bserver-based nonlinear control approaches for tem

ChemicalEngineeringScience63(2008)395–403www.elsevier.com/locate/cesTwoobserver-basednonlinearcontrolapproachesfortemperaturecontrolofaclassofcontinuousstirredtankreactorsShahinSalehia,MohammadShahrokhib,∗aDepartmentofMeasurementandAutomation,PetroleumUniversityofTechnology,Tehran,IranbDepartmentofChemicalandPetroleumEngineering,SharifUniversityofTechnology,P.O.Box11365-9465AzadiAv.,Tehran,IranReceived8March2007;receivedinrevisedform2September2007;accepted17September2007Availableonline29September2007AbstractInthispaper,twononlinearobserverbasedcontrollersfortemperaturecontrolofacontinuousstirredtankreactorinwhichaspecialclassofparallelexothermicreactionstakeplaceareproposed.Areducedordernonlinearobserverisconstructedtoestimatetheconcentrationinthereactor.Theobserveriscoupledwithtwononlinearcontrollers,designedbasedontwowell-knowntechniques,namelyinput–outputlinearizationandbacksteppingforcontrollingthereactortemperature.Fordampeningtheeffectofobservererrordynamics,acompensatingtermisusedineachcontrollaw.Theasymptoticalstabilityoftheclosed-loopsystemisshownbytheLyapunov’sstabilitytheorem.Theeffectivenessoftheproposedcontrollershasbeendemonstratedthroughcomputersimulations.2007ElsevierLtd.Allrightsreserved.Keywords:Chemicalreactor;Nonlineardynamics;Processcontrol;Stability;Backstepping;Feedbacklinearization1.IntroductionTemperaturecontrolofcontinuousstirredtankreactors(CSTRs)isgenerallycrucialandcomplicatedduetosystemnonlinearity,multiplicityofequilibriumpointsandinputcon-straints.Meanwhilecontrolofanunstableequilibriumpointofthereactormakestheproblemworse(Bequette,2003).Recently,alargenumberofcontrollershavebeendesignedtocontrolCSTRs.SomeofthesecontrollersaretraditionalPIDstunedbasedonlinearizedreactormodel(Brownetal.,1998;Leeetal.,1993;Ratto,1998).Moreover,controlofchemicalreactorsbyoutputfeedbackwithPIcontrollershavebeenre-viewedinaPh.D.Thesis(Jadot,1996).Furthermore,basedonfeedbacklinearizationtechnique(Khalil,1996;SlotineandLi,1991),severalcontrollersei-theradaptiveornon-adaptivehavebeenproposedforthetemperaturecontrolofCSTRs(LimquecoandKantor,1990;AdebekunandSchork,1991a,b;Adebekun,1992;Kosanovichetal.,1995;Tyneretal.,1999).Anonlinearoutputfeedback∗Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](M.Shahrokhi).0009-2509/$-seefrontmatter2007ElsevierLtd.Allrightsreserved.doi:10.1016/j.ces.2007.09.040controllercoupledwithanonlinearobserver(usedforestimat-ingconcentration)hasbeendesignedforcontrollingtemper-atureofanexothermicfirst-orderreactiontakingplaceinaCSTR(LimquecoandKantor,1990).TheglobalstabilityofstatefeedbackcontrolforaclassofuncertainreactorshavebeenestablishedbyAdebekunandSchork(1991a,b)andAdebekun(1992).GlobalstabilizationofareactorwithcomplexkineticshasbeenconsideredbyKosanovichetal.(1995).Anadaptivetemperaturecontrollerbasedoninput–outputfeedbacklin-earizationhasbeenproposedforCSTRsbyTyneretal.(1999).GlobalstabilizationofaclassofCSTRhasbeenconsideredbyVieletal.(1997)andtheyhaveproposedanadaptivecontrollerforthispurpose.SistuandBequette(1992)comparedperfor-mancesofagloballylinearizingcontrol(GLC)(KravarisandChung,1987),assumingconcentrationtobeavailable,withanonlinearpredictivecontroller(EatonandRawlings,1990).Theyshowedthatthesetwononlinearcontroltechniquescanleadtothesameperformanceifthedesiredoutputtrajectoryisspecifiedinaconsistencefashion.Inanotherwork,nonlin-earmodelpredictivecontrollercoupledwithstateobserverisusedforcontrollinganunstableCSTR(BiagiolaandFigueroa,2004).Anovelnonlinearadaptivecontrollerbasedonfuzzy396S.Salehi,M.Shahrokhi/ChemicalEngineeringScience63(2008)395–403logicandFourierIntegralhasbeenproposedforreactortem-peraturecontrolassumingthattheconcentrationisavailable(HuaguangandCai,2002).Anothercontroller,basedonfuzzyadaptivecontroltechnique,hasbeenproposedfortemperaturecontrolofafirstorderreactiontakingplaceinaCSTR(Salehietal.,2006).Inmostoftheaboveworks,ithasbeenassumedthattheconcentrationmeasurementisavailableandifanob-serverisused,thestabilityoftheoverallclosed-loopsystemincludingtheobserverdynamichasnotbeenestablished.Besides,recentyearshavewitnessedarapidapplicationofbacksteppingmethodologyfordesigningnonlinearcontrollers.Thistechniqueprovidesapowerfuldesigntool,fornonlinearsystemsinthepurefeedbackandstrictfeedbackforms(Khalil,1996;Krsticetal.,1995).Oneadvantageofusingbackstep-pingnonlinearcontrolschemeisitsrobustness,whichcannotbeobtainedexplicitlybythetraditionalcontrolschemes.ThistechniqueeitheradaptiveornonadaptivehasbeenappliedfortemperaturecontrolofCSTRsaswell.ZhangandGuay(2001)introducedanadaptiveneuralnetworkcontrolschemeforaclassofnon-affineCSTR,usingLyapunov’sstabilitytheoremandbacksteppingtechnique.AnotherexampleofbacksteppingcontrolleristheschemeproposedbyGopalunietal.(2003).TheyhaveappliedthistechniquetodesignarobustadaptivenonlinearcontrollerforabenchmarkCSTRinordertoregulatetheproductconcentration.Theyusedtuningfunctionstoreducethenumberofupdatelaws.Inaddition,anadaptivenonlinearcontrollerbasedonbacksteppingtech