chapter 3. optimal linear state feedback control systems

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1、3OPTIMALLINEARSTATEFEEDBACKCONTROLSYSTEMS3.1INTRODUCTIONInChapter2wegaveanexpositionoftheproblemsoflinearcontroltheory.Inthischapterwebegintobuildatheorythatcanbeusedtosolvetheprob-lemsoutlinedinChapter2.Themainrestrictionofthischapteristhatweassumet

2、hatthecompletestatex(t)oftheplantcanbeaccuratelymeasuredatalltimesandisavailableforfeedback.Althoughthisisanunrealisticassumptionformanypracticalcontrolsystems,thetheoryofthischapterwillprovetobeanimportantfoundationforthemoregeneralcasewherewedonota

3、ssumethatx(t)iscompletelyaccessible.Muchattentionofthischapterisfocuseduponregulatorproblems,thatis,problemswherethegoalistomaintainthestateofthesystematadesiredvalue.Weshallseethatlinearcontroltheoryprovidespowerfultoolsforsolvingsuchproblems.Bothth

4、edeterministicandthestochasticversionsoftheoptimallinearregulatorproblemarestudiedindetail.Importantex-tensionsoftheregulatorproblem-thenonzerosetpointregulatorandtheoptimallineartrackingproblem-alsoreceiveconsiderableattention.Othertopicsdealtwithar

5、ethenumericalsolutionofRiccatiequations,asymptoticpropertiesofoptimalcontrollaws,andthesensitivityoflinearoptimalstatefeedbacksystems.3.2STABILITYIMPROVEMENTOFLINEARSYSTEMSBYSTATEFEEDBACK3.2.1LinearStateFeedbackControlInChapter2wesawthatanimportantas

6、pectoffeedbacksystemdesignisthestabilityofthecontrolsystem.Whateverwewanttoachievewiththecontrolsystem,itsstabilitymustbeassured.Sometimesthemaingoalofafeedbackdesignisactuallytostabilizeasystemifitisinitiallyunstable,ortoimproveitsstabilityiftransie

7、ntphenomenadonotdieoutsufficientlyfast.194OptimnlLinearStnteFccdbackControlSystemsThepurposeofthissectionistoinvestigatehowthestabilitypropertiesoflinearsystemscanbeimprovedbystatefeedback.Considerthelineartime-varyingsystemwithstatedifferentialequal

8、ionIfwesupposethatthecompletestatecanbeaccuratelymeasuredatalltimes,itispossibletoimplementali~iearco~itrollawoftheformwhereF(t)isatime-varyingfeedbacligainniabisandd(t)anewinput.Ifthiscontrollawisconnectedtothesystem3-1,theclosed-loopsystemisdescrib