北理工控制理论基础期末试题

北理工《自动控制理北理工《自动控制理论》详见：网学天地，、考点、典型题、命题规律独；咨讲解PAGEPAGE1TestforcontroltheoryAnRLCcircuitisgiveninFig.1,whereuistheinputvoltage.Takingthe

iL

andthecapacitor

uC

asthestatey

astheoutput,obtainthestatespacerepresentationfortheRLCFigure1:AnRLCAcontrolsystemisgiveninFig.Figure2:AcontrolCalculatetheunitystepresponseDeterminetheumovershootMpandthepeaktimeUnityfeedbackcontrolsystemhastheopen-looptransferG(s)

K(s1)(0.2ss3(0.1s DeterminetherangeforKsothattheclosed-loopsystemisstableusingtheRouth-Hurwitzstabilitytest;DrawtheNyquistplot

G(s)(s1)(0.2s s3(0.1s

anddeterminerangeforKsothattheclosed-loopsystemisstableusingtheNyquiststabilityAcontrolsystemisdescribedbythefollowingstate-spacerepresentationycT 0

0 bA

b

2 1 b3 2

b4 cT yzethecontrollabilityandthe Ifthesystemisuncontrollableand/orunobservable,givethenecessaryandsufficientconditionfortheexistenceanobserver-basedstate-feedbackcontrolthatstabilizesthesystem.

01A1

0 0

2Determinethematrix

eAtConsiderthesystemwithpositionandvelocityfeedbackinFig.3,whereKh>0isthevelocityfeedbackgain.Figure3:AcontrolsystemwithpositionandvelocityShowthatforagivenconstantKh,theclosed-looppolesaredeterminedbytherootlocus 1K(Khs s

ForagivenconstantKh,therootlocus(3)isdepictedinFig.4,anditisthatthebreak-inpointis2.Determinethevelocityfeedbackgainandtheopen-loop

z1oftherootlocusFigure4:TherootFortherootlocusdepictedinFig.4,determinetherootlocusgainKsuchthattheclosed-loopsystemhasapairofcomplexconjugatepolesonthelines1

j.Determinethecorresponding ratio andclosed-loopAunityfeedbackcontrolsystemhastheminimumphaseopen-looptransferG(s)K(1s1)(2s1)(mssl(Ts1)(Ts1)(Ts wherel+u=nandmn.ForK=1theAsymptoteoftheNyquist|G(j)|dBisdepictedinFig.

explicitlyusingthedataprovidedinFig.5,especiallysystemtype,the

T1,T2,,Tu,

1,2,,mDeterminetherangeoftheopen-loopgainKsothattheclosed-loopsystemisCalculatethestatic