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Computers and Chemical Engineering 33 (2009) 1202–1211

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journa l homepage: www.e lsev ier .com/ locate /compchemeng

onlinear control of debutanizer column using profile position observer

ourabh Gupta1, S. Ray, A.N. Samanta ∗

epartment of Chemical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

r t i c l e i n f o

rticle history:eceived 7 June 2005eceived in revised form2 December 2008

a b s t r a c t

In this contribution profile position control for a debutanizer column is presented and a nonlinear profileposition observer is developed using tray temperature measurement. The measurement location is alwaysa well-known problem in industry; moreover it causes capital investment also. In order to overcome thisdifficulty we are proposing the pseudo profile position concept to control a debutanizer column. The

ccepted 30 December 2008vailable online 10 January 2009

eywords:seudo profile positionebutanizer column control

proposed pseudo profile position concept makes the proposed controller scheme to directly applicable inan industrial column with few modifications in the existing control structure of the column and withoutany fixed capital investment. A comparative study has been presented for four cases including control ofdistillation column using only one temperature measurement. The simulation results showed that ourapproach has the potential to meet the industrial process control requirement.

ave propagation modelodel-based control

. Introduction

Distillation columns have been well known to pose a difficultontroller design problem, resulting from unique characteristics,uch as complex dynamics, high nonlinearity and interactionetween the control loops. Choosing the proper control tech-ique for distillation columns and implementing it properly isconomically important due to the controller effect on productuality, production rate, and energy usage. Distillation control ischallenging endeavor due to the inherent nonlinearity of dis-

illation, severe coupling present for dual composition control,on-stationary behavior, and the severity of disturbances.

The highly nonlinear and distributed character of a distillationolumn is represented by its sharp composition and temperaturerofiles. It is because only a small portion of the column is usedor the major separation while other parts are only responsible forefining the products. The attempts of using a partial differentialquation to describe the dynamic behavior of distillation columnave been tried by few researchers (Cho & Joseph, 1983a, 1983b;arquardt, 1986, 1988; Stewart, Levien, & Morari 1985; Wong &

uus, 1980). Most of them have taken an orthogonal collocation

echnique to approximate the composition profiles in the columns polynomials. They cannot explain a highly nonlinear, distributedharacter of distillation columns which is resulted from its sharpomposition and temperature profiles, only providing a polynomial

∗ Corresponding author. Tel.: +91 3222 283948; fax: +91 3222 282250.E-mail addresses: gupta sourabh@hotmail.com (S. Gupta),

ray@che.iitkgp.ernet.in (S. Ray), amar@che.iitkpg.ernet.in (A.N. Samanta).1 Present address: MW Kellogg Ltd., Kellogg Tower, Greenford, Middlesex, UK.

098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2008.12.009

© 2009 Elsevier Ltd. All rights reserved.

approximation of the column profile by mathematical formalism.Gilles and Retzbach (1983) viewed the essential dynamic quality oftheir extractive column as the movement of the regions of high masstransfer that is reflected by temperature fronts. Therefore, theyused the loci of temperature fronts as state variables. Marquardt(1986, 1988) generalized the approach starting from partial dif-ferential material balance of column section to develop a novelmodel for distillation. The approach is satisfactory but its disad-vantage is the high complexity of the proposed model. In 1990,Lang and Gilles presented a full order nonlinear observer for distil-lation columns. Temperatures are measured at different points ofthe column and compared to the observer’s output temperatures.Hwang (1991) proposed a nonlinear wave theory to explain the non-linear behavior of distillation columns and in 1993, Han and Parkproposed a model-based controller design incorporating Hwang’snonlinear wave model of high purity binary distillation column intothe generic model control (GMC) framework by Lee and Sullivan(1988) based on the composition measurements. Shin, Seo, Han,& Park (2000) proposed a profile position observer based on thetemperature measurements for a binary column to overcome thedifficulty of composition measurements.

In the previous research most of the work has been carriedout for binary distillation columns with additional measurements.Moreover, strategies which are applicable to binary distillationcolumns cannot be directly apply to multicomponent distillationcolumns because of the highly nonlinear behavior of multicompo-

nent distillation columns.

The importance of the product quality for a debutanizer columnkeeps it always in focus in a refinery. In the recent years, Huangand Riggs (2002) presented the decentralized PI and MPC controlof gas recovery unit (deethanizer, depropanizer and debutanizer

S. Gupta et al. / Computers and Chemical

Nomenclature

A heat transfer areaB molar flow rate of bottom productD molar flow rate of distillate productfb vapor bypass fractionF molar flow rate of feedG molar vapor holdup of plateh molar liquid enthalpyH molar vapor enthalpylC molar cooling rate of condensateL molar flow rate of liquid stream in rectifying sectionL molar flow rate of liquid stream in stripping sectionM molar liquid holdup of plateMw average molecular weightN number of trays of entire columnq liquid mole fraction of the feedQB reboiler heat dutyr molar holdup ratio of vapor to liquidS profile position of column sectiont timeT tray temperatureTs representative tray temperature corresponding to

profile position of self-sharpening standing waveu normalized wave velocity for specific compositionu� normalized shock wave velocity of self-sharpening

waveU overall heat transfer coefficientV molar flow rate of vapor stream in rectifying sectionV molar flow rate of vapor stream in stripping sectionx liquid mole fractionxs representative liquid mole fraction corresponding to

profile position of self-sharpening standing wavey vapor mole fraction

Greek letters� prefix for difference between the two sides of self-

sharpening wave� normalized distance from bottom of the column,

� = k/N� normalized time, � = tF/NMε heat transfer effectiveness� molar density

Superscriptsˆ observer prediction. derivative* setpointnorm. normalized value

Subscripts0 reboiler tray1 rectifying section2 stripping sectionC critical valueCW cooling waterF feedi tray il, L liquidSP setpointv, V vapor

Engineering 33 (2009) 1202–1211 1203

column). Ansari and Tade (1998) presented the development of anonlinear process model-based control of a debutanizer columnusing the generic model control structure of Lee and Sullivan (1988).In the present work, we are proposing profile position control of adebutanizer column. As the profile position control leads to an addi-tional capital investment in the form of temperature measurementdevice moreover which may also cause noise to the system, we areproposing the pseudo profile concept to control the debutanizercolumn.

2. Process description for debutanizer column

The debutanizer column of the gas recovery unit of FCC unit(Huang & Riggs, 2002) is simulated in this work. The debutanizercolumn has 30 no of trays, reboiler and a total condenser. The feed,a mixture of C3–C6 components, is fed to the column at 16th tray(counted from bottom). The condenser is operated as flooded con-denser, but there is no level measurement of liquid level in thecondenser. The overhead pressure is controlled by adjusting thedistillate product (butane) flow, and is an effective indicator of liq-uid level in the condenser. Detailed dynamic material balance andenergy balance equations have been used for the simulation of thedebutanizer column as shown in Table 1. The vapor liquid equi-librium is calculated using SRK equation of state. For the floodeddebutanizer condenser, the effectiveness is not a constant becausethe heat transfer area decreases as more cooling water tubes arecovered by the condensate (i.e. UA is not constant). To simplify themodel, the heat transfer effectiveness is assumed to be proportionalto the height of vapor volume in the shell side of the condenser.The nominal values required for the distillation column simulationis presented in Table 2.

3. Debutanizer control strategy

In a debutanizer column, the control objective is to removeimpurities (C+

5 components) in the distillate and maintain mini-mum possible amount of butane in the bottom product to maximizethe yield of butane. Keeping this target in mind, butane compositionis measured and controlled at both ends of the column by control-ling the butane wave in the distillation column. The control schemeis shown in Fig. 1.

The heart of the control scheme is the profile position observerand the profile position controller. The composition controllers(CC1 and CC2), simple PI controllers, generate the profile positionsetpoints by using the measurements from analysers (A01 and A02).The profile position observer and controller is designed using non-linear wave theory for distillation column.

4. Nonlinear wave theory

The dynamic behavior of distillation column is characterizedby the propagation of concentration or temperature profile in thecolumn sections. This typical dynamic behavior is summarized byMarquardt (1986) for nonlinear wave propagation where nonlin-ear wave is a spatial structure moving with a constant propagationvelocity and constant shape along a spatial coordinate.

Fig. 2 presents the simulated propagating composition (butane)and temperature waves for the debutanizer column in case of 10%heavier and 10% lighter feed composition (Table 3) disturbance tothe column. A disturbance in the feed composition creates two

shock waves on both sides of the feed plate moving towards theboth end of the column. The difference in wave velocities for heav-ier and lighter feed makes the column nonlinear and complex interms of controlling the column. From the standpoint of controlapplications, the dynamic information of most interest is that after

1204 S. Gupta et al. / Computers and Chemical Engineering 33 (2009) 1202–1211

Table 1Modeling equations for debutanizer column.

Continuity equations and energy balance equations for distillation columnModeling equations for reboiler and column base

Continuity equation (dMB/dt) = L1 − B − VB

Component continuity equation (dxB,j/dt) = [L1x1,j − BxB,j − V0y0,j − xB,j(dMB/dt)]/MB

Energy balance equation V0 = [L1(hL,1 − hL,B) + QB − MB(dhL,B/dt)]/(HV,0−hL,B)

Modeling equations for ith (i /= feed tray) trayContinuity equation (dMi/dt) = (Vi−1 + Li+1 − Li − Vi)/time constantComponent continuity equation (dxi,j/dt) = [Li+1xi+1,j + Vi−1yi−1,j − Vi(yi,j − xi,j) − xi,j(Vi−1 + Li+1)]/Mi

Energy balance equation Vi = [Li+1hL,i+1 + Vi−1HV,i−1 − hL,i(Vi−1Li+1) − Mi(dhL,i/dt)]/(HV,i − hL,I)

Modeling equations for feed trayContinuity equation (dMi/dt) = (Vi−1 + Li+1 + F − Li − Vi)/time constantComponent continuity equation (dxi,j/dt) = [Li+1xi+1,j + Vi−1yi−1,j − Vi(yi,j − xi,j) − xi,j(Vi−1 + Li+1)]/Mi

Energy balance equation Vi = [Li+1hL,i+1 + Vi−1HV,i−1 − hL,i(Vi−1Li+1)−Mi(dhL,i/dt)]/(HV,i − hL,i)

Modeling equations for total condenserContinuity equation (dM/dt) = lC − R − DL

Component continuity equation MD(dxD,j/dt) = lC(yD,j−xD,j) + VN+1(yN+1,j − yD,j)Energy balance equation lC = [MD(dh/dt) − QC − VN(HV,N − HV,N+1)]/(HV,N+1 − hL,N+1)

Condenser pressure can easily be calculated from the following equationP = [RVT/(sp. vol. − bm)] − [am/sp. vol. (sp. vol. + bm)]Condenser cooling duty Cooling duty = ε(mCp) (T − T )

tcttbttvi1&

he wave is formed and before it approaches the column end. Theontrol of distillation columns is dependent on the ability to modelhe state of the column in terms of a continuous butane composi-ion or temperature profile and its dynamics in terms of propagatingutane composition or temperature waves. The wave tends to travelo either one of the column ends unless the balance of convec-

ive transports is carefully maintained to have a zero shock waveelocity with the compositions and flow rates of all streams enter-ng a distillation column. Several researchers (Gilles & Retzbach,983; Gilles, Retzbach, & Silberberger, 1980; Hwang, 1991; LangGilles, 1990; Marquardt, 1986, 1988) successfully approximated

Fig. 1. Schematic diagram of debutaniz

CW CW 1

a = exp((r − 1)NTU) ε = (1 − a)/(1 − ra)NTU = UAmax[(vap. vol.Accu. − vap. vol.col.)/(mCp)CW (tot. vol.accu. − vap. vol.col.)]

the behavior of high purity binary distillation columns with thisapproach.

The travel of such a constant-pattern wave can be characterizedby shock wave velocity and the velocity of this wave is derived fromthe material balance across the wave:( )

u ≡ ∂�

∂�x or y

= − ∂x/∂�

∂x/∂�= V/F(∂y/∂x) − L/F

1 + r(∂y/∂x)(1)

where r is vapor to liquid holdup ratio, � is normalized time(� = tF/NM), and � is normalized distance from bottom of the column

er column with control structure.

S. Gupta et al. / Computers and Chemical Engineering 33 (2009) 1202–1211 1205

Fig. 2. Dynamic composition and temperature profiles of the debutanizer column to a ste

Table 2Operating variables for debutanizer column.

Reflux rate (lb mol/s) 0.318Reboiler duty (btu/s) 3832.84Condenser duty (btu/s) −4803.5

Feed Distillate Bottoms

Stream detailsFlow rate (lb mol/s) 0.314 0.251 0.063Temperature (◦C) 111.8 58.1 121.4Pressure (psia) 233.7 90 99.3

CompositionC3 1.22% 1.53% –C4 76.80% 95.47% 2.0%

(ieo

dt= K1(S − S) + K2

0

(S S) dt (2)

TF

C

F

C5 11.74% 2.90% 47.11%C6 10.24% 0.10% 50.89%

� = k/N). Assuming the liquid flow is so slow that local equilibriums attained, y in Eq. (1) can be substituted with the vapor liquidquilibrium relation. The detail description of this equation can bebtained from the literature (Hwang, 1991).

able 3eed composition in different scenarios.

omposition Normal 10% Lighter

eed compositionC3 1.22% 1.25%C4 76.80% 78.44%C5 11.74% 10.85%C6 10.24% 9.46%

p disturbance of feed composition in open loop (each curve is separated by 5 min).

Therefore, the behavior of distillation column is severely nonlin-ear and sensitive since even a small upset of the balanced conditionwill lead to a large shift of the profile, giving dramatic changes in theproduct purity. In this study, we are applying the nonlinear wavemodel for a debutanizer column as the basis for the profile positionobserver and the generic model controller in the control system.

5. Profile position controller design

Using Hwang’s nonlinear wave model, a profile position con-troller is designed employing a GMC framework. GMC allows theincorporation of nonlinear process models such as a nonlinear wavemodel directly into the control algorithm. The GMC equation for theprofile position S can be written as

dS ∗∫ t

∗ ′

where S and S* are the profile position and its setpoint respectively;dS/dt is the propagation rate of profile. S is expressed in terms ofthe normalized distance from the bottom of the column (S = 0 at

10% Heavier 20% Lighter 40% Heavier

1.19% 1.27% 1.09%75.06% 80.0% 69.19%12.68% 10.01% 15.87%11.06% 8.73% 13.84%

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L

V

wk(

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i

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icswc

no

S

wnmv

206 S. Gupta et al. / Computers and Che

ottom; S = 1 at the top). The propagation rate can be expressedrom the nonlinear wave model as follows:

dS

dt= u = V

F

�y/�x − L/V

1 + r(�y/�x)(3)

Distillation columns, in general, have two sections: one is theectifying section and the other is the stripping section. Combiningqs. (2) and (3) gives one equation for each section as follows:

V

F

�y/�x − L/V

1 + r(�y/�x)− K11(S∗

1 − S1) − K12

∫ T

0

(S∗1 − S1) dt′ = 0 (4)

V

F

�y/�x − L/V

1 + r(�y/�x)− K21(S∗

2 − S2) − K22(S∗2 − S2) dt′ = 0 (5)

here subscripts 1 and 2 represent rectifying section and strippingection respectively. L and V are the liquid and vapor flow ratesespectively in the rectifying section and L and V in the strippingection. The profile position and the slope of the equilibrium curvet the representative concentration can be estimated by the pro-le position observer accurately. Mass balance around the feed trayives

¯ = L + qF (6)

= V + (1 − q)F (7)

here q is the liquid mole fraction of the feed. Therefore, if wenow the feed condition, L, V, L, and V can be determined from Eqs.4)–(7).

Due to the highly nonlinear behavior of the multicomponentistillation column, the controller algorithm has been simplified inhe following order:

i. Calculate reboiler molar vapor flow rate from the available refluxrate (from plant) using Eqs. (5) and (6).

i. Calculate molar reflux rate from the available reboiler molarvapor flow rate from previous step, using Eqs. (4) and (7).

. Profile position observer

The success of the GMC profile position controller is mainlyependent on the ability to estimate the profile positions thatannot be measured directly. Han and Park (1993) used theoncentrations on the pre-specified trays, but the use of such mea-urements is not practical since the composition measurementsre expensive and unreliable. Shin et al. (2000) presented a pro-le position observer based on the temperature measurement, buthis approach is limited only for the binary systems.

The profile position can be regarded as the location of the stand-ng wave. It is more convenient to represent the location of aonstant pattern wave with a single point corresponding to a repre-entative concentration. The profile position of the constant patternave can be determined easily by tracking the representative con-

entration or temperature instead of the entire wave.In this case, the profile position observer is designed using the

onlinear wave model for the debutanizer with additional feedbackf weighted output error of temperature(s) feedback.

˙ = dS

dt= V

F

�y/�x − L/V1 + r(�y/�x)

+m∑i=l

k1(Tnormi )(Tnorm

i − Tnormi ) (8)

�y S + L/F

�x

=V /F − rS

(9)

here i is the measurement tray number and l and m are theumber of first measurement tray and the number of last measure-ent tray in a column section, respectively; indicated the estimated

alue. The representative slope, which is the slope of the equilib-

Engineering 33 (2009) 1202–1211

rium curve at the representative temperature, can be estimatedfrom Eq. (9). The difference in the order of magnitude of the temper-ature and the profile position can result in the poor performance ofthe observer. To make both of them of same order we are proposingto normalize the temperatures between 0 (top) and 1 (bottom) andsteady state temperatures can be taken as the reference tempera-tures. For �y/�x and Tnorm relationship the steady state plant datacan be used which will take care of the tray efficiencies also. Thedifference between the process and model has to be corrected bythe measurement so that the sharp profile regions of both coincide.Thus the profile position can be estimated with sufficient accuracyand the saturation problem can be greatly reduced. The weightingfactor k1(Tnorm

i) has the following form:

k1(Tnormi ) = k0 exp[−b(Tnorm

i − Tnorms )2] (10)

The value of the weighting factor k1(Tnormi

) gets greater as thetemperature of the measurement tray is closer to the representativetemperature with an exponential form. Here, k0 denotes the gainof the weighting function and b adjusts the range of the weight-ing. The weighting gain k0 of the observer is chosen so that theobserver is considerably faster than the process. The parameter bcan be determined by considering the profile shape of the columnsection. The observer response time should be fast enough to pro-vide convergence of the estimates within the time interval of theinterest. Therefore, the sampling time of the observer is chosen as0.2 time unit.

The observer computes the temperature of each measurementtray from the estimated profile position with that the profile has alinear form as follows:

Tnormi = k2(Si − S) + Tnorm

s (11)

where Si is the normalized distance at which ith tray is located andTnorm

iis the normalized temperature at the ith tray and Tnorm

iis

the representative normalized temperature. Ideally temperatureswere measured at different points of the column and comparedwith the observer’s output temperatures. However, in practice thisis not always feasible. One representative tray temperature locationin each section can be selected based on the inflection points inthe temperature waves. In control applications, the nonlinear wavemodel is used to ensure zero wave propagation velocity despite dis-turbances. Subsequently, inflection point should remain unchangedand there will be conformity of profile position. In our case, the rep-resentative tray temperatures with respect to the inflection pointsare on 14th and 18th tray.

7. Pseudo profile position observer

In industrial column, installation of a new measurement deviceis not always feasible. To overcome this problem we have to use theexisting temperature measurement for the calculation of the pro-file position, which is usually available at the top and the bottomstage of the column. Roffel, Betlem, and Blouw (2003) have pro-posed a method to estimate the temperature at representative traybased on Taylor series expansion. In our work we are also usingthe Taylor series expansion approach to estimate the representa-tive tray temperature. The representative tray (14th and 18th tray)temperatures can be calculated from the existing top and bottomtray temperature measurement by the following equations:

T14 = Tbot +(

∂T

∂S

)(S14 − Sbot),

bot

T18 = Ttop +(

∂T

∂S

)top

(S18 − Stop) (12)

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tcp

eat

fttwtbcps

•

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C

S. Gupta et al. / Computers and Che

The derivative ∂T/∂S should be calculated at the measurementray. This derivative can be calculated from the simulation of theolumn and an average value for the derivative can be used forredicting the representative tray temperatures.

The simpler but somewhat inaccurate method is to assume lin-ar temperature profiles between top tray and feed temperaturend bottom tray and feed temperature and calculate the represen-ative tray temperatures by linear interpolation.

During the study of the debutanizer column we have taken dif-erent cases, in which our aim is to find out the temperature athe desired tray of the column. The obtained profile position fromhe inferred tray temperatures can be treated as a ‘pseudo profile’,hich represents the nonlinear wave for the corresponding sec-

ion (rectifying/stripping) and during the control the objective wille to manipulate the pseudo profile position for the compositionontrol. For the study of the pseudo profile position control, theossible cases are listed in Table 4. The algorithm of the observer isummarized in the following steps:

Step 0: Select initial estimates of profile position S and represen-tative slope �y/�x.Step 1: Measure temperatures at measurement trays, infer thetemperatures of representative trays from each section.Step 2: Normalize the temperatures and calculate the errorsbetween the measured and the estimated normalize tray tem-peratures.Step 3: Estimate the propagation velocity and the representativeslope from the equation with the feedback of the weighted errors.Step 4: From the equilibrium relation and the representative slope,find the representative normalized temperature.Step 5: Estimate the profile position by integrating the wave prop-agation velocity.Step 6: Estimate tray temperature from the profile position andthe representative normalized temperature, return step 1.

. Tuning parameters for composition/profile positionascade control

Han and Park (1993) shows that tight control of profile positioneads to fast stabilization of the product concentrations and thathe composition controller can remove the slight offset from theetpoint in product composition. Therefore the sampling time ofhe composition controller was chosen as 2.0 time unit while thatf the profile position controller was 0.2 time unit.

Tuning parameters of the GMC controller, for the stripping sec-ion and the rectifying section can be calculated individually usingntegral absolute error (IAE) optimization by keeping one section’s

stripping/rectifying) control loop closed and the other section’srectifying/stripping) control loop open. As the GMC controllerquations are coupled to each other, a detuning factor is required toeduce the proportional action as well as the integral action. Oncehe GMC controller parameters are identified, the similar way ispplied to calculate the control parameters for the PI control.

able 4ifferent test cases for pseudo profile position estimation of debutanizer column.

Top tray temperature Bottom traytemperature

Representative tray temprectifying section

ase 0 – – Measurementase 1 – – Measurementase 2 – Measurement Measurement

ase 3a Measurement Measurement Estimating it using other(linear interpolation).

a Industrial approach.

Engineering 33 (2009) 1202–1211 1207

9. Results and discussions

Nonlinear profile position observer is implemented on the sim-ulated debutanizer column. The profile position behavior is studiedfor different location of temperature measurement as mentioned inTable 4. The cascaded structure of composition controller to profileposition controller is also designed and implemented on the debu-tanizer column to study the effect on controller performance fordifferent cases of profile position behavior. Tuning parameters foroptimal tuning of debutanizer column is given in Table 5.

10. Effect of measurement location on profile positionobserver

Fig. 3 shows the open loop profile position behaviors of the debu-tanizer column with different cases of measurement location asmentioned in Table 3. The feed composition is changed to makeit 10% heavier and introduced to the column at 10 min. S1 and S2are the composition profiles for rectification and stripping sectionrespectively. Since both representative rectification and strippingtemperatures are measured in Case 0, this can be considered asideal case. Case 1 is a different from other cases because of onlyone measurement (in rectification section) is used and other tem-perature is inferred. In case of pseudo profile (Case 1), gain for therectifying profile position (S1) should be sufficient such that profileposition in stripping section can be estimated. A low gain is allow-able in Case 0, 2 and 3 as it leads to a good control and less sensitiveto noise. As there is only one temperature measurement in Case 1so this is a compromise with profile position (S1) estimator gain inthis case and due to this estimator parameters are also different.

11. Effect of feed composition disturbance

The controller performance has been tested for the specified fourcases and the results show that the proposed controller scheme isable to control within a small time interval. Fig. 4 shows the abilityof the control system to reject the effect of the feed compositionchange. The control scheme with all the cases is shown to providea good performance for the large upset such as a change in thefeed composition of 20% lighter feed followed by 40% heavier feedwith Case 1 showing least integral absolute error. In all the cases,the composition waves are controlled immediately (Fig. 5) and theshock wave velocity is reduced to zero after the initial shock dueto feed composition disturbance. This expectedly, diminishes thepropagation of feed disturbances to the terminal butane composi-tions.

12. Tracking of setpoint for bottom composition

Fig. 6 shows the comparative performance of the profile posi-tion controller with decentralized PI controllers for the closed loopresponse to a desired setpoint change in XB (n-butane) from 0.02 to0.002. This is a large relative change in the setpoint for the systemand the profile position controller is able to move to the setpoint

erature for Representative tray temperature for stripping section

MeasurementEstimating it from the profile position estimatorEstimating it using other two temperatures (linearinterpolation).

two temperatures Estimating it using other two temperatures (linearinterpolation).

1208 S. Gupta et al. / Computers and Chemical Engineering 33 (2009) 1202–1211

Table 5Parameters for the controller and the proposed observer.

Case 0, Case 2, and Case 3 Case 1

Accumulator level control (PI tuning) Accumulator level control (PI tuning)KC = 2.0e−32 �I = 2.0e32 KC = 2.0e−32 �I = 2.0e32

Reboiler level control (PI tuning) Reboiler level control (PI tuning)KC = 2.0e−3 �I = 2000 KC = 2.0e−3 �I = 2000

GMC tuning GMC tuningK21 = 206.82 K22 = 2.55 DT = 3.5 K21 = 206.82 K22 = 2.55 DT = 5K21 = −3.18 K22 = −0.64 DT = 3.5 K21 = −3.18 K22 = −0.64 DT = 5

PI tuning PI tuningKC,1 = −112 �I,1 = 139 DTPI,1 = 5 KC,1 = −112 �I,1 = 139 DTPI,1 = 2KC,2 = −8 �I,2 = 35 DTPI,2 = 5 KC,2 = −8 �I,2 = 35 DTPI,2 = 2

Parameters for profile position observer (rectifying section) Parameters for profile position observer (rectifying section)k0 = 0.4 k2 = −15, b = 0.03 k0 = 0.4 k2 = −3, b = 0.01

Parameters for profile position observer (stripping section) Parameters for profile position observer (stripping section)k0 = 0.6 k2 = −12, b = 0.01 k0 = 0.6 k2 = −12, b = 0.01

e posi

wmofattoI

13. Simultaneous servo and regulatory performance with

F

Fig. 3. Open loop transient response, in profil

ithout any offset in the product concentration in quick time. Theaximum variation in distillate butane composition is ±0.2% is

bserved in case of Case 1, where only one measurement is usedor profile position observers. Although decentralized PI controllers

re also able to track the setpoint change and stabilize the system,heir speed of response is quite slow compared to the profile posi-ion controllers. The speed of response can be increased at the costf higher deviations from the setpoint which contributes to higherAE value. The parameter values (gain, integral time in minutes) for

ig. 4. Closed loop transient response of debutanizer column for a step disturbance of 20%

tion with different cases for 10% heavier feed.

the PI controllers as obtained by minimizing the total IAE are (6.45,6.5) and (−11,380, 5.5) for top and bottom controllers respectively.

noise for the column

A simulation experiment has been conducted on the columnwith imposing disturbance and uncertainties. In this experiment

lighter feed at 10 min followed by a step disturbance of 40% heavier feed at 100 min.

S. Gupta et al. / Computers and Chemical Engineering 33 (2009) 1202–1211 1209

rbanc

fc

•

••

•

F

Fig. 5. Close loop temperature profiles of debutanizer column for a step distu

eed disturbances and setpoint changes have been imposed to theolumn simultaneously.

n-Butane composition setpoint change in bottoms form 0.02 to

0.002 (15 min),20% lighter feed to the column (30 min).High purity product in terms of n-butane composition in distillatefrom 95.6% to 96.2% (60 min).10% heavier feed to the column (90 min).

ig. 6. Closed loop transient response in distillate and bottom n-butane composition for a

e of 20% heavier feed and 20% lighter feed (each curve is separated by 1 min).

• In the above case following uncertainties has been taken intoaccount:

• Random disturbance in feed flow rate (±5%).• Random disturbance in reboiler heat duty (±10%) and reflux flow

rate (∓10%).

• Noisy temperature measurement at top and bottom (±5 ◦C)

This rigorous controller testing is conducted for Case 3 only. InCase 3, top and bottom tray temperature measurement is availableand profile positions are calculated based on these measurements

desired setpoint change in setpoint change in XB (n-butane) from 0.02 to 0.002.

1210 S. Gupta et al. / Computers and Chemical Engineering 33 (2009) 1202–1211

Fig. 7. Closed loop transient response in XD (n-butane), and rectifying section’s profile position (S1).

butan

bNabc

a

Fig. 8. Closed loop transient response in XB (n-

y inferring the represented tray temperatures (14th and 18th).ormally, in existing columns top and bottom tray temperaturesre already available and this new nonlinear control strategy can

e applied without any instrument hardware modification of theolumn.

Figs. 7–9 show the simulation results for the simultaneous servond regulatory performance with noise for the debutanizer col-

Fig. 9. Closed loop transient response of

e), and stripping section’s profile position (S2).

umn. The controller is able to control the column end point butanecompositions to its setpoint despite the setpoint and load changesin the column. The transient behavior of the reflux flow rate and

reboiler heat duty, the two manipulating variable, is shown in Fig. 9.Except at 60 min, both the manipulated variable showed near sta-ble and smooth transition which is a desirable performance of acontroller.

reflux rate and reboiler heat-duty.

mical

1

pscotots

atpdt

R

A

C

C

neering Science, 55, 807–816.Stewart, W. F., Levien, K. L., & Morari, M. (1985). Simulation of fractionation by

S. Gupta et al. / Computers and Che

4. Conclusions

A nonlinear profile position observer has been developed androven to estimate the profile position of the column section withufficient accuracy using temperature measurement in a multi-omponent distillation column. The GMC controller works directlyn the rate of the profile propagation and the tight control ofhe profile position helps to control the end point compositionsf debutanizer column. It has also been shown that proposedechnique is extremely robust and able to control without any off-et.

Pseudo profile position concept is presented in our work for thepplicability of the proposed profile position controller to an indus-rial column without any capital investment. The proposed pseudorofile position concept makes the proposed controller scheme toirectly applicable in industrial column with few modifications inhe existing control structure of the column.

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