Chapter8ApproximatingContinuous-TimeControllers,有時(shí)把模擬控制系統(tǒng)簡單地代換為計(jì)算機(jī)控制系統(tǒng)，因?yàn)楹笳叩挠布阋恕⒖煽?。在這種情況下，自然要尋求把模擬系統(tǒng)轉(zhuǎn)換為有同樣特性的數(shù)字系統(tǒng)的方法。解決這個(gè)問題的捷徑是：采用短的采樣間隔和對(duì)連續(xù)時(shí)間控制器找出某些離散時(shí)間近似法。就平均值而言，離散時(shí)間控制信號(hào)比連續(xù)時(shí)間信號(hào)要滯后半個(gè)采樣周期。這一延遲引進(jìn)一相位落后，使閉環(huán)特性變壞。采樣周期的選擇是重要的。通常用近似替代法轉(zhuǎn)譯連續(xù)時(shí)間控制器將要求用很短的采樣周期。但使用數(shù)字設(shè)計(jì)方法，則可能容許有轉(zhuǎn)長的采樣時(shí)間。,8.1基于傳遞函數(shù)的近似法8.2基于狀態(tài)模型的近似法8.3頻率響應(yīng)設(shè)計(jì)方法8.4數(shù)字PID控制器,8.1ApproximationsBasedonTransferFunctions,8.1ApproximationsBasedonTransferFunctions,DifferentiationandTustinApproximationsBackwardsdifferenceForwarddifference(Eulersmethod),說明：使用向前差分近似法有可能將一個(gè)穩(wěn)定的連續(xù)時(shí)間系統(tǒng)映射為一個(gè)不穩(wěn)定的離散時(shí)間系統(tǒng)。采用向后差分近似時(shí)，一個(gè)穩(wěn)定的連續(xù)時(shí)間系統(tǒng)將總是給出一個(gè)穩(wěn)定的離散系統(tǒng)。不過，還有一些不穩(wěn)定連續(xù)時(shí)間系統(tǒng)轉(zhuǎn)換成穩(wěn)定的離散時(shí)間系統(tǒng)。,Forwarddifference(Eulersmethod),Backwardsdifference,Forwarddifference(Eulersmethod),Forwarddifference(Eulersmethod),Tustinsapproximation(BilinearTransformation),塔斯廷近似的優(yōu)點(diǎn)是：可以將左半S平面轉(zhuǎn)換到單位圓內(nèi)。,FrequencyPrewarping頻率彎翹的預(yù)防頻率彎翹：如果希望設(shè)計(jì)帶通或者是限波濾波器，采用上述的前向差分、后向差分或者塔斯廷近似法得到的數(shù)字濾波器也許都給不出正確的帶通或者限波頻率。這個(gè)效應(yīng)就是頻率彎翹。這里主要是給出采用塔斯廷近似時(shí)，怎么樣來預(yù)防頻率彎翹。,WhenThen,此式給出了頻率標(biāo)度的畸變。,|D(ejh)|,pp,|D(ejh)|,ExampleStep1.Pre-warpingStep2.,針對(duì)頻率彎翹，實(shí)際中采用：考慮了頻率標(biāo)度畸變的塔斯廷變換,ImpulseInvariantTransformationImpulseInvariantTransformation&Hold,ComparisonoftheVariousDiscretizationMethods,MatchedZ-transform,8.2ApproximationsBasedonStateModelsConsiderasystemControllaw,Discretecontrollaw:Forthecontinuoussystem:(8.14)Where:,Forthediscrete-timesystem,(8.15),Let:Suppose:While:,IfThen(8.14)(8.15)Suppose:Then:And:,8.3Frequency-ResponseDesignMethods,DesignProcedureconsistsoffivestepsStep1:GiventhecontinuousplantH(s)andthehold,transformthemodeltothez-plane,Step2:TransformH(z)tothew-planei.e.ThenselecthStep3:DesignD(w)onthew-planeStep4:Transformbacktothez-planeStep5:TransformD(z)toacomputationalalgorithm,Example,r,d,When,M,M,d,d,8.4DigitalPID-Controllers,(1),(2)EulersMethod,Backwardsdifference:,BackwardsDifference:,(3)Bumplesstransfer(4)Antiresetwindup(5)Integrationoffset(6)TuningRules(7)SelectionofSamplingInterval,