chapter3-3.ppt

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1、3.4Transientresponseanalysisofthelinearcontrolsystem3.4.1Time-Domaintransientperformancespecificationofthelinearcontrolsystems.1.StepresponseThestepresponseofthegeneralcontrolsystemsisshowninFig.3.4.1StepResponse8/14/202112.Theperformancecriteria1)Risetimetrforthecurve①forthecurve②8/14/20212k1/sα2.

2、WhyandHowtoresearchthefirst-ordersystem?Thesystemcouldbedescribedbyafirst-orderdifferentialequation—thefirst-ordersystem.Typicalfirst-ordersystemWhy---manyactualsystemscanbeexpressedasafirst-ordersystem.How---solveC(t)andanalyzeC(t).3.Thestepresponseofthefirst-ordersystem1.Whatisthefirst-ordersyste

3、m?3.4.2stepresponseofthefirst-ordersystems8/14/20213Thestepsignalr(t)=A0·1(t)GraphicrepresentationStepresponsePoledistributionReIm3.4.2stepresponseofthefirst-ordersystems8/14/20214performance3.4.2stepresponseofthefirst-ordersystems8/14/202153.4.3stepresponseofthesecond-ordersystemsThesystemcouldbed

4、escribedbyasecond-orderdifferentialequation.2.Whyandhowtoresearchthesecond-ordersystem?1.Whatisthesecond-ordersystem?Why---manyactualsystemscanbeexpressedasasecond-ordersystem.How---solveC(t)andanalyzeC(t).3.stepresponseofthetypicalsecond-ordersystemsHere:8/14/202163.stepresponseofthetypicalsecond-

5、ordersystemsHere:Threecase:1)ξ>1overdampingcasePolesdistributionc(t)tUnitstepresponse8/14/202172)ξ=1.criticaldampingcasePolesdistributiontc(t)Unitstepresponse8/14/202183)0<ξ<1.UnderdampingcaseImS-planeRePolesdistributionc(t)t1Unitstepresponse8/14/202194)ξ≤0.Zeroornegativedampingcasesystemisunstable

6、Polesdistribution:Unitstepresponse:c(t)t18/14/2021104.Thetransientperformanceanalysisofthesecond-ordersystem①Risetimetr②Peaktimetr8/14/202111③Settingtimets④maximumovershootσpNote:8/14/2021123.4.5TheresponseofthelinearsystemsforotherinputsignalsIntermsofthetheoryincourse3.1.4:Wecangetotherresponseba

7、sedonthestepresponse.Suchas:8/14/2021138/14/2021143.5Theunity-stepresponseanalysisofthenth-ordercontrolsystems8/14/202115Discusstheunitstepresponse:Wehave:8/14/202116Wecanusethedominantpolestoapproximateant