基于脉冲响应的参数辨识

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1、Chapter8ParameterIdentificationByImpulseandPulseResponseLiShaoyuanE-mail:syli@sjtu.edu.cnIMPULSERESPONSEBasicPrinciplesThemainstrategyofimpulse-responseidentificationistoobtainprocesstransferfunctionmodelsdirectlyfromexperimentalimpulse-responsedata.Thereisadirectrelationshipbetweenasyste

2、m’stransferfunctionandthemomentsofitstheoreticalimpulseresponse.Onemajordisadvantage:theimpulsefunctionisdifficulttoimplementinpractice.GeneralTheoryBydefinitionoftheLaplacetransformofafunction,therefore:Now,thepowerseriesexpansionfore-st:itbecomes:IdentificationofSimpleModelFormsTheproce

3、dure,usingtheimpulse-responseapproach,isnowsummarized.1.Experimentallyobtainthesystem’simpulseresponse.2.Fromtheimpulse-responsedata,calculatethenormalizedmoments3.Postulateanapproximatetransferfunctionmodel.4.Estimatetheunknownparametersinthepostulated,transferfunctionmodelbyrelatingthet

4、ransferfunctiontothemoments.First-OrderModelSecond-OrderModelSecond-Order-Plus-Single-ZeroModelFirst-Order-Plus-Time-DelayModelObtainingMomentsFromExperimentalDataExperimentalimpulse-responsedataareusuallyobtainedatdiscretepointsintime,usuallyatequallyspacedtimeintervals.Theintegralwillha

5、vetobeapproximatedbyquadraturesorotherefficientnumericalintegrationschemes.Impulse-responseDataFromOtherResponsesInpractice,itmaynotalwaysbepossibletoimplementaninputfunctionthatiscloseenoughtoanidealimpulse;FromExperimentalStep-ResponseDataFromArbitraryInput/OutputDataForeachobservedexpe

6、rimentaldatapointwemaynowwrite,usingthisexpression:whichmaybewrittentogetheras:FrequencyIdentificationFromPulseResponsesingleoutputprocessis:andsincethefrequencyresponsecanbeobtainedbysettings=jωwehave:whereU(jω);andY(jω),are,respectively,theFouriertransformationsoftheinputandoutputpulset

7、estdata,i.e.:FrequencyResponsewhere,fortheoutput:and,fortheinputFrequencySpectraanalyzetheinputandoutputdatafortheir“frequencycontent,”byinspectingthemagnitudesofthefunctionsU(jω)andY(jω)atvariousfrequencies.fortheinput:andfortheoutput:FrequencySpectraofaPulseSignal