自动控制理论第五章习题

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1、第五章习题E5.2Theengine,body,andtiresofaracingvehicleaffecttheaccelerationandspeedattainable.ThespeedcontrolofthecarisrepresentedbythemodelshowninFigureE5.2.(a)Calculatethesteady-stateerrorofthecartoastepcommandinspeed.(b)Calculateovershootofthespeedtoastepcom

2、mand.E5.3Foryears,AmtrakhasstruggledtoattractpassengersonitsroutesintheMidwest,usingtechnologydevelopeddecadesago.Duringthesametime,foreignrailroadsweredevelopingnewpassengerrailsystemsthatcouldprofitablycompetewithairtravel.Twoofthesesystems,theFrenchTGV

3、andtheJapaneseShinkansen,reachspeedof160mph.TheTransrapid-06,aU.S.Experimentalmagneticlevitationtrain,isshowninFigureE5.3(a).TheuseofmagneticlevitationandelectromagneticpropusiontoprovidecontactlessvehiclemovementmakestheTransrapid-06technologradicallydif

4、ferentfromtheexistingMetroliner.TheundersideoftheTR-06carriage(wherethewheeltruckswouldbeonaconventionalcar)wrapsaroundaguideway.Magnetsonthebottomoftheguidewayattractelectromagnetsonthe"wraparound,"pullingituptowardtheguideway.Thissuspendsthevehiclesabou

5、tonecentimeterabovetheguideway.ThelevitationcontrolisrepresentedbyFigureE5.3(b).(a)usingTable5.6forastepinput,selectKsothatthesystemprovideanoptimumITAEresponse.(b)UsingFigure5.3determinetheexpectedovershoottoastepinputofI(s).E5.5Alow-inertiaplotterisshow

6、ninFigureE5.5(a).ThissystemmayberepresentedbyblockdiagramshowninFigureE5.5(b).(a)Calculatethesteadyerrorforarampinput.(b)SelectavalueofKthatwillresultinzeroovershoottoastepinput.Providethemostrapidresponsethatisattainable.Plotthepolesandzerosofthesysteman

7、ddiscussthedominanceofthecomplexpoles.Whatovershootforastepinputdoyouexpect?E5.6Effectivecontrolofinsulininjectioncanresultinbetterlivesfordiabeticpersons.Automaticallycontrolledinsulinjectionbymeansofapumpandasensorthatmeasuresbloodsugarcanbeveryeffectiv

8、e.ApumpandinjectionsystemhasafeedbackcontrolasshowninFigureE5.6.CalculatethesuitablegainK,sothattheovershootofthestepresponseduetothedruginjectionisapproximately7%.R(s)isthedesiredblood-sugarlevelandY(s),istheactual