Regulation of a Steam-generator in an Adaptive Multivariable Way

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Applila li oll s 10 Process COlllrol. ' ·il'Il Il ;1.

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REGULATION OF A STEAM-GENERATOR IN AN ADAPTIVE MULTIVARIABLE WAY E. Fenet* and D. Meizel** ".Y(}llfifl' Fmll(lli,(' rln I't'lm/n HP. HfIj//II(,III' rll' 1)"III.'t'IIf"(', HI' 1 - 51'1. 5l)l.J(J j)""i.-t'llf"l', l ,ll//('{' '"'' l a/NlIlil(}III' d:-I"/(}IIIIi1IIf"I' t'I rlllI/(}/l!l(illlf"I' / 1/(/1/.'/111//1', IW/I/II/ II/(/I/,'//ll/ dll ,\ '(}II/, HI' 1.1', ;l)(,5/ l 'd/I'III'I/"I' rI: -J'I'1f ( /dl'.\', Fill//('{'

Abstra ct . This pap er pr ese nts th e r eal i za tion of the co ntrol of a two-input s-two-outputs pr ocess by use of bo th class ic al PI con tr olle r s t oge the r with an adap tive decoupling precom pe n sator . The co n t r ol - law is implemented on a dece ntraliz ed- mic r op r ocessor-b ase d indu st ri a l process - control system that has been conceived essen ti ally for fixed - ga in s re gulators . From the dif fic ul ti es we me t in the i mpl ementa ti on , ',e propose some specifi cations to in c r ease f l exib i l ity of pr op- r amm ing for in dust ri al -pr ocess - co ntrol sys t ems . Keyword s . Control e n g in eer in ~ comput er ap plicati ons ; multivariable co ntrol systems; adaptive con trol; heat systems . I. I NTRODVCTIO K

is implemented on a process - con trol sys t em (Micro-Z by Con trole- Bayley) that i s det a i led in par ag r a ph I V.

A drastic change in the pur chas in g- politics o f pe t r oleum i ndustry has brought up the demand for a bett er cont r ol of the tra n sient behaviours of the plant s involved. Thi s implies the use of modern contr o l co mp onents based on comp ut e rs and the inte r est for modern contro l-sy s t em-d es i gn me t hodo l ogies the us e of whi ch ca n no more be cons trai ned by the t ec hnology.

Modelization The plant dynamics has been first id en tifi ed by the a nalys i s of step- responses wh il e the supp lied steam fl ow-ra t e was cons t ant . Th is has been done off-line for three significative nominal loads (37, 46 and 57 t ons per hour) by use of the ex t e nd ed-l easts qua r e method.

In the present e d a ppli ca tion, we s how the dia lect i ca l link betwee n the two a s pects . The impl eme n ta tion of an adapti ve control law on a pr ocess - control system i s presented. The difficulties e ncount ered in the realizati on has led uS to formulate some process - co ntrol sys t e ms specifications with th e a im of their more fl exi bl e use .

The results of th e iden tifi cat i on a r e g iv e n unde r the s i mp l e f ol l ow in g form (1) wit h parameters defi ned in Tab l e 1. Y (t ) , u (t)

e

?

]R-

Y(z) = F(z) . V(z)

The paper is organized as fo llo~s . The second sec tion describes the physica l plant and presents its modelization. The adaptive con tr o l s truc ture i s desc ri bed in paragraph three. The process - contro l system (Micro- Z by Con trole- Bayley) is then presented in para graph four. It will lead uS to th e actual implementation of the adaptive control in sec tion five. The co ntr o l system spec ifi ca ti ons th a t come fr om this expe riment consti tut e the conclus ion of this communication.

(1)

Yl

combusti ve - a ir f low r ate (Qa)

Y2

pressure - d iff ere nce in side the fire - box (P f ) inlet-shutter control

u1 u 2

1

II. THE PROCESS AIm ITS MODELIZATIOK The actua l pl ant supplies steam with specifiec' pres sure and temperature to a pe tr o l e um refinery (BP, Dunkerque, France) . The steam flow- rate is imposed by the demand of supplied units. Th is load is he nce hardly predic t ible and i t va r ies withi n the interval 37 through 57 tons per hour.

outlet - shutter co ntrol Parameter- identifi ca tion resu l ts

TABLE 1

~

A schema ti c diagram of the heater is given in Fi g . 1. We conside r here the regulati on of both the pressur e differen ce (P f ) i n side the fire - box toge t her wi t h the combustive - air fl ow-rate (Qa) a r ound fixed se t- points designed to maximiz e the heat e r' s e ffi cie ncy. The two control- inputs are the pos i tion s of t he i nl e t (V l ) a nd outlet (U 2 ) shutte r s.

al l

a

21

a

12

a

22

8 11

82 1

8 12

822

.9 13 . 945 . 876 . 855 .236 .0415 .588 - .605

37

t

/h

46

t

/h

. 853 .9 14 .792 .760

.17

.0629 . 717 - .6 13

57

t

/h

.886 .902 .92 5 .95 1 .13

.0636 .1 57 -. 345

Denotin g t ha t time -constants in F(z) lie columnw i se in a narrow domain , we cons i der the following s i mpl e r linear in parame ters model (2) as a basis of the control - l aw desi gn.

The regula t ion of the various units of the r efi ne r y

229

E. Fencl and D. l\1eizcl

2:~()

y(k+ll = A (load) .y(k) + B (load) .u (k)

I

y e

JR2, u e JR3

(2)

l oa d : supplied flow-rate

Air-fl ow meter (Qa)

e

Fi r e- Box pressure (P ) f

e

Steam flow

,

r-----------~----------~----------------~ +- - - -

.:

+----

FIRE BOX

i

I nl et blower

11

\11

Water supply

-

--~~ ---:: -~

~.~---------~~-----~~-----~~ ~-----~

Inlet shutter (lJ ) 1

i i 11

Heat exchanger

Fuel

i

1 ~

...

-- - ~

---~

---;!Io

Outlet shut ter (U ) 2

Chimney

Heater physical description

Fig. 1.

tes A(k) and B(k) of matrices A and B (5).

I l l. THE CONTROL-LAW For a fixed load a good solution to the regulation problem is ob tained by the block-diagram of Fig. 2.

This estimation is achieved by conside ring the process whose output is the filtered mode l-proce ss er ror Es (k) (6) . E(k)

Oecoupling

~ Ym(k) - y(k)

E (k) ~ E(k) - A .E(k- 1) S

1 Es (k +1)

=

B

m

.r(k~

(6)

+ (Am - A).y(k) - B.u(k)

These equations can be rewritten in the linear-inparameters followin g form (7) : Fig. 2.

Linear control structu r e

E (k+ 1) s

The decoup lin g precompe nsator is designed by modelmatching the following linear s tationnary reference mo del (3). The tuning of the PI cont rollers i s then done by consideration of this constant referen ce mode 1.

m

B .r(k) + q,T (k).8 m

IjIT (k) = [ y 1 (k) ' Y2 (k) ,u (k) , u (k) ] 2 1 q,(k)

E

1R

8X2

T ; q, (k)

[ IjIT(k) =

with

+ B • u(k) m

B

=

o

8T = [ lIa 11 , lIa 12' b 11 , b 12 '

.35 0]

[o

lIa

(3)

21

,lIa

22

,b

21

(7)

,b 22 ]

1.1

The decoupling control law is thus (4) where the matrices A and B (2) depends on the s upplied steamflow-rate.

The decoupling contr ol -l aw (5) is based upon zeroing the prediction of Es(k +1 ) (7) a t time k . Es( k+1) appears then as a predict i on error and the estimate e(k) of 8 is given by Kalman-fi lter equations (8)

(4) 8(k-1) + K(k).E (k) s

The supp lied s t eam flow-rate i s not measured. So, at any mome nt, matrices A and B in (4) are not known exac tl y . An adaptive solution (Landau, 1979) is thus deve-

lopped where u(k) is defined by the cu rrent estima-

o (k+ll

[R (k+1 ) + q,T(k).P(k).q,(k) ]

P (k+ 1)

P(k) - P(k).q,(k).o-1 (k +1 ) . q,T(k) .P( k)

K(k +1 )

(8)

23 1

Regulation of a Steam-Generator with

IV. THE PROCESS - CONTROL SYSTEM p(O) > 0

The above designed co ntrol-law is to be implemented on the "Micro-Z" system by Controle - Bayley (Control e-Bayley, 1983). This system is organized in a hierarchical way (Fig. 4).

{ R(k) is the covariance-matrice of € (k) s

From this c las s i ca l start - point, some modifications in the updating of P(k) in (8) have been propo sed to establish the robustness of the con trol-law ob tained from the estimat es il(k) (Irving, 1979 ; M' Saad, 1984). They are summarized in the procedure below (9), that cons ists to prevent P(k) to be sin gular while keeping its trace inside an interva l (t r , t; ) and to use the updat ing mechanism (8) for significant process model errors. IF (€ (k)

s

Basic contro l operations of a subsystem are executed by decentralized autonomous programmable micro processor ca rds. The man/machine interaction is achieved by classi cal control - stations or by graphical workstations connected to the control card by two indepe ndant buses f or safety's sake . Note that local parame t e rs and variables can be observed and tuned by a micro- console .

> €- s ) THEN

comp ute D(k), P (k), K(k) (8) Work stations

IF ( IE (k) I - IE (k- ll l < ~) THEN s s IF (trace (P(k) < !:.E» THH: P(k)

1.15. P(k)

=

Classical contro l- s t ations

(9)

ENDIF ELSE IF (trace (P(k) < t;» P(k)

TI1EN

1.15 [ P(k) + 0 . 05 Diag (P(k»

=

]

ENDIF ENDIF

Taking in account this modification, simu lati on re sults of the process - model ( 1) governed by this control-law «5) throu gh (9» is given in Fig. 3.

ID....l£C.o

console Process lOT

30 T

50T

70 T

90'

110l

Fi g . 4 .

Micro - Z architectu r e

Programming an application The control algorithm implemented on a decen tralized card is built as a block - diagram featuring ba sic ope rations contained in a soft-library. l OT

30T

SO T

70T

90T

1l0T

The following example (Fig. 5) illustrates this programmation.

1.5

The control - structure being defined and stored in a PROM; the various parameters involved are contai ned in a RAM at the card level and are tuned by the micro - console (Fig . 4) at the local level.

.5

lOT

30 T

50T

70T

t

t

t

37t/h

46t/h

57t/h

90T

The memory-size of a ca rd enables to define applications with up to 99 basic block-operations.

11 0 1

This limitation is a priori not constra ining for standard decentralized subsys tems.

;~Ir____~~__

L_o_ ad___

30

Fig. 3.

70

k

Adaptive contro l-law simulation results

E. Fe nel and D. !\Icizel I imi ter

set-point

y

C

Fo r r obus tness ' sake , the above basic updating of Pi(k) are modified by use of the trace-control algorithm (9) . The practical realization The limited number (99) of basic ope r a t o r s on one con trol- ca r d have l ed us to an implementation with 3 cards (Fig . 6).

Exponential filter

sets-points

c,

,/ Y,

Y2

"- C

2

EA

Structure configuration programming

Fig . 5.

Fig. 6. V. ADAPTIVE CONTROLLER IMPLEMENTATION

The block-d iagram programmation that is a "natural " way to conceive a nd r ealize control operations is constraining when nume ri cal procedures such as Kalman filter equations (8) are considered. The updating of the symetric 8 x 8 P(k) matrix would require more than 96 add i tion a nd 64 summa tion blocks for its own sake while up to 99 opera t ors can be conf i gured on one single ca rd. A simplification of the Kalman-f ilter equat ion is then proposed in o rde r to r eplace the 8 x 8 matrix P(k) to be updated by two 4 x 4 matrices P I (k) and PZ(k) . This is infered fr om both the cho ic e of a d1a gonal P(O) matr i x and the hypothesis that R(k) be diagonal. Considering the definition of ~(k) (7) , P(k) is 1n that case displayed in two diagonal 4 x 4 blocks PI (k) and P2(k) . By u~e of the same part1t 10n on the pa r ameter vec tor 8(k), it comes then a dec o upled version (10) of the original Kalman filter equations (9). i = 1, 2

8( k ) = [ 8;(k) ;

8~(k)

] T

8 1 , 8 2 E 1/.

'l'T(k)

[ Yl (k) ' Y2(k),u 1 (k),u 2 (k) ]

8 . (k)

8.1 (k-1)

1

O.(k+l) 1.

P. (k+l) 1

Implementation architecture

The first card cont ains the linear contro l s tructure (5) together with the reference model (3) and the evaluat i on of Es (6). The r emaini ng cards (2 & 3) impl ement respectively the updating of the model - parameters est imat es 81(k) and 8 (k) (9) & (10) used in the "linear " control 2 structure . They are thu s slaves of the "linear " card 1. It is to note that, from the conception of the "Micro-Z " system , based on app li catio n decentrali -

zation there is no data- bus linking the control cards . ' The transmissions of Es , y, u , 8 1 , 82 between cards ( 1, 2) and ( 1, 3) are then realized by analog transmission. Some r es ults displayed in the adaptive (§ I I)and to

of the so- obtained control-law are Fig . 7 and show a good rob ust ness of control l aw to the modelization error the acrobatic design of the adaptive

precompensato r .

""'-

I~ f-

4

1[\/\

,, ~

:;

;;

;;

::

;

+k. (k).(E (k». S

1.

(10)

[I"V 1::

r- .:= ~ h

--

lif

1

_":-- i:=-- r---ir

P. (k) 1

_ (P.(k).'i'(k). 'i'T(k).P.(k» /O.( k+1) 1

"

-

1

R .. (k+1)+'l'T(k).P.(k).'l'(k) 11

L.

1

il

:\

,"-b ~

1

"

s

-

---

-

k. (k+1) = P. (k) . 'l'(k) / O. (k) E JR4 1

P. (0) 1

1

1

Fig. 7. Ill'p lement at ion resul t s (Dashed-l ine s

set- point s)

Regulation of a Steam-Generator VI. CONCLUSION : CO~ffiNTS AND PROPOSITION FOR PROCESS - CONTROL SYSTEMS Block- diagram programmation is a natural way for control-system design. Nevertheless, it appears as a constra int in some spec ific numerical - like control procedu res as illustrated by the presented adaptive control case . In order to solve the problem, there should be the possibility to extend the basic-operations library by programming specific - functions in assembly or compiled high-level languages. Matrix and vector operatio ns would then be less memory-consuming than when programmed in a block - diagram way . On t he other ha nd, we co nsider hierarch i cal decomposition of a control application is a good prac tice though it has compelled uS to analog transmissio n s between cards coope rating to the same task . In fact, these constraints come from the fact that the hierarchical decomposition of an application is restricted to a two - levels de com position. should be possible , in the near-future, to define an arbitrary multi - levels decomposition in order to implement a control application with arbitrary complex structure in the same way that the one that deserves its analysis. It

REFERENCES Controle - Bayley ( 1983). " Inter-KANA" exposition , Novembe r 1983, Dusseldo rf, ~ Ge rmany. Irving, E. ( 1979 ). "Improving power network stability and unit stress with adap ti ve generator control", Automati ca , 15 , 31.

Landau, I.D. (1979). "Ad aptive control: the model referen ce approach" , M. Dekker Ed ., NewYork, U.S.A .. M' Saad, M. (1984). " Sur la mise en oeuvre des schemas de commande adaptive", Proceedings of

the CNRS Symposium "Commande adaptive, aspects pratiques et theoriques", Grenoble , France,

21 - 23 November, (to be published by CNRS Ed ., Paris , France).