自动控制理论5

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1、Lecture56Analysisinthetimedomain(I)—First-ordersystemNorthChinaElectricPowerUniversitySunHairong2021/7/17TopicsofthisclassFirst-OrderSystems:examplesTransferfunctionoffirst-ordersystemsCommoninputsFirst-ordersystem’sresponsetosomecommoninputsFirst-orderfeedbacksystem

2、Polesandzerosofthefirst-ordersystemExamplesReading:Module31.Examplesoffirst-ordersystemsAssumingzeroinitialconditions,Example1：RCCircuit(1)Example2：Spring-DampersystemExample3：RCCircuit(2)2.Transferfunctionoffirst-ordersystemsItmaybeseenfromthepreviousexamplesthatmany

3、differentsystemsmayberepresentedinfirst-orderform.ThegeneralizedblockdiagrammaybeshowasThegeneralizedtransferfunctionbetweentheinputandtheoutputmayberelatedbytheequation3.CommoninputsUnitimpulsesignalUnitstepsignalUnitrampsignalHarmonicsignalExpression:Unitimpulsesign

4、alLaplacetransforms:R(s)=1UnitstepsignalExpression:Laplacetransforms:UnitrampsignalHarmonicsignalr(t)=Asinωt1(t)Expression:Laplacetransforms:Expression:Laplacetransforms:4.First-ordersystem’sresponsetosomecommoninputsImpulseresponseStepresponseRampresponseImpulseresp

5、onseTakingtheinverseLaplacetransformgivesThefollowingfigureshowstheoutputofthesystem(t≥0)StepresponseLeadingtoTakingtheinverseLaplacetransformgivesThefollowingfigureshowstheoutputofthesystemc(T)=0.632；c(2T)=0.865；c(3T)=0.95；c(4T)=0.98。(t≥0)RampresponseTakingtheinverse

6、LaplacetransformgivesThefollowingfigureshowstheoutputofthesystemInthestead-statetheoutputlagstheinputbyatimeequaltothetimeconstant.(t≥0)ObservationoftheaboveresponsesImpulseStepRampresponsetransientpartstead-statepart01TherelationshipoftheseresponsesAssumingzeroinitia

7、lconditions5.First-orderfeedbacksystemSupposeafirstordersystemisconsideredtobetheplantinafeedbackcontrolsystemwithavariableamplifiergainascontroller,asshowninthefollowingfigureTheclose-looptransferfunctionIftheinputisaunitstep,thenLet’sconsiderthefollowingquestion,Wha

8、t’stherelationshipofthetwosystems?Whatwouldbetheresponsefigureofthefeedbacksystemlike?Howaboutthestead-stateerror?Andwhatist