chapter4.ppt

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1、Chapter4TheRootlocusMethod10/2/20211Chapter4RootlocusMethod4.1Introduction4.2Theconceptsoftheroot-locus4.3Therootlocussketching(conventionalroot-locus)4.4Theparameterroot-locusandthezero-degreeroot-locus4.5TheRootlociofthesystemwiththetime-delay4.6Thecontrolsystemanalysisanddesign

2、utilizingtheroot-locimethod10/2/202124.1IntroductionForinvestigatingtheperformanceofasystem,wehavetosolvetheoutputresponseofthesystem.Buttherearetwodefectswhenwedothis:WecanutilizetheRoot-locustechniquetomakeupforthedefectsabove.(1)Itisadifficultthingtosolvetheoutputresponseofasys

3、tem–especiallyforahigherordersystem.(2)Wecan’teasilyinvestigatethechangesofasystem’sperformancefromthetime-domainsolutionofthesystem’soutputresponsewhenoneortwoparametersofthesystemvariesinagivenrange,or,whenoneormoredevicesareaddedtothesystemtoimprovethesystem’s.Root-locusisagrap

4、hicaltechniquebaseonfthepolesandzerosoftheopen-looptransferfunctionfordeterminingthepolesoftheclosed-looptransferfunctionofasystem.UtilizingRoot-locustechnique,Wecaneasilyinvestigatetheperformancechangewhenoneortwoparametersofthesystemvariesinagivenrange:10/2/202134.1Introductionw

5、hensomeparameterofthesystemvariesinagivenrange;whensomedeviceisaddedtothesystem.Theroot-locustechniquecanbeconvenientlyusedfordesigningandanalyzingthecontrolsystems.History:Root-locusmethodwasconceivedbyEvansin1948.Root-locusmethodandFrequencyResponsemethod,whichwasconceivedbyNyqu

6、istin1938andBodein1945,makeupofthecoresoftheclassicalcontroltheoryfordesigningandanalyzingcontrolsystems.Wediscusstheroot-locusaccordingtofollowingorder:1).whatisRoot-locus?2).Howtheroot-locusplotofasystemissketched?3).Howtheperformanceinformationisanalyzedfromtherootlocusofasyste

7、m.(plotting)(analysisoftherootlocus)(basicconceptionoftheroot-locus).10/2/202144.2TheRootlocusconcept4.2.1Whatistherootlocusofasystem?Example4.1:forthesystemshowninFig.4.1:Fig.4.1C(s)R(s)Theopen-looptransferfunction:Thecharacteristicequation:Therootsofthecharacteristicequation,ort

8、hepolesoftheclosedlooptransferfun