Instrumental variable methods for system identification 2002

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1、CIRCUITSSYSTEMSSIGNALPROCESSINGVOL.21,NO.1,2002,PP.1-9INSTRUMENTALVARIABLEMETHODSFORSYSTEMIDENTIFICATION*TorstenSOderstrOmtandPetreStoicaIAbstract.Thispapergivesatutorialoverviewofinstrumentalvariablemethods.Com-parisonsaremadetotheleast-squaresmethod.Ananalysisin

2、cludingconsistencyandasymptoticdistributionoftheparameterestimatesisincluded.Keywords:Least-squaresestimation,consistencyanalysis,asymptoticdistribution,recur-sivealgorithm.1.IntroductionOneusualwayofdealingwiththemanysystems(orsignals,iftherearenoobservableinputs

3、)weencounterinourendeavorsistomodelthemandthenusethemodeltoachieveourgoals,asifitwereanexactdescriptionoftherealsystem.Thegoalsinclude:

4、Acquiringinformationandknowledgeaboutthesystemunderstudy;

5、Simulatingthebehaviorofthesystemunderconditionsthatmightbedetri-mental

6、totherealobject;

7、Predictingthebehaviorofthesystemoveracertaintimehorizoninthefuture;

8、Designingaregulatorthatcontrolsthebehaviorofthesystem;9Usingthemodelparametersas"datacompressors",e.g.,forfaultdetectionorrecognition.Themodelsusedtoachievesuchgoalscanbeeitherno

9、nmathematical(e.g.,mental)ormathematical(suchasdifferenceordifferentialequations,state-spaceequations,transferfunctions,andsoon).Systemidentificationisoneofthetwo*ReceivedNovember16,2000.WorksupportedinpartbySwedishResearchCouncilforEngineeringSciencesundercontrac

10、t95-800,andtheFoundationforStrategicResearch.DepartmentofSystemsandControl,InformationTechnology,UppsalaUniversity,Uppsala,Sweden.E-mailforSSderstrOm:ts@SysCon.uu.seE-mailforStoica:ps@SysCon.uu.se2SODERSTROMANDSTO~CApossiblewaysofobtainingmathematicalmodelsforacer

11、tainobject(eitherasignalorasystem)byprocessingexperimentaldatacollectedinanoperationregimethatisthoughttobeclosetothatinwhichthemodelisgoingtobeused.Theotherpossibleway,calledmathematicalmodeling,consistsofmakinguseofthelawsthatareknowntogovernthebehaviorofthesyst

12、emtoobtainamathematicalmodelforit.Themaindrawbackofmathematicalmodelingisthatitcannotbeappliedtocomplicatedsystemseitherbecausetheresultingmodelwouldbet