Predictive information in the control room

P R E D I C T I V E INFORMATION IN T H E CONTROL ROOM

Rolf J . van der Veldt; Wim A. van den Boomgaard Delft University of Technology

The Netherlands

The fast advance in computer technology, and the resulting introduction of powerful digital equipment in the control room, offers the possibility of presenting new kinds of information to the operator. One of these novelties is the prédictive

display. New techniques, however, must be applied intelligently, on the right time in the right place.

In this paper a current investigation is described concerning the effect of a prédictive display on the operator's control behaviour, under various process and display conditions. The problem will be treated expérimentally as wel! as theoretically.

INTRODUCTION

Since the early sixties many investigations concerning prédictive displays have been reported. Such a display is meant to show prédictions of a number of process

variables to the human controller.

In some studies it appeared that a prédictive display can especially be of great assistance to the human operator in controlling higher order Systems having l i t t l e damping (e.g. Sheridan et a l . , 1964) and in supervisory control of complex, slowly responding Systems; For low order, simple processes prédictive displays were less effective (Kvalseth, 1978). The effect of prédictions manifests itself particularly by:

- a better control performance of the human controller (Kelley, 1972; Dey, 1972; Laios, 1978; Veldhuyzen, 1976; De Keyser & Van Cauwenberghe, 1979; Widdel & Krais, 1982; and others),

- a decreased mental load, - a shortened learning period.

The causes of these effects can probably be found in the assumption that human

contro') involves making mental prédictions. The genera! aim of control is to satisfy

certain goals into the future (e.g. a desired state, minimal energy consumption) and is thus a future directed activity (Kelley, 1968). Consequently, i t is assumed that making and using prédictions is an inévitable part of controlling. Remarkably enough, by far the most controller mechanisms known in control theory do not make use of prédictions; the so-called prédictive control (see below) has been playing a minor rôle up to now, but is gaim'ng interest.

Based on the assumption that control requires a prédictive activity, the success of a prédictive display is dépendent on the ability of the human controller to make nis own mental prédictions. This capability dépends on f i r s t l y the knowledge of the process (internai model) and, secondly, on the capability of generating prédictions based on that process knowledge. These two aspects are considered to be distinct notions.

Severa! studies of "mental p r e d i c t i o n " have been c a r r i e d out, e . g . Kahneman &

Tversky (1973), and Hussy (1975), being not d i r e c t l y r e l a t e d to a control s i t u a t i o n . Rouse (1973), Van Heusden (1980), and Van Bussel (1980) have i n v e s t i g a t e d mental p r e d i c t i o n of dynamical systems and time s e r i e s , and concluded that humans

apparently p r e d i c t suboptimally. Besides, a l o t of e f f o r t i s put i n studying the nature and accuracy of the i n t e r n a ! model.

Based on the r e s u l t s mentioned above, i t appears to be d i f f i c u l t , however, to know beforehand the s i t u a t i o n s i n which p r e d i c t i o n w i l l be e f f e c t i v e . The same a p p l i e s to the choice of the r i g h t p r e d i c t i v e d i s p l a y parameters (span, accuracy, e t c . ) . Thé a p p l i c a t i o n of a p r e d i c t i v e d i s p l a y i s very broad: operator t r a i n i n g , use as a d i a g n o s t i c a i d (what-if d i s p l a y ) during f a u l t management, v a r i a b l e time scale d i s p l a y i n g f o r norma! control ( S h i r l e y , Campbell, Robinson, 1981).

Other aspects are:

- the p r e d i c t i o n method and the process model used - the accuracy of the p r e d i c t i o n s

- how to d i s p l a y the p r e d i c t i o n s ? - p r e d i c t i o n span.

The f i r s t aspect i s mainly a t e c h n i c a ! problem, while the other aspects al so depend on operator c h a r a c t e r i s t i c s .

In t h i s paper a research e f f o r t i s described that does not involve the t e c h n i c a l problem ("how to make a p r e d i c t i o n ? ) but aims at studying the r e l a t i o n s h i p between process parameters, p r e d i c t i v e d i s p l a y parameters and the o p e r a t o r ' s performance in a supervisory task. The approach i s both experimental and t h e o r e t i c a l .

EXPERIMENTS

In the f i r s t place the experiments are meant to i n v e s t i g a t e a number of aspects of human p r e d i c t i v e control separately. This requires an experimental too! that enables one to ca.rry out c o n t r o l l a b l e and reproducible experiments. Secondly, we f e l t the need f o r doing experiments i n more r e a l i s t i c s i t u a t i o n s , i n v o l v i n g several aspects at the same time.

In the experiments described below, both forms ar used, namely a computer s i m u l a t i o n (MISI = Mini Simulation) of small mul t i - d i m e n s i o n a l processes and a computer

simulation of a more r e a l i s t i c u t i l i t i e s p l a n t . Experiments 1-3 are c a r r i e d out v/ith MISI, i n the 4th experiment the u t i l i t i e s plant has been used.

The M I S I - s i m u l a t i o n

MISI i s a s o f t w a r e p a c k a g e t o s i m ú l a t e any l i n e a r m u l t i - v a r i a b l e System o f up t o t h e 8th o r d e r . The s i m u l a t e d System can have up t o 8 i n p u t s , 8 O u t p u t s and 8 d i s t u r b a n c e s and a t i m e d e l a y ( F i g . 1). up to 8 inputs u p to 8 d i s t u r b a n c e s up to 8 O u t p u t s Figure 1.

The man/machine interface consists of a CRT and a keyboard. The ïnputs and O u t p u t s of the system to be controlled can be displayed on the CRT, as shown in figure 2.

i n p u t s Outputs -i 1 1 r

1, , ,

Display of the MISI man/machine interface for a system with 4 inputs and Outputs.

The desired values and alarm limits of an output can be displayed as well. Besides, it is possible to show a predicted value of each output, with a prédiction span that can be chosen freely. The subject can control the system's outputs by manipulating the inputs. This can be done by moving the dashes, representing the input values. In experiment 1-3 the same process structure is used (Fig. 3), but the process Parameters have différent numerical values. The process consists of four separate first-order Systems, each having one input and one output. The time constant of each system is 100 seconds, while the gains are assigned différent values per system. Interaction between the four sub-s.ystems can be introduced as shown in figure 3.

Vi

Figure 3.

The gains K - H détermine the l e v e l of i n t e r a c t i o n . Appendix I contains a complete summary of the numerical values used i n the experiments.

In the experiments 2 and 3 time delays are introduced, while experiment 1 deals with undelayed Outputs.

The u t i l i t i e s plant s i m u l a t i o n

This second s i m u l a t i o n i s a more r e a l i s t i c , although l e s s f l e x i b l e expérimental t o o i . A u t i l i t i e s p l a n t i s an intégral p a r t of most i n d u s t r i a l complexes and i s well-known i n the process i n d u s t r i e s (Campbell, S h i r l e y , 1979). The p l a n t , a l s o c a l l e d steam p l a n t or b o i l e r house, i s the c e n t r a l f a c i l i t y where natural g a s , o i l or another f u e l i s used to f i r e one or more b o i l e r s which produce steam. With t h i s steam production i t i s p o s s i b l e t o d r i v e a number of turbines and compressors which produce e l e c t r i c i t y and compressed a i r (Shinskey, 1978).

The p a r t i c u l a r u t i l i t i e s p l a n t used f o r our s i m u l a t i o n ( F i g . 4) i s a s i m p l i f i e d process which produces intermediate pressure steam (IP-steam, 300 p s i ) , low pressure steam (LP-steam, 50 p s i ) , e l e c t r i c a l power and compressed a i r (50 p s i ) . The i n i t i a l high pressure steam (HP-steam, 800 p s i ) generated by the f o u r b o i l e r s i s e n t i r e l y used i n the u t i l i t i e s plant i t s e l f as an intermediate energy-resource. A more

d e t a i l e d d e s c r i p t i o n of t h i s s i m u l a t i o n can be found i n Schneider et a l . (1982) and Van der Veldt e t a l . (1984).

fbl fue valve

T

jëT^n 3 fûërYn

%—Ovalve valve ¥—Ovalve *—Ovalve

ip steam to plant electricity to plant _ — — y — letdown valve low <*| pressure), steam header lp steam to plant

The man/machine i n t e r f a c e c o n s i s t s of a colour VDU used f o r s t a t e and status information and a monochromatic VDU as a prédictive d i s p l a y . A s p e c i a l

keyboard i s designed to enable the subject to perform various functions ( d i s p l a y an other template, change a s e t p o i n t or a v a l v e p o s i t i o n , e t c . ) by pressing only a few keys.

Experiment 1

The f i r s t expérimental séries c a r r i e d out with the MISI-simulation concerns the e f f e c t of a prédictive d i s p l a y when system's complexity i s v a r i e d (Van der V e l d t , 1984). In t h i s case, i n t e r a c t i o n i n the S y s t e m i s chosen as a way of representing the complexity, and can be v a r i e d by the K-jj-factors of f i g u r e 3.

The hypothesis of t h e expérimental séries i s :

Prédictive information w i l l cause a l a r g e r increase of the o p e r a t o r ' s performance when the system's i n t e r a c t i o n i n c r e a s e s .

Method of experiment 1

The process to be c o n t r o l l e d i s already described above, while the numerical values can be found i n Appendix I.

To vary the complexity of the System, three différent degrees of i n t e r a c t i o n are used. The prédictions are completely accurate, being a mere e x t r a p o l a t i o n of the actual s t a t e , with a prédiction span of 60 seconds, which has been found to be t h e optimal ( i n terms of a performance measure as defined below) i n préparatory t e s t s . Consequently, there are s i x c o n d i t i o n s , as shown i n f i g u r e 6.

no low h i g h i n t . i n t . i n t . without p r é d i c t i o n 1 2 3 w i t h p r é d i c t i o n 4 5 6 Figure 6. The s i x c o n d i t i o n s of experiment 1. 6 a l i m e • Figure 7.

C a l c u l a t i o n of the absolute e r r o r score. The score i s equal to the sum of a i l dashed areas.

The task of the subjects i s to change the outputs as q u i c k l y as p o s s i b l e from a set of i n i t i a l values to c e r t a i n d e s i r e d f i n a l v a l u e s . The outputs can be c o n t r o l l e d by manipulation of the i n p u t s . The same i n i t i a l and f i n a l values are taken f o r a i l s u b j e c t s .

The performance measure takes the weighted summation of four e r r o r scores, one f o r each output. These scores are i n f a c t integrated absolute e r r o r c r i t e r i a , as shown i n f i g u r e 7. Other measures, l i k e a quadratic e r r o r score, have been c a l c u l a t e d as w e l l , but they turned out to be almost f u l l y c o r r e l a t e d with the absolute e r r o r s measure.

The experiment was c a m ' e d out with 36 subjects i n an i n t e r - s u b j e c t design. A f t e r they were t r a i n e d i n handling the man/machine i n t e r f a c e , but not i n c o n t r o l l i n g the p a r t i c u l a r process, each subject d i d f i v e t r i a l s of ten minutes each. As a r e s u i t , the f i r s t t r i a l was the f i r s t c o n f r o n t a t i o n with the process f o r each s u b j e c t , which can a l s o be noticed i n the l e a r n i n g e f f e c t s that appear i n the r e s u l t s of t r i a l 1 through 5.

Results of experiment 1

When the mean i s taken of a i l performance scores per c o n d i t i o n , the diagram of f i g u r e 8 can be drawn. S i m i l a r p i c t u r e s r e s u i t from the mean scores of each t r i a l per c o n d i t i o n .

A

Mean performance scores of experiment 1, on a s u b j e c t i v e i n t e r a c t i o n s c a l e .

The i n t e r a c t i o n measure, as used i n f i g u r e 8, needs f u r t h e r e x p l a n a t i o n . I n t e r a c t i o n i n f a c t defines the l e v e l of d i f f i c u l t y , which i s b a s i c a l l y a s u b j e c t i v e matter. An adequate measure to q u a n t i f y i n t e r a c t i o n can be achieved as f o l l o w s : In each of the c o n d i t i o n s 1, 2 and 3 ( i . e . without prédiction) the mean i s taken of the

measured performance scores of the s u b j e c t s . Next, thèse mean v a l u e s are used as a ( s u b j e c t i v e ) measure of i n t e r a c t i o n i n the System. The meah scores of c o n d i t i o n

1, 2 and 3 l i e therefore on a s t r a i g h t l i n e under an angle of 45° with t h e two axes.

A f t e r a l l , the f i r s t and second levé! of i n t e r a c t i o n are chosen too c l o s e to each other. Yet, i n t o t a l the r e s u l t s confirm the hypothesis with s u f f i c i e n t

s i g n i f i c a n c y (p < 0 . 0 5 ) . Experiment 2

Systems containing time delays are e s p e c i a l l y i n t e r e s t i n g i n r e l a t i o n with prédictive d i s p l a y s . Such Systems are d i f f i c u l t to c o n t r o l , since the feedback information i s retarded. A method to compensate f o r the d e l a y , i s to make and use a prédiction of the O u t p u t s .

The hypothesis of expérimental séries 2 i s :

Prédiction w i l l h i g h l y increase the o p e r a t o r ' s performance i n C o n t r o l l i n g a delayed System.

Method of experiment 2

The numerical values of the MISI-process are given i n Appendix I; see a l s o f i g u r e 3. The K-jj-values correspond to the medium levé! of i n t e r a c t i o n i n experiment 1. Two différent values of the time delay (Tj) are taken (50 and 150 seconds), while prédictions are shown with a prédiction span of zéro (= no prédiction), a span equal to the delay (T^), and a span equal to the delay plus the time constant

(T = 100 s e c ) . S i x c o n d i t i o n s can thus be d e f i n e d ; see f i g u r e 9.

without pred. pred.

pred. span = Td span = Td + T time 50 s. 1 2 3 delay Td 150 s. 4 5 6 Figure 9. The s i x c o n d i t i o n s of experiment 2.

The task of the subjects i s i d e n t i c a l to the task of experiment 1: change the Outputs from i n i t i a l values to desired values as q u i c k l y as p o s s i b l e .

Also the same performance measure i s used as i n experiment 1. Again, 36 subjects have j o i n e d i n the experiments i n an i n t e r - s u b j e c t design. A f t e r a t r a i n i n g of four 10 minute t r i a l s , a f t e r which l e a r n i n g e f f e c t s had l a r g e l y disappeared, the subjects did another four t r i a l s of 10 minutes counting f o r the scores.

Results of experiment 2

The mean scores of the s i x c o n d i t i o n s are drawn i n the diagram of f i g u r e 10. A n a l y s i s of variance shows a very s i g n i f i c a n t (p < 0.001) e f f e c t of prédiction, while time delay i s only s i g n i f i c a n t i n the c o n d i t i o n s without prédictions. I t

seems as i f prédictions almost e n t i r e l y compensate f o r the time d e l a y , and t h a t the performance improves even more ( a l b e i t s l i g h t l y ) when the prédiction span i s f u r t h e r increased.

As f o r the number of control a c t i o n s again an obvious e f f e c t of prédiction appears. ( F i g . 11). • = 5 0 s . d e l a y • = 1 5 0 s . d e l a y

•^8

Mean number of input changes i n experiment 2.

Experiment 3

So f a r , as a r e s u l t of the exact e x t r a p o l a t i o n of the actual process s t a t e , p r e d i c t i o n s are shown to the subject with a p e r f e c t accuracy. In r e a l i t y

inaccuracies from many sources w i l l be i n e v i t a b l e . This t h i r d experimental s e r i e s deals with inaccurate p r e d i c t i o n s , under the f o l l o w i n g hypothesis:

P r e d i c t i o n i s l e s s e f f e c t i v e when accuracy decreases. Method of experiment 3

This experiment i s i d e n t i c a l t o experiment 2 (process, time d e l a y s , performance c r i t e r i o n , t a s k ) , except f o r the p r e d i c t i o n s . As mentioned above, the p r e d i c t i o n s with a f i x e d p r e d i c t i o n span equal to the time delay plus time constant, are i n a c c u r a t e . This inaccuracy i s reached by f i r s t making an exact e x t r a p o l a t i o n and then adding a f i r s t - o r d e r f i l t e r e d white noise s i g n a ! ( F i g . 1 2 ) . Two d i f f e r e n t noise l e v e l s (with the same mean equal to zero) are used, r e s u l t i n g i n p r e d i c t i o n s with medium and low accuracy (Standard d e v i a t i o n s of the noise: medium, appr.

9% o f nominal output v a l u e ; low , appr . 36%).

accurate prédiction white noise signal inaccurate predict ion Td = 50 s. Td -150 s. low accuracy 1 2 medium accuracy 3 4 Figure 12- Figure 13.

A r t i f i c i a l i n t r o d u c t i o n of inaccuracy The four c o n d i t i o n s of experiment 3. i n the prédiction, as applied i n exp. 3.

four c o n d i t i o n s ( F i g . 13). S i x subjects per c o n d i t i o n (so 24 i n t o t a l ) performed the experiments i n an i n t e r - s u b j e c t design. They d i d 4 regular 10 minute t r i a l s a f t e r 4 t r i a l s of t r a i n i n g , j u s t l i k e i n experiment 2.

Results of experiment 3

The mean performance scores of the four c o n d i t i o n s can be compared with the mean scores obtained i n the c o n d i t i o n s w i t h a p e r f e c t prédiction and without prédiction of experiment 2. From f i g u r e 14 i t can be noticed that the médium and low accuracy c o n d i t i o n s l i e between the performance scores of the c o n d i t i o n s without and w i t h p e r f e c t prédictions.

t

Figure 14.

Results of experiment 3, compared with c o n d i t i o n s without and with perfect prédictions.

Experiment 4

Three important aspects i n r e l a t i o n with p r e d i c t i o n are covered with the MISI-experiments: system complexity, time delay and inaccuracy. The MISI-simulation i s very wel! s u i t e d to i n v e s t i g a t e separated aspects with reasonable s i g n i f i c a n t r e s u l t s . MISI i s l e s s u s e f u l , however, i n studying the b e n e f i t s of a p r e d i c t i v e aid i n r e a l i s t i c s i t u a t i o n s .

In order to acquire some knowledge about the p r a c t i c a l a p p l i c a t i o n of a p r e d i c t i v e d i s p l a y , a f i r s t experiment has been c a r r i e d out with the u t i l i t i e s p l a n t

s i m u l a t i o n . The main aim i s to see whether a p r e d i c t i v e d i s p l a y w i l ! increase performance s i g n i f i c a n t l y at a l l , and secondly, whether a p r e d i c t o r w i l l a i d more i f the task d i f f i c u l t y i n c r e a s e s .

Method of experiment 4

The u t i l i t i e s plant process i s already described above. The p r e d i c t i o n s of the f i v e outputs to be c o n t r o l l e d are generated by means of a nearly p e r f e c t

e x t r a p o l a t o r and thus can be regarded as s u f f i c i e n t l y accurate. The p r e d i c t i v e d i s p l a y i s used i n the o f f - l i n e mode, which means t h a t a new p r e d i c t i o n i s c a l c u l a t e d and displayed only i f the subject demands f o r i t and, moreover, that the subject can evaluate a number of c o n t r o l a c t i o n s by using the p r e d i c t i v e d i s p l a y , before a c t u a l l y applying those a c t i o n s ("what-if" mode).

The p r e d i c t i o n s are represented i n a graphical way on a VDU over a p r e d i c t i o n span of 7 minutes (the time constants of the process vary from 2 seconds u n t i l 6 minutes). The p r e d i c t o r i s made i n such a way that i t takes hardly two seconds to c a l c u l a t e and d i s p l a y a new set of p r e d i c t i o n s .

The task of the subject i s defined as f o l l o w s . The i n i t i a l s t a t e of the process at the beginning of an experimental t r i a l d i f f e r s from the d e s i r e d e q u i l i b r i u m . The subject has to avoid the process outputs from d e v i a t i n g too much and to bring the outputs back between the alarm l i m i t s and next i n the e q u i l i b r i u m again.

A b s l o l u t e e r r o r scores f o r each of the f i v e outputs have been used i n the performance measure, as defined i n the MISI-experiments.

Eight subjects are used to perform the experiments. F i r s t , they were t r a i n e d i n about s i x hours, spread over 3 days, how to use the man/machine i n t e r f a c e and to be able to control the process. A f t e r t h i s p e r i o d , they d i d s i x t e e n experimental t r i a l s of ten minutes (spread over 2 days), each t r i a l s t a r t i n g with one out of e i g h t d i f f e r e n t i n i t i a l process s t a t e s . The sequence of i n i t i a l states over the 8 subjects was balanced by the l a t i n square method.

Two main c o n d i t i o n s with 4 subjects each are d i s t i n g u i s h e d with and without

p r e d i c t i o n s . w i t h i n these c o n d i t i o n s a f u r t h e r d i v i s i o n can be made with respect to the 8 i n i t i a l process s t a t e s .

Results of experiment 4

The performance scores can be d i v i d e d i n t o 16 c a t e g o r i e s , namely the c o n d i t i o n s with and without p r e d i c t i o n s , each having 8 i n i t i a l process states ( F i g . 15). When the scores are normalized i n a way s i m i l a r to experiment 1 (the norms are the mean performance scores i n the c o n d i t i o n s without p r e d i c t i o n ) , the p i c t u r e of f i g u r e 16 can be drawn. Again, as i n experiment 1, we see that p r e d i c t i o n i s of greater b e n e f i t to the operator i n s i t u a t i o n s where the control task i s experienced as more d i f f i c u l t . Two points i n the diagram, however, do not support t h i s statement

( i n i t i a l s t a t e s 7 and 8 ) . Their p o s i t i o n i n the diagram i s close to the l i n e under 45 degrees, caused by the very large scores obtained by only two s u b j e c t s . I f we omit these d e v i a t i n g scores, the mean scores of i n i t i a l states 7 and 8 become as l a r g e as f o r i n i t i a l s t a t e s 1, 2 and 3.

I t f o l l o w s from a n a l y s i s of variance that p r e d i c t i o n s i g n i f i c a n t l y improves the performance.

Figure 15.

Results of experiment 4.

Figure 16.

Normalized scores o f exp. 4. The dotted l i n e represents the hypothesis that prédiction i s more useful as task d i f f i c u l t y increases.

THEORETICAL ANALYSIS

The t h e o r e t i c a l analysis serves as a background f o r the set-up o f the experiments. When the t h e o r e t i c a l a n a l y s i s reveals c e r t a i n control properties under c e r t a i n c o n d i t i o n s , the experiments could be s e t up with thèse c o n d i t i o n s , i n order t o f i n d out whether thèse p r o p e r t i e s also apply t o human C o n t r o l l e r s . The conditions are characterised by the parameters o f the System, man/machine i n t e r f a c e ,

Controller, e t c .

Also the interprétation of the r e s u l t s from the experiments can be supported by the t h e o r e t i c a l a n a l y s i s . Occurring phenomena could be compared o r explained with the p r o p e r t i e s found i n the t h e o r e t i c a l a n a l y s i s . I t must be emphasized, that the goal

of th e t h e o r e t i c a l analysis is not t o f i t a certain Controller model (wit h a

prédictive control strategy) on the measured input/output data gathered with the experiments.

Prédictive c o n t r o l ! e r

From the r e s u l t s o f the experiments we have the i n d i c a t i o n that i n some control s i t u a t i o n s a human operator c o n t r o l s the System according t o a prédictive control s t r a t e g y . This has been the reason t o analyse a c o n t r o l l e r , which i s based on a prédictive contro! s t r a t e g y .

The prédictive control s t r a t e g y , as shown i n f i g u r e 17, w i l l be b r i e f l y explained. At a c e r t a i n moment i n time the f o l l o w i n g four control tasks are s u c c e s s i v e l y c a r r i e d out:

1. Observation of the actual output, from which the state of the System i s r e c o n s t r u c t e d .

2. Given the actua l s t a t e o f the system and the assumed i n p u t , the output response

i s predicted over the prédiction span.

3. On the basi s of the différence between the desire d output response (th e référence

t r a j e c t o r y ) and the predicted output response, the optimal input c o r r e c t i o n s are determined. The optimal input c o r r e c t i o n s are determined by minimization of a quadratic c r i t e r i o n , i n terms of the control e f f o r t and the control r e s u l t (the output e r r o r ) . The sum of the assumed input and the optimal input c o r r e c t i o n s y i e l d the optimal input over the prédiction span.

4 . The f i r s t element of the optimal input i s applie d to the system as the contro l a c t i o n .

One time step l a t e r t h i s procedure i s r e i t e r a t e d .

~ L

Thil}-.

V.

The scheme of the p r e d i c t i v e control i s i l l u s t r a t e d i n f i g u r e 18. The éléments of the c o n t r o l l e r are the référence model, the p r e d i c t o r and the décision mechanism.

reference ftrajectory disturbances s e t -point reference model 'V mecha decision nism, input

i

predicted output trajectory Figure 18.

The C o n t r o l l e r parameters a r e : the length o f the prédiction span, the shape of the référence t r a j e c t o r y and the weighting matrices i n the o p t i m a l i z a t i o n c r i t e r i o n . As an example the control of a s c a l a r f i r s t order system, with gain K = 3 and

T = 100 s e c , i s considered . Thi s system i s i d e n t i c a l t o the f i r s t subsystem

without a time delay as used i n the experiments. As a f i x e d C o n t r o l l e r parameter a f i r s t order référence model, K = 1 and x = 50 s e c , i s chosen. The s e t p o i n t i s 0. 875. The f r e e Controller parameters are the length of the prédiction span and the weighting f a c t o r s q and r, r e s p e c t i v e l y f o r the control déviation and the input c o r r e c t i o n s , i n the o p t i m i z a t i o n c r i t e r i o n .

The performance of the control i s measured with the quadratic c r i t e r i a Jdev/cor a n a

^dev- Jd e v / c o r 1 S a measure of the control r e s u i t and the control e f f o r t together;

1. e. the sum of the quadratic Output déviations, weighted with q , and the quadratic input c o r r e c t i o n s , weighted with r, over the control i n t e r v a l of 600 s e c ; r i s chosen as 1. J t jev only takes the control r e s u i t i n t o account.

In f i g u r e 19, Jdev/cor and J f je v are drawn as f u n c t i o n s of the prédiction span and

the weighting f a c t o r q. I t i s observed that the minimal value of Jdev/cor dépends on q. For a good control performance a long prédiction span i s necessary when q has a small value. On the other hand, a short prédiction span (compensatory c o n t r o l ) w i l l lead to a minimal Jdev/cor w n e n 9 ^s r e l a t i v e l y l a r g e . In t h i s case a long

prédiction span w i l l cause a r e l a t i v e l y large control e f f o r t . For t h i s reason an i n f i n i t e prédiction span w i l l y i e l d the minimal value of Jdev» f o r any value of q.

Figure 19.

Optimal c o n t r o l l e r with p r e d i c t o r

Optimal l i n e a r control of a d e t e r m i n i s t i c delayed system i s achieved by a combination of a p e r f e c t p r e d i c t o r ( i n f a c t an e x t r a p o l a t o r ) , with a p r e d i c t i o n span equal to the time d e l a y , and a l i n e a r optimal c o n t r o l l e r .

When the p r e d i c t i o n span i s lower than the time d e l a y , the performance of the

optimal c o n t r o l l e r w i l l decrease, and thus the (absolute) e r r o r score w i l l i n c r e a s e . This corresponds to the r e s u l t s of experiment 2 ( F i g . 1 0 ) .

Unlike the r e s u l t s of experiment 1, a change of the i n t e r a c t i o n l e v e l i n the

undelayed system has hardly any e f f e c t on the performance of the optimal c o n t r o l l e r . When the accuracy o f the p r e d i c t i o n s i s v a r i e d (as i n experiment 3 ) , only a s l i g h t decrease i n performance of the optimal c o n t r o l l e r can be observed.

Obviously, the optimal control strategy y i e l d s r e s u l t s d i s s i m i l a r t o the experiments 1 and 3. In the experiments, i n t e r a c t i o n and accuracy do have a large e f f e c t on the human c o n t r o l l e r ' s performance. A t e n t a t i v e conclusion may be that the subjects

were a c t i n g suboptimally, p o s s i b l y because they had an imperfect i n t e r n a l model of the process t o be c o n t r o l ! e d .

CONCLUSIONS

The more d i f f i c u l t to control and to p r e d i c t a process i s to the operator, the greater a s s i s t a n c e a prédictive d i s p l a y can provide. In p a r t i c u l a r the experiments have shown that the i n t e r a c t i o n and delay i n the system are f a c t o r s i n f l u e n c i n g the s u b j e c t i v e d i f f i c u l t y . Inaccuracy of the p r e d i c t i o n reduces the e f f e c t i v e n e s s of a prédictive d i s p l a y r a p i d l y .

Comparing the human c o n t r o l l e r with the optimal c o n t r o l l e r we f i n d différences and s i m i l a r i t - i e s . P r e d i c t i o n span has a large i n f l u e n c e on the performance of an

optima! c o n t r o l l e r when delays are i n v o l v e d . However, i n t e r a c t i o n i n a system without delays has a hardly recognizable e f f e c t on the optimal c o n t r o l l e r ' s

performance, while i t influences the o p e r a t o r ' s performance s t r o n g l y . Another feature i s the low s e n s i b i ü t y of the optima! c o n t r o l l e r f o r inaccuracies i n the

Outputs, where agai n human c o n t r o l i s h i g h l y a f f e c t e d .

T h e o r e t i c a l a n a l y s i s of prédictive control shows an optimal performance f o r a c e r t a i n p r e d i c t i o n span. Furthermore, i t appears that the performance i s hardly a f f e c t e d beyond a c e r t a i n value of the p r e d i c t i o n span.

ACKNOWLEDGEMENTS

We thank Mr R. Jansen, Mr D. Broer, Miss M. de Frètes and Miss R. T e t t e l a a r , students of the Man-Machine Systems Group of our laboratory and o f the Dept. of Psychology of the Uni v e r s i t y of Leiden, f o r t h e i r coopération i n preparing and c a r r y i n g out the experiments.

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APPENDIX I G e n e r a l l y , t h e s y s t e m i s g i v e n b y : K K K *1 = xsTT u l ; H = 7STT <u2 + K1 2yl + K32y3 + K42y4^ ; y3 = TsTT (u3 + K13^l) K4 * 4 = T S T T <u4 + K1 4yl + K34y3> •

The n u m e r i c a l v a l u e s f o r the f i r s t - o r d e r Systems a r e :

Parameters: T = 100 se c l<x = 3 l<2 = 1.5 1<3 = 2.5 K. = 2 Desired f i n a l c o n d i t i o n s : y ides = 0.875 ^2d y3d ^4d es es es = 0.5 = 0.625 = 0.375 S t a r t i n g c o n d i t i o n s : y i( 0 ) = 0 U l( 0 ) = 0 y2( 0 ) = 0 u2( 0 ) = 0 y3( 0 ) = 0 u3( 0 ) = 0 y4( 0 ) = o u4( 0 ) = o

The values o f the gains f o r each l e v e l o f i n t e r a c t i o n :

K12 K13 K14 K32 K34 K42

none 0 0 0 0 0 0

medium 2.2 0.6 1.35 -1.5333 -1.5 -1.8