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1、PART2ControlTheoryUNIT3TheFrequencyResponseMethods:NyquistDiagramsIntroductionTherearetimeswhenitisnecessaryoradvantageoustoworkinthefrequencydomainratherthanintheLaplacedomainoftherootlocus.Forsystemanalysis,therootlocusmethodrequiresatransferfunction,whichmaybedifficultore
2、venimpossibletoobtainforcertaincomponents,subsystems.Inmanyofthesecases,thefrequencyresponsecanbedeterminedexperimentallyforsinusoidaltestinputsofknownfrequencyandamplitude.Thenatureoftheinputalsoinfluencesthechoiceoftechniquestobeusedforsystemanalysisanddesign.Manycommandin
3、putsmerelyinstructasystem,tomovefromonesteady-stateconditiontoasecondsteady-statecondition.Thistypeofinputcanbedescribedadequatelybysuitablestepsinposition,velocity,andacceleration,andtheLaplacedomainisappropriateforthispurpose.If,however,theintervalbetweensuchstepinputsisde
4、creasedsothatthesystemneverhastimetoreachthecorrespondingsteadystate,thesteprepresentationandLaplacedomainarenolongeradequate.Suchrapidlyvaryingcommandinputs(ordisturbance)maybeperiodic（adj.周期性的）,random（adj.随机性的）,oracombinationthereof.Thewindloadingofatrackingradarantenna,fo
5、rexample,resultsfromameanvelocitycomponentthatvarieswithplussuperimposedrandomgusts.Ifthefrequencydistributionoftheseinputscanbecalculated,measured,orevenestimated,thefrequencyresponsecanbeusedtodeterminetheireffectsuponthesystemoutput.Thefrequencyresponseisasteady-stateresp
6、onse.Althoughsomeinformationcanbeobtainedaboutthetransientresponse,itisonlyapproximateandissubjecttomisinterpretation(n.曲解，误议).TheFrequencyTransferFunctionItisnecessarytodevelop（v.导出，引入）aninput-outputrelationshipthatcanbeusedinthefrequencydomain,i.e.,afrequencytransferfuncti
7、on.ConsideralinearsystemwithaknowntransferfunctionG(s)andapplythesinusoidalinputr(t)=sintorR(s)=whereistheamplitudeandtheinputorforcingfrequency（强制频率）.ThetransformedoutputisC(s)=G(s)Thepartialfractionexpansion（部分分式展开式）ofC(s)yieldsC(s)=++++…Where-,-,…aretherootsofthecharacter
8、isticequationofthetransferfunction.Theinversetransformisc(t)=++++...whereth
