线性控制系统工程 山东大学

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PartI:ControlSystemModeling（14points）

1.Determinethedisplacementtransferfunctionbetweenxo(s)/xi(s)forthemechanical

systemshowninFig.

i1

C

2o

2.TogetTransferFunctionG(S)=Vo(s)/Vi(s)

R2R1

C1C2ViVoI2I1

PartII:ControlSystemsAnalysis（25points）

1.Forunity-feedbacksystemsdescribedasthefollowingopen-looptransferfunction,Determine:(1)PO_PercentageOvershoot,

(2)Ts_theSettingTimetoanunitstepinput(±5%).

10GH(s)?

s(0.1s?1)

kxxkx

2.Forunity-feedbacksystemsasthefollowingopen-looptransferfunction,

Determine:(1)theresponseofunitstepinput,(2)thevelocityerrorcoefficientsKv,(3)thesteady-stateerrorcorrespondingwiththeinputr(t)=2t.

4

G(s)?s(s?5)

3.Thecharacteristicequationofaclosed-loopsystemisasfollowing.Determinethesystemstablecondition(theacceptablerangeofK)withRouth’sstabilitycriterion.

32

1.SimplifythetransferfunctionY(s)/R(s)

2.Reducethetransferfunctiontoanapproximatefirst-orsecondordersystem,plottheclosed-looppolesonthecomplexplane,andsketchtheunitstepresponse.

3.WhatvalueofKgivesthesystemdescribedbyamagnitudeof–10dBatafrequencyω=5rad/s?

s?3Ks?(2?K)s?4?0

4.Forunity-feedbacksystems,theopen-looptransferfunctionisasfollowing.DrawNyquistdiagramanddeterminetheclosed-loopsystemstabilitywithNyquiststabilitycriterion.

210GH(s)?GH(s)?(5s?1)(2s?1)s(0.1s?1)

5.Forunity-feedbacksystems,theopen-looptransferfunctionisasfollowingequation.Usingstraight-lineapproximation,plottheBodediagramsofthesystemandcheckthestabilityofthesystem.

250GH(s)?

(s?5)(s?2)(s?0.5)

6.Forthefollowingunityfeedbacksystem,designaPhaseLagcompensationelement,tosatisfytheconditionofPhasemarginisnotlessthan135°.

10GH(s)?

(s?1)(10s?1)

1.PleasegiveageneraldiscussionwiththekeypointsofLinearFeedbackControl