现代控制系统 英文 dorf 第12版 modern control

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1、Problems375(a)Showthat/=(/1-Q)2/{2K).(b)DetermineandthezeroofGL(s),wehavethegainKthatwillminimizetheperformanceindex/.0.2917s+1Isthisgainapracticalvalue?(c)SelectapracticalGds)=valueofgainanddeterminetheresultingvalueofthe0.399s2+1.375s+1performanceindex._0.731(

2、s+3.428)P5.12Traintravelbetweencitieswillincreaseastrainsare~(s+1.043)(s+2.4)*developedthattravelathighspeeds,makingthetraveltimefromcitycentertocitycenterequivalenttoair•P5.14FortheoriginalsystemofProblemP5.13,wewantlinetraveltime.TheJapaneseNationalRailwayhasa

3、tofindthelower-ordermodelwhenthepolesofthetraincalledtheBulletExpressthattravelsbetweensecond-ordermodelarespecifiedas-1and-2andTokyoandOsakaontheTokaidoline.Thistraintravelsthemodelhasoneunspecifiedzero.Showthatthisthe320milesin3hoursand10minutes,anaveragelow-o

4、rdermodelisspeedof101mph[17].Thisspeedwillbeincreasedas=0.986s+2=0.986(s+2.028)newsystemsareused,suchasmagneticallylevitatedsystemstofloatvehiclesaboveanaluminumguideway.dS)s2+3s+2(s+1)(5+2)•Tomaintainadesiredspeed,aspeedcontrolsystemisP5.15.Consideraunityfeedba

5、cksystemwithlooptrans•proposedthatyieldsazerosteady-stateerrortoaferfunctionrampinput.Athird-ordersystemissufficient.Deter•minetheoptimumsystemtransferfunctionT(s)foranK(s+1)L(s)=Gc(s)G(s)=ITAEperformancecriterion.Estimatethesettling(s+4)(s2+s+10)*time(witha2%cr

6、iterion)andovershootforastepDeterminethevalueofthegainKsuchthattheper•inputwhen&>„=10.centovershoottoaunitstepisminimized.P5.13Wewanttoapproximateafourth-ordersystembyP5.16Amagneticamplifierwithalow-outputimpedancealower-ordermodel.Thetransferfunctionoftheorig•i

7、nalsystemisisshowninFigureP5.16incascadewithalow-passfil•terandapreamplifier.Theamplifierhasahigh-inputs3+Is2+24s+24impedanceandagainof1andisusedforaddingtheGH(s)=s4+10.53+35s2+50s+24signalsasshown.SelectavalueforthecapacitanceCs3+7s2+24s+24sothatthetransferfunc

8、tionV0(s)/Vin(s)hasadamp•ingratioof1/v2.Thetimeconstantofthemagnetic(s+l)(s+2)(s+3)(s+4)'amplifierisequalto1second,andthegainisK=10.Showthatifweobtainasecond-ordermod