系统的能控性和能观性 英文版

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1、----------专业最好文档，专业为你服务，急你所急，供你所需-------------文档下载最佳的地方Unit13ControllabilityandObservabilityAsystemissaidtobecontrollableattimeifitispossiblebymeansofanunconstrainedcontrolvectortotransferthesystemfromanyinitialstatetoanyotherstateinafiniteintervaloftime.Asystemissaidtobeobserv

2、ableattimeif,withthesysteminstate,itispossibletodeterminethisstatefromtheobservationoftheoutputoverafinitetimeinterval.TheconceptsofthecontrollabilityandobservabilitywereintroducedbyKalman.Theyplayanimportantroleinthedesignofcontrolsystemsinstatespace.Infact,theconditionsofcont

3、rollabilityandobservabilitymaygoverntheexistenceofacompletesolutionofthecontrolsystemdesignproblem.Thesolutiontothisproblemmaynotexistofthesystemconsideredisnotcontrollable.Althoughmostphysicalsystemsarecontrollableandobservable,correspondingmathematicalmodelsmaynotpossessthepr

4、opertyofcontrollabilityandobservability.jCompleteStateControllabilityofContinuous-TimeSystemsConsiderthecontinuous-timesystem(13.1)whereX=statevector(n-vector)u=controlsignal(scalar)A=matrixB=matrixThesystemdescribedbyEquation(13.1)issaidtobestatecontrollableatifitispossibletoc

5、onstructanunconstrainedcontrolsignalthatwilltransferaninitialstatetoanyfinalstateinafinitetimeinterval.Ifeverystateiscontrollable,thenthesystemissaidtobecompletelystatecontrollable.Weshallnowderivetheconditionforcompletestateofcontrollability.Withoutlossofgenerality,wecanassume

6、thatthefinalstateistheoriginofthestatespaceandthattheinitialtimeiszero,or.ThesolutionofEquation(13.1)is----------专业最好文档，专业为你服务，急你所急，供你所需-------------文档下载最佳的地方----------专业最好文档，专业为你服务，急你所急，供你所需-------------文档下载最佳的地方Applyingthedefinitionofcompletestatecontrollabilityjustgiven,weha

7、veor(13.2)Andcanbewritten(13.3)SubstitutingEquation(13.3)intoEquation(13.2)gives(13.4)LetusputThenEquation(13.4)becomes(13.5)Ifthesystemoscompletelystatecontrollable,then,givenanyinitialstateX(0),Equation(13.5)mustbesatisfied.Thisrequiresthattherankofthematrixben.Fromthisanalys

8、is,wecanstatetheconditionforcompletestatecontrollabili