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1、----------專業(yè)最好文檔，專業(yè)為你服務(wù)，急你所急，供你所需-------------文檔下載最佳的地方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----------專業(yè)最好文檔，專業(yè)為你服務(wù)，急你所急，供你所需-------------文檔下載最佳的地方----------專業(yè)最好文檔，專業(yè)為你服務(wù)，急你所急，供你所需-------------文檔下載最佳的地方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
