The effect of preview on pilot describing functions in a simple tracking task

May,

1-972.

THE EFFECT OF PREVIEW ON

PILar DESCRIBING FUNCTIONS

IN A SIMPLE TRACKING TASK

by

N. H. Drewell

THE EFFECT OF PREVIEW ON PILOT DESCRIBING FUNCTIONS IN A SIMPLE TRACKING TASK

by

N. H. Drewe11

SUbmitted, Apri~ 1972.

ACKNOWLEDGEMENT

The author wishes to express his thanks to his supervisor, Dr. L. D. Reid, for his helpful suggestions during the study. Thanks are also extended

to the subjects who donated many hours of their time, and to the National Research Council of Canada, who funded the work under Grant No. 3-301-182-20.

SUMMARY

This report presents a preliminary analysis of the pilot describing functions of six volunteer subjects found by using the new preview display at U.T.LA.S. The tasks were pure pursuit tracking with rate control dYltamics; the pilot being given a preview of the input signal. The amount of preview was varied between zero and 0.8 seconds and where possible, an 8-parameter theoretical pilot model was fitted to the describing fU{lction data in order to enhance the quantitative description of these functions.

1.

2.

4.

5.

INTRODUCTION

THE DESCRIBING FUNCTION THE EXPERIMENT

3.1

Experimental Layout

3.2

Equipment.,

3.3

Random Noise Input

3)~4 Tracking Scores

3.5

Experimental Design

TABLE OF CONTENTS

3.6

Calculation of Pilot Describing Function

RESULTS

4.1

Small Preview Cases

4.2

Large Preview Cases

4.3 Tracking Scores CONCLUSIONS REFERENCES APPENDICES TABLES FIGURES PAGE 1 1 2 2 2

3

4

4

5 5

6

8

9 9 11

1. INTRODUCTION

The pilot describing f~ction has been found previously for many types of tracking tasks. The sensitivity of the function to changes in input signal power spectral density and control dynamics has been investigated in compensa-tory, pure pursuit and pursuit-plus-disturbance tracking tasks. Also investi-gated have been the effects of predictor displays of varying sophistication. This study attempts to widen the data base to include the effects caused by the pilot being able to see the future course öf the input signal in a pure pursuit task where input power spectral density and control dynamics are kept constant. This t~e of situation arises when a driver negotiates a fog shrouded winding road.

2. THE DESCRIBING FUNCTION

Figure la represents the linearized version of a pilot performing a pursuit-plus-disturbance tracking task where Yp(S) and YR(S) are the linear pilot describing functions whic~ use as inputs,the system error eet) and system output met) respectively and whose outputs are summed along with net), an uncorrelated noise signal (remnant) introduced by the pilot,.)to produce the pilot output o(t). The aircraft dynamics A(S),acting on the pilot output,then produces an output which is summed with a second system input g(t) to produce the system output met), which if the tracking is perfect is identically iet).

The two describing functions to be measured must have uncorrelated in-puts. Previous experience (Ref.l) has shown that the magnitude of YRCS) is generally much smaller than that of Yp(S) and A(S), and for this rea~on, the present experimental situation was simplified and modelled by the system shown in Fig. lb where the second system input g(t) and the descri~ng f~ction Ys(S) have been removed. In other words a compensatory model has been used to

re-present a pure pursuit tracking situation. This simplification can be j~s~ified

as will be discussed in connection with the correlation coefficient.

According to Ref. 1, the linear function Yp(S) which best fits the original pilot data in the RMS sense has the form

For thecoompensatory case where defined by

<1> •• (w) is the cross-power spectral density

l.J where

=

~

,

J

e 00 -j WT 21T' R .. _l.J (T) dT R .. (T)

=

l.J _00 lim T ~.oo 1 T T

J

i(t)j(t + Tfdt o

for two time signals iet) and jet). In order to provide an index of fit of Yp(S) to the real pilot data, a correlation coefficient is defined at each

measurement frequency and has the form

where p2 takes on values between 1 (perfect fit) and 0 (no fit). Justification can therefore be established for usi~g the simplified experimental situation of Fig. lb if it can be shown that thé correlation coefficients so found with zero preview 'compare favoUrab ly wi th those found to hold for the si tuation of Fig. la.

3 •

TEE EXPERIMENT

3.1 Experimental Layout

The experiment al situation of'Fig. lb was physical\y realized as shown by the photographs of the interior of the work station in Fig. ,2a and the ancillary equipment in Fig. 2b. A schematic representing the interconnec-tion of, the equipment is presented in Fig.4. The input signal was prerecorded on magnetic tape for purposes of repeatability of input signal and controlla-bility of its magnitude and mean vailue. The tape deck provided the input to the computer where the signal was interfaced with the preview electronics. The display electropics produced appropriate signals for the display and monitoring oscilloscope to create the two dimensional representation of the input signal. A more complete ,des~ription of the display and its interpretation is given in the foltowing paragraph on equipment. The displayelectronics also furnishes the signal which is considered as the system input as represented by Fig. lb. The output of 4he joystick o(t) is iritegrated to create the rate control air-craft dynamics (transfer funct~on

Kis )

'0Utput m( t) • This output is subtracted from i(t) in the computer to generate the system errorsignal e(t) which along with,the system input i(t) and stick output o(t) is fed to the data acquisition

system.

3.2 Equipment

Housed in the work station is the preview display system previously developed at U.T.I.A.S. utilizing digital electronics with a shift register and a Hewlett Packard 143~A oscilloscope with an

8

by 10 inch display screen outfitted with two 1405 A Dual Trace Amplifier plug-ins. A photo of the dis-play screen appears in Fig. 2a. The circle, controlled by the stick, moves along the vertical line 'a', its velocity being proportional to stick deflec-tion. (The line 'a' is for reference purposes onlyand does not appear on the actual display). Pulling back on the stick makes the circle risee The directed vertical distance betwe,en the circ le (the system output) and the wavy line is the system error (positive as shown in the drawing). The heïght above a zero reference at which the wavy line intersects the vertical line 'a' is the system input (again positive as shown). The portion of the wavy li~e to the right of line 'a' represents the future course of the input signal and it is called the preview portion of the display. The left hand side represents

h~tory and is called the postview. In practice, the postview was blanked out

in order to consider the effects of previewalone. Briefly, the operation of

history in digital form is retained in a shift register with 8-bit prec~s~on. A selectable part of the history is displayed as the wavy line shown in Fig.2a. Theline is actually a series of dots spaced every 0.10 inches, the spacing representing 0.020 seconds. The 8-bit precision of the shift register provided a displayed vertical resolution of 0.017 inches. The horizontal position of line 'a' can be continuously varied electrically from the left edge of the wavy line to the right edge, creating a wide range of possible ,combinations of

I

preview and postview. Figure 3 is a time-lapse prese~tation of the pre and postview signals.

The displayed RMS magnitude of the system input signal was kept at 0.50 inches with its mean at zero, and the diameter of the circle was 0.13

inc~es. When sitting in the seat provided, the subjects viewed the display

from a distance of 20 inches on the average.

Also shown in Fig. 2a is the joystick used, which is af low inert~a with aluminum tubing topped by a balsa wood hand grip 18.5 inches from the bali bearing pivot point. Spri;qg loading has been added to gi ve i t a mechan:ic al equilibrium at its center position. It has a spring constant of 0.34 ounces per degree of deflection, a natural frequency of 11.8 radians per second, and a damping ratio of 0.0067. Maximum deflection of the stick was ~imited

to + 17.5 degrees and the overall system gain set to give a 0.94 in.sec/ cirële speed per degree of stick deflection.

The tape deck which played back the random noise tape was a Revox type 1102 outfitted wit)h 10.5 inch reels and used at 7.5 in./sec. to provide a frequency response of 50 Hz. to 15 kHz., + 1.5 db. Appendix A explains how this machine' was used to record and play baëk low frequency signals.

The computer used for the signal processing was a general purpose analogue computer - an Electronic Associates, Inc. TR-48. The data acquisition system built by the Electrönic Engineering Company of California was designed to interface with the Kennedy DS-370 digita1 magnetic tape recorder. The who1e system was driven and synchronized by the crystal output of a General Radio type 1151 - a digital time and frequency meter, which also served to monitor the timing of the "write command" pulses driving the digital recorder.

In the original recording of the input tape using pu1se-width modu-lation, a Wavetek model 116 provided the required waveforms for the modulation process as described in Appendix A.

An air-conditioner for the work station, a monitoring oscil10scope for the operator, and an intercom system between subject and operator rounded out the convenience features.

3.3. Random Noise Input

The power spectral density of the input signal was a close experi-mental approximation to that represented by Fig. 5, which is the theoretical c~ve defined by <1> •. (w) ~~ 1

4

(IC

w :

6)

+ 0.032( _(_.,_).",...2_1.;...2..;..1 _ _ _ _ '\

J~

+ 7.92 jw + <1> .. (0) ~~

This is a standard curve used in previous UfT.I.A.S. work and is c1assed as the High Frequency input (H).

3.4 Tracking Scores

Tracking scores give a crude but iromediate indication of performance and are defined by

T.S.

fT

e

2

dt 0 x lOr;;f'/o =

J

o

T

_.2 dt 1

The integra1s of the error and input squared were ca1cu1ated by the analog~e

computer during the last 150 seconds of all tracking runs, and the score was given to the subject immediately on completion of the task. The lower the score, the better the subjects performed.

3.5 Experimental Design

All controllable task parameters were kept constant except for the amount of displayed preview. Postview was kept at zero for all tracking runs, which were performed at any time of the working day at the convenience of the highly motivated vo1unteers. During the training period four tracking runs were completed during the day in two sessions of two runs each and during the actual experiment, the subjects were given two options(each day:

1) Two sessions of two runs each - the first run being a warm-up and the second being used for performance data. 2) One session of three runs - the first again a warm-up

and the rest being used for performance data.

The amount of preview presented to a subject on any one day was one of 0, 0.1, 0.2, 0.4, 0.8 seconds (referred to as 0, 1, 2, 4, 8 preview) and the sequence in which it was presented day by day was determined as foltows. During training, the preview at which the subject' s performance (his score) was weakest was given preference over the other previews unti1 the deficiency was made up, relative to his performances at the other previews. D,uring the experiment the preview presented was predetermined by consu1ting a random numbers tab le and choosing four permutations of 0, 1, 2, 4, 8 to create the sequence. T~e sequences for all the subjects are repeated in Table. 1.

The input noise tape contained 13 runs of 165 seconds each, the first seven of which were used during training with the remainder used for the experiment. Subjects were never to1d the run number before tracking during the experiment. Tests conducted during the training period indicated that the subjects could not recögnize a given run n~er as having been pre-sented twice, ind~pendent of the disp1ayed preview, if this fact had not been

poin~ed out beforehand. On this basis, the run number used for a given track-ing run durtrack-ing the experiment, as durtrack-ing traintrack-ing, was determined at random by the operator with only one restriction. No run n~er was presented twice during any one session with a s~bject.

. Subjects were told that the rate control dynamics corresponded to the initial pitch motion of an aircraft relative to the horizon and the task was to keep the aircraft in tqe required attitude as represented by the input signal such that their tracking scores were minimized. That is, the circle was to be kept on the wavy line shown in Fig.2a. It was impressed on the subjects that a negative error did not cancel a positive error and that scores vary as the square of the error. Training of a subject was terminated when consistent scores were achieved at all previews. This consti tut~d .. l approxi-mately 40 tracking runs per preview per subject during training and 14 during the experiment. This involved a total of approximately 1609 tracking,runs. Performance data were obtained during

8

tracking runs at each preview for each subject.

3.6 Calculation of Pilot Describing Functions

The pilot describing functions shown in this report were calculated using previously developed software on an IBM system 7094, working with the digital data tapes. A listing of the pertinent subroutines is found in REf. 1. The sampling rate applied was 25/second and record lengths of 150 seconds llsed., Thus, in order to achieve measu.rement frequency intervals compatible

with those used previously, the maximum time delay T used in the calcula-max

tion of the auto and cross-correlation functions R .. (T) was set to 9.96 seconds.

-~J

!

This gave an estimate of the describing functions at int.ervals of 211: T = m

0.63l radians/second starting at ~/Tm

=

0.315 rad./:se~. 4. RESULTS

It' is important to stress that the pilot describing functions pre-sented in this report model the combined .dynamics of the disp~ay, pilot, and

~0Ystick since no data were taken to separate out the individual systems. It

should be noted that the stick is effectively a pure gain and the display a pure negative time deray • The describin~ function yp(w) relates stick out-put to the tracking error disp1ayed on the screen. Eaéh describing function is characterized by three plotsshowing amplitude, phase, and correlati on as a function of frequency in radians/second. The amplitude plot shows the _~tick motion position in degrees produced per inch of error signal displayed. The phase plot represents the phase of the stick oupput relative to that of the erilor signal. The phase in degrees is negative fora:~phase lag and positive for a phase lead. The correlation is defi~ed in chaptèr 2 and takes on values

be~ween 1 and O. The error bars indicate the standard deviations based on

estimates of variance. Some standard deviations when expressed on a logarith-mic scale, as for example in the amplitude plots, will be at minfs infinity,

indicating that the value of the standard deviation exceeds that of the mean.

It has been recently shown that redefiI\ing the correlation produces significantly improved correlation values at frequencies greater than about 5 radians/sec. (Ref. 2). Define

p

=

n /

(1

+

A(S)Y(S»

where p, n indicate ~e Laplace transf®rms of the time signals p(t) and n(t). The correlation used in this report is defined as (Ref. 1)

2

=

.

eI>pp (W) P 1 - eI>

(W)

00 /<I>. (w)

/2

l.0

=

--~---<I> •• (w) eI> (w) l.l. 00

A second possibility would be

2

P = 1

-eI>nn(W)

eI>

(w)

00

The two correlations are plbtted in Fig.6 for a data base similar to that of the 0 preview case in this report. The P12 plot shows higher val\les in gener al than the p2 definition. The same effect could be expected to hold for the other preview cases as weil.

The describing functions for the 0,1,2 preview cases averaged over

all subjects are illustrated in Fig. 7. Inter-subject variab~lity was res-ponsible for rather large standard deviations and has blurred same detail

but the gross effects of increasing preview are apparent. Superimposed on the 0 preview case (Fig. 7a) is the average describing function and

correla-tion found in Ref. 1 in a~ experimental situation modelled by Fig. la with

identical input spectra and aircraft dynamics. The overall system gain in

the present experiment was 2.78 times that of Ref. land to correct for this effect? the latter amplitude data have been divided by 2.78 before being plotted in ~ig. 7a. The similarity of the amplitude and phase plots of the two experiments indicates th at the subjects used in this study comprised of

a fairly normal group. The similarity of the correlation plots indicates that

the simplification of the experimental situation as discussed in chapter 2

was valid, and therefore that the equatio~ used in the calculation of yp(W) :

<I>. (w)

yp(W) = ~l.o _ _

<1>. (w)

l.e

was also valid. If the correlation values of the~ preview case in this experiment had been substantially lower, this would have meant that the

sub-jects utilized inputs other than the displayed error to a much greater extent

than allowed by hypothesizing an experimental situation as shown in Fig. lb.

4.1 Smal 1 Preview Cases - Pilot Model Curve-Fits

Af ter McRuer et al (Ref

.3)

a model described as the "Extended Cross over Model" was fitted to the data. Since the measurement frequencies span the region of the neuromuscular resonance, the third order nepromuscular term was included to form

-j (WT-+a/W)

A computer program was written (see Appendix B for listing and details) to adjust the 8 parameters so as to minimize the RMS difference between thetheoretical curve and the data points. Curve fits were attempted for the small previews

(0,1,2) only, because the •. describing functions for the large previews (4,8) were

of vastly different form than any that could be produced by simply adjusting

parameters of this model. Emphasis was placed on fitting the model to individual

subjects because large systematic inter-subject variability could be expected to

blur detail. Note, for example, the different forms of the describing function

at 0 preview exhibited by subjects 1 and 2 in Figures 8a and 8b respectively.

The parameters for the 0,1;2 preview cases are presented in Table 3

for each subject and the describing functions found by averaging the original

amplitude and phase data over the entire test group. It is noteworthy that the

lag term associated with the neuromuscuiar system is absent in many cases, espec-ially the 0 preview cases. Correspondingly, the time delay is larger to make

up the difference in overall phase lag. In each case where this term is missing,

the computer started the iterations with a value of T

Nl of D.09 seconds and drove

this term to such a small value as to be insignificant in the pilot model. The

routine was then repeated initializing this val~e to zero and a significant

improvement in fit was achieved as evidenced by a lower fit parameter.

The

a

parameter , the approximation for the very low frequency

lag-lead was very small, in most cases insignificant and unreliable considering that

the lowest frequency at which amplitude and phase information was available was

0.32 rad./sec. Similarly at the opposite end of the spectrum, any lead, lag, or resonance terms beyond about 25 rad./sec. were in question since the highest measurement frequency was 21.8 radians/second. The plots of the three describing

functions along'with their associated correlationplots for the 0,1,2 preview

cases are shown in Figures 8,9 and 10. It was found that these subjects effectively

spanned the range of characteristics found for the test group.

The curve that was fitted to the data of subject 1 at 0 preview is of

special interest in that the derived value of damping factor was very sensitive

to changes in the weighting scheme employed by the computer program. It was found that if the relativeweight applied to the experimenta~data was inversely

prç:>portional to t4eir standard deviatiol::\s, the damping factor was much lower than

that show~ in Table 3. (This scheme however gave poor results for most of the

other graphs and was dropped in favour of the one outlined in Appendix B).

Indeed, the large standard deviations in amplitude and phase of subject 1 near

resonance were due not so much to changes in damping factor betwee:q runs but to changes in resonant frequency.

Before proceeding to the describing functions with preview, one more point should be raised. At 0 preview all subjects exhibited what appears to be a double resonance with a separation of about 2.5 radians/second instead of a

single neuromuscular resonance. More detailed analysis is required but this is

beyond the scope of the present report.

With preview, the describing functions changed many of their

character-istics. The describing functions of the 0,1,2 preview cases - the ones to which

curves were fitted - are illustrated in Fig.

7

for overall averages and in

Figures 8, 9 and 10 for three representative subjects. The decreases in phase

lag with increasing preview exhibited in these figures are obvious and Table 3

preview to reduce their time delay by an equal amount, but the next 0.1 seconds

presented was less fully utilized with the resu~t that even with 0.2 seconds pre=

view there still persisted a residual time delay, albeit smalle The break frequ=

ency l/T

L of the lead term may be expected to increase with increasing preview

as more of the lead is generated for the pilot but this is not supported by the

data. The ga in factor increases, however, indicating that subjects are more

confident in their control of the situation with the preview display. The reso

-nant frequency due to the neuromuscular system shifts in each case to a higher

value with larger preview, in most cases exceeding the highest measurement

fre-quency. The damping factors as well as the resonant frequencies are unreliable

in the 2 preview case as previously noted, but the 0.1 second preview resonance

is sharper in general than that of the 0 preview case.

In order to present graphically the alteration to the 0 preview

des-cribing function

Ypo(w)

caused by preview, a transfer function was defined

Y./

(w) ~ ~ 0

Ypi(w)

Ypo(w)

where i represents the preview condition. Thus the modulus of Y./

(w)

represents

~ 0

the amplitude at each frequency and the phase represents the phase 2difference

between the i th preview case and 0 preview. A correlation change 6p was also

defined 6p2

=

Pi2- po2. Figure 11 presents these changes as solid points for

·the comparison of the 2 and 0 preview cases and as open points for the comparison

of the 1 and 0 preview cases. Curve fitting to Yl/O(w) was complicated by the

aforementioned resonance shifts and has not been done. In the y

2/ 0

(w)

case the

second resonance was effectively out the measurement range simplifying curve

fitting. Negative time delays and anti-resonances were fitted and the parameters

are given in Table 2. The assumed form for y

2/0

(w)

was 2

Y2/0(W)

=

Kv.

jWT

v

((~:)

+

2'v

j

_W

₊

_{1 )}

Caution should be exercized in interpreting the data of Table 2. Al=

though the anti-resonances corresponded closely to the resonance parameters of

the 0 preview cases in Table 3, the amplitude factor K and negative time delay

v

T are very sensitive to changes in break frequencies of lead and lag terms which

v

have been ignored. The consistently small value of T can be explained in part

v

by the presence of a lag term attributable to the neuromuscular system in the 2

preview case data whose effect has not heen considered in the simplified model

of y

2/0

(w

).

402 Large Preview Cases

For previews ~arge compared to typical human reaction times (such as

previews of 0.4 and 0.8 seconds) the describing function found varied much more

allong subjects than for small previews. Intra-subject variability was also

larger but not as pronounced as inter-subject variability. The describing func~

tions for the three subjects (numbers 1,3,6) of Figs. 12 and 13 indicate the

however, the graph for subject

3

in Fig. 12 represents only

5

of his

8

tracking runs - the others having a describing function similar to that of subject

6.

The graph representing subject

3

in Fig.

13

is the result of

4

runs - again the rest looking more like those of subject

6

but with larger stanàard deviations.

As the correlation plots show, the fit of the linear describing function at the high end of the frequency spectrum (beyond aoout

8

radians/ second) is poor even though the output power spectral density of the subjects was not much diff -erent from the small preview cases. There may have existed a time variation in control strategy such th at the phase angles at high frequencies changed drastically with time.

One common feature of all the describing functions for these previews is a rapid rise in amplitude in the frequency region roughly between 0.3 and

4

radJsec. where most of the input power is concentrated. Only one subject (subject

6) had a describing function which was a logical extrapolation of the 2 preview case in that the negative phase lag at low frequencies increased, with the mid frequencies characterized by a sma~l phase lag at

4

preview and a small negative lag at

8

preview. The variability of his data was very low, compared to all other subjects. The majority of all the describing functions calculated for the large preview cases were similar in general form to those of subject

6,

b,ut showed larger fluctuations in amplitude and phase (as a function of frequency) and had much larger standard deviations, as noted.

The control strategies, determined independently byeach subject during __ the training period~ may explain the rapid rise in amplitude which is the one

common feature. All subjects reported that they "followed the waves in" (from the right hand side of the screen to the tracking point). They generally focusseQ their attention about 1.5 to 2 inches (no measurements were taken) to the right of the tracking point, which corresponds in time to 0.3 to 0.4 seconds "upstream"_

of the tracking point. Any high frequency disturbances were followed visually right to the tracking point in order that these rapid changes in input could be tracked accurately. High frequency in this case means any wave with apparent period less than twice the time interval of 0.3 to 0.4 seconds, i.e., greater than about

8

rad./sec. As aresult, the low frequencies were tracked somewhat less accurately than the mid-range.

4.3

Tracking Scores

The tracking scores achieved byeach subject at each preview are pre -sented in Fig. 18 and it is evident that previewallows the pilot to reduce his tracking score drastically. The abnormally high amplitude of the describing function of subject 1 correlates with his lower-than-average scores, as does the small relative phase angle of subject

6.

5.

CONCLUSIONS

1) Tracking accuracy is improved (tracking scores reduced) tremendously by dis-playing to the pilot a preview of the input function during a tracking run. 2) For previews between 0 and 0.8 seconds, the low frequency amPlitude of the

· I

3)

The resonant frequency attributed to the neuromuscular system increases monotonically with preview between 0 and 0.2 seconds, and probably beyond this range.

4)

Presenting preview to a pilot al~ows him to compensate for his time delay, and he makes full use of the first tenth of a second of preview presented but does not make full use of the second tenth of a seconde

5)

The lead term TL in the extended crossover pilot model does not appear to be significantly altered by the 0.1 and 0.2 second preview displays.

6) Evidence exists to suggest that the neuromuscular response is doubly peaked in a 0 preview situation.

7) Large scale changes in pilot describing functions occur in the region between 0.2 and 0.4 seconds and additional investigation in this region

1. Reid, L. D. 2. Frostell, G. E. 3. McRuer, D. Graham, D. Krendal, E. Reisener,

w.

Jr. ,

4.

Philbrick & Nexus Research

REFERENCES

"The Measurement of Human Pilot Dynamics in a Pursui t-plus-Disturbance Tracking Task". urIAS Report No. 138, University of Toronto, April,

1969.

-"A Comparison of Pilot Describing Fqnction Measurement Techniques". urIAS Tecll. Note. No. 167, University of Toronto, October,1971. "Human Pilot Dynamics in Compensatory Systerns", AFFDL-TR-65.-15, 1965.

Applications Manual for Operational Amplifiers, 1968.

APPENDIX A: PULSE-WIDTH MODULATION

In order to record very low frequency type tape deck, a modulation system is required signal is within the bandpass of the recorder. was chosen because of:

signals on a home entertainment to ensure th at the recorded Pulse-width modulation (PWM)

1) Insensitivity to tape wow and flutter as compared to

amplitude modulation

(AM).

2) Insensitivity to changes in tape - tapehead contact

as compared to AM.

3) Simplicity of modulating and demodulating the tape

as compared to frequency modulation (FM).

Other than the TR-48 analogue computer used for signal processing,the only instrument required is a signal generator with synchronized square and tri-angular wave outputs (Wavetek 116 or equivalent). The circuit diagram of Fig. 14 shows part of the computer patching used during the recording process. The information signal is summed with the triangular wave output of the signal generator set of 600 Hz and 10 volts peak-to-peak. This frequency gave the best square wave playback response from the tape deck. Also added in is a De voltage to allow setting the modulation to zero (pulse "on" time equals pulse "off" time) for a zero inforrr..ation signal. See Fig. 16a for a typical

summing amplifier. output waveform. This output controls a precision gate (a

modified version of the one described in Ref. 4) through aresistor chosen

to draw maximum current from the amplifier without overloading it. This ensures

fast gate switching. The operation of the gate is simple: The -lOV at point

"a" is converted to + 10V at point "b" for any negative voltage at point "c". For any positive voltage at point "c" greater than about 0.7V, the gate is

turned "off" and point "b" is 0 volts independent of point "a". In this fashion

the instantaneous information voltage determines the time during the cycle at wqich the gate is turned on and off. The signal is now a pulse whose dura-tion depends linearly on the informadura-tion signal voltage, as shown in Fig.16b. Before recording on tape, however, the signal must be made symmetric with respect

to the zero axis - in other words its De content must be zero when integrated

over one cycle. This is achieved by multiplying the pulse by a synchronized

square wave whose DC level is also zero and whose amplitude in this case is ~

10 volts. The output of the multiplier (shown in Fig. 16c) is in this case

divided by ten before being passed to the tape deck. Recording level is adjusted by monitoring the tape playback signal with an oscilloscope, and is set high

enough to saturate the tape but just low enough to preserve De stability of the pulses on playback. By similarly monitoring the recording signal, the amplitude of the information signal is set to ensure that 100% modulation is never

exceeded. The computer patching used during playback is shown in Fig. 15.

First, wave shaping is carried out b,efore demodulation. The output of the tape

deck is summed with a biasing voltage and is again fed into a precision gate

via the same small resistor used during recording. This bias is set to abo~t

+ 2.5 volts to achieve a clean voltage change free of spikes and transients at the output of the amplifier in the region around zero volts (Fig. 17a). The output of the gate is again a pulse whose amplitude is very stabie and whose duration varies directly as that of the original pulse from the tape (Fig.l7b).

Filtering of the signal complet es the demodulation. In this experiment, the

filters employed ai-so served to shape the input' signal power spectrum and second

order filters with natural frequencies of 6 and 11 radians/second and damping

APPENDIX B:

The computer program listed here was written in order to speed up the process of fitting the extended crossover pilot model to experimentally determined amplitude and phase date. It duplicates human decisions regarding the goodness of fit of the model to the data. The inputs to the program are average amplitude

ani average phase values at

35

frequency points along with their standard devia-tions and initial values of the

8

model parameters, selectable by the operator. The program as listed was executed on an IBM System 1~30 with an 1132 printer and a 1627 plot~er. Input data were read in on punched cards by a separate program and left in common core, and during execution, all but 70 of the

8poo

available core locations were used.

The heart of the program is the subroutine MS which calculates either the theoretica~ data points with the model parameters at hand, or the change in the appropriate goodness-of-fit criterion for a given change in one of the model parameters. The main features of the program are outlined below.

The mainline program first applies a condition to the experimental data at the option of the operator (see Itvariance normalizationlt

) in order to weight

each amplitude and phase value according to a Itdeviation", the inverse of which

is the weighting factor. The options are:

1)

The deviation is set equal to the standard deviation for that point except where the standard deviation exceeds the

equiva-lent of 0.1 inches on the original graph.

2) The deviation is set equal to the equivalent of 0.1 inches for all data points.

The vertical scale values of the graph were originally 1 inch per decade in ampli-tude and 0.8 inches per 100 degrees in phase angle, and the distance represented by the standard deviation of the amplitude points was set at ~og(~ + rr) - logrr

where ~ and rr are the experimental average and standard deviation for that point. Option 1 was normally used but option 2 was available for curve-fitting to data with undefined standard deviations - as for example a single record of one trackingrun. Option 1 was arrived at aft er considerable experimentation with various weighting schemes and was found to give the most visually pleasing re -sults for the most data sets.

Af ter weighting the data points, the computer goes into a closed cycle starting at statement number

56

where'" the increment sizes are ini tialized to

10%

of model parameter value and the theoretical curve calculated according to model parameters at ha~d. Subroutine MS is then called to evaluate the change in fit due the change in a parameter. The goodness-of-fit .tests actually used will be elaborated on later. During the first few cycles, the do-loop increment P in the subroutine decreases from 17 (a total of

3

amplitude and

3

phase data points are campared) to 1 (all data points contribute to the relevant goodness-of-fit test) and retains this value till the program terminates. This allows the gross features of the experimental data to be approximate,d. quickly by the computer and contributes to decisive results.

The goodness-of-fit test in subroutine MS is conducted as follows. Each experimental point is compared to its theoretical coun,terpart acc0rding to the model parameters at hand, to find the modulus of the difference between the two

divided by the previously adopted deviation. These data are treated as 2 sets of numbers (35 for amplitude and 35 for phase in the steady-state condition of the previously defined cycle). The RMS values of the two sets is calculated

(SMS1, SMS2) followed by a calculation of the RMS deviations of the sets about their SMSl or SMS2 values (TV1, TSM). All model parameters which affect the shape of the theoretical curves use in their goodness-of-fit test the TV1 or TSM or both values, leav.ing only the pure gain term K which is tested for its SMSl value. Those terms affecting the shape of the amplitude curve only or the phase curve only will have tested only their TV1 or TSM values respectively to determine whether an improvement has occurred in fit as a result of incre-menting th at parameter.

In order to sharten execution time which is typically 10 minutes, the program retains a memory of the direction in which a parameter was incremented the previous time in order to effect an improvement in fit. Thus the parameter is incremented in the same direction on the subsequent test. Whenever a para-meter is located close to a local minimum of its appropriate goodness-of-fit function and incrementing it in both directions yields a poorer fit, the size of the increment for that parameter is decreased by a factor of 0.4. The program terminates when an increment of 0.0125% applied to any model parameter will

not produce an improvement of more than 0.01% in the appropriate goodness-of-fit function, except for the gain term Kwhere an improvement of more than 0.1% is required. Another program is then cal led which reads in more data.

CURVE-F I T MA.l NL! NE PROGRAM

REA\.. K. • P"IAX,PMU\..T.11'12,!).14.",lb,I7.lti DI"IENSJON NII101.UI)~I.XVZIZ451

COM1J.OI'II Nl,XVZ,SITE,TR,rSITV,UIP1l80

SWITCH 0 P\..OTS CURVE A .... VytlolE SWITCH I SUPPRESSES AU P\..OTTING

VERS ION A 7

SwITCH 5 CAUS IN PARAMETER VA\..UES Ta RI::P\..ACE THOSE 1/111 THE "'~O(iRAM SWITCH 8 FOM DISHEGARDING EHROR BAlts

SWITCH U FOIt FORCEO EXI T

SWJTCH 12 WIL\.. Rf START PROGRA'" fROM SCRATCH IFIN1161-101011 810,809,810 809 PI180_lP!0./3.14!59 TH_Zl,764/69. "'X-l1 5-0.1000001 CALL OATSWI8,1 ... 1

DIMENSION CONVERSION FROM 50 TO )S

00808 1-11140 J-1/3!1.01 L_1/4.1 + 1 104_1+50 MO_I+150 N_l!l*J + I UILI-IL*2-11*TH XVZII '-XVIINI IFIJI 800.800,808 800 XVZIII-XVZIII*XYZIII VARIANCE NORMALIZATION GO Ta te07 ,8011 ol'"

801 XI-ALOGll.+XYZI MIISORT I XYI t I111

Irlxz-0.Z31 80Z.80J,80J 801 XYIIMI-xl GO TO 804 80J XVZIM)_0.23 804 IFIXVZIMOI-12.!l1 808.808.806 806 xVIIMOI-12.5 GO Ta 808 807 XVZIMI-O,23 XVZIMOh12.!I 808 CONTINUE AMIN_7.0 AMUL T- 0.4)429448 PMAX-6.!I PMU\.. T -0.008

CAL\.. SCALFI 1.01-1.0,!I.0.0.0 I

CAU DATSWll,INI GO TO 57 1)1) CONTINUE J-O WRlTEIltll01 57 LX-Z "41-1 MZ-l MJ-l Mlo_I 1041)-1 /146-1 M7-1 1048-1 NTT-Nl(1) K.-0.6 T-O.IZ "-O.OZ TL-3.365 Tr_o.!lO TrlI-0.091 ZN-O.1 WN_18. XLM_17.09 J-O N-)5 CALL OATSWI5.MPI GO TO IZOl, '61oMP 201 wRITE 11.1041 PAGE Z

WRITEII,IOll ",.T.A,TL,TI,TN.WN,ZN

READ16.1071 KIT.A.TL.T1.TN,WN.ZH 56 U_I 12-1 U-I 14_1 15-1 U-I 17-4 a-I

CALL NHOMSIK.. T.A .TL, T r. TK ,TMI TN ,WN.ZN ,M.F, SO.MX .V.Dlt.OV .H.J, 1. I LLO-140

Jl CAL.L OATSWlll ,KLMI GO TO 1~0.121. K.LM 32 CALL OATSWIU,INGI GO TC 15~.40ll.ING 401 TlI-l.1T1 TLL-l./T\.. TNN_l.ITN CALL OATS'~lltJSUPJ CALL OATSWIO,LMI GO TO (8).8~I,LM A3 GO TO 185.8411 JSUP !4 00 3S l_l,LLO,LX 1W-1+LX-l IP.-0.0201/11"''''0.991 + 0.0101/11.,,-139.991 -0.OZOl/llw-l.1191 ';_1 ''''.2.'''1. I*TH/".

, ASE' _I_I"'*T+A/." I +AT A:o. 1 TL*. I "AT AN I T I.W I

... ATANI TN.'"n-ATANI2*ZN.W/WN/I 1.-IW/WH 1**2' 11·I8U./3.14J.59 IFC"'-WNI 52152,5) S3 F ASEF-FIISEF-180.

"

Cf Cf CF CF

·

CF

•

37 CF

•

"

"

1 CF • CF

•

CF 10 " 11 " 12 CF 13 CF I . CF " CF " CF 17 ,e CF U

,.

CF

,.

CF 20 8' CF 21 3 CF 22 CF '3 CF 2. CF Z> CF

••

CF

.,

CF zo CF

••

Cf '0 Cf 3l CF 3. CF 33 CF

,.

CF " CF 3. Cf 37 CF 38 CF 3. CF '0 CF

.,

CF

..

CF

.,

CF

..

CF

••

CF

••

CF

.,

CF

..

CF

..

'00 CF '0 .01 CF

"

CF " '0 CF "

••

CF

,.

CF " CF

,.

CF " CF

,.

CF

,.

CF .0 CF b! CF

••

92 CF .3 .3 CF

••

010 CF

.,

CF •• CF 67

..

CF

.-

••

CF

••

101 Cf 10 CF n 10. CF 7' 107 CF 13 108 Cf 7. 110 CF 70 111 CF

,.

Cf 11 CF

,.

CF 7. CF .0 CF Ol CF

••

CF _" CF

..

CF

.,

CF

••

CF

.,

CF

..

CF OY CF .0 CF " CF

••

CF .3 Cf •• CF

.,

CF

••

CF " CF

••

CF

••

CF 100 CF 101 CF 10' CF 103 CF 10. Cf 10. CF 10. CF 101 CF loe CF 10' CF 110 CF 111 CF 112 CF 113 CF u. CF 11. PAGE

,

CONT INUE " 11.

Xl- PMAx+F ASEF.PMUL T-O. A-O. 8.NTT CF 117

YZ_Z .0+\04. CF 11. CAL\.. FPLOTIIP,XZ.YII CF 11' IF(I-701 35.37,]5 CF ILO wRIlEn.1071 FASH.", CF 121 CONT INUE " " 2 00 36 l_l.LLO,LX CF IL' lW-I +Lx- l CF 12'

IP--O.020111 IW-U.991 + u.OlOl/llw-l)9.9'111 -0 .020111 h~-I.Y'll I CF 125 "'_11 W*Z.-I. I *TH/ •• CF 120 AMPP -K.*SQRT II TL**2*.", •• 2+1. 11 1 T 1*.2*w.*2+1.1/ CF 127 I TN •• 2*.",.*Z+I. 111 11. - I W/WH I •• 21.*Z+ I 2*ZN* ... /WN 1 •• 2 I I CF "8 XZ- AMIN+ALOGIZ.*AMPPI*AMULT CF

".

Yz-z.O+w/ •• CF "0 CALL FPLOT II P .xZ,VZ I CF 13l IFtJ-701 36,38,)6 CF 132 wRIfEI].1071 .... ~PP.W CF 133 CONTINUE CF

".

CAL\.. FPLOTII,5.0,O.01 CF

'"

GO Ta 19Z,JI,LX CF 13. F-' CF 137

CALL NHDMS IK.T .A.TL,T I, TK,TM.TN .WH .ZN,M8. F .1.MX ,v .Olt.OY,N.J, 181 CF 138

• -F CF ".

'-TL CF "0

CALL NHOMSI K. T ,A. TL. TI. TK. TM, TH .'0111'11. ZN .M1 • FIJI .MX ,v ,Olt,OV.N.J, 1 1) CF

'"'

TL-F CF ,"2

J-J+l CF ,.,

F-TI CF ,..

CALL Nl·mMS IK. T I A I TL. TI. TK.. TM. TN ,WN .ZN .MZ I '.21,MXIV,OXIOV .N.J .IZI CF 145

TI-F CF ,..

'_TN CF ,.,

CALL NHDMSIK, T ,A ,TL.T 1 .TK.. TH.TN.WN.ZH ,104). F .ZJ.MX .V.OX.OY,N.J, I)) CF h '

T/II_F CF

'"

F-ZN CF " 0

CALL ~HDMS IK.T ... T\...T I, TK ,TM,TN.'liN.ZN IM4. F .11.MX.V ,OX,OY.N IJ. 141 CF 1>1

IN-F CF

".

F-WN CF

'" CALL NHOMSIK.IT,AITL.TI,TK.,TMITN.WN.ZN,M~, F .16 .MX.y.OX.ov ,NIJ. J 5) CF

'"

WH-' CF

'"

F-T CF

".

CALL NHOMS I"" T. AITL.T I. TK.. TM.TH,WNIZN 11'46, F 12 .MX .Y.OX .0'1 .''IIJ .161 CF "7

T _F CF ,,_

F-' CF

,..

CALL HHDMSIK.T tI. .TL.T I. TK.TM,TN ,WN .ZN .1'11, F.J .MX,Y.OX.ov IN.J.ll J CF ,.0

• _F CF '" MXI-MX CF '" XL,,-xLM/Z. CF 103 I F 111+IZ+1 3+14+ 15"16+17+18"'0.0100 I 54.54.S00 <F

".

IFIXLM-l.011 )l,~OI.~OI CF '" MX_XLM CF '" IFIMX-MXlI56,JI.)1 CF

,.,

WRfTEI3.IU) CF

".

WRIfE13.1081 TE,TV CF '" LX-I CF 170 TII-l./TI CF 171 TLL-lt/TL CF 172 TNN-l./TN CF 113 PAGE

.

WRITEI),IOl, K.. T .A.TL.T 1 .TN ._H,ZN CF 17. WRITE13,1011 CF 175

WRITEIJ.I071 IC:.T .A. TLL,T 11 ,TNN.WNIIN CF 17'

GO TO 83 CF 111

GO TO 1810.9)) • JSUP CF 17. CALL FPLOTIl.13.0.0.01 CF 17.

1'111181-] CF 180

CALL OATSWI lO,NRAT) CF 101

GO TO 194.95 I .NRA T CF 18.

N118 '_4 CF I.'

CALL LINKI NHORI , CF 18' FORMAT! lx, 'K' ,9X. 'T' .9X.'A' .7X, '1/TL' .6X,'1/T I' .6lt. CF

,.,

'l/TN' .7X.'WN' .tllt, 'ZN'I CF U.

FORMAT 1 'IC., T ,A,TL.T t, TN.WNtIN IN FlO' I CF 187 FORMATI8FI0.51 CF lO. FORMAT!I 30X,'FINA\.. PLOT',ZOlt,'E-'.F8.5 120X ,'v_',Fe.s , CF

,.,

FORMAT I'RESTART 'I CF "0 FQRMATIIZX.'FORCED E'xfT'l CF

'"

END CF

CURVE-FIT SUBIotOUTJNE )015

ONE WORO INTEGERS

SUP.Ç(OUTINE NHOMS IKoTt80TLoTloTK.T"".THoWNoINoMo V .L.P.O.UP. DOoNoJ.NOI

REl.L K,MSlI351.KK,ND

l"nEGER E.P

DIMENSION N1110 I .... llS I.X 1351 ,VI n I .Ox 1351,0'1' 1)51 ,F.5EI35,

DI~ENSION TlI3~I.TlI..13510C"'RI21

DIMENSIOH OPI35I,QIl51 .OCH") .AMPLI351 . 'ASELl35 I ,A,..P 1351 CO"'MON Nl. X .ox, V .OY ,AMPL .'ASCL, T lL.S' TE. TR ,T$. Tv.", ,p I UlO

KK_K*I{ Ir1L"401 5.,54.55 55 DO 52 1_t.NIP TI"-TI.w 111 TLW_TL.W I11 TNW-TN.W 1II WWN-W III.W III/WN/WH

AMPL III_KK.I TL\r,·*TLW+l.I/IT lW.T IW+l"1 I TNW*TNW+l. 1/IIl,"W\o!N I * I lt-wWN I + •• *lN*ZN*",.,1II1

TlLI 11.''',wll 1*1+8/WIIII+Af ... 1\I I TLW'-AU,HITNWI-... UNITIWII.PJ180 F"'SELC IJ.TlUII- , ... TANI2.*ZN.WIII/WN/, 1,"",WNIII*PI UU IFIWIII-II'NI51.51.53 53 F"'SELIII-F"'SELIII-180. 51 "''''PI I I.AMPLlII TlIJl-nLII! ''''SE 1 I 1_' "'SEL 1 J I 52 CONT INUE GO Ta 92 54 OV-S.V.NO KX-l IFIVI 69,66169 69 GefOI70.1l1.M 70 VN.Y+OV GO TO 72 71 VN·Y-OV 72 IFIL-201 77,77.13 13 00 76 l-l,N,P VW-V·WIII VNw·VN.WCII

.... 1 ... T ... NIVWI ... T ... HIVNWI I.PI180 lFIL-301 74,74.75

74 ... MPI I I· ... MPLI I '.IVW.VW+l.I/IVNW.VHW+l.1

Tllll·TIL.III+ ... FASEe! I.F.SELII)+A GO TO 76 75 ... MPII)· ... MPLII).IVNW.VNW+l.I/lVW.VW+l.1 TlIII·Tlllll-'" F"'SEIII-F"'SELfII-... 76 CONT INUE E-l GO TO 92 71 IFll-I01 85,85,7e 78 IFIL-UI fIt,81.79 79 WNN.VN ZNN·ZN GO TO 82 81 WNN.WN ZNN-VN e2 WN2.WN-WN WNN2·wNN·WNN E_' 00 e_ l.l,N,P WZ-WII I ·wlll WWNZ .W2/WN2 WWNH2·W2/wNN2 P"'GE 2 LUO I L"'G RESO ... "CE "'MPC I 1 .... MPll I J.IIII-WWN21.11.-WWN21+_ •• ZN.ZN.WWN211 Ill.-'"nmNZ J .1 1.-'W,",NN2 1+" •• l.NN*l.NN*,,\ojNN2 I

F "'SE 1 I J _TllIl I-U"'N 12 •• 1.N .... W! lIllIINNI C 1. -W'IIINN211*P 1180

IFI~III-WNNI e.I84,6] 83 FASEIII.FASEIJI-1801 84 CONT INUE GO TO 92 85 IFIL-21 86,88.90 86 C .VH.VN/V/V 00 87 l-l.N,P AMPIII· ... MPLIII.C 87 CONTINUE E-' GO TO 92 88 C.IVN-VI.PI UlO 00 89 l.l,HIP .... -wlll·C F"'SEIII_F"'SEIIII+A TlIII·Tlllll+'" 89 CaNT INUE E_' GO TO 92 90 c.eVN-YI.PI180 DO 91 l.l,N.P ... ·-C/WII. ''''SE 111-FASElCII+A T 1111.TILlII+ ... 91 CONTINUE E-' 92 T ... SI-0. TMSZ·O. TVI-O, TV2·0. DO 95 l.l.N,P

MSllll .... SSI ... LOGI ... MPIIIIXIIIII.O.S/Oxll J

95 T'4S1.T'4S1+1Io4S1111 •• 2 Sp.lSl-saRT I T/oISII/N IFIL-Il 93.93.94 93 CMRIKXI.t.OOl-TRISMSl IFIC~RIKXII 9.,94,.9 9. 00 _Z l-l,N.P VI-C S~Sl-"'Sllll I**Z 42 TVI.TV1+VI 0061 l.l,NIP \4511 J }-AtlSIYIII-FASEC III/OYCI I 61 T'4S2-T"'52."'51111"2 G"'IH DElAV INVERS ION HS 1 MS

,

MS

,

MS • MS

•

MS

•

MS 7 MS • M,

•

MS 10 MS 11 MS 12 MS I I MS

..

MS 1> MS 16 MS 17 M' 18 MS _I' MS 20 MS 21 M, 22 MS

"

MS 2' MS l> MS 26 MS 27 MS 2. MS 29 MS '0 M' II MS

"

MS

"

MS

,.

MS l> MS

,.

MS " HS

"

MS ,. MS .0 MS '1 MS

.,

MS

.,

MS

..

MS

••

HS

..

MS

.,

MS

••

MS

••

MS '0 MS >l MS

"

MS S> MS ,. MS

..

MS

..

HS " MS 58 MS 59 MS 60 MS 61 MS U MS 6l MS 6. MS U MS 66 MS 67 MS 611 MS 69 MS 70 MS Tl MS 72 MS Tl MS 74 MS 75 M$ 76 MS 77 MS 71 HS 79 MS 8Q HS 81 MS lil MS 8l MS 11 • MS U "'s 86 MI 87 MS 118 MS 89 MS 9Q MS '11 MS 9l MS IJl MS 9_ MS 'I~ HS "'6 MS 91 MS 98 MS 99 MS 100 MS 101 MS lOl MS lU3 MS 10_ MS 105 MS 106 MS 107 MS lUS M$ 109 MS 110 MS 111 MS 112 HS 113 HS 114 MS 11~ P"'GE

,

SMS2 .SQRT I T,",S21/N MS 116 00 62 l ·l,N .P MS 117 VZ-I SMS2-"'SIIIII*.2 MS IlO 6' TV2-TV2+V2 MS 11' TVI·SORTITVII/N MS 110 TS"'·SORTITVZI/N MS 121 Tv M .TVl+TS/14 MS 122 IFll-40J .5 •• 5 •• 4 MS 123

..

1.0.1 + 0.7.l MS 12' IFf 1-21 48.46 •• 7 MS 125 '6 C:OCR I KX l . I . 0001-15/T5)o1 HS 12' IFICMRIKXII .8.48 •• 9 MS 127

.,

CMRI KX l.l.0001-TVITVM MS 12. IFCC,..RIKlCI J 48.48,49 MS 12.

•

•

CONTINUE MS 130 GO TO 130,32,3'u361.[ MS 131 '0 DO 31 l·l.N.P MS 1 " A1I4PlIll_AMPIII MS 1 " FASElCII.F"'SEIII MS H4 31 Tllfil-TlIII MS 13. GO TO It_ MS 1,. 32 DO 3l l-l,N.P MS 137 A"'PLI I l .... 1I4PII 1 MS 13.

"

FASEIIII·FASEIII MS 139 GO TO •• MS 140

,.

00 35 I·I,N.P MS h l

,.

... Pli I I .... MPIII MS 142 GO TO 44 MS 10'

,.

DO 31 l·l,NIP MS 1" FASELIII·F"'SEIII MS 1" ]1 H l I l l · T l I l i MS 146 •• TV-TVM MS 147 TS·TSM MS h l TR-SMSI MS _I" l(·SMSl+SMS2 MS .150 V.VN MS UI

..

RETURN /ltS 152 •• GO TO 156.571 • KX MS 153

..

KX·2 MS U-M-3-M MS 155 JFIJ-201 6'''65.65 MS 1~6 57 CONT INUf MS 157 NO·NO·0.6 MS 158 " I CMR Ill-(MR 1211 2).23.59 MS 159 23 104_'_1'4 MS 160 GO TO 59 MS 161

..

NO·NO·0.6 M' 162 M-3-M MS 163 GO TO 59 M5 16_ 66 NO·O.OOI MS 1 " GO TO 59 MS 166 END MS 167

Tabla 1

PREVIEW PRESENTATION SEQUENCES

DAY

1

2 3 4

5

6 7

8

9 10 11 12 13 14 15 16 17 18 19 20

SUBJECT

1

0

4 1 8

2

1 0

4

2

8

0

4

8

2

1

8

0 4 1

2

2

1

2

0

4

8

8

4 0

2

1

4 1 8 0 2

2

8

4 0 1

3

4 1

8

0

2

1 2

4 0 8

2

4 0 1 8

2 1 4

8

0

4

4 1

0

8

2

4 1 0

2

8

0

2

1

8

4

1 8 0

4 2

5

4 1

0

2

8

2

4 8 1 0

8

4 0

2

1

8

0 1 2

4

6

8

4 1 2

0

2 8 0 1 4

2

4 8 1 0

8 2 0 4 1

EACH CELL REPRESENTS 2 TRACKING RUNS RECORDED FOR ANALYSIS

Tabla 2

Y2/o

(w)

MODEL PARAMETERS

SUBJECT Kv

Tv

_w"

~v

1

2-41

0-078

19·04

0-0276

2

1·24

0·014

16-36

0-266

3

1·42

0·078

17·52

0·0803

4

1·88

0·091

18·26

0·0520

Table

3

PILOT MODEL PARAMETERS

SUBJECT

K

T

oe

l/T

L

l/T

y

1/T

N1

WH

~",

NO PREVIEW

1

0-791 0-160 0-0

0-309 1-79

19-09 0-0350

2

0·786 0-212 0·066 0-299 1·23

17·19 0-1130

3

0·813 0·211 0·0

0·303 1·39

18·23 0·0933

4

0·582 0·185 0·0

0-265 1·66

18·46 0·0426

5

0 .. 551 0·203 0·0

0·318 1·98

15·45

,

0·1136

6

0-732 0·210 0-0

0·390 1-60

15·51 0·0710

ALL

0·444 0·219 0·077 0·234 2-09

18·33 0·0806

0-1 SECONDS PREVIEW

1

0·597 0·032 0·090 0·157 3-26

5-55 22-00 0·0349

2

0-815 0·117 0-103 0·274 1-47 12·04 19·80 0·0627

3

1-532 0-103 0·0

0-318 1·01 13·74 21·77 0-0520

4

0-752 0-078 0,0

0·299

1~92

_{15·18 21-57 0-0597}

5

0-593 0·100 0·042 0·281 2·32 10·68 18·17 0·1152

6

0·616 0·164 0-074 0·258 1·66

19·74 0·0228

ALL

0-812 0-104 0-0

0·240 1·41 19·34 20-67 0-0778

0·2 SECONDS PREVIEW

1

1·005 0·020 0·0

0·122 1·53 11·10 29·07 0-0030

2

1-579 0·061 0·0

0-744 3·45

4·85 19·34 0·0905

3

1·549 0·048 0·0

0·247 1·05

8·89 30·21 0·0202

4

1·085 0·046 0·0

0·233 1·48 21·31 34·42 0·0280

5

0·847 0·065 0·0

0·304 2·00 12-00 23-20 0-1930

6

0·852 0·038 0·050 0-222 2·01

8·88 22·13 0-0589

ALL

1·041 0·019 0-0

0.224 4·70

2·45 21·56 0·1175

net)

g(t)

iet)

eet

Yp(S)

..

'

v

o(tl,.

A(S)

L--.J~

met)

,"'~

,.

,.

, -

..

~

11' - '1'

Ys(S)

Model used for pursuit-plus-disturbance tracking.

Figure 1a

net)

iet)

_..

_~

_Yp{S)

_..

_'

vo(t) ..

_A(S)

met)

_...

, -"

,

..

,

,.

Compensatory model used to approxtmate pure pursuit tracking.

Figure 1b

Work Station Interior

Figure 2a

Postview Preview

iet}

.,---=:!~=--e

(

t)

zero re erence

a

Schematic view of the preview display at time t.

View at t+O.4 seconds

Time-lapse Display Presentation.

Input

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