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Ind. Eng. Chem.Res. 1996,34, 4413-4419 4413

A Comparison of Advanced Distillation Control Techniques for aPropylenePropane SplitterVikram Gokhale, Scott Hurowitz, and J amesB. Riggs*p+Department of Chemical Engineeri ng, Texas Tech University, Lubbock, Texas 79409A detailed dynamic simulator of a propylene/propane ((23) splitter, which was bench-markedagainst industrial data, hasbeen used to compare dual composition control performance for adiagonal PI controller and several advanced controllers. The advanced controllers consideredareDMC, onlinear process model based control, and artificial neural networks. Each controllerwas tuned based upon setpoint changes in the overhead product composition using50%changesintheimpurity levels. Overall, there was notagreat deal of differenceincontroller performancebased upon thesetpoint and disturbance tests. Periodic step changes in feed composition werealso used to compare controller performance. In this case, oscillatory variations of the productcomposition were observed and the variabilities of theDMCand nonlinear process model basedcontrollers were substantially smaller than that of the PI controller. The sensitivity of eachcontroller to the frequency of the periodic step changes in feed composition was also investigated.

IntroductionIt has been estimated that there are about 40 000

distillation columns in the U.S. chemical processingindustries (CPI) alone (Humphrey et al., 1991). Thesecolumns are estimated to consume3%of the total U.S.energy usage. Moreover, distillation columns almostalways determine the quality of products produced bythese industries and many times limit process produc-tion rates.Improved distillation control can result in very sig-nificant economic advantages for the CPI. Listed beloware the major benefits of improved distillation control:(1)Reduced utility usage. Industry many times tendsto overflux their columns, producing overpurified prod-ucts, in an effort to maintain product specifications inthe faceof significant process upsets (e.g., feed composi-tion and flow rate changes). Therefore, reduced productvariability would allow them to produce products thathave impurity levels closer to their true specification,resulting in significant energy savings(20-30% energyreduction) in many cases. This can be particularlyimportant in the refining and high-volume chemicalindustries.(2) Reduced product variability. Reduced productvariability means producing products that contain lessvariability in the impurities in the products. There isarapidly growing trend in the chemical industry towardproducing low variability products (Downs and DOSS,1991). For example, many polymer manufacturers haverealized that they produce a better polymer productwhen they use more uniform quality feedstocks. As aresult, the polymer companies are requiring theirfeedstock producers to provide them with a moreuniform feedstock. As the producers of chemical inter-mediates learn the benefits to their business of moreuniform feedstocks, they are placing more and morerestrictive limits on the variability of their feedstocks.Quality has become a watchword of the 199Os, andquality for the chemical industry means low productvariability.(3) Increased processing rates. When a distillationcolumn represents a bottleneck to a process, improvedcontrol on that column can result in increased through-

*To whom correspondenceshouldbe addressed.t Fax: (806)742-3552. Email: cpjbr@ttacs.ttu.edu.

0888-5885/95/2634-4413$09.00/0

put for the whole process. Obviously, for such cases,improved control provides a major economic improve-ment. Improved column control for such a situationallows the column to be operated closer to its productspecifications without violating them, which in turnallows greater processing rates.Distillation control isa challenging field because ofthe following characteristics of industrial columns:(1)The inherent nonlinearity of columns particularlyfor producing high-purity products.(2)The severe coupling present for dual compositioncontrol.(3)The variation in process gains dueto process andoperating changes.(4) Large upsets in feed flow rate and feed composi-tion.These problems are particularly important for dualcomposition control. When single-ended control isused,couplingiseliminated and the resulting control problemisgreatly simplified. Unfortunately, single-ended con-trol results in suboptimal operation in many cases dueto the issues of energy usage and product recovery.Due to the development and implementation of anumber of advanced control techniques over the last 10years, industry isfaced with the decision of whether ornot to use advanced control and if sowhich one shouldthey select for their application. This decision haslargely been based upon a leap of faith. We havebegun a program aimed at developing comparisonsbetween conventional PI controls and several of themajor advanced control options which can help industry

make economic-based advanced control decisions.The control techniques considered in this study areconventional PI controls, inear model predictive control(DMC; Cutler and Ramaker, 19791, nonlinear processmodel based control (nonlinear PMBC; Lee and Sulli-van, 1988), and artificial neural networks (ANN;Bhatand McAvoy, 1990). This paper presents the results ofthese controllers applied to a detailed dynamic simula-tion of a propylene/propane(C3) splitter.Case Study and Simulator

A simulationof an industrial C3splitter has been usedas a test case to compare a conventional PI controllerand the advanced controllers for dual composition0 1995 American Chemical Society

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4414 Ind. Eng. Chem. Res.,Vol. 34,No. 12, 1995Table1. Design Specifications for PropylenePropaneSditter~ ~no. of traysfeed tray location (from bottom)feed flow ratefeed comp. (mol %)light keyheavy keyfactor times minimumreflux for designcolumn diameteroverhead pressureoverhead product impuritybottoms product impurityoverhead flow rateoverhead temperaturebottom flow ratebottom temperaturereboiler vapor flow ratereflux ratiofeed quality

2326413. 44kgls ( 106400 lb./HR)C3- - 70C3 - 301. 33. 96m( 13ft)14. 4atm( 211psia)C3 - 0.3mol %C3- - 2. 0mol %9. 21kg/s ( 73100 lb./HR)34. 7"C (94. 4"F)4. 21kg/s ( 33400 lb./HR)42. 3"C ( 108. 1OF )131.24kg/s (1 041 165 lb./HR)12. 6saturated

Table 2. Modeling Assumptions for PropylenelPropaneSplitterliquid dynamicsneglible vapor holdupvalue dynamics on all flowsaccumulation and reboilerlevel controlanalyzer delays on productcompositioneqimolal overflowresidence time in reboilerresidence time in accumulatorheat transfer dynamics modeledsaturated liquid feedsubcooled refluxpressure dynamics modeledperfect mixing of liquid on traysideal VLE

hydraulic timeconstantYesnoPI5 minYes5 min5 minnoYesnonoYesno

control. Table1contains the design conditions for theC3splitter. The overhead composition is 99.7 mol %propylene, the bottoms composition is 2 mol % propy-lene, and the feed composition is 70mol % propylene.There are 232 trays with a Murphree tray efficiencyof85% and an operating pressure of 14.4 atm. Themodeling assumptions used indeveloping the dynamicmodel of the C3splitter are listed in Table 2.The dynamic column model is based upon dynamicmole balances on propylenefor each tray. A hydraulictime constant is used to model the liquid dynamics forthe trays with one value of the hydraulic time constantfor the entire column. The equimolal overflow assump-tion is used to calculate the flow rate of vapor leavingeach stage. The vaporfliquid equilibrium was describedusing a relative volatility which was modeled as anexplicit function of pressure and composition (Hill,1959). As a result, each tray had its own relativevolatility. Product composition analyzers and feedcomposition analyzers (when used) were assumed tohave5min cycle times.The test column simulator has the (L,B)configurationimplemented on it. Gokhale (1994) evaluated ninepossible control configurations orthiscolumn and foundthat the (L,B) configuration yielded the best perfor-mance for diagonal PI dual composition control. Whenthe simulation was equipped with perfect level control,the control performanceof the (D,B) structure was foundtobe equivalentto the performance of the (L ,B) config-uration.The dynamic model equations were integrated usinga Euler integrator (Riggs, 1994) with a maximum

reliably stable step size of 0.3 s. A 50:l ratio ofsimulated timetoCPU time was obtained for a 66 MHz486 PC using Microsoft FORTRAN 5.1.The dynamic model was bench-marked against dy-namic step test data from an industrial C3splitter. Theindustrial data were based upon the (L,B) configura-tion. The (L,B) configuration is also used industrially(O'Conner, 1993). First, the simulator was found toprovide the same general behavior as the industrialplant data (O'Conner, 1993) oropen-loop step changesin the manipulated variables and the feed rate. Then,based upon response times, the hydraulic time constantof each tray was adjusted to match the industriallyobserved reponse times as closely as possible. Forexample, the overhead composition was observed tohave an open-loop response time of approximately 7 hfor a0.5%change in the reflux rate. In addition, for a1% hange in the bottom flow rate, the response timefor the bottom composition was approximately 25 h(O'Conner, 1993). A hydraulic time constantof 3swasfoundto provide the best overall dynamic match.The following test scenarios were used to test thecomposition controllers.1. Setpoint change to 99.85% propylene in theoverhead product at t=100 min followed by a setpointchanged to 99.55% at t =1000 min.2. A ramp change in pressure from 211to 226 psiafrom t =100 min to t =160 min followed by a stepchange in feed compositionto 65% at t =1000 min.3. Negative and positive 5% step changes in feedcomposition with changes applied every 250 min. Attime (t)equal to 250 min, the feed composition ( z )wasdecreased to 65% propylene. At t=500 min, z was setto 70%. At t=750 min, z was set to 75%,at t =1000min,z was changedto 70% . At t=1250 min,z was setto 65%, etc.Each controller was tuned for scenario1and testedon scenarios 2 and 3. Controller performance wasevaluated by considering the variability in the propyleneproduct while keeping the bottom product in the vicinityof 2% propylene.Implementation Approach for Each Controller

Conventional PI controls, DMC, nonlinear PMBC, andANN were applied to the simulator of the C3 splitterfor dual composition control. The PI and nonlinearPMBC controllers were applied using the (L/F,B/F)configuration and DMC was applied using the (L,B)configuration, but each controller was tuned for testscenario1based upon the overhead composition controlperformance. Setpoint changes using 50% changes inimpurity were chosen for controller tuning in order toprovide a consistent tuning procedure that is likely tobe robust forawide range of upsets. All controllers useda 5 min control interval since new analyzer readingswere available every5min. All controllers were treatedas unconstrained, although the column model did notallow for negative flow rates.The diagonal PI composition controllers were tunedusing Auto Tune Variation tests (A m, Astrom andHagglund, 1988) with on-line determination of theoverall detuning factor. ATV tests were used to identifythe ultimate gain and ultimate period for the overheadand bottoms. The Ziegler-Nichols (Ziegler and Nichols,1942) PI settings were then calculated. Both controllerswere detuned to provide minimum I AE for setpointchanges in the overhead product using 50% impuritychanges (test scenario1).Detuning was accomplished

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by dividing both controller gains and multiplying bothreset times by the same detuning factor. The diagonalPI controllers were also tuned using pulse tests for theidentification of transfer function models followed by theapplication of the BLT tuning procedure (Luyben, 1986)as a comparison to the ATV tuning procedure. Thecontrol performances of the controllers tuned by eachprocedure were found to be essentially equivalent.Since the ATV test with on-line detuning was easier toimplement and is more realistically applied in anindustrial setting, it was chosen as our PI tuningprocedure.A lead-lag feedforward element for the PI controllerswas developed for feed composition changes for thecomposition control loop on the bottom of the columnand for the top. The feed rate used in theL/F and B/Fmanipulated variable configurations was dynamicallycompensated using a dead time plus a lag. The tuningsettings for the PI controllers and the feedfonvardcontrollers are listed in Table 3.The DMC controller was provided to us by theDynamic Matrix Control Corp. The step responsemodels for the DMC controllers were developed for eachinput ( z ,F,L,B)/output ( x, ) pair. The output for theoverhead product was log transformed in an effort tolinearize the overall process behavior:

( 1)' =log(1- )At least 12 ndependent step tests were conducted foreach input variable. Identification software (DMI pro-vided by DMC Corp.) was applied to all the step testdata in order to develop the step response models foreach input/output pair used by the DMC controller. Thestep response models were suppliedto the DMC control-ler, and the final controller tuning was performed fortest scenario1. Since the impurity level in the overheadis 6.67 times lower than the bottoms and sinceit is moreimportant to minimize the variability of the overhead

product, the deviations in the overhead product wereweighted to be 15 times more important than thebottoms product. A move suppression factor of 1.0 forthe reflux and 0.1 for the bottoms flow were selectedfor the DMC controller. Standard tuning of the DMCcontroller was used, i.e., a control horizon of 30controlintervals and a model prediction horizon of 120 controlintervals (the maximum available).The nonlinear PMBC controller using the tray-to-traybinary model was applied using the approach presentedby Riggs et al., 1990. The control law calculates targetsetpoints XSS, yss) based upon proportional and integralfeedback.

Yss=Y+K 12bSP - )+K 22jbSP - ) dt (3)Then, the values of xss andyssare used by the tray-to-tray binary model to calculate the reflux rate. Sinceeqs2 and 3 can result in values of x s s that are negativeand values of ys s that are greater than 1.0, limits areused to restrict the maximum and minimum values ofxss andYSS.An overall material balance was used to calculate thevalue of the bottoms flow rate. Since the columnresponds much faster to energy changes (e.g., refluxflow) than to material balance changes (e.g., bottomsflow), the target product compositions xs s andyss) are

Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4416Table3. Controller Settingsfor PI Controllers

overhead control loop bottom control loop~-Feedback Only ControllerKC 232.15 lb. mol/mol %.s 1.7 lb. moVmol%.sTI 75 min 400 rninKC 309 lb. moVmol % a s 4.53 lb. mol/mol %* s5r 36.3 min 1.50min

Feedforward Controller for Feed Composition Changesgain 5.08 lb. moVmol %-a -0.71 lb. moVmol%.sdeadtime 20 min 10 minlead 120 min 600 min1% 240 min 450 rnindeadtime 5 min 20 min1% 100min 150min

Feedback with Feedforward

Dynamic Compensation for Feed Rate

amplified byK&Baccordingto the following equationsin an effort to improve the response of the bottomproduct composition.(4 )( 5 )

XMB =XSP+&MB(XSS - SP)Y MB =YSP+K ~M B ~SSSP)

Then,(6)

The feed rate and the feed composition used by themodel were each dynamically compensated usingafirst-order lag and a deadtime. When a feed compensationanalyzer is not available, the product purities andproduct flow rate are used to calculate an estimateofthe feed composition. Thisbackcalculated feed composi-tion is filtered, and the filtered valueisused as the feedcomposition by the tray-to-tray steady-state model.When eqs 2 and 3 are used for setpoint changes, theresulting changes in the manipulated variables aremuch too sharp; therefore, a filter on the setpointchanges was used to stabilize the controller for setpointchanges. The nonlinear PMBC controller was tuned fortest scenario1based upon minimizing the I AE for theoverhead product. Table4 contains the tuning settingsfor the nonlinear PMBC controller.The tray-to-tray steady-state controller model usedby the nonlinear PMBC controller used the relativevolatility modeled as a function of liquid compositionand pressure but used a stagewise tray efficiency whilethe dynamic simulator used a Murphree tray efficiency.At the base case the controller model required a stage-wise efficiencyof 92% omatch the simulator at steady-state conditions with a 85% Murphree efficiency.A n ANN steady-state model was used to replace thetray-to-tray steady-state binary model used by thenonlinear PMBC controller. The feedfonvard ANNmodel consistedof three input nodes, three hidden nodes(one hidden layer), and two output nodes. The transferfunctions used were sigmoidal, and the learning algo-rithm applied was the Levenberg-Marquardt method(Marquardt, 1963). TheANN model considersXSS, yss,andz as nput and calculates the reflux rate and bottomflow rate as itsoutput. Since the ANN model did notalways match the simulator at steady state, a filteredbias was usedtokeep theANN model inagreement withthe process (dynamic column simulator). Forexample,for the reflux, the difference between the measuredreflux flow and the value calculated by the ANN modelwas filtered on-line. When control calculations were

B - Y M B - ZF - MB - MB

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4416 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995Table4 Controller Settings for Nonlinear PMBCController

overhead bottomscontrol loop control loopFeedback ControllerKi 3.0 3.0Kz 0.0 0.0material balance gain 10.0 6.0( K y ~ ~nd&MB)

filter factor on feed ratedeadtime on feed ratefilter factor onz 0.10deadtime onz 5 min

Feedforward Controller0.01410 min

-8 6.4-8.2-

1*

Filtersfor model efficiency parametrization 0.025for back calculated feed composition 0.025for setpoint changes for overhead 0.0850.10

Table5. k2ontroller Settings for ANN Controllerfor setpoint changes for bottom

overhead bottomscontrol loop control loopFeedback ControllerK1 3.0 4.0

Kz 0.0 0.0material balance gain 10.0 6.0W y ~ ~nd&MB)Feedforward Controllerfilter factor on feed rate 0.04deadtime on feed rate 10 minfilter factor onz 0.10deadtime onz 5min

Filtersfor model efficiency parametrization 0.02for back calculated feed compositionfor setpoint changes for bottomrequired, the values of XSS, yss, and z were fed to theANN model and the resulting reflux flow rate andbottoms flow rate were added to the current value oftheir respective filtered bias. A similar procedure wasused for calculating an on-line bias for the bottom flowrate. The ANN model was trained over the expectedrangeof inputs using700steady-state data sets from atray-to-tray steady-state simulator. The ANN modelbased controller was tuned for test scenario 1, and theresulting controller settings are listed in Table 5 .

0.0010.0850.10for setpoint changes for overhead

ResultsFigures 1and 2 show the control results for the PI,nonlinear PMBC, and DMC controllers for setpointchanges in the overhead product (test scenario1).Eachcontroller was tuned for this test based upon optimiz-ing the performanceof the overhead composition, andthe resulting tuning parameter remained unchangedthroughout the remainder of the tests. From Figure1,the nonlinear PMBC and DMC had essentially equiva-lent performance, while thePI controller performed wellbut was somewhat slower settling than the multivari-able controllers. There is a slight glitch in the DMCperformance at about700and 1600min. This resultedbecause the model horizon in the DMC controller (600min) was significantly smaller than the actual processsetting time of about 1800 min. We used version4.0ofDMC which limits the number of model coefficientsto 120, while the more recent release (version 5.0) hasup to 600 coefficients which would have easily elimi-

rP 0 IV.@ 0.3-8

0.2 -MB CDMC.1 0 200 400 800 800 1 o M ) 1 2 0 0 1 4 0 0 1 8 0 0 1 8 0 0 2 o O 0Time (min)Figure 1. Comparison of overhead composition control for testscenario1.

I - MBC I- MC00 200 40 0 800 800 1 o o o 1 2 0 0 1 4 0 0 1 8 0 0 1 8 0 0 2 G f J oTime ( min)Figure 2. Comparison of bottoms composition control for testscenario 1.

PI-.88.8-

5.440 200 400 800 800 1 O O O 1 2 0 0 1 4 0 0 1 8 0 0 1 8 0 0 2 O O OTime (min )Figure 3. Reflux flow rate for various controllers for testscenario 1.nated the glitch. Figure 2 shows the performanceofeach controller for the control of the bottom productcomposition during the setpoint changes on the over-head. Note that the nonlinear PMBC controller had theshortest settling times. Overall considering Figures 1and 2, there is not a great deal of difference betweenthe controllers, although the multivariable controllersdid outperform thePI controller. Figures3and4 showthe reflux and bottoms flow rates for each controllerfor test scenario 1. The nonlinear PMBC controllerclearly shows the smoothest use of the manipulatedvariables.The nonlinear PMBC controller that used the ANNsteady-state model is compared with the nonlinear

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Ind. Eng. Chem. Res.,Vol. 34,No. 12, 1995 4417

............... PIDMC-MBC0.2

PI.35

A -MBC- MC0.3

A"PMBC01-I0 200 400 600 800 l oo0 1200 1400 1800 1800 MooTime (m in )Figure 5. Comparison of overhead composition control fornonlinear PMBC andANN controllers for test scenario 1.

44 .. ..............

04 I0 200 400 600 800 1000 1200 1400 1800 1800 MooTime (m in )

Figure6. Comparison of bottoms composition control for non-linear PMBC andANN controllers for test scenario 1.PMBC controller that used the tray-to-tray steady-statemodel in Figures 5 and6for test scenario1. TheA"controller actually performed slightly better for theoverhead composition control, but itwas quite sluggishwith greater deviations from setpoint for the bottomcomposition control.Figures 7 and 8show the control results for thePI,nonlinear PMBC, and DMC controllers for test scenario2 with no feed composition analyzer readings available.Note that each controller seemedtohandle the columnpressure changes moreor less with the same proficiencyfor the overhead composition, while the multivariblecontrollers showed smaller maximum deviation fromsetpoint for the step change in feed composition. Forthe bottoms composition, the nonlinear PMBC control-

-MBCDMC00 200 400 800 800 l o001200 1400 1800 l 8002OOOTime (min )Figure 8. Comparison of bottoms composition control for testscenario 2 without a feed composition analyzer.

0.35

0.34- 0.33a93 0.32E-Q 031- 0.38+ 02 0

0 280 270 500 l o00 1500 Moo 2500 3OOo 3500 4000Time (m in )

Figure9. Comparison of overhead composition control for testscenario 3 without a feed composition analyzer.lers demonstrated tighter control than the DMC andPIcontrollers.

Figures 9 and 10 show the control results for thePI , nonlinear PMBC, and DMC controllers for testscenario3with no feed composition analysis available.For the overhead product the multivariable controllershad variabilities that were about 2.5times lower thanthe PI controller. The DMC controller had a variabilitythat was slightly larger than the nonlinear PMBCcontroller. For the bottom composition, thePI and DMCcontrollers had very nearly equivalent performancewhile the nonlinear PMBC controller performed consid-erably better.

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4418 Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995

PI- MB C5- DMC

PI"I-." PMBC 0.06

0 050.040.030 02

0 0 \ 5 0 NO 250 300 350 400 450 500 550 600Hold Time (minutes)

I + PI + PMBC * DMC 1- I0 5b 1000 1500 2000 25bO 3doo 35bo ab0

Figure 10. Comparison of bottoms composition control for testscenario 3 without a feed composition analyzer.Time (mi n ) Figure 13 Variation in overhead product composition as afunctionofhold time for test scenario3without a feed compositionanalyzer.

.o 5 I 1

0'r500 l o00 1500 2Ooo 2500 3ooo 3500 4OOoTime (min)

Figure12. Comparison of bottoms composition control for testscenario 3with a feed composition analyzer.Figures11and12show the control results for the PI,nonlinear PMBC, and DMC controllers for test scenario3 using a feed composition analyzer. The resultsimproved for the PI and DMC controllers but worsenedfor the nonlinear PMBC controller. This results becausethe feedforward controllers for PI and DMC wereadjusted for the overhead and bottoms products sepa-rately, but the nonlinear PMBC controller has only onefeed composition which is filtered. Moreover, the topand bottom behave quite differently dynamically whichsignificantly penalizes the nonlinear PMBC controller.The bottoms composition control for the DMC and PIcontrollers seemedtobenefit the most from the additionof feedforward from the feed composition analyzer.

6g 4 5-s 4

.2 3E> 3.5

1 .+ L c -+ + + +' 200 250 3bo 350 460 450 560 550 610Hold Time (minutes)

I f PI + PMBC * DMC ',Figure 14. Variation in bottoms product composition as afunctionofhold time for test scenario3withoutafeed compositionanalyzer.

Figure 13 shows the average total variation in theoverhead product for each controller as a function ofhold timefor the periodic feed composition changes (testscenario 3). The DMC controllers showed significantvariability reduction over thePI controller for the fullrangeof hold times with variability reductions rangingbetween 4/1 to 211. The nonlinear PMBC controllershows results equivalent to the DMC controller up to ahold timeof 300min, but above300 min the results ofthe nonlinear PMBC controller approach those of thePI controller. The deteriorating performance of thenonlinear PMBC controller at larger hold times isprobably due to the lack of flexibility of this controllerand the dynamic difference between the overhead andbottomof the C3splitter. Figure 14shows the averagetotal variation in the bottoms product for each controlleras a function of hold time for test scenario 3. The PIand DMC controllers exhibit essentially equivalentperformance, while the results from the nonlinearPMBC controller are consistently better.A PI controller with a log transformed overheadcomposition (i.e.,y'=log(1- y) )wasalso tested'. Itwastuned for test scenario 1using the same procedure aswas used for the conventional PI controller. It wastested for scenario 2and scenario3over the full rangeof hold times and foundto yield results equivalent tothose obtained for the conventional PI controllers.Conclusion

Although the difference in performance for the PI andthe multivariable controllers for setpoint changes andstep changes in disturbances is not large, significantimprovement in performance was observed for the

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Ind. Eng. Chem.Res.,Vol. 34, No. 12, 1995 4419multivariable controllers over the PI controller for aperiodic variation in feed composition. In fact, thevariability reduction observed in the simulation studyfor nonlinear PMBC over PI controls is similar to thoseobserved industrially (Riggs et al., 1993).The periodic variation in disturbances results in aproduct variability with characteritics similar to theproduct variabilities observed industrially (Riggs et al.,1993). Usually industrial feed composition upsets in-volve some variation in feed composition with respectto time but are not well-represented as step changes.Industrial disturbances are likelytohave an amplitude/frequency distribution that would combine with thefrequency sensitivity of the controller to produce theresulting overall product variability performance. Pe-riodic variation of disturbances (preferably sine wavedisturbances) are proposed here as a more criticalanalysis of controller performance than classical steptests particularly if the frequencyof the disturbance ischanged.Acknowledgment

The authors thank Professor Bill Luyben for guidingand reviewing thePI results. DMC Corp. is gratefullyacknowledged for providing DMC software as well as aDMC training course. Dan O'Conner and Dave Hoff-man of DMC Corp. provided guidance during theimplementation phase. Financial support for this workwas provided by the member companies of the TexasTech University Process Control and OptimizationConsortium and the U.S. Department of Energy (Con-tract No. DR-PC04-94A l 98747).NomenclatureB =bottom product flow rateF =column feed rateKl =the proportional gain in the GMC control law (eqs2Kz =the integral gain in the GMC control law (eqs2 andL =reflux flow ratex =the mole fractionofpropylene in the bottoms producty=the mole fractionofpropylene in the overhead producty' =the log transformed valueofyz =the mole fractionof propylene in the feedSubscripts

and3)3)

MB =material balancesSP=setpointSS=steady-state targetLiterature CitedAstrom, K. J .; Hagglund, T.Automatic Tuning of PZD Controllers;ISA Research Triangle Park, NC, 1988.Bhat, N.; McAvoy, T. J .Use ofNeural Nets for Dynamic Modelingand Control of Chemical Process Systems. Comput. Chem. Eng.1990,4,517-532.Cohen, G.H.; Coon,G.A. Theoretical Considerations of RetardedControl Trans ASM E 1953,75, 827.Cutler, C. R.; Ramaker, B. L. Dynamic Matrix Control: AComputer Control Algorithm. Presented at the AIChE 86thNational Meeting, San Francisco, CA, 1979; also in J oint Autom.Control Conf . Proc. 1979.Downs,J . .;Doss, .E. Present Status and Future Needs-A Viewfrom North America Industry. Proceedings of CP CN; ElsieverPublishing: New York, 1991.Gokhale, V. B. Control of a PropylenePropane Splitter. M.S.Thesis, Texas Tech University, Lubbock, TX , 1994.Hill, G. E. Propylene-Propane Vapor-Liquid Equilibria. Pre-sented at the AIChE National Meeting, Atlantic City, NJ , 1959.Humphrey, J . L.; Seibet, A. F.; Koort, R. A. Separation Tech-nologies-Advances and Priorities. DOE Contract AC07-901D12920, Feb 1991.Lee, P. L.; Sullivan, G.R. Generic Model Control. Comput. Chem.

Eng. 1988,12, 573-83.Luyben, W. L. A Simple Method for TuningSISO Controllers inMultivariable Systems. Znd. Eng. Chem. Process Des. Dev.1986,25, 654.Marquardt, D. W. A n Algorithm for Least-Squares EstimationofNonlinear Parameters. Z Soc. Znd. Appl. M ath. 1963,11(2),OConner, D., DMC Corp., Houston,TX,personnel communication,1993.Riggs, J . B.An Introduction to Numerical Methods for ChemicalEngineers, 2nd ed.; Texas Tech University Press: Lubbock,TX,1994.Riggs, J . B.; Beauford, M.; Watts, J . Using Tray-to-Tray Modelsfor Distillation Control. InAdvances in Industrial Control; P.L., Lee, Ed.; Springer-Verlag: New York, 1993.Ziegler, J . G.; Nichols, N. B. Optimum Settings for AutomaticControllers. Trans. ASME 1942, 54, 759.

431-441.

Received for review January 17, 1995Accepted September 6, 1995@IE9500511

@ Abstract published inAdvance A CS Abstracts, November15,1995.