实验备课教案4(讲义)

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1、实验四根轨迹法的MATLAB自控实现一．实验目的1．熟悉并掌握MATLAB的工作环境。2．了解根轨迹控制技术的基本理论。3．在MATLAB工作环境下，选择适当的例子，实现根轨迹法控制，讨论控制效果。二．实验内容Closed-LoopPolesTherootlocusofan(open-loop)transferfunctionH(s)isaplotofthelocations(locus)ofallpossibleclosedlooppoleswithproportionalgainkandunityfeedback:Theclosed-looptransferfunc

2、tionis:andthusthepolesoftheclosedloopsystemarevaluesofssuchthat1+KH(s)=0.IfwewriteH(s)=b(s)/a(s),thenthisequationhastheform:Letn=orderofa(s)andm=orderofb(s)[theorderofapolynomialisthehighestpowerofsthatappearsinit].Wewillconsiderallpositivevaluesofk.Inthelimitask->0,thepolesoftheclosed-l

3、oopsystemarea(s)=0orthepolesofH(s).Inthelimitask->infinity,thepolesoftheclosed-loopsystemareb(s)=0orthezerosofH(s).Nomatterwhatwepickktobe,theclosed-loopsystemmustalwayshavenpoles,wherenisthenumberofpolesofH(s).Therootlocusmusthavenbranches,eachbranchstartsatapoleofH(s)andgoestoazeroofH(

4、s).IfH(s)hasmorepolesthanzeros(asisoftenthecase),minfinityiszero.Thenumberofzerosatinfinityisn-m,thenumberofpolesminusthenumberofzeros,andisthenumberofbranchesoftherootlocusthatgotoinfinity(asymptotes).Sincetherootlocusis

5、actuallythelocationsofallpossibleclosedlooppoles,fromtherootlocuswecanselectagainsuchthatourclosed-loopsystemwillperformthewaywewant.Ifanyoftheselectedpolesareontherighthalfplane,theclosed-loopsystemwillbeunstable.Thepolesthatareclosesttotheimaginaryaxishavethegreatestinfluenceontheclose

6、d-loopresponse,soeventhoughthesystemhasthreeorfourpoles,itmaystillactlikeasecondorevenfirstordersystemdependingonthelocation(s)ofthedominantpole(s).PlottingtherootlocusofatransferfunctionConsideranopenloopsystem（出发点）whichhasatransferfunctionofHowdowedesignafeed-backcontrollerforthesystem

7、byusingtherootlocusmethod?Sayourdesigncriteriaare5%overshootand1secondrisetime.MakeaMatlabfilecalledrl.m.Enterthetransferfunction,andthecommandtoplottherootlocus:num=[17];den=conv(conv([10],[15]),conv([115],[120]));rlocus(num,den)axis([-223-1515])ChoosingavalueofKfromther