MODELLING THE HUMAN OPERATOR'S SUPERVISORY BEHAVIOR Ted N. W h i t e *
D e l f t U n i v e r s i t y o f T e c h n o l o g y , Dept. o f Mech. Eng. Lab. f o r Measurement & C o n t r o l
Man-Machine Systems Group D e l f t , The N e t h e r l a n d s
ABSTRACT
The i n v e s t i g a t i o n r e p o r t e d h e r e d e a l s w i t h t h e d e s c r i p t i o n o f t h e b e h a v i o r o f t h e human O p e r a t o r p e r f o r m i n g t h e s u p e r v i s i o n o f a s e t p o i n t c o n t r o l l e d p r o c e s s under s t e a d y s t a t e c o n d i t i o n . The d e s c r i p t i o n w i l l be g i v e n i n terms o f a ma-t h e m a ma-t i c a l model.
I n v e r i f y i n g t h e model s t r u c t u r e , c e r t a i n t a s k \ r a r i a b l e s have b e e n d e f i n e d . Then, t o each o f t h e s e t a s k v a r i a b l e s , t h e p a r t i c u l a r i n f l u e n c e o f t h e v a r i a b l e on t h e p a r a m e t e r s o f t h e human O p e r a t o r model h a s b e e n p o s t u l a t e d . The d a t a a n a -l y s i s i s b a s e d on S t a t i s t i c a l and s t o c h a s t i c procédures.
I t i s s h o w n t h a t t h e model s t r u c t u r e I s a p p l i c a b l e t o t h e d e s c r i p t i o n o f t h e h u -man s u p e r v i s o r y b e h a v i o r . However, t h e p a r a m e t e r e s t i m a t i o n procédures a r e com-p l i c a t e d , t i m e consuming and t h u s e x com-p e n s i v e .
1. INTRODUCTION
The p r o p e r f u n c t i o n i n g o f t e c h n o l o g i c a l S y s t e m s , d l v e r g i n g f r o m v e r y s i m p l e t o v e r y c o m p l e x , needs t h e a b i l i t y o f human i n t e r v e n t i o n i n most c a s e s . More s p e -c i f i -c l y , I t -c a n range f r o m a d i r e -c t manual -c o n t r o l t o a s u p e r v i s o r y -c o n t r o l mode. Because o f t h e e v e r i n c r e a s i n g a u t o m a t i z a t i o n i n i n d u s t r y , new demands have b e e n p u t on now-adays O p e r a t o r s . They a r e no l o n g e r f u n c t i o n i n g as d i r e c t , manual C o n -t r o l l e r ; -t h e i r -t a s k s became more and more -t h e s u p e r v i s i o n o f m u l -t i - v a r i a b l e , s l o w l y r e s p o n d i n g , and complex S y s t e m s . As a conséquence, t h i s t a s k i s composed o f m o n i t o r i n g t h e d i s p l a y e d s y s t e m O u t p u t s , C o n t r o l l i n g t h e s e t p o i n t s o f t h e a u -t o m a -t i c C o n t r o l l e r s and p e r f o r m i n g t h e f a u l t management.
Due t o sudden p r o c e s s changes o r d i s t u r b a n c e s , t h e O u t p u t v a r i a b l e s m i g h t e x c e e d t h e b o u n d a r i e s w h i c h a r e s p e c i f i e d b y t h e management o r by s a f e t y régulations. B a s e d on t h e p e r c e i v e d déviations, t h e S u p e r v i s o r décides t o change one o r more s e t p o i n t s . M o r e o v e r , when t h e i n f o r m a t i o n needed t o s u p e r v i s e t h e p l a n t i s i n -s u f f i e i e n t , t h e O p e r a t o r m i g h t décide t o a-sk f o r a d d i t i o n a l i n f o r m a t i o n w h i c h may l e a d t o a s e t p o i n t c o r r e c t i o n . T h i s s t e a d y s t a t e c o n t r o l a s p e c t o f t h e s u p e r v i s o r y b e h a v i o r i s i n gênerai i m p o r t a n t i n p r o c e s s c o n t r o l , t h a t i s i n t h e c o n -t r o l o f c o n t i n u o u s p r o c e s s e s . I t i s c a l l e d t u n i n g . The shut down and s t a r t - u p procédure, a l s o an i m p o r t a n t c o n t r o l mode, i s m o s t l y e x e c u t e d b y s p e c i a l teams o r a u t o m a t i c C o n t r o l l e r S y s t e m s .
I n n u c l e a r power p l a n t s , however, t u n i n g i s f a r l e s s i m p o r t a n t t h a n f a u l t manage-ment. These p l a n t s -are h i g h l y a u t o m a t e d , and t h e main t a s k o f t h e O p e r a t o r i s t o s e a r c h f o r m a l f u n c t i o n s , f a u l t d i a g n o s i s and f a u l t management.
I n t h i s i n v e s t i g a t i o n t h e a t t e n t i o n i s f o c u s s e d on t h e t u n i n g t a s k o f t h e S u p e r -v i s o r .
2 . MODELLING HUMAN CONTROL BEHAVIOR
The b e h a v i o r o f an O p e r a t o r p e r f o r m i n g a s u p e r v i s o r y t a s k , o r any o t h e r manual / c o g n i t i v e t a s k , can be d e s c r i b e d i n différent ways.
F o r many y e a r s , s c i e n t i s t s t r y n o t o n l y t o d e s c r i b e t h e b e h a v i o r o f t h e s u b j e c t s
* T h i s r e s e a r c h I s p a r t l y s p o n s o r e d b y t h e N e t h e r l a n d s O r g a n i z a t i o n f o r t h e Advancement o f Pure R e s e a r c h (ZWO).
o f i n t e r e s t s after t h e e x p e r i m e n t s , b u t , t h e y a l s o t r y t o make p r e d i c t i o i . s u p o n t h e b e h a v i o r t o b e e x p e c t e d , t h u s before t h e e x p e r i m e n t s . Among t h e many t h e o r i e s w h i c h a r e a p p l i e d i n o r d e r t o p r e d i c t human o p e r a t o r b e h a v i o r d u r i n g m a n u a l c o n t r o l t a s k s , t h e c y b e r n e t i c m o d e l s a r e w e l l - k n o w n . I n t h i s p h y l o s o p h y t h e human o p e r a t o r i s r e g a r d e d as a s y s t e m , a c e n t r a l p r o c e s s o r , w i t h i n p u t s a n d o u t p u t s . S o , human o p e r a t o r s c a n b e d e s c r i b e d as i n p u t - o u t p u t r e l a t i o n s . T h i s i d e a I s n o t n e w ; b a c k i n t h e t w e n t i e s , t h e b e h a v i o r i s t s a l r e a d y d e s c r i b e d human b e i n g s as d a t a p r o c e s s o r s w i t h an u n -known c e n t r a l p r o c e s s o r , t h e s o c a l l e d " b l a c k b o x " , w h i c h t r a n s f e r r e d s t i m u l i i n t o c e r t a i n r e s p o n s e s . B y t h e a p p l i c a t i o n o f a w i d e v a r i e t y o f s t i m u l i a n d b y m e a s u r i n g a l l r e s p o n s e s , t h e i n p u t o u t p u t r e l a t i o n s h i p s c o u l d b e d e t e r -m i n e d . On t h e b a s i s o f s y s t e -m t h e o r y , f r o -m t h e i n p u t - o u t p u t r e l a t i o n s a -m o d e l , t h a t i s a m o d e l s t r u c t u r e a n d m o d e l p a r a m e t e r s , c a n be d e r i v e d . C o n s e q u e n t l y t h e " b l a c k b o x " i s w h i t e n e d . A l t h o u g h i n m a n u a l c o n t r o l s i t u a t i o n s c y b e r n e t i c m o d e l s c a n b e a p p l i e d s u c c e s s -f u l l y t o p r e d i c t human b e h a v i o r [ACMC 196k - 1 9 8 1 ] , up t o now i t i s s t i l l n o t p o s s i b l e t o d e v e l o p s u c h p r e d i c t i o n m o d e l s f o r s u p e r v i s o r y c o n t r o l s i t u a t i o n s . The m a j o r d i f f e r e n c e s b e t w e e n d i r e c t m a n u a l c o n t r o l o f v e h i c l e s a n d t h e d i s c r e t e c h a r a c t e r i s t i c s o f s u p e r v i s o r y c o n t r o l i n p r o c e s s i n d u s t r y c a n b e i l l u s -t r a -t e d b y T a b l e I . [ B e a v e r s -t o c k , S -t a s s e n , W i l l i a m s o n , 1977] D a t a P r o c e s s i n g A s p e c t s V e h i c l e C o n t r o l P r o c e s s C o n t r o l l INFORMATION T y p e D i m e n s i o n Time c o n s t a n t s A b s t r a c t n e s s O r i g i n d i s t u r b a n c e s S y s t e m p r o p e r t i e s D i r e c t A b o u t 10 F r o m s e c . t o m i n . Low Known L i n e a r C o n s t a n t I n d i c a t i v e B e t w e e n 100 a n d 1500 F r o m m i n . t o h o u r s H i g h Unknown N o n - L i n e a r T i m e - v a r y i n g PRESENTATION I n t é g r a t i o n P a r a l l e l / s e r i e s Number o f d i s p l a y s Time w i n d o w Modes O v e r v i e w I n t e g r a t e d d i s p l a y s M o s t l y p a r a l l e l s Low I n s t a n t e n e o u s a n d p r e d i c t i v e V i s u a l , a u d i t i v e , v e s t i b u l a r Good N o n - i n t e g r a t e d d i s p l a y s P a r a l l e l a n d / o r s e r i e s H i g h I n s t a n t e n e o u s a n d h i s t o r y ( t r e n d ) V i s u a l , a u d i t i v e P o o r MANIPULATION D i r e c t f e e d b a c k R e s p o n s e S t r a t é g i e s A c c u r a c y P r o p r i o c e p t i v e I m m e d i a t e E r r o r c o r r e c t i o n M o r e o r l e s s c o n s i s t e n t Q u a n t i t a t i v e No p r o p r i o c e p t i v e N e x t s h i f t B o u n d a r y c o n t r o l V a r i a b l e M o r e o r l e s s q u a l i t a t i v e CONFIGURATION P h y s l c a l s i z e P e r s o n n e l t r a i n i n g Human f a c t o r s S m a l l H i g h l y a n d c o n s i s t e n t l y W e l l d e v e l o p e d L a r g e L e s s r i g o r o u s l y V e r y l i t t l e d e v e l o p e d T A B L E 1 : COMPARISON BETWEEN V E H I C L E CONTROL AND PROCESS CONTROL
3. MODELING HUMAN SUPERVISORS BEHAVIOR
3 . 1 Definition of the system state and model description
The human o p e r a t o r ' s s u p e r v i s o r y b e h a v i o r i n a s t a t i o n a r y c o n t r o l mode, where a d y n a m i c , s l o w l y r e s p o n d i n g , and complex s y s t e m i s s e t p o i n t c o n t r o l l e d i s c h a r a c t e r i z e d b y p e r i o d s o f w a i t i n g a n d o f o b s e r v i n g o u t p u t v a r i a b l e s f o l l o w e d by p e r i o d s o f e x e c u t i n g c o n t r o l a c t i o n s . The p r o c e s s t o be s u p e r v i s e d I s d e s c r i b e d b y a l i n e a r , dynamic s y s t e m w i t h s t a t e x ( k ) . The System i s d i s t u r b e d b y a n o i s e w ( k ) . I t h a s a c o n t r o l l e d i n p u t u ( k ) whereas t h e o u t p u t y ( k ) c o n s i s t s o f a l i n e a r c o m b i n a t i o n o f t h e s t a t e v a -r i a b l e s x ( k ) ; t h e s y s t e m can be o b s e -r v e d by t h e human o p e -r a t o -r v i a a d i s p l a y . T h i s o b s e r v a t i o n can be a c o n t i n u o u s o b s e r v a t i o n o r an a d d i t i o n a l s a m p l i n g o f a p a r t i c u l a r s y s t e m o u t p u t .
System t h e o r y d e f i n e s t h e s t a t e o f a d i s c r e t e s y s t e m as "some compact
représen-tation of the past activity of the system complete enough to allow us to predict, on the basis of the inputs, exactly what the Outputs will be and also to update
the state itself" [ P a d u l o , A r b i b , 197M- "S° the future values of the state as well as the Outputs are only determined by the initial values of the state and
the following inputs" [Kok, Van W i j k , 1 9 7 8 ] . T h e r e f o r e , t h e i n p u t o u t p u t r e l a t i o n o f a dynamic s y s t e m c a n be d e s c r i b e d b y two équations : One équation y i e l -d i n g t h e p r o g r e s s i v e change i n t i m e o f t h e s y s t e m s t a t e -due t o t h e i n p u t s , a n -d a second équation a s s o c i a t i n g t h e O u t p u t s o f t h e s y s t e m t o t h e a c t u a l v a l u e o f
t h e s y s t e m s t a t e , t h u s :
x ( k + 1) = A x ( k ) + B u ( k ) + Gw(k) ; y ( k ) = C x ( k ) .
The m a t r i c e s A, B and G c a n be r e g a r d e d as s y s t e m p a r a m e t e r s , and t h e m a t r i x C i s t h e d i s p l a y p a r a m e t e r .
I n o r d e r t o d e s c r l h e human o p e r a t o r ' s s u p e r v i s o r y b e h a v i o r , t h e model s u g g e s t e d by Kok and Van W i j k [ 1 9 7 8 ] w i l l be a p p l i e d . T h i s model i s b a s e d on t h e p h y l o s o phy t h a t t h e human s u p e r v i s o r a c t s as some k i n d o f s u b o p t i m a l c o n t r o l l e r , t a k i n g i n t o a c c o u n t t h e i n h e r e n t l i m i t a t i o n t h a t h i s o b s e r v a t i o n o f t h e ouput p r o -c e s s v a r i a b l e s -c a n be i n a -c -c u r a t e . T h i s l i m i t a t i o n i s m o d e l l e d b y a n o i s e vQ( k ) ,
c a l l e d t h e o b s e r v a t i o n n o i s e . I t i s assumed t h a t t h e human s u p e r v i s o r p o s s e s s e s e x a c t knowledge o f t h e g e n e r a t e d c o n t r o l s i g n a i s u ( k ) . Hence, t h e model
con-s i con-s t con-s o f t h r e e S u b con-s y con-s t e m con-s : an observer, a controller and a décision making element,
DME, t h e l a s t one a c t i n g on each o f t h e two o t h e r Subsystems ( F i g . 1 ) .
control input system dist urbane es d(k) system dynamics system stote x(k) display
observed output ytkP «uj*™lsed system I automatic control-, control-, I 1er and interface lobserved input
uCk)
CONTROL ACTIONS OBSERVATION ACTIONS i OBSERVATIONS L J control decjTsion t
±
Idecision-making -1 part icontrollerl part x(k) I error I variance Observationcfëcision"' Observation input
noise. state estimate idynamic|_ X observer**""" ° ,v;(k) part uTk) *ÎTk 1 observer/controlter/ décision model of the human supervisor output pt(k) observation noise
The s t r u c t u r e o f t h e observer i s d e p i c t e d i n F i g . 2; i t i s modeled as a Kalman
f i l t e r , t h u s i t c o n t a i n s a r e p l i c a o f t h e s y s t e m i n c l u d i n g t h e d i s p l a y .
Based on t h e o b s e r v e d o u t p u t v a r i a b l e s , on t h e knowledge o f t h e dynamics o f t h e s y s t e m , on t h e knowledge o f t h e s t a t i s t i c a ! p r o p e r t i e s o f t h e n o i s e a c t i n g upon t h e s y s t e m , and on t h e s e t p p i n t changes w h i c h have been made a l r e a d y t h e o b s e r -ver estimâtes t h e s t a t e o f t h e s y s t e m x ( k ) and t h e a s s o c i a t e d v a r i a n c e o f t h e e s t i m a t i o n e r r o r V^. I n t h i s p a r t o f t h e m o d e l , t h e n o i s e v e c t o r s vQ( k ) w i t h t h e
c o v a r i a n c e m a t r i x 4» I s assumed t o be w h i t e and n o r m a l l y d i s t r i b u t e d . As a c o n -o
séquence t h e m a t r i x \\> i s a d i a g o n a l m a t r i x . The q u a n t i t y \p models t h e r a t e
o o o f u n c e r t a i n t y o f t h e s u p e r v i s o r about t h e p e r c e i v e d O u t p u t s o f t h e s y s t e m . The
q u a n t i t y i s a p a r a m e t e r o f t h e o b s e r v e r s u b s y s t e m .
commanded input i^lkl
1 model of the correction of observer gain
1 system dynamics e s t i m â t e s K 1
reconstructed
1
estimoted state 1 internal model
x(k! 1 1 of the system to
1
model of the 1 be controlled i 1 display 1 innovation L _ observed output corrupted by observât ion noisey i k l . v . l k )
'reconstructed or estimated output
y(k)
Figure 2: Structure of the observer
The s u b s y s t e m , t h e controller, can be r e g a r d e d as a v a r i a n t o f t h e optime,! c o n
-t r o l l a w . I -t i s s u p p o s e d -t h a -t -t h e human o p e r a -t o r w i l l c o n -t r o l dévia-tions, f r o m o u t s i d e t h e l i m i t s , b a c k t o t h e n o m i n a l v a l u e i n a c e r t a i n p e r i o d . Hence, when t h e p e r i o d , i n w h i c h t h e o u t p u t v a r i a b l e w i l l r e a c h t h e n o m i n a l v a l u e , i s d e t e r m i n e d , t h e n t h e a m p l i t u d e o f t h e s e t p o i n t c o r r e c t i o n I s a l s o f i x e d ; a s h o r t p e -r i o d -r e q u i -r e s a l a -r g e -r a m p l i t u d e t h a n i n a l o n g e -r p e -r i o d . T h i s t -r a d e - o f f between p e r i o d a n d a m p l i t u d e I s modeled b y t h e p a r a m e t e r "p" i n t h e s i n g l e s t e p c o n t r o l l a w w h i c h w i l l be u s e d as controller.
From t h i s c o n t r o l l a w : u ( k ) = u nom(p) - L ( p ) x ( k ) , where u nom dénotes t h e nomin a l I nomin p u t v a l u e , L dénominotes t h e g a i nomin f a c t o r anomind u ( k ) t h e magnominitude of' t h e c o r r e c -t i v e a c -t i o n , a i l -t h e q u a n -t i f i e s a r e known e x c e p -t p , -t h e model p a r a m e -t e r , w h i l e t h e g a i n f a c t o r , L , i s dépendent o f p. I t i s supposed t h a t t h e human o p e r a t o r b a -ses t h e q u a n t i t y u ( k ) on t h e e s t i m a t i o n o f t h e a c t u a l s y s t e m s t a t e , x ( k ) , a n d i s s u p p o s e d n o t t o t a k e i n t o a c c o u n t e f f e c t s o f t h e s y s t e m n o i s e d u r i n g t h e p e r i o d i n w h i c h t h e a c t i o n i s k e p t c o n s t a n t . W i t h t h e s i n g l e s t e p c o n t r o l l a w i t w i l l be p o s s i b l e t o r e a c h i n p t i m e s t e p s an o u t p u t v e c t o r y ( k + p ) w h i c h i s e q u a l t o t h e n o m i n a l o u t p u t v e c t o r , y nom, as l o n g as t h e s y s t e m n o i s e i s z e r o w i t h i n t h a t p e r i o d . Because t h e s y s t e m n o i s e i s p r o b a b l y n o t z e r o a " s u b g o a l " w i l l be r e a c h e d . The DME p r o v i d e s two f u n c t i o n s : F i r s t l y i t models t h e moments on w h i c h an a d d i
a s e t p o i n t c o r r e c t i o n has t o he p e r f o r m e d . The i n p u t s o f t h e DME a r e t h e s y s t e m s t a t e e s t i m a t e x ( k ) and i t s v a r i a n c e V^; t h e f i r s t f u n c t i o n makes use o f x ( k ) and V^, t h e l a s t one uses x ( k ) o n l y .
The a d d i t i o n a l o b s e r v a t i o n s a m p l i n g i s modeled a c c o r d i n g t o a h y p e r b o l i c d e c i s i o n r u l e ( F i g . 3 ) . Whenever the c o m b i n a t i o n o f t h e a b s o l u t e v a l u e o f t h e e s t i m a t i o n o f t h e d e v i a t i o n ! y . ( k ) - y .1 w i t h r e g a r d t o t h e nomi-X Il OBI, 1 n a l v a l u e , y ., o f an o u t p u t , y . ( k ) , and t h e u n c e r t a i n t y about t h a t p a r t i c u l a r e s t i m a t i o n , O y - ( k ) , exceeds a c r i t e r i o n v a l u e , a sample w i l l be t a k e n . The q u a n t i t i e s fj_{k) and av^ ( k ) are d e r i v e d as a l i n e a r f u n c t i o n o f
t h e s t a t e e s t i m a t e , x ^ ( k ) , and t h e a s s o c i a t e d v a r i a n c e , V^, r e s p e c t i v e l y . The m o d e l i n g p a r a m e t e r s are t h e c u r v a t u r e o f t h e h y p e r b o l i c l i n e , CE-j_, and t h e asymptot v a l u e o r m i n i m a l a c c e p t e d u n c e r t a i n t y , a ., where i
deno-t e s deno-t h e i - deno-t h o u deno-t p u deno-t v a r i a b l e . ^ min 1
The c o n t r o l l e r d e c i s i o n s a r e modeled as a s t r a i g h t l i n e ( F i g . h). Whenever,
t h e a b s o l u t e v a l u e o f t h e d e v i a t i o n between t h e e s t i m a t e d o u t p u t and t h e n o m i n a l v a l u e , |y. - y .1, exceeds t h e l i n e q., a c o r r e c t i v e a c t i o n w i l l
1 l nom l . . i .
be made. The upper o r Tower t o l e r a n c e l i m i t , q^, i s t h u s a l s o model parame-t e r .
u n c e r t a i n t y
Figure 3: The hyperbolic decision-rule Figure 4: The linear decision-rul
3.2 Separation Theorem / Model hypotheses
As p o i n t e d out a l r e a d y i n t h e p r e c e e d i n g s e c t i o n , t h e O b s e r v e r / C o n t r o l l e r / D e c i s i o n - m o d e l , 0CDmodel, i s b a s e d on t h e c o n c e p t u a l framework o f t h e O p t i -mal C o n t r o l M o d e l o f B a r o n , e t . a l [ 1 9 6 9 ] , K l e i n m a n , e t . a l [ 1 9 7 0 , 1 9 7 1 ] . The b a s i c a s s u m p t i o n o f t h i s model i s t h a t a w e l l - t r a i n e d and h i g h l y m o t i v a t e d human o p e r a t o r w i l l a c t i n a n e a r o p t i m a l way, s u b j e c t t o h i s i n t e r n a l c o n -s t r a i n t -s w h i c h l i m i t h i -s p e r f o r m a n c e , and -s u b j e c t t o t h e e x t e n d t o w h i c h he u n d e r s t a n d s t h e t a s k o b j e c t i v e s . T h i s model can a p p r o p r i a t e l y be u s e d t o p r e d i c t manual c o n t r o l b e h a v i o r ACMC,[196H - 1980]. The OCD-model i s an ex-t e n s i o n o f ex-t h e O p ex-t i m a l C o n ex-t r o l M o d e l , j u s ex-t by ex-t h e i n ex-t r o d u c ex-t i o n o f a DME.
I t i s a l s o d i f f e r e n t by t h e f a c t t h a t a s i n g l e s t e p c o n t r o l law as a m o d i f i -c a t i o n o f t h e o p t i m a l -c o n t r o l law i s p r o p o s e d , i n s t e a d o f t h e o p t i m a l , -c o n t i nuous c o n t r o l l a w . F i n a l l y i t d i f f e r s by t h e f a c t t h a t most o f t h e i n t e r n a l
c o n s t r a i n t s w h i c h were t a k e n i n t o a c c o u n t i n t h e OCM a r e assumed t o be ne-g l e c t a b l e . T h i s a s s u m p t i o n seems s e n s i b l e due t o t h e l a r ne-g e t i m e c o n s t a n t s i n v o l v e d i n t h e s t e a d y - s t a t e s u p e r v i s o r y c o n t r o l mode; hence a s p e c t s l i k e r e a c t i o n t i m e s o f 0.1 sec and n e u r o m u s c u l a r dynamics w i t h t i m e c o n s t a n t s o f 100 t o 200 m s e c , i m p o r t a n t i n the OCM, can be n e g l e c t e d i n t h e OCD-model.
I n t h e case o f the' O p t i m a l C o n t r o l Model t h e w e l l - k n o w n séparation t h e o r e m i s v a l u a b l e as a b a s i c t o o l . No arguments can he f o u n d , t o p r o o f t h a t t h e séparation p r i n c i p i e can a l s o he a p p l i e d i n t h e case o f t h e OCD-model, s i n c e w i t h t h e i n t r o d u c t i o n o f t h e DME, t h e model becomes n o n - l i n e a r , whereas l i n e a r l t y i s one o f t h e n e c e s s a r y c o n d i t i o n s i n o r d e r t o be a l l o w e d t o a p p l y t h e séparation p r i n c i p i e . The i m p o r t a n c e o f t h e séparation t h e o r e m , however, makes t h a t i t may be f r u i t f u l t o s t u d y t o what e x t e n d t h e DME I n f l u -ences t h i s i m p o r t a n t p r i n c i p i e ; t h e r e f o r e t h e f o l l o w i n g hypothèses have been s t a t e d :
. V a r i a t i o n s i n t h e i n t e n s i t y o f t h e s y s t e m d i s t u r b a n c e s a r e c h a n g i n g t h e p a -r a m e t e -r v a l u e s o f t h e o b s e -r v e -r ; t h e y a -r e n o t I n f l u e n c i n g t h e p a -r a m e t e -r s o f the c o n t r o l l e r . Changes o f t h e p a r a m e t e r v a l u e s o f t h e décision making élé-ment f o r O b s e r v a t i o n a c t i o n s w i l l a l s o t a k e p l a c e .
. V a r i a t i o n s i n t h e d i s p l a y s t r u c t u r e a r e a l s o c h a n g i n g t h e p a r a m e t e r v a l u e s o f t h e o b s e r v e r , and t h e décision making élément f o r t h e o b s e r v a t i o n a c t i o n s ; t h e y a r e n e i t h e r c h a n g i n g t h e p a r a m e t e r v a l u e s o f t h e c o n t r o l l e r , n o r t h e p a -r a m e t e -r s o f t h e décision making élément f o -r t h e c o n t -r o l l e -r a c t i o n s .
. V a r i a t i o n s i n t h e t a s k t o be p e r f o r m e d a r e c h a n g i n g t h e p a r a m e t e r v a l u e s o f t h e c o n t r o l l e r and t h e décision making élément f o r t h e c o n t r o l l e r a c t i o n s ; t h e y a r e n o t c h a n g i n g t h e p a r a m e t e r v a l u e s o f t h e o b s e r v e r and t h e décision making élément f o r t h e o b s e r v a t i o n a c t i o n s .
. V a r i a t i o n s i n t h e dynamics o f t h e s y s t e m t o be s u p e r v i s e d a r e c h a n g i n g a l l t h e p a r a m e t e r v a l u e s I n t h e model.
I n T a b l e I I t h e p o s t u l a t e d r e l a t i o n s between t h e t a s k v a r i a b l e s and t h e p a r a -meters o f t h e model a r e r e p r e s e n t e ! , where a p l u s , +, denotes a dependency and where a zéro, 0, denotes i n d e p e n d e n c y .
Table II: Postulated relations between task variables and model parameters.
P a r a m e t e r s o f : O b s e r v e r p a r t O b s e r v e r Décision p a r t C o n t r o l l e r Décision p a r t C o n t r o l l e r P a r t Task v a r i a b l e s : System D i s t u r b a n c e s + + 0 0 D i s p l a y S t r u c t u r e + + 0 0 Task R e q u i r e m e n t s 0 0 + + System Dynamics + + + + S i n c e t h e p a r a m e t e r s t h e m s e l v e s a r e d i f f i c u l t t o i n t e r p r e t , and s i n c e t h e y cannot be i d e n t i f i e d e a s i l y , a smooth way o f verificatión o f t h e s e h y p o t h e s e s cannot be f o u n d d i r e c t l y . T h e r e f o r e , i t i s w o r t h w h i l e t o t r a n s f o r m t h e hypo-t h e s e s hypo-t o d i r e c hypo-t l y m e a s u r a b l e q u a n hypo-t i hypo-t i e s . S i n c e q u a n hypo-t i hypo-t i e s l i k e hypo-t h e number o f o b s e r v a t i o n a c t i o n s , t h e number o f c o n t r o l l e r a c t i o n s and t h e a m p l i t u d e o f t h e c o n t r o l a c t i o n s can be measured, and s i n c e t h e y a r e d i r e c t l y r e l a t e d t o t h e s t r u c t u r e o f t h e s y s t e m t o be s u p e r v i s - e d , one can r e f o r m u l a t e t h e h y p o t h e s e s as f o l l o w s :
. V a r i a t i o n s i n t h e i n t e n s i t y o f t h e s y s t e m d i s t u r b a n c e s w i l l be r e f l e c t e d i n t h e number o f o b s e r v a t i o n a c t i o n s , and w i l l be r e f l e c t e d i n an a d d i t i o n a l way i n t h e number o f c o n t r o l l e r a c t i o n s . However, i t w i l l n o t be r e f l e c t e d
i n t h e mean a m p l i t u d e o f t h e c o n t r o l l e r a c t i o n s . . V a r i a t i o n s o f t h e d i s p l a y s t r u c t u r e w i l l o n l y be r e f l e c t e d i n t h e number o f o b s e r v a t i o n a c t i o n s ; t h e y w i l l n e i t h e r i n f l u e n c e t h e number o f c o n t r o l l e r a c t i o n s n o r t h e mean o f t h e a m p l i t u d e s o f t h e c o n t r o l l e r a c t i o n s . . V a r i a t i o n s i n t h e t a s k r e q u i r e m e n t s w i l l be r e f l e c t e d i n t h e number o f c o n -t r o l l e r a c -t i o n s ; -t h e y w i l l n o -t be r e f l e c -t e d i n -t h e number o f o b s e r v a -t i o n a c t i o n s ( T a b l e I I I a n d F i g . 5 ) .
Two remarks have t o be made i n r e l a t i o n t o t h e s e h y p o t h e s e s :
a c c o u n t h e r e , because t h e vérification o f h y p o t h e s i s on t h e i n f l u e n c e o f t h e s y s t e m dynamics as a t a s k v a r i a b l e w i l l i n c r e a s e e n o r m o u s l y t h e number o f ex-p e r i m e n t s .
In t h e s e c o n d p l a c e t h e s u p p l e m e n t a t i o n " i n an a d d i t i o n a l way" i n t h e f i r s t h y p o t h e s i s needs some e x p l a n a t i o n . To v e r i f y t h e séparation t h e o r e m , i t h a s t o be shown t h a t o p t i m i z a t i o n of t h e f i l t e r i n g and t h e c o n t r o l p r o b l e m , s e p a r a t e l y , w i l l l e a d t o t h e same r e s u l t s as o p t i m i z a t i o n o f t h e combined p r o blem. E e f e r i n g t o t h e model f i r s t d i s c u s s e d , a n d t a k i n g i n t o a c c o u n t t h e i n -f l u e n c e s o -f t h e t a s k v a r i a b l e s j u s t - m e n t i o n e d , a conséquence o -f t h e sépara-t i o n sépara-t h e o r e m i s sépara-t h a sépara-t sépara-t h e s u p e r - p o s i sépara-t i o n p r i n c i p l e s h o u l d h o l d . Hence, sépara-t h e t a s k v a r i a b l e s y s t e m d i s t u r b a n c e s i s t h o u g h t t o c o n t r i b u t e , i n an a d d i t i o n a l way, a number o f c o n t r o l l e r a c t i o n s w h i c h i s i n d e p e n d e n t o f t h e number o f c o n t r o l l e r a c t i o n s a t t r i h u t e d b y t h e t a s k v a r i a b l e t a s k r e q u i r e m e n t s .
Table III: Postulated relation between task variables and direct measurdble quantities. Q u a n t i t y : Number o f O b s e r v a t i o n a c t i o n s Number o f C o n t r o l l e r a c t i o n s Mean A m p l i t u d e o f C o n t r o l l e r a c t i o n s Task v a r i a b l e : System D i s t u r b a n c e s + + 0 D i s p l a y S t r u c t u r e + 0 0 Task R e q u i r e m e n t s 0 + + Number o f ob- 4 s e r v a t i o n a c -t i o n s D i s p l a y S t r u c t u r e System D i s t u r b a n c e s Task R e q u i r e m e n t s Number o f c o n t r o l l e r a c t i o n s
Figure 5: Postulated relation between task variables and direct measurable quantities
4. EXPERIMENTAL DESIGN
k.\ Description of. the research vehicle
I n t r y i n g t o v e r i f y t h e h y p o t h e s e s s t a t e d i n t h e l a s t s e c t i o n , one needs a r e s e a r c h v e h i c l e on w h i c h e x p e r i m e n t s can be p e r f o r m e d . F o r t h i s r e a s o n a s e t p o i n t c o n t r o l l e d p r o c e s s s i m u l a t i o n h a s been i m p l e m e n t e d on a PDP 11/34 computer. The p r o c e s s , a U t i l i t y P l a n t , i s c o n s i d e r e d t o be a l i n e a r s y s t e m and i t c o n s i s t s o f a B o i l e r , a Back P r e s s u r e T u r b i n e and a C o n d e n s i n g T u r -b i n e . The B o i l e r p r o d u c e s h i g h p r e s s u r e steam w h i c h i s , p r e s s u r e c o n t r o l l e d . The Back P r e s s u r e T u r b i n e consumes H.P.-steam a n d p r o d u c e s l o w p r e s s u r e steam a n d e l e c t r i c a l power; t h i s l o w p r e s s u r e steam i s f l o w c o n t r o l l e d . T h e C o n d e n s i n g T u r b i n e consumes H.P.-steam a n d p r o d u c e s o n l y e l e c t r i c a l power. The t o t a l amount o f e l e c t r i c a l power p r o d u c e d i s power c o n t r o l l e d ( F i g . 6 ) .
steam
Figure 6: Structure of the Utility Plant
h,2 Description of the task of the Supervisor
The t a s k o f t h e human O p e r a t o r i s t o keep t h e t h r e e o u t p u t v a r i a b l e s , i . e . t h e p r e s s u r e o f t h e H.P.-steam, t h e f l o w o f L.P.-steam and e l e c t r i c a l power w h i c h a r e c o r r u p t e d b y s y s t e m d i s t u r b a n c e s , w i t h i n s p e c i f i e d b o u n d a r i e s . These b o u n d a r i e s a r e s y m e t r i c a l l y l o c a t e d a r o u n d a c e r t a i n n o m i n a l v a l u e . The Outputs a r e d i s p l a y e d d i g i t a l l y ; t h e b o i l e r o u t p u t can be o b s e r v e d c o n -t i n u o u s l y whereas -t h e -two o -t h e r Ou-tpu-ts can be sampled o n l y on r e q u e s -t . The t a s k o f t h e O p e r a t o r i s t o sample as few as p o s s i b l e , and t o c o r r e c t t h e s e t - p o i n t s as few as p o s s i b l e . The c o n t r o l s h o u l d be p e r f o r m e d o n l y w i t h s m a l l c o r r e c t i v e a c t i o n s .
The O p e r a t o r s w i l l be m a s t e r s t u d e n t s o f t h e L a b . f o r Measurement & C o n t r o l o f t h e department o f M e c h a n i c a l E n g i n e e r i n g .
h.3 The expérimental set-up
Three t a s k v a r i a b l e s have been chosen f o r t h e expérimental s e t - u p , i . e . a v a r i a t i o n i n System d i s t u r b a n c e s , i n d i s p l a y s t r u c t u r e and i n t a s k r e q u i r e -ments.
V a r i a t i o n s i n t h e system disturbances: Each output v a r i a b l e i s d i s t u r b e d by
a f i r s t o r d e r n o i s e w i t h a l o w i n t e n s i t y , d e n o t e d as n , o r w i t h a h i g h i n -t e n s i -t y , d e n o -t e d as ïï.
V a r i a t i o n s i n t h e display structure: Each déviation between output and a
s p e c i f i e d b o u n d a r y can be i n d i c a t e d i n one o f t h e two f o l l o w i n g ways. By t h e l o c a l a l a r m s t r u c t u r e , d e n o t e d as d, a d i r e c t i n d i c a t i o n i s g i v e n w h i c h o u t p u t i s o u t o f t h e b o u n d a r i e s and i n what d i r e c t i o n t h e v a r i a b l e i s chan-g i n chan-g . By t h e c e n t r a l a l a r m s t r u c t u r e , d e n o t e d as D, i t i s o n l y i n d i c a t e d w h e t h e r one o f t h e o u t p u t v a r i a b l e s i s d e v i a t e d f r o m one o f t h e s p e c i f i e d
l i m i t s . The human O p e r a t o r has t o i n v e s t i g a t e w h i c h o u t p u t i s d e v i a t i n g and i n what d i r e c t i o n t h e o u t p u t i s c h a n g i n g ; he even has t o make s u r e t h a t t h e r e i s o n l y one o u t p u t d e v i a t i n g f r o m t h e s p e c i f i e d l i m i t s . More i n f o r m a t i o n can be a s k e d f o r by means o f t a k i n g a d d i t i o n a l s a m p l e s .
V a r i a ^ i o n i n t h e task requirements: The l o w e r and upper l i m i t s o f each o u t
-put v a r i a b l e a r e s p e c i f i e d . F o r t h e case t h a t l o w e r and u p p e r l i m i t a r e c l o s e t o each o t h e r t h e t a s k i s d i f f i c u l t ( B ) ; f o r t h e case t h e y a r e f a r away f r o m each o t h e r , t h e t a s k i s r a t h e r e a s i l y ( b ) .
I n t h e expérimental s e t - u p each c o n d i t i o n c o n s i s t s o f a c o m b i n a t i o n o f one o f t h e two l e v e l s o f t h e t h r e e t a s k v a r i a b l e s i n v o l v e d . T h e r e f o r e , e i g h t c o n d i t i o n s can be formed. I n t h e f i r s t vérification phase f o u r c o n d i t i o n s were c o n s i d e r e d , t h e y w e r e : n.d.b; n.D.b; N.d.b; N.D.b. I n t h e s e c o n d
véri-f i c a t i o n phase t h e c o n d i t i o n s were: n.d.B; n.D.B; N.d.B; N.D.B.
5. TESTING THE HYPOTHESES
I n t r y i n g t o v e r i f y t h e h y p o t h e s e s , one needs t o be s u r e t o base t h e véri-f i c a t i o n on a r o b u s t s e t o véri-f d a t a o véri-f w e l l - t r a i n e d o p e r a t o r s . The c r i t e r i a i n o r d e r t o c o n c l u d e w h e t h e r t h e d a t a i s o r i g i n a t i n g f r o m w e l l t r a i n e d s u b -j e c t s , a r e t w o f o l d . A t f i r s t , t h e number o f samples t a k e n and t h e number o f c o r r e c t i v e a c t i o n s p e r f o r m e d s h o u l d a p p r o a c h a c o n s t a n t l e v e l f o r e a c h c o n -d i t i o n . S e c o n -d l y , t h e compute-d a b s o l u t e v a l u e o f t h e -déviation intégrais, b a s e d on t h e t i m e t h a t t h e s i g n a l i s o u t s i d e t h e s p e e l l i e d b o u n d a r i e s , s h o u l d be as c l o s e as p o s s i b l e t o z e r o . F o r t e s t i n g t h e h y p o t h e s e s on t h e b a s i s o f t h e f i r s t f o u r c o n d i t i o n s t h e d a t a o f n i n e t r i a l s were c o n s i d e r e d . The n e c e s s a r y c o n d i t i o n s i n o r d e r t o a p p l y p a r a m e t r i c s t a t i s t i c s were c h e c k e d . T h e r e a f t e r , an i n v e s t i g a t i o n w h e t h e r t h e c o l l e c t e d d a t a were s t a t i s t i c a l l y s e e n , i n f l u e n c e d b y p o s s i b l e l e a r n i n g e f -f e c t s was p e r -f o r m e d . No l e a r n i n g e -f -f e c t s c o u l d be d e t e c t e d . As an i n d i c a t i o n , more t h a n 100 ( c a t c h ) t r i a l s p r e c e e d e d t h e a c t u a l 36 t r i a l s . F i g . 7 shows
t h e 99% c o n f i d e n c e i n t e r v a l o f a T-Student d i s t r i b u t i o n o f t h e number o f samp l e s t a k e n a n d t h e number c o n t r o l a c t i o n samp e r f o r m e d , f o r each o f t h e f o u r c o n -d i t i o n s . The f i g u r e shows t h a t a change i n t h e -d i s p l a y s t r u c t u r e e f f e c t s o n l y t h e number o f samples t a k e n and n o t t h e number o f c o n t r o l l e r a c t i o n s e x e c u t e d ; T a b l e I V r e v e a l s t h e e x a c t r e s u l t s .
Table IV: Results of a T-test
V a r i a b l e Number o f c a s e s Me an SD 2 - t a i l p r o b Sampl group n,d,b group n,D,b 9 9 0 . 7 2 1 . 7 2 . 0 3.1 0 . 0 0 0 C o n t r group n,d,b group n,D,b 9 9 7 7 . 2 7 9 . 8 3 . 6 7 A 0 . 3 5 3 Sampl group N,d,b group N,D,b 9 9 l U . 8 U T . O 6 . 5 1 1 . 0 0 . 0 0 0 C o n t r group N,d,b group N,D,b 9 9 1 1 5 . 9 1 0 8 . 2 1 6 . 6 9 . 1 0.21+2 F u r t h e r m o r e I t can be s e e n , t h a t v a r i a t i o n i n t h e i n t e n s i t y o f t h e s y s t e m d i s t u r b a n c e s I s r e f l e c t e d i n t h e number o f o b s e r v a t i o n a c t i o n s , whereas i t i s a l s o a d d i t i v e i n t h e number o f c o n t r o l l e r a c t i o n s ; T a b l e V shows t h e e x a c t r e s u l t s .
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n u m b e r o f c o n t r o l a c t i o n s160
Figure 7: Obtained results of four expérimental conditions
Table V: Results of a T-test
V a r i a b l e Number o f c a s e s Me an SD 2 - t a i l p r o b . Sampl group n,d,b group N,d,b 9 9 0 . 7 1 4 . 8 2 . 0 6 . 5 0 . 0 0 0 C o n t r group n,d,b group N,d,b 9 9 7 7 . 2 1 1 5 . 9 3 . 6 1 7 . 6 0 . 0 0 0 Sampl group n,D,b group N,D,b 9 9 2 1 . 7 U 7 . 0 3 . 1 1 1 . 0 0..000 C o n t r group n,D,b group N,D,b 9 9 7 9 - 9 1 0 8 . 2 7 . ^ 9-1 0 . 0 0 0
As l o n g as t h e t a s k r e q u i r e m e n t s have n o t been changed i n t h e f o u r c o n d i t i o n s , t h e mean a m p l i t u d e o f t h e c o n t r o l l e r a c t i o n s was s u p p o s e d t o r e m a i n c o n s t a n t . F o r vérification t h e r e s u l t s o f t h e T - t e s t showed no s i g n i f i c a n t différence between t h e f o u r c o n d i t i o n s ( F i g . 8 ) . So t h e hypothèses w i t h r e s p e c t t o t h e
t a s k v a r i a b l e s , d i s p l a y s t r u c t u r e , a n d s y s t e m d i s t u r b a n c e s , can be a c c e p t e d c o m p l e t e l y .
The t h i r d t a s k v a r i a b l e t h e " t a s k r e q u i r e m e n t " , i s s u p p o s e d t o have o n l y a e f f e c t on t h e number o f c o n t r o l l e r a c t i o n s and n o t on t h e number o f o b s e r v a -t i o n a c -t i o n s . By c o m p a r i n g F i g . 9 and F i g . 7 , i t can be seen t h a t o n l y i n one
case t h e r e s u l t s o f a v a r i a t i o n i n t h e t a s k r e q u i r e m e n t s déviâtes f r o m t h e p o s t u l a t e d e f f e c t s ; i n c o n d i t i o n n,D,B more samples a r e t a k e n t h a n i n c o n d i -t i o n n,D,b.
. 30 r
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n.D.b N,d.b controLLer 4 b o i t e r controLLer " back p r e s s u r e — t u r b i n e • r controLLer -TTTr.condensing t u r b i n eFigure 8: Number of set-point corrections of three output variables in four expérimental conditions
tn
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N.D.B n.D.B N.d.B n.d.B0 20 40 60 80 100 120 140 160
n u m b e r of controL a c t i o n sFigure 9: Obtained results of four expérimental conditions
R e s u l t s o b t a i n e d w i t h a l e s s t r a i n e d s u b j e c t were s i m i l a r w i t h r e s p e c t t o t h e t a s k v a r i a b l e s , d i s p l a y s t r u c t u r e a n d System d i s t u r b a n c e s i n t h e c o n d i t i o n s : n,d,b; n,D,b; N,d,b; N,D,b. The r e s u l t s were s l i g h t l y l e s s s i g n i f i c a n t (p<.02). The r e s u l t s w i t h r e s p e c t t o t h e t a s k v a r i a b l e t a s k r e q u i r e m e n t s do n o t agrée w i t h t h e hypothèses; even t h e r e s u l t s i n t h e c o n d i t i o n s n,d,B; n,D,B; N,d,B; N,D,B where t h e t a s k v a r i a b l e s d i s p l a y s t r u c t u r e System d i s t u r b a n c e s were v a r i e d s y s t e m a t i c a l l y , were r a t h e r p o o r , a l t h o u g h . t h e t r e n d s were i n t h e p r e d i c -t e d d i r e c -t i o n .
In t r y i n g t o u n d e r s t a n d why t h e h i g h l y s i g n i f i c a n t r e s u l t s w i t h t h e w e l l -t r a i n e d s u b j e c -t were no-t r e p l i c a -t e d by -t h e l e s s - -t r a i n e d s u b j e c -t , and i n p a r t i c u l a r f o r t h e case o f t h e t a s k v a r i a b l e t a s k r e q u i r e m e n t , an a d d i t i o -n a l i -n v e s t i g a t i o -n was made.
Due t o t h e f a c t t h a t t h e s e c o n d s u b j e c t s a m p l e d about t h r e e t i m e s more t h a n t h e w e l l - t r a i n e d s u b j e c t i n each c o n d i t i o n and due t o t h e f a c t t h a t he a l s o c o n t r o l l e d about 1.3 t i m e s more t h a n t h e f i r s t s u b j e c t , t h e i d e a o f a r o o f o r c e i l i n g e f f e c t , s p o i l i n g t h e e x p e c t e d r e s u l t s , was p r o b e d . I n a new expérimental s e t u p t h e w e l l t r a i n e d s u b j e c t was e x c l u d e d f r o m any a l a r m i n d i c a t i o n when he was s u p e r v i s i n g t h e U t i l i t y P l a n t . So t h e t a s k v a r i a b l e d i s p l a y s t r u c t u r e got a t h i r d l e v e l . Here i t s h o u l d be n o t e d t h a t no a l a r m i n d i -c a t i o n i n t h e o t h e r two l e v e l s , l o -c a l a l a r m and -c e n t r a l a l a r m , -c a r r i e s a t l e a s t t h e i n f o r m a t i o n t h a t none o f t h e o u t p u t s i s out o f t h e b o u n d a r i e s . I n t h e new, expérimental s i t u a t i o n , he even d i d n o t get t h i s i n f o r m a t i o n , so t h e s u b j e c t had t o sample much more than b e f o r e , Independent o f w h e t h e r t h e
S y s t e m d i s t u r b a n c e s were h i g h o r l o w , and w h e t h e r t h e b o u n d a r i e s were s m a l l
o r l a r g e . The number o f samples became about e q u a l t o t h e number o f samples o f t h e s e c o n d s u b j e c t . The r e s u l t s , o b t a i n e d from more t h a n 90 t r i a l s , i n d i c a t e d v e r y s t r o n g l y t h a t a r o o f e f f e c t c o u l d have been t h e cause o f t h e d i f -férences between t h e r e s u l t s o b t a i n e d w i t h t h e w e l l t r a i n e d s u b j e c t and those w i t h t h e l e s s t r a i n e d s u b j e c t .
6. PARAMETER IDENTIFICATION
In o r d e r t o v e r i f y t h e h y p o t h e s e s w i t h r e s p e c t t o t h e p a r a m e t e r s o f t h e m o d e l , no a n a l y t i c a l method f o r p a r a m e t e r e s t i m a t i o n c o u l d be d e r i v e d . T h e r e f o r e , c e r t a i n itération p r o c e d u r e s have been used. D u r i n g t h e p a r a m e t e r i d e n t i f i -c a t i o n , many d i f f i -c u l t i e s showed up. One d i f f i -c u l t y a p p e a r e d i n t h e p r o b l e m o f n o t c o n v e r g i n g t o a minimum o f one o f the a c c e p t e d c r i t e r i a , a n o t h e r d i f f i -c u l t y a p p e a r e d w i t h t h e l a r g e Computing t i m e o f 45 se-conds CPU o f a l a r g e s c i e n t i f i c o f f - l i n e computer System f o r o n l y one itération s t e p . T h e r e f o r e , much e f f o r t has been p u t i n r e d u c i n g t h e number o f itérations.
The main p a r a m e t e r o f t h e O b s e r v e r p a r t , ^ yQ, nas been chosen c o n s t a n t ; t h e
p a r a m e t e r v a l u e was chosen 1% o f t h e v a r i a n c e o f t h e a s s o c i a t e d o b s e r v e r o u t -p u t v a r i a b l e a c c o r d i n g t o r e s u l t s o b t a i n e d w i t h t h e O -p t i m a l C o n t r o l M o d e l
[ L e v i s o n , e t . a l . , 1969]- T h i s p a r a m e t e r w i l l be i d e n t i f i e d i n t h e n e a r f u t u r e . The p a r a m e t e r s f o r t h e o b s e r v a t i o n p a r t o f t h e DME, t h e c u r v a t u r e p a r a m e t e r CE^_, and t h e a s s y m p t o t Oy m^n ^ o f t h i s c u r v e , had t o be i d e n t i f i e d f o r e a c h
o f t h e o u t p u t s t o be sampled.. T h e r e f o r e , an a d a p t i v e random s e a r c h method be-ca.me t o o e x p e n s i v e . F o r t h i s r e a s o n a g r a p h i c a l method was p r o p o s e d .
Suppose t h e human o p e r a t o r s a m p l e d t h e i - t h o u t p u t v a r i a b l e a t t i m e :
t i i , ^ i k ' M n - aP P l y inS t h e o b s e r v e r p a r t , t h e a b s o l u t e v a l u e
o f t h e déviation between t h e e s t i m a t i o n o f the i - t h o u t p u t v a r i a b l e , y^, and t h e n o m i n a l v a l u e o f t h e i - t h o u t p u t v a r i a b l e , ynom i» and t h e a s s o c i a t e d
un-c e r t a i n t y about t h i s e s t i m a t i o n a •, can be d e r i v e d ; r e s p e c t i v e l y :
| y i 1 ~ Ynom i l ' I^ik ~ yn o m i t ' I^in ~ ^norn i l a n d- ay i 1 ' ••••• Gy i k s ay i n - ^n e k - t h sample i s l o c a t e d on t h e h y p e r b o l i c décision l i n e : ! i CEik '^Ik' ^nom i ' a - a y •, y • J Í K Jm m ík F o r t h e k - t h s a m p l e , t h e q u a n t i t l e s y ^ , yn 0m i and °y ík a r e c o n s t a n t s ; so t h e r e l a t i o n o f t h e s e q u a n t i t i e s w i t h the p a r a m e t e r s C E i k and c rymin ^ i s known. T h i s r e l a t i o n can be g i v e n as t h e s t r a i g h t l i n e , C Ei k = - | yi k - ynom i\ * aynom i k + | yi k - yno m ±\ * a and can be
p l o t t e d i n a ^ym^n ^ - CE^ p l a n e . T h i s r e l a t i o n can be g i v e n f o r a l l samples
o f the I - t h o u t p u t v a r i a b l e .
F i g . 10 shows the envelop l i n e s o f a l l t h e n "décision l i n e s " . In t h e a r e a o f convergence o f t h e e n v e l o p l i n e s , t h e o p t i m a l p a r a m e t e r s e t i s s u p p o s e d t o be l o c a t e d . T n i s i d e a can be e x p l a i n e d when 2 samples a r e t a k e n ; t h e c r o s s i n g o f
t h e two l i n e s , F i g . 11, shows t h e o n l y s o l u t i o n f o r two samples t o be l o c a t e d a t t h e same h y p e r b o l i c l i n e w i t h t h e a s s o c i a t e d a s y m p t o t . I n t h i s case c o n -v e r g e n c e i s n a r r o w e d down t o one p o i n t , a n d t h e -v a r i a n c e i s r e d u c e d t o zéro.
C E
' y m i n i
•
a.
ymm •cr, y m mExqure 10: Envelop Irnes %n a CE-a . Etqure 11: Two deoiston-lrnes •plane
By a p p l y i n g t h i s method, v e r y good r e s u l t s were o b t a i n e d , i . e . t h e number o f s a m p l e s , t a k e n b y t h e model b a s e d on t h e a c q u i r e d p a r a m e t e r s e t , a g r e e d w i t h t h e number o f O p e r a t o r samples t a k e n i n t h e same c o n d i t i o n . T h i s r e s u i t how-e v how-e r , dohow-es n o t g u a r a n t how-e how-e t h a t t h how-e i n s t a n t s i n t i m how-e o f O p how-e r a t o r s a m p l i n g a n d t h e I n s t a n t s i n t i m e o f s a m p l i n g o f t h e model agrée w i t h each o t h e r . T h e r e -f o r e , t h e d i s t r i b u t i o n o -f t h e s a m p l i n g i n v e r v a l s o -f t h e m o d e l , g i v e n c e r t a i n p a r a m e t e r v a l u e s o f CE^ and ay m^n j_, i s compared w i t h t h e d i s t r i b u t i o n o f
s a m p l i n g i n t e r v a i s o f t h e human O p e r a t o r . The d i s t r i b u t i o n s have t h e shape o f b i n o m i n a l d i s t r i b u t i o n s . A c l o s e r e s e m b l a n c e between t h e two d i s t r i b u t i o n s
o f O p e r a t o r s a m p l i n g and model s a m p l i n g f o r t h e two t o be sampled Outputs i s i l l u s t r a t e d i n F i g . 12 and F i g . 13. iJJ_Lli± Ç 0 9'i 6 P '•ai ü i o <P n i 20 ¿0 L'ft'fr-i'ml ifft.1 60 80 mtervol t e n g t h ( s e c ) s a m p l i n g o u t p u t h u m a n O p e r a t o r s a m p l i n g o u t p u t m o d e l 100 40 20 V 11111. rt r t i i . Li 20 ¿0 60 80 i n t e r v a l l e n g t h (sec) s u m p h n g o u t p u t h u m a n O p e r a t o r s a m p l i n g o u t p u t m o d e l 100
The p a r a m e t e r , p , o f t h e c o n t r o l l e r s u b s y s t e m , détermines t h e number o f t i m e s t e p s , t h e s e t p o i n t c o r r e c t i o n w i l l r e m a i n c o n s t a n t and détermines the a m p l i t u d e o f t h a t c o r r e c t i o n ; t h a t p a r a m e t e r , p , have t o be i d e n t i f i e d . In t h i s i n v e s t i g a t i o n différent p a r a m e t e r v a l u e s have been u s e d , whereas p = 22 t u r n e d out t o be t h e l o w e s t v a l u e b e f o r e i n s t a b i l i t y o f t h e H.P.-steam c o n t r o l l o o p o c c u r s . - W i t h p = 22 a l s o t h e b e s t c o n t r o l performances were o b t a i n e d . I n o r d e r t o r e l a t e thèse r e s u l t s w i t h o t h e r c o n t r o l s i t u a -t i o n s . T a b l e V I shows -t h e a b s o l u -t e v a l u e o f -t h e dévia-tion in-tégrais o f the t h r e e o u t p u t v a r i a b l e s o f t h e s u p e r v i s o r System f o r s e v e r a l c o n t r o l s i -t u a -t i o n s .
Table VI: Déviation scores of System outputs
D e v i a t i o n s c o r e o f : B o i l e r Back P r e s s u r e C o n d e n s i n g o u t p u t o u t p u t o u t p u t S i t u a t i o n : Non O p e r a t o r i n t e r v e n t i o n 1+00 106 50 O p t i m a l O p e r a t o r c o n t r o l 0 . 0 0.01 0 . 0 0 1 OCD-model c o n t r o l ; 137 73 58 S i n g l e s t e p c o n t r o l l a w (p=22) OCD-model c o n t r o l ; 0 . 3 5 10 9 - 5 O p t i m a l ( c o n t i n u o u s ) c o n t r o l l a w
The r e s u l t s a r e c l e a r : The o p t i m a l ( c o n t i n u o u s ) c o n t r o l l a w déviation s c o r e agrées m o s t l y w i t h t h e déviation s c o r e o f t h e human O p e r a t o r . However, t h e c h a r a c t e r i s t i c s o f t h e way o f C o n t r o l l i n g o f t h e model do n o t agrée a t a i l w i t h t h e discrète a c t i o n p a t t e r n o f t h e human O p e r a t o r . The number o f con-t r o l l e r a c con-t i o n s , i n i con-t i a con-t e d by con-t h e OCD model ( p= 2 2 ) , agrées w i t h t h e number o f c o n t r o l a c t i o n e x e c u t e d by t h e human O p e r a t o r ; a l s o , t h e discrète a c t i o n p a t t e r n o f t h e s i n g l e s t e p c o n t r o l l a w agrées w i t h human O p e r a t o r c o n t r o l a c t i o n s , b u t t h e o v e r a l l p e r f o r m a n c e o f t h e model e x p r e s s e d by t h e dévia-t i o n s c o r e s , i s s dévia-t i l l somewhadévia-t dévia-t r o u b l e s o m e .
7. CONCLUSIONS AND FINAL C0MMENTS
Whether t h e séparation t h e o r e m i s v a l i d o r n o t f o r t h e OCD-model, c a n n o t be answered r i g h t now. However, i t can be s a i d t h a t t h e r e s u l t s o b t a i n e d w i t h a h i g h l y t r a i n e d and m o t i v a t e d s u b j e c t showed t h e p o s t u l a t e d independency o f o b s e r v a t i o n and c o n t r o l .
I t can a l s o be s a i d t h a t most o f t h e model p a r a m e t e r s can be i d e n t i f i e d , a l t h o u g h t h e C o m p u t i n g t i m e i s s t i l l a l a r m i n g . T h e r e f o r e , t h e r e s e a r c h w i l l be c o n t i n u e d w i t h h i g h l y t r a i n e d s u b j e c t s ; i t w i l l d e a l w i t h changes i n t h e p a r a m e t e r c h o i c e o f t h e c o n t r o l l e r p a r t o r even a c c e p t i n g a n o t h e r c o n t r o l l a w and i t w i l l d e a l w i t h o p t i m i z i n g t h e p a -r a m e t e -r i d e n t i f i c a t i o n p-rocédu-res. REFERENCES
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