Adaptive behavior of human operators to failure transitions in controlled element dynamics, and identifying unknown sampling frequencies in dynamic system

Bekey, G. A.

English

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USCEE Repor t  262 
https://ntrs.nasa.gov/search.jsp?R=19680010461 2020-03-12T08:46:59+00:00Z
~~ 
USCEE Report  262 
PROGRESS REPORT NO. 5 
June 16, 1967 - December 15, 1967 
NASA Grant NGR 05-018-022 
RESEARCH ON N E W  TECHNIQUES FOR THE 
ANALYSIS OF MANUAL CONTROL SYSTEMS 
George A. Bekey 
January 1968 
E le c t r oni c Sci e nc e s Lab0 r a to r y 
Electrical  Engineering Department 
University of Southern California 
Los Angeles, California 90007 
. .  
I. INTRODUCTION 
The major  effort  dur,ng this reporting period was concentrated i n  the 
following areas :  
following transit ions in controlled element dynamics; (2) identification 
of unknown sampling frequencies i n  dynamic systems;  (3)  modification of 
the data acquisition sys tem used with manual control experiments,  and 
(4) software development. 
11. ADAPTIVE BEHAVIOR O F  HUMAN CONTROLLERS 
Personnel:  A. V. Phatak, G. A. Bekey 
(1) study of the adaptive behavior of human opera tors  
Research  efforts for the past  six months have mainly been in  the study 
of models 
in response to step changes i n  effective vehicle dynamics. 
our P r o g r e s s  Report No. 4 
basic a i r f r ame  with ra te  and attitude gyro augmentation. 
both of these two augmentation loops causes a step change in the effective 
vehicle dynamics controlled by the operator.  
may be accompanied by failure transients ( ramp o r  hard-over)  which in  turn 
require  the operator to introduce a bias in  his control effort i n  o r d e r  to 
maintain stability. 
dynamics fo r  the four different levels of augmentation. 
to descr ibe the adaptive charac te r i s t ics  of the human operator  
As  descr ibed in  
(1) the human operator  is  controlling a pure  iner t ia  
Fa i lure  of one o r  
The fai lure  of the gyro feedbacks 
Table I of P rogres s  Report 4 shows the effective vehicle 
Two different sets  of transit ions were explored experimentally. These 
F o r  the f i rs t  set ,  there  a r e  three distinct post-  
The 
a r e  given in Table I below. 
fa i lure  vehicle dynamics and six different types of transit ion possible. 
"soft" failure r e f e r s  to the absence of any failure transient, while the I 'ramp''  
and "hard" failures indicate the type of transient, namely, a l inear o r  step 
change in feedback signal. 
Table I. List  of Failures Simulated 
- 
Rate only - soft 
Rate plus Attitude Rate only - ramp 
R a t e  only - hard 
I I I 
2. 
Pr e- Failure 
Augmentation 
None - soft 
None - soft 
Post-Failure 
Augment a t  ion 
1. 
Attitude only 1
None - hard 
For  each of the four levels of augmentation, i t  is possible to predict, f rom 
existing data,  the steady-state describing function models. They f i t  a four- 
parameter  model of the form: 
Approximate values fo r  the four parameters  based on closed-loop servo 
analysis and available operator datk2&re presented in  Table 11. Notice that 
there  is  a la rge  difference in  the describing function parameter  values for  the 
four different levels of augmentation, and i s  quite akin to a change in  s t ructure  
of the compensation itself. 
Table 11. Approximate Values of Pa rame te r s  f o r  Steady-State 
Describing Functions 
Any adaptive model for  the operator must satisfy the boundary constraints 
of prefai lure  and postfailure steady- state describing function pa rame te r s  ( 3 )  . 
Also, the model must incorporate the decision p rocesses  involved in  making 
a successful change of s t ruc ture  while maintaining stability. 
many alternative dynamics possible after fa i lure ,  the operator adaptation 
algorithm must  be of a sequential nature where the s t ructural  changes in compen- 
sation can be carried to conclusion o r  terminated in  the middle depending upon the 
post-failure dynamics. 
(4) Since there  a r e  
In other words,  the adaptation philosophy must  be 
based on the Principle of Optimality f rom Dynamic Programming concepts. 
At present ,  the following i s  being done: 
1. Data f r o m  str ip  char t  records i s  being digitized and the resul ts  used to obtain 
phase-plane plots for  various transitions. 
the adaptation seems to accur in three distinct phases: 
Pre l iminary  resul ts  indicate that 
a )  Detection of occurrence of failure 
b) Sequential s t ructural  adaptation to  the required post-failure 
compensation. 
a t  a given point in  the sequence. 
c)  Adjustment of parameters  to minimize e r r o r .  
The detection of failure seems to be based on values of e r r o r ,  e r r o r  
This incorporates decision logic to stop the adaptation 
ra te  etc. and the cr i ter ion may be taken a s  deterministic in  nature to a f i r s t  
approximation. The operator t racks the maximum (or mean- square) values 
of the e r r o r ,  e r r o r  ra te  and so on, for  the prefailure vehicle dynamics and 
retains these values in  memory a s  upper bounds f o r  the various signal 
magnitudes. 
cer ta in  factor (say two), then failure i s  assumed to have occurred. Initial 
resul ts  using such a cr i ter ion for detection seem promising. 
2. Following detection of a failure,  the modification of the operator compen- 
sation must  be car r ied  out with sufficient speed to maintain system stability. 
I 
If the e r r o r  and/or i t s  derivatives exceed the above limits by a 
One such structural  modification scheme with stops at places in between i s  
presently being tested using digital simulation. Again, results look encouraging. 
REFERENCES 
1. Bekey, G. A. , "Research on New Techniques for  the Analysis of 
Manual Control Systems", University of Southern California P r o g r e s s  
Report No. 4. USCEE Report 227 
2. McRuer, Duane, et. a l . ,  "Human Pilot Dynamics i n  Compensatory 
Systems-Theory, Models, and Experiments with Controlled Element 
and Forcing Function Variations", AFFDL--TR -65-15, Systems 
Technology Inc, Aug. 1965. 
3. Weir, D. H. ,  Phatak, A. V., "Model of Human Operator Response to 
Step Transit ions i n  Controlled Element Dynamics", NASA CR-671, 
Jan. 1967 
4. Elkind, J. I. , Miller, D. C., "Adaptive Character is t ics  of the Human 
Controller of Time-Varying Systems", AFFDL-TR-66-60, April 1966. 
111. IDENTIFICATION O F  UNKNOWN SAMPLING FREQUENCIES I N  
DYNAMIC SYSTEMS 
Personnel: C. B. Neal, G. A. Bekey, M. J. Merrit t  
The overall problem of identifying an unknown sampling frequency 
in  a sampled-data system is currently thought of a s  being described by the 
following collection of increasingly difficult problems: 
la.  
the system i s  fairly well approximated by the model. 
lb. 
model poorly approximates the system. 
2. 
model is  approximate, but the system output is noise-corrupted. 
Identification when the system and sampling a r e  deterministic and 
(see Figure 1) 
Identification when the system and sampling a r e  deterministic, but the 
Identification when the system and sampling a r e  deterministic and the 
-Z.O.h, 
3 .  
random parameter  and the system output i s  noise-corrupted. 
4. 
Identification when the sampling is deterministic but the system has 
Identification when the sampling is random, the system has random para-  
' 
Y = f ( t ,  Tx, Y, e l )  
me te r s ,  and the system output i s  noise-corrupted. 
Low 
41 
Frequency 
-~ 
E r r o r  
Processing 
by 
Gradient o r  
Search 
Technique 
Adjust T and Model P a r  a 
Figure 1 Sampling Interval Identification Scheme 
The solution to problems (la) and (lb) has been found and was discussed in  
P rogres s  Report No. 4 (I) ,  a f i r s t  draft  of a report  covering this phase has  
been prepared. During the las t  period most of the attention was given to 
Problem 2. However, a comprehensive l i terature  search  was conducted 
for analytical techniques for Problem 3 and 4. The following observations 
a r e  possible concerning these problems: 
1. While analytical treatments of the problem of estimation of movements 
of random parameters  i n  l inear systems have been given by Brainin(2), by 
Cumming ( 3 ) ,  and by Bogdanoff and K o ~ i n ' ~ ) ,  the methods have been applied 
to only the simplest cases .  Considerable work would be  necessary before i t  
might be possible to t rea t  the case  of both random parameter  variations and 
observation noise. It is  typical of these treatments that, in  general, they 
necessitate the solution of a Fokker-Planck partial  differential equation of 
the same o rde r  a s  the order  of the system 
1. 
the 
differential equations. 
2. 
paramete r s  a r e  random. 
noise) can be treated by this technique. 
technique of the Kalman type is  ruled out; again, because noise must  be 
additive in order  to apply the Kalman estimation procedure. 
(4) . Two simple cases  occur: 
When the parameter  variations a r e  white noise o r  when they.aregaussian. Then 
moments a r e  described by a system of deterministic ordinary l inear 
It i s  not possible to apply any f o r m  of regression analysis when the sys tem 
This is because only additive noise (not multiplicative 
Additionally, a sequential estimation 
In treating Problem 2 the following approaches were  considered: 
1. 
theory following the approaches of K a l ~ n a n ' ~ )  and the la te r  work of Steiglitz 
The application of conventional least- squares  and weighted least  squares  
( 6 )  and Mc Bride . These techniques yield an  i terative estimate of the d iscre te  
t ransfer  function representation of the closed loop system the the form 
-1 n- 1 a t a z t.. . tan-l  Z 
= o l  N(z 1 
-1 -n 
Z 1 t b z t . . . + b n  1 
-1 - zT 
Here  z = e where T is the interval of sampling at  the input and output 
of the measurement  configuration (Figure 2) and does not directly re fer  to the 
internal sampling interval (T ) of the closed loop system. Further  
X 
nois e 
closed loop 
system 
- 
I 
work would be necessary to establish whether T 
small  amount of t ime was spent with this scheme because of the comparative 
could be derived. Only a 
X 
promise of stochastic approximation which i s  discussed below. 
2. 
Problem 2. 
analytical work, but only a few engineering application. Of these, the work 
of S a k r i ~ o n ' ~ )  can be used directly. 
The technique of stochastic approximation appears attractive fo r  solving 
Li terature  search disclosed a considerable body of purely 
It i s  a multiparameter Kiefer-Wolfowitz 
stochastic gradient technique(8) and provided that the i teration process  i s  
such that the measurement  noise t e r m  approaches ze ro  (along with a few 
easily-met conditions on the cost function) 
mean square;  i. e. i f  P 
then convergence is no worse than 
i s  the n-th estimate of the parameter  vector,  n 
where 3 i s  the t rue  value of the system parameter  vector. The overall 
advantage of this method i s  that i t  is quite straight forward to compute the 
Kiefer- Wolfowitz algorithm for the iterative correction to the parameter  
vector. 
Programming of the equations for stochastic approximation of a 
simple 1st order  sys tem (under Problem 2) has been completed. 
sampling interval will  be varied. 
a s  well. 
Only the 
I 
Later,  other parametem will be varied 
The IBM CSMP 1130 P rogram for digital simulation of continuous 
systems i s  currently being used in the basic arrangement  of Figure 1. 
Work i s  a lso beginning in an attempt to develop a general  stochastic 
approximation treatment for the case  of noisy parameters  and observation 
noise. 
REFERENCES 
1. 
2. 
3. 
4. 
I 
5. 
I 
6. 
7. 
8. 
Bekey, G. A. ,  "Research on New Techniques for the Analysis of 
Manual Control Systems", University of Southern California P r o g r e s s  
ReDort No. 4. 
Brainin, S. M., "The Estimation of Randomly Varying Pa rame te r s  in  
Linear Systems",  Ph. D. Dissertation, University of Southern California, 
April  1966. 
Cumming, L. G. , "Derivation of Moments of Continuous Stochastic 
Systems",  International Journal of Control, Vol 5, No. 1, 1966. 
Bogdanoff, J. L . ,  and Kozin, F., "Moments of the Output of Linear  
Random Systems", Journal Acoustical Society of America, Vol 34, 
No. 8, August 1962. 
Kalman, R .  E . ,  "Design of a Self-optimizing Control System", Trans .  
ASME, Vol 80, pp. 468-478, February 1958. 
Steiglitz, K . ,  and McBride, L. E. , "A Technique for the Identification 
of Linear  Systems", IEEE Transactions of Automatic Control, Oct. ,1965. 
Sakrison, D. J. , "Application of Stochastic Approximation to Optimum 
Fi l te r  Design", IRE National Convention Record, Vol 9, P a r t  IV, 1961, 
pp. 127-135. 
Kiefer,  J. and Wdfowitz, J, "Stochastic Estimation of the Maximum of a 
Regress ion  Function", Annals of Mathematical Statistics, Vol 23, No. 3,1952. 
IV.  MODIFICATION TO THE DATA ACQUISITION STATION 
Personnel: M. J. Merr i t t  
The IBM 1710 digital computer described in previous reports  has  been 
replaced by an IBM 360 model 44 digital computer. The new IBM 360 computer 
is almost a thousand t imes fas te r  and has eight t imes m o r e  memory  than 
the IBM 1710 sys tem and will allow f o r  greater  freedom in  the design of 
experiments than was possible previously. Unfortunately, the two systems 
a r e  sufficiently different that an  entirely new interface system and software 
program a r e  required. 
The interface system contains all of the communication between the 
analog and digital computers: 
a) analog to digital converters 
b) digital to analog converters 
c) digital outputs 
d)  digital inputs 
e )  analog mode control 
f) cross-bar  control fo r  address  selection and sot setting 
An interface system has been designed and constructed under support f rom 
other sources  and checkout is  in  progress .  
The operating system and monitor provided with the 360 system a r e  
very complex and some difficulty was encountered in  operating the ADC's 
and DAC's at  the speeds required for the human pilot and the modeling 
experiments planned. Many of the difficulties have been overcome by 
modifying the operating system so that direct control of the converters 
can be obtained. A comprehensive software package which will allow high 
speed processing of ADC and DAG data as well a s  discrete  data i s  being 
developed under a contract with IBM. The resultant software package will 
also be available to FORTRAN use r s  and will be essential in our future 
manual control experiments. 
V.  ADAPTATION OF IBM 1130 CONTINUOUS SYSTEM MODELING 
PROGRAM (CSMP) TO THE IBM 360 MODEL 44. 
Personnel: M. J. Merr i t t  
The Continuous System Modeling P rogram (CSMP) i s  a block 
structured digital simulation language. Many of the block elements a r e  
I 
identical i n  function to the components of an  analog computer; summers ,  
inverters ,  integrators,  potentiometers, etc. Since the computations a r e  
car r ied  out digitally, no amplitude scaling o r  time scaling is  necessary.  
The p rogram a s  supplied by the SHARE Library was written.for an IBM 1130 
computer. The program was modified to meet  the requirements of the 360 
system and was subsequently loaded on a disk file. 
p rograms have been run successfully and the program is considered fully 
op e r ational . 
unknown sampling intervals i n  human pilot models is  being performed 
entirely using CSMP, at  a large 
i n  reliability as compared to purely analog methods. 
Both tes t  and production 
Current  r e s e a rch  using stochastic app r oximation to identify 
savings in  computer t ime and increase  


Research on new techniques for the analysis of manual control systems Progress report, 16 Jun. - 15 Dec. 1967

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