控制工程(周川)a课件

1,Ch2Mathematicalmodelsofsystems,IntroductionModelsintime-domain(Differentialequations)Modelsinfrequency-domain(Transferfunction)BlockdiagrammodelsSignal-flowgraphmodelSimulationandExamples,2,2.1Introduction,Mathematicalmodelscanhelpustounderstandandcontrolcomplexsystemeffectively.Soitisnecessarytoanalyzetherelationshipsbetweenthesystemvariablesandtoobtainamathematicalmodel.Becausethesystemsaredynamicinnature,thedescriptiveequationsareusuallydifferentialequations,iftheycanbelinearized,thenLaplacetransformcanbeusedtosimplifythemethodofsolution.,3,TwoTasksinControlTheory,AnalysisProblems:SynthesisProblem:,GivenaController,determineifthecontrolledsignals(includingoutputs,trackingerror&controlsignal,etc.)satisfythedesiredperformanceforalladmissibleexternaldisturbanceandmodeluncertainties.,Designacontrollersuchthatthecontrolledsignalssatisfythedesiredpropertiesforallexternalandinneruncertainties(suchasnoise,extraneousdisturbance&modelingerrors).,4,Modelingmethod,AnalyticalmethodExperimentalmethod,Goalsofmodeling,AnalysisDesignorControl,5,1Analyticalmethod(解析法)：,Routh判据,英国E.J.Routh建立（Routh-HurwitzStabilityCriteria）（1875年）,J.C.Maxwellformulatesamathematicalmodelforaflyballgovernor,6,2Experimentalmethod(实验法)：,实际系统,7,Hypothesis(猜想法)：,宇宙大爆炸理论,8,ModelsunderConsideration,LinearTime-invariant(constant)Parameter-lumped,9,2.2Differentialequationsofphysicalsystems,Through-variableandacross-variableAnalogousvariables,Voltage-VelocityanalogyForce-currentanalogy,Referto(P39-40),10,HowtoobtainDE?,NewtonslawsforMechanicalsystemKirchhoffslawsforelectricalsystemsTwoexamples,(Refertoscript2-2),11,弹簧阻尼系统如图示：其中，f为阻尼系数k为弹簧系数试确定该系统的模型。,例1机械力学系统,12,解：系统的微分方程如下拉氏变换后（零初始条件下）,13,例2电学系统,RLC无源网络如图所示，其中：电阻为R，电感为L，电容为C，确定其输入输出模型。,R,L,C,14,解：系统的微分方程如下拉氏变换后（零初始条件下）,15,Solvingtheequation,AnalyticalorclassicalmethodLaplacetransformmethodExampleofsolvingdifferentialequation,(Refertoscript2-3,4),16,Modesofdynamicsystem,ModesisdeterminedbyCharacteristicroots:realanddistinctrootsrealandrepeatedrootscomplexconjugateroots,17,2.3Linearapproximationsofphysicalsystems,Non-linearityisessentialandpervasiveAsystemisdefinedaslinearintermsofthesystemexcitationandresponse.PrincipleofsuperpositionHomogeneityAlinearsystemsatisfiesthepropertiesofsuperpositionandhomogeneity,18,Linearapproximationsmethod,TaylorseriesexpansionExample:pendulumoscillatormodel,RefertonextpageorP45,19,Pendulumoscillator,20,2.4TheLaplacetransform,Reviewcomplexalgebraic(refertoP46-52):,LaplacetransformInverseLaplacetransformresidueevaluationFinalvaluetheorem,21,TimeresponsebyLaplacetransform,Timeresponsesolutionisobtainedby:1.obtainthedifferentialequations2.obtaintheLaplacetransformationofdifferentialequations3.solvethealgebraicequationofthevariableofinterest4.obtaintheresponsebytheinverseLaplacetransform,22,2.5Thetransferfunctionoflinearsystem,TransferfunctionisdefinedastheratiooftheLaplacetransformoftheoutputvariabletothelaplacetransformoftheinputvariable,withallinitialconditionsassumedtobezero.Examples:(refertoP53),23,CharacteristicsofTF（传递函数的特性）,Black-boxmodelrationalrealfractionalfunctiontransitionbetweenTFandDETFandimpulseresponse,TransferfunctionistheLaplacetransformoftheimpulseresponseandviceversa.,24,ImplicationofTF（传递函数的含义）,ZeroinitialconditionRepresentationofTF,Inputsandoutputsofsystemarezeroatt=0-,25,TFoftypicalelementsanddynamicsystems,Gain：ZerosatOrigin：PolesatOrigin：Zeros：Poles：,26,ComplexConjugateZeros：ComplexConjugatePoles：Time-Delay：,RefertoP55-63andTable2.5(P64-67),ExamplesofTF,27,ExamplesofTF,1.Potentiometer：(线位移或角位移变换为电压量的装置)（a）,28,（b）whereEVoltageofSource；maxMaximumangleofpotentiometer,29,(c)Potentiometererrordetector,2.DCMotor:,M,+,-,R,a,L,a,E,b,i,a,u,a,(),31,3.Tachometer：,32,4.RCpassivenetwork：,33,5.SeriesofRCpassivenetwork(无源网络级联),34,SeriesofRCpassivenetwork(withoutloadeffect),35,6.IntegratingCircuit(有源网络),36,2.6Blockdiagrammodels（结构图或方框图模型）,Blockdiagramsrepresentationisprevalentincontrolengineering,andconsistofunidirectionaloperationalblocksthatrepresentthetransferfunctionofthevariablesofinterests.Representationofblockdiagram,RefertoP68,37,TransformationofBlockDiagram,BD=Scheme+EquationFourComponentsofBD(referto2-14,15),SignallinePickoffpointSummingpointBlock,38,TransitionbetweenTFandBD,Referto2-15,16,17AnexampleofRCpassivenetwork,i,Ur,39,BlockDiagramofRCpassivenetwork,40,41,42,TheBlockDiagramofthesystem,43,CharacteristicsofBD,UnidirectionalPrincipleWithoutloadeffectConnectionways:,Seriesparallelandfeedbackconnection,44,Blockdiagramreduction,CombinationofblocksincascadeCombinationofblocksinparallelEliminationoffeedbackloopMovingpickoffpointsandsummingpoints,Principle:Keepeverysignaltobeequivalent,45,1.Combinationofblocksincascade,46,2.Combinationofblocksinparallel,47,3.Eliminationoffeedbackloop,48,4.Movingpickoffpointsandsummingpoints,a)Movingasummingpointbehindablock,49,b)Movingasummingpointaheadofablock,50,c)Combinationofsummingpoints,51,d)Movingapickoffpointaheadofablock,52,e)Movingapickoffpointbehindablock,53,ExamplesofBDreduction,Refertotextbook(P70-72)Otherexamples:referto(2-19,20,21),54,Example1,55,-,-,-,56,Example2,57,U,