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1、Module3First-ordersystemsContentsandRequirementsontheModulesConceptandexamplesofFirst-ordersystemsConceptoffirst-ordersystemsAfirst-ordermechanicalsystemAfirst-orderelectricalsystemAfirst-orderhydraulicsystemFirst-orderresponseanalysisfortypicalinputsImpulseresponseStepresponseRampresponseHarmonicr
2、esponseComplex-planerepresentationFirst-orderfeedbacksystemsConceptsofpolesandzerosPolesandzerosoffirst-ordersystemsDominantpolesMechanicalfirst-ordersystemEquatetheforcesatA,TakeLaplacetransforms,assuminginitialconditionstobezero,Leadtothetransferfunction,where,TiscalledTimeConstant,havingunitsofs
3、econdsCAKxoxiElectricalfirst-ordersystemApplyKirchhoff’slawtothecircuitdirectlyinLaplacetransforms,Leadtothetransferfunction,+ui--+uo--iRCHydraulicfirst-ordersystemAccordingtothepropertyofalaminarrestrictor:pressuredropbetweenbothsidesisproportionaltotheflow,withKasflow-pressureconstant,weget,Apply
4、thelawofmassconservationinaddition,TakeLaplacetransforms,leadingtothetransferfunction,h1h2A1A2qRHydraulicfirst-ordersystemThepreviousmodelingresultisinsufficient,becausetheimpressionofflowqonh1hasnotbeentakenintoaccount,Applyblockdiagramalgebra,Applyfinal-valuetheorem,1R1A2s1A1sH1H2Q__ContentsandRe
5、quirementsontheModulesConceptandexamplesofFirst-ordersystemsConceptoffirst-ordersystemsAfirst-ordermechanicalsystemAfirst-orderelectricalsystemAfirst-orderhydraulicsystemFirst-orderresponseanalysisfortypicalinputsImpulseresponseStepresponseRampresponseHarmonicresponseComplex-planerepresentationFirs
6、t-orderfeedbacksystemsConceptsofpolesandzerosPolesandzerosoffirst-ordersystemsDominantpolesTypicalinputsforcontrolsystemUnit-stepfunctiontr(t)10Unit-impulsefunctiontr(t)1/h0Unit-rampfunctiontr(t)10SinefunctionhStepresponseoffirst-ordersystemFirst-ordersystemoutputunderstepinputbecomes,TakeinverseLa
7、placetransforms,Treflectssysteminertia.ThelessTis,thefastertheresponseistc(t)R0AT0.632Rampresponseoffirst-ordersystemFirst-ordersystemoutputunderrampinputbecomes,TakeinverseLaplacetransforms,Forr(t)=At,Impo
