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MATLAB和Simulink的建模与控制.doc

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出处:http://www.dcsc.tudelft.nl/~sc4050/transp/refresher.pdfMatlabandSimulinkforModelingandControl1IntroductionWiththehelpoftwoexamples,aDCmotorandamagneticlevitationsystem,theuseofMATLABandSimulinkformodeling,analysisandcontroldesignisdemonstrated.ItisassumedthatthereaderalreadyhasbasicknowledgeofMATLABandSimulink.ThemainfocusisontheuseoftheControlSystemToolboxfunctions.WerecommendthereadertotrythecommandsoutdirectlyinMATLABwhilereadingthistext.Theexampleshavebeenimplementedbytheauthorsandcanbedownloadedfromhttp://lcewww.et.tudelft.nl/.et4092.TheimplementationisdoneinMATLABversion5.3andhasalsobeentestedinversion5.2.2ModelingaDCMotorInthisexamplewewilllearnhowtodevelopalinearmodelforaDCmotor,howtoanalyzethemodelunderMATLAB(polesandzeros,frequencyresponse,time-domainresponse,etc.),howtodesignacontroller,andhowtosimulatetheopen-loopandclosed-loopsystemsunderSIMULINK.2.1PhysicalSystemConsideraDCmotor,whoseelectriccircuitofthearmatureandthefreebodydiagramoftherotorareshowninFigure1.Figure1:SchematicrepresentationoftheconsideredDCmotor.Therotorandtheshaftareassumedtoberigid.Considerthefollowingvaluesforthephysicalparameters:momentofinertiaoftherotorJ=0.01kg_m2damping(friction)ofthemechanicalsystemb=0.1Nms(back-)electromotiveforceconstantK=0.01Nm/AelectricresistanceR=1electricinductanceL=0.5HTheinputisthearmaturevoltageVinVolts(drivenbyavoltagesource).Measuredvariablesaretheangularvelocityoftheshaftωinradianspersecond,andtheshaftangleθinradians.2.2SystemEquationsThemotortorque,T,isrelatedtothearmaturecurrent,i,byaconstantfactorK:Thebackelectromotiveforce(emf),Vb,isrelatedtotheangularvelocityby:FromFigure1wecanwritethefollowingequationsbasedontheNewton’slawcombinedwiththeKirchhoff’slaw:2.3TransferFunctionUsingtheLaplacetransform,equations(3)and(4)canbewrittenas:wheresdenotestheLaplaceoperator.From(6)wecanexpressI(s):andsubstituteitin(5)toobtain:ThisequationfortheDCmotorisshownintheblockdiagraminFigure2.Figure2:AblockdiagramoftheDCmotor.Fromequation(8),thetransferfunctionfrom