Improved closed loop identification of transfer function model for unstable systems

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1、ARTICLEINPRESSJournaloftheFranklinInstitute343(2006)152–160www.elsevier.com/locate/jfranklinImprovedclosedloopidentificationoftransferfunctionmodelforunstablesystemsR.PadmaSree,M.ChidambaramDepartmentofChemicalEngineering,IndianInstituteofTechnology,Chennai600036,IndiaAbstractThemethod

2、ofidentifyingfirstorderplustimedelaytransferfunctionmodelproposedforunstablesystemsbyAnanthandChidambaram[Closedloopidentificationtotransferfunctionmodelforunstablesystems,J.FranklinInst.336(1999)1055–1061]ismodifiedtoavoidthestabilityproblems[Cheres,Parameterestimationofanunstablesystemw

3、ithaPIDcontrollerinaclosedloopconfiguration,J.FranklinInst.,2005,acceptedforpublication]ofthemethod.Twomodificationsareproposed.Inthefirstmodificationofthemethod,theunder-determinedalgebraicequationsproblemisconvertedintoanoptimizationproblemforcalculationofthethreeparametersofthefirstorder

4、plustimedelay(FOPTD)model.Asimplemethodisgivenfortheinitialguessvaluesofthemodelparameters.Inthesecondapproach,fromthedefinitionofLaplacetransformoftheoutputresponse,athirdequationisformulated.Theresultedthreeequations,intermsofthethreeparametersofthetransferfunctionmodel,arethennumeric

5、allysolved.SimulationresultsaregivenforthesecondorderplustimedelaytransferfunctionconsideredbyCheres2005[ParameterestimationofanunstablesystemwithaPIDcontrollerinaclosedloopconfiguration,J.FranklinInst.,2005,acceptedforpublication].TheresponsesoftheidentifiedmodelswiththesamePIDcontrolle

6、rsarecomparedwiththatoftheactualsystem.PIDcontrollersaredesignedbasedontheidentifiedmodels.Theclosedloopresponsesofthecontrollersontheoriginalsystemareevaluatedandcompared.Thepresentmethodsgivebettercontrolperformances.r2005TheFranklinInstitute.PublishedbyElsevierLtd.Allrightsreserved.1

7、.IntroductionTransferfunctionmodelsareusedtodesignPI/PIDcontrollers[1,2].ClosedloopidentificationmethodispreferredoverthatoftheopenloopmethodsincetheformerisCorrespondingauthor.E-mailaddress:chidam@iitm.ac.in(M.Chidambaram).0016-0032/$30.00r2005TheFranklinInstitute.PublishedbyElsevie