. 

PURDUE UNIVERSITY I ~ ~~~ SCHOOL OF AERONAUTICS AND ASTRONAUTICS 

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(hASA-CE-160k56) BIALXSIS CE bLB 

CCNPIGUBA?ICNS &SING GCB PGB €IIFC!I llODELIIIG 

lateria Status €&Fort (Purdue Uaiv,) 108 p cscz 01c 

63/08 

N87-2C289 I 

Unclas 

45360 

b 

West Lufuyetfe, Indiana 47907 
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ILIEMO: Infomial 

Subject: Analysis of NLR Configurations Using OCM for Pilot Modeling 

From: M.H. Dcijeske 

To: D.K. Schmidt 

INTRODUCTION 

The purpose of this memo is to present a summary of the results obtained from an analytic handling qualities analysis of the rate-commandattitude-hold aircraft configurations 

originally presented in an NLR report by Mooij[’]. Pilodvehicle performance is 

evaluated using an optimal control technique for pilot modeling. Numerical and graphical results for a closed-loop frequency-domain analysis are presented and discussed and 

comparisons with experimental results are made. Finally, the results from this study are 

compared with those from another study that dealt with similar configurationsi2]. 

NLR CONFIGURATIONS 

The aircraft configurations studied by Mooij were variations of a medium-weight, twinengine jet transport (a modified Foker F28W6000) with a rate-commandattitude-hold 

control system for both pitch and roll. Two aircraft and a total of 12 configurations were 

studied. The theta-to-stick and gamma-to-stick transfer functions for the 12 

configurations are presented in Appendix I. As shown in Table 1, the 12 configurations 

constitute three groups: E,F and G. Further details concerning the aircraft configurations 

and control system implementation are contained in Chapter 7 of [ 13. 

Pa ra-,e t e r 

varied rat ion n 

Conf i ruI 

1 

1 

short- E- 1 

period E- 2 

frequency E- 3 4.71 

E-4 

E-5:’ 

n unie ra tor E-5:. 

4.71 t ime F- 3 

constant F- 2 

F- 1 

Ran oe uv r e G- 1 

enhancement G- 2 

1 

1 

3.41 

G- 3 

G-4 

I --1 Equivalent transfer 

function parameters 

Table 1 

NLR Configuration 

Sets 
-2- 

CRITICAL TASK MODELING 

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Two separate tasks were modeled in this analysis: (1) The precise control of attitude (i.e., 

attitude tracking) and (2) The precise control of flight path (i.e., flight-path tracking). The 

modeling of the attitude and flight-path tracking tasks are discussed in detail in [3] and 

[4] respectively. The multi-loop nature of the flight-path tracking task is reflected by the 

block diagram in Fig.1. The describing functions Pu,,Pu and P, in Fig.1 are estimated via 

the OCM. Using block diagram manipulation, one may reduce Fig.1 to Fig.2 and obtain 

the equivalent single-loop pilot describing function, Peq. 

Figure 1 : Flight-Path Tracking Task 

Figure 2 : Equivalent Flight-Path Tracking Task 
-3- 

Similarly, the nature of the precision attitude tracking task is reflected by the block 

diagram in Fig.3. In this case, Pee and Po may be combined in order to find a single-loop 

equivalent pilot function as shown in Fig.4. The equations for the above manipulations I are presented in Appendix II. 

Figure 3 : Attitude Tracking Task 

Figure 4 : Equivalent Attitude Tracking Task 

PILOT MODELING USING AN OCM 

The pilot-related parameters used in the OCM for the flight-path and the attitude tracking 

tasks are presented in Tables 2 and 4 respectively. The values selected for z,the pilot’s 

observation delay, and TN, the pilot’s neuromuscular lag time constant, were chosen to 

represent the human operator in his most aggressive mode. This is done in order to 

expose handling qualities digs in the various configurations by modeling the pilot’s most 

aggressive control techniquesi4]. The rationale behind the selection of the other parameters is discussed in [3] and [4]. Sample input files for the local implementation of the 

OCM code (PIREP) are presented in Appendix m. 

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-4- 

RESULTS 

Presented in Appendix V are the graphical results of the frequency domain analysis of 

the flight-path and attitude tracking tasks. Included are representations of the pilot functions Pye,Pee,Py and Po as well as the equivalent single-loop pilot function P,. Open-loop 

and closed-loop Bode plots for all 12 configurations are also presented. Quantities such 

as crossover frequency, therefore, can be determined directly from these plots. 

A number of key quantities (ref. fig.2 and 4) for both the flight-path and attitude tracking 

tasks are summarized in tables 3 and 5 respectively. The following definitions are used: 

5NS 

TOTAL 

COST 

crossover frequency - the frequency at which the magnitude of the openloop pilot/vehicle system equals 0 dE3 

phase angle of the equivalent pilot function P, at the crossover frequency 

phase angle of PW at lower frequencies 

bandwidth - the frequency at which the closed-loop pilothehicle response 

has phase = -90 deg 

pilot phase compensation for the attitude tracking task adjusted to be comparable to a quantity discussed by Neal-Smith 

5NS = $Peg I Bw + 57.3 z Bw + tan-'(TN Bw) 

maximum magnitude of the closed-loop pilotjvehicle response for the attitude tracking task 

predicted rms gamma error 

predicted rms theta error 

predicted rms stick rate 

value of OCM objective function 
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Parameter 

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Value 

Config. 

~~ 

Observation Vector 

Objective Function 

Weights 

Observation Thresholds 

E- 1 

E-2 

E-3 

E-4 

E-5 

F-3 

F-2 

F- 1 

G- 1 

e-2 

G-3 

G-4 

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7; = [ye ie 9 y 9 i 9 e 9 61 

qi = 1 9 0 0 0 9 0 01 

rF, = 0 , gi, to yield TN 

TYe , Tu, To = 0.05 deg 

Tie, Ti, Tb = 0.18 deglsec 

-5- 

Observation Noise 

Ratio 

T;lble 2 : Pilot Model Parameters 

-20 dB All 

Observed Variables 

Command Signal 

(n=white noise) 

0Jn = .25/(s2 + .5s + .25) 

yc/ec = S/(s + .5) 

Fractional 

Attention 

fi = 0.3333 All 

Observed Variables 

Observation Delay z=O.2 sec 

Neuromuscular Lag zNz0.2 sec 

Motor Noise Variance 

Control Input I F, (Stick Force in lbs.) 

Table 3 : Performance Measures for Flight-Path Tracking Task 

8.00/ - 

5.17/5.67 

4.00/ - 

3.00/ - 

2.33/3.67 

3.33/ - 

4.331 - 

6.3 3f7.67 

5.67/6.00 

4.171 - 

4.00/5.3 3 

3.001 - 

0, 

(radsec) 

1.800 

1.819 

1.858 

1.892 

1.922 

1.967 

1.97 1 

2.077 

1.935 

2.342 

2.348 

2.344 

57.19 

55.63 

53.31 

46.66 

40.09 

, 36.06 

36.12 

23.69 

38.09 

-53.24 

-59.7 1 

-6 1.07 

61.20 

58.43 

55.16 

54.07 

53.72 

50.07 

50.02 

29.86 

52.88 

48.62 

45.53 

43.20 

.4843 

.4743 

.4562 

.4414 

.4287 

.4099 

.408 1 

.3740 

.3897 

.3410 

.3455 

.3502 

Total Cost 

21.77 

19.07 

15.18 

13.29 

12.17 

9.43 

5.7 1 

3.37 

15.17 

7.85 

5.02 

3.84 

.3544 

.3399 

.3140 

.2933 

.2764 

.2528 

.2506 

2094 

.2384 

.17 19 

.1707 

.1740 
-7 TV? 4’ 

Pxanie ter 

Observation Vector 

-6- 

Value 

7; = [e, 9 e,, 0 9 e1 

Table 4 : Pilot Model Parameters 

Objective Function 

Weights 

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Si=[ 1 ,O,O,O] 

rF, = 0 , gk, to yield 2, 

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Observation Thresholds Tee, TO = 0.05 deg 

Tie , Ti, = 0.18 deg/sec 

E-5 

F-3 I 

Observation Noise 

Ratio 

G- 1 

G-2 

-20 dB All 

Observed Variables 

Fractional 

Attention 

f; = 0.5 All 

Observed Variables 

Observation DeIay 

Neuromuscular Lag 

z=O.2 sec 

~Nz0.2 sec 

0% OF, Total Cost 

Motor Noise Variance I -25 dB 

(deg) 

1.186 

1.179 

1.163 

1.146 

1.132 

1.107 

1.076 

1.07 1 

1.143 

1.141 

1.139 

1.137 

Control Input F, (Stick Force in lbs.) 

(n=white noise) 

(lbs/sec) 

15.83 

13.85 

11.08 

9.68 

8.92 

7 .OO 

4.7 1 

2.42 

8.93 

8.86 

8.80 

8.73 

Table 5 : Performance Measures for Attitude Tracking Task 

IF E-2 

1.737 

1.747 

1.774 

1.804 

1.829 

1.872 

1.928 

1.939 

1.810 

1.814 

1.817 

1.821 

26.21 69.04 4.155 

24.86 68.22 4.188 

21.13 66.05 4.265 

16.29 62.99 4.320 

11.54 59.82 4.354 

6.03 55.98 4.39 1 

0.64 52.79 4.480 

-4.30 48.90 4.465 

12.63 60.40 4.335 

12.18 59.99 4.335 

11.57 59.54 4.335 

11.09 59.15 4.335 

1.832 

1.806 

1.751 

1.697 

1.654 

1.578 

1.488 

1.478 

1.687 

1.681 

1.674 

1.668 
- 7- 

DISCUSSION 

Using the data presented, one should be able to address the following questions: 

1. Are there correlations between model-based performance measures and experimental 

pilot ratings, and if so, are these correlations comparable to the results presented in [3] 

and [4]. 

2. Do the results of the attitude-tracking task offer any additional insight beyond that 

gained via the flight-path tracking task results. 

3. How do the results for the NLR configurations compare with the results for the TIFS 

configurations as presented in [2]. 

When analyzing the model-based performance memcs for the flight-path tracking task, a 

number of trends were expected. Anderson and Schmidti4] have shown previously that in 

the flared landing task, a strong correlation exists between pilot rating and achievable 

bandwidth (or crossover frequency), required pilot phase compensation, rms gamma 

error, and total cost. Comparing these quantities for the E configuration set in Figs.5-8, 

we note that there is strong correlation between experimental and model-based performance memcs within this subset of the configurations. 

Pilot workload (and thereby pilot rating) has been shown to correlate with the pilot phase 

compensation required. Pilot phase compensation here refers to the phase angle of the 

equivalent single-loop pilot function, P,,, at crossover. In Fig.6 we see that there is a 

consistent trend for configurations E-1 to E-5. Configuration E-5 has the best pilot rating 

(CH 2.33) and the lowest pilot phase required (40 deg). Likewise, configuration E-1 has 

the worst pilot rating (CH 8.0) and the highest pilot phase required (57 deg). 

A model-based measure of pilothehicle performance is the rms gamma-error computed 

by the OCM. Fig.7 shows the correlation between pilot rating and rms gamma-error for 

the E configuration set. In addition, total cost is a model-based measure that has correlated with pilot rating in previous studies[51. Fig.8 shows the correlation between total 

cost and pilot rating for the E configuration set. 
-8- 

8- 

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0 - 6- 

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e 

e 4- 

n 

- 0 - 

2- 

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Crossover Frequency vs. Pilot Rating 

(E conf~gurotions) 

0 E-1 

0 

0 

0 

0 E-5 

0 

1.7 1.8 1.9 2.0 

crossover frequency (rad/sec) 

Figure 5 

Fiiot Phase Comp. vs. Pilot Rating 

(E configurations) 

10 

i E-5 0 

21 

E-1 0 

0 

0 

0 

o! I # 

30 40 50 60 

pilot phose comp. (deg) 

Figure 6 

70 
RMS Gamma Error vs. Pilot Rating 

0- 

n 

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6- 

0) 

- C 

c 

e 

c 4- 

n 

0 - 

2- 

1 

(E configurations) 

n 

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V - 6- 

0, 

- K 

c 

e 

c 4- 

n 

0 - 

2- 

E-5 0 

0 

0 

E- 1 

0 

0 

o! 1 I I I I 

0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.40 0.49 0.50 

rms gamma error (dag ) 

Figure 7 

Total Cost vs. Pilot Rating 

(E configurotlons) 

10 

8 €-1 0 

0 

E-5 G 

0 

0 

0 

0.20 

1 

0.22 0.24 0.26 0.28 0.3Q 0.32 0.34 0.36 0.38 0.40 

total cost from OCM 

Figure 8 
- 10- 

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While the model-based measures for the E configuration set correlated well with experimental pilot rating, such is not the case across all of the configuration sets. It would be 

exceptional if we could find a single model-based performance metric that always correlated with pilot rating in a predictable manner. However in this case, because of the lack 

of consistent correlations over all configurations studied, we need to take a closer look at 

the configuration dynamics in the attempt to explain the subjective pilot ratings. 

Bode Analysis 

In the attempt to explain the experimental pilot ratings for configuration sets F and G, the 

vehicle-alone dynamics (namely y/F, and €IF,) for configuration sets E,F and G are now 

considered. Vehicle transfer functions are derived and presented in Appendix I. Bode 

plots for y/F, and 8/F, are presented in Figs.9-14. 

For good closed-loop stability margins in a tracking system, the desired shape of the 

open-loop frequency response in the crossover region is well known (i.e. constant slope 

of -20 dB/decade and constant -90 deg phase). Assume that the critical task for a pilot in 

the approach and flared landing task is the precise control of flight-path angle (or sink 

rate). If this is indeed the case, we would expect to find the configurations that have a y/F, 

frequency response more like K/s in the region of crossover to also be rated better by the 

pilots. Note that crossover frequency for all configurations studied is below 2 rad/sec. 

From Figs.l0,12 and 14 we find that the y/F, frequency responses that appear more Klslike in the critical frequency range (0.5-2.0 radsec) invariably correspond to the better 

rated configurations. More specifically, those configurations with (y/F,)-phase tending to 

be more uniformly equal to -90 deg in the critical frequency range also tend to be rated 

better. 

Comparison of NLR and TIFS Analyses 

A pilothehicle analysis of pitch-rate command aircraft configurations in an approach and 

landing task was also conducted by Wendelf2]. In Wendel’s analysis, 26 configurations, 

originally studied using Calspan’s Total Inflight Simulator (TIFS) were evaluated using 

the OCM for pilot modeling. Of those 26 configurations, six had dynamics free of any 

added dynamics due to pre-filters,etc. A quick comparison of results from the two analyses is made here in an attempt to find some sort of consistency between studies. 
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Config. 

1- 1 

1-2 

1-3 

2- 1 

2-2 

7- 1 

- 11 - 

Pilot 

Rating 

6.00 

6.83 

5.33 

6.50 

3.75 

2.75 

The 5 pitch-rate comnmnd configurations from Wendel's TIFS study having dynamics 

comparable to the NLR configurations discussed are presented in Table 6. Configuration 

7-1 is also included in this comparison for it represents an aircraft with conventional 

dynamics. The 8/F, and y/F, transfer functions for the 6 configurations presented in 

Table 6 are presented in Appendix N. Model-based metrics for the flight-path tracking 

task are summarized in Table 7. Configuration 7-1, which has the best pilot rating out of 

the 6, has a very small value for required pilot phase compensation (PqIo, = 7 deg). 

Configuration 7-1 also has the largest crossover frequency (0, = 1.90 radsec). Presented 

in Fig.16 are the frequency responses for y/F, for configurations 1-1,2-1 and 7-1. Note 

that the shape of the Bode plots for configurations 1-1 and 2-1 in the region of crossover 

are very similar, as are their respective pilot ratings (CH=6). Configuration 7-1, looking 

much more like K/s in the region of crossover (0.5-2.0 radsec), ems a much better pilot 

rating (CH=2.75)! 

Table 6 : TIFS Configuration Sets 

0, 

(radsec) 

1.65 

1.85 

1.80 

1.65 

1.65 

1.90 

Config. 

1-1 2.79 0.8 0.38 

1-2 2.76 0.8 0.72 

1-3 2.73 0.8 1 .oo 

2- 1 1.78 0.6 0.38 

2-2 1.75 0.6 0.72 

7- 1 2.84 0.8 0.72 

SPeq ' 0, Bw 

(deg) (radsec) 

39.2 1.86 

24.0 1.96 

16.2 1.96 

60.0 1.79 

43.8 1.82 

7.0 2.06 

0.93 - - 

- 0.16 0.01 

Table 7 : Performance Measures for Flight-Path Tracking Task for Comparable TIFS Configurations 
- 12- 

-270. - 

-360. 

NLR Vehicle Frequency Responses 

60. I 

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40. 

20. 

0. 

-20. 

-40. 

-60. 

0. 

- 

- 

- 

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- thrta/rtlok : E-1 

- - - thota/rtick : E-3 . . . . . . . thrto/rtick : E--3 

1 

e, 

0, -180. 

C 

0 

- 

-270. 

0) 

v) 

0 -360. 

I 

0. .01 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 9 

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Q, 

73 

3 

C 

P 

+J .- 

; 

P 

0) 

73 

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e, 

tn 

C 

0 

0) 

v) 

0 

L 

0. 

- 

NLR Vehicle Frequency Responses 

40. 

20. 

0. 

-20. 

-40. 

-60. 
- 13- 

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a, 

U 

3 

C 

0 

+J .- 

E 

P 

a, 

U 

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a, 

P 

C 

U 

a, 

u) 

U 

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- 

n 

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7J 

a, 

U 

3 

c 

0 

13 

.cI .- 

E 

P 

a, 

73 

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a, 

P 

f 

U 

a, 

u) 

U 

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- 

n 

NLR Vehicle Frequency Responses 

60. 

20. 40‘ h.... 

-40. 

-=O- 1 

y,.. ............... 

. ‘1. 

. ’.

-60. I I I I 

-theto/dlok : F--3 

- - - thota/otlok : F-2 ....... thota/stlck : F-1 

0. 

............ 

-90. 

-180. 

-270. 

-360. 

.o 1 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 11 . 

NLR Vehicle Frequency Responses 

40. 

-gamma/rtlck : F-3 

--- gamma/dlck : F-2 

....... gamma/rtick : F-1 

0. 1 

-270. 

-360. 

.01 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 12 
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- 14- 

NLR Vehicle Frequency Responses 

60 I 

40. 

20. 

0. 

-20. 

-40. 

-60. 

0. 

- theto/mtlck : ' 0-1 

--- thrto/atick : C-2 

, . , . . . . . theta/8tick : 0-3 

, -90. 

-180. 

-270. 

-360. 

60, 

40. 

20. 

0. 

-20. 

-40. 

-60. 

0. 

-90. 

-1 80. 

-270. 

-360. 

.01 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 13 

NLR Vehicle Frequency Responses 

- gornma/mtick 

I I 

: G-1 

1 -1 

--- gammo/mtlck : C-2 . . . . . . , gornmo/stick : C-3 

1 

.Ol 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 14 
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0) 

U 

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c 

P 

0 

& .- 

E 

P 

al 

U 

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al 

P 

C 

0 

a, 

v) 

0 

L 

- 

a 

TlFs Vehicle Frequency Responses 

- theta/.tlok : 1-1 

- - - thota/mtlck : 2-1 

....... thota/atlck : 7-1 

90. , 1 ........ ............. 0. 4 ....... 

I I 

-270. I 1 I 

.01 0.1 1 .o 10. 100. 

frequency - rad/sec 

Figure 15 

TlFs Vehicle Frequency Responses 

20. , 

0. 

-20. 

-40. 

-60. 

-80. -I 

- gammo/mtlck : 1-1 

--- gamma/mtick : 2-1 

....... gamma/atlck : 7-1 

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

-90. - 

-180. - \ 

-270. SI 

.01 0.1 1 .o 7 0; 100. 

frequency - rad/sec 

Figure 16 
- 16- 

Attitude Tracking Analysis 

Up to this point, very little has been said about the analysis of the attitude tracking task. 

Certainly for an aircraft to have acceptable performance in an outer-loop such as flightpath (refer to Fig.l), it must first have good inner-loop, attitude dynamics. This is the 

reason for conducting an attitude tracking analysis - to insure that the configuration under 

study has good attitude dynamics before beginning the flight-path analysis. Another reason for conducting an OCM analysis of the attitude tracking task might be that attitude 

tracking has been argued by some to be the critical task. 

Yet, as stated earlier, it is hypothesized that the critical task for approach and landing is 

the precise control of flight-path angle. If this hypotheses is true, one should expect to 

find correlation between experimental pilot ratings and model-based memcs from the 

flight-path tracking analysis. Having shown through this study that there is a strong 

correlation between the y/F, frequency response in the region of crossover and experimental pilot rating offers evidence that precise control of flight-path is indeed the critical 

task. For this reason, it is more sensible to draw conclusions based upon the results from 

the flight-path analysis and not the attitude analysis. 

CONCLUSION 

This informal memo was written in order to summarize the results of an analytic han- 

&ng qualities analysis of the rate-command, attitude-hold aircraft configurations originally presented in an NLR report by Mooij. While the discussion contained is rather limited in scope, there were a few key ideas that were brought forward: 

1. Model-based performance metrics, such as required pilot phase compensation, appear 

to correlate well with experimentally obtained pilot ratings within a configuration class, 

but not necessarily over all classes. This was true for both the TIFS database as well as 

for the NLR study. 

2. Vehicle configurations that exhibit Ws behavior in the flight-path response, especially 

in the frequency range 0.5-2.0 rad/sec, elicit better pilot ratings in the landing task. 

3. For the approach and landing task, the OCM analysis of the attitude tracking task, 

while a necessary step in the complete analysis procedure, does not seem to offer as 

much insight as the OCM analysis of of the flight-path tracking task. This offers evidence for the hypotheses that the critical tusk for a pilot in the approach and landing task 

is the precise control of flight-path. 
Mooij, H., " Criteria for tow-Speed Longitudinal Handling Qualities," 

National Luchten Rumtevamlaboratorium (NLR), Netherlands, 

December 1984. 

[31 

[41 

r51 

Wendel, T., " Closed-Loop Pilot1 Vehicle Analysis of Approach and Landing of Pitch Rate Command Aircraft," M.S. Thesis, Purdue University, 

December 1985. 

Bacon, B., Schmidt, D., '' An Optimal Coutrol Approach to PilotlVehicle 

Analysis and the Neal-Smith Criteria," Journal of Guidance and Control, 

Vo1.6, Sept.-Oct. 1983, pp. 339-347. 

Anderson, M., Schmidt, D., " Closed-Loop PilotlVehicle Analysis of the 

Approach and Landing Task," Journal of Guidance and Control, Vol.10, 

Mar.-Apr. 1987, pp. 187-193. 

Hess, R., " Prediction of Pilot Opinion Rating Using an Optimal Pilot 

Model," Human Factors, Vol.19, Oct. 1977, pp. 459-475. 
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1.000 )5** 5 ( -0. 5780E-01) + J( 

11.39 )Saw 5 ( -1. 100 1 + J( 

20. 12 IS** 4 ( -10.00 + J( 

12. 17 IS** 3 ( -0. 3682 ) + J( 

3.555 IS*-* ( -9. 3682 1 + J( 

0. l&06 )S+* 1 ( 0. 1 + JC 

0. 1 

Gamrna/stick E-1 

0. 9667 IS** 4 ( -0. 166OE-011 + J( 

1.394 IS** 3 ( -0. 3920 1 + J( 

7. 564 IS** 2 ( -0. 5168 1 + 3( 

c-. 929 IS** 1 ( -0. 5168 1 + J( 

0. 4652E-01) 

0. 

0. 

0. 

0. 3600 

-0. 3600 

0. 

0. 

0. 

2. 670 

-2.670 

( 1.000 )S** 6 ( -0. 5780E-01) + J( 0. I 

( 11.39 IS** 5 ( -1.100 ) + J( 0. 1 

( 20.12 1399 4 ( -10.00 1 + J( 0. 1 

( 12. 17 IS** 3 ( -0. 3682 1 + J( 0.3600 1 

( 3.555 IS** 2 ( -0. 3582 1 + J( -0. 3600 

( 0. 1686 IS*+ 1 ( 0. 1 + J( 0. 1 

( 0. 1 

Configuratian E-2 

----------------------------------------------------------- i, 

Thota/stick E-2 

( 11.00 )S-+* 3 ( -0. 8310E-*S1) + J( 0. f 

( 13. 77 1s+* 2 ( -0. 3620 ) + J( 0. 1 

( 4. bo4 IS*+ 1 ( -0.7oco 1 + J( 0. 1 

( o. 2958 ) 

3 ( 0. 1 + J( 

5 ( -0. 6450E-01) + J( 

4 ( -I. cao 1 + J( 

3 ( -10.90 1 + J( c 7 ( -0. 4226 + J( 

1 ( -0. 4224 1 + J( 

0. 

0. 

0. 

0. 

0. 4203 

-0.4z03 

0. 

0. 

2.570 

-2. 670 

( 1. GOO )SSS i? ( 0. 1 + J( 0. 1 

( 11.99 IS** 5 ( -0. 645GE-01) + J( 0. 1 

( 21.23 13U-F 4 ( -1. 030 1 + J( 0. 1 

( 14. 37 )Si+++ 3 ( -10.00 1 + J( 0. ) 

( 4. ,577 Isle* 2 ( -G. 3220 1 + J( G. 42.03 ) 

( 0.2475 )S+U 1 ( -3. 9226 1 + J( -0. 3TO3 1 

( 9 ) 

____________--______--------------------------------------- 

9 ref'er ta last page of Appendix I far derivation 
I 

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I. 

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I 

1. 

1. 

14. 20 

19. 97 

7. 747 

0. 5140 

1.000 

12. 19 

23.31 

19. 94 

7. 719 

0. 4631 

0. 

1. 441 

2. 402 

11. 62 

6. 768 

0. 1092 

1.000 

12. 19 

23. Et1 

19.94 

7.719 

0. 4631 

0. 

Thetalstick E-3 

IS** 3 ( -0.8310E-01) + J( 0. 

IS** 2 ( -0. 6170 1 f J( 0. 

IS** 1 ( -0. 7060 1 + J( 0. 

1 

6 ( -0. 7240E-01) + J( 

5 ( -0. SEI70 1 + J( 

3 ( -0. 5651 + J( 

2 ( -0. 5651 ) + J( 

4 ( -10.00 1 + J( 

1 ( 0. 1 + J( 

Gammalstick E-3 

4 ( -0. 166OE-01) + J( 

3 ( -0.6170 1 + J( 

2 ( -0. 5168 1 + J( 

1 ( -0. 5168 1 + J( 

0. 

0. 

0. 

0. 5733 

-0.5733 

0. 

0. 

0. 

2. 670 

-2.670 

IS** 6 ( -0. 7240E-01) + J( 0. 

IS** 5 ( -0. 9870 + J( 0. 

IS** 4 ( -10.00 ) + J( 0. 

IS** 3 ( -0. 5651 1 + J( 0. 5733 

)SO* 2 ( -0. 5651 + J( -0. 5733 

IS** 1 ( 0. 1 + J( 0. 

1 

17. 00 

25. 91 

10. 36 

0. 7331 

1.000 

12.39 

26. 38 

25. 50 

10.82 

0. 6827 

0. 

1. 719 

3. 059 

14. 07 

3. 577 

0. 1551 

1.000 

12.39 

26. 38 

25. A0 

10.92 

0.6827 

0. 

Theta/stick E-4 

IS** 3 ( -0.9310E-01) + J( 

IS** 2 ( -0. 7060 ) + J( 

)S** 1 ( -0. 7350 ) + J( 

) 

IS** b ( 0. 1 + J( 

IS** 5 ( -0. 7560E-01) + J( 

IS** 4 ( -0. 9030 + J( 

IS** 3 ( -10.00 + J( 

)Sa* 2 ( -0. 7070 1 + J( 

)S** 1 ( -0. 7070 ) + J( 

1 

)S** 4 ( -0. 166OE-011 + J( 

IS** 3 ( -0. 7350 + J( 

IS** 2 ( -0. 5168 + J( 

IS** 1 ( -0. 5168 1 + J( 

) 

Garnmals t i c k E-4 

)S** 6 ( 0. 1 + J( 

IS+* 5 ( -0.7550E-01) + J( 

IS** 4 ( -0. 9030 1 + J( 

IS** 3 ( -10.00 + J( 

IS** 2 ( -0. 7070 1 + J( 

1s** 1 ( -0. 7070 ) + J( 

) 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 7072 

-0. 7072 

0. 

0. 

2. 670 

-2. 670 

0. 

0. 

0. 

0. 

0. 7072 

-0. 7072 
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1. 

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I 

Configuration E-5 -----------------------------^------------------------------- 

Thetalstic k E-5 

( 19. 20 )SO* 3 ( -0.8310E-011 + J( 0. 1 

( 31.85 )SO* 2 ( -0. 7060 1 + J( 0. 

( 14. 31 IS** 1 ( -0. 8700 + J( 0. 1 

( 0.9800 1 

1.000 

12.59 

28. 97 

31. 83 

14. 37 

0.9352 

0. 

1.951 

3.746 

16. 25 

12. 82 

0.2084 

Is** 6 ( -0. 7750E-01) + J( 

)SO* 5 ( -0. 5380 ) + J( 

IS%++ 4 ( -10.00 1 + J( 

)Si?* 3 ( -0. 8398 ) + J( 

IS** 2 ( -0. 8383 1 + J( 

IS** 1 ( 0. 1 + J( 

1 

IS+* 4 ( -0. 1660E-011 + J( 

IS** 3 ( -0. 8700 1 + J( 

IS** 2 ( -0. 5168 1 + J( 

IS** 1 ( -0. 5168 1 + J( 

Gammalstic k E-5 

0. 

0. 

0. 

0. 8581 

-0. 3581 

0. 

0. 

0. 

2. 670 

-2. 670 

( 1.000 IS** 6 ( -0.7750E-01) + J( 0. 1 

( 12.59 IS** 5 ( -0. 8380 1 + J( 0. 1 

( 28.97 IS** 4 ( -10.00 1 + J( 0. 1 

( 31.83 IS** 3 ( -0. 8388 1 + J( 0.8581 1 

( 14. 37 )SO* 2 ( -0. 8388 I + J( -0.a5ai 1 

( 0.9352 IS** 1 ( 0. + J( 0. 1 

( 0. 1 

Configuration F-3 

Theta/stick F-3 

( 26.90 IS** 3 ( -0.8310E-01) + J( 0. 

( 37.73 IS** 2 ( -0.6210 1 + J( 0. ) 

( 14.76 IS** 1 ( -0. 7060 1 + J( 0. 1 

( 0.9801 1 

1.000 

12. 59 

28.97 

31. 33 

14. 37 

0. 9352 

0. 

2. 730 

4. 562 

22.02 

12.90 

0. 2081 

)S** b ( 0. ) + J( 

IS** 5 ( -0.7750E-01) + J( 

)S** 4 ( -0.83~10 1 + J( 

)Sa* 3 ( -10.00 1 + J( 

IS** 2 ( -0. 8388 + J( 

IS** 1 ( -0. 8388 1 + J( 

1 

IS*+ 4 ( -0. 1660E-01) + J( 

IS** 3 ( -0. 6210 1 + J( 

IS** 2 ( -0. 5168 1 + J( 

)S** 1 ( -0. 5168 + J( 

1 

Gamma/stick F-3 

0. 

0. 

0. 

0. 

0. 8581 

-0. 8581 

0. 

0. 

2. 370 

-2. 670 

( 1.000 IS*+ 6 ( 0. 1 + J( 0. 1 

( 12.59 IS** 5 ( -0.7750E-011 + J( 0. 1 

( 28.97 )S** 4 ( -0. 8380 1 + J( 0. 1 

( 31.83 )S** 3 ( -10.00 I + J( 0. 1 

( 14.37 )Sa* 2 ( -0. 8398 + J( 0.3531 1 

( 0.9352 IS+* 1 ( -0. 8388 1 + J( -0.5591 1 

( 0. 1 
Configuration F-2 

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Thetalstick F-2 

( 44. a0 )S** 3 ( -0.8310E-01) + J( 0. 1 

( 52.02 IS** 2 ( -0. 3720 1 + J( 0. 1 

( 15. 78 IS** 1 ( -0. 7C60 1 + J( 0. 1 

( 0.9777 1 

1.000 

12.59 

31. 33 

14.37 

0. 9352 

28. 97 

0. 

4.547 

6. 467 

35.48 

13. 10 

0. 2077 

b ( -0. 7750E-011 + J( 0. 

5 ( -0. 8380 ) + J( 0. 

4 ( -10.c10 1 + JC 0. 

2 ( -0. €3583 1 + J( -0. 3531 

1 ( 0. 1 + J( 0. 

3 ( -0. a383 + J( o. 8581 

Gamma/ s t i c k F-2 

4 ( -0. 1660E-011 + J( 0. 

3 ( -0. 3720 1 + J( 0. 

2 ( -0. 5168 + J( 2.670 

1 ( -0. 5168 1 + J( -2.670 

1.000 

12. 59 

28.97 

31. 83 

14.37 

0. 9352 

0. 

9. 130 

11. 29 

69. 47 

13. 71 

0. 2085 

6 ( -0. 7750E-01) + J( 

5 -0. 8580 1 + J( 

3 ( -0. 8339 1 + J( 

1 ( 0. ) + J( 

4 ( -10.00 1 + J( 

2 ( -0. 8388 1 + J( 

Gamma/stick F-1 

4 ( -0. 16eOE-01) + J( 

3 ( -0. 1860 1 + J( 

c 7 ( -0. 5168 + J( 

1 ( -0. 5168 1 + J( 

0. 

0. 

0. 

0. 85al 

0. 

-0.8581 

0. 

0. 

2. 670 

-2. 670 
I 

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I. 

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I. 

1. 

18. 50 

26. 36 

9. 923 

0. 6986 

1.000 

12. 31 

25. 53 

26.22 

9. 835 

0. 6527 

0. 

1. 880 

3. 031 

11.43 

a. 559 

-0. 126lE1.000 

12. 31 

25. 59 

26.22 

0. 6527 

9. a35 

0. 

Thetalstick G-1 

)S** 3 ( -0. 9100E-011 + J( 0. 

)S** 2 ( -0. 4940 ) + J( 0. 

IS** 1 ( -0. 8100 1 + J( 0. 

) 

Is** 6 ( -0. 8350E-01) + J( 0. 

IS** 5 ( -0. 5520 1 + J( 0. 

)S*% 4 ( -10.GO 1 + J( 0. 

IS** 3 ( -0. 8354 1 + J( 0.3475 

IS** 2 ( -0. 8354 1 + J( -0. 8475 

IS** 1 ( 0. 1 + J( 0. 

Gamma/stick G-1 

)S** 4 ( 0. 1470E-02) + J( 0. 

IS** 3 ( -0. 8400 1 + J( 0. 

IS*+ 2 ( -0. 3868 1 + J( 2.295 

IS** 1 ( -0. 3868 1 + J( -2. 293 

a1 1 

IS** 6 ( -0. 8350E-01) + J( 0. 

IS** 5 ( -0.5520 1 + J( 0. 

IS** 4 ( -10.00 1 + J( 0. 

IS+* 3 ( -0. 8354 1 + J( 0.8475 

)S** 2 ( -0. 8354 I + J( -0.8475 

IS+* 1 ( 0. 1 + J( 0. 

1 
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1 

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I. 

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I 

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I 

Configuration 6-2 

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

Theta/stick 6-2 

( 18. 80 )S+* 4 ( -0. 9110E-01) + J( 0. 

( 30.06 IS** 3 ( -0. 1980 1 + J( 0. ) 

( 15.21 1599 2 ( -0. 5250 1 + J( 0. 

( 2. 684 IS** 1 ( -0. 7350 1 + J( 0. 

( 0. 1398 1 

( 1.000 

( 12. 51 

( 29.05 

( 31.33 

( 15. 08 

( 2. 620 

( 0. 1305 

( 0. 

IS** 7 ( -0.8350E-01) + J( 0. ) 

)S** h ( -0.2000 1 + J( 0. 1 

)Sa+ 5 ( -0.5520 1 + J( 0. ) 

IS** 4 ( -10.00 1 + J( 0. 1 

)S** 3 ( -0.5354 1 + J( 0.8475 1 

IS++* 2 ( -0.8354 1 + J( -0.8475 1 

)S** 1 ( 0. 1 + J( 0. 1 

Gamma/stick 6-2 

( 4. 332 IS** 5 ( 0. 1470E-02) + J( 0. 1 

( 7.681 IS** 4 ( -0. 2190 1 + J( 0. 1 

( 15. 82 )S** 3 ( -0. 6580 + J( 0. I 

( 10. 88 IS** 2 ( -0. 4488 1 + J( 1. 589 1 

( 1. 684 )S** 1 ( -0. 4488 + J( -1.589 1 

( -0. 2499E-02) 

( 1.000 IS** 7 ( -0.8350E-01) + J( 0. 1 

( 12. 51 IS** 6 ( -0. 2000 1 + J( 0. 1 

( 28.05 IS+* 5 ( -0. 5520 + J( 0. 

( 31.33 IS** 4 ( -10.00 1 + 3( 0. 

( 1s. 08 IS** 3 ( -0. 8354 I + J( 0.8475 I 

( 2. 620 IS** 2 ( -0. 8354 + J( -0.8475 ) 

( 0. 1305 >sa* 1 ( 0. 1 + J( 0. I 

( 0. 1 

----------------------------------------------------------- 

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I. 

I. 

19. 10 

30. 01 

15. 22 

2.699 

0. 1421 

1.000 

12. 51 

28. 05 

31. 33 

15.08 

2. 620 

0. 1305 

0. 

7. 098 

12. 48 

20.26 

11.00 

1. 666 

-0. 2473E1. GOO 

12. 51 

28.05 

31.33 

15. 08 

2.620 

0. 13C5 

0. 

Thetalstick 6-3 

IS** 4 ( -0. 9310E-01) + J( 0. 

)S** 3 ( -0. 1960 + J( 0. 

IS** 2 ( -0. 5860 1 + J( 0. 

IS** 1 ( -0. 6960 + J( 0. 

IS++* 7 ( -0.835OE-01) + J( 0. 

IS** b ( -0.2000 + L'( 0. 

)SO* 5 ( -0. 5520 1 + J( 0. 

IS** 4 ( -10.00 + J( 0. 

IS** 3 ( -0.9354 1 + J( 0.8475 

IS** 2 ( -0. 8354 1 + J( -0.3475 

IS** 1 ( 0. 1 + J( 0. 

I 

Gammalstick 6-3 

)S*W 5 ( 0. 1470E-02) + J( 0. 

IS** 4 ( -0. 2590 + J( 0. 

IS** 3 ( -0.4600 ' + J( 0. 

)S*u 2 ( -0. 5203 1 + J( 1.311 

IS** 1 ( -0. 5203 + J( -1.311 

02 1 

IS** 7 ( -0. 8350E-01) + J( 0. 

IS** 6 ( -0.c7000 + J( 0. 

IS** 5 ( -0. 5520 1 + J( 0. 

IS** 4 ( -10.00 1 + J( 0. 

IS** 3 ( -0. 8554 1 + J( 0.8475 

IS** 2 ( -0. a354 ) + J( -0. 8475 

IS** 1 ( 0. 1 + J( 0. 

I 

e 
Configuration G-4 ........................................................... Theta/stick 6-4 

( 19. 40 )S** 4 ( -0.9140E-01) + J( 0. 1 

( 29.98 )Sa* 3 ( -0. 1940 1 + J( 0. 

( 15. 19 IS** 2 ( -0. 6300 + J( 0. 9420E-01) 

( 2. 680 IS*+ 1 ( -0. 6300 + J( -0. 942OE-01) 

( 0. 1396 1 

I 

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I. 

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I 

I 

( 1.000 

( 12. 51 

( 2’3.05 

( 31. 33 

( 15. 08 

( 2. 620 

( 0. 1305 

( 0. 

)Sa* 7 ( -0. 8350E-01) + J( 0. 

)SE* b < -o.,?oco 1 + J( 0. 1 

IS** 5 ( -G. 5520 1 + J( 0. 

)S** 4 ( -10.00 1 + J( 0. 1 

IS** 3 ( -0.8354 1 + J( 0.8475 1 

IS** 2 C -0. 8354 + J( -0.8475 1 

)S*U 1 ( 0. ) + J( 0. 1 

1 

Gamma/stic k 6-4 

( 9.578 IS*+ 5 ( 0. 147OE-02) + J( 0. 1 

( 16. 89 IS** 4 ( -0. 3072 1 + J( 0.9310E-01) 

( 24.43 IS** 3 ( -0.3072 + J( -0. 9310E-01) 

( 11.35 )SU+ 2 ( -0.5755 1 + J( 1. P88 1 

( 1. 703 IS** 1 ( -0.5755 1 + J( .-1. 188 1 

( -0. 2529E-02) 
I 

13. 

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I9 

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I ‘. 

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L 

1. 

I 
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1 

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1 

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1 

I I I I 

L b L 

I 

PP 

1 - I 

Pea 
I. 

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1. 

J 
APPEbIOI,( I I I 

- OCM Input File For Cdnfiq E-1 231nR1.3 Tracking Task I 

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I 

I 

t=. 21 

identu=2, I. . vu( 1 )=-25. I 

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I 

I 
OCM Input File for Config. E-1 Theta Tracking Task 8 

1 

I. 

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I 

I 

( 1. 000 IS** 5 c 0. ) + de 0. I 

( 4. 866 IS** 4 -0. 3320~-01) + J( 0. 1 

( 10.19 IS** 3 ( -0.434b + J( 0. 1 

( 4. 203 IS** 2 ( -2. 174 1 + Ji 1.757 1 

I 0.2925 )S** 1 ( -2. 174 1 + J( -1.757 1 

( 0. 1 
( 1.Oc)O IS** 5 ( 0. 1 + J( 0. 1 

( 5.452 IS** 4 ( -0. 3560e-011 + J( 0. 1 

( 12-67 IS+* 3 { -1. 190 1 + J( 0. 1 

( 3.302 IS** 2 ( -2. 113 1 + J( 1.72h 1 

( 0. 3154 IS** 1 ( -2. 113 1 + J( -1.726 1 

( 0. 1 

Gammalstic k 1-3 

4 0. 5230e-0115** 4 ( 0.2230~-02) + J( 0. 1 

t 0.2022 IS** 3 ( -2.000 1 + J( 0. 1 

( 1.075 IS** 2 ( -0.9343 1 + J( 3.5’92 1 

( 1.756 IS** 1 -0. 9343 1 + Ji -3. 432 1 

( -0. 392le-021 

I 1. coo )S** 5 0. 1 + 31 0. 1 

4 5.452 IS** 4 ( -0. 356Oe-011 + J( 0. 1 

( 12.67 IS** 3 ( -1. 190 1 + J( 0. 1 

( 3.302 IS** 2 ( -2. 113 1 + J( 1.725 1 

( 0. 3154 IS** 1 ( -2. 113 1 + J( -1.726 1 

( 0. 1 

( 1.060 IS** 5 0. 1 + J( 0. 1 

( 2.702 )SU* 4 ( -0. 7390e-01) + J( 0. 1 

( 4.415 )S** 3 ( -0.4997 1 + JI 0. 1 

( 1. 990 1399 2 ( -1.063 1 + J( 1.423 1 

( 0. 1156 IS** 1 -1. 064 1 + J( -1.423 1 

( 0. 1 

Gamma/stick 2-1 

( 0. 2435e-Ol)S*+ 4 .( 0. 1450~-02) + J( 0. 1 

( 0. 5770e-O11S** 3 ( -2.000 1 + J( 0. 1 

( 0.1932 IS** 2 -0. 1355 1 + J( 2. 599 1 

( 0.3301 IS** 1 ( -0. 1955 1 + J( -2. 598 1 

( -0. 479le-031 
( 1.009 IS++* 5 ( 0. I + J( 0. 1 

( 3.005 IS** 4 ( -0. 4830e-011 + J( 0. 1 

( 5. 036 IS** 3 ( -9. 921Q 1 + J( 0. 1 

( 3. oa5 IS** 2 ( -1.033 1 + J( 1.425 1 

( 0. 1375 IS** 1 ( -1.013 1 + J( -1.425 1 

I 0. 1 

Gammalstic k 2-2 

{ 0.2435e-01 IS** 3 ( -2. 000 1 + J( 0. 1 

( 0. 7639e-01)S++ 2 ( -0. 5686 1 + J[ 2.623 1 

( 0.2308 IS** 3 ( -0. 5686 + J( -2. 623 1 

< 0.3503 ) 

( 1.000 IS** 4 ( -0.4930e-01) + J( 0. 1 

( 3.005 )SO* 3 ( -0. 9310 1 f J( 0. 1 

t 5. 08& IS** 2 ( -1.033 I + J( 3.425 1 

( 3.085 IS** 1 -1. 033 1 + J( -1.425 1 

( 0.1375 1 

( 3. 000 IS** 4 I -9. 1610e-01) + 3( 0. lb33 1 

4. 630 IS** 3 ( -0. 363Oe-031 + 3( -a. 1633 1 

3.253 )S** 2 t -2.324 1 + J( 3.633 I 

( 0.3355 IS** 1 ( -2.324 1 + J( -1.&33 1 

( 0. 2177 1 

Gamma/stick 7-1 

< 0.4159e-91)S** 3 0. 4000e-021 + J( 0. 1 

( 0. 4673e-0115** 2 ( -0. 5644 1 + J( 3.935 1 

I 0.6580 IS** 1 < -0. 5544 1 + J( -3. 933 1 

( -0. 2533e-02) 

APPENCIX V 
NLR Cc.nfigur-ation E-1 : Gommo Trocking 

so. - 

40. - 

20. - 

0. - 

-20. {’ 

‘54 -- b 

.-.. ...- e.. 

. .-- . .. 

+ 

a 

+= .t ++ 

=* +++ + +++ ++a 

LEGEND: 

- pilot reeponae to gamma error 

+ pilot response to gamma 

pilot reapanse to theta 

270. - 

IBQ. A’ 

SO. - 

0. - 

-go. - 

-1 80. 

*t 

+ II 

II * 

+ Ir *** ;t ;&e I 

i 

* 

#- a*\ 

.. .. .* 

. .- 

1 I 1 

frequency - rod /sec 
N LR 

8 6. 

40. 

20- 

0. 

-2.. 

-40. 

Gonfigur-uticln E--2 : Gamma Tracking 

\ .-.e- .... ... 

.. 

LEGEND: . pilot reeponae to gommo error 

+ pilot reaponse to gamma 

Y pilot response to theto 

270. 

1ao. 

90. 

0. 

-90. 

+ tgjt 

i 

i 

I 

i 

mf 

I 

0 I -180. 

U 

I .1 1. 10. 100. 

frequency - rad/sec 
tdLR Configuration €--3 : Gornrna Tracklng 

_. .---.... \ 

.... . ... 

-20, ++ ++ + +++ 

-40- -3

-1 1, 10, 100, 

frequency - rad/sec 

LEGEND: 

- pilot reeponae to gamma error 

+ pilot reaponse to gomma 

r pilot ra~sponsa to theta 

270, 

1 ao, 

90. 

0. 

-!2 0, 

+ =+ 

I+ 

I+ 

m 

+ 

. .. =+ 

m+ 

-1 €30. I 

I I 1 

.1 1. 7 0. 100. I frequency - rod/sec 
Im 

270. - 

lao90. - 

0. - 

-QO. - 

-1 80. 

m 

-!t*& + 

m+ 

I+ 

.I+ 

.I + .. 

. ... a+ . .- 

1(+ 

m+ 

II+ 

rct 

*G 

I + 

I( 

+ 

I I 1 

.- 

C 

IF .- 

t 

IdLH Coniiyurotion E-4 : Gamma Trocking 

40. 

Bo- 1 

-20. + ++ + +++ + 

i+ 

.I++ 

-40, I I I 

-1 1. IO, 100, 

frequency - rad/sec 

LEGEND: 

- pilot reeponae to gomma error 

+ pilclt rsaponse to gamma 

i pilot response to theta 
NLH 

- 

- 

- 

- 

BO. 

40. 

20. 

0, 

-20.. 

-40- 

.... ... 

7.-, ++ + +++ +++p 

Configuraticbn E-5 : Gotnrna Tracking 

I+ 

Y ++ 

=I 

I I I 

.. ... ... ...... \ 

- 

- 

- 

. .- 

II+ - .. .. e. . 

a+ 

I+ 

m+ 

w+ 

=k 

II + 

= 

I I 1 

LEGEND: 

- pilot reeponae to gamma error 

+ pilot reaponse to gamma 

at pilot reaponse to theta 

270. 

1 BO, 

90, 

0. 

-90, 

-1 80. 

m + 

+ 

It+ 

a+ 

I+ 
I 1. 

w 

m: r 

rg 

t4LR C,onfiguration F--3 : Gan- ma Track.in(j 

f.. 

--.- 

a+ 

si f+ 

-40- 1 I 1 

-1 1. IO, 

frequency - rad/sec 

LEGEND: . pilot reeponae to gamma error 

+ pilot reaponae to gamma 

i pilot reaponae to theta 

270. 

180, 

90. 

0. 

-90- 

-1 80, 

1 m+ 

i+ 

.. i+ 

r+ - *. 1 M+ 

100- 

+ 

M+ 

i 

m+ 

r, 

Y 

.1 

1 

1. 10, 100. 

frequency - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

I 

I, 

Q, 

I" I 

Ig 

C 

I" a, 

m 

BO. 

40. 

20. 

0. 

-20. 

-40. 

.. ... 

-1 1- IO. 100, 

f req u e ncy - rad/sec 

LEGEND: . pilot reeponae ta gamma error 

+ pilot response to gamma 

pilot reapansm to theta 

270. 

1 so, 

9 0. 

+ 

m+ 

+ *+ 

w 

-9 0, 

.. E+ 

tM .. + 

-1 80. I 

I 1 I 

.1 1. IO. 100. 

frequency - rad/sec 
14 L F-' 

BO. 

40. 

0. 

-20. 

-44- I I I 1 

-1 1. 10- 100. 

frequency - rad/sec 

LEGEND: . pilot reeponae to gamma error 

+ pilot response to gamma 

*! pilot response to theto 

270. 

1 am 

90. 

0. 

-90. 

-I ao. 

+ 

% ++ 

11 

11+ 

++ .. a+ 

11 

11 + : 

-3s + + 

M+ 

e. 

I 

*,++ 

M+ 

M+ 

1( I( L-F****.. la ... 

I I 1 

,1 1. IO. 100. 

frequency - rad/sec 
I' 

C 

L 

I CP 

I$ I 

40. 

20- .. . . 

-20. O- 1 

+ m +?e + + ++ 

+ ++ + +++ 

+ +* 

-1 1. 1 a- 100- 

frequency - rad/s6c 

LEGEND: . pilot reeponae to gamma error 

+ pilct reapense to gamma 

)* pilot reapclnse to theta 

270. 

1 am 

9 0. 

0. 

-9Q- 

-1 80. 

.1 1. IO. 100. 

frequency - rod/sec 
I 

I 

I. 

1. 

I 

I 

rg 

I' 

IF 0 

I: 0 

1% 

I. 

Ql 

-20. 7. 

1: -40, 

I 

I 

I 

I 

I 

I 

++ +++cH***u*sl +++ 

i *t* 

+ 

3s 

+++ 

*til* = 

3s 

I 

- 

I I 

I.4l-K Configuration 

90. - 

0. - 

-go, - 

-1 80. 

.. 

++ It 

+ 

+i 

+It 

+T mi 

1( i 

*++ r 

+a 

* . . . . .- *. 

1 

c-7; - 2' : 

.. ._.......-I--- 

Gammo Trackirig 

-1 1, IO, 100, 

frequency - rad/sec 

LEGEND: 

- pilot reeponae to gamma error 

+ pilot response to gamma 

Y pilot response to theta 
I 

I 

I 

I 

I 

I 

I. 

I. 

I 

I 

I; 

I; 

In, m 

I. 

0 

0 

1: 

1 

t4LK 

-60 

40. 

20. 

0. 

-20. 

-40, 

+++ ++++* 

m 

j+++ + I 

... 

#(% Mi m* > 

Bt +Y 

s* 4 

I I I 

-1 1. IO. 100. 

frequency - rad/sec 

LEGEND: . pilot reeponae to qornma error 

+ pilot reaponse to gamma 

*i pilot reaponse to thsta 

270. 

180, 

90. 

0. 

-9 0, 

-1 80. 

*( 

+ 1 ** 

++ 

I I 1 

.I 1. 10. 100. 

frequency - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

I 

TI 

0 

-BO. 

40. 

20- 

Q. 

-20. 

-40- 

1 

.. 

. 0. ..... ...... -.--- 

+++ ++ +++ j+++ + ,It lE= z222ia 

s- i 

IR +*I 

*a .c 

I I I 

-1 1. 1 CI- 100- 

frequency - rad/sec 

LEGEND: . pilot reeponae to gamma error 

+ pilot reHponse to gamma 

*I pilot reaponse to theta 

270. 

1 €lo9 o. 

0. 

-90, 

-1 80. 

I 

+ *E 

++ 

. .. +I 

I I I I 

I I 

.1 1. IO. 100. 

frequency - rad/sec 
Id LR 

80. 

Configuration E- 1 : Gamma Trocklng 

40. 

.. . 

\ --c '..__ ... . ... 

0. 

-20. 

-40- 

LEGEND: 

equivalent mingle loop pilot function 

180. 

9 0, 

0. 

-9 0. 

-1 80. 

-270. 

. .. . .-- 

-- 

I I 1 

.1 1. 10. 100. 

frequency - rad/sec 
I 

I 

I. 

b W 

ti .- 

6 

I‘ 

E 

I 

I 

I. 

I 

I 

I 

- I 

f” 

i 

I 

0 

60. 1 

40. - 

20- - 

0. - 

-20. - 

-40. 

NLR Configuration E--2 : Gamma Tr-mcking 

I I 1 

.. . . 

frequency - rad/sec 

LEGEND: . equivalent mingle loop pilot function 

780. 

QQ, 

0. 

-90. 

-. 

II 

io-’aQ- -270. m .1 1. 10. 100, 

frequency - rad/sec 

I 
I 

I 

I. 

Im 73 

I; .- 

I! 

I' 

0 

E 

I 

I 

I 

I 

I 

Iv 

1. 

B 

B 

d 

19 

I 

I 

NLR 

(30. 

Configuraticn E--5 : Gamma Trocklng 

40. 

20- 

Q. 

-20. 

--.- cs .-... .. . .-. 

-40. 

-1 1, 10, 

frequency - rad/sec 

LEGEND: 

- equivalent mingle loop pilot function 

180. 

0 0, 

0. 

-90. 

-1 UO, 

-270. 

- .. .. 

1 1 1 

.1 1. 10. 100. 

frequency - rad/sec 
I 

I 

I 

td LR 

40. 

20. 

0. 

-2.. 

Configuration E--4 : Gamma Tracking 

-40, I 

-1 

.. --.- \ . ...... . .. 

I I I 

1, 10- 100, 

frequency - rad/sec 

LEGEND: . equivalent single loop pilot function 

180. 

8 0, 

0. 

-90. 

-1 80- 

-270. 

.. 

.. 

I 

.1 

I I I 

1. 10. 100. 

frequency - rad/sec 
m 1 

Iy 

NLR Configuration E-5 : Garnma Tracking 

60. 

40. 

20- 

0. 

-20. 

-40. 

-1 1. 10, 100. 

frequency - rad/sec 

LEGEND: 

equivalent mingle loop pilot function 

180, 

90, 

a. 

-90, 

-1 ao- 

-270. I 

.1 

.- 

-. 

.I 

I 

1. 

I 

10. 

I 

100. 
I 

I 

I' 

I 

I 

I 

I 

I< 

la, 

I 

P) 

rd ~fi 

60, 

40. 

20- 

0. 

-20, 

-40- 

Configuration F-3 : Gamma Tracking 

.. 

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

1, 10- 100- 

frequency - rad/sec 

LEGEND: 

equtvolent mingle loop pilot function 

i ao. 

0 0, 

Q. 

-90, 

-1 80, 

-270. 

- .. 

I I 

frequency - rad/s:ec 

-1 1. 7 0. 100. 

I 

frequency - rad/s:ec 

.. 

.. 

1 

-1 

I I 

7 0. 100. 
I 

I 

I. 

t.4 L R 

SO. 

40. 

20. 

0. 

-2. 

-40. 

Cc,nfigur-atimrl F-2 : Gamma Tracklnq 

1, IO. 

frequency - rad/sec 

LEGEND: . equivalent mingle loop pilot function 

180. 

9 0. 

0. 

-9 0. 

-1 so. 

-270. 

.. .. 

.1 1. IO. 100. 

freauencv - rod/sec 
Id L R 

BO. 

40. 

20- 

0. 

-20. 

-40- 

Cc,niigurrotic.r-t F- 1 : Gamma Tracking 

.....-,-- e.. 

.. .. 

.. 

-1 1, 10, 100, 

f re q u e n cy - rad/sec 

LEGEND: . eq~~ivalent einqle loop pilot function 

180. 

90, 

0. 

-90. 

-1 so. 

-270. 

.. 

.. 

I I 1 

.1 1. IO. 10-3. 

frequency - rad/sec 
NLH Configuration G-I : Gamma Traching 

I. BO. 

I 40. 

I 

I 

Q! 

W 

3 

e 

C 

20.. 

0. 

-20. I -t 

I. 

I 

-40- 

-1 1. IO, 100, 

frequency - rad/sec 

LEGEND: . equivalent single Iaop pilot function 

180. 

9 0, 

0. 

-9 0. 

-1 €50. 

-270. 

.1 1. 10. 100. 
I 

I 

I. 

I 

I 

I 

I 

1 

I 

I 

I 

r4LH Cor-1figurotic.n e---2 : Gornrna TracLing 

BO40. 

20. 

0. 

-20. 

-40- 

*. . .. ...... -.--- .. . .. *. 

-1 1, 7 0, 100- 

frequency - rad/sec 

LEG END: 

- equivalent eingle loop pilot function 

180. 

90. 

0. 

-9 0. 

-1 ao. 

-270. 

. .. 

.. .* 

I I 1 

.1 1. 10. 100. 

frequency - rod/sec 

-. . .. .. 

.1 1. 10. 100. 

frequency - rod/sec 
I' Q) 

L 

NLR Configuration G-3 : Gomrno Tracking 

SO. 

40. 

20. 

0. 

-20. 

-40, I 

-1 

. .. - * ...........*---- 

I 

1, 

I 

IO, 

frequency - rad/sec 

LEGEND: 

- equivalent mingle loop pilot function I 

I" I 

1.1 CP 

I" 0 

180, 

8 0, 

* .. 

0. 

-go. 

-1 ao, 

-270. 

... 

I 

100- 

I 

.1 

I 

1. 

I I 

10. 100. 

frequency - rad/sec 
NLR Corlfigurotiorl G-4- : Gamma Tracking 

40. - 

m 

'0 

20. - I 

a> 

W 

3 

t 

P 

4J 

0. - .- 

-2.. - 

-40. 

1 I 

1. 

I I 1 

. - . ......_....e*-*- 

-1 1, 7 0, 100, 

frequency - rad/sec 

LEGEND: 1. - equivalent mingle loop pitot function 

U 

i ao. 

90, 

0. 

-90. 

-1 so, 

-270. 

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

.1 1. 10. 100. 

frequency - rod/sec 
I 

I 

1% 

I' 

IS .- 

IF 

I 

I 

1. 

I 

I 

I 

E 

I. 

a) 

t 

B I 

f 

i 

Ii 

I 

40. - 

NLH Configuration E- 1 : Gamma Tr-ocking 

... . 

eo. 

40. 

+ I 

+ 

-40- I I L 

t 

-1 1, 10, 100, 

frequency - rad/sec 

LEGEND: . gamma to gamma command - open 

+ gomma to gomrna command - closed 

180, 

5) 0, 

0. 

-9 0. 

-1 so. 

-270. 

1. 10. 100. 

freauencv - rad /sec 
u 

- 

- 

- 

1 

- 

t-4 LR 

ad. 

. .. 

+ ++ 

I I & 

1 

40. 

20- 

0. 

-20. 

-40, 

Configurotion E--2 : Gamma Trocking 

.. 

++*+ 

++++++ . ---\ + 

-? 

+ 

LEGEND: . gammo 

+ gamma 

180. 

90, 

0. 

-90. 

to gamma commond - open 

to gamma command - C los6d 

+ +++ ++ 

+ 

+ 

+ 

+ 

+ 

0 

-270. 

*1 1. 10. 100. 

frequency - rad/sec 
I 

I 

k 

Is 

I 

I 

I. 

I 

I 

I. 

I' V 

If 

U 

C 

a, 

F I 

f Iu 

I& 

CP 

E 

I 

~.ILR 

80. 

40. 

20- 

0. 

-20. 

-40- 

Cmnfiguraxtion E--3 : Gamma Tracking 

++*+ 

+ +++ ++ .. + 

.--\ 

+ 

I + 

1 I 

frequency - rad/sec 

+ 

1 

-1 1, 10, 100. 

LEGEND: 

gamma 

+ gamma 

180. 

80. 

0. 

-Q0. 

-1 aa 

-270. 

+ ++ 

to gamma command - open 

to gamma command - closed 

+ +++ ++ 

+ 

+ 

+ 

+ 

+ *. +% - . . .'.j+ .. 

t 

%. 

I I 1 

.1 1. 10. 100. 

frequency - rad/sec 
I 

1 

I. 

I 

I 

I 

m 

I 

T) 

Q> 

W 

3 

C 

0 

0 

3 .- 

E 

CP 

NLR 

80. 

40. 

20- 

0. 

-20. 

-40, 

Cunfiguration E-4 : Gamma Trocking 

++*+ 

++++++ *. + 

--e\ 

+ 

+ 

1, 10- 100. 

frequency - rad/sec 

LEGEND: 

- gamma to gamma command - open 

+ gamma to gamma command - closed 

180. 

9 0, 

0. 

-9 0, 

-1 SO. 

-2770. 

.1 1. IO. 100. 

frequency - rod/sec 
NLR 

450- 

40. 

20- 

0. 

-20. 

-40. 

Configuration E-5 : Garnmo Trocklng 

* +? ++ 

--*\ 

++++++ - 

'. 

+ 

+ 

+ 

LEGEND: 

- gamma 

+ gamma 

180. 

go0. 

-90. 

-1 so, 

-270. 

to gamma command - opmn 

to gamma cornmond - closed 

+ +++ ++ 

+ 

+ 

+ 

+ 

+ 

I 

.1 

I 

1. 

I I 

IO. 100. 

frequency - rod/sec 
I 

I 

I. 

Im T) 

I' 

NLR Configuration F-3 : Gamma Trocking 

cia- 1 

. .. . . 

20. 

40- i .- * 

,?++++ 

*."\ 

+++ ++++++ - 

t -20. j + 

+ 

-40- I + 

I I I 

-1 1, IO. 100- 

frequency - rad/sec 

LEGEND: 

- gamma to gamma commond - open 

+ gamma to gamma cornmond - closed 

I 

4 80. 

8 0- 

0. 

-90. 

+ +++ ++ 

+ + 

+ 

+ 

+ 

.1 1. 7 0, 100. 

frequency - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

f..J L F: 

BO. 

40. 

20- 

0. 

-2.. 

-40- 

I 

m 

Cc\niigurotic\rl F-2 : Gamma Tracking 

1, IO. 

frequency - rad/sec 

LEGEND: 

gamma to gamma command - opgn 

+ gamma to gamma command - closed 

1 BO. 

90, 

0. 

-90. 

-1 ao, 

-270. 

+ +++ ++ 

+ 

+ 

+ 

+ 

+ 

.1 1. IO. 100. 

frequency - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

I 

I 

Is 

r.1 L F: 

SO. 

40. 

20- 

0. 

-200. 

-40- 

Configuration F- 1 : Garnmo Tracking 

+ 

+ 

+ 

I 

-1 

1 

1. 

I 

10- 

frequency - rad/sec 

LEGEND: 

gamma 

+ gamma 

180. 

90, 

0. 

-9 0. 

-1 eo. 

-270. 

I 

100. 

to gamma command - open 

to gamma command - closed 

1 + ++ + +++ ++ 

+ + 

+ 

+ 

+ 

+ *+* 

.1 1. 7 0. 100. 

frequency - rad/sec 
1 

I 

I. 

I 

I 

I 

CP I:, 

rdLFi 

BO. 

40. 

20. 

-20.. 

-40. 

Configuration G-I : Garnn~o Tracking 

+ +++ 

++*+ 

++ *-1, 

1 , ,*++ , 

-1 1- I a- 100, 

frequency - rad/sec 

LEGEND: 

gamma to gommo command - open 

+ gamma to gamma command - c lossd 

180. 

9 0, 

0. 

-90. 

-1 SO. 

-270. 

+ ’+++ +++++++ 

+ ~ 

I 

+ 

+++ 

++ + . . . ..*a*.*++ 

.1 1. IO. 100, 

freauencv - rad /sec 
+ 

+ 

-40- 

I 

I 

I I 1 

-1 1, 10, 100, 

frequency - rQd/SeC 

LEGEND: 

gamma to gamma command - open 

+ gamma to gammo command - closed I 

180. 

I. -270, 

.1 1. 10. 100. 

frequency - rod/sec 
I 

I 

I. 

60. - 

40. - 

20- - 

0. 1. 

-20. - 

-40. 

I 

I 

I 

I 

I 

I 

... . 

+++ + +++ ++++\ **. *. .. 

+ 

+ 

+ 

I I -L 

1 

NLR Configuration G--3 : Gommo Trocking 

-1 1, 10, 100, 

frequency - rad/sec 

U - 

II 

I 

b 

1: 

LEGEND: 

- gamma to gamma command - opsn 

+ gammo to gommo commond - closed 

180. 

9 0, 

0. 

-9 0. 

-1 so, 

-270. 

1. 7 0. 100. 

frequency - rad/sec 
m 

I 

I” 

& .- I& 

u 

IE 

- 80. 

40. 

20. 

0. 

-20, 

-40- 

-1 1- IO, 100, 

frequency - rad/sec 

LEGEND: 

gamma to gomma command - open 

+ gamma to gamma commond - closed 

I 

T3 

I’ 

0 

180, 

9 0. 

0. 

-90. 

-1 ao. 

-270. 

.1 1. 10. 100. 

frequency - rad/sec 
I 

I 

I 

I 

I 

I 

I 

I 

U 

1 SQ9 0. 

E. 

-9 G. 

-1 eo. 

1. 10. 100. 
+ T + +' ++ 

1 

I I I 1 

270. 

i ao. 

90. 

0. 

-90- 

-1 80. 

.1 1. IO. 100. 

frequency - rad/sec 
I ++ 

-4 Cf. 1 I I i 

++ + 

+ 

+ + 

+ 

+ 

+ 

+ 

0. 

--so. 

-1 BO. 

.1 1. 10. 100. 

frequerlcy - rod/- -eC 
I 

I 

I 

B 

I 

I 

I 

I JI f.! 

4 C). - 

0. - 

-20. - 

++ 

r 7 .- L / CIA 

180. 

90. 

G. 

-GIG- 

-1 eo. 

++ + 

+ 

+ 

+ 

+ 

+ 

+ 

t.. ... .. .. . . 

+ 

+ 

+ 

+ 

+ + + + + 

++ 

+, 

.1 1. IO. 100. 

f req u e rl cy - r a d /' 5 e c 
I 

1 

I. 

. .. .. . 

+++ + +++ 

+++ ++ A 

+ + 

++ 

LEGEND: . pitat reeponae ta theta error 

+ pitat rsapclnse to theta 

270. 

1 ao. 

9 0. 

0. 

-9 0, 

-1 80. 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ 

+ + + + + + + + + + 

.1 1. 10. 100. 

frequency - rad/sec 
I 

8 

e 0. 

3 1:) . 

20. 

0. 

-20. 

-4 0. I 

-1 

.. .. . .. . 

+ ++ + +++ 

++ ++- 

+ 

++ 

I 

1. 

frequency - r u ci j’s e c: 

270. 

1 ao, 

9 0. 

0. 

-9 0- 

-1 80. 

+ ++ 

+ 

+ 

+ 

+ 

+ 

. ... .. + 

. .+’ 

+ + + 

++ 

++ 

+% 

% + + + + 

1 

100. 

.1 1. IO. 100. 

frequency - rad/E.:ec 
r, 7 .-. L .( 1,'. 

i eo, 

9 0. 

0. 

-90- 

-1 80. 

.1 1. 10. 100. 

frequency - rad/sec 
1 

I 

I 

1 

I 

I 

4 r:, . - 

-20. - 

-413- - 

_. ... 

270. 

1 am 

9 0. 

0. 

-9 0- 

-1 80. 

.1 1. IO. 100. 

frequency - rad/- 4ec 
.. ... 

r 

+ ++ + ++* 

' ++++A 

+ + 

++ 

LEGENP: . pilclt t-empanse tc, theta error 

+ pilclt rmapon3e to theta 

270, 

1 eo, 

9Q. 

0. 

-90- 

-1 ao. 

++ 

+ 

+ 

+ 

+ 

+ 

+ 

+. .. . .. . . 

+ 

+ 

+ 

+ 

+ 

+ ++ 

+ 

+ 

+ 

+ 

+ 

+ 

+. .. . .. . . 

+ 

+ 

+ 

+ 

+ 

+ + + + + + + + + 

I I I 

+ + + + + + + + 

4 

.I 1. 3 0. 100. 

frequency - rad/sec 
U 

t. 13 - 

4 I.-J . -- 

2c. - 

0. - 

4 

-20. - 

-40. 

I’ . -. 

__- 

.. . . .. 

.. 

+ ++ + +++ 

+++ ++ A 

i + 

++ 

I 1 I 

. -- 

r 

L 18‘ 

t 

CL 

I 

.I 7. 

270. 

1 eo. 

9 0. 

0. 

-9 0. 

-1 eo. 

+ 

+ 

+ 

+ 

+ 

+ 

. +. . ... .. -. 

+ 

+ 

+ + 

+ 

I 

I I I 1 

.l 1. IO. 100. 

frequency - rod/- dec 
1.19 . - 

4 7,. -' 

>' L 

0. - 

4 -2u. - 

-40- 

-1 

1 EO9r3. 

-I ++ + +++ 

+++ ++ A 

+ + 

++ 

I 

1- 7 0. 100- 

0. 

-% 0- 

-1 eo. 

- 

-%0- - 

-1 eo. 

++ 4- 

+ 

+ 

+. . ...._ .. 

+ 

+ 

+ 

+ 

+ + + + + + + + + + 

I I 1 

+ 

+ 

+ 

+ 

I + + + + + + + + + + 

I + 

I I I 1 
1 I 

L 

1 

L 

a i 

.. . . .. 

+ ++ + +++ 

. ++++A 

+ + 

++ 

270. 

1 eo. 

9 0. 

0. 

--9 0, 

-1 80. 

+ ++ 

+ 

+ 

+ 

+ 

+ 

+ 

+. . .-._ _. . . .. + 

+ 

+ + + + + + + + + + + + 

I I I 

.l 1. IO. 100. 

frequency - rod/sec 
1 

I 

I. 

i 

1 I I 1 

I 

I 

t 

I 

B 

I 

I, Qr 

20. 

0. 

- 4- c', 

.. '. 

. . . . ... 
r I L_-- . : 1 t bc~"t.0 7 t-ac I-airig 

- 

- 

1 

I 

I. 

I I 1 

1 

1 

I 

u 

I 

I 

.. .. 

Bingle loop pilot function 

-e. 

180. 

9 0, 

0. 

-9 0. 

-I am 

-270. 

75 

.. 
I 

I I a? 

T! 

7 

. . ._ 
I 

I 

I 

1 

I 

I 

I. 

I 

I 

I 

I 

I 

l 

I 

I J1 f 

CCj. 

0. 

-40. 

-1 1- IO. -ic*afrequency - radjsec 

LEGEND: 

equivalent mingle loop pilot function 

I 

.1 

I I I 

1. IO. 100. 

f re y u e n c~,,~ - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

I 

eo. 

4 0. 

20- 

0. 

- 7- i I-' . 

-4 0. I 

-1 

I 

1- 

I 

IO. 

I 

100. 

frequency - rad/sec 

LEGEND: 

equivalent eingle Iaop pilot function 

180. 

9 0. 

Q. 

-9 0. 

-1 so- 

-270. 

I 

..._ .. 

1 I 1 

.I 1. 7 0. 100. 

frequency - rad/sec 
I 

I 

I. 

I 

I 

I 

I 

I 

I 

BY 

I 

u I t-l 

Im 

m 

0 

... 

LEGEND: . equivalent single Iaop pilet function 

18rj. 

9 Q. 

0. 

-9 0. 

-1 80, 

-270. 

. ..... .. 

I I 1 

.1 1. IO. 100. 

freauencv - rod /sec 
I 

I 

I 

I 

I 

I 

1 

I 

I. 

I 

I 

I 

I. 

1 

-1 

I 

1- 

180. 

90. 

0. 

-9. 

-I am 

-270. 

. . . ... 

.1 1. IO. 100. 

frequency - rad/sec 
I 

I 

I 

I 

I 

I 

I, 

IC 

I. 

I. 

I 

I 

I 

I 

1 

I 

I 

ps 

I 

80- 

4 o. 

20. 

0. 

-20. 

-40- 

. .. 

. . .. 

-1 1- 10- 100. 

frequency - rad/sec 

LEG END: 

equivalent eingla loop pilot function 

180. 

9 0, 

0. 

-9 0. 

-1 so- 

-270. 

.1 1. 10. 100. 

frequency - rod/sec 
I 

I 

I 

I 

I 

I 

I 

I 

I. 

1 

1 

I 

I 

I 

I 

I 

1. 

I. c 270. 

c c71 . 

I 

I I 1 

4 0. 

Q. 

-20. 

-40- 

.. ..-- -. 

\ 

.. 

.. 

LEGEND: 

equi;iaIent single lcop pilot func:ticln 

1 1 IBO. BO - 

90, - 

. .... 0. - .- 

-9G. - 

-180- - 

c 270. I I 1 

.1 1. IO. 100. 

f req u e rl cy - t-ad/sec 
I - (‘(l’ - I 

180. - 

90. - CP 

I 

12 

I 

Q. - I, - 

1: -30. - 

I! L 

la 

--lea, - 

I. -270. 

2 iJ . 

. ...* .. 

I I I 

.. 

LEG EN C’: 

equivalent Binale loop pilot function 

frequency - i-ad/sec 1 
1 

1 

1 

1 

I 

m 

-E 

a! 

-D 

3 

E 

4-a .- 

E 

I 

I. 

1 

1 

I 

1 

I 

I 

[LI 

6'1 

0 

i 

LL 

. ,. . 

180, 

9 0. 

0. 

-3 0. 

-1 so- 

-270. 

.1 1. IO. 100. 

frequency - r-od/sec 
f 4 1 f 1: I40. -' 

I -20. 

LEG E td D: 

equivalent eingle loop pilot function 

frequency - rod/- 3CC 
1 

I 

I. 

I 

1 

I 

EOG. 

-20. 

-4 Elm& m6 m 

arm- 

++ + + ++ 

LEGEND: . theta tc. thmta c~,mmarld - open 

+ theta tr_. thBta ~=.z~mmarrld - c: I CZI E. e d 

180. 

9 0, 

0. 

-90. 

-1 80, 

-270. 

+ ++ 

.. 

,/ 

+ +++ 

+ ++ 

+ 

+ 

+ 

+ 

+ *. + 

.+ 

+ 

+ +'. +* +* +. 

y. 

1 I I 

100. 

I 

.1 1. IO. 

frequer-Icy - rad ,/'s;.ec 
-&v. - 

4 0. 

2G. 

0. 

-20. 

.. 

-40. I I I 

+ 

1 

LEGENC>: . theta to theta cctrnrnarld - open 

+ theta tc, theta cmmmand - closmd 

180, 

9 0, 

0. 

-go. 

-1 ao. 

-270. 

7 

*-?++ + +++ 

+ ++ 

+ 

+ 

+ 

+ 

+ -. + 

+ 

+ +'. +. +' +' ++'. 

I I I 

+- . 

I 

+' +' ++'. 

I I I 

.1 1. I a. 100. 

frequency - rod /-. 4cc c-x 
'I 

U 

L 

3 r:.* . 

1- 

i c:. 

0. 

.. 

LEG Et4 D: 

180. 

9 0. 

rJ. 

-90. 

-1 ao. 

--- 2 7 0. 

theta c.=,mmand - op-n 

theta cclmmartd - clclsmd 

+ +++ 

+ ++ 

++' 

.I 1. IO. 100. 

frequency - rod/sec 
I 

Bo 

I 1 a?’ 

w 

I 

I 

I 

1 

1 

I 

I 

LEG EN D: . theta tc theto cc~mmand - open 

+ theta tc theto ~c~rnmond -cIaBed 

’8Q* 1 

1 -90. 

+ 

+. I + 

+ 

+ 

*. + 

+ 

-l j , .-”: . , , 

+‘ 

+’ 

-270. 

-1 1. IO. 100, 

frequency - rad/sec 
I 

le(.. - 

90- - 

a. I. 

-90. - 

-1ao. - 

-270. 

-40- I + 

I I 1 

?++ + +++ + 

+ + I + 

+ 

+ 

+ 

-. + 

+ 

.. + * +. +* +' . +* +' +' 

y. 

I I i 

-1 1. 10- 7 00- 

frequency - rad/sec 

LE G E P4 D : Io . theta tc. theta command - open 

+ theta tc theta cmmrnond - c1oE-d 

I 

U 

I' 
I 

1 

I. 

I 

I 

I 

u 

1 

I 

I i 

e 0- 

40. 

0. 

-20. 

-40. 

-1 

. .. 1 + 

LEG EN D: . theta to theta cc~rnrnand - open 

+ theta tc:. thbta caminand - clozed 

180. 

9 0, 

0. 

-9 0. 

-1 so, 

- e, L70. 

+ +++ 

++ 

+ 

+ 

+ 

+ 

+ 

+ 

+' +' . +. +' 

+ *. 

+,. I 

I 1 I 1 

.1 1. IO. 100. 

frequency - rad/- dec 
2 13 I I. 

-0 

0. 

I 

I -1 1- IO. 

f r-eq u e n cy - raci/sec 

LEG END: . theta tc- theta cclmrnand - open 

+ theta tc: thflta cctmrnand - closad 

1 'do. 

. .. 

+ ++ + + ++ + +++ 

0. 

1 

1. IO. 100. 

frequency - rod/sec 
I 

I 

I 

I 

I 

I 

I 

I 

I. 

i. 

1ao. - 

90, - 

0. 1, 

-90. - 

-iao. - 

-270. 

I 

I 

I 

I 

1 

I 

I 

+ ++ + +++ 

+ ++ 

+ 

+ 

+ 

+ 

+ 

+ **. + 

..+ 

4 +. +. +' 

+ *. +. +. +. 

I I 1 

60. 

40. 

212)- 

0. 

-20. 

-40- 

-1 1. 7 0, 100, 

frequency - ruci/sec 

LEGEND: . theta to theta command - open 

+ theta tc thQta c~lrnrnarld - closed 
'I I 

I 

I 

I 

I 

I 

I 

I 

I. 

I 

I 

I 

I 

1 

I 

I 

I 

I. 

I. 

-40. - I 

-b 

I I 

LEG END: . theta tc. theta cgrnmand - open 

+ theto tc th-to command - closmd 

180. 

9 0. 

0. 

-9 0. 

+ ++ 

~ *- 

+ +++ 

++ + 

+ 

+ 

+ 

+ 

.. +. 

+ 

'.+ 

+ 

/. +' 

-180. - 

+'. +' +' ++'. 

-2770. I 

-e' 

I 1 

.1 1. 7 0. 100. 

frequency - rad/sec 
I 

I 

I 

I 

I 

I 

i 

I" 

4 0. 

20. 

0. 

-2. 

-40- + 

I 

-1 

I 

1. 

I I 

IO- 100- 

f t'F g u e 1-1 cy - rad/, CFr, 

LEG END: . theta to thBta ccmmartd - open 

+ theta tc 

1 EO. 

9 0, 

0. 

-90. 

-1 230. 

-270. 

theta carnrnand - clomed 

+ +++ 

+ ++ 

+ + 

+ 

+ 

+ *. + '.+ 

Y 

+. +'. +- 

I I 1 

.1 1. IO. 100. 

frequency - rad/sec 
I 

I 

I 

I 

I 

I 

I 

I 

I. 

I 

I 

I 

I 

1 

I 

I 

I 

I. 

I. 

4 0. 

0. 

---eQ_ 

.. 

++ + +++ 

LEGEND: 

1 ao. 

9 0- 

C. 

-9 0. 

-1 am 

27Q. 

theta command - open 

theta cctmrnand - c:lclBed 

+ +++ 

++ + 

+ 

+ 

+ 

+ 

.. + 

+ 

'.+ 

-t +. 

+'. +. +' 

+ .. 2. 

I 1 1 

.1 1. IO. 100. 

frequency - rod/sec 
-4-1- 1 + 

1 1 I 

-1 1- IO, 100- 

frequency - rad/',* -=ec 

LEG EN Ea: 

. theto tc th-ta cammarid - open 

+ theta tn th-ta carnrnand - closed 

I 1 180, 

I 

I 

I 

I 

0. 

-9 0. 

-1 80. 

-270. 

it++ + +++ 

++ 

-I * +. 

I".? ++ + +++ 

+ ++ 

+ 

+ 

+ 

*. + 

+ 

*. + 

- * +. +'. +* +- 

+ .. 

\.. 

I I I 

+'. +* +' 

+ .. 

I \.. 

I I I 

.1 1. 10. 100. 

frequency - rad/s.ec