自控原理习题教程文件.docx
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自控原理习题教程文件.docx
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自控原理习题教程文件
自控原理习题
习题一
1.Thedifferentialequationofasystemshownbelow,trytoestablishthedynamicstructurediagramofthesystemanddeterminethetransferfunctionY(s)/R(s),Y(s)/N1(s),Y(s)/N2(s).
2.AFeedbackcontrolsystemhasthestructureshowninfigure2.DeterminetheK1andK2sothattheunitstepresponsey(t)hasTp=0.5sandP.O=2%.
Figure2
3.Whentheinputsignalofthesystemis,
themeasuredoutputresponsefor.
(1)Determinethesystemtransferfunction.
(2)Foraunitstepinputandaunitrampinput,calculatethesteady-stateerrorrespectively.
4.Anegativefeedbacksystemhasalooptransferfunction.
(1)UsingtheRouth-Hurwitzcriterion,findthevalueofthegainKwhentheclosed-loopsystemhastwopolesontheimaginaryaxis.
(2)FindthevalueofthegainKwhens=-3andotherrootsofthecharacteristicequation.
5.Aunityfeedbacksystemhasaplant
(1)Sketchtherootlocusoftheclosed-loopsystem.
(2)DeterminetherangeofKforstability.
(3)FindthegainKatthebreakawaypoint.
6.Logarithmamplitudefrequencycharacteristiccurveofminimumphasesystemsshownbelow,writeoutthesystemtransferfunctionrespectively.
7.Aunityfeedbackcontrolsystemhasaplant
(1)PlottheBodediagramofG(s).
(2)DeterminethephasemarginPMandgainmarginGM.
(3)PlotthepolarplotandMarkGM,PMonthethismap.
习题二
1.Aunitynegativefeedbackcontrolsystemhastheplant
(1)Determinethepercentovershootduetoaunitstepinput.
(2)ForwhatrangeofKisthesettlingtimelessthan1second?
2.Acontrolsystemisshowninfigure2.
(1)whenr(t)=tandn(t)=t,determineallsteady-stateerrorofthesystem.
(2)whenr(t)=1(t)andn(t)=0,determinetheP.OandTs.
Figure2
3.Acontrolsystemshowninfigure3.onecontrolleristheproportionalcontroller,Gc(s)=Kp.determinetherangeofKpofstablesystem.
Figure3
4.Theunit-stepresponseofaunityfeedbacksystem
(1)Findthetransferfunctionofthesystem.
(2)Findtheopen-looptransferfunctionG(s).
5.Aunityfeedbacksystemhasaplant
(1)whenT=1,Sketchtherootlocusfor0 (2)whenK=10,sketchtherootlocusfor0 6.thefollowingopen-looptransferfunctionG(s)H(s)havenopolesontherighthalfs-plane,theirpolarplotsshowninfigure6.Pleaseanalyzethestabilityofthecorrespondingsystem. Figure6 7.Aclosed-loopcontrolsystemshowninFigure7. (1)DrawtheBodeplotoftheopen-looptransferfunction G(s). (2)Calculatethephasemargin. (3)Provethephaseis-180°whenandfindoutthe gainmargin. Figure7 习题三 一、AcontrolsystemisshowninFigure2.1(a)andFigure2.1(b),findthetransferfunction(),(), (), Figure2.1(a) Figure2.1(b) 二、Aunityfeedbacksystemhasaplant . (1)Plotthepolarplotforwhen; (2)Calculatethephaseandmagnitudeat; (3)DeterminetherangeofKforwhichthesystemisstable; (4)Calculatethesteady-stateerrorforinput. 三、AcontrolsystemisshowninFigure4.1, Where=1+,=. Figure4.1 (1)Toassurethesystemisstable,determinetheconditionthat,shouldsatisfy; (2)When=0,0,determinethevalueofwhenthepercentovershoot(P.0%)is16.3%;() (3)Fortheconditionof (2),findthetimeresponsey(t)forastepinputr(t)=A,fort>0; (4)When0,0,findthesteady-stateerrorforinputr(t)=10+2t. 四、Aunityfeedbacksystemhasaplant (1)Sketchtherootlocusfor0 (2)DeterminethevalueoftherootsontheandthegainKrequiredforthoseroots; (3)DeterminetherangeofK,thatresultinasystemthatsatisfystepresponsewithnoovershoot. 五、Theopen-loopbodeplotofaunityfeedbacksystemareshowninFig.6. (1)Findtheopen-looptransferfunctionG(s);. (2)Determinethephasemarginandgainmargin;. (3)WhenK=20,whetherthesystemisstable.; 六、Theunityfeedbacksystemhasopen-looptransferfunction, ThebodeplotofisshowninFig.7. Fig.7 (1)DeterminethetransferfunctionofcompensatorGc(s) (2)When,determinethephasemarginofthesystemaftercompensation. 习题四 1.DeterminethetransferfunctionY(s)/R(s). 2.AFeedbackcontrolsystemhasthestructureshowninfigure2. Figure2 (1)ShowthepermissibleareaforthepolesofY(s)/R(s)inordertoachieveP.O≤16.3%andts≤4s. (2)Whenζ=0.5andωn=10,determinethevalueofKandβ. (3)Determinethesteady-stateerrorforastepandarampinput. 3.Asystemhasthetransferfunction Determineitsunitystepresponseanditsunityimpulseresponse. 4.Aunitynegativefeedbacksystemhasalooptransferfunction . (1)Sketchtherootlocusofq(s)=1+G(s)=0. (2)DeterminetherangeofKforstability. (3)FindthevalueofthegainKwhens=0andotherrootsof
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