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END3.1TheTransferFunctionModelReviewofLaplaceTransformsTheBasicPropertiesofLaplaceTransformsIntegralTheoremInitialValueTheorem用留数法分解部分分式II.whenhassamerootsolutionTheLaplacevariablescanbeconsideredtobedifferentialoperatorImportantLaplaceTransformPairsInverseLaplaceTransformationSolvethedifferentialequationsusingtheLaplacetransformWecangetFindthefinalvalueofthesystemcorrespondingtoTheIncorrectUseofFinalValueTheoremWhentheinitialconditionsareDCgainistheratiooftheoutputofasystemtoitsinput(presumedconstant)afteralltransientshavedecayed.SolutionMathmodelinn-orderdifferentialequations:SomeCommentsabouttheTransferFunctionAcertaintransferfunctioncorrespondacertainportraitofzero-polesdistribution.Themethodofthetransferfunctionhassomelimitation.SolutionExample3.9ModelsofElectricCircuits(2)Transferfunction1.ProportionalUnitExample3.10Geartrainratio3.DifferentialUnitExample3.11Theop-ampintegratorTopaymoreattentionto4.First-orderInertiaUnitas2Y(s)+bsY(s)+cY(s)=kX(s)6.PIDUnitTheresponseofoutputisdelayedintimecomparedwithinputs.TheLaplacetransformofTimeDelay8.First-orderUnitWithTimeDelay3.2TheTransferFunctionofOtherUnitThetransferfunctionmodelofActuatorMotortorqueHomework
