chapter5.ppt

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1、Chapter5FrequencyResponseMethodConceptGraphicsmodeAnalysisIntroductionFrequencyResponseofthetypicalelementsofthelinearsystemsBodediagramoftheopenloopsystemNyquist-criterionSystemanalysisbasedonthefrequencyresponseFrequencyresponseoftheclosedloopsystems5.1Introd

2、uctionThreeadvantages:*Frequencyresponse(mathematicalmodeling)canbeobtaineddirectlybyexperimentalapproaches.*easytoanalyzetheeffectsofthesystemwithsinusoidalvoices.*easytoanalyzethestabilityofthesystemswithadelayelement5.1.1frequencyresponseForaRCcircuit:urucRC

3、Wehavethesteady-stateresponse:5.1IntroductionHere:Wecall:FrequencyResponse(orfrequencycharacteristic)oftheelectriccircuit.Wehave:then:Make:5.1IntroductionGeneralizeabovediscussion,wehave:Definition:frequencyresponse(orcharacteristic)—theratioofthecomplexvectoro

4、fthesteady-stateoutputversussinusoidinputforalinearsystem,thatis:Here:Andwename:(amplituderatioofthesteady-stateoutputversussinusoidinput)(phasedifferencebetweensteady-stateoutputandsinusoidinput)5.1.2approachestogetthefrequencycharacteristics1.Experimentaldisc

5、riminationMeasuretheamplitudeandphaseofthesteady-stateoutputInputasinusoidsignaltothecontrolsystemGettheamplituderatiooftheoutputversusinputGetthephasedifferencebetweentheoutputandinputArethemeasureddataenough？DataprocessingChangefrequencyyN5.1.2approachestoget

6、thefrequencycharacteristicsTheorem:IfthetransferfunctionisG(s),wehave:Proof:Where—piisassumedtobedistinctpole(i=1,2,3…n).2.DeductiveapproachInpartialfractionform:Here:5.1.2approachestogetthefrequencycharacteristicsTakingtheinverseLaplacetransform:Forthestablesy

7、stemallpoles(-pi)haveanegativerealparts,wehavethesteady-stateoutputsignal:5.1.2approachestogetthefrequencycharacteristicsTheamplituderatioofthesteady-stateoutputcs(t)versussinusoidinputr(t):Thephasedifferencebetweenthesteady-stateoutputandsinusoidinput:Thenweha

8、ve:Comparewiththesinusoidinput,wehave:thesteady-stateoutput:5.1IntroductionExamples5.1.1aunityfeedbackcontrolsystem,theopen-looptransferfunction:1)Determinethesteady-statere