A hybrid computer identification program has been developed which determines and displays those parameter values of a model of the compensatory control system that existed over the last fifteen seconds of operation. These values are up-dated every 0.05 sec so that a visual display of the parameters appears to be continuous. Presently, a closed loop crossover model is being used as the compensatory system model with the parameters K and tau displayed, however, any suitable model could be used in its place

Brabant, G.

Jackson, G. A.

English

NASA Technical Reports Server

5. A Hybrid Computer Program for the Visual Display 
of Compensatory System Model Parameters* 
GLENN A. JACKSON AND GERALD BRABANT 
Odkldnd University 
A hybrid computer identification program has been developed which determines and displays 
those parameter values of a model of the compensatory control system that existed over the 
last fifteen seconds of operation. These values are up-dated every 0.05 sec so that a visual 
display of the parameters appears to be continuous. Presently, a closed loop crossover model is 
being used as the compensatory system model with the parameters K and 7 displayed, however, 
any suitable model could be used in its place. 
INTRODUCTION 
The hydrid computer program discussed in this 
paper is the outgrowth of research that is dedi- 
cated to the development of a system that will 
meet two main specifications: 
(1) Develop a parameter identification method 
that will quickly and accurately identify the 
parameters of a compensatory control system 
model using only short Iengths of input-output 
data from the compensatory system under test. 
(2) Convert this method into an on-line system 
that will continuously display to the operator the 
average values of his associated compensatory 
system model. These average values should again 
be calculated over as short a time span as possi- 
ble so that the display will indicate to the operator 
essentially his present parameter state. The 
hybrid computer method developed, referred to 
as “hybrid parameter tracking” (ref. l), satisfies 
both of these specifications. 
Parameter identification via hybrid parameter 
tracking is accomplished by using short lengths of 
sampled input-output data from the compensa- 
tory system. These data, 1 1 5  sec in length, are 
used repetetively as the driving signals for a 
fast-time analog continuous parameter tracking 
* This research was supported by NASA contract 
NGR 23-054-003. 
system utilizing the crossover model (refs. 1 
and 2). Since only 5 to 10 iterations of these data 
are required for parameter convergence, and since 
each iteration requires only 0.05 sec, parameter 
identification is achieved less than half a second 
after the data are taken. In addition, once 
started, the program continues sampling the com- 
pensatory system input-output signals, while 
simultaneously iterating these data through the 
continuous parameter tracking system. 
The final result is that every 0.05 sec new values 
of the crossover model parameters, K and T, are 
calculated and displayed with each calculation 
using only the last 15 sec of compensatory system 
data. The visual display is thus a running record 
of the K and T values that existed over the last 
15 sec of operation. 
A BRIEF DESCRIPTION 
OF THE PROGRAM 
A simplified block diagram of the overall hybrid 
system is given in figure 1. In this figure only 
main signal lines are shown. All sense lines and 
control lines have been omitted for simplicity of 
presentation. 
The basic operation of the system is as follows: 
(1) The compensatory system input and out- 
put signals, r(t)  and c(t ) ,  are sampled via ADPs 
47 
https://ntrs.nasa.gov/search.jsp?R=19730001382 2020-03-17T07:16:24+00:00Z
48 SEVENTH CONFERENCE ON MANUAL CONTROL 
.1 i 
I 
Closed Low Compensatory c ( t )  
Control System 
ADC 1 
K value at end o f  
jth iteration jth fteratlon 
I t value a t  end of 
FIGURE 1.-Simplified block diagram 
of the identification system. 
1 and 2 at a rate of 20 samples/sec with the 
samples stored alternately in a 600 word table in 
digital core. 
(2) After 600 samples have been taken (300 
samples of both r ( t )  and c ( t ) ) ,  and before the 
301st samples of r( t )  and c(t) arrive, the sampled 
input and output values are fed via DAC’s 1 and 
2 into a fast-time analog continuous parameter 
tracking identification system. The analog time 
scale is 500 times normal time. At the end of this 
fast-time run three things occur: 
(a) The parameter values present at the end 
of the run are recorded using ADC’s 3 and 4. 
These values are stored so they can be analyzed 
later; sent to the visual display; and also used 
as initial conditions for the next fast-time 
analog iteration. 
(b) The 600 values in the input-output table 
are moved down two words in core. This eli- 
minates the first samples of r(t)  and c( t )  that 
were taken, and provides room for the next 
samples to be taken. In  addition, the gradient 
gains on the K and r integrators of the con- 
tinuous parameter tracking system are ad- 
justed. These gains are reduced systematically 
for five iterations and then recycled back to 
their initial values. This is done to ensure that 
a short length of high remnant data will not 
cause the continuous parameter tracking sys- 
tem to go unstable. 
(c) The system waits for the next samples of 
r( t )  and c( t )  to arrive. 
(3) At t =  15.05 sec the 301st samples of r(t)  
and c(t) are taken and placed in the 600 word 
table. The program returns immediately to (2) 
above, and the next fast-time identification run 
begins. 
The timing sequence used during a single period 
of operation is given in figure 2, with the timing 
intervals labeled to correspond to the word 
descriptions given above. In  this figure it is 
assumed that the system has been in operation 
for a t  least 15 see. Figure 3 presents the general 
functional level flow diagram of the system. 
TESTS IDENTIFYING A KNOWN 
CROSSOVER MODEL WITH 
STEP CHANGES I N  K AND T 
To check the accuracy and transient response 
of the identification method, three tests were run 
using a known model in place of the normal 
compensatory system. A crossover model with 
nominal values of Ko=3.8 and ~ ~ = 0 . 2 3 5  was 
used. The input signal r( t )  was pseudo random 
gaussian white noise passed through a third order 
low pass filter of the form l / (&~+l)~.  After the 
identification system was on-line, step changes 
T = 50 rnillisec. 
FIGURE 2.-Timing sequence for a single iteration. 
A HYBRID COMPUTER PROGRAM 49 
Set a11 po- 
tentiometers 
on EAI-680 
-4 
Put X and T 
integrators 
in IC and 
preset 0a) . counter 
I 
Initialize 
DACS 0 thru 
5 
I 
Put EAI-680 
i n  OP and 
!iQRMI.-SEC 
I 
I 
PAUSE FFFO: 
(1111 1111 
1111 moo) 
Push START to 
continue 
FIGURE 3.-Functional level flow chart for 
the hybrid parameter tracking program. 
in KO and 7 0  were made in the known model, and 
the resulting identified values were recorded. 
Figure 4 shows the response to a step change 
in KO from 3.8 to 4.8 with 7 0  held fixed at 0.235. 
The total transient response time is seen to be 
15 sec, which is the time it takes for the 600 word 
data table to be converted from “K = 3.8 data” 
to “K =4.8 data.” Figure 5 shows the response to 
a step change in ro from 0.235 to 0.285 with KO 
held fixed at 3.8. Again, the response time is 
15 sec, as expected. Figure 6 shows the system 
response to simultaneous step changes in both 
KO and roe The responses are similar to those 
found following individual step changes in KO 
or ro. It can be seen that in these particular cases, 
the determination of one parameter was relatively 
independent of the other. This is undoubtedly 
not always the case. 
TESTS ON HUMAN OPERATORS 
Following the tests on a known model, the 
hybrid parameter tracker was evaluated on a 
standard compensatory control system. The com- 
K 
- _____ 
FIQURE 4 . - r 0  held at 0.235 while KO is 
step changed between 3.8 and 4.8. 
I: 5.0 
L.0 
3.0 
9.0 
1.0 
0.0 
0.5 
I 0.4 0.3 
0.8 I 
- 
II 
1.0 
-1.0 
-3.0 
FlWR 5 - K. R l d  A t  1.8 mil. -, I s  S l f P  C M n c (  2% r* 2s 
FIQURE 5.--Ko held at 3.8 while TO is step 
changed between 0.235 and 0.285. 
FlW 6 - ‘i ld f. u. flultmw+li SW MmWi 1. wmm 3.4 I a.8. 7. .zs ld .m 
FIQURE &-KO and T~ are simultaneously step changed; 
KO between 3.8 and 4.8, TO between 0.235 and 0.285. 
50 SEVENTH CONFERENCE ON MANUAL CONTROL 
pensatory system used an arm movement control 
stick, a k / s  plant, and the same l / ( + ~ + l ) ~  filter
that was used on the known model. The main 
point of concern prior to the running of these 
tests was the distinct possibility that remnant 
would cause high variability in the K and r values 
being identified and displayed. Fortunately, thesp 
fears appear to have been unwarranbed, a t  least 
when data lengths of 15 sec are used. 
Figure 7 is a typical section of data found 
while identifying an untrained subject. Figure 8, 
on the other hand, is a similar section of data 
obtained from a subject who had some previous 
tracking experience. In  both cases the variability 
of K and r was not large enough to degrade the 
visual display by any significant amount. As 
-- 
+ +Lo- 
lnplt Sigl.1 %5- - - 
r(t) 1.5- 
0.5- 
-0.5- 
-1.5- 
-2.5- 
FIGURE 7.-Hybrid parameter identification 
of an untrained human operator. 
- 
I 10.0 
8.0 
0.4 
0.3 
0.2 
0.1 
0.0 
r(t) 1.5 
I lpyt  Slgl.1 2.5 
0.5 
-0.5 
-1.5 
-2.5 
I I 
FIGURE 8 .-Hybrid parameter identification 
of a trained human operator. 
expected, parameter variability was greater in 
the untrained case (ref. 3). 
CONCLUSIONS 
The hybrid parameter tracking identification 
method has been shown to accurately identify 
crossover model parameters using input-output 
data only 15 sec in length. Theoretical analysis 
indicates that with an input filter of the form 
l/(#s+ 1) the method should be successful using 
data only 7 sec long (ref. 1). This has not been 
tried to date. However, since the identification 
time, even in the present state, is relatively short 
when compared to the times required by other 
identification methods, several specific uses for 
the method are proposed. 
(1) The method can be used as a test device 
to display to the human operator his present 
parameter state. In  this manner several interest- 
ing experiments could be run: Can the operator 
alter his parameters on command? Can he learn 
his tracking task more quickly by monitoring his 
progress? Can he reduce parameter variability? 
Can he reduce remnant by reducing parameter 
variability? Can he adjust K and r in some 
specified optimum sense? 
(2) The method can be used as a data analysis 
device to determine the correlation between 
short-term parameter variability and other perti- 
nent system variables: How does the variance of 
the short-term average parameter values change 
with practice? How does i t  vary between sub- 
jects? Is  parameter variability a function of 
parameter magnitude? Is it directly related 
to remnant? Is it related to the plant being 
controlled? Some of these questions will be 
investigated during the coming year. 
To date only a limited amount of human 
operator testing has been completed using the 
hybrid parameter tracking technique. Thus, no 
firm statements concerning its utility can be made 
a t  this time. However, it has the potential of 
becoming a valuable tool in the measurement of 
human performance. 
NOTE ON COMPUTATION 
The hybrid facility used in evaluating the 
hybrid parameter tracking method consists of an 
A HYBRID COMPUTER PROGRAM 51 
IBM 1130 digital computer, an EA1 680 analog 
computer and an EA1 693 interface package. 
The digital program was written in Assembler 
language. 
REFERENCES 
1. JACKSON, G. A.: An Investigation of Two Hybrid 
Computer Identification Techniques for Use in 
Manual Control Research. Final Report on NASA/ 
ERC contract No. NGR 23-054-003, vol. 11, June 30, 
1970. 
2. JACKSON, G. A.: A Method for the Direct Measure- 
ment of Crossover Model Parameters. IEEE Trans- 
actions on Man-Machine Systems, vol. MMS-IO, 
no. 1, Mar. 1969, pp. 27-33. 
3. BURGETT, A. L.: A Study of the Variability of Human 
Operator Performance Based on the Crossover Model. 
Fifth Annual Manual Control Conference, Mar. 27-29, 
1969. 


A hybrid computer program for the visual display of compensatory system model parameters

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