控制工程3(英文)PPT课件

精选,1,Ch6TheStabilityofLinearFeedbackSystems,TheconceptofstabilityTheRouth-HurwitzstabilitycriterionTherelativestability,精选,2,6.1Theconceptofstability,Astablesystemisadynamicsystemwithaboundedoutputtoaboundedinput(BIBO).,Theissueofensuringthestabilityofaclosed-loopfeedbacksystemiscentraltocontrolsystemdesign.Anunstableclosed-loopsystemisgenerallyofnopracticalvalue.,absolutestability,relativestability,精选,3,Absolutestability:Wecansaythataclosed-loopfeedbacksystemiseitherstableoritisnotstable.Thistypeofstable/notstablecharacterizationisreferredtoasabsolutestability.,Relativestability:Giventhataclosed-loopsystemisstable,wecanfurthercharacterizethedegreeofstability.Thisisreferredtoasrelativestability.,精选,4,精选,5,精选,6,6.2TheRouth-Hurwitzstabilitycriterion,精选,7,where,精选,8,Anecessaryandsufficientconditionforafeedbacksystemtobestableisthatallthepolesofthesystemtransferfunctionhavenegativerealparts.,精选,9,Anecessarycondition:Allthecoefficientsofthepolynomialmusthavethesamesignandbenonzeroifalltherootsareinleft-handplane(LHP).,Thecharacteristicequationiswrittenas,精选,10,HurwitzandRouthpublishedindependentlyamethodofinvestigatingthestabilityofalinearsystem.Thenumberofrootsofq(s)withpositiverealpartsisequaltothenumberofchangesinsignofthefirstcolumnoftheRoutharray.,Routh-Hurwitzstabilitycriterion,精选,11,CASE1Noelementinthefirstcolumniszero.,CASE2Zerointhefirstcolumnwhilesomeotherelementsofrowcontainingazerointhefirstcolumnarenonzero.,CASE3Zerosinthefirstcolumn,andotherelementsoftherowcontainingthezeroarealsozero.,精选,12,Considerthecharacteristicpolynomial,TheRoutharrayis,精选,13,Case3,Considerthecharacteristicpolynomial,TheRoutharrayis,Theauxiliarypolynomial,精选,14,精选,15,Designexample：weldingcontrol,精选,16,6.3Therelativestability,Therelativestabilityofasystemcanbedefinedasthepropertythatismeasuredbytherelativerealpartofeachrootorpairofroots.Axisshiftandexamples,精选,17,精选,18,Considercontrolsystem,DeterminetherangeofKsatisfyingthestabilityandallpolesM.Step4Therootlocusontherealaxisalwaysliesinasectionoftherealaxistotheleftofanoddnumberofpolesandzeros.Step5Determinethenumberofseparateloci,SL,thenumberofseparatelociisequaltothenumberofpoles.,精选,34,Example7.1Second-ordersystem,精选,35,Step6Therootlocimustbesymmetricalwithrespecttothehorizontalrealaxiswithangles.Step7Therootlociproceedtothezerosatinfinityalongasymptotescenteredatandwithangles.TheselinearasymptotesarecenteredatapointontherealaxisgivenbyTheangleoftheasymptoteswithrespecttotherealaxisis,精选,36,Example7.2Fourth-ordersystem,精选,37,精选,38,Step8Determinethepointatwhichthelocuscrossestheimaginaryaxis(ifitdoesso),usingtheRouth-Hurwitzcriterion.TheactualpointatwhichtherootlocuscrossestheimaginaryaxisisreadilyevaluatedbyutilizingtheRouth-HurwitzCriterion.Step9Determinethebreakawaypointontherealaxis(ifany).LetorStep10TheangleoflocusdeparturefromapoleisTheangleoflocusarrivalfromazerois,精选,39,精选,40,精选,41,精选,42,精选,43,Step11Determinetherootlocationsthatsatisfythephasecriterionatroot.Thephasecriterionisq=1,2.Step12Determinetheparametervalueataspecificrootusingthemagnituderequirement.Themagnituderequirementatis,精选,44,Example7.4Fourth-ordersystem,精选,45,精选,46,7.3ParameterDesignbytheRootLocusmethod,Thismethodofparameterdesignusestherootlocusapproachtoselectthevaluesoftheparameters,Theeffectofthecoefficienta1maybeascertainedfromtherootlocusequation,精选,47,精选,48,精选,49,精选,50,精选,51,精选,52,7.4SensitivityandtheRootLocus,TherootsensitivityofasystemT(s)canbedefinedas,thesensitivityofasystemperformancetospecificparameterchanges,wehave,精选,53,精选,54,精选,55,精选,56,精选,57,7.5Three-term(PID)Controllers,Thecontrollerprovidesaproportionalterm,anintegrationterm,andaderivativeterm,精选,58,精选,59,精选,60,精选,61,精选,62,精选,63,Summary,Inthischapter,wehaveinvestigatedthemovementofthecharacteristicrootsonthes-planeasthesystemparametersarevariedbyutilizingtherootlocusmethod.Therootlocusmethod,agraphicaltechnique,canbeusedtoobtainanapproximatesketchinordertoanalyzetheinitialdesignofasystemanddeterminesuitablealterationsofthesystemstructureandtheparametervalues.Furthermore,weextendedtherootlocusmethodforthedesignofseveralparametersforaclosed-loopcontrolsystem.Thenthesensitivityofthecharacteristicrootswasinvestigatedforundesiredparametervariationsbydefiningarootsensitivitymeasure.,精选,64,Assignment,E7.4E7.8,精选,65,Ch8FrequencyResponseMethods,BasicconceptoffrequencyresponseFrequencyresponseplotsDrawingtheBodediagramPerformancespecificationinthefrequencydomain,精选,66,8.1Basicconceptoffrequencyresponse,Thefrequencyresponseofasystemisdefinedasthesteady-stateresponseofthesystemtoasinusoidalinputsignal.Theresultingoutputsignalforalinearsystem,isalsoasinusoidalinthesteadystate;itdiffersfromtheinputwaveformonlyinamplitudeandphaseangle.,精选,67,Letinput,TheLaplacetransformation,Theoutput,undeterminedcoefficient,精选,68,精选,69,iscomplexvector,精选,70,FrequencyCharacteristics,TransferfunctionandLaplacetransformFrequencycharacteristicsandFouriertransform,精选,71,Frequencycharacteristic,Transferfunctionanddifferentialequationareequivalentinrepresentationofsystem.,精选,72,FrequencycharacteristicandTransferfunction,精选,73,Computationoffrequencyresponse,精选,74,8.2Frequencyresponseplots,PolarplotBodediagramNicholschartFrequencyresponseplotsoftypicalelements,精选,75,精选,76,frequencyresponseofanRCfilter,精选,77,精选,78,精选,79,Theprimaryadvantageofthelogarithmicplotistheconversionofmultiplicativefactorintoadditivebyvirtueofthedefinitionoflogarithmicgain,精选,80,BodediagramofanRCfilter,精选,81,精选,82,Nicholschart,0o,180o,-180o,w,0,-20dB,20dB,精选,83,Frequencyresponseplotsoftypicalelements,GainPoleatoriginZeroatorigin,精选,84,Poleontherealaxis(jwT+1)Zeroontherealaxis(jwT+1)TwocomplexpolesTwocomplexzeros,精选,85,精选,86,精选,87,精选,88,精选,89,Bodediagramofatwin-Tnetwork,精选,90,精选,91,8.3DrawingtheBodediagram,精选,92,精选,93,精选,94,精选,95,精选,96,精选,97,DrawingBodediagram:(1)(2)DrawtheasymptoticapproximationofL()inthelowfrequencyrange；(3)Changetheslopeatthebreakfrequency;(4)Thisapproximationcanbecorrectedtotheactualmagnitude.,精选,98,(1)La(w)=20lgK20lgw(2)w1，La(w)=20lgK(3),-20dB/dec,1,20lgK,w,精选,99,8.4Performancespecificationinthefrequencydomain,Attheresonantfrequency,amaximumvalueofthe