计算机控制系统 课件.ppt

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1、Chapter2ThezTransform12Contents2-1Introduction2-2Theztransform2-3ztransformsofelementaryfunctions2-4ztransformcalculationmethods2-5Importantpropertiesandtheoremsoftheztransform2-6Theinverseztransform2-7ztransformmethodforsolvingdifferenceequations2-8Co

2、ncludingcomments22-1IntroductionztransformAmathematicaltoolcommonlyusedfortheanalysisandsynthesisofdiscrete-timecontrolsystems.Theroleoftheztransformindiscrete-timesystemsissimilartothatoftheLaplacetransformincontinuous-timesystems.JustastheLaplacetran

3、sformationtransformslineartime-invariantdifferentialequationsintoalgebraicequationsins,theztransformationtransformslineartime-invariantdifferenceequationsintoalgebraicequationsinz.3Inconsideringtheztransformofatimefunctionx(t),weconsideronlythesampledv

4、aluesofx(t),thatis,x(0),x(T),x(2T),…,whereTisthesamplingperiod.x(kT)canbewrittenasx(k)tosimplifythepresentation.1.One-sidedztransformTheztransformofatimefunctionx(t),wheretisnonnegative,orasequenceofvaluesx(kT),wherektakeszeroorpositiveintegersandTisth

5、esamplingperiod,isdefinedbythefollowingequation2-2Theztransform42-2Theztransform2.Two-sidedztransformTheztransformofatimefunctionx(t),where-

6、owersofz-1.One-sidediscommonlyused.5Assumption:Functioniscontinuousfromtheright.1.Unit-StepFunction2-3ztransformsofelementaryfunctions62.Unit-RampFunction2-3ztransformsofelementaryfunctions73.PolynomialFunctionak2-3ztransformsofelementaryfunctions84.Ex

7、ponentiaFunction2-3ztransformsofelementaryfunctions95.SinusoidalFunction2-3ztransformsofelementaryfunctions102-3ztransformsofelementaryfunctions112-3ztransformsofelementaryfunctions122-4zTransformsCalculationMethods1.Partial-fraction-expansionmethodThe

8、LaplacetransformX(s)ofacontinuous-timefunctionx(t)canbeexpandedtoapartial-fractionformAccordingtotheformulaforthez-transformoftheexponentialfunction,wecanconcludethat132-4zTransformsCalculationMethods142-4zTransformsCalculationMethods15