系统的能控性和能观性英文版本

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1、Unit13ControllabilityandObservabilityAsystemissaidtobecontrollableattimeifitispossiblebymeansofanunconstrainedcontrolvectortotransferthesystemfromanyinitialstatetoanyotherstateinafinite矚慫润厲钐瘗睞枥庑赖。intervaloftime.Asystemissaidtobeobservableattimeif,withthesystemin

2、state,聞創沟燴鐺險爱氇谴净。itispossibletodeterminethisstatefromtheobservationoftheoutputoverafinitetime残骛楼諍锩瀨濟溆塹籟。interval.TheconceptsofthecontrollabilityandobservabilitywereintroducedbyKalman.Theyplayan酽锕极額閉镇桧猪訣锥。importantroleinthedesignofcontrolsystemsinstatespace.Infac

3、t,theconditionsof彈贸摄尔霁毙攬砖卤庑。controllabilityandobservabilitymaygoverntheexistenceofacompletesolutionofthecontrol謀荞抟箧飆鐸怼类蒋薔。systemdesignproblem.Thesolutiontothisproblemmaynotexistofthesystemconsideredis厦礴恳蹒骈時盡继價骚。notcontrollable.Althoughmostphysicalsystemsarecontr

4、ollableandobservable,茕桢广鳓鯡选块网羈泪。correspondingmathematicalmodelsmaynotpossessthepropertyofcontrollabilityand鹅娅尽損鹌惨歷茏鴛賴。observability.jCompleteStateControllabilityofContinuous-TimeSystems籟丛妈羥为贍偾蛏练淨。Considerthecontinuous-timesystem(13.1)whereX=statevector(n-vector)

5、預頌圣鉉儐歲龈讶骅籴。u=controlsignal(scalar)A=matrixB=matrixThesystemdescribedbyEquation(13.1)issaidtobestatecontrollableatifitis渗釤呛俨匀谔鱉调硯錦。possibletoconstructanunconstrainedcontrolsignalthatwilltransferaninitialstatetoany铙誅卧泻噦圣骋贶頂廡。finalstateinafinitetimeinterval.Ifevery

6、stateiscontrollable,thenthesystemis擁締凤袜备訊顎轮烂蔷。saidtobecompletelystatecontrollable.Weshallnowderivetheconditionforcompletestateofcontrollability.Withoutlossof贓熱俣阃歲匱阊邺镓騷。generality,wecanassumethatthefinalstateistheoriginofthestatespaceandthattheinitial坛摶乡囂忏蒌鍥铃氈淚。t

7、imeiszero,or.ThesolutionofEquation(13.1)isApplyingthedefinitionofcompletestatecontrollabilityjustgiven,wehave蜡變黲癟報伥铉锚鈰赘。or(13.2)Andcanbewritten(13.3)SubstitutingEquation(13.3)intoEquation(13.2)gives買鲷鴯譖昙膚遙闫撷凄。(13.4)LetusputThenEquation(13.4)becomes(13.5)Ifthesys

8、temoscompletelystatecontrollable,then,givenanyinitialstateX(0),Equation綾镝鯛駕櫬鹕踪韦辚糴。(13.5)mustbesatisfied.Thisrequiresthattherankofthematrix驅踬髏彦浃绥譎饴憂锦。ben.Fromthisanaly