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1、EngineeringCyberneticsPartFourFrequencyResponseAnalysisofControlSystemsFrequencyResponseAnalysisofControlSystems4.1Concepts4.2GraphicalDescriptions:NyquistandBodeDiagrams4.3MinimumPhaseSystems4.4FrequencyCharacteristicsofClosed-loopControlSystems4.5PerformanceSpecificationinFrequencyDomain4.6Determi
2、netheTransferFunctionofaControlSystemsthroughExperimentsThefrequencyresponseisdefinedasthesteady-stateresponseofasystemtoasine-wavesignalinput.ConceptsThefrequencyresponseThesine-wavesignalinputis:orConceptsThetransferfunctionofasystemis:Thesystemsteady-stateresponseis:ConceptsevaluatingG(s)ats=jω:A
3、sinewaveinputsignalforcesasinewaveattheoutputsignalwiththesamefrequencyforalinearsystem.ConceptsConclusion:theamplitudeismodifiesbyafactorequaltothegainofAiG(jω).thephaseisshiftedbyaquantityequaltothephaseofG(jω).ConsiderthetransferfunctiongivenbyandinputsignalisDeterminethefrequencyresponseoutput.E
4、xampleConceptsSolutionPut,thenConceptsWhen,thenConceptsthegainandthephaseofthefrequencyresponseoutputofsystemareasfollowthefrequencyresponseoutputsignalisConceptsFrequencyresponsesaretypicallydepictedgraphicallyintwoforms:GraphicalDescriptions:NyquistandBodeDiagramsNyquistdiagramBodediagramNyquistdi
5、agramNyquistdiagramTakeXaxisandYaxisastherealpartandtheimaginarypartofthefrequencycharacteristicfunctionrespectivelyintheX-Yreferenceframe,whenfrequencyischangedin(-∞,+∞),thegraphofG(jω)iscalledtheNyquistdiagramorthepolarcoordinatediagram.NyquistdiagramExamplePlottheNyquistdiagramforthesystemwiththe
6、transferfunctionSolutionStep1:put,determine,and.NyquistdiagramStep2:at,wecandetermine,and.,Step3:at,wecandetermine,And.,Step4:put,wecandetermineand.With,andthatmeanstheNyquistdiagrampassing(0,0)pointofthereferenceframe.HereNyquistdiagramthusdetermineand.SotheNyquistdiagrampassespoint(K,0)and(0,0)oft
7、hereferenceframe.Step5:put,andgotand,offromstartpoint(K,0)withtoendpoint(0,0)with,thatcandescribetheNyquistdiagramasfig.4-3.Step6:inthecomplexplane,accordingtochangingNyquistdiagramNyquistdiagramrules
