r- ,y . d AqL5 -r/ 

v 

<* 

L, ”- 

NASA Contractor Report 4058 

1 

Optimal Cooperative Control 

Synthesis of Active Displays 

Sanjay Gary and David K. Schmidt 

GRANT NAG2-228 

JUNE 1987 
NASA Contractor Report 4058 

Optimal Cooperative Control 

Synthesis of Active Displays 

Sanjay Gary and David K. Schmidt 

Purdue University 

West Lafayette, Indiana 

Prepared for 

Ames Research Center 

Dryden Flight Research Facility 

under Grant NAG2-228 

National Aeronautics 

and Space Administration 

Scientific and Technical 

information Off ice 

1987 
iil 

-- TABLE OF CONTENTS 

Page 

LIST OF TABLES..........................................v 

LIST OF FIGURES........................................d 

LIST OF SYMBOLS........................................xi 

ABSTIZACT..............................................xiv 

CHAPTER 1 INTRODUCTION.................................1 

CHAPTER 2 ANALYSIS OF DISPLAYS FOR A K/s PLANT........8 

2.1 K/s Plant and Task Descrietion ................ 8 

2.2 Display Quickening For K/s Plant.............lZ 

2 

2 

CHAPTER 3 OPTIMAL COOPERATIVE CONTROL/DISPLAY 

DESIGN METHODOLOGY,.........................l9 

3.1 Problem Formulation...........................l9 

3.2 Design Objectives - .............................ZO 

3.3 Solution for u ............................... 23 

3.4 Solution for u and u ........................ 24 

3.5 Application to Pilot-fn-the-Loop Synthesis.. . .26 

3.6 Numerical Solution -Alg orithm..................29 

-1 

2 

CHAPTER 4 APPLIC$TION OF DISPLAY DESIGN METHODOLOGY 

TO K/s PLANT....... ........................ 34 

4.1 Problem Formulation and Synthesis Results.....34 

4.2 Evaluation of the Display quickening 

Control Law~..................................38 

4.2.1 Mean-Square Analysis.. ................ -38 

4.2.2 Power Spectrum Analysis ................ 42 

4.2.3 Frequency Domain Analysis .............. 44 

CHAPTER 5 APPLICATION OF COOPERATIVE METHODOLOGY TO A 

MORE COMPLEX DISPLAY DESIGN.........52 

5.1 System D~amics ...............................52 

5.2 Task modeling .................................54 

5.3 Optimal Display Synthesis for F-15 Mode1......65 

fTiECEDiN(3 PAGE BUNK NOT FullD 
iv 

Page 

5.4 Comparison of the Displays .................... 68 

5.4.1 Time FIIstorles ......................... 68 

5.4.2 Frequency Domain Analysis .............. 73 

5.4.3 RMS Analysis ........................... 76 

5.4.4 Spectral Analysis ...................... 78 

CHAPTER 6 S.Y ................................ o.oo.83 

APPENDICES 

APPENDIX A DERIVATION OF NECESSARY CONDITIONS 

FOR CONTROLLER 2 (u2) .................. 89 

APPENDIX B THE OPTIMAL CONTROL PILOT MODEL ........ 94 

APPENDIX C ANALYSIS RESULTS FOR K/s PLANT ....... 102 2 

APPENDIX D DATA AND ANALYSIS RESULTS 

FOR F-15 AIRCRAFT ..................... 120 

f.. ..... 
V 

-- LIST OF TABLES 

Table Page 

2.1 OCM RESULTS FOR VARYING DISPLAY BANDWIDTH.........13 

2.2 OCM RESULTS FOR VARYING DISPLAY CONTROL GAINS.....17 

4.1 OPTIMAL DISPLAY DESIGNS FOR K/s PLANT............37 

4.2 OCM ANALYSIS RESULTS FOR VARIOUS CASES............39 

5.1 PILOT PERCEPTION THRESHOLDS.......................64 

5.2 OCM ANALYSIS RESULTS..............................77 

APPENDIX TABLES 

D.l TRIM CONDITIONS FOR F-15 MODEL...................121 

D.2 MATRICES A AND B FOR F-15 MODEL.. .............. 122 

D.3 PILOT OBSERVATION MATRICES FOR STATUS DISPLAY....123 

2 

V V 
vi 

-- LIST OF FIGURES 

Figure Page 

1.1 Simplified Block Diagrams for 

Control/Display Augmentation........ ............... 3 

1.2 Control vs. Display Augmentation ................... 4 

2.1 Display for K/s Plant............................lO 2 

2.2 Parametric Performance - Manual Control Rate......l4 

2.3 Parametric Performance - Manual Control Activity..l5 

3.1 Block Diagram for Control 

and Display Augmentation..........................21 

3.2 Simplified Pilot Model Block Diagram .............. 28 

3.3 Flowchart for Numerical Procedure..................31 

4.1 Error vs. Manual Control Rate 

for Various Displays ............................*. 40 

4.2 Error vs. Manual Control Activity 

for Various Displays.. ............................ 41 

4.3 Comparison of Human Operator's 

Control Spectrum, A(~)....~.......................43 

4.4 Block Diagram for Display Augmented Plant.........45 

4.5 Comparison of Display Augmented Plants, G(s)......47 

4.6 Comparison of Human Describing Functions, P(s)....48 

4.7 Comparison of Human's Phase Compensation 

(adjusted phase) .................*.O.OO.- =49 

4.8 Comparison of Closed-Loop Frequency Response 

for Displays 1,3 and 5..........................0051 
Figure Page 

5.l(a) az Response to Step Elevator Input 

(6 = 0.01 rads, +ve down)............55 

Mach Response to Step Elevator Input. .......... 56 

ec 

5.l(b) 

5.l(c) 8 Response to Step Elevator Input........... ... 57 

5.2(a) a Response to Step2Throttle Input 

(6Tc = 1 ft/sec , +ve thrust) ...... . ...... -58 

5.2(b) Mach Response to Step Throttle Input ........... 59 

z 

5.2(c) 8 Response to Step Throttle Input .............. 60 

5.3 Conceptual Display Format for Status Display ...... 61 

5.4 Conceptual Display Format for Augmented Display ... 63 

5.5(a) xdl Response to Step Elevator Input 

= 0.01 rads, +ve down)..........69 

xd2 Response to Step Elevator Input ............ 70 

xdl Response to Step Thro5tle Input 

(6Tc = 1 ft/sec , +ve thrust)........71 

xd2 Response to Step Throttle Input ............ 72 

Block Diagram for Status Display ................* .74 

( 'ec 

5.5(b) 

5.6(a) 

5.6(b) 

5.7 

5.8 Block Diagram for Augmented Display.... .......... -75 

5.9 Comparison of e Power Spectr um................. -79 

5 . 10 Comparison of Pilot Commanded Elevator Spectrum.. -80 

az 

5.11 Comparison of Pilot Commanded Throttle Spectrum...81 

APPENDIX FIGURES 

B.1 OCM Block Diagram .................................95 

C.1 

C.2 

Control Spectrum for Limiting Case - A...........103 

Control Spectrum for Display 1...................104 

C.3 Control Spectrum for Display 2...................105 
viii 

Figure Page 

(2.4 Control Spectrum for Display 3...................106 

C.5 Control Spectrum for Display 4...................107 

C.6 Control Spectrum for Display 5...................108 

C.7 Bode-plots of K/s2 Plant Plus Display 1. . . . . . . . . .lo9 

C.8 Bode-plots of K/s2 Plant Plus Display 2 .......... 110 

C.9 Bode-plots of K/s2 Plant Plus Display 3.. . . . . . . . .111 

C.10 Bode-plots of K/s Plant Plus Display 4..........112 

C.ll Bode-plots of K/s Plant Plus Display 5..........113 

2 

2 

C.12 Pilot Describing Function for Limiting Case-A....114 

C.13 Pilot Describing Function for Display 1..........115 

C.14 Pilot Describing Function for Display 2..........116 

C.15 Pilot Describing Function for Display 3..........117 

C.16 Pilot Describing Function for Display 4..........118 

C.17 Pilot Describing Function for Display 5..........119 

D.l Pilot Describing Function P 6e 

- 

a 

zc for Status Display ............................ ...124 

D.2 Pilot Describing Function P 

- 

e 

az for Status Display ....................... .....0..125 

6e 

M 

D.3 Pilot Describing Function P 

- 

for Status Display ............................... 126 

D.4 Pilot Describing Function P6= 

- 

8 for Status Display ............................... 127 

D.5 Pilot Describing Function P 6T 

- 

a 

ZC 
Figure 

ix 

Page 

for Status Display...............................l28 

D.6 Pilot Describing Function P 

6T 

az 

- 

e 

for Status Display.................................129 

6T 

M 

D.7 Pilot Describing Function P 

- 

for Status Display...............................130 

6T 

0 

D.8 Pilot Describing Function P 

- 

for Status Display...............................131 

D.9 Pilot Describing Function P 

- 6e 

a 

ZC for Augmented Display............................l32 

D.10 Pilot Describing Function P 

6e 

dl 

- 

X 

for Augmented Display............................133 

D.ll Pilot Describing Function P 

- 6e 

d2 X 

for Augmented Display.. ......................... -134 

D.12 Pilot Describing Function P 6e 

B for Augmented Display ............................ 135 

6T D.13 Pilot Describing Function P 

- 

a 

ZC for Augmented Display........ ................... .136 

D.14 Pilot Describing Function P 6T 

- - 

^d 1 for Augmented Display....... ..................... 137 

D.15 Pilot Describing Function P 6T 

d2 

- 

X 

for Augmented Display ............................ 138 

D. 16 Pilot Describing Function PgT 

- 

8 
X 

Figure Page 

for Augmented Display ............................ 139 

D.17 ea= Power Spectrum for status Display.... ........ 140 

D.18 Pilot Commanded Elevator Spectrum 

for Status Display..... .......................... 141 

D.19 Pilot Commanded Throttle Spectrum 

for Status Display. .............................. 142 

D.20 eaz Power Spectrum for Augmented Display ......... 143 

D.21 Pilot Commanded Elevator Spectrum 

for Augmented Display ............................ 144 

D.22 Pilot Commanded Throttle Spectrum 

for Augmented Display ............................ 145 
xi 

-- LIST OF SYMBOLS 

Symbol Me ani n g 

2 

a .................. normal acceleration (ft/sec ) 

A........... ........p lant matrix 

B................ ... system control distribution matrix 

C...................output state distribution matrix 

D...................system noise distribution matrix 

D(s). ............... display system transfer function 

e........... ........p lant position error 

z 

2 

e ................. normal accleration tracking error (ft/sec ) 

E .................. output control distribution matrix 

az 

fi.. ............... .fractional attention allocation for ith observation 

g...................control rate weighting 

gd..-...............display control gain 

G...................gain matrices 

G(s) ................p lant transfer functiodmatrix 

I..... .............. identity matrix 

J .................. cost functional 

K.. .................p lant gain 

K1..................control gain matrix 

M...................~ch error (-001 Mach) 

M1..................Kalman filter gain matrix 

P...................solution to Ricatti equation 

P(s)................htl~~~an operator transfer functlon/matrix 

q........ ...........p itch rate (-01 rads/sec) 

q. .................. au~ented system state vector 

qe..................error weighting 
Symbol 

xi i 

Meaning 

Q...................state weighting matrix 

r...................control weighting 

R,F.................control weighting matrices 

T(s). .............. .closed-loop transfer function 

~...................control vector 

v .................. motor noise vector 

v .................. observation noise vector 

V....... ............p erturbed forward velocity (ft/sec) 

V .................. measurment noise intensity 

-Y 

w...................system noise input vector 

W.............. .....sy stem noise intensity 

x.... ............... K/s plant position 

 state vector 

%..................display variable 

y...................system output vector, measurment vector 

- 

- 

* 

Y 

2 

- 

a...................angle of attack (.01 rads) 

a ................. .perception threshold value for ith observation -i 

- augmented system state vector 

 augmented system state estimate vector 

6...................human operator's control input vector 

6 .................. elevator control input (-01 rads) 

6T..................throttle control input (ft/sec ) 

u...................pilot input 

u .................. optimal pilot input 

- 

2 e 

* 

pu..................motor noise ratio 

u .................. root mean square value of x 

C...................state error covariance matrix 

Cx(w) ...............p ower spectral density of x 

f...................time delay 

fd...........8......display lag time constant 

................. observation noise ratio for ith observation pYi 

X 
Symbol 

xiii 

Meaning 

T .................. neuromotor lag time constant 

e...................pitch rate (.01 rads) 

n 

operat ions 

(*).................time derivative of (') 

E(.} ................ expected value operator 

(.> .............. ..transpose of (.) T 

( . I-'. ............. .inverse of (.I 

subscripts 

l...................refers to Controller 1 

2...................refers to Controller 2 

aug.................augmented system 

A...................augmented system 

c...................closed loop system, command 

d...................display augmentation system 

o...................nominal values, unaugmented system matrices 

p...................human operator/pilot 

v...................vehicle 
CHAPTER - 1 

1 

INTRODUCTION 

The utility of providing augmented displays to the human operator 

as an aid in the closed-loop control of high order dynamical systems is 

well known, and discussion of some of the early work done in evaluating 

various types of augmented displays can be found in [l]. With the 

advent of high performance aircraft, the amount of information to be 

processed by the pilot to successfully accomplish the assigned task has 

continued to increase. It has, therefore, become more critical to 

determine the best informational set and display dynamics needed by the 

pilot so as to reduce the pilot's workload and improve performance. For 

example, the use of flight directors to achieve this objective has been 

analytically evaluated in 121 using closed loop or "pilot - modeling" 

techniques, and validated through man-in-the-loop simulation in [3]. 

Ongoing research in the area of automatic flight test trajectory 

controllers [4,5] has demonstrated the usefulness of such controllers, 

rather than manual control, for accurately following specified complex 

trajectories. These controllers, however, take the pilot out of the control loop, and it is desirable to avoid this. The possibility of doing 

so while aiding the pilot with an appropriate display is worth exploring, and that is the subject of this work. 

In general, the design of active displays for the human controller 

requires extensive real time man-in-the-loop simulation to evaluate 

various candidate designs. Although simulator validation is always 

appropriate, the objective of this study is to develop an analytical 

technique to aid in the design of pilot-optimal display augmentation 
2 

systems. 

In the past, analytical methods have been proposed in which models 

of human behaviour were used to identify, investigate and evaluate the 

properties of augmented aircraft dynamics. In all these methods, hop 

ever, the "pilot model analysis" was added a posteriori. The idea that 

the augmentation system works in cooperation with the pilot and a technique which considers the augmentation system and the pilot to be two 

controllers working in "parallel" was first suggested by Schmidt [7]. 

This technique was later modified and its application to synthesize control augmentation that directly optimizes pilot opinion rating was 

demonstrated for a modern control configured aircraft [8,9]. The 

cooperative control synthesis technique has the advantage that it incorporates a mathematical model of the pilot behaviour and uses optimal 

control theory to synthesize control gains that are pilot-optimal as 

modeled. 

Since display augmentation, like control augmentation, has to be in 

harmony with the pilot's abilities and limitations in order to be 

acceptable to him as an aid in accomplishing his task, the cooperative 

synthesis technique is considered to provide an appropriate framework 

for synthesizing pilot-optimal display augmentation. 

Even though the objective of both the control augmentation and the 

display augmentation is to aid the pilot, the way this is achieved is 

fundamentally different for the two types of augmentation. The differences between these two types of augmentation are best understood by 

considering the simplified block diagrams of Figures (1.1) and (1.2). 

Figure (l.l(a)) depicts the pilot controlling an unaugmented vehicle. 

For this case, the responses (7) observed by the pilot are those being 
3 

- 

P U ' 

r-------- 1 

I I7 I 

- 

Unaugmented Y 

Vehicle 

Unaugmented 

Vehicle 

Pilot ---El- 

(a) Unaugmented Vehicle 

Lc7-1 Pilot 

Control 

I il Law 1-1 I 

I I 

Pilot 

(b) Control Augmentation 

i coE:"l t 

ai

I I 

Pilot 

(c) Display Augmentation (d) Control and Display Augmentation 

Figure 1.1 Simplified Block Diagrams for 

Control/Display Augmentation 
4 

* 

U 

Y Augmented 

Vehicle 

G'(s) 

- 

(a> Control Augmented Vehicle 

(b) Display Augmented Vehicle 

Figure 1.2 Control vs. Display Augmentation 
5 

controlled by the pilot. 

Figure (l.l(b)) shows the case of a pilot controlling an augmented 

vehicle. Note that the control augmentation changes the effective plant 

dynamics being controlled by the pilot, and may be designed so as to aid 

the pilot in accomplishing his task and to achieve desired dynamics for 

improved handling qualities. 

observed by the pilot are still those he is directly controlling. 

Here again, however, the responses (7) 

Figure (l.l(c)) shows a simplified case of display augmentation, 

wherein the vehicle responses drive a display observed by the pilot. 

Note that any display dynamic augmentation does not change the characteristics of the vehicle dynamics being controlled (i.e. y/u is 

unchanged). It only modifies the dynamics being observed by the pilot 

(or x /u ). Here, clearly, though the pilot observes and controls xd 

(the displayed signal), the controlled variables of interest are still 

the vehicle responses 7. 

mentation is shown in Figure (l.l(d)). 

P 

dP 

The case of combined control and display augConsider the manual control of a vehicle G(s), with control augmentation such that the augmented vehicle is G'(s), as in Fig. (1.2(a))- 

The closed-loop transfer function, Including the pilot, from some disturbance u to the vehicle output y is 

W 

u (SI G'(s) 

= 1 + G'(s) P'(s) w 

where P'(s) represents the pilot describing function. Next consider the 

pilot controlling the vehicle without control augmentation but with 

display augmentation, as in Fig. (1.2(b)). The closed-loop transfer 

function for this case is 

('1 . 2) 
6 

Now if the display dynamics D(s) are chosen, for example, such that 

G(s)D(s)=G'(s), then the pilot describing function P(s) of the display 

augmentation'case (Fig. (1.2(b))) is approximately the same as P'(s) for 

the control augmentation case. Then Eqn. (1.2) becomes 

uw( s1 G(s) 

= 1 + G'(s) P'(s) 

Comparing Eqn. (1.3) to Eqn. (1.11, it is apparent that though the stability characteristics in terms of the closed-loop characteristic polynmial are the same for the two cases of augmentation, the closed loop 

transfer functions are not. The point here is that the closed-loop system dynamics obtained through control augmentation may be quite different from that obtined through display augmentation. 

Chapter 2 of this report provides motivation for display augmentation through analytical evaluation of various display "quickening" control laws, synthesized essentially through trial and error, for a simple 

K/s plant. 2 A compensatory tracking task is analyzed using an Optimal 

Control Yodel (OCM) [6] of human behavior. 

In Chapter 3 a methodology to synthesize pilot-optimal 

display/control laws which is sensitive to the control and information 

processing limitations of the human controller is proposed. This methodology is an extension of the cooperative control synthesis technique 

previously developed to design pilot-optimal control augmentation 

[7,8,9]. Though the proposed methodology has been developed so as to be 

applicable to simultaneous synthesis of pilot-optimal control augmentation and display augmentation, the present discussion focuses on the 

application of the technique to display design only. 

The application of the cooperative display design technique to 
7 

2 again synthesize-display laws for the K/s 

discussed in Chapter 4. When compared to the results of Chapter 2, the 

results of this application tend to analytically validate the synthesis 

procedure. The displays lead to predicted reduction in pilot workload 

when evaluated using the OCM. Also the ability of the methodology to 

provfde task tailoring of the displays is demonstrated. 

plant in the tracking task is 

In Chapter 5 the application of the methodology to high order 

dynamical systems in a multi-control task.scenario is demonstrated for a 

modern aircraft. The chosen model closely represents the unaugmented 

longitudinal dynamics of the F-15 aircraft, and the task is that of 

tracking a normal acceleration command while regulating Mach number. 

The control inputs available to the pilot are the elevator stick and 

throttle. Model-based evaluation of the synthesized display again indicates reduction in pilot workload in accomplishing the task. 

Finally a summary of the work is presented in Chapter 6 and recommendations made for future research. 
8 

ANALYSIS - OF DISPLAYS -- FOR A K/s2 PLANT 

Motivation for providing the human controller with augmented 

displays is explored through analytical evaluation of various 

emperically-derived 

plant. The results of this evaluation agree with the known fact that 

the human operator's workload can be significantly reduced and his performance improved by a proper design of the signal being displayed to 

him. 

2 display "quickening" control laws for a simple K/s 

2 

-- 2.1 K/s --- Plant and Task Description 

2 Consider the K/s plant dynamics as discussed, for example, by 

Kleinman et al. in [6]. The system state equations are 

(2.1 .1) 

where x(t) is the plant position and 6(t) is the input from the human 

controller. 

A velocity disturbance is applied to the plant. It is modeled as a 

first order Markov process having a break frequency of 2 rads/sec and is 

given by 

xp = -2xp + w(t) (2.1.2) 

where w(t) has intensity W = 0.217 to give E(xl} 2 = 0.054 in.2 Defining 

. the plant position error (e) and the error rate (e) as 

(2.1.3) A e(t) - = x2(t) ; kt) : xp + x3(t) 

and letting K = 1 in./in., the plant equations (2.1.1) can be combined 
9 

with the disturbance equation (2.1.2) to get 

(2.1.4) 

or in concise form 

- 

X= AT+B u + D w 

0 0 0 

The human operator's task is to minimize the position error x (t) in the 

presence of the disturbance. 

2 

Next consider a display exhibiting some transport lag modeled in 

the form 

( 2.1 .5) 

The dynamics of the disturbance, plant, and display can then be written 

as 

- 1 

-1 Bo] 0 6 + DO]" 0 (2.1.6) 

The human operator's observations for this system are 

Y1 = Xd (2.1.7) 

Y2 = Xd 

where it is assumed, in accordance with the known abilities of the human 

controller, that he is able to reconstruct the displayed-variable rate 

by observing the displayed variable itself. 

As shown in Fig. (2.1), the human operator's task with the display 

is to keep the needle on the display centered to the best of his 
10 

Figure 2.1 Display for K/s2 Plant 
11 

abilities, subject to reasonable workload. This performance objective 

can be reflected in terms of minimizing the cost 

... '2 -1 Jp(6) = E{lirn r 1 /(xi + g6 )dt) 

T+- o 

(2.1.8) 

With the above formulation in mind, the performance of the manually 

controlled system is evaluated using the OCM model for various values of 

T A brief description of the OCM modeling technique is given in 

Appendix B. For all the analysis carried out in this section, the 

parameters that define the OCM model were set to the following values: 

d' 

(i) Ruman operator's observation time delay, T, set to 0.2 

seconds 

(ii) Observation noise ratio set at -20 dB for both observations 

(iii) Motor noise ratio was set at -25 dB 

(iv) The weighting, g, on the control rate in the human 

controller's objective function was always adjusted to yield a neuromotor lag time constant,T of 0.1 secs. n' 

(v) Very low values of thresholds were used for the observations 

available to the human,and he was assumed to devote full attention 

to the displayed signal. 

The OCM model obtained for the above values of the parameters has been 

shown to correlate very well with the experimentally observed behaviour 

of the human controller [6], especially in single-axis tasks such as the 

one being discussed here. The significance of these parameters in 

modeling the human operator dynamics is explained in Appendix B. 
12 

The results for various values Of display lag T are presented in d 

Table 2.1, in terms of the mean square values of the variables of 

interest. These results are also plotted in Figures (2.2) and (2.3) (to 

be discussed later) and correspond to the curve marked 

figures. From these results it is clear that with only error e driving 

0 in these 

the display, the pilot's performance improves as the display bandwidth 

is increased. As - + the pilot's performance approaches a limiting 

case where the error is displayed instantneously to the human, or the 

1 

d T 

limiting case where there is no display lag. This limiting idealized 

case (labeled A in the figures) assumes that the error can be sensed and 

displayed without any computational delay or lag, and may not be achievable. The question now is whether the performance (or pilot's workload 

situation) can be improved by augmenting the display dynamics. 

2 

-- 2.2 Display Quickening - For K/s Plant 

Consider the augmented display dynamics of the form 

1 + -1 

Xd = Txd TX2 + gdx3 (2.1.9) 

where g is a gain to be adjusted. 

state, the above form of display will provide some lead information to 

Since x,(t) is the plant velocity d 

the human. Note that this form of display dynamics can be written in 

general as 

. 

xd = adxd + ud 

(2.2.1) 

- 

where yd = Cdx is the vector of plant responses available for driving 

the display, and ud is the display control law to be determined. 

formulation of display dynamics as above, the choice of ad determines 

In the 
13 

TABLE 2.1: OCM RESULTS FOR VARYING DISPLAY BANDWIDTH 

d 

T 

(set) 

0.20 

0.10 

0.05 

0.02 

0.01 

-> 0 

M.S. Error (e) 

1 

(in.') 

0.0215 

0.0177 

0.0157 

0.0142 

0.0135 

0.0131 

M.S. Input (6) 

(in. 2, 

~ 

2.176 

1.543 

1.261 

1.. 223 

1.141 

M.S. Control Rate (6) 

(in.2/sec 2 ) 

106.91 

76.47 

67.44 

62.9 

60.98 

54.73 
14 

- 02 

-019 =O’F 

.013 

-014 1 

Q 

I 

! 

\ 

\ 

? 

! 

I 

! 

-012 L I Ill 1i1111111 111 il I I .- - 

0 20 40 60 €33 I00 1 20 

Mean 2 2 Square Control Rate (in. /sec ) 

Nomen cl a t ure 

@ Only e driving display, T~ = .20 - -> 0 

@ 

@ 

Td = .lo, gd = 1, 2, 3, 4, 5, 6; B : gd r: 2 

T = .os, gd = 1, 2, 3, 4, 5, 6; c : gd = 3 d 

T in seconds d 

.Figure 2.2 Parametric Performance - Manual Control Rate 
15 

\ 

/ 

11~111 Ill I II IIlllll II lllll 

1.6 1.6 2 2 

\ 

-. 6 

*-- 

4 \ 6 

-0 12 

0 -2 -4 -6 .8 1 1-2 1.4 

Mean Square Control Input (in. 2 ) 

Nomenclature 

@ 

@ 

Only e driving display, T = .2O - -> 0 

T~= .lo, gd= 1, 2, 3, 4, 5,6; B: gd=2 

d 

@ la= .05, gd= 1, 2, 3, 4, 5, 6; c: gdz3 

Td in seconds 

Figure 2.3 Parametric Performance - Manual Control Activity 
16 

the bandwidth of the display. 

With the same OCM parameters as above, an analysis was performed 

for two values of T : .10 and .05 secs. These values were chosen so 

that the display dynamics are near the bandwidth of the human controller 

d 

as modeled. For each of these values, g is varied from 1 to 6. The 

results are presented in Table 2.2 and are also plotted in Figures (2.2) 

d 

and (2.3) so as to compare them with the previous results. In the two 

figures, the curve marked @ corresponds to T = .IO SecS and that d 

marked @ to T~ = .05 secs. 

Fig. (2.2) is a plot of mean square error (e) vs. mean square 

manual control rate (6) for the various display cases discussed above. 

Fig. (2.3) is a plot of mean square error vs. the mean square manual 

control input (6). From these two figures it is clear that the mean 

square control input and control rate both decrease as the display control gain gd is increased. 

gd is increased, and then increases beyond a certain value of gd that 

depends on the choice of display bandwidth. 

The mean square error initially decreases as 

Note that earlier work [10,11] has shown that the human operator’s 

workload is directly related to his mean-square control rate. This means 

that it should be possible in this case to improve performance (of which 

mean square error is a measure), while at the same time decreasing workload. 

there is an optimal choice of display control gains. 

C in Figures (2.2) and (2.3) is such an optimal display for T~ = .05 

secs, and for this case the performance is slightly better than even the 

Moreover, the results indicate that for a given display bandwidth 

For example, point 

idealized limiting case at point A. 
17 

TABLE 2.2: OCM RESULTS FOR VARYING DISPLAY CONTROL GAINS 

- 

gd 

- 

1 

2 

3 

4 

5 

6 

M.S. Error (e) 

(in.2) 

0.0144 

0.0138 

0.0143 

0.0157 

0.0175 

0.0195 

(b) Td = .05 secs 

gd Y.S. Error (e) 

(in. ) 2 

0.014 

0.013 

0.0127 

0.0128 

0.0131 

0.0136 

M.S. Input (6) 

(in. 2> 

1.113 

0.733 

0.486 

0.339 

0.248 

0.187 

~ 

1.175 

0.968 

0.789 

0.639 

0.521 

0.427 

M.S. Control Rate (6) 

22 (in. /sec ) ~~ 

54.75 

35.92 

23.71 

16.52 

12.05 

9.01 

M.S. Control Rate (6) 

(iL2/sec 2 ) 

58.06 

47.47 

38.49 

30.97 

25.15 

20.46 
18 

It would then appear desirable to develop a systematic approach to 

display augmentation which will make it possible to directly synthesize 

the optimal display gains without having to resort to trial and error. 

In the following chapter an extension of the optimal cooperative control 

synthesis technique [7-91 is proposed as a methodology to accomplish 

this. 
OPTIMAL COOPERATIVE CONTROL/DISPLAY DESIGN METHODOLOGY 

The problem formulation for the cooperative control/display design 

methodology is presented and the necessary conditions for optimality are 

derived in detail. Application of the methodology to pilot-in-the-loop 

synthesis is demonstrated and various special cases of augmentation are 

discussed. 

3.1 Problem Formulation 

In this section the mathematical formulation of the cooperative 

control synthesis technique is presented. Necessary conditions for the 

simultaneous optimality of the display and control augmentation systems 

are developed in the sections that follow. The procedure followed here 

is very similar to that of [8,9]. 

Consider a dynamic system acted upon by two controllers, and 

described by the linear time invariant set of first order differential 

equations 

- = Ax + B + B20~2 + Do; (3.1.1) 0 lo 1 

- ml - m2 with ZcRn, ulcR , u2sR 

with intensity W. The two controls represent two physically independent 

and w a zero-mean Gaussian white noise process 

controllers, and in section (3.5) it is shown how the controller 1 (u,) 

can be made to closely approximate the OCM model of human behaviour. 

The display dynamics are assumed to be of the form 

(3.1.2) 

with FdcRd, ud€R md , and ud is the display quickening controller. The 
20 

objective is to find the optimal cooperative controllers 1 and 2 

(il and v2) along with the optimal display control law Ud. 

Controller 1 (u ) is assumed to have noisy observations available 1 

for feedback given by 

- =clox+c x +cu +v - 

Y1 dld ud y (3.1.3) 

where is also a zero-mean Gaussian white noise process with intensity 

V This controller will be shown to include state estimation. 

Y 

Yo 

The augmentation controller c2 and the display control law Kd are 

assumed to have noise-free system outputs y2 and yd, respectively, 

available for feedback, where 

r- i 

- - - 

'd = 'd y2 = c x; 20 (3.1.4) 

Note that the above formulation does not allow feedback of the display 

states x 

controllers are constrained to have the direct output feedback form 

to the augmentation controller c2. Finally, these two latter d 

- - - 

u2 = G2y2 = G C x 2 20 

- 

ud = Gdyd = GdCd 

The interaction between the different controllers 

(3.1.5) 

is shown in the block 

diagram of Figure (3.1). 

-- 3.2 Design Objectives 

Controller 1 is to be optimal with respect to the cost 

m 

in the presence of the action of control inputs z2 and Td. Here E{'} 
21 

COSTROL 

1 LAW 2 

7-- I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

- - - "d DISPLAY Xd 

DT!:.Q!ICS 

DISPLAY 

LAW, Gd C I' 

'd 

'- 

DISPLAY 

I 

I Eo 

I 

KALMAN 1 

I 

I 

FILTER I 

LAW 1, ' 

i 

Figure 3.1 Block Diagram for Control and Display Augmentation 
22 

indicates the expected 

> 0, old 0, R1 > 0 lo 

display control law d 

T 

J = E{lim - 1 

in the presence of the 

1 

T+- TO 

value operator and the weighting matrices are 

0, F1 > 0. 

are to be optimal with respect to the cost 

Conversely, Controller 2 (T2) and the 

--T - -T - -T - -T - 

(~T~20x+xd~2d~d+~1R2ul+u2F2~2+~dF2d~d) dt } ( 3.2.2) 

control action u The weighting matrices are 1' 

0, F2 > 0, F2d > 0. 

Augmenting the system dynamics (3.1.1) with the display dynamics 

(3.1.2), the state-space description of this augmented system is 

ri LJ 

(3.2.3) 

Defining = COL (x, x ), (3.2.3) can be written in a compact form with d 

appropriate definitions for the matrices as 

The measuments can similarly be written as 

- 

y1 = clx + CUGd + v Y 

- 

Y2 = c2x 

(3.2.4) 

(3.2.5) 

The two cost functions can then be expressed in terms of the augmented state vector as 

-T - 1 T -T - + ZTR u + U2F1u2)dt} 

= E{limT / (X Qlx, 1 1 1 T+= 0 

J1 
23 

where the weighting matrices Q, and O2 are appropriately defined. 

that this formulation is formally that for a multi-player non-zero sum 

game, and we seek a Nash solution [22]). 

(Note 

-- 3.3 Solution for U1 

- 

In the presence of the action of control inputs u2 and ud, as given 

by (3.1.5), the dynamics of the augmented system (3.2.4) are 

where 

A (A + B2G2C2 + BdGdCd) aug = 

c (c, + CUGdCd> 

aug - 

1 

where is the minimum 

x. The gain matrix K 1 

(3.3.1) 

(3.3.2) 

and the performance index J becomes 1 

Equations (3.3.1) and (3.3.3), in the case of uncorrelated process 

and measurement noises (w and 7 ) and for V > 0 (i.e. V - positive 

definite), describe the standard non-singular linear quadratic Gaussian 

regulator problem for controller u 1' 

Y Y Y 

The optimal controller is known 

[12] to have the form 

(3.3.4) 

mean-square estimate of the system state vector 

is given by 

-1 T K1 = -R 11 B P (3.3.5) 

with P > 0 and symmetric, the solution of the algebraic Ricatti equation 
24 

AT P + PA + (Q~+c%;F~G~c~) - PB~R~ T -1 B~P = o (3.3.6) aug aug 

The dynamics of the Kalman state estimator are 

where the Kalman filter gain matrix M is given by 1 

with C (> 0) the solution of the algebraic Ricatti equation 

- -- 3.4 Solution - for u and ud 2- 

The optimal controller Tl as derived above has the form 

(3.3.7) 

(3.3.8) 

(3.3.9) 

(3.4.1) 

+B K -M C ). Then in the presence of this control A 

1 ‘Aaug 1 1 1 aug 

where A 

action u the system dynamics (3.2.4, 3.3.4, 3.3.7) can be written in 

terms of the augmented state vector Tf - COL (x, $) as 

1’ 

[A BIKl [jZ2 + [ “]Zd + [” ‘1 r] (3.4.2) 

V 

Y 

MICl M1 cu O M1 qwhich can further be written in a compact form, with appropriate definitions of matrices, as 

(3.4.3) 

The intensity of the process %’ is W‘ = 

- 

The index of performance to be minimized by u2 and ud then becomes 

(3.4.4) 
25 

with 

Q'i - c' To ] . K1R2K1 

The design objective can then be stated as that of finding the optimal 

controller u and optimal display control zd which minimize the cost J2 

as given by (3.4.41, subject to (3.4.3). 

2 

Proceeding in a way as detailed in Appendix A, it can be shown that 

the gains G 

the two controllers u2 and ud are given by 

and Gd which correspond to the simultaneous optimality of 2 

- 

and 

- -T Here, L = E{q q } satisfies the relation 

A L + LA: + D'w'D'~ = o 

C 

and H satisfies 

A~H + HA^ + = o 

C 

(3.4.5) 

(3.4.6) 

(3.4.7) 

(3.4.8) 

where the following definitions have been used 

r 1 

BIKl c~~F~G~ c~+c%~F~~G~c~ 

Ac z A [ M1 Aaug 'g A']; 5: Q' + I 0 

The solutions (3.4.5) and (3.4.6) are derived from the gradient condi- 
26 

tions 

LJ L 

and 

F2dGd 

(3.4.9) 

respectively, as shown in Appendix A. 

Equations (3.4.7) to (3.4.10) then give the four necessary conditions for the simultaneous optirnality of the display and control augmentation for the task, as defined by the performance index J given that 

Controller 1 is of the form stated in (3.4.1). 

2' 

-- 3.5 Application ---- to Pilot-in-the-Loop Synthesis 

In the preceding sections, a dual performance optimization problem 

was discussed and the necessary conditions for the optimality of the 

various controllers, and the expressions for the resulting gain 

matrices, were derived. The association of Controller 2 (G2) with plant 

augmentation, and of display control (id) with the display augmentation 

should be apparent in the above formulation. In this section it will be 

shown that Controller 1 6,) can be made to closely approximate the OCM 

model of human behaviour by an appropriate choice of the relevant parameters. In this manner the cooperative methodology, as developed above, 

can be used to do "pilot in the loop" synthesis of the display/control 

augmentation design. 

Consider the Optimal Control Model as discussed in Appendix B. 
27 

-T A -T -T With < 4 uo(t) and x - [x , up(t)l, the dynamics of the augmented systern in Equation (B.4) are 

P= P= 

(3.5.1) 

with Ao, Blo, and Do as in (3.1.1). 

The observations available to the pilot, as given by (B.2) can be 

rewritten as 

- 

yp(t) = C ;; (t-T) +V(t-T) (3.5.2) OP 

where C = [C I d], and the pilot's cost function (B.3) becomes 

0 

(3.5.3) 

Comparing the above formulation for with that for Controller 1 

0 

(u,) as in Section (3.3) we notice that Equations (3.5.1) to (3.5.3) 

have the same form as Eqns (3.3.1) to (3.3.3), but for the simplification that the time delay, T, has been eliminated in the observations for 

- 

The absence of the time delay simplifies the dynamic order of the u1 

pilot model by eliminating the linear predictor in the control Structure 

(B.17, B.18). The motor noise (v in (B.12)) is however accounted for 

in this formulation in that it may appear as an additional disturbance 

m 

in Eqn. (3.3.1). 

Controller 1 (u ) is as shown in Figure (3.2). 1 

The structure of the pilot model as represented by 

It is worth mentioning here that, though the simplified pilot model 

is used in the synthesis procedure presented in this report, the complete model (with predictor, etc.) is used to evaluate these deagns. 

Moreover, at each iteration of the synthesis process, the parameters 

(e.g. noise intensities) in the simplified model are updated to yield 
28 

C 

0 

.r 

U 

0 I"; 

a 

1% 

r 1 II 

-- 

fa 0- 

YLL 

4 

n. 

e 
29 

results that are consistent with the complete OCM model. It has been 

shown in [9] and [16] that by selecting proper noise intensities for the 

control noise 7 and the measurement noise 7 

yield the same human operator dynamics as the complete OCM model. 

the simplified model may 

m Y’ 

-- 3.6 Numerical Solution Algorithm 

For the case of only control augmentation (G ) being designed, the 2 

problem reduces to one discussed extensively by Innocenti in [8,9] as 

the Linear Optimal Cooperative Regulator (LOCR) problem. With the 

display-related terms removed from the problem formulation, the necessary conditions for optimality as derived above reduce to those in 

[~l 

For the case of only display control law being designed, the necessary conditions simplify, with the terms related to Controller 2 (c2) 

removed from the problem formulation. The block diagram for the controller interaction is the same as in Figure (3.1) but without Controller 2. 

flow chart for the computer program written to implement the display 

synthesis procedure, is provided here. Since the algorithm is very 

similar to that in [8,9], the reader is referred to the references for a 

more detailed description. 

A brief description of the solution algorithm, alongwith a 

The problem formulation for the case of display augmentaion only 

can be summarized as follows: 

Given the linear time invariant system 

(3.6.1) 
30 

- 

Yd = cdx 

we wish to determine the optimal controllers 5 

respect i ve 1 y 

and ud that minimize 1 

and 

rn 

(3.6.2) 

(3.6.3) 

subject to the constraint 

In Equations (3.6.1) to (3.6.4) all the vectors and matrices are as 

defined in Section (3.2). 

The numerical procedure solves for the display control law (Ed) 

2 which satisfies the necessary conditions of optimality for the cost J 

(3.4.7 to 3.4.101, given that the corresponding Controller 1 (cl) is 

optimal with respect to the cost J1 (or satisfies 3.3.5 to 3.3.9). 

algorithm for the solution procedure is summarized in Fig. (3.3) and a 

step-by-step description of the algorithm is given in the following. 

The 

- 

Step-1. This step consists of selecting a starting display control 

law u 

able choice (as is shown in later application) is to select G such 

that the display variables xd, as given by (3.1.2) , closely approximate those observations of the pilot which are of primary importance 

to initialize the numerical optimization procedure. A reason- d 

d 

for accomplishing the assigned task. 

Another important choice to be made, before starting the iterative 
31 

t 

- Starting Display 

Control 'Gains, G 

d 

Con jugate 

no 

Figure 3.3 Flowchart for Numerical Procedure 
32 

procedure, is that for the intensities of the noise processes W and 

v These should be chosen such that the optimal Controller 1, for 

the starting display augmentation, closely represents the OCM pilot 

model. 

- 

Y' 

Step-2. Solve for the optimal Controller 1 (Ll), as detailed in 

Section (3.3), for the initial display augmentation, and compare with 

the corresponding OCM pilot model to confirm that the choice for the 

noise intensities is appropriate. 

Step-3. Form the closed loop system, as in (3.4.3) and (A.4 of 

Appendix A), for the current display augmentation (cd) and the 

corresponding optimal Controller 1. Solve the Lyapunov equations 

(3.4.7) and (3.4.8) for the matrices L and H, respectively. Obtain 

aT2 

the cost J as in (A.6) and the gradient - as in (3.4.10). 

2 aGd 

Step-4. Next a conjugate gradient search procedure is used to 

upgrade the display control law This consists of making incremen- d' 

tal changes in the gain matrix G in the negative gradient direction 

till a value of G 

as compared to its value over the previous step. Note that at each 

incremental step the controller u is updated to be the LQG con- 1 

troller for the current display law; 

d 

is reached for which the cost J2 shows an increase d 

d' 

aY2 

Step-5. Calculate - for the display control gains Gd obtained at 

the end of Step 4 and check whether the necessary condition (3.4.10) 

for J to be minimum is satisfied. If yes, then go to Step 6 otheraGd 

2 
wise go back to Step 3. 

Step-6. Check for the convergence of the entire iterative process. 

This is done by evaluating the difference between the display control 

gains G obtained at the end of Step 5 and those at the start of Step 

3. If this difference is less than some bound 8, then proceed to 

Step 7, otherwise gosback to Step 3 and repeat the gradient search 

procedure. 

d 

Step-7. The Controller and the display control law ud at the end 

of Step 6 are the optimal solution for the problem formulated as 

above. But we further require that the Controller 1 be an approximate 

representation of the human behaviour as modeled by the optimal 

control- theoretic model. Therefore the control gains and closed loop 

statistics obtained at the end of Step 6 are compared with the 

results of the evaluation of the corresponding display augmented system using the OCM model. If a reasonable agreement is obtained 

between the two results, then the display control law obtained is 

pilot-optimal and the iteration process is stopped. Otherwise the 

noise intensities 7 

started anew from Step 1. 

and f; are updated and the iteration process Y 
34 

I'sinE the algorithm discussed in Chapter 3, various display augmen- 

- 2 tation control laws, u will be synthesized for the K/s plant. The 

control laws are evaluated, using the full-order OCN model, in terms of 

the mean sauare valiles of the variables of interest, and the power spectrum of the human operator's control input. Detailed frequency domain 

d' 

analysis is also carried out for the various displays. 

-- 4.1 Prohlen Formulation and Synthesis Results - - -- 

2 The dynamics of the K/s plant augmented with the 

expressed in the form 

displav may he 

with Ao, Ro, go and the intensity TJ of the white noise process w as 

defined in Section (2.11, and B = 1. Here the display dynamics are as d 

in (2.2.11, and u is the display control law to be determined. d 

As discussed in Chapter 3, Controller Zl in the cooperative problem 

formulation is analogous to the control rate u So defining 

u 

of the OCM. 

P 

4 i, the dynamics of Eqn. (4.1.1) can be written as 1= 

where 

(3 f ad 

0 

the control noise 

r 7 

L 

term, v is the human's "motor 

rn' 

J 

noise". The 
35 

outputs available for feedback to Controller 1 (u ) are the same as the 

hunan’s ohservations. Therefore for the display auRvtented case 

1 

where 7 is the human‘s ohservation noise. To be consistent with the 

analysis of Chapter 2, the responses driving the display are chosen to 

be 

Y 

(4.1.4) 

where x,(t) and x?(t) are the position error and the plant velocity, 

respectively, and are as defined in Seciion (2.1). Then the display 

& 

controller, to he designed, has the form 

d id = adxd + u 

(4.1.5) 

with G = [a,,, gd3]. 

augmented system is to regulate the displayed variahle x Thus the 

controller u 

The human operator’s objective for the display- d 

do 

minimizes the cost function J1, where 1 

2 T 

/(xi + rlul)dt) 

T- o 

J1 = E{lim (4.1.6) 

Here the choice of r depends on the desired neuro-muscular-lag time 

constant T of the human as modeled. For the purposes of the display 

design for the K/s plant, r was continually adjusted to yield T Z 0.1 

1 

n 

2 

1 n 

secs. 

The objective in the display design is to help the human opehator 

regulate the tracking error e (= x,), in the presence of the velocity 

disturbance, and with minimal workload. This objective can be formulated as that of finding the optimal display control law ud of the form 
36 

(4.1.5) which minimizes the cost function J where 2' 

m 

1' 2 J = E{lim - j<a e e2 + r 21 u2 + f2dud)dtj 

T- o 

2 (4.1.7) 

Foliations (4.1.2) to (4.1.7) then define the problem formulation 

. for the display design for the K/sL plant, within the framework of the 

cooperative methodologv. ITsinR the algorithm discussed earlier, the 

optimal display control gains, G are deterninerl for various values of 

relative weighting on the error in cost function .J Here relative error 

d' 

2' 

'e weighting is defined as the ratio - which is varied by chanaing Q 

e 2 r 

and/or r The results are presented in Tahle 4.1. *:ate that in 2' 

(k.1.7), f2d needs to be positive definite in order to pet a finite 

optimal solution to the problem. However, since the display control 

does not reflect any measure of energy, the weighting f may be chosen 

to achieve some selected overall display gain, or sensitivity. For the 

2d 

results presented in this section, simply a constant value of € = .no1 

is used, and note that the display sensitivity - is not constant. 

Since the algorithm that synthesizes the optimal gains is itera2d l:dlss 

tive, a starting display gain matrix has to be specified. For the 

results presented in Table 4.1, C, = 120, 01 is used for the starting d 

dislay control law. (Note from Section (2.1), the startinf? gains are 

such that the displayed variable xd is just tagged error). Also, for 

comparison with the results of Section (2.2), ad = -20 sec 

(this corresponds to T = 0.05 secs). 

variances for the noise processes and v are constantly updated in 

the iteration process in order to make the controller u closely approximate the OM model with the parameters selected as in Section (2.1). 

-1 

was chosen 

.s 

The weighting rl in J1, and the d 

Y m 

1 
37 

Case 

1. 

2. 

3. 

4. 

5. 

TABLE 4.1 : OPTIMAL DISPLAY DESIGNS FOR K/s2 PLANT 

d Optimal G 

q, r 2 

1 2x 1 o-~ [36.6, 11.91 

2 2x1~-4 [49.2, 13.01 

2 1x1~-4 [64.4, 16.31 

4 ixl o-~ L85.1, 17.31 

4 ~xIO-~ [118.2, 22.61 
38 

From the results presented in Table 4.1 it is noted that as the 

relative mighttng on the error is increased, the display sensitivity 

(f g ) becomes larger. This is because a low value for f2d was chosen 

as discussed earlier. But, as the analysis in the following section 

d d2 

will show, it is the relative position and velocity gain magnitudes in 

the display which are of most interest, rather than the absolute values 

of the display gains. 

4.2 Evaluation -- of the Display Quickening Control - Laws 

The display gains obtained in Section (4.1) are now to be evaluated 

-- 

using the €ulL-order human operator model, with the same parameters in 

the model as given in Section (2.1). For the purposes of comparison, 

the initial display case (G = [20, 01) and the limiting case of no 

display lag are also evaluated. 

d 

The display designs of Section (4.1) are referred to as Designs 1 

to 5, as defined in Table 4.1. The limiting case of no display lag is 

referred to as "A", the initial display case as "B" and the case of best 

performance obtained through trial and error in Section (2.2) as "C". 

---- 4 . 2 . 1 Mean-Square Analysis 

The OCM analysis results, in terms of the mean-square values of the 

tracking error, the human's control rate, and control input for the 

varlous cases of display augmentation mentioned above, are listed in 

Table 4.2. These results are also plotted in Figures (4.1) and (4.2). 

Fig. (4.1) is a plot of mean-square error vs. mean-square control rate, 

and Fig. (4.2) is a plot of wan-square error vs. mean-square control 

input. The scales are choren to be compatible with Figs. (2.2) and 

(2.3). 
Case 

1. 

2. 

3. 

4. 

5. 

A. 

B. 

C. 

39 

TABLE 4.2: OCM ANALYSIS RESULTS FOR VARIOUS CASES 

M.S. Error (e) 

(in.2> 

0.014 

0.0132 

0.0131 

0.01272 

0.01269 

0.0131 

0.0157 

0.0127 

M.S. Input (6) 

(in. 2 1 

0.389 

0.492 

0.514 

0.650 

0.665 

1.141 

1.353 

0.789 

M.S. Control Rate <S) 

(in.2/sec 2 

18.64 

23.72 

24.78 

31.58 

32.4Q 

54.73 

67.44 

38.49 
40 

1 Nomenclature 

2 : Gd = [49.2, 13.01 A : No Display-Lag 

3 : Gd = [64.4, 16.31 

-01 9 

4 : Gd = [88.1, 17.31 1 

0) 

.Ol3 i z 

B : Gd = [20, 01 

C : Gd = [20, 31 

5 : G = l118.2, 22.61 d 

Beg. Display -F 

0 

/z Increasing Weight on Error 

15 20 25 30 55 40 45 50 55 GO 65 70 

Mean Square Control Rate (in. / sec ) 2 2 

Figure 4.1 Error vs. Manual Control Rate for Various Displays 
41 

- --- .022 : 

- Komenclature 

1 : Gd = [36.6, 11.91 

2 : G = [49.2, 13.01 

3 : G = [64.4, 16.31 

4 : Gd = [88.1, 17.31 

5 : G = [118.2, 22.61 

d 

d 

d 

A : No Display-Lag 

B : Gd = [20, 01 

C : Gd = [20, 31 

v t 

,013 1 

Beg. Display-)( 0 

.3 .4 .5 .6 .7 .e .g I 1.1 1.2 1.3 1-4 

Mean Square Control Input (in. 2, 

Figure 4.2 Error vs. Xanual Control Activity €or Various Displays 
42 

From these results it is clear that as the relative weighting on 

the error in the cost function J is increased, the optimal cooperative 

display design methodology leads to display gains which give improved 

2 

perforaance at the expense of increased control activity. It is noted 

that for all the 5 cases obtained using the cooperative methodology, the 

final optimal display gains are such that the performance is significantlv .improved as compared to the starting display (R), and at the same 

time the "workload" (6) and the control effort (6) are considerably 

reduced. If the weighting; on the error is high (Cases 4 and S), perforinance comparahle to the limiting case (A) and the best performance case 

(C) is ohtained, along with reduced workload and control effort. b'oteover it appears that €or the selected display bandwidth (a = -20 

sec ), tracking performance (ms error) better than that of Case 5 cannot he obtained. Increasing the weight on error in the cost function J, 

any further would only have the effect of leading to a display design 

d 

-1 

- 

requirinp: higher control effort without any noticeable improvement in 

perf ormance . 

---- 4.2.2 Power Spectrum Analysis 

Using the Oc41 modeling technique, the power spectra of the human's 

control inputs and the system responses can also be estimated. Note 

that the mean-square value u2 of a zero mean process x is related to the 

area under its power spectral density C (w), or 

X 

X 

(4.2.1) 

Figure (4.3) provides a comparison of the power spectra of the human 

operator's control input (6) for the displays 1, 3, and 5, and the llm- 
43 

Figure 4.3 Comparison of Human Operator’s Control Spectrum, b (UJ) 
44 

itiny! case A. The plots in Fipure (4.3) show that the control power 

required is lower for all the optimally synthesized displays when compared to the idealized Case A with no display lap,. bloreover, the peak 

value increases 3s the weighting on the error in the cost .I, is 

increased, corresponding to the human's task becomes increasingly more 

difficult from display design 1 to design 5. The power spectral densities of the human's control input 6 for all the displays are shown in 

the Figures (C.1) to (C.6) in Appendix C. These figures include: 1) the 

total control input power (in dR), 2) the portion of the control correlated wlth the command driving the system, and 3) the human operator's 

remnant, or the uncorrelated portion of the control input. 

- 

Since the mean-square value of the errors €or the display cases 1 

to 5 and the limitintg Case A were not significantly different, (see 

Tahle 4.21, the power spectral densities of the errors €or these cases 

would he expected to be similar. This was indeed found to be the case 

and so the error power spectral density plots are not included in the 

report. 

--- 4.2.3 Frequency Domain Analysis 

The human operator model can also be represented in the frequency 

domain in terms of the transfer matrix between the human's observations 

and his control inputs (6,131. Since the Rode characteristics of the 

plant and the display are known, frequency-domain analysis of the 

manually-controlled display-augmented systems can be carried out, once 

the human describing functions are estimated from the model. 

With the human operator so represented, the block diagram for the 

task is shown in Fig. (4.4). The display-augmented system is defined as 
45 

r 

r--- 

I 

I 

I 

I 

I 

I 

I '7 

I- I LQ- 

- $1 

,"I 

"I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

i 

I 

.- 
46 

x (SI 

C(s) - -- Ad 

= 6(s) 

and the human descriSing function is 

For the displays 1, 3, 5, and A, G(s) and P(s) are compared in "igures 

(4.5) and (4.h), respectively. (The Bode-plots of G(s) and P(s) for the 

cases 1 to 5 and the Case 4 are show in Appendix C.) From these frequency responses in Fiz.(4.5) and Fis.(h.6), the open-loop Sode-plots 

may also be deter-nined (not shown). 'It appears that open-loop magnitude 

crossover (w such that 1 "( iw) C( iw) I = 0 dS) is approximately constant 

at between 2-2.5 ratls/sec for all these cases, consistent with the command signal bandwidth (break at 2 rads/sec). Also, as the weighting on 

error increases (Case 1 -> Case 5), the sensitivity (gain) of the total 

plant plus display increases. From Fig. (4.5) it is clear that all the 

synthesized displays provide additional lead between 1 and 10 radslsec. 

As the weighting on the error in the cost J is increased (Case 1 -> 

Case 5), this phase lead provided by the synthsized display gains 

decreases. 

2 

The human operator's phase compensation in Fig. (4.6) is more 

easily interpreted by looking at this phase compensation with the time 

delay (T) of 0.2 seconds removed. This adjusted phase is then given by: 

pc(w) = 4 ?(jw) + 57.3 T w (4.2.2) 

A comparison of this adjusted phase €or the various display cases is 

provided in Figure (4.7). From these plots it appears that the human 

would need to generate much higher phase lead for Case A as compared to 

all the optimal display augmentation cases. For Cases 1-5, the required 
47 

60 

40 

20 

0 

- 20 

-40 

- 60 

-7 30 

-1 40 

n 

M 

a 

0) 

c 

p1 

u -150 W 

-160 

-170 

- 180 

.I ?O 7 oc 

c 

1 70 

Frequency (rads/ sec) 

1 oc 

Figure 4.5 Comparison of Display Augmented Plants, G(s) 
48 

150 

30 

20 

10 

0 

-1 0 

c - 

Et Q/ 

700 

I- / -La 

-100 1 

-150 I I , I I I III I I I I I141 I 

.I I 10 

Frequency (rads/sec) 

Figure 4.6 Comparison of Human Describing Functions, P(s) 
49 

Frequency (rads/sec) 

Figure 4.7 Comparison of Human’s Phase Compensation 

(adjusted phase) 
50 

phase lead increases with the increase of error weighting in the cost 

function J,. 

trends in Figure (h.7) indicate that the display augmentation reduces 

the human‘s workload. ‘loreover, the plots predict increasiqp, workload 

as the error weighting (q ) is increased in the synthesis of the 

display. 

Thus, usirig the phase lead as a measure of workload, the & 

e 

Vith G(s) and P(s) known, the closed loop transfer function, 

x( S) T(s) = ~7, is easily obtained, through alEebraic manipulations usiqg 

the hlock diarram of Fig. (4.G), to he 

C 

Mere De(s) =y-- A ”* and D.(s) zz- , x (s) is the commanded position A ‘d3 

d X dC sa 

and x(s) is the plant position state. Closed-loop frequency response 

for Cases 1,3 and 5 of display augmentation is compared in Fig. (4.8). 

The maanitude and phase plots in Fig. (4.8) indicate that as the error 

weighting (qe) is increased, the synthesized display is such that tracking performance is improved. 

Hence, both by comparing these results from the display augmentation synthesis technique with the results of Chapter 2, and through 

additional closed-loop analysis, one can conclude that this synthesis 

technique appears to lead to desirable results. 
51 

0 

-5 

-10 

-75 

- 20 

0 

- 39 

- 60 

- 90 

-120 

IO 

I I I I I IIII 1 I I 11 Ill 

.I I 

Frequency (rads/sec) 

10 

Figure 4 .a Comparison of Closed-Loop Frequency Response 

for Displays 1,3 and 5 
52 

APPLICATION OF COOPERATIVE *ETHODOT,nCY TO A 

MORE CO?TPLEX DISPLAY T)ESIcN 

- .- - 

__. 

In this chapter, an example application of the optimal cooperative 

methodology to a higher-order system in a multi-input task is presented. 

The intent is to demonstrate tbe application of the cooperative methodology to complex systems and the design presented here should not be 

considered a finalized design. The chosen plant to be controlled 

represents the unaugmented Longitudinal dynamics of sn aircraFt, and the 

task is that of tracking a normal-acceleration command vhile rewlating 

Mach number. The control inputs available to the pilot are the elevator 

stick and throttle, and the pilot may Se assumed to he controlling the 

aircraft remotely from the ground, for example. The chosen mow1 and 

the task formulation are discussed in detail. 

The task is first described and modeled, using an initial unaugrnented status display. Then an optimal display augmentation control law 

is synthesized using the proposed algorithm. The pilot's performance 

€or the unaugmented and the augmented display systems is then evaluated 

and compared. Based on these evaluations, improvement in performance and 

reduction in the pilot workload is predicted for the optimally augmented 

display. 

-- 5.1 System Dynamics -- 

The dynamics are those for an F-15 type aircraft without any flight 

control augmentation, but including a Mach sensor (with lag), a thrust 

lag modeling the engine, and a fast first order actuator €or the eleva- 
53 

tor control. ('%is model is fron ?ef.[21], ?ut without the command aliamentation syster.) The vehicle state vector is 

--T 

x 

angle of attack (.nl rads), nitch rate (.01 rads/sec), pitch attitude 

= [17,a, a, 0, 6e, ?', 6TI - the perturbed forward velocity (ft/sec), V 

( .O1 rads), the elevator deflection (.01 rads), sensed Yach niimher (.On1 

Mach), and the thrust acceleration (ft/sec ). 2 

tor deflection and the comnanded thrust acceleration. The state-space 

r2~rescntation of the model is 

- 

x = Ax + gvT V vv (5.1.1) 

xhere the matrices A and R are as given in Appendix E. The states are 

the perturbed values ahout the trin conditions also listed in Appendix 

V V 

D. 

The pilot's assumed objective here is to track a normal acceleration command (a ) while regulating Xach number to the best of his ahility. Rather than the deterministic normal acceleration command (a ) 

used for the pushup-pullover maneuver in previous studies [4,5], the 

ZC 

ZC 

command signal to be tracked is generated, for the purpose of display 

control law synthesis, by using a second order Markov process with a 

break frequency of 1 rad/sec and a damping ratio of 0.7. With 

a 1, the command system is represented in the state variable -7- A 

xc z [azc, zc 

form as 

(5.1.2) 

The intensity of the white noise process w is chosen to be W = 181 so C C 
54 

as to yield the rns comnand of Q = 8 €t/sec2 (or 0.25 g’s). a 

2C 

-T A -T -T Oe€inina xo [xc, xv], the vehicle dynamics augmented with the 

command system are written in the state-space form as 

- 

x =Ax +BT+3w 

0 00 0 oc (5.1.3) 

with appropriate definitions of A S and n . The time response of the 

variables a $1 and 8 is obtained €or unit step control inputs. The 

time histories €or step elevator input are shown in Figures (5.1 (a)- 

(c)) and those for step throttle input i? Figures (5.2 (a)-(c)). 

0’ 0 0 

z’ 

5.2 Task ‘‘odeling - - - --- 

For the initial unaiigmented status display, the pilot’s observations arc assumed to be the normal acceleration command signal, the a 

trackina error (e 

attitude. It will again be assumed that the pilot can reconstruct the 

rates of the displayed signals. Then the pilot‘s observation vector, 

z 

= a -aZ), the sensed (lagged) Nach number and pitch az ZC 

-T - a e ?I, bi, 8, e], is of the form Yp - zc’ az’ 

- 

Yp = COT + EoT (5.2.1) 

with C and E as given in Appendix D. A conceptual display format for 

this status display is shown in Fig. (5.3). 

0 0 

For the augmented display system, the pilot’s observations are to 

a and 8, along with the associated rates. (Note that be Xdl’ ‘d2’ zc 

compared to the status display case, e and M are replaced by the 

“intelligent” display variables x and x 

tained in the pilot’s observation vector). Therefore the outputs available for feedback by the pilot are 

az 

dl d2 ’ while aZc and 8 are main- 
55 

3 

h 2 

v 

N 

rd 

1 

‘5 

0 1 2 3 4 5 6 7 6 9 10 

Time (Set) 

Figure 5.l(a) a Response to Step Elevator Input z (6e,= 0.01 rads, +ve down) 
56 

6 

5 

4 

3 

2 

1 

0 

-1 

0 2 3 4 6 6 

Time (sec) 

7 6 9 TO 

Figure 5.l(b) Mach Response to Step Elevator Input 
57 

0 

-1 

-2 

-3 

n 

v) 

a 

2 -$ 

d 

0 

C 

W 

a -5 

-6 

-7 

Figure S.l(c) 8 Response to Step Elevator Input 
58 

Time (sec) 

Figure 5.2(a) a Response to Step Thr ttle Input 

s 2 

( 6Tc= lft/(sec 1, +ve thrust) 
’1 ‘2 

1 

.2 

Time (sec) 

Figure 5.2(b) Mach Response to Step Throttle Input 
60 

t 

1 2 3 ';I 5 6 7 a 9 .I 0 

Time (sec) 

Figure 5.2(c) 8 Response to Step Throttle Input 
61 

50 

40 

30 

20 

n 

.=a 

0 

-10 

z" 

d 

0 

0 

0 

W 

-20 

- 30 

- 40 

- 50 

C RT 

(Assumed Markings at 0.5 ft/sec2 and 0.5 M) 

Pilot's objective: (a) Keep 0 over the a bar 

zc 

(b) Keep a within -f (15) M 

2 

(ft/sec ) 

IO-ID 

Attitude 8' 

(blarkings at lo) 

Figure 5.3 Conceptual Display Format for Status Display 
62 

.4 conceptual display format for the augmented system is shown in Fig. 

(5.4). 

Reasonable pilot modeling parameters for this analysis are as fol1 ows : 

(i) Pilot‘s observation tine delay, T, set to 0.2 seconds. 

(ii) Observation noise ratio set at -12 dT? for all observations. 

(iii) !.‘otor no’,se ratio set at -12 d? €or hoth control channels. 

(iv) The weighting on the control rates in the pilot’s cost frinction adjusted to yield a neuromotor lap, tine constant of 0.2 secs 

in the elevator channel and 5 secs in the throttle channel. 

(v) The pilot’s fractional attention allocation (f ) was set at i 

0.3 €or each of the observations a e and M, and 9.1 for 8. zc’ az 

(vi) The pilot’s indifference thresholds €or the various ohservations are set to values listed in Table 5.1. 

Though parametric performance analysis is not too sensitive to many 

of these variables, the values of observation and motor noise ratios are 

chosen to be higher than in Chapter 2 in order to he consistent with the 

pilot behaviour observed in real-time simulations of complex tasks. 

Also the pilot’s neuromotor lag time constant for the throttle channel 

is set at 5.0 secs to reflect the fact that the pilot changes the throttle setting very slowly, since the engine response is slow. Finally, 

from Fig. (5.3), it is seen that though the pilot observes a e and zc’ az 
63 

50 

40 

u 30 

n 

v) 

rl 

C 

h fa 

p. 

cn 

’ 20 

r’lD 

zo 

a -10 

W 

hl 

X 

-u -20 

C 

m 

-30 

- 40 

a 

x 

-50 

I 

0 

J xd2 I O-PL ’d I i 

50 

40 

30 

20 

10 

0 

-10 

-20 

- 30 

-40 

-50 

a ZC 

2 (ft/sec ) 

Attitude 8 0 

(Efarkings at I 0 ) 

C RT 

(Assumed Markings at 0.5 display units for x and x dl d2 

Pilot’s objective: (a) Keep 0 at 0 marking for Xdl 

(b) Keep a at 0 marking for Xd2 

Figure 5.4 Conceptual Display Format for Augmented Display 
64 

TABLE 5.1 PILOT PERCEPTION THRESHOLDS 

I Observation 

az 

M(.001 Mach) 

8 (.01 rads) 

x (display units) 

x (display units) 

dl 

d2 

Threshold 

0.5 

0.5 

0.5 

0.2 

0.5 

0.5 

Lte Thresholc 

1.0 

1 .o 

1 .o 

0.4 

1.0 

1 .o 
‘.f x and x for the case of augmented display - Fig. (5.4)) from 

the same physical display, he still needs to scan their values 

dl d2 

separately. So we will consider his attention to be divided equally 

between the three primary observations, with attitude information only 

secondary to the task. The choice of the values for pilot’s thresholds 

is based on the assumed display size and minimum resolution in the conceptual display formt of Figs. (5.3) and (5.4). The thresholds for the 

rates are twice the thresholds for the corresponding displayed variable, 

for all the pilot’s Observations. 

For the unausmented status display, the pilot’s objective function 

is taken to he 

(5.2.2) 

which reflects the pilot’s emphasis on tracking the a command, and also 

is consistent with the units of a and Pi in the dynamic model. This 

objective corresponds to the pilot attempting to keep the square, in the 

z 

z 

display format of Fig. (5.3), over the a bar, while at the same time 

maintaining the Yach needle within 2 (15). 

ZC 

Note in this case the 

pilot’s Commanded thrust (6T ) is explicitly included in the cost objective. This was found to be necessary to keep the commanded thrust within 

limits deliverable by the engine. The weightings in (5.2.2) were determined after a few trials of the modeling procedure. Finally, in 

C 

(5.2.21, and g are chosen 

neuromotor lag time constants 

2 

-- 5.3 Optimal Display Synthesis 

to be consistent with the assumed pilot’s 

for the two control channels. 

for F-15 Nodel ---- 
66 

For designing display auventation for the aircraft discussed 

ahove, the basic display dynamics may be taken to be of the €orm 

or 

with 

(5.3.2) 

- 

where x 

designer, and the display gains Gd are to he synthesized so as to be 

optimal for the task to be performed. For the display design presented 

is as defined in (5.1.3). Tn (5.3.2), yd is chosen hy the 0 

- 

in this section, yd is chosen to he 

(5.3.3) 

which means that all the vehicle states as well as the command states 

are available for driving the display. Note that in (5.3.1), the 

display bandwidth is chosen to be faster than the pilot's dynamics. 

Also two display states (along with two display control laws) are 

chosen. 

A 

13 Defining Controller 1 to he the pilot's inputs,or 'iT - T, the 

dynamics of (5.1.3), augmented with the display system and pilot's control inputs can be written as 
67 

w!iere the two-dirensionnl rhite-noise process 7 is the pilot's notor 

noise in the two control channels. 

m 

With the auzmented display (see Fig. (5.4)), the pilot's task is 

that of regulating the display states x and x This can be modeled 

as finding the optimal Controller 1 (u ) which minimizes the cost function J piven by 

dl d2' 

1 

1 

m 

*7 *7 

+ !zl(6ec)- + ~~(6T~)~)dt) (5.3.5) 

The ohjective function .J, to be nrininized hy the displav control 

c.1 

L 

- 

law ti is, however, taken to he 

T 

T- o 

J2 = .Jp(T) + E{lim I.(3nnnl(~i~ + u2 d2 )dt) (5.3.6) 

Note here that J (3) is as in (5.2.2), or the pilot's ohjective with the 

status display. The weights on the display controls (u 

chosen to he very small initially, at least, so that their contribution 

P 

and ud2) are dl 

to J2 is negligible as compared to J (T). 

consistent with our objective of finding a display control law which 

The choice of J as above is P 2 

helps the pilot perform his overall task of tracking the a command 

while regulating the Mach number. 

2 

In order to initialize the numerical solution technique, an initial 

guess for the display control gains is made such that x corresponds to 

-e (i.e. a -a ) and x to 0.01 X in the steady state. Qecalling 

Eqns.(5.3.2) and (5.3.3), then, the starting display control gains are 

a1 

az z zc d2 

(5.3.7) 

Gd start -[ 00 0 0 00 0 0.2 7 -20 0 -0.082 -32.21 0 0 -5.096 

For this choice of Gd, J1(UI) for the initial display law closely 
68 

reoresent5 .T (7) of the original status-disp:sy case. 

2 

The ontimal 3isplav control gains detenined fron the algorithm 

c on ve r ged to 

I -fi.32~ -1.475 -38.n5 -12.06 -4.n19 4.~23 3.213 

-16.74 0.8258 -13.44 -36.74 -15.41, 33.06 -0.202 

(5.3.8) 

In the synthesis process for the optimal display, the weightings z, 

2 11 

1 

and :: in the cost function J (u ) and the variances for the noise 

processes v and < 

u cl-osely approximate the full-order pilot model. 

- 

are constantly updated so as to make the controller 

nl Y - 

1 

- 5.4 Conparison of the nisplays - ___-- I - 

The pilot's periornance, as predicted by model-based evaluation, is 

compared for the two cases - the status display and the "optimal" 

display augmentation synthesized as ahove. 4s in the case of K/s 

plant, the criteria used for comparison are - r;ns values of the variables of interest, control and error spectra, and frequency domaix 

analysis. Time histories for step control inputs are also provided to 

gain a better understanding of the significance of the "intelligent" 

display varlables x and x 

referred to as Display A and the optimal display as %splay B in the 

following discussion. 

2 

For brevity, the status display is dl d2' 

---- 5.4.1 Time Wistories 

dl For Display B, the time histories for the two display variables x 

d2 and x €or a unit step elevator input are shown in Figs. (5.5 (a)-(b)) 

and those for a unit throttle input are shown in Figs. (5.6 (a)-(b)). 

Significant coupling is evident in this case, especially for elevator 
69 

0 I 2 3 4 5 6 7 8 9 10 

Time (sec) 
70 

10 

n 

LI a0 

E: 

J 

x 

a 

74 

P 

26 

-c 

v 

N 

XU 

4 

2 

U 

Time (sec) 

Figure 5.5(b) x Response to Step Elevator Input d2 
71 

-.06 h 

v) 

u 

P 

v) 

cl 

a 

W 

-.18 

-.21 

0 

I::!! :I,:!:::* !:::* .. i.........i.... . . . . . ! . . . . . . . . . . 

1 2 3 4 5 6 

Time (sec) 

7 8 9 10 

Figure 5.6(a) x Response to Step Throttle Input 

2 (6Tc= lft/(sec ), +ve ihrust) 

dl 
72 

N 

ZI 

X 

I 2 3 4 5 6 7 a 9 

Time (sec) 

Figure 5.6(b) x Response to Step Throttle Input d2 
73 

commands. 

for the pilot might he to attempt to "control" x with the throttle and 

x 

uncontrollahle from throttle inputs. For a step normal acceleration conmand, there will be an instantaneous change in both x and x (as is 

apparent from the optimal display gains C in (5.3.9)). In order to follow the command, then, the pilot's strategy would appear to be to apply 

the elevator to regulate x and si.nultaneously use the throttle to null 

out the effects of the elevator cmmand and the normal acceleration com- 

;land on Y . T'le ultimate siiccess of this stratep;y as well as comparison 

vith that for the case of status display (nisplay A), of course, 

requires additional analysis and simulation. 

Frm these time responses, it would appear that the strategy 

dl 

with the elevator. This is due to the fact that x is essentially d2 d 2 

dl d2 * 

d 

d2 

r! 1 

--- 5.4.2 Frequency Domain Analysis 

The block diagram representations for the pilot's task formulated 

as above are shown in Figures (5.7) and (5.8) for Displays A and R, 

respectively. Note that in each case the pilot has four observations 

and two controls available to him. (The rate observations, as stated 

earlier, are reconstructed by the pilot from the displayed signals.) So 

the frequncy-domain representation of the pilot consists of a 2 x 4 

transfer matrix. For Display A the pilot representation is 

P(s) = 

and for Display R 

P(s> = 

' 6e- 6e '&e '6e 

-- zc - az _1 a e zc az 

P ---- 6T 6T '6" '6T 

a e M e 

(5.4.1) 

(5.4.2) 
74 

4J 

d 
I 

75 

-4 

1 h 

m 

E 

m 

$4 

M 

a 
76 

l'ere P is the pilot descri5ing function fron the normal acceleration 

- 6e 

a 

ZC 

command observation a to the commanded elevator input 6 . The other 

elements of (5.4.1) and (5.4.2) are similarly defined. The Rode-plots 

ZC ec 

for rhe eight pilot describing functions for Display A are presented in 

Figures (n.1) to (n.8) and those for Display B in Figures (D.9) to 

(n.16) in .Appendix n, for reference. 

1Jith the pilot represented by eight transfer €unctions, it is not 

straightforwaril to define a meaningful ieasure of pilot workload in the 

f renuency-dnmai 7. since the vehicle rlvnnmics and the displ3v dynnics 

are knom and the various pilot descrihinp €unctions are avaitahle as 

above, additional frequency-domain analysis, as in the case of the Y/s' 

3 

plant, may in principal be performed using the block diagrams of Figures 

(5.6) and (5.7). However, the results presented in Chapter 4 showed that 

the performance and workload information ohtained fron statistical and 

spectral analysis of the nodel-based predictions is consistent with that 

derived from the other frequency-domain analysis. Therefore, results 

from statistical and spectral analysis will be used to evaluate and compare the two Displays A and B. 

---- 5.4.3 RMS Analysis 

Using the complete human operator model, closed-loop analysis was 

performed for both the status display (A) and the optimal augmented 

display (B). The rms values €or the variables of interest €or the two 

a. 

displays are shown in Table 5.2. From these results it is clear that 

there is a slight improvement in a tracking performance for the case 

with display augmentation, and Mach number regulation is much improved. 

2 

Both the pilot control inputs and control rates are lower for the 
77 

TABLE 5.2 OCM ANALYSIS RESULTS 

e e M Classification az az 

ftlsec 2 .001 Mach 

A: Status Display 7 .OO9 11.920 39.11 

B: Optimal Display 6.659 9.349 11.32 

0 

.01 rads 

8.45 

3.36 

ec 

.01 rads 

Classification 6 

A: Status Display 2.95 

B: Optimal Display 1.78 

0.1742 

C 

6T 

f t/sec 

13.21 2.566 

8.06 0.819 

ec 

6 

2 
78 

optilal iisp13y cAse, iridicatinp that the desizned display auyentation 

should lead to reduction in pilot workload. 

--- 5.4.4 Spectral Analysis 

The power spectra of the a tracking error and both t!ie control 

z 

inputs for the Displys A and R are shown in Fizures (D.1) to (n.6) in 

the 'Ippendix 3. 

correlsted with the cornman6 drivinp, the system, and the uncorrelated 

part, or the contribution due to the pilot's rmnant. 

These plots show the total power (in dR), the portion 

The a trackinr error power spectrum for the nisplqvs I and P, i4 

z 

covpdred in Cig~ire (5.q). This power for Display R (aiigmented case) is 

slightly higher than 3isplay A at Low frequencies, brit is less than 

qisplay 4 for frequencies above 0.7 rads/sec. Fven though the rms 

tracking error with the optimal Idisplay (B) is not too nuch lower than 

that with the status display (A), the augmentation appears to reduce the 

errors at the more-demanding higher frequencies. 

The pilot's commanded elevator power spectrum and commanded thrust 

power spectrum €or Displays A and B ar2 compared in Figures (5.10) and 

(5.11), respectively. From these figures it is clear that the power €or 

both pilot control inputs is much lower at all frequencies €or the 

optimal display case. As was the case of K/s plant, this is an indication that the pilot's workload in accomplishing the task should be 

reduced. 

2 

Thus, from this initial example application, it appears that the 

suggested display augmentation synthesis technique can lead to desirable 

results when applied to manual control of complex dynamics. As further 

experience is gained in applying the technique, even better performance 

my 5e achieved. 
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83 

The objective of this effort was to develop an analytical technlque 

to aid in the design of display augmentatlon. The main differences 

Setween display auzaentation and control augmentation were pointed out 

usi2g simplified block diagrams. Although different from augmenting 

plant dynamics, it is usually possible to improve human operator performance in manual-control tasks hy providing the human with an augmented 

display. 

:fodel-hased evaluations were performed for various emperically2 derived display "quickening" control laws for a simple K/s plant in a 

compensatory tracking task. The results of this analysis, in terms of 

mean square values of tracking error and manual control activity and 

rate, showed that significant reduction in human operator workload and 

improvement in performance is possible through a proper design of the 

signal being displayed to the human. 

The cooperative control synthesis technique previously developed to 

design pilot-optimal control augmentation was then extended to incorporate the simultaneous design of pilot-optimal display augmentation. 

The problem formulation for the cooperative synthesis technique was discussed in detail and the necessary conditons for optimality were 

derived. A numerical algorithm for applying the methodology to.gerform 

pilot-in-the-loop synthesis of optimal display augmentation control laws 

was then presented. 

The application of the methodology to a simple system was demonstrated by synthesizing various display augmentation control laws for 
84 

3 

the Y/ sL plant. Ry varyin? the weightinp paraneters in the cost function, it was shown that this methodolo?y has the potential of providing 

a systematic approach to design of task tailored display augmentation. 

The synthesized display designs were evaluated, using the full-order 

hunan operator nodel, in terns of the mean square values of the variahles of interesl: anfl the power spectrup of the human operator's control 

input. The evaluation results predicted a reduction in hiiman operator 

wor'tload and improveFent in tracking error performance with the angmented displays. Yoreover, when compared to the emperically-derived 

display "quickening" control lards, tlie results tended to vaiidate the 

cooperative approach to display design. 

Detailed frequency domaii analysis was also perforned for the synthesized displays, using the frequency-domain representation of the 

human operator model. All the augmented displays were shown to provide 

the human operator with some lead information, reducing the required 

human operator phase compensation from the case with no display augmentation. A comparison of the closed-loop frequency responses for the 

various synthesized displays i3dicated that the cooperative methodology 

does lead to desired results. 

An initial application of the methodology to high-order system 

dynamics with a multi-control task was then demonstrated, using a 

normal-acceleration tracking task and an F-15 type aircraft model. The 

problem formulation was discussed in detail and a preliminary di-lay 

design was synthesized using the cooperative technique. Analytical 

methods for evaluating the synthesized display for the complex task were 

again employed, and the results of the analysis were compared with those 

€or an unaugmented status display. Rased on the statistical analysis 

-8 ' . 
85 

rssults, ir?provment i.2 performance and pilot workload is predicted for 

the synthesized optimally aumented display. 

Since the model-based evaluation of the display designs predicts 

pronisiny! gains i? pilot workload, it is suggested that these rssults he 

validated throuEh real-time, man-in-the-loop siTulation. For the display 

design syntbesized for the aircraft model, further insizht needs to he 

gained into the significance of the two display varlables. Finally, the 

application of the cooperative methodology to display design for coilplcx 

systems should 5e further explored, and systems considered for which 

ot’:er nethods !:ave +?en used to s:znthesize t?ie displav, to provir‘e 

furtb-er conparison and validation. 
86 

REFERENCES 

[ 11 Poulton, "Tracking Skill and Manual Control ,I1 Academic Press, 

1974. 

[2] Hoffman, W.C., Yleinman, D.L., and Young, L.R., "Display/Control 

Requirements for Automated VTOL Aircraft," NASA-CR 158905, ASITR-76-39. 

[3] Yorn, J., Gully, Sol W., and Kleinman, D.L., "Validation of an 

Advanced Cockpit Display Design hiethodology via 

WorCloadfXonitoring Tradeoff Analysis ,I1 18th Annual Confere'nce on 

Yanual Control, Dayton, Ohio, June 1982. 

[4] Duke, E.L., Jones, F.P., and Roncoli, R.R., "Development of a 

Flight Test Maneuver Autopilot for a Highly Maneuverable Aircraft," AIM Paper 83-0061, Jan. 1983. 

(51 Walker, R.A., Cupta, N.K., Duke, E.L., and Patterson, B., 

"Developments in Flight Test Trajectory Control," AIAA Paper 84- 

0240, Jan. 1984. 

[6] Kleinman, D.L., Raron, S., and Levison, W.H., "An Optimal Control 

Model of Human Response," Parts I and 11, Automatica, vo1. 6, pp. 

357-383 , 1970 . 

(71 Schmidt, D.K., "Optimal Flight Control Synthesis via Pilot Modeling," AIM Journal of Guidance and Control, July-August 1979. 
87 

[ 8) Schmidt, D.K., and Innocenti, M., "Pilot Optimal Multivariable 

Control Synthesis by Output Feedback," NASA CR-16312, July 1981. 

[ 91 Innocenti, M., "Cooperative Pilot-Optimal .4ugmentation System Synthesis for Complex Flight Vehicles ,I1 Ph.D. Thesis, Purdue University, West Lafayette, Indiana, May 1983. 

[lo] Schmidt, D.K., "On the Use of the Om's Quadratic Objective Function as a Pilot Rating Pfetric," 17th Annual Conference on Manual 

Control, Los Angeles, CA, June 1981. 

[ 11 J Wierwille, Walter W., and Connor, Sydney, A., "Evaluation of 20 

Workload Neasures Using a Psychomotor Task in a Moving-Rase Aircraft Sinulator," Human Factors, Vol. 25, pp. 1-16, 1993. 

[ 121 Kwakernaak, H., and Sivan, R., "Linear Optimal Control Sys terns ,I1 

Wiley-Interscience, 1972. 

[In] Bacon, B.J., and Schmidt, D.K., "An Optimal Control Approach to 

Pilot/Vehicle Analysis and the Neal-Smith Criteria," NASA Contractor Report 170416, April 1984. 

11 [14] McRuer, D., Graham, D., Krendel, E., and Reisener, W. Jr., Human 

Pilot Dynamics in Compensatory Systems," AFFDL-TR-65-15, July 

1965. 

[15] Curry, R.E., Hoffman, W.C., and Young, L.R., "Pilot Modelling for 

Manned Simulation, Vols. I and TI, AFFDL-TR-76-124, Dec. 1976. 

[ 161 Phatak, Ani1 V., "Investigation of Alternate Human Operator 

Optimal Control Hodel Structures ,I1 Air Force RMRL, contract 
88 

/IF3361 5-78-C-0501. 

[ 171 Noble, B., Daniel, J.W., "Applied Linear Algebra," Prentice-Hall 

Inc., 1977. 

[18] Joshi, S.X., "Design of Optimal Partial State Feedback Controllers 

for Linear Systems in Stochastit Environments," Paper hD-4, TEEE, 

Souteascon, Charlotte, N.C., 1975. 

[19] Neal, T.P., and Smith, R.E., "An In-flight InvestCgation to 

Develop Control System Design Critera for Fighter Airplanes," 

AFFDL-TR-70-74, Vol. I, Dec. 1790. 

[20] Anderson, M.R., and Schmidt, D.Y., "Closed-loop, Pilot/Vehicle 

Analysis of the Approach and Lending Task," ATAA Paper ?.io. 

1851-CP, 1985 Guidance and Control Conference, Snowmass, Colorado. 

85- 

[21] Walker, R.A., and Gupta, N.K., "Flight Test Trajectory Control 

Analysis," NASA Contractor Report170395, Feb. 1983 

(221 Pavassilopoulos, G.P., Medanic, J.V., Cruz, J.R. Jr., "On the 

existence of Nash Strategies and Solutions to Coupled Riccati 

Equations in Linear-Quadratic Games", JOTA, Vol. 28, No. 1, May 

1979. 

[23] McRuer, D.T., and Krendel, E.S., "Dynamic Response of Human Operators", Wright Air Dev. Center WADC TR 56-524, Wright-Patterson Ait 

Force Base, Ohio, Oct. 1957. 

[24] Levison, W.H., Kleinman, D.L., and Baron, S., A Model for Human 

Controller Remnant", IEEE, Trans. Man-Machine Syst., Vol. 10, Dec. 1969 
APPENDIX - A 

DERIVATION - OF NECESSARY CONDITIONS FOR CONTROLLER 2 (T ) - 2 - 

As stated in section (3.4), the system dynamics in the presence of 

the control actionul can be written in terms of the augmented state 

vector 5 as 

. 

- ’- I# 

q = A 1 q + B’u 22 + B’u dd + Dw (A. 1) 

I I I I 

B2, Bd, and D are as defined in section (3.4). The out- 1’ where 7, A 

puts 7 and yd are given in terms of by 2 

and the index of performance J becomes 2 

I 

with Q again as defined in section (3.4). 

The closed loop system under the action of Controller 2 (L2) and 

the display control law with the control laws as given by (3.1.5)’ d’ 

can then be written in a compact form as 

. 

- #I 

q = ACT+ D w 

where 

C and A as defined in Chapter 3. aug’ aug 1 with A 

The system given by (A.4) is identified as a linear stochastic time 
90 

I 

invariant system driven by a white noise process w . From linear stochastic system theory [12], In the steady state case the system state 

covariance matrix L is obtained as the solution to the following 

Lyapunov equation 

A L + LA: +, D’w’D’~ = o 

C 

I I - AT 

where W is the intensity of the process w and L=E[q q 1. 

Using the trace operator [17], J can be expressed as 2 

J2 = tr[qL] 

where 

- Q-Q ‘[ + 0 i 0 

C;G;F~G~C~ + c%~F~~G~c~ 

(A.5) and (A.6) can now be treated as a constrained parameter 

optimization problem [18]. Defining H as a symmetric matrix of Lagrange 

multipliers, the cost J can be augmented with the constraint (A.5) to 

get 

2 

(A.7) - ’T J2 = tr[qL] + tr[H(AcL + LA: + D W D 11 

The necessary conditions for optimality applied to (A.7) yield the 

following relations 

#I 

- aJ2 = A~L + LA: + D w D ’T a 0 

aH 

aT2 

aT2 

-= 0 

aG2 

-= 0 

aGd 

(A.ll) 
Equations (A.10) and (A.ll) need further elaboration because the 

augmentation gains G and the display control gains G are embedded in 

the dynamics of the closed loop system. 

2 d 

In T2, the terms containing G2 are and Ac. Therefore 

aT2 

-=- a (tr[qL] + 2tr[HLA:]} 

aG2 aG2 

(A. 12) 

T where the trace identity tr[HA L]=tr[HLA ] has been made use of. 

Further note that in A G appears both in A as well as in A But 

A 

(3.4.1), and since we are looking for a Nash solution, Controller 1 is 

C C 

c' 2 aug 1' 

is part of the optimal Controller 1 (il), as is apparent from 1 

to be considered fixed in the minimization process for J Thus the 

only gains that may be adjusted in Controller 2 are those in A 

2' 

where 

aug 

A = A + B G C + BdGdCd. Then 

aug 222 

r 

- a 

aG2 

Noting that 

tr[HLAc] T = "I'l 0 

(A.13) can be simplified to get 

= [B; 0 

(A. 13) 

(A. 14) 

(A. 15) 

Also from the definition of we have 
92 

- tr[q~] = - a tr{ a 

aG2 3% L 

-1 

=- a tr{ 

aG2 O1 

C;G;F~G~C~ o I 

-2 

= 2F2G2[C2 OIL (A. 16) 

Combining (A.15) and (A.16), the condition (A.lO) can be written in the 

expanded form as 

as', L -- - 2{F2G2[C2 OIL 

aG2 

+ [Bl 0 }=O (A. 17) 

In j2, the terms containing G are 5 and A . Therefore as before d C 

aT2 

-=- a {tr[qL] + 2tr[HLAT]} aGd aGd C (A. 18) 

Again noting that in A A and M are part of the optimal conc' 1 1 

troller 1 (u ), the only free gains Gd to be adjusted are those appearing in A and Caug. Then 

1 

aug 

The matrix on the right hand 

a =- 

aGd 

side of (A.19) can be written as 

(A.19) 

(A. 20) 
93 

which gives 

- a 

aGd 

(A.21) 

Further, similar to the procedure used to get (A.16), we have 

tr[qL] = 2F2dGd[Cd OIL (A.22) - a 

aGd 

Combining (A.21) and (A.22), (A.ll) can be written in the expanded form 

as I 0 + ' Bd ] THL } ( A. 2 3) 

M1 cu 

(A.81, (A.9), (A.17) and (A.23) together give the necessary conditions for the simultaneously optimality of the augmentation controller 

u2 and the display control law Ed. - 
94 

APPENDIX - B 

- THE OPTIMAL CONTROL -- PILOT MODEL 

The optimal control approach to human operator modeling was 

developed by Kleinman, Baron and Levison in the early 1970's. Since 

that time it has been used successfully to model manual pilot behaviour 

in a variety of complex tasks. A brief discussion of the actual model. 

is given here as it forms the basis for the synthesis and analysis of 

display augmentation designs presented in this report. More detailed 

discussion of the structure of the model can be found in [6] and [13]. 

The model is based on the assumption that a "well-motivated" human 

pilot adjusts his gains and compensation for the vehicle and task such 

that an objective function, J is minimized, subject to human limitations. Typically a piloting task, aircraft and display dynamics are 

represented in the block diagram shown in Figure (B.l) and by the time 

invariant differential equation 

P' 

- 

x(t) = z(t) + bu (t) + Di(t) 

P 

where the A matrix can be an agregation of task, plant and control system dynamics. The vehicle states are represented by the vector x(t) 

while u (t) is the pilot input (assumed to be scalar here for the purposes of explanation - multi-input tasks are easily accomodated within 

P 

the framework of the model) and w(t) is a "white" noise disturbance with 

intensity W. 

An output vector 7 (t) represents those variables which the pilot 

can observe, either through the cockpit display, out the windows or by 

P 

the "seat of his pants". His observations are given by the relation 
95 

t 

0 > I> 

--- 

1 

Q 

3 
- 

YP(t) = 

where T is a pure delay a 

96 

CX(t-T) + du (t-T) + V (t-T) 

P Y (B.2) 

sociated with the inherent d-lay in the 

pilot’s perception, and 

sity V. which models the imperfection in the pilot‘s observations. 

Y 

is a vector white noise process with intenY 

The pilot’s task is reflected in the minimization of a quadratic 

performance index of the form 

* lT 2 ‘2 Jp(p ) = E{lim r I ( C qix: + N + gu )dt} P P T+- 0 i=l 

subject to pilot observations y (a) for time u < t and with cost functional weightings q > 0, r > 0, and g > 0. 

P 

i 

Inclusion of the control rate, u in the cost function naturally 

leads to a first order lag in the pilot’s control law analogous to the 

neuromotor lag of the McRuer crossover pilot model [14]. The time conP’ 

stant of the lag, furthermore, may be adjusted through variation of the 

control-rate weighting constant, g. 

By defining a new state vector as 

the augmented system can be represented as (u (t) = pO(t)) P 

with 

Ab 

*o = [. .] ’ bo = r] ’ Do = F] 

The minimizing control law is 

with 
97 

A 

where T(t) is the current estimate of the state y(t), and KO is the 

unique positive definite solution of the Ricatti Equation 

ATK +KA +Q -- K b bTK = .O 

00 00 0 g 0000 

with Qo = diag(qi, r). Expanding the optimal control law as 

(B.7) 

where p (t) is the current estimate of the system state x,(t), and letting 

i 

by iterating the control-rate weighting, g, the equivalent lag time constant, T = - , can be adjusted to a desired value. The control law 

ln+l 

1 

can then be written as 

where 

* 

u (t) = -feat) 

with 

(B.lO) 

(B. 11) 

1 e = Tn[lls 12, In] 

From the human operator viewpoint, an exact control input is not 

possible. 

in the control equation, or 

This uncertainty is modeled by the addition of motor noise vm 

(B.12) 

where vm(t) is a Gaussian "white" noise source with intensity, V,. The 
98 

controller gains previously calculated are assumed to remain, the same in 

the presence of motor noise. This assumption reduces the human operator 

model to sub-optimal control behadour. 

The current state estimate is derived from the combination of a 

Kalman state estimator and a least mean square predictor. The system is 

rewritten as 

(B. 13) 

where 

A1 = 1 - '1' bl = rl] - 

n n 

c1 =[C I dl , Dl=l 2 

n 

The disturbance noise has the form <:(t) = [GT(t), v (t)] with covariT 

m 

ance matrix 

E{<l(t)<:(a)) = WIG(t-o) (B.14) 

- 

The Kalman filter generates an estimate, X(t) of the model states 

(B.15) 
99 

where the error covariance matrix, C is the solution of 1’ 

A~C~ + z,AT + D~~D~ - c c T v -1 clcl = o 

11 (B.16) 

The least mean squared predictor is governed by the equation 

- 

S(t) = Alr(t) + blp(t) (B.17) 

Finally, the current state estimate is found by combining the Kalman 

state estimate and the predicted state through the relation 

- - *IT 2. - 

dt) = Ut) + e [x(t--T) - S(t-~)l (B.18) 

In order to apply the optimal control model, it is necessary to 

know the various human response parameters T,T ,V ,V introduced above. 

Published data in manual control [14] indicates that typical values for 

the effective time delay are ~=0.15-0.25 secs. The neuromotor lag time 

nym 

constant T is of the order of T =0.1-0.6 secs with T -0.1 being typical 

[23]. It should be noted that results reported in [14] indicate that T 

varies inversely with forcing function bandwidth. 

n n nn 

Investigation of the properties of human controller remnant [24] 

have shown that the sources of remnant can be modeled on the basis of 

constant noise to signal ratios. Thus the observation noise associated 

with the ith observed variable yi has an intensity 

= Pyi EIYiI (B. 19) 

where the constant p is based on the human controller’s attention 

Yi 

being limited to the ith observation only. Similarly, the motor-noise 

v,(t) is modeled to have an intensity given by 

(B.20) 2 v m = Pu EIupI 

The constants p and p are referred to as observation noise ratio and Yi U 
100 

motor-noise ratio respectively, and are generally specified in terms of 

their decibel values. Model matching analyses have shown values of 

P =0.01n (-20 dB) and pu=0.003a (-25 dB) to provide a good fit with 

experimental data for manual control tasks involving single-axis trackYi 

ing. These ratios have much higher values for complex multi-control 

tasks. Since the noise intensities are specified as ratios of the closed 

loop intensities of the corresponding signals, an iterative process is 

necessary to determine the optimal control model for which the relations 

(B.19) and (B.20) are satisfied. 

Studies of human perception abilities have shown that if a quantity 

y. is displayed explicitly to the human operator, he can extract the 

1 

rate of change of that quantity, y Thus the rates of the displayed 

quantities should be included in the pilot's observation vector 7 . 

Furthermore, if the human controller has more than one explicitly 

i' 

P 

displayed observation available to him, his attention is divided between 

the various displays. The error induced due to this division of attention is modeled by modifying the observation noise corresponding to the 

ith displayed variable as 

(B.21) 

where (Vo) 

total attention allocated to the ith observed variable and has limiting 

is as given by Eqn. (B.19). Here f is the fraction of Y ii i 

values at no attention (f =0) and full attention (f -1) [15]. The values 

of f are generally determined on the basis of the importance of that 

particular observation in successfully accomplishing the task as modeled 

i i 

i 

by (B.3). 
101 

If a particular signal y is very small in magnitude, the human i 

controller may not be able to detect its non-zero value (visual threshold) or may choose not to react to the small perturbations (indifference thresholds). This aspect of the human controller is modeled by 

modifying the observation noise intensity corresponding to the i th 

displayed variable as 

(B.22) 

2 where a = E(y } and N is the describing function of a dead-zone element [6]. (V ) is as obtained from (B.21) and a is the value of the 

threshold for the ith observation. Pyscophysical studies have shown that 

Yi i I 

Y ii i 

these thresholds typically correspond to values of 0.05 deg and 0.15 

deglsec at the pilot's eye. Also, a reasonable value for these thresholds is the minimum resolution marking on the display. 

Finally, combining (B.191, (B.211, and (B.221, the intensity of the 

obsevation noise v to be used in (B.2) to model the imperfections in 

the pilot's observations, is obtained to be 

Yi 

with all the relevant quantities defined as above. 

(B.23) 
102 

APPENDIX - C 

ANALYSIS RESULTS FOR K/s 2 PLANT -- 
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-- DATA AND ANALYSIS RESULTS FOR F-15 AIRCRAFT --- 
TABLE D.1: TRIM CONTIIONS FOR F-15 MODEL 

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1. Report No. 

NASA CR- 4058 

National Aeronautics and Space Administration 

Washington, DC 20546 

2. Government Accession No. 3. Recipient's Catalog No. 

14. Sponsoring Agency Code 

4. Title and Subtitle 

Optimal Cooperative Control Synthesis 

of Active Displays 

7. Author(sJ 

4 

Sanjay Gary and David K. Schmidt J 

9. Performing Organization Name and Address 

School of Aeronautics and Astronautics 

Purdue University 

West Lafayette, IN 47907 

2. Sponsoring Agency Name and Address 

I 

5. Supplementary Notes 

NASA Technical Monitor: Eugene L. Duke, Ames Research Center, 

Dryden Flight Research Facility, Edwards, California 93523-5000. 

5. Report Date 

6. Performing Organization Code 

June 1987 

8. Performing Organization Report No. 

H-1378 

10. Work Unit No. 

RTOP 505-66-1 1 

11. Contract or Grant No. 

NAG2- 2 28 

13. Type of Report and Period Covered 

Contractor Report-Final 

6. Abstract 

7. Key Words (Suggested by Author(sJ) 

Aircraft control 

Control law synthesis 

Control systems 

Handling qualities 

A technique is developed that is intended to provide a systematic 

approach to synthesizing display augmentation for optimal manual cont r o l i n complex, closed-loop tasks. A cooperative control synthesis 

technique, previously developed to design pilot-optimal control augmentation for the plant, is extended to incorporate the simultaneous 

design of performance enhancing displays. The technique utilizes an 

optimal control model of the man-in-the-loop. It is applied to the 

design of a quickening control law for a display and a simple K/s2 

plant, and then to an F-15-type aircraft in a multichannel task. 

Utilizing the closed-loop modeling and analysis procedures, the 

results from the display design algorithm are evaluated and an analytical validation is performed. Experimental validation is recommended for future efforts. 

18. Distribution Statement 

Unclassified - Unlimited 

Subject category 63 

19. Security Classif. (of this report) 

unclassified 

20. Security Classif. 21. No. of Pages 22. Rice' (of this page1 

Unclassified 156 A08