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ROBUST DECENTRALIZED CONTROL OF REACTIVE

DISTILLATION PROCESS IN DIMETHYLACETAMIDE PRODUCTION

Andrei Yu. Torgashova1

, Kyung-Chul Parkb, Nam Sig Kang

b

aInstitute of Automation and Control Processes FEB RAS,

690600, 5 Radio Str., Vladivostok, Russia, E-mail: torgashov@iacp.dvo.ru

bTechnical Team, Samsung Fine Chemicals Co., Ltd.,190, Yeochun-dong, Nam-ku, Ulsan, 680-090, Korea

E-mail: kyungchul.park{namsig.kang}@samsung.com

Abstract: The paper deals with the sequential synthesis procedure of decentralized (multi-loop) PID-controllers based on the estimation of control loops interaction in the form of

multiplicative plant uncertainty. It is shown that the each synthesis iteration isaccompanied by the correction of the robust performance criteria for the coupled SISO-systems. The results of industrial application of proposed sequential design for reactivedistillation unit is cited as well as comparison analysis with the other techniques is given.

Copyright 2005 IFAC

Keywords: Decentralized control, Distillation columns, PID controllers, Robustperformance, Uncertain dynamic systems.

1. INTRODUCTION

Nowadays the widespread technology for controlperformance improvement of multivariable chemicalprocesses is an application of model predictive

control (MPC) software packages as RMPCT, DMC,IDCOM and etc (Qin and Badgwell, 2003). However

for their successful realization it is necessary to havespecial interfaces and sometimes DCS configurationwork is not available. Because of the encounteredtechnical problems of MPC application the finetuning of multi-loop PID controller still remains asimportant task in industry.

It was proposed to consider the synthesis of robustmulti-loops PID controllers as direct optimizationproblem solution using successive quadraticprogramming or linear matrix inequalities (Bao et al,

1Present address: Samsung Fine Chemicals Co. Ltd,

190, Yeochun-dong, Ulsan, 680-090, Korea

1999; Huang and Huang, 2004; Zheng et al, 2002).Such kind of methods are characterized by the high

dimensionality of the vector of optimized parameters.Also the analysis will be more complicated when theuncertainty or transport delays of the non-diagonal

elements of the process transfer matrix areconsidered. The alternative sequential design isconsiderably easy used in practice (Hovd and

Skogestad, 1994) because of the low calculationefforts and based on the independent analysis of eachclosed loop systems. The bandwidths of SISO-systems are estimated. The final target is to find thePID parameters which can provide the fulfilment ofthe inequality imposed of the MIMO-system

structured singular value. The previous investigationsregarding the sequential approach did not handle therobust stability and performance conditions ofseparated SISO closed loop systems in the

straightforward manner with their interactions. Theadditional lack is the absence of the strict

mathematical guidance for the selection of the loopsbandwidths.

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In the present work we are developing the sequentialapproach for robust multi-loop PID controllersynthesis based on the example of reactivedistillation column in dimethylacetamide production.

It has been proposed to use the multiplicativeuncertainty form in order to express interaction

among the loops on the each iteration of designprocedure. The high bound of interaction (by its

multiplicative presentation) is estimated when theinfluence from the other SISO-systems has themaximum effect. The tuning of the single controllercan be simplified when the high bound of the so-

called interaction equivalent uncertainty is less thenprocess model uncertainty.

2. REACTIVE DISTILLATION COLUMNMODEL AND ROBUST

CONTROL PROBLEM FORMULATION

The integrated chemical processes are becoming

more popular nowadays in industry. Theiradvantages consist in the low energy consumptionand capital cost due to the concurrent

implementation of several physical-chemicalprocesses in the same apparatus. For example, thecombination of chemical conversion of thesubstances with their distillation is realizing in thereactive distillation (RD) column (Taylor R. and R.Krishna, 2000; Noeres et al, 2004). The RD columnis essentially nonlinear and non-stationary plant

because of the drift of reaction rates undertemperature and pressure variation, changes of thecatalyst activity, inconstancy of the hydrodynamic

conditions and etc. The features of RD columns

Fig. 1. Multi-loop control system configuration ofreactive distillation column.

operation make challenge for the nonlinear controldesign (Chen et al, 2003; Gruner et al, 2004).However, the accurate analytical synthesis of thenonlinear controller for industrial column is so

complicated by the high dimensionality of thedistillation model having a system from hundreds

nonlinear differential and algebraic equations(Krivosheev and Torgashov, 2002). Therefore, the

robust performance optimization of PID-controllersis motivated based on the empirical dynamic modelswhich commonly used in practice (Engell andFernholz, 2003). Moreover, according the work of

Kienle and Marquardt, 2003 the stabilization ofcertain RD column steady-state in industry can bedone in many cases using conventional PI-controllers.

The investigated RD column of dimethylacetamide

(DMAC) production is depicted on the Fig. 1. It hasthree available manipulated variables u=[u1 u2 u3]

T

and three controlled outputs y=[y1 y2 y3]T. The

pressureP (y1) is regulated by the molar flows ratio(FRC u1) of S1 (acetic acid - AcOH) and S2(dimethylamine - DMA). The RD column product D

contains about 25% of impurities (DMA, AcOH).They are removed by subsequent distillation columns(not considered in the present paper). Thetemperature T (y2) is held by the manipulation ofsteam V (u2) used for the creation of vapor stream

inside the column. The part of the vapor returns intothe column as reflux after condensing. The level L

(y3) in the bottom is controlled by the distillate D(u3). The reflux drum level is maintained by refluxR.The interaction of the vapor and liquid is

accompanied by the chemical reaction DMA +AcOH DMAC + H2O with the distillation ofreactants and reaction products. The some operation

conditions details can be found in the work of Kerberet al, 1971. The reaction mechanism and kinetic were

introduced by Fabrizio et al, 1973.

The chemical interaction among the reactants has socomplex nature. At the first step thedimethylammonium acetate is formed by thefollowing reversible reaction:

CH3COOH+(CH3)2NH(CH3)2N+H2,CH3COO

-.

At the second step the catalytic decomposition of the

derived salt solution on the final product isprocessing:

(CH3)2N+H2,CH3COO

Catalyst

CH3CON(CH3)2+H2O.

In order to prevent the azeotrope formation between

DMAC and AcOH the DMA flow is supplied inexcess. Therefore, the pressure in the top of columnis sensitive with respect to variation of ratio betweenS1and S2. The following RD column transfer matrixwas derived for nominal operating point:

...

88.377.3

106

1.119.30

003.0

16.21193

2.066.3

14.121.23

17.0 18.20109

14.08.5

61.9

026.082.0

)(

5

23

56

23

5

2

5

2

2

2

3

2

++

++

++

++

++

+

+

+

=

ss

ss

ss

esss

esss

ess

se

ss

e

ss

se

ss

s

sG

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.

1.40

007.01.014.37

207.09.26116

006.01.06.3

...

5

2

2

2

23

2

+

+

++

s

s

s

ess

s

es

esss

ss

(1)

The PID-controllers were implemented in Yokogawa

DCS, therefore the all gains of the transfer function(1) were scaled for the range of y from 0 to 100%and the time constants are indicated in minutes. Theinvestigation of industrial plant showed its verynonlinear and complex behavior (Fig.2).

The control system configuration on the fig. 1 wasselected based on the RGA analysis

(j)=G(j)(G(j)-1)T (Skogestad andPostlethwaite, 1996). The modules of the diagonal

elements of (j) have the values around unityexcepting the range from 0.1 rad/min to 1.0 rad/min(fig.3). The interaction is appearing in that frequency

range, i.e. the non-diagonal elements in (1) ij|ij(j)

are approaching to unity. The condition number of

G(j) is increasing from 15 to 97 and hunting around55 in the high frequency domain (fig.4). The fig.3-4are confirming the validity of robust PID-controllersdesign for RD column.

Fig. 2. Nonlinear steady-state characteristic of

reactive distillation column: plant data; regression model.

The multiplicative form of plant model uncertaintyrepresentation is common and useful method in orderto express robust performance and stability of closedloop system. The following weighted transferfunctions for multiplicative uncertainty descriptionare chosen for diagonal elements description in (1)

02.018.0

01.0)(11 +

+=

s

ssW ;

06.029.0

02.0)(21 +

+=

s

ssW ;

03.02.0

009.0)(31 +

+=

s

ssW . (2)

The expressions (2) were derived from the conditionsof real parametric and structural uncertainty of

G(j). The upper indexes in (2) correspond to thenumbers of diagonal elements in (1).

The statement of the robust H-optimal PIDcontroller design problem for i-th closed loop has thefollowing form

iCC iimax

21 , (3)

under constraints

,1)()(