vipin chawla - cmbc paper - acs i&ec 1990 - ie00097a021

8/3/2019 Vipin Chawla - CMBC Paper - ACS I&EC 1990 - Ie00097a021

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134 I n d . Eng. Chem. Res. 199 0,2 9, 134-138

A New Control Algorithm for Single-Input-Single-Output andMultiple-Input-Multiple-Output Systems: Applications to Multiloop

Control Systems

A new control algorithm called Conservative Model-Based Control (CMBC) was presented in theliterature recently, and its applications to single-input-single-output SISO) systems were describedby the authors. In this paper, we examine the potential of CMBC as a multiloo p controller. Severa ls imulated d is t il la t ion co lumns , wi th d im ens ions ranging f rom 2 X 2 t o 4 X 4, re selected for thes tudy . T h e a lgor i thms tes ted are CMBC and P I / P ID con tro l tuned by the B iggest Log modu lusTuning (BLT)method. T he results indicate the supe rior capability of CMBC as a mu ltiloop controllerin compar ison with the o ther a lgor i thms s tudied .

Th e control system design procedure for multivariablesystems consists of the following steps: (1) interactionanalysis, to find the exten t of interactio n present an d toselect the proper pairings of controlled and m anipulatedvariables from among the competing sets; (2 ) multiloopcontroller selection and design for modestly interactin gsystems; (3) decoupling procedures tha t provide explicitinteraction compensation; and (4) use of a full multiv ar-iable control strategy that provides for inherent interactioncompensation and constraint handling capabilities.

T he results of the interaction analysis may suggest the

use of multiloop controllers. Indeed , industria l processesare often controlled by multiloop PID-type controllers.

Luybe n (1986) and Monica e t al. (1988) described thetuning procedures for multiloop PI and PID controllersoperating in a multivariable environm ent. These con-trollers contain up to th ree tunin g constan ts per loop, andtherefore, tuning them in the presence of m odeling errorscould present difficulties to the operator.

Against this background, the recen tly developed Con-servative Model-Based Control (CMBC) algorithm(Chawla et al., 1989) may offer significant adva ntages, asit contains a single tunin g constant. Also, it has beenshown to give superio r performance in a comparison withP I and PI D control for first-order with dead-tim e single-input-single-output (SISO ) processes.

Review of Conservative Model-Based Control

The algorithm is based on the philosophy that, in theworst case, the closed-loop response should be a t least asgood as the norm alized open-loop response. For a typicalSISO sampled-data control system shown in Figure 1,th eabove condition may be state d mathe matically as follows:

DG, 1

1+ .c, = 6 " pNote th at the z-transform operator has been om itted fromall the equ ations in this section for brevity. Solving forD, we get

1D = -KP - G P

but from Figure 1,we get

D = M / E (3 )

From eq 2 and 3, we find that

1M = -( E + G@)

KP(4 )

where G p may be represented with th e aid of an impulseresponse model.

Now, desirable properties such as robustness anddead-time compensation are built in to the algorithm bymultiplying a first-order lead term on the right side of eq4, giving

0 s an adjustable tuning parameter which may be ma-nipulated to satisfy a user-specified performance criterionsuch as ISE. The detailed derivation and discussion of the

properties of the algorithm are given by Chawla et al.(1989).

For first-order with de ad-time S ISO processes, Chawlaet al. (1989) have shown th at excellent servo-performanceand regulatory performance can be obtained. A wide rangeof modeling errors was introd uced by assu min g th at all th emodel parameters were off by as high as 60%, both on thepositive and negative sides. In all the cases studied, ef-fective control was obtained, giving a good indication ofthe robustness of the algorithm.

Multiloop Control

In m ultiloop control, the n X n multiple-input-multi-ple-output (MIM O) system is partit ioned into n input /

output pairs, each of which is controlled by an SISOcontroller. We assume th at , by some suitable interactio nanalysis method, the selection of controlled variables,manipulated variables, and variable pairings has alreadybeen made. Let the process transfer function matrix beformed of the elements g l l ,12, ..,g l n ,..,grin. Then, theprocess model, G, used in the CMBC algorithm is chosenas the diagonal matrix:

= diag [~ll,g22,...,gnn1 (6 )

Th e omission of the off-diagonal elem ents may be lookedupon as an impositio n of modeling error. Satisfac toryperformance under these circumstances would furtherprove the capability of CMBC as a multiloop controllerfor multivariable systems.

Application to Distillation Columns

Th e performance of CM BC has been tested on severalsimulated distillation columns. Th e open-loop transferfunction matrices of these systems may be found in Lu-yben (1986). The column configurations range from 2 X

2 to 4 X 4 systems.Luyben (1986) presented the B iggest Log modulus

Tuning (BLT -1) procedure for tuning m ultiloop PI con-trollers. Monica et al. (1988) extended th is method todesign multiloop PID controllers by the so-called BLT-4procedure.

All simulation work in this stud y was carried o ut on th eVAX 8650 system . T he use of impulse response repre-

0888-5885/90/2629-0134$02.50/0 0 990 American Chemical Society



Ind. Eng. Chem. Res., Vol. 29, No . 1, 1990 135

Table I. BLT-1/CMBC Tuning Parameters and ISE's

Figure 1 . Typical samp led-data control system.

sentation considerably simplified th e computations.Minimization of ISE was used as the performance cri-

terion for tunin g the CMBC controllers. Th e tuning pa-ram eters giving the least ISE were obtained by using anoptimization procedure described by Luus and Jaakola(1973).

Several distillation columns were simulated. These arereferred to as VL (Vinante and Luyben, 1972),WB (Woodand Be rry, 1973),OR (Ogunnaike e t al., 1983), and A1 andA2 (Alitiqi, 1985). The P I controller parameters tuned bythe B LT -1 procedure were obtained from Luyben (1986).Th e responses of th e above processes to a u nit step changein distillate composition under P I an d CM BC control were

simulated.Th e graphs for both PI an d CMl3C control are presented

in Figures 2-6. Also presented a re the m ovements of theman ipulate d variables. Deviation variables have been usedin these figures. The ISE's indicated on these figures areth e sum of the ISE's of all the variables. Tab le I sum -marizes the results of the above comparative study.It may be noted that the performance of CMBC is

definitely superior to the P I algorithm in term s of ISE.Th e controlled variables can be seen to reach the desired

0 l " " " ' " " l4

0 . 10. 40. 60.

TIYE

I

0 . 10. 40. eo.

nm

xD.=

MULTILOOP P I

Figure 2. Vinante-Luyben multiloop PI/CM BC.

BLT-1parameters ISE

process K , T I C M B C p B L T - 1 CMBC

Vinan te-Luy ben -1.07 7.1 0.8077 4.25 3.571.97 2.58 0.8658

Wo od-B erry 0.375 8.29 0.9342 7.55 5.050.075 23.6 0.9197

Ogunnaike-Ray 1.51 16.4 -0.7977 1411 396-0.295 18.0 -0.3079

2.63 6.61 0.9159Alatiqi case 1 2.28 72.2 0.9771 115.3 37.8

2.94 7.48 -0.57391.18 7.39 0.94572.02 27.8 0.9819

1.16 13.2 0.73600.727 13.2 0.95152.17 40.0 0.9823

Alatiqi case 2 0.923 61.7 0.0941 80.8 58.8

Table 11. BLT-4 Tuning Parameters and ISE's

BLT-4 parameters

process KO 71 ~n BLT-4 ISE

Wood-Berry 0.1910.161

Ogunnaike-Ray 1.213-0.477

4.879

Alatiqi case 1 5.1300.9641.7053.889

16.31510.856

20.3511.04

3.57

32.122.877

5.13214.391

0.074 6.140.890

0.319 3710.706

0.297

2.537 5800.03830.1670.831

set points much faster tha n in the case of P I control. Also,the movements of the manipulated variables do not in-dicate any undesirable trends. T he improvement in per-

0. 10. 40. 00 .

nuc



136

a

m

2g x

Pm

a

9

f1 :

c;z0

0 ..0

Ind. E ng. Chem . Res., Vol. 29, No . 1, 1990

0 80 40 60 .

TlYE

E* '-.___ _ _ _ . - _ _ _ _ _ _ _ _ _ _ _ - - - - - - -

t l

..

T5o x

P00

a

0 . W . 40. W.

TIYE

0 . 20. 40. 60 .

ffyE

l " ' l " ' l " ' 1

0 . m. 40 . 0. m. 40. W . 0. m. 40.

TIYE nuc TIUE-D.RR

MUTLILOOP PI YULTILOOP CYBC

Figure 3. Wood-Berry multiloop PI/CM BC/P ID.

I I i9

I I

0

ma

v-.. B .'\ % , \\

5$ 2

P '"', ---,---.

.-x:>\ , \I'

x i I I

0 . 20 . 40. .o. 0. M . 40. 40 . 0 . ao. 40. 0.

"IUE T lME TIME, -_ -1 I \ a ,i '\\ ,,'--..e/--

! \ \,

I /\ II /

0 . 20. 40. 80 . 0. Do. 40. W. 0 . W . 40 . bo.

TlYE TIME TIME

~ PI pm _-_-------cyst

Figure 4. Ogunnaike-Ray multiloop PI/CM BC/P ID.

formance of the CMBC algorithm over PI is particularlynotable as the order of the system increases.

The PID settings for the WB, OR, and A1 columnsobtained by th e BLT-4 m ethod are given by Monica et al.(1988). Th e responses of these columns on P ID controlto a unit step change in the distillate composition areincluded in Figures 3-5. Table I1 gives the parameters andthe ISE's obtained for these simulations.

The ISE's obtained by PID control, in the W B and ORcases, are comparable to those obtained by CMBC . In theA1 case, the response by PID control is highly oscillatoryand is not satisfactory.

Th e use of P I/ PI D controllers involves the use of up tothree tuning parameters per loop. In the case of CMBC,a single param eter is used per control loop. Th e advantageof having a single tuning parameters would become par-ticularly evident as the order of the system increases andthe interactions between the various loops become sig-nificant.

Conclusions

The applicability of CMBC as a multiloop controlleroperating in a m ultivariable environment ha s been dem-



Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990 137

0 . W.

TIME

Di I ” ‘

1OO. 0. eo. 180. 0. 90. 180.

TlyE TIME

t

i f

s I , ’ ’ , , , (

0 . eo.

TIME

100. 0 . so. 0. eo. 180.

TIME TlYE

MULTILOOP P I MULTILOOP CMBC

Figure 5. Alatiqi case 1 multiloop PI /CMBC/PID.

5

s0

D

MULTILOOP PID

9r I I

0. eo.

RYE

1.0.

t 1

0 . 90. 180. 0. W. 180.

TIME TlYE

AT.-- - -S.eD8-----.em_-_--_---0.m

MULTILOOP P I MULTILOOP CMBC

Figure 6. Alatigi case 2 multiloop PI / CM BC.

onstrated. A comparison of the results with several dis-tillation columns shows that CMBC is superior to PIcontrol. Th e performance of PID control is comparablewith CMBC in some cases but is inferior in one casestudied. Since CMBC contains a single tuning constantand has been show n to give excellent performanc e, it may

be the preferred choice as a m ultiloop controller in processapplications.

Nomenclature

D = digital control algorithmE = error



138 Ind. Eng. Chem. Res., Vol. 29, No. 1, 1990

g,, = transfer function of the ith input-ith outpu tG , = process transfer functionhi = impulse response coefficient at th e ith insta ntISE = integral of the square of errorsK , = proportional constant of a PID controllerK = process gainL 4 = side-stream draw-off (in figures)M = manipulated variablesQB = boiler heat supply (in figures)RR = reflux ratio (in figures)T b = temperature of th e bottoms plate (in figures)AT = temperature difference across the side-stream draw-off

XB = bottoms composition (in figures)XD = distillate com position (in figures)XS = side-stream com position (in figures)

G re e k Symbols

@ = CMBC tuning parameterT,, = derivative constant of a PID controlleriI= integral constant of a PID controller

Literature Cited

Alatiqi, I. Composition Control of Distillation Systems SeparatingTern ary Mixtures with Sm all Intermediate Feed Concentrations.Ph.D . Dissertation, Lehigh Un iversity, Bethlehem, PA, 1985.

Chawla, V. K. Development of an E xpert System Framework forMultivariable Con trol System Design. Ph.D. Dissertation, Univ-ersity of Louisville, Louisville, KY, 1988.

Chawla, V. K.; Prasad, P. R.; Deshpande, P. B. A New Digital Con-trol Algorithm for SISO and MIMO systems. Hydrocarbon Pro-CPS b . 1989. Oct.

tray (in Figures)

Luu s, R.; Jaakola, T. H. I. Optimization by D irect Search and Sys-tematic Reduction of the Size of Search Region. AIChE J . 1973,19 (4 ), 760-66.

Luyben, W. L. Simple Method for Tuning SISO Controllers inMultivariable Systems. Ind . Eng. Chem. Process Des. Deu. 1986,

Monica, T. J.; Yu, C.; Luyben, W. L. Improved Multiloop Single-input Single-output (SISO) Controllers for Multivariable Pro-cesses. Ind. Eng. Chem. Res. 1988, 27, 969-973.

Ogunnaike, B. A.; Lemaire, J. P.; Morari, M.; Ray, W. H. AdvancedMultivariable Control of a Pilot-plant Distillation Column.AIChE J . 1983,29, 632.

Prasad, P. R. Contro l Strategies for Multiva riable Processes: Dis-tillation Colum ns and Polymerization Reactors. M.S. Thesis,University of Louisville, Louisville, KY , 1989.

25,654-660.

Vinante, C. D.; Luyben, W. L. Kern. Teollisuus 1972, 29, 499.Wood, R. K.; Berry, M. W. Termin al Composition C ontrol of a Bi-

nary Distillation Column. Chem. Eng. Sci. 1973, 28, 1707.

*T o whom correspondence should be addressed.+Presentaddress: Chemical Engineering Department, T he Ohio

f Present address: Technology A pplications Inc., Jacksonville, FLState University, Columbus, OH 43201.

32216.

P. Ram anatha n Prasad,' Vipin K. Chawla'Pradeep B. Deshpande*

Depar tment o f Chemical Engineering

University of LouisvilleLouisville, Ke ntu cky 40292

Received for reuiew February 21, 1989Revised manuscript received October 6 , 1989

Accepted October 27, 1989

vipin chawla - cmbc paper - acs i&ec 1990 - ie00097a021

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