

necessary practice to prevent unwanted circumstances occurring in real-world vehicle 

training. Simulators can be used in research to test different tasks not achievable and not 

safe in the real-world vehicle. Using simulator research, real-world vehicles can be 

improved, a better understanding of human control can be sought and future accidents 

can be prevented Simulators have to provide realistic cues to the operator in order to 

train them effectively (Wiener, 1988) [19]. 
2 

 Vehicle simulation uses principles of human perception to closely replicate the 

vehicle it is simulating. Visual, vestibular, and proprioceptive feedback are the main 

components of human perception employed for vehicle control. These components work 

together with the cognitive system to stimulate a characteristic human control strategy. 

The fidelity of the simulation depends on how closely the performance of the simulator 

matches the vehicle. The purpose of simulation is to maintain high fidelity while keeping 

within the constraints of the simulator. The simulator has motion limitations that make it 

difficult to recreate the same accelerations, velocities, and displacements experienced in 

the vehicle. 

A vehicle simulator uses cueing algorithms, i.e. control laws which stimulate 

perceptions in the simulator sufficient to produce a pilot control strategy similar to the 

criterion vehicle. The visual system on a simulator should also have high fidelity, 

recreating the scenery with details necessary for training preserved. The motion system 

should be correlated with visual cues otherwise the cues will conflict and provide 

misleading information to the pilot. Another system component involved in simulation is 

the force feel feedback in the vehicle. The fidelity of the control loader has fewer 

limitations than both the motion and visual systems. The control inceptor is the main 

interface of the pilot with the vehicle dynamics. Therefore, control loader force feedback 

can have a significant impact on the control strategy of the human operator. The control 

loader force feedback effect on human test subject performance is the primary focus of 

the research discussed in this report. 
3 

1.2 Objectives and Scope of Research 

 The control inceptor is the main operator-vehicle interface. Control loader 

systems provide the force feel feedback necessary to train test subjects efficiently. 

Initially, control loaders used mechanical springs, dashpots, cams, and friction brakes. As 

aircraft flight controls systems became more complicated, control loader systems had to 

provide more realistic force feedback cues (Takats, 2011) [18]. The updated control 

loader systems are able to match the non-linear parameters involved in vehicle control. 

Maintaining a high fidelity control inceptor wherein the control inceptor dynamics in the 

real world vehicle are accurately reproduced in the simulated vehicle is important. A 

quasi transfer of training experiment was conducted in order to investigate the effect of 

training operators on either a high fidelity or low fidelity control inceptor simulation. 

The real-time training experiment which was conducted at NASA Langley 

Research Center provides the necessary data for analysis. Using objective metrics, an in 

depth analysis of test subject performance is discussed in the final chapters. Also, any 

future recommendations will be discussed to improve the control loader experimentation. 

The main objectives of these experiments are listed below. 

 Objectives of this research: 

Fundamental objective is to determine if the fidelity of a control loader affects 

training 

Define high and low fidelity control loader parameters 

Verify control loader parameters 

Develop a compensatory disturbance tracking task 

Develop the quasi-transfer of training study 
4 

Implement experimental task on fixed base simulator 

Run test subject experiments and analyze results 

Develop test plans for future experimentation 

1.3 Report Organization 

This report is organized as follows. The second chapter gives a brief background 

on control systems in aircraft, control loader systems, the neuromuscular system, transfer 

of training experiments, and compensatory tasks. Chapter 3 presents a review of literature 

on different neuromuscular models and the different experiments to test the effect of the 

control loader system dynamics on human control performance. Chapter 4 describes the 

design of the quasi-transfer of training roll disturbance compensatory task. In this 

chapter, the two control loader dynamics representing a high fidelity and low fidelity 

control loader system were defined and implemented on a simulator located at NASA 

Langley Research Center. Frequency responses and step responses were obtained to 

verify the implemented force gradient, natural frequency, damping ratio, and breakout 

force. This chapter is important to understand how the experiment was performed. 

In Chapter 5, the test setup of the experiment is discussed. The protocol, 

experimental measurements, experimental pseudo code as well as the simulator used for 

experiments are presented here. This is a useful chapter for those that need to recreate the 

experiment presented in this research. Chapter 6 discusses the results of test subject 

performance and control strategy using RMS tracking error and PSD analysis. Chapter 7 

gives conclusions for this research and future recommendations to improve the 

experiment. 
5 

Chapter 2 Background 

2.1 Fidelity Assessment 

The force feedback cues provided to the operator are very important for the 

control strategy within different vehicles. The effect of training on a control inceptor with 

different force feedback characteristics than the real world vehicle is unknown. This 

report will ascertain important information on these force feedback cues and the 

significance of control inceptor fidelity. 

 Fidelity has been defined by Hess (1991) [6] as “the degree to which 

characteristics of perceivable states induce adequate pilot psychomotor and cognitive 

behavior for a given task and environment.” Typically, simulators cannot match the full 

motion capabilities of the vehicle being simulated. Therefore, simulators rely on the 

principles of human perception to provide the cues which induce proper operator control 

of the vehicle. This is a key component in maintaining motion fidelity and part of the 

difficulty to obtain adequate simulator fidelity. On the other hand, the visual system 

fidelity is obtained by replicating the simulator visual scene as closely as possible to the 

real-world visual scene. Maintaining visual fidelity requires synchronizing the visual to 

the motion characteristics. A conflicting visual and motion cue can have adverse effects 

on test subject’s control of the simulated vehicle. The force feel system dynamics are 

easily replicated although there are still limitations. The limitations include non-linear 

effects such as friction and the ability to maintain sufficient bandwidth while preserving 

the force gradient. In the research conducted, the control behavior between the high 

fidelity and low fidelity simulation is investigated to ascertain if force feedback is 

necessary for adequate control behavior. 
6 

 There has been considerable focus for fidelity assessment on motion systems and 

visual systems. Hess (2000) [4] proposed the Handling Qualities Sensitivity Function 

(HQSF) as a method for assessing simulator fidelity. This function uses the Hess 

structural model (Hess, 1985) [8] of the human pilot to determine how the input power is 

transferred to output control power of the pilot. It is consistent with a transfer function 

which relates the input to the output of the pilot. The fidelity metric relates the area below 

the HQSF between the real world vehicle and the simulated vehicle. As the value of the 

fidelity metric becomes larger, the simulator fidelity is lower. Another approach is the 

Sinacori technique (Schroeder, 1999) [17], which compares the gain and phase distortion 

between the nominal vehicle and the simulated vehicle. The gain and phase distortion 

should be minimal for the simulation to be considered high fidelity. 

2.2 Aircraft Control System Dynamics 

 Many new aircraft have moved to mechanical hydraulically boosted and fly-bywire force feel control systems which have unknown effects on pilot performance. The 

mechanical hydraulically boosted and fly-by-wire control systems do not have any direct 

physical connection to the control surfaces of the aircraft. Both mechanical hydraulically 

boosted and fly-by-wire control systems use hydraulics to reduce the forces required to 

move the control surfaces. Mechanical hydraulically boosted and fly-by-wire control 

systems utilize an artificial force feel device to create the force feedback cues that arrive 

from the aerodynamic forces on the control surfaces. In the same manner, simulators use 

a control loader system to simulate the control inceptor dynamics in the real world 

vehicle. Within this section, there is a discussion on the background of aircraft and 

simulator flight control systems. 
7 

The flight control systems in aircraft prior to World War I consisted of direct 

mechanical linkages to the control surfaces (Takats, 2011) [18]. This type of flight 

control system is referred to as a reversible flight control system whereby the 

aerodynamic forces on the control surfaces are felt directly by the pilot. An example of a 

reversible flight control system is shown below in Figure 2.2.1. 

Figure 2.2.1 Reversible Flight Control System (Takats, 2011) [18] 

In Figure 2.2.1, the input force by the operator causes the control inceptor (1) to 

deflect. Through a series of direct linkages and hinges, a hinge moment is applied to the 

control surface (5). This causes an increased aerodynamic force on the control surface (5) 

which is directed back to the control inceptor via the linkages and hinges. The gearing of 

the linkages provides a certain amount of mechanical advantage but is limited by the 

space available within the aircraft. Also shown in Figure 2.2.1 is the autopilot (2) system. 

The autopilot applies a signal to a servo valve to increase hydraulic flow, therefore 

increasing the applied force. The force from the hydraulic actuator is applied by way of 

linkages to deflect the control surface (5). 

On larger aircraft, hydraulically boosted flight control systems are typically used. 

Two types of hydraulically boosted flight control systems exist: mechanical and fly-by-
8 

wire. The mechanical hydraulically boosted flight control system utilizes mechanical 

linkages to control a hydraulic valve actuator instead of direct connection to the control 

surfaces. For the fly-by-wire systems either an analog circuit or a digital computer is used 

to measure pilot control inceptor inputs and apply a command to an actuator to drive the 

control surfaces. The fly-by-wire and mechanical hydraulically boosted control systems 

are examples of irreversible flight control systems. For both systems, the aerodynamic 

forces cannot be felt by the pilot because of the absence of the direct linkage to the 

control surfaces. For these systems, an artificial feel system is implemented to simulate 

any force feedback characteristics (Takats, 2011) [18]. An example of a fly-by-wire 

flight control system is shown in Figure 2.2.2. 

Figure 2.2.2 Fly-By-Wire Flight Control System (Takats, 2011) [18] 

In Figure 2.2.2, the deflection of the control inceptor (1) from the operator is 

analyzed by an analog or digital computer. The computer then sends the proper command 

to a hydraulic valve actuator (6) which provides the hinge moment to deflect the control 

surface (5). An autopilot system (2) can bypass the control by the operator by directly 

controlling the command to the hydraulic valve actuator (6). 
9 

The flight control system characteristics are divided into two groups; the aft mass 

and the forward mass. For an irreversible flight control system, the forward mass includes 

the control inceptor and the linkages to the control surfaces. The aft mass includes any 

linkages, hinges, and aerodynamic forces on the control surface itself. Some of the 

components to consider when modeling the aircraft control system are the spring and 

damping forces due to the linkages and the mass attached. Also, the hinge moments due 

to aerodynamic forces are considered for the aft mass model. When modeling a 

hydraulically boosted system, the dynamics of the hydraulic actuator must be included. 

The forward mass simulation for most irreversible systems represents a spring mass 

damper system with: force gradient, natural frequency, and a damping coefficient term. 

With modern fly-by-wire systems, nonlinear characteristics can be present such as 

breakout force, friction, and detents. The fly-by-wire system allows for the choice of 

certain characteristics, which can affect the stability of the aircraft. This is why many 

aircraft have digital systems that help stabilize the aircraft (Takats, 2011) [18]. 

Control loader systems are utilized in simulators to simulate the control inceptor 

characteristic dynamics. These dynamics include the force gradient, damping, natural 

frequency, friction, detents, breakout force, and any other nonlinear dynamics. Early 

control loader systems used a position feedback control loop. An example of a position 

feedback control loader system is shown in Figure 2.2.3. As the control inceptor is 

moved, both the force and position on the control inceptor are measured. The force is fed 

through the aft mass and forward mass simulations, which creates the appropriate 

dynamics. 
10 

+

-

Servo Drive Servo

Valve

Hydraulic

Actuator

Force

Transducer

Position

Transducer

Aft Mass Simulation

Force Feedback

AFT Mass Position

FWD Mass Position

+

+

Position

Command

Cable

Simulation -

+

Figure 2.2.3 Position Servo Control Loader Model (Takats, 2011) [18] 

The combination of the aft and forward mass simulation results in a commanded 

position. The servo drive command is produced when the position of the control inceptor 

is subtracted from the commanded position. The position servo control loader has limits 

on the achievable bandwidth. Therefore, force feedback control loader systems were 

implemented to obtain a higher bandwidth and because human test subjects 

predominantly use force to control a vehicle (Takats, 2011) [18]. 

The forward mass simulation can either be computed in the control loader 

computer or a similar analog circuit. In Figure 2.2.4, a hybrid analog/digital control 

loader system is shown. In this system, an analog circuit computes the forward mass 

dynamics such as the force gradient, damping, and natural frequency while the control 

loader computer computes the cable and aft mass simulation. As the control inceptor is 

deflected, a force transducer measures the force applied by the operator. This force is fed 

through the forward mass simulation to produce a commanded velocity. The velocity 
11 

command computed is then multiplied by the damping coefficient (C) to produce the 

damping force. The position of the control inceptor goes through the control loading 

computer, which applies a force gradient calculated from the cable and aft mass 

simulation. The cable and aft mass simulations depend upon the aircraft being simulated. 

If a specific aircraft is not being simulated, a linear force gradient can be set without 

implementing the cable or aft mass simulation. 

Figure 2.2.4 Analog/Digital Control Loader S ystem (Takats, 2011) [16] 

 The force feedback control loader, Figure 2.2.5, uses a force command to drive 

the servo. As the control inceptor is deflected, both the position and force are measured. 

The position of the control inceptor is implemented through the forward mass, aft mass, 

and cable simulations to produce a force command to the servo valve. The servo drive 

command is produced when the force of the control inceptor is subtracted from the 

calculated commanded position. A control loader system commands the control inceptor 

to the proper position based on the force applied by the operator. 
12 

+

-

Servo Drive Servo

Valve

Hydraulic

Actuator

Force

Transducer

Position

Transducer

-

Cable +

Simulation

Aft Mass Simulation

Force Feedback Force CMD

AFT Mass Position

FWD Mass Position

+

Figure 2.2.5 Force Servo Control Loader Model (Takats, 2011) [18] 

The control loader system used in the experiments is a force feedback control 

loader system developed by McFadden Simulator Systems. The block diagram of its 

internal control structure is shown in Figure 2.2.6. When the test subject applies a force, 

the position of the control inceptor is fed back through the implemented dynamics. The 

parameters that create the force feel dynamics consist of the forward damping, the force 

gradient, the breakout force, and forward stop force. The position is fed through the force 

gradient to produce a force command which could be non-linear. The velocity of the 

control inceptor is fed through the damping coefficient to produce a force due to the 

damping. The breakout force applies a high force gradient and a certain force level 

around the neutral position of the control inceptor. The control inceptor will not move 

until the breakout force level is reached. The forward stop position sets the maximum 

deflection of the control inceptor in either direction. 
13 

The force that is applied to the control inceptor by the operator is first summed 

with the force command developed from the characteristic forward mass dynamics to 

produce an applied force. The applied force is then subtracted from the measured force 

on the control inceptor, which produces a force error command that drives the servo to 

the correct position. A force can be developed by a computer or analog circuitry and then 

injected in the control loader system at the same summing junction where operator force 

input is usually added. This allows for frequency sweep and step response data to be 

collected from the control loader system. 

Fwd

Damping

+

Actuator

Valve Drive

Input Force

Position

transducer

Actuator

Position

Pressure

transducer

Force

gain

+

Position

Derivative gain

Stop Position

Compensation

Fwd Stop

Positions, Fwd

Stop Slope

+

Force

Gradient

+

Breakout

Force

+

+

-

Figure 2.2.6 McFadden Control Loader Model (McFadden Systems Inc., 1999) [15] 

2.3 Neuromuscular Models

 The neuromuscular system is an important component in the control of a vehicle. 

The visual, vestibular, and somatosensory systems give feedback to the operator and 
14 

relay important information regarding vehicle control. The information is processed by 

the central nervous system and a command is applied by the neuromuscular system. The 

output of the neuromuscular system is a force. The neuromuscular system has its own 

internal feedback loop. The Golgi tendons and muscle spindle relay information on the 

muscle extension and force applied by the muscles in the limbs. This allows for coarse as 

well as fine motor control within a task. This allows the pilot to be adaptable and able to 

control many varying dynamic tasks. One question brought up by the study of the 

neuromuscular system is the limitation of the neuromuscular system and the situations 

that cause a task to be uncontrollable. 

 Don R. Gum (1973) [2] proposed a lateral head motion model. This model 

includes the muscle dynamics, head dynamics, and muscle spindle feedback. The transfer 

function for the muscle is defined as a first order system. The muscle spindle represents a 

lead/lag and the head dynamics represents a typical spring mass damper second order 

system. The lateral head motion model is shown in Figure 2.3.1. 

Gravity Torque

h

m

m

f

I

T s

d

T

K

) 1 ( 

2 2

1

2 n n s s    

) 1 (

) 1 (

1

1

1

1

T

T s

T

T s

  



Disturbance

Input

 d



 i

Head Angle

Input

 o

Head Angle

Ouput

Muscle Dynamics

Head Dynamics

Muscle Spindle Feedback

e 



 g



 s

h

h

I

M gr

+

- +

+

+

Figure 2.3.1 Lateral Head Motion Block Diagram (Gum, 1973) [2] 
15 

R. E. Magdaleno and D. T. McRuer (1971) [13] have also investigated many 

aspects of the neuromuscular system and proposed similar neuromuscular models. One 

such model is the neuromuscular subsystems model which was developed using test 

subject describing functions using an input/output relationship. To obtain a specific 

model for the muscle and muscle spindle feedback, EMG signals were recorded from 

each test subject. This allowed for the measurement of the effective muscle activation 

signal and average tension in the muscle. The neuromuscular subsystems model is shown 

in Figure 2.3.2. 

+

+

1

2

2

2 (1 ) 1

as

a N

a a

K e

s Ts s





 

	 	


     


 

Manipulator

Position

c

Muscle/Manipulator

Spinal Cord Dynamics

( )

( )

sps

sp sp

sp

sp

K sZ e

H

s P

	 	 

 

js H Ke j j

	 

+

+

c s K ee

	

Display

Input

e

Retinal and

Central

Equalization

Figure 2.3.2 Neuromuscular Subsystems Model (Magdaleno & McRuer, 1971) [13] 

 Another model proposed is from Ronald A. Hess (1985) [8]. Hess developed a 

structural model in which each transfer function is defined for the components of the 

neuromuscular system. The model is then matched to pilot input/output relationships 

through various tasks. Hess uses the crossover model to equalize the structural model and 

chose parameters to have K/s dynamics around 2 rad/s. The structural model proposed by 

Hess (1985) [8] is shown in Figure 2.3.3. 
16 

Display

+

-

+

- +

+

nu

-

Central Nervous System Neuromuscular System

2

2 2 2

n

nn n s s



    Yc

1

1 1/

K s

s T 

2

1 ( 1/ ) 2

K

k s T 	 

1

Yp os

e

	

Ke

1s

se



e Yd Ke

Figure 2.3.3 The Structural Model of the Human operator for Compensatory Tracking (Hess, 1985) [8] 

 A neuromuscular model has recently been proposed by Ruud Hosman and David 

Abbink (Hosman, 2010) [9]. This model also takes a structural approach by using test 

subject input/output relationships to define the parameters. The neuromuscular model 

proposed by Hosman (2010) [9] is shown in Figure 2.3.4. A detailed description of the 

neuromuscular models presented above is discussed within the Literature Review. 

 Many performance effects are noted throughout the research when the control 

loader dynamics are changed. It is shown that phase lag due to the control force feel 

dynamics has less impact since both the input and output of the control inceptor are 

known to the test subject. The natural frequency of the neuromuscular system is typically 

around 14 rad/s. It seems that reducing the natural frequency of the control loader below 

that of the neuromuscular system causes roll ratchet tendencies. Also, the sensitivity of 

the control loader can cause pilot induced oscillations (Johnston, 1988) [10]. The reason 

for many of these effects is not very clear, and this is a matter for continuing research. 
17 

+

+

-

He

Fex Xe

Hc

+

-

+

-

Hint

+

-

1/kse

Hact +

+ +

-

+

τdelay Hgto

-

+

Hce

τms Hms

Fc

Environment

Human

Admittance

Supraspinal

Input

Fmus

xse

x

xce

a

Figure 2.3.4 Neuromusculoskeletal Model (Hosman, 2010) [9] 

2.4 Transfer of Training 

A transfer of training experiment usually involves a simple control task in which a 

test subject control strategy is tested. Typically, the amount of time and runs completed to 

reach a certain performance metric will determine when the test subject has trained on a 

specific task. A transfer of training experiment involves a test subject training in a 

simulator and then transferring to the real-world vehicle. By comparing how well the test 

subjects perform in both the simulator and the real world vehicle; the training 

effectiveness can be measured. Certain aspects of test subject control strategy such as the 

training benefits of maintaining visual, motion, and force feedback fidelity are 

investigated. Usually, two different test subject groups are used to test training advantage. 

One group is trained on a high fidelity simulation and another group is trained on a 

simulation with certain variables changed. The two groups will then transfer to the realworld vehicle. 

A variation of a transfer of training study is a quasi-transfer of training study. 

Since using a real-world vehicle is cost ineffective and time consuming, a quasi-transfer 
18 

of training study can be conducted. A quasi-transfer of training differs in that a simulator 

is used to test both training and transfer tasks. One group will train on a high fidelity 

simulator and another group will train on a simulator with certain variables altered. The 

two groups will then transfer to the same high fidelity simulator which represents the 

real-world vehicle. A quasi-transfer of training study is easily replicable and can be 

performed for a wide variety of tasks. 

An example of a quasi-transfer training study is an experiment conducted by 

William H. Levison (1979) [12]. Five groups of test subjects trained on a roll-axis 

tracking task. One group trained with only visual cues. A second group trained with 

synchronized visual and motion cues. The other three groups trained with motion cues 

delayed 80, 200 and 300 msec. The groups were trained on the Roll Axis Tracking 

Simulator (RATS) at the Aerospace Medical Research Laboratory. One group trained 

with no motion in the RATS and then transferred to the RATS with synchronized motion 

and visual cues turned on. Another group trained with the synchronous motion and visual 

turned on and then transferred to the synchronous motion and visual simulation. The 

groups that trained on the delayed motion cues, trained in the RATS with motion delayed 

80, 200 and 300 msec and then transferred to the synchronous motion and visual 

simulation. The test subjects all trained to an asymptotic mean square tracking error 

before transferring to the synchronous motion and visual simulation. 

2.5 Tracking Tasks 

Tracking tasks are implemented most of the time when determining human control 

strategy because of their simplicity and transportability to multiple simulators. There are 

two types of tracking tasks, compensatory and pursuit. 
19 

In a compensatory tracking task, a forcing function moves an indicator on a 

display. An indicator and a zero reference point are shown on the display. The indicator 

can represent a bank angle, altitude, or deflection in the horizontal direction. The operator 

is required to maintain the indicator on the zero reference point. This task is similar to 

driving on a road, a wind gust moves the car off course, and you have to return the car on 

course again. The compensatory task employed in experiments is usually a roll 

disturbance or pitch disturbance compensatory task. In the roll disturbance compensatory 

task, the test subject tries to return the cursor back to level flight or zero degrees bank 

angle. For the pitch disturbance compensatory task, the test subject nulls the forcing 

function in the vertical direction returning the cursor back to a target altitude labeled on 

the display. 

In a pursuit tracking task, the operator is presented with a display consisting of 

two indicators, the target and the follower. The target moves according to the defined 

forcing function. The operator has to follow the target to keep the follower superimposed 

on the target indicator. This task can be utilized for horizontal and vertical motion. 

Usually, the percent on target and tracking error are used to measure test subject 

performance. 

For a compensatory tracking task, the tracking error is the difference between the 

indicator and the reference point. For a pursuit tracking task, the tracking error is the 

difference between the target and the follower position. Typically, the forcing function is 

a pseudo-random disturbance employed by a sum of sinusoids. This mitigates operators 

from recalling the disturbance in previous runs. 
20 

Chapter 3 - Literature Review of Control Force Feedback 

Dynamics 

3.1 Introduction 

 Research involving simulator dynamics and controls has improved simulator 

training and the transfer of training to real-world vehicles for pilots. Research exists for 

the different mechanisms that the human uses to control a vehicle. These mechanisms 

involve the visual system, the vestibular system, and the somatosensory system. Much of 

the knowledge is focused on the visual and vestibular systems. Vestibular cues are the 

main source for motion sensation, but somatosensory cues could offer additional 

information that could be beneficial to the pilot’s control of the vehicle. 

 Simulators create the effect that the pilot is controlling the real-world vehicle. A 

high fidelity simulator matches the response of the vehicle’s motion closely. Simulators 

cannot duplicate the actual dynamics of the vehicle but use basic principles of human 

perception to create cueing algorithms to allow the pilot to perceive the same vehicle 

motion. To create a high fidelity simulator, human perception of motion has to be well 

understood. In particular, this research focuses on the somatosensory system and the 

effect of control inceptor dynamics on a human test subject. 

 Within this literature review, both an understanding of the somatosensory system 

involvement in stick control of the aircraft, and the different effects that the control stick 

dynamics have on pilots was sought. The first topic discussed is the somatosensory 

system, particularly the neuromuscular system involved with limb movement and the 

different pilot models involving this system. The second topic discussed is the 
21 

experiments that have been conducted in the past to clarify the effects of changing the 

control inceptor dynamics. 

 This literature review together with knowledge on human in the loop control tasks 

has provided the necessary information to design and conduct experiments to test the 

effect of force feedback cues on human test subjects. 

3.2 Neuromuscular/Pilot system models 

The neuromuscular system is a complex system consisting of the neural pathways, 

the motor neurons, the muscle fibers, and many proprioceptors. Two of the most 

important proprioceptors are the muscle spindle and the Golgi tendon. The muscle 

spindle is responsible for sensing the change of length and the rate of change of length in 

the muscle fiber. This gives a sense of the position of the limb. The Golgi tendon has a 

linear relationship with the muscle force. These two sensors are very important in 

controlling the position of the limb. The muscles within the limbs have both damping and 

spring characteristics. The muscle works in antagonistic pairs to move the limb. An 

example of antagonistic pairs working to move a control stick is shown in Figure 3.2.1. 

Figure 3.2.1 Antagonistic Muscle Pairs (Magdaleno & McRuer, 1968) [14] 

 

 A motor neuron creates a firing rate that causes the overlapping muscles to contract. This 

causes tension in the muscle which moves the limb. Some of the major neuromuscular 

models that have been described in the literature will be discussed within this section. 
22 

3.2.1 Precision Model 

 A neuromuscular model for limb dynamics that was proposed by Magdaleno and 

McRuer (1968) [14] is the precision model. The transfer function representation of this 

neuromuscular model is presented in Equation 3.2.1 (Magdaleno and McRuer, 1968) 

[14]. 

1

2

2 2

1 1

1 1 ( 1) 2

L K s N

p p

I K N NN N

Ts T s YK e

Ts T s Ts s s

 

 

	



  
 
        
 
  

              

 Equation 3.2.1 

The Kp term is a gain used to adjust the open loop crossover frequency. The equalization 

term is used to allow the open loop frequency response to have a slope of -20 dB/decade 

at the crossover frequency. There is also a delay term which represents the delay of the 

nervous system. A lead/lag term exists which represents the low frequency phase lag seen 

by higher order aircraft dynamics. 

 To accurately describe each subsystem of the neuromuscular system, Magdaleno 

and McRuer (1971) [13] conducted experiments to determine the describing function for 

the muscle/manipulation actuation element. These experiments involved both hand and 

leg control manipulators. The experiment performed was a tracking compensation task in 

which the describing functions were obtained. The results obtained led to the block 

diagram of the neuromuscular system with muscle spindle and effective joint sensor 

feedback shown below in Figure 3.2.2. The values for each parameter are shown below in 

Table 3.2.1. 

Neuromuscular System Equalization 

Term 
23 

+

+

1

2

2

2 (1 ) 1

as

a N

a a

K e

s Ts s





 

	 	


     


 

Manipulator

Position

c

Muscle/Manipulator

Spinal Cord Dynamics

( )

( )

sps

sp sp

sp

sp

K sZ e

H

s P

	 	 

 

js H Ke j j

	 

+

+

c s K ee

	

Display

Input

e

Retinal and

Central

Equalization

 

3.2.2 Lateral Head Motion Model 

 Another neuromuscular model presented is a lateral head motion control model 

developed by Gum (1973) [2]. This model represents the motion of the head in response 

to an input from the nervous system. Head motion consists of multiple components. 

These components are the muscle dynamics, the head dynamics, and muscle spindle 

feedback. The block diagram of the lateral head motion control model by Gum (1973) [2] 

is shown in Figure 3.2.3. The values for the terms within the lateral head motion control 

block diagram are shown in Table 3.2.2. 

Gravity Torque

h

m

m

f

I

T s

d

T

K

) 1 ( 

2 2

1

2 n n s s    

) 1 (

) 1 (

1

1

1

1

T

T s

T

T s

  



Disturbance

Input

 d



 i

Head Angle

Input

 o

Head Angle

Ouput

Muscle Dynamics Head Dynamics

Muscle Spindle Feedback

e 



 g



 s

h

h

I

M gr

+ - + -

Values for Neuromuscular 

Subsystems Model 

Tn 1/30 sec 

ζa .8 

ωa 10 rad/sec 

τa .017 sec 

Zsp 11 rad/sec 

Psp 40 rad/sec 

τsp .023 sec 

Values for Lateral Head 

Motion Block Diagram 

Kf 43 N 

d 0.075 m 

Tm 0.08 s 

Ih 0.0304 kg-m2

ζ 0.64 

ωn 7.81 rad/s 

Mh 4.6 kg 

g 9.8 m/s2 

r 0.0498m 

α 0.2 

T1 0.25 s 

 Figure 3.2.3 Lateral Head Motion Block Diagram (Gum, 1973) [2]

Figure 3.2.2 Neuromuscular Subsystems Model (Magdaleno & McRuer, 1971) [13] 

Table 3.2.1 Neuromuscular 

Subsystems Model Parameter Values 

(Magdaleno & McRuer, 1971) [13] 

Table 3.2.2 Lateral Head Motion 

Parameter Values (Gum, 1973) [2] 
24 

The system input is a commanded head angle input (θi) from the nervous system. 

The sensed angular output of the head (θs) is subtracted from (θi) to create the error (θe) 

which drives the system. At this summation point gravity applies a torque on the head 

through an angular acceleration which is represented by (  g ). The gravity torque constant 

has units of rad/s2

. These angular accelerations from the muscle dynamics, disturbance 

input, and gravity torque are applied to the head, which creates a head angle output (θo). 

 The control of muscle dynamics is a low pass filter. At low frequencies the 

magnitude is about 40 dB and has a corner frequency of 12.5 rad/sec. The frequency 

response for the muscle dynamics along with its transfer function is shown in Figure 

3.2.4. 

1326

( 12.5) e s



  

 13

Figure 3.2.4 Muscle Dynamics Frequency Response 

10-1 100 101 102 103 0

20

40

60

Muscle Dynamics Frequency Response

Magnitude (Decibels)

10-1 100 101 102 103 -100

-50

0

Phase (Deg)

Frequency (rad/sec)
25 

At low frequencies the muscle has zero phase. At high frequencies the muscle has 

a phase lag of 90 degrees. The muscle has more sensitivity to slower movements and will 

drop down to a gain of 0 dB at 1,000 rad/sec. Between 0.1 and 1 rad/sec, there is a 

constant gain and zero phase lag. 

In the neuromuscular model proposed by Gum (1973) [2] the muscle spindle 

feedback is represented as a high pass filter. The muscle spindle is more sensitive to 

smaller muscle movements at higher frequencies since it increases its gain at frequencies 

beyond 1 rad/s. The phase of the muscle spindle dynamics seems to peak at 10 rad/sec at 

a phase angle of about 45 degrees. The frequency response of the muscle spindle along 

with its transfer function is shown in Figure 3.2.5. 

5( 4)

( 20)

s

o

s

s





  

Figure 3.2.5 Muscle Spindle Feedback Frequency Response.

10-1 100 101 102 103 0

5

10

15

Muscle Spindle Feedback Frequency Response

Magnitude (Decibels)

10-1 100 101 102 103 0

20

40

60

Phase (Deg)

Frequency (rad/sec)
26 

 The frequency response of the total lateral head motion control is shown in Figure 

3.2.6. The frequency response acts as a low pass filter allowing for a constant gain 

sensation at lower frequencies. The system has a gain margin of 6.43 dB and a phase 

margin of 149 degrees. In the head motion range of 0.1 Hz (0.628 rad/sec) and 1 Hz 

(6.283 rad/sec), the movement of the head has zero phase and zero gain. At frequencies 

above 100 rad/s, the output lags the input by 270 degrees. An increase in gain by a factor 

of 2.4 times or a phase lag of 149 degrees will cause instability. The total head motion 

control has a peak frequency of 14 rad/s. If you increase the damping ratio, a smaller 

peak occurs which leads to less head motion ratcheting. 

43 2

1326 26,520

42.5 562.2 8,714 23,320

o

i

s

ss s s





    

 

Figure 3.2.6 Lateral Head Motion Control Frequency Response 

10-1 100 101 102 103 -150

-100

-50

0

50

Lateral Head Motion Control Frequency Response

Magnitude (Decibels)

10-1 100 101 102 103 -300

-200

-100

0

Phase (Deg)

Frequency (rad/sec)
27 

The step response for the total head motion control is shown in Figure 3.2.7. This 

response has a rise time of 0.583 seconds and a settling time of 1.15 seconds. The 

response has an oscillation that is not sinusoidal in nature. This behavior is due to a 

second order peaking shown in the total lateral head motion frequency response (Figure 

3.2.6). The neuromuscular peaking in pilot control of a center stick on an airplane is 

shown to cause roll ratcheting. The final value of the system is 1.13 degrees which is 

greater than the commanded head angle of 1 degree. The step response shows a slight 

muscle ratcheting which occurs when the neuromuscular peak magnitude is above 0 dB 

at -180 degrees of phase. 

 

43 2

1326 26,520

42.5 562.2 8,714 23,320

o

i

s

ss s s





   

 

Figure 3.2.7 Lateral Head Motion Control Step Response 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0

0.2

0.4

0.6

0.8

1

1.2

1.4 Lateral Head Motion Control Step Response

Time (sec)

Ouput Head Angle (Deg)
28 

3.2.3 Hess Structural Model 

 A structural pilot model was proposed by Hess (1985) [8]. The model is shown in 

Figure 3.2.8. This model includes muscle manipulator dynamics, muscle spindle 

feedback, and Golgi tendon feedback. The model represents the response of the pilot’s 

neuromuscular system via visual feedback. It is a disturbance compensation task in which 

the pilot compensates for a disturbance. The error between the disturbance and the output 

of the plant are visualized by the human. In this model, the human operator tries to 

minimize this error through visual and proprioceptive feedback cues. 

e Yd

Display

+

-

1s se Ke

Ke os

e

	 1 Yp +

-

2

2 2 2

n

nn n s s



    Yc ++

nu

1

1 1/

K s

s T 

2

1

2 ( 1/ )k

K

s T 	 

-

Central Nervous System Neuromuscular System

 Figure 3.2.8 The Structural Model of the Human operator for Compensatory Tracking (Hess, 1985) [8] 

 The parameters T1, K1, K2, and Ke are chosen using the crossover model proposed 

by Johnston & McRuer (1986) [11]. The crossover model states that the form of the 

combined open loop transfer function for the pilot and the plant should be K/s for the 

crossover frequency. The crossover frequency of the pilot model is the frequency at 

which the response crosses 0 dB or a magnitude of one. Typically the crossover 

frequency is between 3 and 6 rad/s. 
29 

 The crossover model is used by Hess to determine the proper proprioceptive 

feedback which equalizes the plant to have K/s dynamics. When the dynamics of the 

system are equal to K/s2

, the pilot adapts to the different dynamics by applying different 

control strategies and these are typically compensated within the feedback of the system. 

 An updated structural model presented by Hess (2000) [4] is shown in Figure 

3.2.9. In contrast to the original structural pilot model proposed by Hess, the revised 

model includes one term for the proprioceptive feedback. The revised model also 

includes a vestibular feedback loop. The equations presented below in Section 3.2.3 are 

obtained from Hess (2000) [4]. 

+

- Ke os

e

	

-

propioceptive

feedback

Pilot

C + YNM YFS YC

M

Vehicle

δF δm

YPF

YPF

Um

Us

vestibular

feedback

visual

feedback

Figure 3.2.9 Revised Structural Model of the Human O perator for Pursuit Tracking (Hess, 2000) [4] 

The term YNM is represented by the transfer function in Equation 3.2.2. 

 

2

2 2 2

NM

NM

NM NM NM

Y

s s



    

Equation 3.2.2 

 

The nominal parameters for the neuromuscular transfer function (YNM) are equal to a 

damping ratio (ζNM) equal to 0.7 and a natural frequency (ωNM) equal to 10 rad/s. The 

force feel system term (YFS) is typically represented as a second order spring mass 

damper system with the transfer function represented by Equation 3.2.3. 
30 

 

2

2 2 2

FS

FS

FS FS FS

Y

s s



    

 Equation 3.2.3 

 

 

The proprioceptive feedback term (YPF) is in the form of KPF(s+a), KPF, or KPF/(s+a) 

when the vehicle dynamics are equal to Kc, Kc/s, and Kc/s2

 respectively. The 

proprioceptive gain (KPF) is chosen so that the minimum damping ratio of 0.15 is 

obtained for any of the closed-loop poles. The equalization term (Ke) is chosen to allow 

(YpYc) to have a crossover frequency of 2 rad/sec. The parameter “a” is chosen so that 

(YpYc) represents K/s dynamics around a crossover frequency of 2 rad/s. The transfer 

function (Yp) is represented by Equation 3.2.4. 

 1

os NM FS

p e

NM FS PF

Y Y

Y Ke

Y YY

	 
    
    Equation 3.2.4 

 

 

The term Ke and os e	 represent the pilot equalization term and the central processing time 

delay respectively. The term τo is equal to 0.2 seconds. 

3.2.4 Neuromusculoskeletal Model 

 A neuromusculoskeletal model presented in the American Institute of Aeronautics 

and Astronautics (AIAA) 2010 Modeling and Simulation Technologies Conference is 

shown in Figure 3.2.10 (Hosman, 2010) [9]. This model represents motion of the 

neuromusculoskeletal system in response to an externally applied force disturbance. The 

equations presented below in Section 3.2.4 are obtained from Hosman (2010) [9]. The 

model includes feedback from both the muscle spindle and the Golgi tendon. As shown 

in this model, the Golgi tendon receives force feedback from the muscle as opposed to 

receiving feedback from the muscle extension. 
31 

+

+

-

He

Fex Xe

Hc

+

-

+

-

Hint

+

-

1/kse

Hact +

+ +

-

+

τdelay Hgto

-

+

Hce

τms Hms

Fc

Environment

Human

Admittance

Supraspinal

Input

Fmus

xse

x

xce

a

 Figure 3.2.10 Neuromusculoskeletal Model (Hosman, 2010) [9] 

 In the above block diagram Hact and Hgto represent the muscle activation dynamics 

and the Golgi tendon feedback respectively. Hms and Hint represent the muscle spindle 

feedback and the limb dynamics respectively. Hce and Hc represent the visco-elasticity of 

the muscle and the contact dynamics respectively. He represents the inceptor dynamics. 

The transfer function for the muscle activation is shown in Equation 3.2.5. 

2

1

()2 1

act

o o

H

s s 

 



  

Equation 3.2.5 

 

 

 

This equation is typical of a second order spring mass damper system which has been 

seen throughout all of the previously proposed neuromuscular dynamics. The afferent 

response of the muscle spindle is described by Equation 3.2.6.

 

2 H k ks ks ms p v a   

Equation 3.2.6 
32 

The terms kp, kv, and ka represent the position feedback gain, the velocity feedback gain, 

and the acceleration feedback gain respectively. The control inceptor transfer function 

(He) is represented by Equation 3.2.7. 

2

1 e

e ee

H

ms bs k

   Equation 3.2.7 

 

The limb dynamics (Hint) are also described by a second order system in Equation 3.2.8. 

 

int 2

1

q qq

H

ms bs k

   Equation 3.2.8 

In this case the terms bq and kq represent the passive viscosity and passive elasticity of the 

muscle within the limb. The term (mq) represents the mass in kilograms of the arm. 

3.3 Force Feel Research 

Bailey (1990) [1] conducted experiments on how force feel characteristics 

affected pilot performance. The experiments consisted of using a USAF variable stability 

NT-33A aircraft. Pilots tested 200 configurations in which the roll-mode time constant, 

roll command gain, time delay, and the roll pre-filter break frequency were changed. The 

block diagram showing the implementation of the experiment is shown in Figure 3.3.1. 

Equation 3.3.1, Equation 3.3.2, and Equation 3.3.3 below are obtained from Bailey 

(1990) [1]. 

FS FS s

2 2 2(.7)( )

.25

   2 2

1

2(.7)( ) PF PF s s    

Ds e

	 Augmented

Aircraft

Fas δas δac

ωFS = 26 rad/s

= 13 rad/s

= 8 rad/s

ωPF = 26 rad/s

= 13 rad/s

= 8 rad/s

= none

τd = 0 ms

= 55 ms

= 110 ms

= 175 ms

Figure 3.3.1 Lateral Flying Q ualities Experimental Set Up (Bailey, 1990) [1] 
33 

 In Figure 3.3.1, the feel system dynamics are represented by a second order 

transfer function shown in Equation 3.3.1. 

 

2

2 2 2(.7)( )

as FS FS

as FS FS

k

F s s

 

     Equation 3.3.1 

 Equation 3.3.1 represents the output lateral deflection of the control inceptor (δas) 

due to the input lateral force applied to the control inceptor (Fas). The term (kFS) 

represents the force gradient. Two force gradients of 2.75 lb/in and 4 lb/in were tested 

within this experiment. The term (ωFS) represents the natural frequency. The natural 

frequencies tested were 8 rad/s, 13 rad/s, and 26 rad/s. The damping ratio was held 

constant at 0.7. The pre-filter shown directly after the command type can either be in 

terms of a second order system transfer function shown in Equation 3.3.2 or a simple 

time delay (τPF). 

 

2

2 2 2(.7)( )

c

s

a PF

a PF PF s s

 

      Equation 3.3.2 

 

The pre-filter natural frequencies were chosen as 8 rad/s, 13 rad/s, and 26 rad/s. The 

augmented aircraft dynamics are shown below in Equation 3.3.3. 

 

.04 '

1

Fas R s

ac R

L

e

s

 

 

	   

Equation 3.3.3 

 

The term (L’Fas) and (τR) are referred to as the roll rate command gain and the roll 

mode time constant respectively. The units of the roll rate command gain are deg/sec2

/lb 

and the units of the roll mode time constant are seconds. The roll mode time constant and 

roll rate command are chosen based on a specified roll sensitivity (P/Fas) which is the 

slope of the roll rate command gain divided by the roll mode time constant. The units of 
34 

the roll sensitivity (P/Fas) are deg/sec/lb. The roll sensitivity represents the roll rate of the 

augmented aircraft with respect to the force input. Figure 3.3.2 shows this correlation of 

the roll mode time constant and the roll gain. 

Figure 3.3.2 Roll Command Gain vs. Roll Mode Time Constant (Bailey, 1990) [1] 

The roll mode time constants used in this experiment were 0.15, 0.25, and 0.40 sec. The 

roll sensitivities used were 10, 18 and 25 deg/sec/lb. For the different configurations, the 

roll command gain was chosen based on Figure 3.3.2 above. 

 The two experiments conducted were a power approach and an up-and-away task. 

The power approach task involved a visual landing task with a lateral offset. The up-andaway task consisted of a Heads Up Display (HUD) generated tracking task. The 

experimental data consists of pilot ratings, pilot comments, and task performance records. 

The pilot ratings were obtained using the Cooper-Harper pilot rating scale. 
35 

 The results show that performance decreases when the roll mode time constant 

decreases from 0.40 to 0.15 sec. Also a change in the feel system natural frequency from 

26 rad/sec to 8 rad/sec and all other parameters fixed causes performance degradation. 

The reduction of the natural frequency produces a greater chance of roll ratchet. When 

the feel system natural frequency is reduced from 26 rad/s to 13 rad/s, very little change 

in the pilot’s flying qualities occurs. When the force gradient was decreased from 4 

lb/inch to 2.75 lb/inch an improvement was seen. The phase lag caused by force feel 

dynamics has less effect on the pilot’s performance as compared to other control system 

phase lags. The force feel is a part of the control system in which the pilot can sense both 

the input and output of the control inceptor. 

 High performance flight control system bandwidths could be affecting the 

neurological system of the pilot. Some of the issues in new control loader systems 

include high roll control sensitivity, pilot induced oscillations, and roll ratchet in 

precision control. 

 Dynamic models for the pilot and the closed loop Arm/Manipulator/Feel system 

are obtained from the frequency responses obtained within experiments conducted by 

Johnston (1988) [10]. The experiment consisted of a roll tracking task where the pilot 

matched the bank angle of the plant with the target, which was defined by a pseudo 

random motion. The pseudo random motion was created from a sum of cosines 

waveform. The difference between the target bank angle and the plant bank angle was 

recorded. The block diagram for the experiment is shown in Figure 3.3.3. 
36 

Ф 

rad s CF   0,14,26 /

Display Pilot Manipulator

Analyzer

-

-

+

I/O

Ф e F pc

Ф=Σ sin ωi

( 1) 

	

s Ts

K e Y

s

c



 

YcY!YCF



! Y c 

CF CF CF

CF

CF

s s

Y 2 2

2

2  



  

 CF .7

Figure 3.3.3 Roll Tracking Task Block Diagram (Johnston, 1988) [10] 

 The control plant (Yc) is equal to the transfer function (Yφ) multiplied by an 

optional pre-filter (YCF). The output of the manipulator above was converted into digital 

signals that were analyzed using STI’s (System Technology Inc.) describing function 

analyzer program. This allowed pilot/vehicle transfer functions to be extracted from the 

experiments. The transfer functions were used to analyze the effect of the force feel 

system on the neuromuscular system. 

 The manipulators used were McFadden force loader systems. Both a center stick 

and a side stick were used for the different configurations. Different sets of feel system 

dynamic characteristics were implemented. These characteristics are shown in Table 

3.3.1. The disturbance that was implemented was a sum of different cosine waves at 

different frequencies and amplitudes. The form of the sum of cosines is φ = ΣAicos(ωit). 

This created a pseudo random target for the pilot to follow. The parameters for the 

frequencies and amplitudes of each cosine wave are shown in Table 3.3.2. 
37 

Sidestick YFS1 YFS2 YFS3

KFS (lb/in) 14 7.5 3.75 

 (lb/deg) 1.22 0.65 0.33 

 (deg/lb) 0.82 1.53 3.1 

ωFS (rad/sec) 31.4 22.4 18 

ζFS 0.7 0.6 0.6 

Breakout (lb) 0.75 0.75 0.75 

Centerstick YFS4 YFS5

ωFS (rad/sec) 4 4 

ζFS 26 14 

Breakout (lb) 1 1 

Table 3.3.1 Force Feel Characteristics (Johnston, 1988) [10] 

Cosine Wave 1 2 3 4 5 6 7 8 9 

Frequency (ωi rad/s) 0.467 0.701 1.17 1.87 3.51 7.01 11/2 14 18.7 

Amplitude (Ai) 15.2 15.2 15.2 7.6 3.04 0.76 0.38 0.228 0.152 

Relative Amplitude 1 1 1 0.5 0.2 0.05 0.025 0.015 0.01 

Table 3.3.2 Disturbance Sum of Cosines Parameters (Johnston, 1988) [10] 

The performance level to be met by each pilot was short periods of 1 to 2 degrees 

tracking error and peak errors less than 22 degrees. A Cooper Harper Pilot Rating 

(CHPR) was given by each pilot after each task was performed. 

 A simple block diagram, shown in Figure 3.3.4 below, represents the control 

apparatus used by the test subject to create a commanded roll angle. The block diagram 

includes the force feel system, a command gain which represents a roll rate per unit force, 

and the vehicle dynamics. This block diagram represents a position sensing control effort 

in which the deflection of the control inceptor controls the vehicle. The input to the 

vehicle dynamics is a commanded roll rate and the output is a roll angle of the vehicle. 

The roll rate is converted into a roll angle of the vehicle by the s term in the denominator 

of the vehicle dynamics. This acts as an integrator, which integrates a velocity (roll rate) 

into a displacement (roll angle). 
38 

2 2

1 /

2(.6)(22.4) (22.4)

K F S

s s   KFSKC

F D Pc

(  1)

	

s T s

e

R

s

Feel System

Command

Gain

Vehicle

Dynamics

Ф 

Figure 3.3.4 Effective Controlled Element (Johnston, 1988) [10]

 For the two test subjects that performed these experiments, the neuromuscular 

natural frequency was around 14 rad/s. The peak magnitude for the neuromuscular 

system was affected slightly by the feel system gradient. By increasing the control stick 

stiffness, a small increase in the peaking of the neuromuscular system occurred. It was 

shown that if the neuromuscular peak goes above the 0 db line at a phase angle close to 

-180 degrees, roll ratchet could occur. Figure 3.3.5 represents the neuromuscular 

amplitude ratio peaking as a function of frequency from the range of 11-19 rad/s. 

Figure 3.3.5 Amplitude Ratio Peak as a Function of Force Gradient Constant (Johnston, 1988) [10] 
39 

Figure 3.3.5 compares three different force gradients along with three different 

time delays added. The roll rate per unit force was kept at 10 deg/sec/lb and the vehicle 

dynamics were K/s dynamics. As shown, increasing the force gradient increases the 

neuromuscular peaking slightly. Also, the displacement sensing cases presented for the 

0.65 lb/deg force gradient case show greater neuromuscular peaking as opposed to force 

sensing configurations. 

 Tracking performance for the experiments was measured from the RMS roll error 

(σe) and the crossover frequency (ωc). The crossover frequency is the frequency at which 

the Pilot/Vehicle frequency response crosses the 0 db line. A higher crossover frequency 

corresponds with lower root mean square (RMS) tracking error. The manipulator control 

effort (σc) was also recorded as a performance measure. The Cooper Harper rating was 

used to obtain pilot ratings. The tracking bandwidth increased as the roll rate per unit 

force increased. At around 10 deg/sec/lb, the tracking bandwidth remains constant. This 

is shown in Figure 3.3.6. 

Figure 3.3.6 Task Bandwidth vs. Roll Command Gain (Johnston, 1988) [10] 
40 

Figure 3.3.6 represents the crossover frequency as a function of the roll rate per unit force 

gain. At a low roll rate per unit force, the pilot has a hard time moving the control 

inceptor to the proper position in a short time. The optimal command gains reported by 

Johnston (1988) [10] are between 10 and 20 deg/sec/lb. This report suggests that high 

stick forces, particularly consistent with the force gradient, limit how fast the pilot can 

compensate. For a higher force gradient, a higher roll rate per unit force is needed to 

allow for higher bandwidth control. 

 The measure of pilot workload was conducted using both the root mean square 

tracking error and the root mean square manipulator displacement or force input. A good 

measure of pilot workload is done by plotting the product of the tracking error and the 

manipulator input versus the reciprocal of the crossover frequency and the command 

gain. A plot of the pilot workload versus the reciprocal of the product of the command 

gain and the crossover frequency is shown in Figure 3.3.7. 

Figure 3.3.7 Workload vs. the Reciprocal of the Product of Roll Command Gain and Task Bandwidth 

(Johnston, 1988) [10] 
41 

The workload parameter is equal to the product of the tracking error and the manipulator 

input. Decreasing the crossover frequency or the command gain causes the pilot 

workload to increase. The Cooper-Harper ratings also show that a decrease in the 

command gain causes performance degradation. 

 The highest force gradient of 1.22 lb/deg causes higher pilot workload at a low 

roll command gain of 10 deg/sec/lb. The forces were too high to command fast 

maneuvers. The lower force gradient of 0.33 lb/deg caused large stick deflections and the 

command gain was increased to avoid the control stick going beyond the travel limits. 

The force gradient that had the best Cooper-Harper ratings from pilots was 0.65lb/deg. 

This trend is shown in Figure 3.3.8 below. As shown, the increase in command gains for 

the different force gradient cases corresponds to a lower Cooper-Harper rating. This 

suggests that increasing the command gain results in typically better pilot ratings within 

these experiments. For the highest feel gradient of 1.22 lb/deg, increasing the roll 

command gain leads to pilot induced oscillation PIO. 

Figure 3.3.8 Cooper Harper Rating vs. Roll Command Gain (Johnston, 1988) [10] 
42 

 Experiments were conducted on a center stick installed in the USAF NT-33 

aircraft, and were presented in Johnston (1988) [10]. The block diagram describing the 

experiments performed on the center-stick is shown in Figure 3.3.9. 

 

KC δa Ф 

F F

D

2 2 2(.6)( ) ( )

FS C

FS FS

K K

s s     2 2

1

2(.7)( ) ( ) CF CF s s    

	.0335 e (.15 1)

1

s s 

KFS = 4 lb/in KC = 10 and 20

deg/sec/lb

Command

Filter

Aileron

Servo

Figure 3.3.9 Center-Stick Experimental Setup (Johnston, 1988) [10] 

The input into this system is a force. A force sensing or displacement sensing task can 

both be performed. A force sensing configuration is where the force applied to the control 

inceptor commands the plant and a displacement sensing configuration involves the 

displacement of the control inceptor commanding the plant. For the displacement sensing 

configuration, the force feel dynamics convert the force input into a displacement of the 

control inceptor. The force system dynamics are represented by a second order system 

shown in Equation 3.3.4 (Johnston, 1988) [10] below. 

 

2 2 2(.7)( )

fs c

fs fs

K K

F s s



     Equation 3.3.4 

 

The term (Kfs) represents the feel system force gradient. The term (Kc) represents 

the roll command gain with units of deg/sec/lb. The term (ωfs) represents the force feel 

natural frequency. In this block diagram a command filter is optional. The command 

filter represents a second order transfer function in the form of Equation 3.3.5 (Johnston, 

1988) [10]. 
43 

 2 2

1

2(.7)( )

cf

cf cf cf F s s



     Equation 3.3.5 

 

The aileron servo block represents a delay added to the system. The 1/(s(.15s+1)) block 

represents the plant dynamics. The result of the effect that the feel system and filter 

dynamics has on the tracking bandwidth is shown below in Figure 3.3.10. 

Figure 3.3.10 Task Tracking Bandwidth as a Function of Feel System Natural Frequency (Johnston, 1988) [10] 

As shown, as the command is increased from 10 deg/sec/lb to 20 deg/sec/lb the tracking 

bandwidth increases. When the natural frequency of the force feel system is increased 

from 14 rad/s to 26 rad/s the tracking bandwidth decreases for the displacement sensing 

configuration. An increase in tracking bandwidth allows for better control of the plant 

dynamics. Although the tracking bandwidth changes dramatically when the natural 

frequency is increased, the tracking error does not change much between the two. The 

tracking error as a result of each configuration is shown below in Figure 3.3.11. 
44 

Figure 3.3.11 Task Tracking Error as a Function of Feel System Natural Frequency (Johnston, 1988) [10] 

 The tracking error does improve with an increase in the roll command gain from 

10 deg/sec/lb to 20 deg/sec/lb. The Cooper-Harper rating also corresponds with these 

results. As the roll command is increased, the Cooper-Harper rating improves. The 

Cooper-Harper ratings for each configuration are shown in Figure 3.3.12. The two 

configurations that have the best Cooper-Harper ratings and lowest tracking errors are the 

force feel system with a natural frequency of 14 rad/sec and 26 rad/sec, a roll command 

gain of 20 deg/sec/lb, force sensing configuration, and no command filter. 
45 

 Figure 3.3.12 CHPR as a Function of Feel System Natural Frequency (Johnston, 1988) [10] 

 The case for the 10 deg/sec/lb command gain shows a lower bandwidth for the 

higher natural frequency case, but shows a similar tracking error and a better Cooper 

rating than the lower natural frequency case. Test subject A consistently held a higher 

tracking bandwidth and lower tracking error. Also, test subject A held a more consistent 

control strategy. Looking at the performance of test subject A, it seems that the 14 rad/s 

feel system with no pre-filter has a slightly better tracking performance, and a higher 

bandwidth. Changing the force gradient to cause a lower control inceptor natural 

frequency can affect tracking performance. 

 Mitchell (1992) [16] reported that in order to obtain a Level 1 Handling Qualities 

Rating (HQR), a minimum control inceptor natural frequency should be set to 10 rad/s 

for a control inceptor mass of 5 lbm (0.0133 lb•s2

/in). Typically with a low force 

gradient, a high natural frequency is not obtainable for a low control inceptor mass. Most 
46 

experimental aircraft show that a higher frequency control inceptor with a low mass 

typically has a higher force gradient. If the mass of the control inceptor is very light, then 

more inceptor deflection will occur. 

 LATHOS is an abbreviation for Lateral High Order System Experiments which 

are discussed by Mitchell (1992) [16]. A USAF NT-33 aircraft was used during these 

experiments. The best reported system had 1.5 lb control inceptor breakouts, a 3.81 lb/in 

force gradient and an optimal command gain of 6.6 to 8.4 deg/sec/lb. In this report it was 

suggested that the command gain should be set just above 8 deg/sec/lb, the force gradient 

should be set just below 4 lb/in, and to use some nonlinearity in the force gradient. 

 In the literature, it was shown that the neuromuscular system can be characterized 

with a transfer function that matches results from experiments involving human test 

subjects. The proposed characteristics of a roll compensatory task found throughout the 

literature were utilized when designing a quasi-transfer of training study discussed in 

Chapter 4. In conclusion, a natural frequency between 14 and 26 rad/s and a damping 

ratio of 0.7 leads to high performance from each test subject. The roll command of the 

control inceptor should be set just above 8 deg/sec/lb and the force gradient should be set 

to 4 lb/in for the high fidelity control inceptor. It was shown that these characteristics 

produce the best tracking error and task bandwidth for the compensatory tasks conducted. 

By increasing control inceptor roll command gain to 20 deg/sec/lb it was shown to 

improve tracking bandwidth. The increased roll command gain was shown to increase 

pilot induced oscillation (PIO). To avoid neuromuscular ratcheting and PIO, a control 

inceptor sensitivity of 10 deg/sec/lb is chosen. 
47 

Chapter 4 - Design of Transfer of Training Study 

4.1 Introduction 

 

The design of the experimental task to test the effectiveness of transfer of training 

on a simulator will be discussed within this chapter. This particular transfer of training 

experiment is focused on the control loader system and its interaction with the 

neuromuscular system. To focus in on the particular effect of the neuromuscular system 

by altering the control loader dynamics, the simulator is fixed base and a simple out the 

window display is used. A roll disturbance compensatory task is used within the 

experiments. A description of the roll compensatory task as well as the parameters that 

were determined to design the experiment is presented within this chapter. 

4.2 Roll Disturbance Compensation Task 

A quasi transfer of training experiment is conducted where a high and low fidelity 

control inceptor is interchanged to test transfer of training effectiveness. The reason for 

pursuing a study in the force feel system provided by a control loader is to develop an 

understanding of the prominence of force feedback cues to the pilot. To test each human 

test subject, a disturbance compensatory roll tracking task with 1/s and 1/s2

 plant 

dynamics will be used. The quasi transfer of training study consists of training test 

subjects to null a roll disturbance maintaining level flight using a high and low fidelity 

control loader simulation. The reason for using a roll disturbance compensatory task is to 

keep the task as simple as possible to mitigate effects other than those caused by the 

neuromuscular system of the human test subject. Implementation of the experiment will 

be described in the following sections. 
48 

The roll disturbance compensatory task used in the experiment is shown in 

Figure 4.2.1. A disturbance consisting of a sum of nine sinusoids deflects a bank angle 

line viewed on the display. The disturbance input that is applied is discussed in section 

4.5. 

Feel 

System Pilot Kc

Plant 

(1/s or 1/s2

)

Forcing Function 

(Sum of Sines)

Commanded Roll Rate (Degrees/sec) or 

Roll Acceleration (Degrees/sec2

) 

Roll Angle 

(Degrees)

Feel 

System

Stick Displacment (in)

Force 

(lb)

Display

Breakout 

Force (1.5 lb)

+

-

0

+

+

Figure 4.2.1 Developed Roll Disturbance Compensatory Tracking Task 

The commanded plant input is equal to the test subject control inceptor deflection 

multiplied by a roll rate per inceptor deflection command gain (Kc). The commanded 

plant input is then passed through plant dynamics to produce a roll angle. The roll angle 

of the vehicle is displayed as an angle displaced from an artificial horizon line 

representing level flight. The visual feedback and proprioceptive feedback are the main 

cues to the test subject. The test subject will have to compensate for this disturbance and 

maintain level flight, an angle of zero degrees from the horizon line. For 1/s2

 dynamics 

the roll command gain (Kc) of the plant will represent roll acceleration per unit deflection 

of the control inceptor. 
49 

The displayed roll angle causes the test subject to output a force from muscle 

activation on the control inceptor. The deflection of the control inceptor in inches is 

multiplied by a roll command gain (Kc). The roll command gain converts the deflection 

of the control inceptor to a roll rate command ( c ) and roll acceleration command ( c ) 

for 1/s and 1/s2

 plant dynamics respectively. The roll rate command ( c ) and roll 

acceleration command ( c ) are displayed as a roll angle (φ) after being passed through 

1/s and 1/s2 dynamics respectively. 

The roll command gain Kc will be set initially to a value of 40 deg/in•s and 40 

deg/in•s2 for plant dynamics of 1/s and 1/s2 respectively. When the deflection output of 

the control inceptor in inches is multiplied by the roll command gain it creates a roll rate 

given in deg/s and roll acceleration in deg/s2

 for 1/s and 1/s2 dynamics respectively. For 

both 1/s and 2 1/ s plant dynamics, the roll command gain is adjusted during preexperiment trials. The roll command gain is kept constant for both 1/s and 1/s2 plant 

dynamics. 

In section 4.3, the determination and implementation of the force feel parameters 

on the McFadden control loader are discussed. The Kfs in the block diagram represents 

the force gradient and Kc represents the roll command gain. When the test subject 

deflects the control inceptor, a roll rate command or roll acceleration command is 

produced which will then be integrated once for the 1/s plant dynamics or integrated 

twice for the 1/s2

 plant dynamics. The integration of the roll rate command or roll 

acceleration command can be obtained using the Euler numerical integration method 

represented by Equation 4.2.1. 
50 

 n nn 1 h  "  

Equation 4.2.1 

 The term ( n1 ) represents the new calculated roll angle at every time step. The 

current roll angle ( n ) is summed with the current roll rate ( n  ) multiplied by the step 

size (h). The roll angle output ( c ) commanded by the pilot is summed with the 

disturbance which drives the image generation. The roll rate at each time step ( n  ) is 

represented by Equation 4.2.2. The term Xc represents the commanded control inceptor 

displacement in inches. The term Kc represents the roll command gain in deg/s•in and 

deg/s2

•in for 1/s and 1/s2 plant dynamics respectively. 

 

 

Equation 4.2.2 

4.3 Force Feel Parameter Determination 

4.3.1 High Fidelity Control Loader Parameters 

 

 The high fidelity control loader parameters were adapted from the literature 

presented in the literature review. These parameters were determined to produce a good 

task performance from test subjects within the many experiments conducted in the 

literature. Two of the characteristics that determined good flying performance were test 

subject tracking error and tracking bandwidth. Throughout the literature, many 

experiments were conducted in which different control inceptor characteristics were 

tested. The parameters were chosen that produced the smallest tracking error, and the 

highest tracking bandwidth. 

 The parameters that defined a high fidelity control inceptor were a force gradient 

of 4 lb/in, a damping ratio of 0.7, a natural frequency of between 14 and 26 rad/s, and a 

 n cc

  " X K
51 

breakout force of 1.5 lb. These parameters lead to a system that has a small peak 

overshoot and that settles to its final value fairly quick. A step response of the high 

fidelity control inceptor with a natural frequency set to 26 rad/s is shown below in Figure 

4.3.1. 

 Figure 4.3.1 Simulated High Fidelity Control Loader Step Response 

 Shown in Figure 4.3.1, an overshoot of around 4.6 corresponds to a damping ratio 

of 0.7. The natural frequency is difficult to measure using the time response so the 

frequency response method is used. The natural frequency of the system should be 

anywhere between 14 rad/s and 26 rad/s to be considered a high fidelity control inceptor. 

Since the mass changes from simulator to simulator it will be difficult to maintain the 

natural frequency without changing the inertia of the control inceptor. The inertia of a 

High Fidelity Control Inceptor Simulated Step Response

Time (sec)

Control Inceptor Deflection (inches)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

System: tf1

Peak amplitude: 1.05

Overshoot (%): 4.6

At time (sec): 0.17
52 

system can only be increased; therefore only allowing the natural frequency to be 

decreased while maintaining the force gradient. 

4.3.2 Low Fidelity Control Loader Parameters 

For the control loader quasi transfer of training experiment, the low fidelity 

parameters are determined from a computer joystick. The computer joystick used is a 

Logitech Force 3D Pro and is used frequently in flight simulator games. These 

parameters are all measured in the horizontal direction of the computer joystick. The final 

measured parameters of the computer joystick are a natural frequency of 34.5 rad/s, a 

damping ratio of 0.135, and a force gradient of 0.7 lb/in. The damping ratio and 

corresponding natural frequency are found using the log decrement. 

The first step in determining the natural frequency is to calculate two successive 

peak times. In this case, two successive zero crossings on each of the peaks are used to 

find the period of the transient decay of the computer joystick. The damped frequency is 

found using the formula 2π/T where T is the period of transient oscillation. The natural 

frequency is then calculated using 2 / 1   n d  	 where (ωd) is the damped natural 

frequency and (ζ) is the damping ratio found using the log decrement. The force gradient 

is found using a force gauge to measure the maximum force at the maximum deflection 

of the joystick. 

 To obtain the time response of the computer joystick, the program MMS (Man 

Machine Systems) Laboratory was used as a baseline test. The MMS Laboratory software 

was created to test different compensatory tasks. The program runs a simple background 

with a cursor and a target box in which the person has to compensate for a disturbance of 

the plant. The program has the ability for keyboard, mouse, or joystick input from the 
53 

subject performing the tests. The measured response from the program is the power 

spectral density of the input and output, input response from the joystick, and the tracking 

error. The computer joystick is held at its maximum deflection in either direction. It is 

then released when the program is run to obtain the transient behavior of the joystick. 

This type of test is referred to as a free release response. 

Using the time response of the computer joystick, the natural frequency and the 

damping ratio is calculated. To find the force gradient, the force is found at the maximum 

deflection of the joystick using a force gauge. The force gradient is then found by 

dividing the maximum force by the maximum deflection of the joystick. The output of 

the joystick is not known since it communicates through USB. The USB accepts packets 

of data in bits, which can represent a voltage, current, or resistance from the joystick. 

Since the log decrement is utilized to obtain the damping ratio and natural frequency, the 

ratio between two successive peak amplitudes should be the same if a voltage, current or 

resistance is being read by the computer. 

The MMS Laboratory software gave results that were not consistent for each run. 

Successive peak times varied between 0.21seconds and 0.25 seconds which changed the 

damped frequency and therefore natural frequency. From 0.21 seconds to 0.25 seconds 

successive peak time, the difference in natural frequency differs by 4.83 rad/s. The time 

response obtained using MMS Laboratory software is shown in Figure 4.3.2. The 

maximum deflection of the computer joystick is normalized in the MMS Laboratory 

software by dividing the response by the maximum deflection. The results for the MMS 

Laboratory software show a damping ratio of 0.133, and a natural frequency of 26.18 

rad/s. 
54 

 Figure 4.3.2 Logitech Computer Joystick Transient Response O btained from MMS Laboratory 

To obtain a more accurate measurement of the computer joystick, a built-in 

program in Labview [20] that measures the input of the joystick was used. A built-in 

function was used to measure the length of time the program ran. This timer was verified 

against a stopwatch and computer time to make sure that it was measuring the time 

accurately. A while loop used a metronome device which set the duration of each 

iteration that occurred. This was utilized to find the sample time and to determine the 

accuracy of collecting data at specific time intervals. 

The while loop was used to collect data at a specific time rate so that each sample 

of the joystick data represented a set time that had elapsed. The while loop time was 

compared to the time selected for each iteration. The time response for the computer 

joystick obtained using Labview [20] is shown in Figure 4.3.3. The y-axis is the 

normalized deflection of the computer joystick. The deflection of the computer joystick 

0.8 1 1.2 1.4 1.6 1.8 2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Time (sec)

Control Inceptor Deflection (Normalized)

Time Response of Computer Joystick
55 

was normalized by dividing the response by its maximum deflection. The x-axis 

represents the time in seconds. 

 

 Figure 4.3.3 Logitech Computer Joystick Transient Response O btained using Labview [20] 

The results obtained using Labview [20] were more consistent for successive peak 

times. This gave a more accurate natural frequency. The results for the transient response 

obtained using Labview [20] were a damping ratio of 0.135, and a natural frequency of 

34.5 rad/s. Since the mass of a control inceptor from simulator to simulator is never the 

same; it is important to maintain the force gradient which corresponds to the natural 

frequency. Since typical control inceptors in simulators have a greater mass, the 

obtainable natural frequency will be much lower. 

The average natural frequency obtained using Labview [20] of approximately 34 

rad/s might not be able to be replicated within the control loaders available with such a 
56 

low force gradient. Also, the low damping ratio of 0.135 and force gradient of 0.7 lb/in 

can cause the control stick to oscillate. The low fidelity control inceptor will be 

represented by a low force gradient, a low damping ratio, and a low natural frequency. 

These parameters are implemented and analyzed in Section 4.4 to ensure proper setup of 

the control loader for further experimental testing. 

4.4 Analysis of Control Loader Parameters 

To verify that the control loader parameters are implemented correctly, a 

frequency response and step response of the control loader for both the high fidelity and 

low fidelity system is required. The control inceptor dynamics have to be such that they 

match the characteristics that are defined below in Table 4.4.1.

Table 4.4.1 Control Inceptor Characteristics 

 

To perform either a frequency response or a step response, a signal is injected into 

the control loader to obtain an output response. The control loader used for these 

experiments was manufactured by McFadden Systems. This type of control loader uses a 

force command servo as opposed to a position command servo. To inject a signal, the 

Simulation Evaluation System (SIMES) was used. The SIMES unit has the capability to 

output analog signals through an analog output port. Wiring from the analog output on 

the SIMES unit is connected to the control loader circuitry. The SIMES unit analog 

McFadden Control Loader: 

Control Inceptor 

Fidelity: 

Force 

Gradient: 

Damping Ratio ζ Damping 

Coefficient β:

Breakout 

Force: 

High Fidelity 4 lb/in 0.7 0.25 lb•s/in 1.5 lb 

Low Fidelity 0.7 lb/in 0.135 0.0243 lb•s/in 0 lb 
57 

output is connected at the force command summing junction within the control loader 

circuitry shown below in Figure 4.4.1. 

Simplified Force

Servo Control Loader

Model

+

-

Servo Drive Servo

Valve

Hydraulic

Actuator

Force

Transducer

Position

Transducer

-

Cable +

Simulation

Aft Mass Simulation

Force Feedback

Force CMD

AFT Mass Position

FWD Mass Position +

+

 Figure 4.4.1 Force Servo Control Loader Model (Takats, 2011) [18] 

 The input voltage to the control loader circuitry is chosen so that the control 

inceptor deflects 10% of its maximum travel in one direction. The maximum travel of the 

control inceptor was set to 2 inches in either direction so 10% of travel is equal to 0.2 

inches. The input analog signal is created within Matlab [21] as digital data. This data 

then passes through a digital to analog converter which then goes into the control loader 

circuitry. 

The step response input that was created in Matlab [21] is actually a series of 

pulses with a 10 second pulse width. The response of the control loader to the pulse train 

results in a sharp spike right when the signal is injected. The reason for a sharp spike 

when injecting a step input is that a step input has a large change in amplitude very 

quickly and the control loader system might not be able to handle a fast changing input. 

To simplify the results, a free release response is used instead. A free release response 
58 

consists of manually deflecting the control inceptor to its maximum deflection in one 

direction and releasing the control inceptor. The SIMES unit is used to record the 

position of the control inceptor straight from the position transducer within the control 

inceptor. 

To calculate the damping ratio using the free release response either the maximum 

percent overshoot or the logarithmic decrement method is utilized. To find the damping 

ratio (ζ) using the maximum percent overshoot, Equation 4.4.1 is used. The term PO 

refers to the maximum percent overshoot. 

 

2 2

ln( /100)

(ln( /100))

PO

PO



#

	 

 Equation 4.4.1 

To obtain the damping ratio using the logarithmic decrement method, Equation 

4.4.2 is used first. The term (δ) represents the logarithmic decrement. The term (n) refers 

to the number of periods between two successive peaks. The terms (x0) and (xn) refer to 

the first peak amplitude and the successive peak amplitude n periods away. 

 

1 0 ln

n

x

n x

  Equation 4.4.2 

After the logarithmic decrement is calculated, the damping ratio (ζ) is found using 

Equation 4.4.3. 

To obtain the frequency response, a frequency sweep is first conducted. A 

frequency sweep consists of inputting a constant small amplitude sinusoid with varying 

 

2

1

2 1



#






    
  

Equation 4.4.3 
59 

frequencies. To implement this on the McFadden controller the following procedure 

shown in Figure 4.4.2 is conducted. 

- +

Force

Command Servo

Drive

Servo

Valve

Hydraulic

Actuator

Force

Transducer

Force Feedback

Record

Input &

Feedback

 Figure 4.4.2 Frequency Sweep Configuration (Takats, 2011) [18] 

 A sinusoid with varying frequencies is fed into the control loader force command 

summing junction and the force feedback measured by the control inceptor force 

transducer is recorded. Two different sinusoids were chosen for the high fidelity and low 

fidelity frequency sweep. The amplitude and frequency range for both the high fidelity 

and low fidelity frequency sweep are shown in Table 4.4.2. 

Control Loader 

Fidelity 

Frequency Range 

0.1 to 1 rad/s 1-18 rad/s 19-21 rad/s 22-25 rad/s 

High Fidelity Frequency 

Interval 

0.1 rad/s 

interval 

1 rad/s 

interval 

0.1 rad/s 

interval 

1 rad/s 

interval 

Amplitude 1 inch 1 inch 1 inch 1 inch 

Control Loader 

Fidelity

Frequency Range 

0.1 to 1 rad/s 1-7 rad/s 7-9 rad/s 9-20 rad/s 

Low Fidelity Frequency 

Interval 

0.1 rad/s 

interval 

1 rad/s 

interval 

0.1 rad/s 

interval 

1 rad/s 

interval 

Amplitude 1 inch 1 inch 1 inch 1 inch 

Table 4.4.2 Frequency Sweep Input Sinusoid Formulation 

Once the input force command and the force feedback are recorded, an offline 

analysis of the input/output is conducted. Using a Fast Fourier Transform technique 

within Matlab [21], the time domain signals are converted to the frequency domain. The 
60 

Matlab [21] code to accomplish this technique is located in Appendix D. The command 

in Matlab [21] referred to as spectrogram computes the Fast Fourier Transform and also 

applies a window function to a signal. The Fast Fourier Transform is computed for both 

the input and the output of the system. The cross spectrum which relates the similarity of 

two waveforms is then computed. The equation to compute the cross spectrum is shown 

in Equation 4.4.4. 

Cross Spectrum FFT Input FFT Output  $ ( )* ( ) Equation 4.4.4 

The auto spectrum which is equal to the cross spectrum of a signal with itself is computed 

for the input. The equation to compute the auto spectrum is shown in 

Equation 4.4.5. 

AutoSpectrum FFT Input FFT Input  $ ( )* ( ) 

 

Equation 4.4.5 

The term FFT(Input)* denotes the complex conjugate of the Fast Fourier Transform of 

the Input. Next, the frequency response function (FRF) is obtained by using Equation 

4.4.6. 

 

Cross Spectrum FRF

Auto Spectrum  

Equation 4.4.6 

From the frequency response function (FRF), both the magnitude ratio in dB and the 

phase between the Output and Input Signals can be calculated. The magnitude in dB is 

obtained by using Equation 4.4.7.

 MagnitudedB FRF  $ 20 log ( ) 10 

 

Equation 4.4.7 

To find the phase difference in degrees between the Input and Output Equation 4.4.8 is 

used. 
61 

 

1 Phase imag FRF real FRF pi tan ( ( ) / ( )) (180 / ) 	  $ 

 Equation 4.4.8 

The terms imag(FRF) and real(FRF) represent the imaginary and real part of the FRF 

respectively. 

 To test the above signal processing technique, a frequency sweep was conducted 

on the control inceptor dynamics within Simulink [22]. The response using the above 

signal processing technique is compared with the true response using the transfer 

function. The simulated frequency response of the high fidelity control inceptor is shown 

below in Figure 4.4.3 using both the signal processing technique and the transfer function 

response. The transfer function used to simulate the high fidelity control inceptor is 

shown in Equation 4.4.9. The natural frequency was found using the square root of the 

defined force gradient of 4 lb/in divided by the mass of the McFadden control inceptor 

(0.01 lb•s2

/in). 

 

2

2 2

(20)

s s   2(.7)(20) (20)

 

Equation 4.4.9 

The frequency response is limited from 0.0159 to 4 Hz (0.1 to 25 rad/s). The 

frequency is limited to this range to decrease computation time for the signal processing 

technique. Also, the control loader is limited to a 5 Hz (31 rad/s) input signal. The 

average error in magnitude between the simulated and true frequency response is 0.0014 

dB. The average error in phase between the signal processed and true frequency response 

is 0.00015 degrees. 
62 

 Figure 4.4.3 Simulated High Fidelity Frequency Response 

 The simulated frequency response for the low fidelity control inceptor is shown in 

Figure 4.4.4. The transfer function used to simulate the low fidelity control inceptor is 

shown in Equation 4.4.10. The natural frequency was obtained using a force gradient of 

0.7 lb/in and the McFadden control inceptor mass of 0.01 lb•s2

/in. 

 

2

2 2

(8.366)

s s   2(.135)(8.366) (8.366)

 

Equation 4.4.10 

The response for the low fidelity control inceptor using the signal processing technique 

matches the true response very well. The average magnitude and phase error between the 

signal processed response and the true response is equal to 0.0035 dB and 0.09 deg 

respectively. The signal processing technique produces good results, but has issues with 

noisy signals. 

10-1 100 101 102 -6

-4

-2

0

2

Frequency Response of High Fidelity Control Loader

Amplitude (dB)

Frequency (rad/s)

Experimental Response

Simulated Response

10-1 100 101 102 -150

-100

-50

0

Phase (Degrees)

Frequency (rad/s)
63 

 Figure 4.4.4 Simulated Low Fidelity Frequency Response 

Another technique used when computing the frequency response is to select the 

different frequency sinusoids within the input and output of the control loader system and 

compare the magnitudes and phase difference between the two. This results in one value 

per frequency producing a smooth frequency response. 

 To measure the force gradient of both the high fidelity and low fidelity control 

inceptors, a push/pull test was conducted. To perform this test the control inceptor is 

pushed to its maximum deflection in one direction then pulled to its maximum deflection 

in the other direction. Both the force applied to the control inceptor in pounds and its 

position in inches are recorded. The force applied is plotted against the position of the 

control inceptor. The slope of this plot is equal to the force gradient. 

10-1 100 101 102 -20

-10

0

10

20

Frequency Response of Low Fidelity Control Loader

Amplitude (dB)

Frequency (rad/s)

Experimental Response

Simulated Response

10-1 100 101 102 -200

-150

-100

-50

0

Phase (Degrees)

Frequency (rad/s)
64 

4.4.1 Experimentally Obtained High Fidelity Characteristics 

 The characteristics for the high fidelity control inceptor that were experimentally 

measured from the McFadden control inceptor are presented within this section. The first 

measured characteristic is the force gradient obtained by plotting the force applied versus 

the displacement of the control inceptor. The force versus displacement for the high 

fidelity control inceptor is shown in Figure 4.4.5. 

 Figure 4.4.5 High Fidelity Force vs. Displacement 

As shown in Figure 4.4.5, the control inceptor contains hysteresis. The control 

inceptor follows a different force vs. displacement path when being loaded as opposed to 

being unloaded. The hysteresis is caused by the difference in energy dissipation due to 

viscous damping when loading the control inceptor as opposed to unloading the control 

inceptor. The area in between the force vs. displacement hysteresis loop represents the 

energy loss of the system ΔE. Using the formula ΔE = πcωX2

, the damping coefficient 

can be calculated. The term X represents the amplitude of motion, c represents the 

damping ratio, and ω represents the natural frequency. The loss of damping energy in one 

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-10

-8

-6

-4

-2

0

2

4

6

8

10

High Fidelity Force vs. Displacement

Displacement (inches)

Force (lbs)
65 

direction makes it harder to load the control inceptor as opposed to unloading the control 

inceptor. The force gradient obtained from the slope in Figure 4.4.5 is equal to 4.09 lb/in. 

The implemented force gradient for the high fidelity control inceptor is 4 lb/in. At zero 

inches of deflection, there exists a non-linearity corresponding to the breakout force. The 

control inceptor starts deflecting when the force applied is around 1.5 lb.

 To obtain an effective mass of the control inceptor and to investigate the effect 

that friction has on the damping, a free release was conducted with the damping 

coefficient set to a low value of 0.01 lb•s/in. The free release for this system is shown in 

Figure 4.4.6. By obtaining the effective mass, the damping coefficient corresponding to 

the defined damping ratio of 0.7 for the high fidelity control inceptor can be calculated. 

The low damping ratio allows multiple peak amplitudes to appear in the transient 

response allowing for the investigation of the change in damping ratio as the motion of 

the control inceptor decreases. 

Figure 4.4.6 High Fidelity Free Release Response with Low Damping Ratio 

2 2.5 3 3.5 4 4.5 5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Experimental High Fidelity Free Release Response

Time (sec)

Control Inceptor Position (inches)
66 

Using every two successive peaks, the logarithmic decrement was used to 

determine the damping ratio as the amplitude of motion decreases. Since the force 

gradient of 4 lb/in was confirmed, this was used along with the natural frequency 

obtained from every two successive peaks to find the effective mass. The effective mass 

is then calculated using Equation 4.4.11.

 

e 2

n

k

m

  

Equation 4.4.11 

A list of the damping ratios for different successive peaks along with the effective mass is 

shown in Table 4.4.3. As shown, the damping ratio increases as the motion of the control 

inceptor becomes smaller. This can be due to coulomb friction that exists very close to 

the neutral position of the control inceptor. 

Successive 

Peaks 

Logarithmic Decrement 

δ

Damping Ratio 

ζ 

Natural Frequency ωn 

(rad/s) 

1st 0.446 0.071 18.311 

2nd 0.537 0.085 18.493 

3rd 0.624 0.099 18.408 

4th 0.748 0.118 18.34 

5

th 0.55 0.087 17.918 

Successive 

Peaks 

Effective Mass (lb•s2/in) 

1st 0.0119 

2nd 0.0117 

3rd 0.0118 

4th 0.0119 

5th 0.0125 

Table 4.4.3 Acquired High Fidelity Effective Mass with Low Damping Ratio 

For larger motion, the friction does not affect the damping nearly as much as for 

low amplitude motion. This occurs because at a higher deflection of the control inceptor, 

a higher restoring force overcomes the resistance due to friction. The effective mass of 

the control inceptor generally stays consistent and is not affected by an increase in the 
67 

damping ratio. The effective mass was compared with previous results conducted by 

NASA Langley Research Center, and the average values of the effective mass have a 

difference 0.00197 lb•s2

/in. 

The free release response was conducted for the high fidelity control inceptor with 

an implemented damping coefficient of 0.0243 lb•s/in. The response is shown below in 

Figure 4.4.7. As shown, the response contains a small amplitude peak and settles fairly 

quickly. This response is typical of a highly damped second order system. The overshoot 

for this system is equal to 4.022% which corresponds to a damping ratio of 0.715. This is 

consistent with the damping ratio of 0.7 that is implemented for the high fidelity control 

inceptor. Because of friction, the measured damping ratio is slightly larger. 

Figure 4.4.7 Experimental High Fidelity Free Release Response 

The frequency sweep technique described above in Section 4.4 was implemented 

on a McFadden control loader to verify the control inceptor dynamics before conducting 

4.5 5 5.5 6

-2.5

-2

-1.5

-1

-0.5

0

0.5

Experimental High Fidelity Free Release Response K= 4 lb/in  = .7

Time (sec)

Control Inceptor Position (inches)
68 

the main transfer of training study. The input frequency sweep was developed in Matlab 

[21] with a force amplitude of 1.5 lbs and the frequencies of the sinusoids presented in 

Table 4.4.2 in Section 4.4. The input represents a force command to the force servo of the 

control loader. The output is the measured force from the force transducer located within 

the McFadden control inceptor. 

Using the signal processing technique produces a noisy Bode diagram. This is 

mitigated by plotting only the phase and magnitude at the frequency intervals used in the 

frequency sweep. The damping coefficient used for the high fidelity was lowered to .01 

lb•s/in. The damping coefficient was lowered so that a resonance peak can be seen 

around the natural frequency of the system. Otherwise, a system with a damping ratio of 

0.7 has no peaking and therefore harder to locate the resonance peak. 

From the free release response of the high fidelity control inceptor with the 

damping coefficient lowered to 0.01 lb•s/in, a damping ratio of 0.118 was obtained. 

Using the obtained force gradient of 4.09 lb/in and an effective mass of 0.0119 lb•s2

/in, 

the calculated natural frequency is equal to 18.54 rad/s. A damping ratio of 0.118 along 

with a natural frequency of 18.54 rad/s is used when simulating the frequency response. 

Using the signal processing technique the following frequency response is obtained in 

Figure 4.4.8. 
69 

Figure 4.4.8 Experimental High Fidelity Frequen cy Response with Low Damping Ratio 

The resonance peak frequency is equal to 18.32 rad/s, which corresponds to a natural 

frequency of 18.57 rad/s. This value is 0.16% different than the natural frequency 

obtained from the simulated frequency response. 

The phase relation between the input and output obtained experimentally shows 

some phase lead at around 7 rad/s. There is a time shift that occurs in the output when the 

input sinusoid changes frequencies. It could be that the momentum of the control inceptor 

keeps the control inceptor from responding to a change in frequency promptly. The time 

response of the input and output shows the input leading the output at this frequency. 

10-1 100 101 102 -5

0

5

10

15

Frequency Response of High Fidelity Control Loader

Amplitude (dB)

Frequency (rad/s)

Experimental Response

Simulated Response

10-1 100 101 102 -200

-150

-100

-50

0

50

Phase (Degrees)

Frequency (rad/s)
70 

4.4.2 Experimentally Obtained Low Fidelity Characteristics 

 The same tests performed above for the high fidelity control inceptor were again 

performed for the low fidelity control inceptor. One of the tests performed was the force 

vs. displacement test. Shown below in Figure 4.4.9 is the force vs. displacement of the 

low fidelity control inceptor. 

 Figure 4.4.9 Experimental Low Fidelity Force vs. Displacement 

The mean slope of the low fidelity control inceptor force vs. displacement was 

found to be 0.66 lb/in which is 0.04 lb/in different than the defined value of 0.7 lb/in. The 

non-linearity at 0 inches of deflection that is present for the high fidelity control inceptor 

is not present for the low fidelity control inceptor. The breakout force that causes the nonlinearity is set to 0 lb for the low fidelity control inceptor. There still exists hysteresis for 

the low fidelity control inceptor caused by energy dissipation while unloading the control 

inceptor due to viscous damping. 

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-1.5

-1

-0.5

0

0.5

1

1.5

Low Fidelity Control Inceptor Force vs. Displacement

Control Inceptor Deflection (inches)

Force Input (lbs)
71 

 The free release response was also conducted and is shown in Figure 4.4.10. As 

shown, the free release response for the low fidelity control inceptor represents a low 

damped system. 

Figure 4.4.10 Experimental Low Fidelity Free Release Response 

The overshoot of 48.2% corresponds to a damping ratio of 0.226. Using the log 

decrement on the first two successive peaks a damping ratio of 0.233 is obtained. The 

defined damping ratio is equal to 0.135 but because of added friction to the system, the 

damping ratio is larger than what is defined. The natural frequency obtained from the free 

release response is equal to 5.26 rad/s. 

Both the experimentally obtained frequency response using a signal processing 

technique proposed in Section 4.4 and a simulated response are shown in Figure 4.4.11. 

A damping ratio of 0.226 and a natural frequency of 5.26 rad/s that are both obtained 

from the free release response (Figure 4.4.10) are used to simulate the frequency 

0 1 2 3 4 5 6 7

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Experimental Low Fidelity Free Release Response K= .7 lb/in c= .0243 lb•s/in

Time (sec)

-

-0

0

Control Inceptor Deflection (inches)
72 

response. The peak magnitude of the simulated and experimental frequency response is 

equal to 7.125 and 7.4 dB respectively. The peak magnitude corresponds to the damping 

ratio of the system. The simulated peak magnitude corresponds to a damping ratio of 

0.226. A peak magnitude of 7.4 dB corresponds to a damping ratio of 0.219. Therefore 

the difference is equal to 3%. 

Figure 4.4.11 Experimental Low Fidelity Frequency Response 

The peak magnitude for the simulated and experimental response occurs at 5 rad/s 

and 4.965 rad/s respectively. The natural frequencies that correspond to the peak natural 

frequencies for the simulated and experimental responses are equal to 5.26 rad/s and 5.24 

rad/s respectively. The difference between these two natural frequencies is equal to 0.4%. 

 The expected natural frequency for this system using the effective mass of the 

control inceptor of .0119 lb•s2

/in and a force gradient of 0.7 lb/in is equal to 7.67 rad/s. 

The control inceptor contains friction which effectively damps the system which acts as 

an added mass. The calculated effective mass for the low fidelity control inceptor is equal 

10-1 100 101 102 -60

-40

-20

0

20

Low Fidelity Control Inceptor Frequency Response

Frequency (rad/s)

Amplitude (db)

Experimental Response

Simulated Response

10-1 100 101 102 -200

-150

-100

-50

0

Phase (degrees)

Frequency (rad/s)
73 

to 0.025 lb•s2

/in. The effective mass for the low fidelity control inceptor is 0.0131 lb•s2/in 

greater than the high fidelity control inceptor. 

4.5 Disturbance Input & Performance Metric Tests 

The disturbance shown below in Table 4.5.1 was chosen from an experiment 

conducted by Bailey (1990) [1]. The disturbance consists of a series of sine waves in the 

form of sin( ) %A t i i  with different amplitudes and frequencies. This allows the task to be 

pseudo random which tests each of the test subjects for a wide range of human 

performance. This also removes any effect of improved performance solely to learning 

the task. 

Plant 

Dynamics 

Sine Wave 1 2 3 4 5 6 7 8 9 

1/s & 1/s2 Frequency (ωi 

rad/s) 

.467 .701 1.17 1.87 3.51 7.01 11/2 14 18.7 

Amplitude 

(Ai) 

15.2 15.2 15.2 7.6 3.04 .76 .38 .228 .152 

Table 4.5.1 Sum of Sines Disturbance Input 

The frequencies for each sinusoid were chosen to effectively test the neuromuscular 

system. The neuromuscular system is represented by a second order mass damper with a 

natural frequency typically around 14 rad/s. The sum of sines disturbance includes the 

frequency of 14 rad/s. 

 The response of the disturbance is shown below in Figure 4.5.1. The root mean 

square (RMS) of the disturbance over a 30 second interval is equal to 20.85 deg. The 

maximum roll angle that occurs from the disturbance input is 38 deg. The disturbance 

switches direction 10 times over the duration of 30 seconds. 
74 

Figure 4.5.1 Plot of Roll Angle Disturbance 

As shown in Figure 4.5.1, the disturbance reaches approximately the same 

maximum amplitude in both directions and is evenly centered around zero degrees roll 

angle. The disturbance contains numerous low frequencies as compared to higher 

frequencies. 

The disturbance input was implemented within the MMS (Man Machine Systems) 

Laboratory software. This software allows for the testing of compensatory tracking tasks 

with test subjects. It has the ability to test 1/s and 1/s2

 plant dynamics with a disturbance 

input. It can measure performance attributes such as RMS tracking error, RMS input, 

STD input, and time on target. A Logitech computer joystick, the same used to obtain the 

low fidelity control inceptor characteristics, was used to test the ability to null the 

disturbance. 

 At the same time that the disturbance was tested, the performance metric RMS 

tracking error was tested to determine if the test subject reached an asymptotic tracking 

error. To test the disturbance within the MMS Laboratory software, it was scaled down to 

0 5 10 15 20 25 30 -40

-30

-20

-10

0

10

20

30

40

Disturbance Input (Sine Function) 30 sec

Time (sec)

Roll Angle Output (deg)
75 

stay within the limits of the display. The disturbance that is implemented within the 

MMS Laboratory software is normalized. The full deflection of the cursor on the display 

is represented by an amplitude of 1. The disturbance was normalized by dividing by the 

maximum amplitude multiplied by a factor of 5. The disturbance that was implemented 

within the MMS Laboratory is shown below in Table 4.5.2.

Plant 

Dynamics 

Sine Wave 1 2 3 4 5 6 7 8 9 

1/s & 1/s2 Frequency (ωi 

rad/s) 

.467 .701 1.17 1.87 3.51 7.01 11/2 14 18.7 

Amplitude 

(Ai) 

.2 .2 .2 .1 .04 .01 .005 .003 .002 

Table 4.5.2 Disturbance Input Implemented in MMS Laboratory 

Using the MMS Laboratory software, the running cumulative average RMS 

tracking error was recorded for each run which lasted for 30 seconds. A plot of the 

running cumulative average RMS tracking error is shown in Figure 4.5.2. 

 Figure 4.5.2 RMS Tracking Error O btained from Test within MMS Laboratory 

0 5 10 15 20 25 30

0.4

0.41

0.42

0.43

0.44

0.45

0.46

RMS Tracking Error (30 second runs, Averaged data over runs)

Run number

RMS Tracking Error
76 

As shown in Figure 4.5.2, the running cumulative average RMS tracking error 

reduces drastically from the first run to the fourth run. After the fourth run it seems that 

the running cumulative average RMS tracking error starts to level off and approach an 

asymptote. This shows that the test subject has reached his/her maximum performance. 

From Figure 4.5.2 it is hard to tell that the RMS tracking error has reached an 

asymptote. Since the RMS tracking error differs by an order of 10-2 between each run, the 

slope of the running cumulative average tracking error is obtained. The slope of the RMS 

tracking error is calculated between every two successive runs. The slope is shown in 

Figure 4.5.3. 

 

Figure 4.5.3 Slope of RMS Tracking Error O btained from Test within MMS Laboratory 

As shown, the slope in the beginning is much higher and then it eventually starts 

to approach a zero slope meaning that the response is reaching a horizontal asymptote. It 

has been determined that if a consistent slope of 0.01 or less exists for 3 runs, the test 

0 5 10 15 20 25 30

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

Slope of RMS Tracking Error (30 second runs, Averaged data over runs)

Run number

RMS Slope
77 

subject has reached his/her performance asymptote and has trained successfully on the 

task. 

 The reason for using the running cumulative average of the RMS tracking error is 

that there exists a small fluctuation of the RMS tracking error from run to run. This 

distorts the behavior and the RMS tracking error appears to not reach an asymptote. The 

running cumulative average does not distort the values but gives a general trend for the 

behavior of the RMS tracking error. 

The running cumulative average RMS control inceptor deflection was also 

considered when conducting these tests. The RMS control inceptor deflection is shown in 

Figure 4.5.4. It appears that the behavior of RMS control inceptor deflection is very 

similar to that of the RMS tracking error. The RMS control inceptor deflection also 

decreases in value with each successive run. This suggests that the test subject has less 

control inceptor movement as the task is being learned. 

Figure 4.5.4 RMS Control Inceptor Deflection O btained from Test within MMS Laboratory 

0 5 10 15 20 25 30 0.4

0.41

0.42

0.43

0.44

0.45

0.46

RMS Input (30 second runs, Averaged data over runs)

Run number

RMS Input
78 

The slope of the RMS control inceptor was calculated and plotted in Figure 4.5.5. 

Although the RMS input shows a general trend of reaching an asymptote, less control 

inceptor deflection does not necessarily show an improvement in performance. It does 

show an improvement in test subject workload. More important is the bandwidth of the 

test subject input. Higher bandwidth corresponds to increased test subject performance.

Figure 4.5.5 Slope of RMS Control Inceptor Deflection O btained from Test within MMS Laboratory 

0 5 10 15 20 25 30 -0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

Slope of RMS Input (30 second runs, Averaged data over runs)

Run number

RMS Slope
79 

Chapter 5 - Experimental Setup 

5.1 Introduction 

 

 Experiments are conducted on a high fidelity or low fidelity control inceptor in a 

manner to effectively test the performance of each test subject. The importance of 

maintaining the proper force feedback to the test subject is not known, and these 

experiments will illuminate the effects of force feedback. The task performed by each test 

subject is a roll disturbance compensatory task. The plant dynamics used in the 

experiments are 1/s and 1/s2

. Plant dynamics 1/s represents a simple control task while 

1/s2

 plant dynamics represent a more difficult task. Each test subject will complete the 

roll disturbance compensatory task for both the 1/s and 1/s2

 dynamics. The test subjects 

will complete a run lasting for 30 seconds. They will conduct as many runs as necessary 

to reach a performance asymptote that is described within this chapter. The following 

chapter will present a background of the experiment performed, an experimental setup, 

and a protocol. 

5.2 Background 

 The experiments within this study were conducted in the Cockpit Motion Facility 

(CMF) at the NASA Langley Research Center. Shown in Figure 5.2.1 is an artist 

conception of the Cockpit Motion Facility. The motion platform is located in the center 

of the facility. The motion platform has six degrees of freedom and has six 76 inch 

hydraulic actuators. Within this facility, there exists the ability to use each one of the 

three flight cockpits with motion or as a fixed base simulation. The flight cockpits used in 

a fixed based simulation are located on either side of the Cockpit Motion Facility. The 

three flight cockpits include the Research Flight Deck Simulator (RFD), the Integration 
80 

Flight Deck Simulator (IFD), and the Generic Flight Deck Simulator (GFD). Within this 

study the GFD was chosen because of the flexibility of changing the characteristics of the 

control loader system. In this experiment the GFD was used as a fixed based simulator. 

Figure 5.2.1 Cockpit Motion Facility (NASA LaRC) 

 The GFD cockpit uses four CRT monitors to present an out-the-window display 

image. The image is passed through a beam splitter and then collimated to provide the 

out-the-window image. These particular displays are referred to as WAC window 

displays which stands for wide angle collimated displays. 

5.3 Implementation of Transfer of Training Study 

A description on the experimental setup and protocol is discussed within this 

section. A quasi-transfer of training experiment is conducted where test subjects with no 

prior flight experience will train on a roll disturbance compensatory task. A control 
81 

inceptor representing high fidelity force feedback dynamics and a control inceptor with 

very minimal force feedback will be interchanged. This experiment is conducted on a 

fixed base simulator with an out-the-window display. 

This experiment focuses on feedback cues that arise solely from the 

neuromuscular and visual systems. This experiment will ascertain important information 

on the effect of training on two different control inceptor dynamics. The simple setup 

allows the experiments to be repeated with other simulators. 

5.3.1 Protocol 

A quasi-transfer of training study consists of training test subjects to null a roll 

disturbance maintaining level flight using a high and low fidelity control inceptor 

simulation. After the test subjects are trained, they will then transfer to the high fidelity 

control inceptor simulation. The test subjects will be drawn from the general population 

in which they have no formal flight training experience. The simulation will be fixed base 

and will have a simple horizon out-the-window display. Implementation of the 

experiment will be described in the following paragraphs as well as a procedure for 

training the test subjects on each of the simulations. A step by step experimental protocol 

is located in Appendix A. 

Before running tests with test subjects, a simple check on the equipment should be 

conducted. The display should show the target clearly. The display should also react 

accordingly to test subject input with the roll rate of the bank angle on the display 

increasing with increased control inceptor deflection. Also, the recorded force output and 

control inceptor deflection should have very little signal noise. The disturbance should be 

applied without any test subject input and the output bank angle should be recorded. This 
82 

should be compared with the disturbance generated in a computer simulation. The control 

inceptor should be calibrated properly making sure that at the neutral position the 

position being sensed is a value of zero inches. Also the force should be zero pounds 

when the control inceptor is at rest. 

 To conduct the transfer of training task, two separate groups each consisting of 10 

test subjects will be used. The two groups represent the high fidelity control inceptor 

transfer group and the low fidelity control inceptor transfer group. One group termed the 

high fidelity control inceptor transfer group will train on the high fidelity control inceptor 

simulation. The other group termed the low fidelity control inceptor transfer group will 

train on the low fidelity control inceptor simulation. The test subjects will each conduct a 

30 second run. The RMS tracking error and RMS control inceptor deflection will be 

recorded for each run. The RMS cumulative running average will be computed for both 

the tracking error and control inceptor deflection. 

When each test subject reaches an asymptotic running cumulative average RMS 

tracking error, the training task will be completed for each test subject. To assist in 

determining if the test subject has reached an asymptote, the slope of the running 

cumulative average RMS tracking error between every two points is calculated. When the 

slope reaches a consistent value for three consecutive runs of 0.1 or less, asymptote has 

been reached. At the conclusion of the training session a break is administered. After 

each test subject trains, they will then be transferred to the high fidelity control loader 

simulation. The test subjects will again complete 30 second runs until they reach an 

asymptotic running cumulative average (RMS) tracking error. A description for the 

measured and the calculated parameters is described in section 5.3.2. 
83 

Each test subject is given a label HF# and LF# for the high fidelity and low 

fidelity transfer group respectively. Each test subject will be given a certain time slot in 

which they will conduct both the 1/s and 1/s2

 plant dynamics experiments. The test 

subjects will each be briefed on the task they are to perform with a briefing statement that 

is located in the Experimental Protocol in Appendix A. The test subject will perform four 

phases of the experiment that include the familiarization phase, evaluation phase, training 

phase, and transfer phase. A break of 5 minutes is administered between the training and 

transfer phase. The test subject will then transfer to the high fidelity control loader 

simulation. After they have completed the task for 1/s plant dynamics, the test subjects 

will get another break of 5 minutes. After the break they will return to complete all four 

phases for 1/s2 plant dynamics. An experiment run time that gives an estimated 

experiment completion time is located in Appendix C. 

5.3.2 Test Setup 

Two different transfer of training configurations exist for the 1/s and 1/s2 plant 

dynamics. Experiment pseudo code is created to run these two tasks within the 

experiment. Much of the code implements the disturbance, Euler integration techniques, 

roll angle that is displayed, as well as a way to measure data associated with test subject 

performance. The experimental pseudo code is located in Appendix E. Figure 5.3.1 

describes the general configuration for both the 1/s and 1/s2

 plant dynamics. 

The main difference is that the roll command is represented by a roll rate 

command and a roll acceleration command for 1/s and 1/s2 dynamics respectively. In 

Figure 5.3.1 a forcing function described in Table 4.5.1 in Section 4.5 is first generated 
84 

and then summed with the output roll angle of the plant that is commanded by the test 

subject. 

Feel

System

Subject

Input Kc Plant (1/s)

Forcing Function

(Sum of Sines)

 c 

Roll Command Roll Angle

(Degrees)

Stick Displacment (in) Force

(lb)

Image

Generation

+

+

Visual

Feedback

Feel

System

Subject

Input Kc Plant (1/s2

)

Forcing Function

(Sum of Sines)

 c 

Roll Command Roll Angle

(Degrees)

Stick Displacment (in) Force

(lb)

Image

Generation

+

+

Visual

Feedback

Figure 5.3.1 Q uasi Transfer of Training Experimental Configuration 

When the experiment starts, the forcing function will disturb a bank angle line 

located on the display. The test subject will view the disturbed roll angle and apply a 

command to the control inceptor to return the bank angle back to zero degrees. In the 

implementation of the experiment code, the feel system parameters are modified through 

the control loader software within the GFD simulator. The control inceptor deflection is 

measured in real time and then multiplied by the roll command gain (Kc). For 1/s and 1/s2 

dynamics the roll command gain (Kc) converts the inceptor deflection into a roll rate and 

roll acceleration respectively. The initial value of the roll command gain (Kc) is set to 40 
85 

deg/in•sec and 40 deg/in•sec2

 for 1/s and 1/s2 dynamics respectively. To simulate the 

plant dynamics of 1/s and 1/s2

, Euler integration is applied once or twice to the roll plant 

command respectively. The integration technique produces the commanded roll angle 

that is summed with the forcing function to produce the output bank angle displayed on 

an out-the-window display. A general flow chart of the experiment is shown in Appendix 

F. 

For this experiment, a variety of parameters will be measured that will be further 

analyzed offline. Some of the parameters to be measured include test subject horizontal 

control inceptor deflection, horizontal control inceptor force, and tracking error. Some of 

the calculated parameters include the running cumulative average RMS tracking error, 

the slope of the average RMS tracking error, RMS control inceptor deflection, and PSD 

of the control inceptor deflection. A list of parameters along with the frequency of 

measurement is shown in Appendix B. One of the most important parameters is the RMS 

tracking error, which is used to tell if the test subject has reached a performance 

asymptote. To calculate the RMS tracking error, the bank angle is recorded. Each data 

point is squared and summed together then divided by the total number of data points. 

This is represented in Equation 5.3.1. 

 

222 2

123 n rms

xx x x

x

n

  """  Equation 5.3.1 

The term (xrms) represents the RMS of any data that is recorded. The symbol “n” 

represents the total number of data points. The term (xn) represents each data point 

recorded at a discrete time interval. To calculate the running cumulative average of the 

RMS tracking error, Equation 5.3.2 can be used. 
86 

 

( 1) ( 1) ( ) ( ) rms rms rmsj xj xj x j j	" 	  Equation 5.3.2 

The term j represents the run number. The term x ( j) rms and x ( j 	1) rms represents the 

current RMS running cumulative average and the previous RMS running cumulative 

average respectively. The term x ( j) rms represents the current run RMS tracking error. 

The RMS running cumulative average has to be initialized to the RMS of the first run. 

The averaging technique in Equation 5.3.1 will take place on the second run, when two 

RMS data points are obtained. The running cumulative average of the RMS tracking error 

for the first run is just the RMS tracking error of the first run. 

 To determine if the RMS running cumulative average has reached an asymptote, 

the slope between every two runs will be calculated. As the slope between two runs 

reaches 0.1 for 3 consecutive runs, asymptote has been reached. The formula for the 

slope between two runs is listed in Equation 5.3.3. 

 ( ) ( ) ( 1) rms rms rms &  		 x j x jx j Equation 5.3.3 

 

The term x ( j) & rms represents the slope of the running cumulative average RMS between 

two runs. The terms x ( j) rms and x ( j 	1) rms represent the current and previous run RMS 

tracking error respectively. 

5.3.3 Display Setup 

The display consists of a horizon line and a bank angle reference line that will 

displace at an angle from the horizon reference line. The image will be displayed on an 

out-the-window display. A simple example of this is shown in Figure 5.3.2. The 
87 

background is black and the horizon reference line is white. The roll reference line is 

green in color to distinguish from the horizon reference line. To obtain the dimensions of 

the visual scene, a computation of the viewing dimensions for the test subject at a 

distance away from the display is conducted. To compute the horizontal viewing 

dimension Hv, Equation 5.3.4 is applied. 

 Hv = 2 tan(HFOV/2) DEP " " Equation 5.3.4 

The term HFOV represents the horizontal field of view angle, and DEP equals the 

distance from the display screen that the eye of the test subject is located. To determine 

the vertical viewing dimension Vv, the following Equation 5.3.5 is applied. 

 Vv = 2 tan(VFOV/2) DEP " " Equation 5.3.5 

The term VFOV represents the vertical field of view angle, and DEP again 

represents the distance from the display screen that the eye of the test subject is located. 

The length of the horizon reference line should be approximately 80% of the horizontal 

viewing dimension. The length of the roll reference line should be 80% of the vertical 

viewing dimension. The dimensions of the target on the display are shown in 

Figure 5.3.2. These dimensions are calculated using a vertical FOV of 27 ̊, a horizontal 

FOV of 44 ̊, and an eye point distance from the collimator of 50 inches. 
88 

 Figure 5.3.2 Out-the-Window Display Setup 

5.3.4 Force Feel Parameters Implementation 

 In Chapter 3, the force feel parameters for the high and low fidelity control 

inceptors were implemented on the McFadden control loader system that is located 

within the GFD simulator and verified. The McFadden control loader software allows 

one to input certain parameters. A list of some of the parameters available for the 

McFadden control loader is shown in Table 5.3.1. 

Parameter Name: Units: 

Inertia (lbf/in/sec2) 

Minus Stop inches 

Plus Stop inches 

Dead Band inches 

Breakout Level lbf 

Breakout Slope lbf/inch 

Damping lbf/inch/sec 

Friction lbf 

Plus Grad Slope lbf/inch 

Minus Grad Slope lbf/inch 

 Table 5.3.1 McFadden Control Loader Parameter Table 

19”

Bank Angle Reference 

Line 

Horizon Reference Line 

32”

Bank Angle 

Angle Tick Marks 
89 

A parameter, such as inertia, is considered to be added to the inertia of the system. 

This parameter does not define the actual inertia of the system. The minus and plus stop 

are hard stops and limit the motion of the control inceptor to a negative and positive 

motion range in inches. The dead band creates a portion of the deflection where force 

feedback is not felt. The breakout level is the force required for the control inceptor to 

begin deflecting. Corresponding to the breakout level is the breakout slope which is 

usually set to a high value typically around 100 lb/in so that very little deflection occurs 

before the breakout force level is met. 

The damping parameter is in terms of damping coefficient and not the damping 

ratio. This should be considered carefully when implementing the characteristics of the 

control inceptor. The friction parameter gives added friction force to the system. The plus 

grad slope and minus grad slope refer to the force gradient in lb/in. This allows the user 

to set the force gradient differently when pushing the control inceptor as opposed to 

pulling the control inceptor. Also, the McFadden control loader is able to apply different 

force gradients over different intervals of the deflection of the inceptor. This allows the 

user to create a nonlinear force gradient. Within this study only a linear force gradient is 

implemented and is equal in the push and pull directions. 

The force feel parameters implemented on the McFadden control loader are 

shown below in Table 5.3.2. These parameters are shown for the test subject control 

inceptor which is a sidestick manipulator. The damping ratio that is defined for both the 

high fidelity and low fidelity control loader was converted to the damping coefficient 

using Equation 5.3.6. Since there still exists nonlinearities in the system due to Coulomb 
90 

friction; the apparent mass of 0.0119 lb•s2

/in is used. This apparent mass was determined 

in Chapter 3. 

 2   """ m n

Equation 5.3.6 

Although the apparent mass is consistent for large deflection of the control 

inceptor from the neutral position, there exists greater damping when the control inceptor 

is close to neutral. This is due to a Coulomb friction force. The friction force near neutral 

causes the system to have a higher damping ratio. The calculated damping coefficient for 

the high fidelity control inceptor is equal to 0.3 lb•s2

/in using the apparent mass. With 

this implemented damping coefficient, the system exhibited a higher damping ratio in the 

time response. The damping coefficient was then lowered to obtain a value closer to the 

defined damping coefficient of 0.7. The low fidelity damping coefficient was not tuned to 

obtain the exact damping ratio of 0.135. As long as the measured damping ratio is below 

0.3, it can be considered a low fidelity control inceptor. The damping coefficient will 

have to be changed depending on the mass of the control inceptor being used. 

The control loader should be tuned so that the time response and frequency 

response verifies the force gradient, damping ratio, and breakout force proposed in Table 

5.3.2. It is very important to verify the control loader characteristics before conducting 

the quasi transfer of training study. 

McFadden Control Loader 

Control Inceptor 

Fidelity: 

Effective 

Mass

(Roll Axis) 

(lb•s2/in) 

Force 

Gradient: 

Damping 

Ratio ζ

Damping 

Coefficient β:

Breakout 

Force: 

High Fidelity 0.0119 4 lb/in 0.7 0.25 lb•s2/in 1.5 lb 

Low Fidelity 0.025 0.7 lb/in 0.135 0.0243 lb•s2/in 0 lb 

 Table 5.3.2 Implemented Control Inceptor Characteristics 
91 

Chapter 6 - Results and Discussion 

6.1 Introduction 

The results for the quasi-transfer of training study are presented within this 

section. Only quantitative results were obtained during the experiments. Subjective 

results were not recorded because of the inexperience of the test subjects and their ability 

to rate the control task accurately. First, average tracking error performance for the test 

subjects is presented. The tracking error was obtained by calculating the root mean square 

(RMS) tracking error for the duration of each run for each test subject and for both 1/s 

and 1/s2 plant dynamics. A cumulative average over the number of runs completed is 

shown. This removes any small fluctuation in a test subject’s tracking error and gives a 

general trend for the data. Second, power spectral density (PSD) analysis and coherence 

analysis is presented. 

A very important concept when measuring human performance is the workload 

used to perform each task. To measure the test subject’s workload, power spectral density 

(PSD) analysis was employed. This technique shows the frequencies and power that each 

test subject uses when performing the task. Generally, a test subject will use more power 

and operate at a higher frequency when the task workload is greater. The power spectral 

density (PSD) analysis only gives insight on test subject workload and it does not give us 

direct insight on the test subject’s performance level. This analysis is conducted to 

evaluate if either group has a higher workload when completing the roll disturbance 

compensatory tracking task. 

The results presented in this section are used to evaluate the differences or 

similarities between training on a high fidelity or a low fidelity control loader. 
92 

6.2 Performance Metrics 

Shown in Figure 6.2.1 is the average root mean square (RMS) tracking error for 

the high fidelity training group for the 1/s plant dynamics. The RMS tracking error is 

obtained by recording the roll angle that is shown on the display at each sampling 

interval, squaring the data points, dividing by the total number of data points and taking 

its square root. 

 Figure 6.2.1 Average Tracking Error for High Fidelity Training Group (1/s Plant Dynamics) 

The subjects reach an asymptotic performance level in the training phase. The asymptotic 

performance level is determined if the slope of the tracking error reaches a value of 0.01 

or less for three consecutive runs. The asymptotic performance level that they reach is 

equal to 13.61 deg. The improvement rate is equal to 0.1736 degrees per run. The 

standard error of the tracking error for test subjects is also shown. The standard error is 

equal to the standard deviation divided by the square root of the sample size. Through 

both the training phase and transfer phase the spread of data is consistent. When the test 

0 10 20 30 40 50

11

12

13

14

15

16

17

18

19

20

21

Results for High Fidelity training Group (1/s Plant Dynamics)

Number of Runs

Average Tracking Error Across the Group of Subjects (deg)

Training Phase

+/- Standard Error

Transfer Phase

+/- Standard Error

Results for High Fidelity Training Group (1/s Plant Dynamics)
93 

subjects transfer, the tracking error remains close to the average asymptote achieved in 

the training phase. The difference between the asymptotic tracking error in the training 

phase and the initial tracking error in the transfer phase is equal to 0.31 degrees. The test 

subjects continue to improve slightly in the transfer phase with an improvement rate of 

0.06 degrees per run. The final average tracking error is 12.6 degrees. The average 

number of runs to reach asymptote in the training phase is 18 runs. The average number 

of runs to reach asymptote in the transfer phase is 16 runs. 

 Shown in Figure 6.2.2 are the tracking error results for the low fidelity training 

group for 1/s plant dynamics. 

 

Figure 6.2.2 Average Tracking Error for Low Fidelity Training Group (1/s Plant Dynamics) 

The low fidelity training group starts off with an average tracking error of 20.94 degrees. 

The low fidelity group is able to train to a tracking error of 16.57 degrees. The 

improvement rate is 0.1748 degrees per run. When this group transferred to the high 

fidelity control loader simulation, the tracking error initially increased. The difference 

0 10 20 30 40 50

12

14

16

18

20

22

24

26

Results for Low Fidelity training Group (1/s Plant Dynamics)

Number of Runs

Average Tracking Error Across the Group of Subjects (deg)

Training Phase

+/- Standard Error

Transfer Phase

+/- Standard Error

Results for Low Fidelity Training Group (1/s Plant Dynamics)
94 

between the initial tracking error in the transfer phase and the asymptotic tracking error in 

the training phase is 1.74 degrees. Although the low fidelity group has an increased initial 

tracking error when they transfer, they are able to adapt and improve their performance. 

Their final asymptotic tracking error is 13.99 degrees and the improvement rate for the 

transfer phase is 0.196 degrees per run. With approximately 13 runs completed, there is a 

54% increase in tracking error due to one subject within the group causing the sudden 

increase in tracking error. The average number of runs to reach asymptotic in the training 

phase and transfer phase is 20 and 16 runs respectively. 

 To compare the tracking error performance for both groups, the results are plotted 

together in Figure 6.2.3. The two best and two worst test subjects were removed from 

each group consisting of 10 test subjects to obtain a group closer in tracking performance 

with a smaller variance in data. 

Figure 6.2.3 Average Tracking Error Results for Both Training Groups (1/s Plant Dynamics) 

The two groups reach a final tracking error within one standard error of each other. This 

shows that some of the test subject data for the high fidelity group lies in the vicinity of 

0 10 20 30 40 50

10

12

14

16

18

20

22

24

26

28

Average Tracking Error Results (1/s Plant Dynamics)

Number of Runs

Average Tracking Error (deg)

High Fidelity Group

+/- Standard Error

Low Fidelity Group

+/- Standard Error
95 

the low fidelity group. This usually suggests no significant difference between the final 

mean tracking errors. A t-test is performed between the groups for each run to determine 

if the average tracking error for each run is significantly different for each group. Using a 

confidence level of 95%, the t-value required for a significant difference is equal to 

1.812. The t-value for the last run between the high and low fidelity group is equal to 

1.54. This suggests that there is not a significant difference between the two test subject 

groups. In the training phase, the high fidelity and low fidelity group take 18 and 20 runs 

respectively to train. In the transfer phase, the high fidelity and low fidelity group take 16 

runs to train. 

The average tracking error results for the high fidelity training group for 1/s2

 plant 

dynamics are shown in Figure 6.2.4. 

 Figure 6.2.4 Average Tracking Error Results for High Fidelity Training Group (1/s 2 Plant Dynamics) 

0 10 20 30 40 50

25

30

35

40

45

50

55

Results for High Fidelity training Group (1/s2 Plant Dynamics)

Number of Runs

Average Tracking Error Across the Group of Subjects (deg)

Training Phase

+/- Standard Error

Transfer Phase

+/- Standard Error

Results for High Fidelity Training Group (1/s

2

Plant Dynamics)
96 

The results plotted in Figure 6.2.4 illustrate that the tracking error is greater for 1/s2 plant 

dynamics. The initial average tracking error is 48.49 degrees. The asymptotic tracking 

error is 33.32 degrees which is equal to an improvement rate of 0.6 degrees per run. The 

tracking error directly after the high group transfers is equal to 33.11 degrees which is 

0.21 degrees different than the asymptotic tracking error in the training phase. In the 

transfer phase the improvement rate is equal to 0.112 degrees per run. The high fidelity 

group reaches their final asymptotic tracking error of 30.31 degrees in 40 runs. The 

average number of runs to reach asymptote in the training and transfer phase is equal to 

24 and 22 runs respectively. 

The low fidelity tracking error performance is plotted in Figure 6.2.5. The low 

fidelity group maintains a higher tracking error than the high fidelity group. The low 

fidelity group started with an average tracking error performance of 62.63 degrees and 

then trained to an average tracking error of 43.78 degrees. This is an improvement rate of 

0.754 degrees per run. As shown for 1/s plant dynamics, the low fidelity group again has 

a sudden increase in their tracking error for 1/s2

 plant dynamics right when they transfer. 

They are able to adapt their control and reduce the tracking to a value lower than their 

asymptotic tracking error in the training phase. The low fidelity training group increased 

their tracking error to 67.3 degrees when they transferred, which is 4.67 degrees larger 

than their initial tracking error. The group reaches a final asymptotic tracking error of 

39.7 degrees which is an improvement rate of 1.104 degrees per run. The final asymptotic 

tracking error is 4.11 degrees less than the asymptotic tracking error in the training phase. 

The average number of runs to reach asymptote in the training and transfer phases is 25 

and 23 runs respectively. 
97 

 

Figure 6.2.5 Average Tracking Error for Low Fidelity Training Group (1/s 2 Plant Dynamics) 

Figure 6.2.6 compares the high fidelity tracking error to the low fidelity tracking 

error data. Four test subjects including the two best and two worst were again removed 

from the population in each group. 

Figure 6.2.6 Average Tracking Error Results for Both Training Groups (1/s 2 Plant Dynamics) 

0 5 10 15 20 25 30 35 40 45 50

20

30

40

50

60

70

80

90

100

Average Tracking Error Results (1/s2 Plant Dynamics)

Number of Runs

Average Tracking Error (deg)

High Fidelity Group

+/- Standard Error

Low Fidelity Group

+/- Standard Error

0 10 20 30 40 50

30

40

50

60

70

80

90

Results for Low Fidelity training Group (1/s2 Plant Dynamics)

Number of Runs

Average Tracking Error Across the Group of Subjects (deg)

Training Phase 

+/- Standard Error

Transfer Phase

+/- Standard Error

Results for Low Fidelity Training Group (1/s

2

 Plant Dynamics)
98 

A positive standard error for the high fidelity does not overlap the average tracking error 

for the low fidelity group. To determine if there is a significant difference between the 

average tracking errors for the high and low fidelity group, a t-test was performed. The 

two worst test subjects were removed from analysis of the data since they could not 

maintain adequate performance. These two test subjects obtained a tracking error beyond 

180 degrees for more than one run and were not able to reach a tracking error 

performance asymptote. A t-value above 1.812 using a 95% confidence level suggests a 

significant difference between the mean of the two groups. A t-value of 2.62 is calculated 

for the final run of the experiment. This suggests that for 1/s2 plant dynamics, there is a 

significant difference between the final tracking error scores for the high and low fidelity 

training groups. 

 Some of the test subjects did not reach a true asymptote and therefore continued 

to improve their tracking error after transfer. These test subjects were re-tested with 

experiments consisting of 80 runs and 40 runs in the training and transfer phase. Two test 

subjects were chosen from each group. Both test subjects did not reach asymptote with 

one having better tracking error performance. Shown in Figure 6.2.7 is test subject 

HF001 with 1/s plant dynamics. 
99 

Figure 6.2.7 Average Tracking Error with Greater Amount of Runs (Test Subject HF001 1/s Plant Dynamics) 

This plot shows the training data for the original experiments and the new experiments 

with more runs implemented. As shown, the longer runs allow the test subject to reach a 

performance asymptote while the original experiments show continued improvement in 

both the training and transfer phase. The tracking error for test subject LF009 with 1/s 

plant dynamics is shown in Figure 6.2.8 Average Tracking Error with Greater Amount of 

Runs (Test Subject LF009 1/s Plant Dynamics) 

0 20 40 60 80 100 120

11

12

13

14

15

16

17

18

19

20

21

Cumulative Average RMS Tracking Error (1/s Plant Dynamics Subject HF001)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented
100 

Figure 6.2.8 Average Tracking Error with Greater Amount of Runs (Test Subject LF009 1/s Plant Dynamics) 

Test subject LF009 reaches an asymptote when given more runs to train. The other 

results using a greater number of runs to train are shown in Appendix I. 

In conclusion, for the 1/s plant dynamics the high fidelity and low fidelity training 

groups have a similar final tracking error. The final tracking error of either group is 

within one standard error of each other. Both groups maintain their tracking performance 

as they transfer. The low fidelity group shows more improvement than the high fidelity 

group when they transfer and eventually reach a similar tracking performance. The low 

fidelity group has an improvement rate of 0.196 degrees per run while the high fidelity 

group has an improvement rate of 0.06 degrees per run in the transfer phase. The low 

fidelity group improves more drastically when they transfer suggesting that that the high 

fidelity control loader allows the test subject to perform better. Table 6.2.1 shows the 

0 20 40 60 80 100 120

12

14

16

18

20

22

24

Cumulative Average RMS Tracking Error (1/s Plant Dynamics Subject LF009)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented
101 

average number of runs for each group to reach asymptote. Both groups train within the 

same number of runs. The performance results for 1/s plant dynamics shows that there is 

no distinct advantage in training on the high fidelity control loader. For 1/s2 plant 

dynamics there is a greater difference in final tracking performance between the two 

groups. The two groups do not train to the same tracking error performance in the 

training phase and transfer phase. The tracking error for the two groups is not within one 

standard error of each other. For more difficult tasks, it is important to train on the high 

fidelity control loader. There is no significant difference in how many runs each group 

takes to reach asymptote for 1/s2 plant dynamics. Figure 6.2.9 and Figure 6.2.10 show the 

average tracking error for the first and last run in the training and transfer phase for 1/s 

and 1/s2 plant dynamics respectively. 

Average Number of Runs to Reach Asymptote Criterion 

Group: Training: Transfer: 

1/s Plant Dynamics 

High Fidelity 18 16 

Low Fidelity 20 16 

1/s2 Plant Dynamics 

High Fidelity 24 22 

Low Fidelity 25 23 

Table 6.2.1 Average Number of Runs to Reach Asymptote 
102 

Figure 6.2.9 Average Tracking Error (1/s Plant Dynamics) 

Figure 6.2.10 Average Tracking Error (1/s 2 Plant Dynamics) 

0

5

10

15

20

25

30

 Training Phase Transfer Phase 

Average Tracking Error 

 (1/s Plant Dynamics) 

Average First Run Tracking

Error (deg) High Fidelity

Average Last Run Tracking

Error (deg) High Fidelity

Average First Run Tracking

Error (deg) Low Fidelity

Average Last Run Tracking

Error (deg) Low Fidelity

0

10

20

30

40

50

60

70

80

Training Phase Transfer Phase 

Average Tracking Error 

(1/s2 Plant Dynamics) 

Average First Run Tracking

Error (deg) High Fidelity

Average Last Run Tracking

Error (deg) High Fidelity

Average First Run Tracking

Error (deg) Low Fidelity

Average Last Run Tracking

Error (deg) Low Fidelity
103 

6.3 PSD Analysis 

To conduct Power Spectral Density analysis on the test subjects, the control 

inceptor deflection throughout each run is used. The units of power for the control 

inceptor deflection are in2

/Hz. To assess if the control inceptor deflection data meets the 

requirement of stationarity, the variance and mean square were computed for each data 

set. The recorded data were sampled at 50 Hz and every 4th data point was saved, 

therefore the effective sampling interval was 0.08 sec or 12.65 Hz. The highest frequency 

expected in the control inceptor deflection is 3 Hz because the disturbance input does not 

have frequencies beyond this. The sampling rate satisfies the Nyquist criterion. To 

improve the PSD, the data were re-sampled to 100 Hz to obtain more data points. When 

calculating the variance, the data were split into 48 windows consisting of 65 data points 

for a total of 3120 data points. The variance of the control inceptor deflection for every 

test subject in the high fidelity and low fidelity groups using 1/s plant dynamics is 

presented in Figure 6.3.1 and Figure 6.3.2 respectively. The variance does not grow in 

amplitude as a function of time. A wide sense stationary signal has a constant variance 

and mean at any time. There is a small fluctuation in the variance from segment to 

segment. Although the data are not the most stationary data, the portion of the data that 

had the smallest mean square and variance was chosen when analyzing the PSD to ensure 

credible frequency analysis. The variance and mean square for 1/s2 plant dynamics and 

the other runs that were analyzed are presented in Appendix G.
104 

 Figure 6.3.1 Variance of Roll Stick Deflection 1st Run (High Fidelity Group 1/s Plant Dynamics) 

 Figure 6.3.2 Variance of Roll Stick Deflection 1st Run (Low Fidelity Group 1/s Plant Dynamics) 
105 

Since 20 test subjects were used with multiple runs, only the peak power and peak 

frequency for each test subject were calculated for the first and last runs in the training 

and transfer phases. The peak power for 1/s plant dynamics is presented in Figure 6.3.3. 

Figure 6.3.3 Average Peak Power (1/s Plant Dynamics) 

Shown in Figure 6.3.3 above, there is an overlap in data for the high and low fidelity 

training group in the training session. There is no significant difference in the power in 

the training phase. There is an increase in the power from the first to the last run in the 

training session for both groups. This would suggest that the test subjects increase their 

workload as they train. This does not necessarily suggest that, because their workload is 

higher, they will decrease their performance. The task presented to the test subjects could 

cause the test subjects to become more involved in their control behavior further reducing 

their tracking error. 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Training Phase Transfer Phase 

Average Peak Power 

(1/s Plant Dynamics) 

Average First Run 

Peak Power (in2/Hz) 

High Fidelity 

Average Last Run Peak 

Power (in2/Hz) High 

Fidelity 

Average First Run 

Peak Power (in2/Hz) 

Low Fidelity 

Average Last Run Peak 

Power (in2/Hz) Low 

Fidelity 
106 

 In the transfer phase, the low fidelity group has reduced their power while the 

high fidelity group maintains their peak power. Using a t-test to determine if there is a 

significant difference in the average power between the two groups, t-values of 0.0844 

and 0.939 were calculated for the first and last runs of the transfer phase. Using a 95% 

confidence level, a t-value above 1.812 suggests a significant difference. Both values 

suggest there is no significant difference in the power used for either the high or low 

fidelity group. The reduction in power of the low fidelity group from the last run of the 

training phase to the first run of the transfer phase suggests that their control inceptor 

deflection is reduced, that their peak frequency increases, or that both the control inceptor 

deflection reduces and their peak frequency increases. The low fidelity group adapts and 

continues to increase their power within the average of the high fidelity group. 

The peak frequencies for the high and low fidelity training groups using 1/s plant 

dynamics are presented in Figure 6.3.4. 

Figure 6.3.4 Average Peak Frequency (1/s Plant Dynamics) 

0

0.05

0.1

0.15

0.2

0.25

Training Phase Transfer Phase 

Average Peak Frequency 

(1/s Plant Dynamics) 

Average First Run Peak

Frequency (Hz) High Fidelity

Average Last Run Peak

Frequency (Hz) High Fidelity

Average First Run Peak

Frequency (Hz) Low Fidelity

Average Last Run Peak

Frequency (Hz) Low Fidelity
107 

During the training phase, the peak frequency of the low fidelity group is lower than the 

high fidelity training group. The t-value between the two groups for their first run in the 

training phase is equal to 2.992, which is greater than the significant t-value of 1.812 

suggesting these peak frequencies are different for the two groups. Eventually, after both 

groups train they reach approximately the same peak frequency between 0.18 and 0.2 Hz. 

One of the higher amplitude sinusoids in the disturbance has a frequency of 0.1868 Hz. 

When the high fidelity transfer group transfers they maintain their peak frequency but 

when the low fidelity group transfers there is an increase in the peak frequency. The tvalue between the first run peak frequency in the transfer phase for the high fidelity and 

low fidelity group is 1.055 suggesting no significant difference. Eventually, the low 

fidelity group reaches an average peak frequency closer in value to the high fidelity 

training group around 0.173 Hz. 

 The peak power for 1/s2

 plant dynamics is shown in Figure 6.3.5. The peak power 

used for the test subjects is around 10 times the amount used for 1/s plant dynamics. This 

shows that a higher workload is necessary for this task. The 1/s2 plant dynamics is a much 

harder task since it creates a higher sensitivity and adds delay for the test subjects. When 

the test subjects apply a control inceptor deflection, it is multiplied by a roll command 

gain which creates roll acceleration command. The test subjects are trying to control the 

bank angle with roll acceleration. This gives more sensitivity to control inceptor inputs 

and also makes it harder to predict the commanded bank angle based on control inceptor 

deflection input. 
108 

 

Figure 6.3.5 Average Peak Power (1/s 2 Plant Dynamics) 

 For both training groups, the peak power is similar and within one standard error 

of each other. Generally, the high fidelity group reduces their power from the first run to 

the last run in the training phase. The transition from training phase to transfer phase is 

important in determining if training on one control inceptor has a training advantage. 

The low fidelity group does not drastically increase or reduce their power when they 

transfer. This is also shown in their tracking error performance in which the two groups 

tend to maintain their tracking error when they transfer. The power level between groups 

is not significantly different. 

 Presented in Figure 6.3.6 is the peak frequency for the 1/s2 plant dynamics. The 

low fidelity group initially has a lower peak frequency than the high fidelity training 

group. As they train, the low fidelity training group increases their peak frequency. As 

the high fidelity group transfers, the average peak frequency increases 25%. The majority 

of high fidelity test subjects increase their peak frequency with one test subject increasing 

0

2

4

6

8

10

12

Training Phase Transfer Phase 

Average Peak Power 

(1/s2 Plant Dynamics) 

Average First Run 

Peak Power (in2/Hz) 

High Fidelity 

Average Last Run 

Peak Power (in2/Hz) 

High Fidelity 

Average First Run 

Peak Power (in2/Hz) 

Low Fidelity 

Average Last Run 

Peak Power (in2

/Hz) 

Low Fidelity 
109 

his/her peak frequency from 0.293 Hz to 0.5615 Hz. The high fidelity test subjects are 

maintaining a higher peak frequency than the low fidelity group. There is a greater 

difference in the peak frequency than for 1/s plant dynamics. The peak frequencies and 

peak power for each test subject is shown in Appendix H. 

 

Figure 6.3.6 Average Peak Frequency (1/s 2 Plant Dynamics) 

 The average peak power and peak frequency gives us a general sense of where 

test subjects are using most of their power. The peak power used by most test subjects is 

between 0.18 and 0.2 Hz. One of the frequencies contained in the disturbance is 0.1862 

Hz. The peak power and frequency gives an observation of the test subject’s workload at 

one peak frequency that is not always equal between test subjects. To determine the 

difference between the two groups, the average Power Spectral Density (PSD) for 1/s is 

plotted in Figures 6.3.8 through 6.3.10. The PSD is averaged by adding up the power at 

each frequency and dividing by the total number of test subjects and plotting this against 

the frequency vector that is common to all test subjects. There is a plot for the last run 

training phase, the first run transfer phase and last run transfer phase for both 1/s and 1/s2

0

0.05

0.1

0.15

0.2

0.25

0.3

 Training Phase Transfer Phase 

Average Peak Frequency 

 (1/s2 Plant Dynamics) 

Average First Run Peak

Frequency (Hz) High

Fidelity

Average Last Run Peak

Frequency (Hz) High

Fidelity

Average First Run Peak

Frequency (Hz) Low

Fidelity

Average Last Run Peak

Frequency (Hz) Low

Fidelity
110 

plant dynamics. As a comparison to the test subject’s Power Spectral Density, the PSD of 

the disturbance forcing function is shown below in Figure 6.3.7. 

Figure 6.3.7 PSD of Disturbance Forcing Function 

The peak frequencies within the PSD of the disturbance correspond with the frequencies 

of the nine sinusoids used to develop the sum of sinusoids disturbance. The power at 

higher frequencies is in the vicinity of 104 times smaller than the highest power. 

 The average PSD for the high fidelity and low fidelity training groups in the last 

run of the training phase is very similar. They have the same peak power around 0.45 

in2

/Hz and peak frequency around 0.1953 Hz. The three other peak frequencies include 

0.293 Hz, 0.5615 Hz, and 1.11 Hz. These peak frequencies are around the frequencies of 

the sum of sinusoids disturbance. When the high fidelity training group transfers they 

maintain a similar peak frequency and peak power in the transfer phase. The low fidelity 

group reduces their peak power and maintains the same peak frequencies as the high 

fidelity group. The low fidelity group increases their peak power and maintains a similar 

10-1 100 101 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: 0.1114

Y: 0.997

PSD of Disturbance

Frequency (Hz)

Normalized Power

X: 0.07401

Y: 0.9775

X: 0.1862

Y: 1

X: 0.2975

Y: 0.2478

X: 0.5585

Y: 0.04015

X: 1.115

Y: 0.002576

X: 0.8751

Y: 0.0007942

X: 2.228

Y: 0.0002383

X: 2.975

Y: 0.0001245
111 

power spectral density as the high fidelity training group in the last run transfer phase. 

The similarity in peak frequencies and peak powers for both groups suggest very similar 

control strategy. The similar control strategy results in similar tracking error 

performance. 

Figure 6.3.8 Average PSD for High Fidelity and Low Fidelity Training Test Subjects Last Run Training 

(1/s Plant Dynamics) 

Figure 6.3.9 Average PSD for High Fidelity and Low Fidelity Training Test Subjects First Run Transfer 

(1/s Plant Dynamics) 

10-2 10-1 100 101 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Average PSD for High Fidelity and Low Fidelity Subjects LRTG (1/s Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity

10-2 10-1 100 101 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Average PSD for High Fidelity and Low Fidelity Subjects FRTF (1/s Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity
112 

Figure 6.3.10 Average PSD for High Fidelity and Low Fidelity Training Test Subjects Last Run Transfer 

(1/s Plant Dynamics) 

For 1/s2

 plant dynamics there is a difference in peak power. The average power 

spectral density (PSD) for 1/s2

 is plotted in Figures 6.3.11 through 6.3.13. In this case, the 

low fidelity group maintains a higher peak power and fewer peak frequencies than the 

high fidelity group. The high fidelity group maintains greater power at the higher 

frequencies and has less power at frequencies below 0.1 Hz. As both groups transfer they 

increase their power with the low fidelity group containing a higher peak power. The 

high fidelity group has increased their power at 0.293 Hz. Still, the high fidelity group is 

able to operate in more than one frequency and at the higher frequencies. In the final run 

of the transfer phase, the low fidelity group adapts and operates at the extra frequencies 

that the high fidelity group initially operated at. The high fidelity group increases their 

peak frequency while the low fidelity group reduces their peak power adopting a similar 

control strategy with the same power and frequency peaks. The dissimilar power 

10-2 10-1 100 101 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Average PSD for High Fidelity and Low Fidelity Subjects (1/s Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity
113 

spectrum in the training phase gives insight into the significant difference in tracking 

performance. 

Figure 6.3.11 Average PSD for High Fidelity and Low Fidelity Training Test Subjects Last Run Training 

(1/s2

 Plant Dynamics) 

Figure 6.3.12 Average PSD for High Fidelity and Low Fidelity Training Test Subjects First Run Transfer 

(1/s2

 Plant Dynamics) 

10-2 10-1 100 101 0

0.5

1

1.5

2

2.5

3

Average PSD for High Fidelity and Low Fidelity Subjects LRTG (1/s2 Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity

10-2 10-1 100 101 0

0.5

1

1.5

2

2.5

3

3.5

4

Average PSD for High Fidelity and Low Fidelity Subjects FRTF (1/s2

 Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity
114 

Figure 6.3.13 Average PSD for High Fidelity and Low Fidelity Training Test Subjects Last Run Transfer 

(1/s2

 Plant Dynamics) 

To understand how each test subject’s power is related to performance, the PSD 

of the two best and two worst test subjects, based on their tracking error performance, is 

utilized. Shown in Figure 6.3.14 and Figure 6.3.15 is the PSD for the two worst and two 

best performing test subjects for the high fidelity and low fidelity group using 1/s plant 

dynamics respectively. Shown in Figure 6.3.16 and Figure 6.3.17 is the PSD for the two 

worst and two best performing test subjects for the high fidelity and low fidelity group 

using 1/s2

 plant dynamics respectively. The test subjects that have the best performance 

have the two largest power amplitudes and are operating with more power in the upper 

frequencies. Reduced power at the same frequencies between two test subjects suggests 

less workload. Less workload does not necessarily indicate that the test subject is 

performing better. Increased power at the specific peak frequencies implies that the test 

subjects are using higher control inputs. A higher control input correlated well with the 

10-2 10-1 100 101 0

0.5

1

1.5

2

2.5

3

3.5

4

Average PSD for High Fidelity and Low Fidelity Subjects LRTF (1/s2 Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

High Fidelity

Low Fidelity
115 

disturbance gives the test subject greater control authority. A small control input is not 

enough to null the difference while too much control input overcompensates for the 

disturbance. 

 Figure 6.3.14 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(High Fidelity 1/s Plant Dynamics) 

 Figure 6.3.15 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(Low Fidelity 1/s Plant Dynamics) 

10-2 10-1 100 101 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PSD of Control Inceptor Deflection for High Fidelity Subjects (1/s Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

HF002 (Best Performance)

HF009 (2nd Best Perfomance)

HF007 (2nd Worst Performance)

HF008 (Worst Performance)

10-2 10-1 100 101 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PSD of Control Inceptor Deflection for Low Fidelity Subjects (1/s Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

LF006 (Best Performance)

LF005 (2nd Best Perfomance)

LF003 (2nd Worst Performance)

LF004 (Worst Performance)
116 

 Figure 6.3.16 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(High Fidelity 1/s 2

 Plant Dynamics) 

 Figure 6.3.17 PSD of Control Inceptor Deflection for Best and Worst Test Subjects 

(Low Fidelity 1/s2

 Plant Dynamics) 

10-2 10-1 100 101 0

1

2

3

4

5

6

PSD of Control Inceptor Deflection for High Fidelity Subjects (1/s2 Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

HF002 (Best Performance)

HF009 (2nd Best Perfomance)

HF005 (2nd Worst Performance)

HF006 (Worst Performance)

10-2 10-1 100 101 0

0.5

1

1.5

2

2.5

3

3.5

4

PSD of Control Inceptor Deflection for Low Fidelity Subjects (1/s2 Plant Dynamics)

Frequency (Hz)

Power (in2/Hz)

LF006 (Best Performance)

LF005 (2nd Best Perfomance)

LF010 (2nd Worst Performance)

LF007 (Worst Performance)
117 

6.4 Coherence Analysis 

 The next analysis involves the coherence of each test subject’s control inceptor 

deflection to the disturbance. Coherence analysis shows the correlation between two 

signals. The two best and two worst test subjects were removed from both the high 

fidelity and low fidelity training groups. This leaves us with six test subjects in each 

group. Since it is difficult to interpret the data from all 12 test subjects from both groups 

at one time, only three test subjects from each group are presented in each coherence 

figure. 

Shown in Figure 6.4.1 is the coherence for test subjects using 1/s plant dynamics. 

The two groups typically have the highest coherence between 0.18 and 0.2 Hz. There is 

also a peak in the coherence at 0.5371 Hz and 1.123 Hz. These values correspond to the 

frequencies contained within the disturbance. At the upper frequencies the test subjects 

are less correlated with the disturbance. There is a lot of noise beyond 1.2 Hz which is 

due to the sparse frequency information from the disturbance input and control inceptor 

deflection. This portion is disregarded for analysis. 

Figure 6.4.1 Coherence between Control Inceptor Deflection and Disturbance Forcing Function 

(1/s Plant Dynamics) 

10-1 100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Coherence Between Control Inceptor Deflection and Disturbance (1/s Plant Dynamics)

Frequency (Hz)

Amplitude

HF001

HF004

HF005

LF010

LF008

LF009
118 

 Shown in Figure 6.4.2 is the coherence for 1/s2

 plant dynamics. For 1/s2 plant 

dynamics there seems to be less coherence across all frequencies. Also, the test subject’s 

coherence between 0.05 and 0.3 Hz is much lower for 1/s2

 plant dynamics. The 

frequencies in this range are very important since most of the power in the disturbance 

signal is dedicated to the lower frequency range. The lower coherence at the lower 

frequencies has an adverse effect on the test subject’s control strategy. The test subjects 

tend to adapt to a low frequency high amplitude motion in which most of the test subjects 

reach the maximum deflection of the control inceptor in both directions. The coherence 

for 1/s2

 is much more diversified between test subjects than the coherence for 1/s plant 

dynamics. The harder task causes test subjects to be highly uncorrelated with the 

disturbance. Test subjects need to be highly correlated with the disturbance across its nine 

frequencies to perform with a minimum tracking error. 

Figure 6.4.2 Coherence between Control Inceptor Deflection and Disturbance Forcing Function 

(1/s2

 Plant Dynamics) 

10-1 100 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Coherence Between Control Inceptor Deflection and Disturbance

Frequency (Hz)

Amplitude

HF1

HF3

HF4

LF1

LF2

LF4
119 

6.5 Frequency Responses of Test Subjects 

 In pursuing an investigation of human control strategy, the frequency response 

relating the input roll error as seen by the test subject and the output control inceptor 

deflection was sought. The frequency response function is related to PSD by means of a 

Fast Fourier transform (FFT) which is a faster algorithm to calculate the Discrete Fourier 

transform (DFT). The periodogram method was used to calculate the PSD and is equal to 

the Discrete Fourier Transform (DFT) of the autocorrelation. Equation 6.5.1 corresponds 

to the PSD calculation using the periodogram method. 

 

1

2

0

1 [][ ] [ ]

M N m k j n N

mMi

PSD x i x i m w m e

N

# 	 	 	

	 

  ' ' Equation 6.5.1 

To implement this method, the input signal was first zero-padded which is conducted by 

adding zeros to the end of the signal and making the signal length equal to a power of 

two. Next, a Hamming window function is applied to the zero-padded signal equal to the 

length of the signal. Next the autocorrelation is found by obtaining the convolution of the 

signal with the signal at a different time. The signal vector was flipped making its first 

value a value at the end of the signal so that the signal is being convolved with future 

values of itself. The absolute value is taken to calculate the magnitude of the complex 

number obtained when computing the Discrete Fourier Transform (DFT). The code to 

obtain the PSD is shown in Appendix J. 

 The frequency response of a linear system relates the amplitude and phase of the 

output to the input. There are many ways to measure the frequency response of a system. 

A frequency sweep, a sum of sinusoids, band-limited white noise, and an impulse can be 

injected into a system to be measured. Obtaining the frequency response converts the 

time-domain signal into the frequency domain representation. This is conducted using the 
120 

Fourier transform which represents a time domain signal as a sum of sinusoids with 

different amplitudes, phases and frequencies. When a sinusoid is passed through a linear 

time invariant (LTI) system, only the amplitude and phase change for the sinusoid. By 

measuring the difference of the amplitude and phase between the output and input at each 

frequency, a frequency response can be obtained. 

 Traditional methods include exciting the system by applying a frequency sweep 

consisting of sinusoids of different frequencies and constant amplitude to the input. The 

output response is measured and the amplitudes and phases of each sinusoid at each 

frequency are individually calculated. New techniques exist which allow the user to 

excite the system with a frequency sweep, sum of sinusoids, or an impulse and use the 

quotient of the Fast Fourier Transform (FFT) of the output and the input. The frequency 

response analysis has been discussed previously in Chapter 4 in Section 4.4. This 

technique was used to obtain the frequency response of the control inceptor used in the 

quasi-transfer of training experiment. 

 To better understand the behavior of the test subjects, the frequency response was 

attempted for each test subject. However, testing multiple test subjects is time consuming 

when implementing a frequency sweep. The roll disturbance compensatory experiment 

was designed with a sum of sinusoids disturbance. The sum of sinusoids method has been 

used in the past by Johnston and Aponso (1988) [10] to obtain frequency response 

functions for test subjects. The system to be measured in this case is the human control 

strategy. The input to the human is the roll error shown on the display and the output used 

is the control inceptor deflection. The FFT technique shown in Chapter 4, Section 4.4 

was employed. 
121 

 The FFT is an efficient way to compute the Discrete Fourier Transform (DFT) of 

a signal. The Fourier transform is a way of converting the time domain into the frequency 

domain. The Fourier transform is similar to the Fourier series. The Fourier series 

represents any periodic signal as a sum of sinusoids in the complex form o jk t

k

k

c e 

(

	(

' . 

To estimate the Fourier coefficients ck, Equation 6.5.2 is used. 

 0

1 ( ) o o

t T jk t

k

t

c xt e dt

T

  	  ) Equation 6.5.2 

The term ck is a complex number which represents both the amplitude and phase of a 

periodic sinusoid. The Fourier coefficients ck can only be analyzed at a multiple of the 

periodic signal frequency. The Fourier transform is similar to the Fourier coefficients in 

that it builds the signal out of a sum of sinusoids of different frequencies. The difference 

is that the Fourier transform can be used for non-periodic signals. The formula for the 

Fourier transform is shown in Equation 6.5.3. 

 

( ) () j t X xt e dt   ( 	

	(

 ) Equation 6.5.3 

 The Fourier transform has a very similar structure to the Fourier coefficients 

except that the Fourier transform can be calculated at any frequency of importance when 

dealing with a signal that is not composed of harmonic frequencies. As shown, the 

Fourier transform is applied over an infinite time scale. This can only be solved 

analytically and cannot be analyzed with discrete data points over a finite time signal. 

The Discrete Time Fourier Transform (DTFT) is used for discrete data sets. The DTFT is 

shown in Equation 6.5.4. 
122 

 

( ) [] j n

n

X xne

(

	 *

	(

*  ' Equation 6.5.4

The structure again is very similar to the continuous time Fourier transform shown in 

Equation 6.5.3 except that it is a summation of discrete data points. Again, this requires 

an infinite number of data points. To deal with a finite number of data points, the Discrete 

Fourier Transform (DFT) shown in Equation 6.5.5 is used. 

 

1

2 /

0

() []

N

j kn N

n

X k xne #

	

	



' Equation 6.5.5 

 

 The DFT represents the DTFT sampled at integer intervals. By having a limited 

number of data points, it limits the accuracy of the computed DFT. The number of data 

points limits the spacing of frequencies that the DFT is calculated at. The frequency 

interval is limited by Equation 6.5.6. 

 

2 s kkF

N

#

  Equation 6.5.6

This formula shows that the sampling rate and number of data points has an effect of how 

closely spaced the samples of the DTFT are. Increasing the number of points without 

increasing the sampling frequency can be done two ways. The length of the signal 

collected has to be sufficiently long for a specific sampling rate to get more frequency 

points. The higher the sampling rate, the longer the signal has to be to produce a finer 

DFT frequency vector. Increasing the sampling rate of a data set that is time-limited, does 

not improve the number of frequency points for the DFT. One way to increase the 

number of points is to run the signal for a longer time period. The problem with this is 
123 

that it can only be done when collecting data. If you already have data for a certain time 

period, the method of zero-padding can improve the DFT calculation. 

 Since the data collected from each test subject was run for only 30 seconds, the 

method of zero-padding was used. To also remove the effect of spectral leakage a 

Hamming window function was applied to each signal. To show the effect of zeropadding and lengthening the time signal, the single sided amplitude spectrum of the sum 

of sines disturbance is plotted in Figure 6.5.1. 

Figure 6.5.1 Single Sided Amplitude Spectrum of Disturbance 

The corresponding amplitudes and frequencies of the sinusoids present in the disturbance 

are shown in Table 6.5.1. 

Sine Wave 1 2 3 4 5 6 7 8 9 

Frequency (ωi rad/s) 0.467 0.701 1.17 1.87 3.51 7.01 11/2 14 18.7 

Amplitude (Ai) 15.2 15.2 15.2 7.6 3.04 0.76 0.38 0.228 0.152 

Table 6.5.1 Disturbance Sum of Sinusoids Parameters 

10-1 100 101 102 0

2

4

6

8

10

12

14

16

X: 1.87

Y: 7.602

X: 0.4679

Y: 15.2

Single-Sided Amplitude Spectrum of Disturbance

Frequency (rad/s)

|Y(f)|

X: 0.7018

Y: 15.2

X: 1.17

Y: 15.2

X: 3.511

Y: 3.04

X: 5.499

Y: 0.38

X: 7.01

Y: 0.7603

X: 14

Y: 0.2281

X: 18.7

Y: 0.1519

No Zero Padding

Zero Padded 5,808 zeros

Longer Run Time 200 sec
124 

The FFT of the disturbance signal with a 31.28 second length and a 12.5 Hz 

sampling rate does not correspond well with the frequencies contained in the disturbance. 

Zero-padding the signal improves the location of the peaks. The zero-padded signal still 

does not match the amplitudes and frequencies of the sum of sinusoids accurately. 

Increasing the length of the signal from 31.28 seconds to 200 seconds has the best 

improvement. When zero-padding, the added zeros create a higher frequency resolution, 

but do not add any more information to the DFT. By collecting longer data samples, it is 

adding more information to process the DFT. The only thing that can be concluded is that 

for the sample data that was taken in the experiments; zero-padding and the use of a 

window function other than a rectangular window can improve the DFT calculation. The 

frequency response results with zero-padding and windowing are shown in Figure 6.5.2. 

Figure 6.5.2 Test Subject HF002 Experimental Frequency Response 

10-1 100 101 102 -60

-40

-20

0

20

Experimental Subject Frequency Response (Subject HF002)

Frequency (rad/s)

Amplitude (dB)

10-1 100 101 102 -1000

0

1000

2000

3000

Frequency (rad/s)

Phase (Degrees)

Points corresponding to input Signal

Experimental Frequency Response

Precision Model Frequency Response
125 

In this plot, the frequency response of the test subject along with a precision model 

adopted from Magdaleno & McRuer (1986) [11] are plotted. The precision model used is 

shown in Equation 6.5.7. 

 

2 2

4082.328

( 11.8)( 2(.138)(18.6) (18.6)

Yp

ss s   

Equation 6.5.7 

The response does not correspond well with the precision subject model. Also the 

phase representation diverges at above 10 rad/s. The frequency response was going to be 

used to determine bandwidth, crossover frequency, gain margin, and phase margin 

calculations. From this frequency response the bandwidth cannot be clearly determined. 

This response represents only one run completed by test subject HF002. To improve the 

frequency response, four runs at the end of training were combined and the frequency 

response was averaged across the four runs. The response is shown in Figure 6.5.3. 

Figure 6.5.3 Test Subject HF002 Experimental Frequency Response Averaged O ver Four Runs 

10-2 10-1 100 101 102 -60

-40

-20

0

20

Experimental Subject Frequency Response (Subject HF002)-Averaged over 4 Runs

Frequency (rad/s)

Amplitude (dB)

10-2 10-1 100 101 102 -400

-200

0

200

400

Frequency (rad/s)

Phase (Degrees)

Points corresponding to input Signal

Experimental Frequency Response

Precision Model Frequency Response
126 

In this figure, there seems to be a better frequency response but it is limited by the 

number of input frequencies that stimulated the system. Above 18.7 rad/s, the highest 

frequency in the input disturbance, there is noise and the phase is not reliable. Looking at 

the coherence (Figure 6.5.4 & Figure 6.5.5) between the input signal represented by the 

roll error and the output control inceptor deflection, the coherence drops off drastically 

after 10 rad/s. Because the coherence between signals is small after 10 rad/s, our 

frequency response will be unreliable above this frequency. 

Figure 6.5.4 Coherence Between Roll Error and Control Inceptor Deflection for O ne Run (Test Subject HF002) 

Figure 6.5.5 Coherence Between Roll Error and Control Inceptor Deflection Average over Four Runs (Test 

Subject HF002) 

10-1 100 101 102 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Coherence Between Roll Error and Control Inceptor Deflection

Frequency (rad/s)

Amplitude

10-2 10-1 100 101 102 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Coherence Between Roll Error and Control Inceptor Deflection

Frequency (rad/s)

Amplitude
127 

 To test the frequency response method using a sum of sinusoids input disturbance 

function on a linear time invariant (LTI) system, the disturbance was passed through a 

second order transfer function in Matlab [21]. The second order transfer used is shown in 

Equation 6.5.8. The frequency response was found using the Matlab [21] program in 

Appendix D. 

 

2

2 2

(6) ( ) 2(0.135)(6) (6)

H s

s s   

 

Equation 6.5.8 

Shown in Figure 6.5.6 is the frequency response with input disturbance as defined by 

Table 6.5.1. This was the disturbance used within the compensatory tracking task. The 

frequency response is only reliable at the points corresponding to the frequencies in the 

input disturbance signal. These points are represented by circles on the plot. This is 

because the frequency response is a comparison of output amplitude and phase to input 

amplitude and phase. For a linear system, the experimenter will only have outputs at the 

same frequency as the input signal. If output information exists at different frequencies 

than the input, the experimenter has a non-linear system, and frequency response methods 

are unreliable. 

 The same frequency response with more frequency points included in the input 

disturbance signal is shown in Figure 6.5.7. Also, the frequency was extended up to 25 

rad/s. As shown, the points corresponding to the input frequencies line up better with the 

true frequency response. After 25 rad/s, no comparison can be made between the output 

and input, so the results are not consistent with the true response. This behavior is shown 

in the experimental response, where the lack of frequency points causes unwanted noisy 

behavior between sucessive frequency points. This shows how increasing the number of 
128 

frequencies and extending the frequency to a higher frequency in the input disturbance 

can improve results. 

 Figure 6.5.6 Frequency Response for LTI System (O rigi nal Disturbance Forcing Function) 

Figure 6.5.7 Frequency Response for LTI System (Finer Frequency Vector Input) 

10-2 10-1 100 101 102 103 -100

-50

0

50

Frequency Reponse for Second Order Transfer Function 36/(s2+2(.135)(6)+(6)2)

Frequency (rad/s)

Amplitude (dB)

10-2 10-1 100 101 102 103 -600

-400

-200

0

200

Frequency (rad/s)

Phase (Degrees)

Points corresponding to input Signal

Experimental Frequency Response

True Frequency Response

10-2 10-1 100 101 102 103 -100

-50

0

50

Frequency Reponse for Second Order Transfer Function 36/(s2+2(.135)(6)+(6)2

Frequency (rad/s)

Amplitude (dB)

10-2 10-1 100 101 102 103 -300

-200

-100

0

100

Frequency (rad/s)

Phase (Degrees)

Points corresponding to input Signal

Experimental Frequency Response

True Frequency Response

Frequency Response for Second Order Transfer Function 36/(s2+2(.135)(6) +(6)2)
129 

 The frequency response (Figure 6.5.8) using a chirp signal with closely spaced 

frequencies was input into the transfer function. The response matches the true response 

very well. The input forcing function presented to the test subjects needs higher 

frequencies and finer spaced frequencies. Since a sum of sinusoids is presented to the test 

subject, including higher frequencies may cause the test subject to have a more difficult 

time responding with the same frequency motion. 

 Figure 6.5.8 Frequency Response for LTI System (Chirp Input Signal) 

 In conclusion, the frequency response results were not sufficient to accurately 

determine bandwidth and other control strategy differences between test subjects. To get 

a better frequency response function for each test subject, the input forcing function has 

to be investigated. The forcing function as is has to include more in-between frequencies 

and the amplitude for each frequency has to be set accordingly so test subjects are able to 

respond to those frequencies. Longer runs of 2 to 4 minutes will also aid in better FFT 

10-2 10-1 100 101 102 103 -150

-100

-50

0

50

Frequency Reponse for Second Order Transfer Function 36/(s2+2(.135)(6)+(6)2

Frequency (rad/s)

Amplitude (dB)

10-2 10-1 100 101 102 103 -300

-200

-100

0

Frequency (rad/s)

Phase (Degrees)

Points corresponding to input Signal

Experimental Frequency Response

True Frequency Response

Frequency Response for Second Order Transfer Function 36/(s2+2(.135)(6) +(6)2)
130 

results. The sampling rate should also be increased to at least 100 Hz when recording 

data. 

6.6 Remnant 

Remnant is defined as the portion of the operator’s output that is not related to the 

system input. The remnant is the result of the non-linear behavior of the test subjects. 

This gives rise to the quasi-linear model of the human. The describing function is 

represented by the linear correlated input and output of the test subject. The remnant 

describes the remaining non-linear behavior of the test subject. Shown in Figure 6.6.1 and 

Figure 6.6.2 are the PSDs of test subject HF002 and test subject HF005. 

Figure 6.6.1 PSD of Control Inceptor Deflection for Test Subject HF002

Examples of remnants are labeled in these figures. The points labeled in this figure are 

the frequencies that are near the frequencies of the input disturbance. These frequencies 

are very close to the disturbance input frequencies but not the exact frequencies. From 

test subject to test subject, the peak powers occur near the disturbance input frequencies. 

The power not corresponding to the spikes in the power spectral density is considered the 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

X: 0.1953

Y: 1.127

PSD of Control Inceptor Deflection First Run Training Phase (HF-002 1/s)

Frequency (Hz)

Power

X: 0.3052

Y: 0.4799

X: 0.5493

Y: 0.4754

X: 0.1099

Y: 0.4669

X: 0.8911

Y: 0.1187

X: 1.123

Y: 0.2104

Remnant 
131 

remnant. Most of the test subjects do not contain a significant remnant suggesting they 

maintain a mostly linear behavior. 

Figure 6.6.2 PSD of Control Inceptor Deflection for Test Subject HF005

Chapter 7 – Conclusions and Future Recommendations 

7.1 Summary 

This research was conducted in order to ascertain differences that exist when 

training on a high fidelity or a low fidelity control loader simulation. This will either 

dispute or verify the importance of maintaining a high fidelity control loader when 

training pilots. Along with comparing the difference between the two training groups, it 

provides examples of frequency domain methods to analyze test subject control strategy. 

These experiments can be modified to better characterize the human control strategy. 

Techniques using power spectral density (PSD) to characterize human control behavior is 

a fairly new concept and this has to be further analyzed to understand how the PSD is 

related to human control. 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 X: 0.293

Y: 0.6214

PSD of Control Inceptor Deflection First Run Training Phase (HF-005 1/s)

Frequency (Hz)

Power

X: 0.1831

Y: 0.5734

X: 1.111

Y: 0.06557

X: 0.5493

Y: 0.2788

X: 0.8911

Y: 0.08539

Remnant 
132 

The first step in this research was to review the neuromuscular system and the 

many experiments conducted to understand how to effectively test two different control 

loader dynamics and the effect it has on the test subject performing the task. This 

literature review together with knowledge about control systems was the basis for 

developing an experiment to test subjects. 

The second step was to develop the experimental task. The experiment consisted 

of a roll disturbance compensatory task. This is a typical task used to test human 

performance in a simulator because of easy implementation and transportability to other 

simulators. The two tasks used were a simpler task consisting of 1/s plant dynamics and a 

harder task using 1/s2 plant dynamics. 

The next step was to determine the proper dynamics to represent the high fidelity 

and low fidelity parameters. The high fidelity parameters were determined from the 

literature and the low fidelity from a computer joystick. The low fidelity control inceptor 

represents a low damped, small force gradient control inceptor. These dynamics were 

implemented and then verified by determining the damping ratio and force gradients from 

the time and frequency responses. 

Finally 20 test subjects were split into two groups consisting of 10 each. One 

group trained on the high fidelity control inceptor and the second group trained on the 

low fidelity control inceptor. After training both groups were then transferred to the high 

fidelity control inceptor simulation. 

7.2 Conclusions 

The results show that for 1/s plant dynamics the two groups maintain a similar 

control strategy throughout the training and transfer phases. Their performance measured 
133 

using the root mean (RMS) tracking error for each run over the course of the experiment 

shows very similar performance without a significant difference. The power spectrum 

density for the two groups shows similar peak power and peak frequency. Typically, the 

test subject’s peak power coincided with a portion of the 9 frequencies in the sum of 

sinusoids disturbance. This shows that they are responding directly to the disturbance in 

their control strategy. 

The test subjects also have a maximum peak power at a frequency between 0.18 

and 0.2 Hz which is one of the highest amplitudes in the sum of sinusoids disturbance. 

Two sinusoids with a frequency of 0.074 Hz and 0.112 Hz in the sum of sinusoids 

disturbance have the same amplitude of 15.2 degrees roll angle as the 0.2 Hz sinusoid. 

Test subjects maintain power below 0.2 Hz but do not peak within this region. The power 

also decreases beyond 0.2 Hz as does the disturbance amplitude. The disturbance shows 

lower frequency behavior more so then high frequency behavior. The amplitude 

decreases for the higher frequency sinusoids. An interesting behavior shown is that the 

low fidelity control loader training test subjects generally have a lower peak frequency 

for their first run but they train to a higher peak frequency similar to the high fidelity 

group even before they transfer. The high fidelity group maintains their peak power better 

when they transfer than the low fidelity group, but the low fidelity group adapts very 

quickly and soon increases their peak power. By the last run, both groups have similar 

peak power and peak frequencies. 

For 1/s2

 plant dynamics, the difference between the two groups is greater. The 

high fidelity group performs better in terms of having a smaller asymptote tracking error. 

Also, the power spectrum density suggests a different control strategy by either group. 
134 

The low fidelity group uses all their power at one frequency around 0.2 Hz, while the 

high fidelity group uses their power at higher frequencies. The power dedicated to one 

frequency, especially a low frequency, suggests a high amplitude oscillatory behavior at 

one frequency. This is a typical strategy when the test subject cannot keep up with the 

disturbance. Both groups use much higher power for 1/s2 plant dynamics suggesting high 

amplitude control inceptor deflection. The low fidelity training group adapts this high 

amplitude nature through the training phase and first run transfer phase. They eventually 

use their power at the higher frequencies suggesting that the high fidelity control inceptor 

allows them to operate in the higher frequencies. The PSD for both groups is very similar 

during the last run of the experiment showing that the low fidelity test subjects adapt and 

pick a strategy similar to the high fidelity test subjects. The results show that maintaining 

a high fidelity control loader system is more important for the harder task. The test 

subjects that performed the worst in each group for both 1/s and 1/s2

 plant dynamics 

generally use less power and use this power at fewer frequencies than the best performing 

test subjects within the group. 

In conclusion, there is no significant difference in the performance and power 

spectral density between the high fidelity group and the low fidelity group for 1/s plant 

dynamics. The similar control behavior represented by the PSD agrees with the similar 

tracking error achieved by both training groups. The low fidelity test subjects trained with 

similar peak power and peak frequencies through the training phase and transfer phase. 

This allows the low fidelity test subjects to adapt when they transfer to the high fidelity 

control dynamics. For 1/s2 plant dynamics there is an advantage to training on the high 

fidelity control loader. Both the tracking error and power spectrum density is different for 
135 

both groups using 1/s2

 plant dynamics. The low fidelity group adapts their use of peak 

power and frequencies to match the high fidelity group in the last run transfer phase, but 

only maintain one peak frequency in the training phase and first run transfer phase. The 

low fidelity group has low coherence at the peak frequency they operate at. The use of 

one peak frequency combined with a highly uncorrelated test subject leads to degraded 

tracking error performance. 

7.3 Future Recommendations 

There are many improvements that can be implemented to further analyze the 

human control strategy. In the experiments only 20 test subjects were used. Although 20 

test subjects are significant to test differences, some test subjects were removed. These 

experiments will be repeated with more test subjects and will be grouped accordingly to 

statistical properties. 

The experiment could be improved by refining the asymptotic criterion when a 

test subject has trained. To determine when test subjects reached training asymptote, the 

slope of the tracking error between two runs was computed. A criterion was set that the 

slope should reach a value of 0.1 or less for three consecutive runs. This value was set 

based on tests performed off-line. It was observed that some test subjects didn’t reach an 

asymptote. A new definition of horizontal asymptote can be derived for new experiments 

or a longer number of runs can be conducted to ensure test subjects reach asymptote. 

Another improvement to be made is to the disturbance forcing function. The 

disturbance forcing function was adopted from the literature and represents a sum of 9 

sinusoids with increasing frequencies and decreasing amplitudes. The higher frequency 

sinusoids might not be seen by the test subjects with the diminished amplitude. It would 
136 

be beneficial to analyze the disturbance and change the amplitudes to see the effect it has 

on the test subject. The test subjects might adopt a different control strategy or shift their 

peak power. This would show the limitation of the neuromuscular system and the effect 

of changing vehicle dynamics. 

The implementation of a non-linear force gradient for the control inceptor 

dynamics could enhance the study further. Only a linear force gradient was implemented 

in this study. The experiments could test if non-linear force gradients are better than 

training with a linear force gradient. This change could mimic the effects of the nonlinear aerodynamics on the control surfaces. 

 This research is ongoing and is important to vehicle simulation. The main 

interface to the vehicle is the neuromuscular limb interaction and it is very important to 

understand the effects of poorly simulating control inceptor dynamics. Many experiments 

can be tested concerning different control inceptor dynamics and to develop a better 

understanding of human control strategy. 
137 

Appendices 

Appendix A: Control Loader Quasi Transfer of Training Experimental Protocol 

Pre-Experiment 

Description 

 The purpose of the pre-experiment phase is to make sure the implementation of 

the roll compensatory task is ready for experimentation. The pre-experimental tests are 

conducted with a simulator pilot. 

Initial Tests

1. Ensure that the display is showing the target clearly. 

2. Ensure that the system responds properly to test subject input. Deflect the control 

inceptor at increasing amplitudes and hold. The roll rate of the display bank angle 

reference line should consistently increase with increasing control inceptor 

deflection. 

3. Activate disturbance and ensure the output of the display responds to the 

disturbance. The roll reference line on the display should show a quasi random 

response. 

4. Test data recording. Make sure output sensor measurements are within the 

operating range. 

a) Deflect control inceptor one direction and then the other. In one direction, the 

output control inceptor position sensor should show decreasing values and 

increasing values in the other direction. The control inceptor position should 

be at a value of 0 when centered and is not deflected. Force values should 

increase in either direction as one deflects the control inceptor further. The 

force should also be calibrated to zero when no input is applied to the control 

inceptor. 

b) Activate disturbance and do not apply any control inceptor input. Obtain the 

bank angle measurement. This should be the same as the disturbance input 

that has gone through the plant dynamics defined in the Control Loader Quasi 

Transfer of Training Experimental Plan. 

Roll Command Gain Tuning 

Plant Dynamics 1/s 

High Fidelity/Low Fidelity 

1. Initialize roll command gain at 40 deg/sec/in. 

2. Run roll compensatory task and note if the system is controllable 

3. Adjust gain if needed. 
138 

Plant Dynamics 1/s2

High Fidelity/Low Fidelity 

1. Initialize roll command gain at 40 deg/sec2

/in. 

2. Run roll compensatory task and note if the system is controllable 

3. Adjust gain if needed.

Experiment 

Description 

Each test subject will go through all four phases of the experiment before the next test 

subject conducts the experiment. A break will be administered in between the training 

and quasi transfer sessions for each test subject. The high fidelity transfer group will train 

on one day and the low fidelity group will train on another day. A break will be 

administered after each training session and then again before the test subjects start 

training on 1/s2

 plant dynamics. 

Familiarize 

1. Test subjects will be briefed on the task they are to perform. 

2. Allow test subjects to perform a single run of the experiment for both 1/s and 1/s2

dynamics. 

Evaluation 

1. 10 test subjects will be assigned to the low fidelity control loader transfer group 

and another 10 test subjects will be assigned to the high fidelity control loader 

transfer group. Test subjects will be assigned a number associating them with 

either group. The high fidelity group will start with HF001 and the low fidelity 

group will start with LF001. 

2. For subsequent tasks the control inceptor deflection, bank angle, control inceptor 

force, and tracking error will be recorded throughout the run. The RMS & STD 

input will be calculated for each test subject for the one run length at a later time. 

Also, a PSD analysis of the control inceptor deflection and control inceptor 

bandwidth input will be calculated at a later time. This is the baseline 

performance level for each test subject. 

3. Each test subject in the high fidelity control loader transfer group is to perform a 

30 second run of the high fidelity control loading roll tracking compensatory task 

for 1/s and 1/s2 plant dynamics. 

4. Test subjects will give a Modified Cooper Harper Rating (CHR) for both runs of 

1/s and 1/s2

 dynamics. They may also give any comments on tasks. 

5. Repeat Steps 2-5 for the low fidelity control loader transfer group. 
139 

Training 

1. The high fidelity control loader transfer group will train on the high fidelity 

control loader simulation and the low fidelity transfer group will train on the low 

fidelity control loader simulation. 

2. The test subjects will perform the roll compensatory tracking task for 1/s and 1/s2

plant dynamics. Each run will last for 30 seconds. 

3. They will conduct as many runs as necessary to reach a performance asymptote. 

In this case, the cumulative running average of the RMS tracking error will be 

used as the performance metric. As the slope of this performance metric 

approaches zero, asymptote has been reached. 

Throughout each run, the following parameters will be recorded. These parameters along 

with frequency of measurement are listed in the Control Loader Quasi Transfer of 

Training Experiment Plan. 

a) Bank Angle 

b) Control Inceptor Deflection 

c) Control Inceptor Force 

d) RMS Control Inceptor Deflection 

e) Running Cumulative Average of RMS Tracking Error 

f) Running Cumulative Average RMS Control Inceptor Deflection 

g) Slope of the Running Cumulative Average of the RMS Tracking Error 

4. After the training session has ended for each test subject, they will give a 

Modified Cooper Harper Rating (CHR) and comment on tasks performed. 

Quasi-Transfer 

1. Run roll compensation tasks again for 1/s and 1/s2 plant dynamics. The low 

fidelity control loader transfer group will transfer to the high fidelity control 

loader simulation for further experimentation. The high fidelity control loader 

transfer group will continue experimentation in the high fidelity control loader 

simulation. 

2. The test subjects will again conduct as many runs as necessary to reach a 

performance asymptote. 

3. The cumulative running average of the RMS tracking error is also used to 

measure when test subjects have reached a performance asymptote. 

4. The same parameters recorded for the training sessions will also be recorded for 

the transfer sessions. 

5. A Modified Cooper Harper Rating and test subject comments are recorded at the 

end of the experiment. 
140 

Data Analysis 

1. Record the control inceptor deflection, bank angle of the plant, and control 

inceptor deflection for every run for the entire run. 

2. From these recorded parameters, the RMS tracking error should be calculated. 

Obtain the RMS running cumulative average tracking error over the runs 

completed. 

3. When the RMS running cumulative average tracking error reaches an asymptote 

the run has completed. Take the slope of every two runs for the RMS running 

cumulative average. When the slope reaches 0.001 for a consistent 5 runs, 

asymptotic performance has been reached. 

4. From the recorded parameters, the standard deviation (STD) of the control 

inceptor deflection, the RMS control inceptor deflection, the RMS Tracking 

Error, the PSD of the control inceptor deflection, and the control inceptor input 

bandwidth will be calculated. 

5. A comparison will be made between all of the calculated parameters for the low 

fidelity transfer group and the high fidelity transfer group. Also, each transfer 

group will be analyzed for variation within. The comparison will reveal any 

effects of training on one simulation as opposed to the other. 

Experimental Briefing 

The experiment that will be performed today is a roll compensatory task. A roll angle will 

be shown on the display as a roll reference line. There will also be a horizon reference 

line representing a zero roll angle. A disturbance that is somewhat random will cause the 

roll reference line to move with unexpected behavior. The task is to return the roll 

reference line to a zero roll angle. This occurs when the roll reference line overlaps the 

horizon reference line. You will be given one run of the task to familiarize yourself with 

the experiment. 
141 

Appendix B: Experimental Measured and Calculated Parameters 

Experimental 

Parameters

Required 

During 

Training 

Sessions 

Required 

During 

Transfer 

Sessions 

Frequency of 

Measurement Parameter 

Training Type 

Sessions 

Transfer 

Sessions 

RMS Control 

Inceptor Deflection Yes Yes Every Run Every Run Calculated 

Running 

Cumulative 

Average of RMS 

Tracking Error over 

Runs 

Yes Yes Every Run Every Run Calculated 

RMS Tracking 

Error Yes Yes Every Run Every Run Calculated 

Slope of Running 

Cumulative 

Average of the 

RMS Tracking 

Error 

Yes Yes Between 2 

Runs 

Between 2 

Runs Calculated 

STD Control 

Inceptor Deflection No No None None Calculated 

PSD Control 

Inceptor Deflection No No None None Calculated 

Control Inceptor 

Input Bandwidth No No None None Calculated 

Roll Rate No No None None Calculated 

Bank Angle Yes Yes

Every Run 

for Entire 

Run 

Every Run 

for Entire 

Run 

Recorded 

Control Inceptor 

Deflection Yes Yes

Every Run 

for Entire 

Run 

Every Run 

for Entire 

Run 

Recorded 

Control Inceptor 

Force Yes Yes

Every Run 

for Entire 

Run 

Every Run 

for Entire 

Run 

Recorded 

Cooper Harper 

Rating Yes Yes After Each Trial 

After Each 

Trial Recorded 
142 

Appendix C: Experiment Run Time 

Estimated Run Time for Each Experiment Phase ( High & Low Fidelity 1/s & 1/s2 Plant 

Dynamics) 

Test Subject 

Number 

Familiarize 

Phase 

Evaluation 

Phase 

Training 

Phase 

Breaks QuasiTransfer 

Phase 

Total 

Run 

Time 

HF001 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF002 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF003 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF004 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF005 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF006 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF007 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF008 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF009 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

HF010 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

Total 

Experiment 

Time 

10 min 10 min 3 hrs 20 

min 

1 hr 40 

min 

1 hr 40 

min 

7 hrs 

LF001 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF002 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF003 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF004 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF005 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF006 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF007 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF008 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF009 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

LF010 2×30 sec 2×30 sec 2×10 min 2×5 min 2×5 min 42 min 

Total 

Experiment 

Time 

10 min 10 min 3 hrs 20 

min 

1 hr 40 

min 

1 hr 40 

min 

7 hrs 
143 

Appendix D: Matlab [21] Code to Calculate Frequency Response 

%Man Machine Systems (FRF Frequency Response Function) 

%Slicing the Input and Output Signals

numseg=1

lengthseg=round(length(Input)/numseg);

for i=1:numseg

M1(i)=(i-1)*lengthseg+1;

M2(i)=(i)*lengthseg;

if M2(i)>length(Input);

 M2(i)=length(Input);

end

end

 

%Calculating the Fourier Transform, Cross Correlation and Auto 

Correlation

for n=1:length(numseg)

 win1=hamming(lengthseg);

Ninput=Input(M1(n):M2(n));

Noutput=Output(M1(n):M2(n));

[y1,F,T] = spectrogram(Ninput,win1,0,[.6:.01:3.97],100);

[y2,F,T] = spectrogram(Noutput,win1,0,[.6:.01:3.97],100);

Tin=205;

CCin(:,n)=conj(y1).*y2;

ACout(:,n)=(abs(y1)).^2;

end

%Calculating Magnitude and Phase between Output and Input

AC=mean(ACout,2);

CC=mean(CCin,2);

FRF=CC./AC;

figure(4)

subplot(2,1,1)

[mag,phase,F1]=bode(tf_hf,{.1,18.95})

mag=20*log10(mag);

 semilogx(F1,mag(:,:),'r')

 hold on

Mag=20*log10(abs(FRF));

semilogx(2*pi*F,Mag); grid on

title('Frequency Response of Low Fidelity Control Loader')

ylabel('Amplitude (dB)')

xlabel('Frequency (rad/s)')

subplot(2,1,2)

Phase=unwrap(angle(FRF))*180/pi; 

semilogx(2*pi*F,Phase); grid on

hold on

 semilogx(F1,phase(:,:),'r')

ylabel('Phase (Degrees)')

xlabel('Frequency (rad/s)') 
144 

Appendix E: Experiment Pseudo Code 

Create output table for each test subject that includes the Control 

Inceptor Deflection, Control Inceptor Force, Roll Angle Output, over 

the entire run and for each run. The data should be stored at every 

sampling interval. 

% Pseudo Code for Quasi Transfer of Training Control Loader Experiment 

 

%Initialization

SubjectNum %Subject Number 1:10 for Both High Fidelity & Low Fidelity 

Simulation. Label this differently such as SubjectNum=HF001 and 

SubjectNum=LF001 to distinguish between High Fidelity and Low Fidelity 

Data.

t=0; % sec

h=.001; % Sampling Time (seconds) Depends on simulation sampling time

runL=30; % Run Time (seconds)

RollA1(1)=0;

RollA2(1)=0; 

RunN=0; %Run number. Initialized to the zero runs before program starts 

---------------------------------------------------------------------- -

------------------------------------

%% Code for 1/s Plant Dynamics

n=t/h; %Iteration number. The time divided by the sampling time

%Commanded Plant Input

% ContIncpPos is the Test Subject Control Inceptor Deflection in 

inches. Store these values at each sampling interval throughout the 

run. Also store these values for every Run.

KC=80; %Roll Command Gain (deg/lb*sec)

CPI(n)=ContIncpPos(n)*KC; %Commanded Plant Input. Store at every 

sampling interval throughout the run. Also store these values for every 

Run. 

%Development of Disturbance

Freq=[.467,.701,1.17,1.87,3.51,7.01,11/2,14,18.7]; % Frequencies of the 

9 sinusoids 

Amp=[15.2,15.2,15.2,7.6,3.04,.76,.38,.228,.152]; %Amplitudes of the 9 

sinusoids 

%t represents Time in seconds

Dist=Amp(1)*sin(Freq(1)*t)+Amp(2)*sin(Freq(2)*t)+Amp(3)*sin(Freq(3)*t)+

Amp(4)*sin(Freq(4)*t) 

+Amp(5)*sin(Freq(5)*t)+Amp(6)*sin(Freq(6)*t)+Amp(7)*sin(Freq(7)*t)+Amp(

8)*sin(Freq(8)*t) 

+Amp(9)*sin(Freq(9)*t); %Disturbance 

%Euler Integration to Obtain Roll Angle of the Plant Dynamics 

%Commanded Plant Input Passed through One Integration. 

RollA1(n+1)=RollA1(n)+CPI(n)*h; % Roll Angle when Plant Command is 

Integrated Once. This is calculated at every sampling time of 

simulation 

RollF1(n)=RollA1(n)+Dist(n) %Output Roll Angle for 1/s dynamics. Sum of 

commanded plant roll angle and disturbance. Store these values at every 

iteration and for every run. This drives display 
145 

if t=30 

RunN = RunN+1

end

%Tracking Error, Cumulative Running Average Tracking Error and RMS 

Tracking Error (Post Processed)

%1/s Plant Dynamics

%n represents each data point. Have to record Output Roll Angle RollF1 

for every sampling interval

N=length(RollF1) % Total number of data points of Output Roll Angle

for n=1:N % This for loop goes through every data point collected for 

the Output Roll Angle

RollF1Sq(n)=RollF1(n)^2; %Each Data Point of Output Roll Angle Squared

end

TrackError(RunN)=sqrt(sum(RollF1Sq)/N); %RMS Tracking Error of Each Run

%Cumulative Running Average of RMS Tracking Error

if RunN >=2 % Start calculating Cumulative Running Average Tracking 

Error when RunN =2 

TrackErrorC(RunN)=(TrackError(RunN-1)*(RunN-1)+TrackError(RunN))/N 

%Cumulative Tracking Error

end

%Slope of the Cumulative Running Average of RMS Tracking Error

if RunN >=2 %Start calculating Slope at Run # 2

diffTE(1)=0 %initialize the slope to zero. 

diffTE(RunN)=(TrackErrorC(RunN)-TrackErrorC(RunN-1)); % Slope at every 

two points.

end 

if diffTE<=.001

end 

-----------------------------------------------------------------------

------------------------------------

%% Code for Plant Dynamics of 1/s^2

n=t/h; %Iteration number The time divided by the sampling time

% Commanded Plant Input

% ContIncpPos represents the Test Subject Control Inceptor Deflection 

in inches. Store these values at each sampling interval throughout the 

run. Also store these values for every Run. 

KC=80; %Roll Command Gain (deg/lb*sec)

CPI(n)=ContIncpPos(n)*KC; %Commanded Plant Input. Store at every 

sampling interval throughout the run. Also store these values for every 

Run. 

%Development of Disturbance

Freq=[.467,.701,1.17,1.87,3.51,7.01,11/2,14,18.7]; % Frequencies of the 

9 sinusoids 
146 

Amp=[15.2,15.2,15.2,7.6,3.04,.76,.38,.228,.152]; %Amplitudes of the 9 

sinusoids 

% t represents Time in seconds

Dist=Amp(1)*sin(Freq(1)*t)+Amp(2)*sin(Freq(2)*t)+Amp(3)*sin(Freq(3)*t)+

Amp(4)*sin(Freq(4)*t) 

+Amp(5)*sin(Freq(5)*t)+Amp(6)*sin(Freq(6)*t)+Amp(7)*sin(Freq(7)*t)+Amp(

8)*sin(Freq(8)*t) 

+Amp(9)*sin(Freq(9)*t); % Disturbance 

 

%Euler Integration. Conducted at each time step 

%Commanded Plant Input Integrated Twice

RollA1(n+1)=RollA1(n)+CPI(n)*h; %Commanded Plant Input Integrated Once

RollA2(n+1)=RollA2(n)+RollA1(n)*h; % Roll Angle when Plant Command is 

Integrated Twice

RollF2(n)=RollA2(n)+Dist(n); %Output Roll Angle for 1/s^2 dynamics. Sum 

of commanded plant roll angle and disturbance. Store these values at 

every iteration and for every run. This drives displays 

if t=30; 

RunN = RunN+1 

end 

%Tracking Error, Cumulative Running Average Tracking Error and RMS 

Tracking Error (Post Processed)

% n represents each data point. Have to record Output Roll Angle RollF1 

for every sampling interval

N =length(RollF1) Total number of data points of Output Roll Angle

for n=1:N % This for loop goes through every data point collected 

for the Output Roll Angle

RollF2Sq(n)=RollF2(n)^2; %Each Data Point of Output Roll Angle Squared

end

TrackError2(RunN)=sqrt(sum(RollF2Sq)/N); %RMS Tracking Error of Each 

Run

if RunN >=2 %Have to start at Run #2 Have to start calculating 

Cumulative Running Average Tracking Error when RunN =2 

TrackErrorC2(RunN)=(TrackError2(RunN-1)*(RunN1)+TrackError2(RunN))/RunN 

end

%Slope of the Cumulative Running Average of RMS Tracking Error

if RunN >=2 %Start calculating Slope at Run # 2

diffTE2(1)=0 %initialize the Slope to zero. 

diffTE2(RunN)=(TrackErrorC2(RunN)-TrackErrorC2(RunN-1)); % Slope at 

every two points. 

end

if diffTE2<=.001

end 
147 

Appendix F: Experiment Flow Chart 

What are Plant 

Dynamics? Start Program

End Experiment

Initialize Program 

as defined in 

Pseudo Code

Use 1/s2 plant 

dynamics code

1/s2 Plant 

Dynamics

1/s Plant 

Dynamics

Use 1/s plant 

dynamics code

Obtain Pilot Input 

and 

Corresponding 

Commanded Plant 

Input

Develop 

Disturbance

Record 

Subject 

Number

Use Euler Integration to 

Calculate Plant 

Commanded Roll Angle 

from Command Plant 

Input

+

+

Drive Display

Store the Output 

Roll Angle. Used 

later to calculate 

RMS Tracking 

Error

Store the Subject 

Inceptor Input 

Deflection 

throughout each 

run and for every 

run

Calculate RMS 

Tracking Error and 

Cumulative Running 

Average Tracking 

Error

Calculate Slope of 

Cumulative Running 

Average Tracking 

Error at every two 

points

Is Slope <= .1 

Post Process

YES

NO

Continue with next 

Run
148 

Appendix G: Mean Square and Variance for High Fidelity and Low Fidelity 

Training Groups 

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Mean Square of Roll Stick Deflection HF FRTG 1/s

Time (sec)

Mean Square (in2)

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mean Square of Roll Stick Deflection HF LRTF 1/s

Time (sec)

Mean Square (in2

)
149 

0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mean Square of Roll Stick Deflection HF FRTG 1/s2

Time (sec)

Mean Square (in2)

0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mean Square of Roll Stick Deflection HF LRTF 1/s2 TF

Time (sec)

Mean Square (in2

)
150 

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Mean Square of Roll Stick Deflection LF FRTG 1/s

Time (sec)

Mean Square (in2

) e (i

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Mean Square of Roll Stick Deflection LF LRTF 1/s

Time (sec)

Mean Square (in2

)
151 

0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mean Square of Roll Stick Deflection LF FRTG 1/s2

Time (sec)

Mean Square (in2

)

0 5 10 15 20 25 30 35 40 45 50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Mean Square of Roll Stick Deflection LF LRTF 1/s2

Time (sec)

Mean Square (in2

)
152 

0 5 10 15 20 25 30 35 40 45 50

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Variance of Roll Stick Deflection HF LRTF 1/s

Time (sec)

Variance (in2)

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Variance of Roll Stick Deflection HF LRTF 1/s2

Time (sec)

Variance (in2)
153 

0 5 10 15 20 25 30 35 40 45 50

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Variance of Roll Stick Deflection LF LRTF 1/s

Time (sec)

Variance (in2)

0 5 10 15 20 25 30 35 40 45 50

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Variance of Roll Stick Deflection LF LRTF 1/s2

Time (sec)

Variance (in2)
154 

Appendix H: Peak Power and Frequency for Every Test Subject

0

0.2

0.4

0.6

0.8

1

1.2

HF001HF002HF003HF004HF005HF006HF007HF008HF009HF010

LF001LF002LF003LF004LF005LF006LF007LF008LF009LF010

Peak Subject Power (1/s Plant Dynamics) 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

HF001HF002HF003HF004HF005HF006HF007HF008HF009HF010

LF001LF002LF003LF004LF005LF006LF007LF008LF009LF010

Peak Subject Frequency (1/s Plant Dynamics) 

First Run Peak Frequency 

(Hz) (Training) 

Last Run Peak Frequency 

(Hz) (Transfer)

First Run Peak Power (in2/Hz) 

(Training) 

Last Run Peak Power (in2

/Hz) 

(Transfer) 
155 

0

2

4

6

8

10

12

14

16

HF001HF002HF003HF004HF005HF006HF007HF008HF009HF010

LF001LF002LF003LF004LF005LF006LF007LF008LF009LF010

Peak Power (1/s2 Plant Dynamics) 

First Run Peak Power (in2/Hz) 

(Training) 

Last Run Peak Power (in2/Hz) 

(Training) 

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

HF001HF002HF003HF004HF005HF006HF007HF008HF009HF010

LF001LF002LF003LF004LF005LF006LF008LF009

Peak Frequency (1/s2 Plant Dynamics) 

First Run Peak Frequency 

(Hz) (Training) 

Last Run Peak Frequency 

(Hz) (Transfer)
156 

Appendix I: Average Tracking Error Using More Runs to Train 

 

 

0 20 40 60 80 100 120

20

25

30

35

40

45

50

55

60

Cumulative Average RMS Tracking Error (1/s2 Plant Dynamics Subject HF001)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented

0 20 40 60 80 100 120

8

10

12

14

16

18

20

22

24

Cumulative Average RMS Tracking Error (1/s Plant Dynamics Subject HF005)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented
157 

0 20 40 60 80 100 120

30

35

40

45

50

55

60

Cumulative Average RMS Tracking Error (1/s2 Plant Dynamics Subject HF005)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented

0 20 40 60 80 100 120

15

20

25

30

35

40

45

50

55

60

Cumulative Average RMS Tracking Error (1/s Plant Dynamics Subject LF003)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented
158 

 

 

0 20 40 60 80 100 120

20

40

60

80

100

120

140

160

180

Cumulative Average RMS Tracking Error (1/s2 Plant Dynamics Subject LF003)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented

0 20 40 60 80 100 120

30

35

40

45

50

55

60

65

Cumulative Average RMS Tracking Error (1/s2 Plant Dynamics Subject LF009)

Run Number

Cumulative Average RMS Tracking Error (deg)

Set Number of Runs

Asymptote Criterion Implemented
159 

Appendix J: Smoothed Periodogram Matlab [21] Code 

% Calculating the smoothed periodogram 

function s = smooper(x,w); 

% Input parameters: 

% x: the data vector 

% w: the window; 

% Output: 

% s: the smoothed periodogram, of length equal to that of x. 

if (rem(length(w),2) == 0), 

error('Window in SMOOPER must have an odd length'); 

end 

x = reshape(x,1,length(x))'; 

%x = x - mean(x); 

kappa = (1/length(x))*conv(x,fliplr(x)); 

%kappa = conv(x,fliplr(x)); 

n = 0.5*(length(kappa)-length(w)); 

s = fft([zeros(1,n),w,zeros(1,n)].*kappa); 

s = abs(s(1:length(x))); 

function [P, f] = smPSD(x, T, ifNorm, N, n) 

% input: x--the signal 

% input: T--the sampling rate of the signal 

% input: ifNorm--flag for normalization (1) or not (0) 

% input: N--window size 

% input: n--window overlap 

% output: P--the PSD 

% output: f--the frequency (Hz) 

% perform "slicing" of the signal 

j=1; 

L=0; 

while L<=length(x) 

 intvec(j,:)=[(j-1)*(N-n)+1, j*(N-n)+n]; 

 L=j*(N-n)+n; 

 if intvec(j,2)>length(x) 

 dta=intvec(j,2)-length(x); 

 X(:,j)=[x(intvec(j,1):end); zeros((intvec(j,2)-length(x)),1)]; 
160 

 else 

 X(:,j)=x(intvec(j,1):intvec(j,2)); 

 end 

 j=j+1; 

end 

% ----------- proceed with PSD calculation ---------- 

for j=1:size(X,2) 

 x=X(:,j); 

 len=length(x); 

 

 % determine the length of FFT 

 i=-1; 

 K=0; 

 while K<length(x) 

 i=i+1; 

 K=2^i; 

 end 

 % zeropad the signal to the length of FFT 

 xz=[x' zeros(1, K-len)]; 

 

 if (rem(len,2) == 0), % determine the length of the window, it must be odd 

 lwin=len-1; 

 else 

 lwin=len; 

 end 

 w = window(@hamming,lwin); % use hamming window. other window can also be 

used 

 %w = window(@hann,lwin); % use hann window. other window can also be used 

 %w = window(@rectwin,lwin); % use rectangular window. other window can also 

be used 

 P(:,j) = SMOOPER(xz,w'); 

 if ifNorm==1 

 P(:,j) = P/max(P); % normalization, optimal 

 end 

 

 Fs = 1/T; 

 df = Fs/length(P)/2; 

 f = 0:df:Fs/2-df; 

 

end 

P=mean(P,2); 

figure(2) 
161 

hold on 

plot(f,P,'r') 

title('PSD of Control Inceptor Deflection (HF001-1/s)') 

xlabel('Frequency (Hz)') 

ylabel('(control inceptor deflection)^2/Hz') 

INT_PSD=trapz(P) 

%% 

% M=round(sqrt(length(Input))) 

% [cxyM,F]=mscohere(Input,Output,M,0,256) 

% figure(1) 

% hold on 

% plot(F,cxyM,'r') 

% title('PSD of Control Inceptor Deflection (Data Set-Last Run)') 

% xlabel('Frequency (Hz)') 

% ylabel('(control inceptor deflection)^2/Hz') 

% 

% Gxy=(abs(P1)).^2; 

% Gxx=P2; 

% Gyy=P3; 

% 

% Cxy=Gxy./(Gxx.*Gyy); 

% plot(f,Cxy) 
162 

References 

[1] Bailey, R.E. and Knotts, L.H., Interaction of Feel System and Flight Control 

System Dynamics on Lateral Flying Qualities, NASA Contractor Report 179445, 

1990 

[2] Gum, Don R., Modeling of the Human Force and Motion-Sensing Mechanisms, 

Air Force Human Resources Laboratory-Advanced Systems Division, AFHRL-TR72-54, June 1973 

[3] Herzog, James H., Matched Control Using the Matched Manipulator Control 

Technique, IEEE Transactions on Man-Machine Systems, Vol. MMS-9, No. 3, 

September 1968 

[4] Hess, Ronald A. and Zeyada, Y., Modeling Human Pilot Cue Utilization with 

Applications to Simulator Fidelity Assessment, Journal of Aircraft, Vol. 37. No. 4, 

July/August 2000 

[5] Hess, Ronald A. and Malsbury, T., Flight Simulator Fidelity Assessment in 

Rotorcraft Lateral Translation Maneuver, Journal of Guidance, Control, and 

Dynamics, Vol. 16, No. 1, January/February 1993 

[6] Hess, Ronald A. and Malsbury, T., Closed-Loop Assessment of Flight Simulator 

Fidelity, Journal of Guidance, Control, and Dynamics, Vol. 14, No. 1, 

January/February 1991 

[7] Hess, Ronald A., Analyzing Manipulator and Feel System Effects in Aircraft 

Flight Control, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 20, No.4, 

July/August 1990 

[8] Hess, Ronald A., A Model-Based Theory for Analyzing Human Control 

Behavior, Advances in Man-Machine Systems Research, Volume 2, 1985, pp. 129-

175 

[9] Hosman, Ruud J.A.W, Abbink, David A., and Cardullo, Frank M., The 

Neuromuscular System, AIAA Modeling and Simulation Technologies Conference, 

Toronto, Canada, August 2010 

[10] Johnston, Donald E. and Aponso, Bimal L., Design Considerations of 

Manipulator and Feel System Characteristics in Roll Tracking, NASA Contractor 

Report 4111, 1988 

[11] Johnston, Donald E. and McRuer, D.T., Investigation of Interactions Between 

Limb-Manipulator Dynamics and Effective Vehicle Roll Control Characteristics, 

NASA Contractor Report 3983, 1986 

[12] Levison William H., Effects of Simulator Delays on Performance and Learning in 

a Roll-Axis Tracking Task, Fifteenth Annual Conference on Manual Control, Wright 

State University, Dayton, Ohio, 1979 

[13] Magdaleno, R.E. and McRuer, D.T., Experimental Validation and Analytical 

Elaboration for Models of the Pilot’s Neuromuscular Subsystem in Tracking Tasks, 

NASA Contractor Report 1757, April 1971 

[14] Magdaleno, R.E. and McRuer, D.T., Small Perturbation Dynamics of the 

Neuromuscular System in Tracking Tasks, NASA Contractor Report 1212, December 

1968 

[15] McFadden Inc., Hydraulic Control Loader System Instruction Manual, 1999 
163 

[16] Mitchell, David G. and Aponso, Bimal L., Effects of Cockpit Lateral Stick 

Characteristics on Handling Qualities and Pilot Dynamics, NASA Contractor Report 

4443, June 1992 

[17] Schroeder, Jeffery Allyn, Helicopter Flight Simulation Motion Platform 

Requirements, NASA/TP-1999-208766, July 1999 

[18] Takats, J., Flight Control System Simulation, Flight and Ground Vehicle 

Simulation Update, 2011 

[19] Wiener, Earl L., Nagel, David C., Human Factors in Aviation, pg. 229-260, 

Academic Press, 1988 

[20] National Instruments Corporation (2012), NI LabVIEW Technical Resources: 

Getting Started, Support, and Downloads, http://www.ni.com/labview/technicalresources/ 

[21] The MathWorks (1994-2013), Documentation Center/Matlab, 

http://www.mathworks.com/products/matlab/ 

[22] The MathWorks (1994-2013), Documentation Center/Simulink,

 http://www.mathworks.com/products/simulink/ 
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Technical Memorandum

 4. TITLE AND SUBTITLE

Investigation of Control Inceptor Dynamics and Effect on Human Subject 

Performance 

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Stanco, Anthony A.; Cardullo, Frank M.; Houck, Jacob A.; Grube, Richard 

C.; Kelly, Lon C.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

L-20288

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category 54

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The control inceptor used in a vehicle simulation is an important part of adequately representing the dynamics of the vehicle. The inceptor characteristics are 

typically based on a second order spring mass damper system with damping, force gradient, breakout force, and natural frequency parameters. Changing these 

parameters can have a great effect on pilot control of the vehicle. A quasi transfer of training experiment was performed employing a high fidelity and a low 

fidelity control inceptor. A disturbance compensatory task was employed which involved a simple horizon line disturbed in roll by a sum of sinusoids 

presented in an out-the-window display. Vehicle dynamics were modeled as 1/s and 1/s2. The task was to maintain level flight. Twenty subjects were divided 

between the high and the low fidelity training groups. Each group was trained to a performance asymptote, and then transferred to the high fidelity simulation. 

RMS tracking error, a PSD analysis, and a workload analysis were performed to quantify the transfer of training effect. Quantitative results of the experiments 

show that there is no significant difference between the high and low fidelity training groups for 1/s plant dynamics. For 1/s2 plant dynamics there is a greater 

difference in tracking performance and PSD; and the subjects are less correlated with the input disturbance function. 

15. SUBJECT TERMS

Control inceptor; Vehicle simulation

18. NUMBER

 OF 

 PAGES

179

19b. TELEPHONE NUMBER (Include area code)

(443) 757-5802

a. REPORT

U

c. THIS PAGE

U

b. ABSTRACT

U

17. LIMITATION OF 

 ABSTRACT

UU

Prescribed by ANSI Std. Z39.18

Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

 160961.01.01.01 

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

NASA/TM-2013-218026

16. SECURITY CLASSIFICATION OF:

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and 

Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person 

shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

01- 07 - 2013