Model algorithmic control of industrial processes

Digi tal Computer Applications to Process Control, Van Nauta Lemke, ed. © IFAC and North-Holland Publishing Company (1977)

A G RI H IC C ichalet,

R

A. Rault,

C-10

F I D S RIAL PROCESSES J.L.

Testu

,

_ apon

ADERSA/GERBIOS

53, Avenue de l'Europe 78140 Velizy (France)

A new method of igital process control is described. It relies on three principles a) the multi-fariable plant is represented y its impul e responses which will be used on line by the control computer for long range prediction b) the behavior of the closed loop system is prescribed y means of reference trajectories initiated on the actual outputs ; c) the control variables are computed in a heuristic way with the same procedure used in identification which appears dual of control under this formulation. This method has been continuously and successfully applied to a dozen large scale industrial processes for more than a year's time. Its effective success is due to the ease of its implementation (e.g. constraints on the control variables) and to its amazing robustness as concerns structural perturbations. The economics of this control scheme is eloquent and figures can be put forward to demonstrate its efficiency. Optimality does not come from extraneous criteria on the control actions but from minimization of the error variance which permits to compute in a hierarchical way the set points of the dynamic control.

The principles of this al orithmic control scheme for industrial systems ave een presented in previous public at ion s [1], [5]. The r e for e in t his paper, the emphasis will be placed on applications since a ignifican number of complex industrial system have been ontrolled this procedure for more han wo year

I

The achievements of modern control theory are well known. Successful applications to aerospace guidance pro lems are remarkable. However the im le entation of suc techniques to indu trial control is not so successful. Industrial pro esses are qui e different, they are highly multivaria le sys ems, he clas ical no ion of order of the system no 10 ger mak e, er ur ations affec e lant s r c more of en han he easura le varia nd s rial processes erformance cri re

p

co tarole a

n

1

rol tree

103

104

.ODEL A COR T .'.IC CO .. TRO

S RIAL

aCE

he choice 0

C-IO

an

e

o 1

such

a

>

'T

i e 1el, con rol opera or or i era i e

R

e

'vi

ere s e

R

is

he

i

e re ponse of

hould u e as t - sa pli pure ef ec

1.1.1

Impulse Re ponse Represen ation

he main fea res of t are li ed elow.

is re_resen a

ion

Universali y Each ou

.(n)

J

0

a mul

sys em is a wei h ed s m of inpu s ej(n) (Fig. 1)

aria le

he

E

past

i

e

e

sa e

e- ela s or .on are ea il taken

- If the s stems were to be naturally unsta le - which rarely happens we could sta ilize them b some standar procedure with no claim on performance while I CO.' in a supervi or way would optimize this performance (see implementation). - The main criticisms hat were raditionally put forward against this representation dealt with the non-minimality of this modeling. They were pertinent but the ~resent cost of fast access memory is such that we can afford a redundant representation. The ill-posed nature of the identificaion invol ed ca e avoided y a proper condi ioni g of relaxa 'on fac ors (Ref. [18] ) .

e E E

.(

L k=

-

is represen are ect to per i ed to 0= e follo-

Fig re

(n) or

In a

-ec or =or j (

aU

~

T

2.

~

~

ek(

- i )

J

.2

s(

s( -

) +

(n)

C-10

i

EL ALGOR

'.0

o

pleme i al

l

a

s

TH.·~IC

CO. TROL OF I

D STRIAL PRO

E

E

105 ranspsrent" ) ill the e

all on-line

T e o~l criti al hase are ex eriment I nning and a a olle ing. Active e signals should pertur a l i tIe a ossible normal operating con itions and give he est informa ion on 1e stem ructure. These eman s e a i fie without 0 e o not comp L tions. It is neces ary to arefully select he nat re of es signal that will be a ed to the ac ual controls. PRB has proved to be onvenie rovide ~ts spectrum and cross-correlation of lnpu s were appropriate. Identification can be performed in di ferent ways

l-

are an

.1.3 "\-1 emu s

po i n 0 u t hat ex p r e i 0 nI' R e rence 0" el" lS u ed in a way which iffers from ~ha is usually meant y ifferent authors. (Re [ ] , [11], [ 13] ) .

Given a sim le one-impu , 0 e-output sys em, let C e the cons ant value of the prescribed output and O() the actual out ut value at time. (Fig. 2)

-

- System is open-loop. A weak manual control is tolerate on ome outputs inducing a negligible bias on th~ pa;ameters.

H.P.

c

Desired output

--easured output

Predic

ed output

Reference trajectory Past .........- .....- .....~

eas red i

Future

p

Co ~T

-

Fig re 2

-

dic

l

e

e-

'~ '

106

-,.:e i

Il

i

t

i .:;. 1 i

2.

e

e

"t

~

Ij

e

.

C-IO

.:.....

Ccr:troJ..

:c" (::)

-,': 1-. i c

~:.

....... :-,

~-.

r~~l""'erer:ce

I'

e -S- c ~. C.3

c.: ~ 1

C

e ~.~ 8.. \,. i c ~-- .

r

e~·~·

~.

en 't

t :i en

reCt;r~,lve c e :-r, ~ ',; "t e j [ J' t l~ e ~:i ~ pIe ~ t (1.3 t er j er)

1 i n ear" ::';~.:R ( n ) = 0. ~\:R (n) '1' Le!' e i' ere n c e

2.

( 1-0.)

="l..i

~

e

3.1 i t 2. 1..1

'.'; i t r

par2.~eters.

let '.,' e e r; fol}c~:

2.S

E:

respect tc

(?ig.

.2.

S_ ( il )

I!1

c :l e 1

t e ~ ng

c r: c s e r,

a r: en&.

In t~e identi~icutio~ ccheme s(n), e(~) are g j \' e n :~ i r; cl 2.? ~ r. t:; e c CJ!'1 t re 1 pro [, 1 e ~ s (L ) 1 S ~: Le',: n, i ~ t LeT.: 3. s t fro~ the collected data, in tte future by t~e re~erence model trajectory, ~ i s g i v e n t y t 1-: e !) rev i 0 u::::. i i,'i p n t if i c 2~ t i G n . e ( n) ~ s :::; i ''- t; n i n t; , e pas t : " r er:: t b e 3toreJ cc~p~ted co~trcls, in the fut~re ~, y t}, e ~, a met y ;:. e o:~ 2. 1 g cri t :. rn •

" "'- ell [: e ; ; 2. V e -j " s y s t er::, i t.3 r~, 2. i ne', 2. r 2. C t er i s tic i s i t s t if.": ere s !':l 0 n s c T~,: R T r i.3 par 2. D: e t e r i s c nee:' t :-, e :: e v.- t. c '[ e ::' ~j e cif i e din t 1: e p r c g r 3.!!l 3. n J m '...: s t b e a c c e S 2, i 11 l e t c, er s . 1

It is to be noteJ t~at d~e to state and structural pert'_~r1:ation:3 and comp"L.t2.tional errors, the actual trajectory ::1 0 e s n G t !~ i t t o t Le:' 0 l' e see n r e fer e !1 c e r; '::' J. e l i t i S O!'1 1 Y 1 0 c a 11 y tan g e n t .

Constrai~ts

cn the

i nt r

Li

0

cl u. c e j .

2.ctU3.~crs

reJi,lces to the cor:lJ-;;~taticn centrols acting on 2. known sY.3te~ so t ~'. a t the- f 1...: t l..l l' e C ',1 t put fro m .' t 0 in~i~ity is as close as possible to t~e

1':.12 -;)rcblem

central: should be ita t ion s i IT: !:: C ~ e ,j 'c y iescribed ty

r1

are

0:

re=~eren2e

le(n)

r1sdel

(n)

nstraint sec c n ,1 2, r

~.,..

-

e(n-l)1

cn

< ~: ....

i:~terna:l.

2. ~"'

i El~' 1 e s c r i n ~::" C C e d

c '~

=

S(N)

I DEn T I FIe A '=' I 0 :J

!

( !1) E.

1

:,:e8, s:.::r e

S(N)

=

!

=

.7"+-'re t ~

A

!

I::e::ti::icaticn

LA

--------

~:e2.s:.:re

Past ~~e

-

Figure 3.a -

as ur e

t

Refere::.ce ~.~cdei

.. ODEL ALGORITH IC CO TROL OF I

C-IO

n er his form lation the roblem an e sol ed y different me ho s linear progra ml ,quadratic ... with direc or i era ive metho s. The choice depen s on practical and financial possibilities

DUSTRIAL PROCE SES

computation time, emory allocation, software por a ility. A flow chart of the con rol algorithm (Fig. ) ives the outline of the control compu ation.

Predictive Control Initialisation

Computation of the reference trajectory

(loop on the control computation)

(loop on the outputs)

I

(loop on the predictive inputs)

Computation of £IS(K) Computation of predictive control inputs

Test on constraints

Application of the control input at time +1

-

Figure 3.b -

107

Flow chart of the control algorithm

__ aCE

108

E

C-I0

ions

1.2

ion

I

1.

- Internal mo el ~ (s = ~T ~) where control varia les will e is inguishe rom ea ura le per ur ations se a fee forwar pre ic ion. i

-

Reference o el ime re on e T R

-

Cons rain s

s

for a given cIa s,

on con rol max, min, elocit max on internal varia les if nece ary.

The e parameters should e let at the i posal of the process operator and h 0 s e non -- 1 i ne. I n par tic u 1 a r when t e control is implemente ime-re ponse an constrain scan e s ri ly set an o~ timize aftervards.

1.3

Performan e

Takin ln in"e men fin ncial are me el of he ~roce or on line on a o

e

- Direct Digi al Control

(DDC)

Computer control the process control variable which are often e -points of casca e level PID controllers. Internal mo el is in hi case the rocess mo el. In his implemen a ion, constraints on the actuators are easil formulated. On t e 0 her and iden ifica on roceure and ~ per i or SOl ',,'are (wa ch do ) re_ulre careful en ion (Fig. )

IDCO C~NS

I PROCESS

- - - - - - - I.~I .

f--,

-----

Figure

':::'ra

-

ea e

0

ear l.e

irect

I

..s ..-J

igita

Co

rol

C-IO

ODEL ALGORITH IC CO TROL OF I 2)

in a direct or supervisory way, ensures optimal control of the process (FiG. 5).

109

DUSTRIAL PROCESSES

Optimiza ion of the set-poin s wi h minimization of cost functions ensuring quality and quantity of production. Time and space scheduling of production (planning- operation research) .

The economical benefits induced by levels and 1 are in practice usually negligible.

o

Figure 5 -

1.5

In contrast, level 2 optimization can bring valuable improvements in the economics of the systems. However, a necessary but not sufficient condition for satisfactory level 2 optimization is first to have level 0 and 1 optimized. If a regulator is operating around a fixed set-point, no significant gain in energy and raw material consumption can be obtained by a sophisticated dynamic control. On the contrary, an optimized level 2 setting needs a good quality of control around level 1 set-points. Reducing the variance of the actual output around their prescribed mean values allows level 2 to be set in better way, closer to the spec~fied quality variables.

Transparent Control

ecessi ty of a sophisticated control algorithm?

Effective control schemes used in practical industrial applications are nowadays digital transcriptions of analog control la\ls· (Ref. [19]). What is the purpose of anindustrial controller? What are the criteria? Strict dynamic control must be imbedded in a larger problem which can be divided into 4 hierarchical levels 0)

1)

Control of ancillary systems (e.g. servo-valves) where PID controllers are quite efficient.

A diagram of great generality is given by Figure 6 where we plotted the distrib tion of the measured quality of the product which is specified to be q ~ q (See application 1 for example). s

Dynamic control of the plant - multivariable process perturbed by state and structural non measured erturbations.

I

J

W2

I

I

I

I /

qs

I

I

q

I

I

Quality

ql

2

/ 1Ml

1M2

-

Figure 6 -

Operating Point

110

C-10

E::L A 2.1

>

an

<

-2 -s will ion

e

~e

0

~s

1)

D

~

>

e

1

loser fune "

0

ion

( -2 )

Thu o s a Cons raints rianee of minimized.

the

s ee ru of he time re ponse of e hen .e main parame er

fre~ueney

To o on

a ears 0 e arame er' of e 00 h on e

o

~r---..,.,.~ RD209

Light il er

2.

,.----.,

~:t---------J

Steam

ig re

C-I0

ODEL ALGORITH1IC CO TROL OF I DU TRIAL

A physical cons rain epen s ver much on the ou flows e products i i oul e kep wi in e "pan" level a fixed i erval to en ure correct working con itions of the i tillation column. he mathematical model representative of the problem is given y the block diagram of Figure 8 on which each input variable is relate to each output through an im~ulse re 0 se to be identified. Two varia les are 0 be controlled with a physical constraint on a hird one, us i n g wo con t r 01 v a r i a l e s. It i s a c as e of non controllabili y. The procedure followe then, is to check on the "pan" level and each time it goe beyond its allot t e din t er v aI, 0 pro g res i vel y change the set points of TI 62 and TI 63 in order to satisfy the "pan" level. This is only possible with an al orithmic type of control. The control is a direct digital one with a sampling period of a 3 minutes. The steam generation process in the power plant is represented on Figure 9. The problem here is to control the steam pressure P delivered to the turbine and the steXm temperatures at the superheater Ts and at the resuperheater Tr using as control variables

-

Fig re

ROCE

III

ES

e deheater flo Q~ he rec- cling air flow R y , the fuel inflow Qf submitted to loa variation of he plant, measured the steam outflow Qv'

RD208 1163 .. -

RD209 TI62 1118

---

PAN. 1161

-

Figure 8 -

..

112

e

i

Le ruc ure is a mixe ran pare con rolled in on Fi ure 11.

followi e on

~R

... AL

RO E.. SE

C-IO

i~ ile re iner Fi Le mo el re 7 12 im o 1 e

la is re

exaillple

0_

i

a

io has sen realized on line are shown in Fi ure 13. Eac onse is 0 pose 0 0 Oln s. of he ehavior 0 he lant ema ical mo el i .ow o

OF

PV

OD TS

T i im lementa ion ar icularly interes ing eca se it provi es evidence of e generali five proce e are con rolled and wi hin each proces se eral t e of controls are performed (te _ era re ,level impuri ie ). The particular analysi of eac process is qui e similar to he rece ing ones and t u ~ill not e repeated. 2.2

Proce

s

~o

eling and

RY TRS

OV

Identification

ig re

PV ref

10 -

PV QO

TS

PROCESS

ref

IS

Ry

TRS ref

TRS

-

Figure

11

:' I:.

C-10

AIR

012

113

ETHYLE E

OXYCHL RATIO

HCl

DISTILLATIO COLU S

COLD CHLORATIO

012

------,

I I I I I

DIS C

FUR ACES

r:::::J

KA

1

I 012 I

c:::J KB c:::J I{C

I I

o111

0 131

I I I

012.

c::::J

Process under IDCO

~ Transformation

Process

C==.=J Separation Process

-

Figure 12 -

:--:----.......

TI62

5"C=

. ~.: -:..:.-..._~",-::::::-

--. - --_.::-:.=---- ---:

.-

TI63 _ 'r

Fig re

(

'. -.':0 .

I

114

ODEL ALGORITH IC C

TROL OF I DUSTRIAL PROCESSES

TI62

C-10

TI63

-

Figure

Results of the identification of the pressure of the steam generator are given on Figure 15. These identifications have been performed on open loop systems. In most applications, the control algorithm used thereafter ( .A.C.) being sufficiently robust, it was not necessary to have an on-line identification scheme, bec~use generally the processes work around the same operating point. In the case where the load of the process is liable to change (as for example in the power plant application) on-line a aptation becomes necessary. This problem requires a more so histicated sol~tion and in general we are faced wi h a dual con rol situation. In he power plant case it was fo n af er identification at different load levels (100%, 8 0 " 5 0 ;0) t h a t he" t i me con san t s ' 0 f the transfers related to e e pera ures aried as an inverse function of e loa Qv' If one observes the process with a sa pling perio var ing in t e same way it appears as a stationar s s e . This has been implemented and gi es full sa isfaction ; the only identifica ion left to be one on line is he ain of each impulse response.

14 -

It should also be mentione that the non linearities of actuators have been included in the internal model of the process as for example in the recycling air inflow R y such cases should be identified independently. 2.3

Parameters of the control algorithm

The main parameters of the control algorit m are the time constants of the reference model. _hey define the desired behavior and stability of the controlled variables. sually in in us rial processes, t e desired behavior is to accelera e he nat ral res onse of the stem within the li itati ns of the cons raints on the actuators. ype s are of t e ax, min The cons rai of variation e ampli ude and spee on e water e con rol. For exa ple of ower plant as well as i s in the flow Q ot li ited. aria ion are spee of .. odels of the processes were not - except for the gain of he s ea generatorodified on line, no ada a ion was necessary. For a inputs x 2 outpu s" syste t e whole sof ware nee s less than 2 K words of 16 bits,including data and programs.

,,0 EL. LG o. I ' _,1 C

C-I0

PV

L.l.

;PVC

:--I-r-

F-"

o TROL OF I

I--"'~ I-

T%V(

I-

-

TRI L

P.=

TR :¥VC

PO E

~4U

R -i~1I1·

E

115

II-

it

,V ?IV

,

:/

.~

l.I1t»,.., ~

100

,

"

~

TR~

0

..

\

-

""

205 I

"

100

~nrt le "'-

SOl tie

..-

-~

nt liet

{' kJ h

I~

\~

I

} W r lOde j\ ~

~

~~

1

1

IL ~~

~ L?/U

V

T( mn)

10

'en

ica

10.

40

30

20

0

60

50

70

80

90

F~

.e ,., ea.

ve

ra or -

2

re

ro le,. :'rom w.o e a .alene:'i coul e erive

a)

~e

cr~~

g

1-,

rea

116

o

ODEL ALGORITH IC

TROL OF I

scheme can give results which may seem positive but are in fact often short lived. However, operators who are used to having a direct insight into the system through the recorder data, will decide on that basis if any improvement has occurred.

c)

Economics

As described above the level 1 optimization is significant only on level 2 management of the process. A few exa~les are given. - I~ the PVC plant on a distillation column (D 131 Purificat ion), a small variance of the outputs and security feeling, induced by the new control, allowed to reconsider, after a few months of a satisfactory continuous operating conditions, the specifications of level 2. Step by step in a year's time, specifications were almost doubled and the minimal constraint on the outflow was lowered from 45 T/H to 32 T/H. That induced an economy of energy on this col urn n 0 f ab 0 ut 1. 5 T / H 0 f s team ( ~ 1 5 %) which on a 8000 hou~s/year basis represents about 120.000 $ a year.

In the steam generator example,a standard triangular 10 MW/minute power perturbation was applied, with regular analog control and with IDCOM (Figure 17). b) Variance A more objective way wLich yields numerical results is to compute on line the mean value and variances of the variables to be controlled. This has been done on the distillation column (refinery).

desired output

t--------H ~

1 ho r

..

A ALOG

CONTROl. ., 14

IDCOM

T1621:

---....

.

2701 260.

des 1 red

~ __.

- v-

~lg

~----A

LEVEL

ALOG

COR 0 Lr----i.,~1.....4 ._.---

~ IDCO

(l201)% c ana190'%-62~

100 80

~....,...

60

40 20 -I-

our

-

C-10

ariances on the two temperatures are divided by a factor which permits the shift of the set points to better level 2 operating conditions (Figure 18).

For the oil refinery distillation column a shift from analog control to IDCOM is presented (Figure 16). ote that the pan constraint was not respected at time inducing a lower quality of the temperature controls.

210 205 200 195 190 185

DUSTRIAL PROCESSES

Figure

16 -

0

u t put

= u

C-10

o

EL ALGORI H IC CO TROL OF I DUSTRIAL PROCESSES

M Watt

Bar

..IS -,

1

r24(

.

/

--r\

OV

~~

5

PV

\ 1/

OF

r4

,

'r\

u

If

t'N.. ..

le;

c ~

TS rn'

8 I

4

1\

I ,

~i'-

,

1,- .........

,

,

I\.... '{

- -.... v

\

l/

/1---- I'...l.r I---~

'\..

, \

8t~ I

I I1

~'

\ '"

\

,/

I

I

"

4

/1\

I \

I

~6

.'

I

\

,/ '- ,

~

I

1

--

I

\

~?

I--~~

,

1"\ \

/

\

(

/1\ I1

f-t]

RV

I

I

1

20

,

I

2

Fd

L.-,,-

j 'V

I'

L.-.

J (

\

A

OD kJ

/t-A~

i\ ,

-1,-

.....

\ f

-1~

,

11

~

11

[\

]

j

V.'

~5

d n

'h

n - ~'

\

-1 u

"

..

11

~

r2' 5 2025

117

1

T"" ~

0

\

I

\

'oF;.

,...-

-'f

- - - - ,..., '~

~~

-

-

l£'

v.. . I

'1\

,/~

v

'.\

'~

- .... .JJ"""-

'\ f \ (

Analog Con rol---·---------IDCO -

Figure

17 -

Human

as~ects

ODEL ALGORITH IC

118

o

TROL OF I

complexity since all control parameters have a straight forward physical significance (time response - constraints ... ). Last, but not least, innovation should make control easier. For example the oxychloration furnaces were difficult to drive, taking too much of the operator's attention - the "pan" level constraint was so hard on operators that most of their time was occupied by this nonchallenging but dangerous task : after a few months of application of IDCOM,

DUSTRIAL PROCESSES

as confidence gra ually pervade the operators were relieved from preoccupation, to such an extent they would never accept a return previous situation.

Temperature TI

30

62

Control IDCOM----I IDCOM

20

10

230°C

11

62°c

11 62 set !> 0 in t

50

Temperature TI 63 IDCO Control

40 A ALOG

30 I

20

10

Figure

them, that that to the

Being no longer concerned with hat is fact a minor problem : dynamic control level 1, more significant improvements - level 2 settings - can be looked for a sound basis. The way is then opened true optimization.

Number of points

-

C-I0

18 -

ean

St andard deviation

in at on for

C-10

ODEL ALGORlTH lC CO TROL OF I

119

DUSTRlAL PROCESSES

el P. ew met 0 of control is propose (IDCO). It uses t e mo el of the plant in a irect ay and avoi s t.e clas i al but trou lesome approach which onl - proces es the error control - in a ?im_le or sophisticated way. It uses to he utmost the memory and optimization capabilitie of igital computers - the only hardware on whic it can e implemented. On s ch f n amental , it is po si le to tackle large in ustrial processes in a glo al an multivariable way, taking constraints into account. Wealth of information (past values of inputs and outputs) insures a surprising robustness and ease of implementation.

is ance

A

Significant applications have been rea 1 i zed 0 n d i f fer e n t i n d u s t r i a 1 pr 0 c e s s e s for a long period of time. The number of processes controlled full time by IDCO is on the increase. The theoretical basis of the method is simple an stur y, some problems like s a ility an adaptativity are esensitize but there is s i l l a lot to e one on various aspects: edicated hardware - computational software - auto-adaptation - dual control, etc ... The field is wide open.

ifica ion,

2

rague, [ 5]

"IDCO - Con uite algorithmique des roces us industriels de fabrication" Procee i gs of the conference organize ADER /GERBIOS on he Algorit ic vontrol o~ In ustrial stems, e 197 aris (Frenc )

[ 6]

Turtle D., Philli son P. "Simultaneous identification and control" Automatica, 01.7, 5- 53, 1971

[7 ]

Kurz H., Isermann R. ",etho s or on-line _rocess entification in close loop" Preprints 6th IFAC Worl Congress,

1975 [8 ]

stavson I. o erstrom T., Lj n L. , On the accurac ro lem in i en l fication" Con res Preprints 6th IFAC orl

1975 [ 9]

We want to thank the Electricite e France, the Rhone-Poulenc Industries, the Compagnie Fran~aise de Raffinage, who have worked wit us on the mentioned ap lications an so kindly ro ide us wit t e r e s It of e economic ap_raisal of e JA proce re.

[ 10]

[

1]

RE ERE-CES [1 ]

Ra ic

Co

es rol

. L. ,

rial

0

ifica io ima ion,

[ 2]

~e

[2] 's

e

6 [3 ]

es iscre s ar i istr c re

°2

3]

.. ODEL ALGORlTH lC CO TROL OF I D STRlAL PROCESSES

120

l

14]

r 15]

[16 ]

[

7]

Be1anger P.R. " 0 ment on a 1ear g me s s em ifica io " IEt..t-, P , 2C7-20 T pki Y.Z. lA apta ion an Aca emic Pre s, Graupe "I en ifica an os ran

C-10

[ 18]

o

for

le.

6

rol

r 19]

1earnin" 1971

"

onaghey L. icrocomputer sy ems for roce s con rol" rocee ing of .e I~EE, 01-

1

\

76 y,

9 2 [20 ]

a .. , aren ra K. "An i en ifi ation roce r e ~ or ,- t eLl I' discrete ultivaria le IEEE, Trans. on A oma lC ontrol, AC-19, 5 -552, 1 7

[21 ]

~ichale

endel J . . . "Discrete techniques of Parameter Esti ation" Decker Inc ewYork, 73

K

., Rault A., "I e ificat'on e ro e la ho e u mo 'le' Cordon & Brea h Lon on, 71

me

ar