sensitivity analyses敏感性分析

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1、SENSITIVITYANALYSESCHAPTER13SENSITIVITYANALYSESThepreviouschaptershintedattheimportanceofthesensitivityofasystemtoitsparameters.AsmentionedinSection4ofChapter3,intheabsenceoffeedback,controlforcesdonotreallymoveasysteminahighlypredictablemanner.Thefeedbackactsasacontinuously-actingcorrectionoferrors

2、resultingfromnotknowingpreciselythesystem’sparameters,theexternaldisturbances,andeventhecontrolforcesbeingapplied.Thequestionariseshowonecanstudythesensitivityofasystemtogainconfidencethatacontrolsystemdesignwillstabilizeasystemasintended.Sensitivityanalysescanbeperformednumericallyoranalytically.Th

3、enumericalapproachconsistsofrepeatedlysimulatingtheresponseofasystemmodelwhilevaryingdifferentparameters,likethesystem’sphysicalparameters,thecontrolparameters,andthedisturbances.Thisapproachcanbeextremelyeffective.Anotherapproachistogainmoreinsightintothenatureoftheerrors.Thisisaccomplishedbyanalyt

4、icalmethods.Theeffectofthechangesinthesystem’sparameterscanbedescribedbyrelationshipsthatexpressthechangesintheclosed-loopdecayratesandclosed-loopfrequenciesintermsofchangesinthesystem’sparameters,thatis,thephysicalparametersandthecontrolgains.Below,wefirstshowhowaperturbationanalysiscanbeperformedt

5、odetermineformulasforthechangesintheclosed-loopdecayratesandthefrequenciesofoscillationintermsofchangesinthesystem’sphysicalparameters.Then,weshowhowanapproachcalledtheroot-locusmethodcanbeperformedtodeterminethechangesintheclosed-loopdecayratesandthefrequenciesofoscillationintermsofchangesinthecont

6、rolgains.1.PerturbationAnalysisPerturbationanalysisdatesbackovermanyhundredyears.Itisanoldandpowerfultrickforfindingthesolutiontoanonlinearproblemintheneighborhoodofalinearproblem.Inparticular,let’sfindthedecayratesandfrequenciesofaclosed-loopsystem.Thedecayratesandthefrequenciesofoscillationofthesy

7、stemaredeterminedfromtheeigenvalueproblemassociatedwiththeclosed-loopsystem.Assumethatamulti-degree-of-freedomsystemandalinearfeedbackcontrollawaredescribedby(13–1)Theclosed-loopeigenvalueproblemisCON