feedback control-5-1

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1、LaplaceTransform&ODESolutionReviewDoremembersomeimportantLaplacepropertiesLaplaceTransform&ODESolutionReviewLaplaceTransform&ODESolutionReviewTosolveaODEwithorwithoutinitialcondictionsTakeLaplacetransforminbothsidesLaplaceTransform&ODESolutionReviewFortheleftsidewheretheis

2、apolynomialofwhichorderlessthannLaplaceTransform&ODESolutionReviewFortherightsidewheretheisapolynomialofwhichorderlessthanmTheresponsetotheinputLaplaceTransform&ODESolutionReviewthenTheresponsetotheinitialconditionstransientresponsesteadystateresponseLaplaceTransform&ODESo

3、lutionReviewSupposeandLaplaceTransform&ODESolutionReviewthenOncetheTFhasbeendeterminedbyanyofavailablemethods,wecanstarttoanalyzetheresponseofthesystemitrepresents.3.3EffectofPoleLocationWhenthesystemequationsaresimultaneousordinarydifferentialequations(ODEs),theTFthatresu

4、ltswillbearatioofpolynomials:SothevalueswhichmakeA(s)=0aredefinedassystem’spolesIftheinputsignalisunitimpulse,3.3EffectofPoleLocationSo,theoutputisThentheinverseLaplacetransformofG(s)istheunitimpulseresponseofthesystem.Italsocalledthenaturalresponseofthesystem.3.3EffectofP

5、oleLocationThepolesandzerostocomputethecorrespondingtimeresponseandthusidentifytimehistorieswithpolelocationinthesplane.3.3EffectofPoleLocationThepoleissplanesplane3.3EffectofPoleLocationIfExample3.22ResponseVersusPoleLocationExample3.22ResponseVersusPoleLocation3.3Effecto

6、fPoleLocationIfthepolynomial’scoefficientsarereal,therootsofitarerealorconjugatepairs.Thenfora2ndordersystem,therootsdistributionmay3.3EffectofPoleLocationFora2ndordersystem,whereisthedampingratioofthesystem.istheundampednaturalfrequencyofthesystem.3.3EffectofPoleLocationt

7、hen3.3EffectofPoleLocation3.3EffectofPoleLocationsinceThepolesofthesystemare