自动控制理论六作业

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1、第六章习题E6.1Asystemhasacharacteristicequation:s3+3Ks2+(2+K)s+5=0.DeterminetherangeofKforastablesystem.E6.7Anegativefeedbacksystemhasalooptransferfunction矚慫润厲钐瘗睞枥庑赖。(a)Findthevalueofthegainwhentheζoftheclosed-looprootsisequalto0.707.聞創沟燴鐺險爱氇谴净。(b)Findthevalueofthegainwhentheclosedsystemhastw

2、orootsontheimaginaryaxis.残骛楼諍锩瀨濟溆塹籟。E6.11AsystemwithatransferfunctionY(s)/R(s)is酽锕极額閉镇桧猪訣锥。Determinethesteady-stateerrortoaunitstepinput.isthesystemstable?彈贸摄尔霁毙攬砖卤庑。E6.14Asystemhasacharacteristicequationq(s)=s4+9s3+45s2+87s+50=0.(a)Determinewhetherthesystemisstable,usingtheRouth-Hurwitz

3、criterion.(b)Determinetherootsofthecharacteristicequation.謀荞抟箧飆鐸怼类蒋薔。E6.23Aclosed-loopfeedbacksystemisshowninFigureE6.23.ForwhatrangeofvaluesoftheparametersKandpisthesystemstable?厦礴恳蹒骈時盡继價骚。P6.3Arcweldingisoneofthemostimportantareasofapplicationforinstustrialrobots.Inmostmanufacturingwel

4、dingsituation,uncertaintiesindimensionsofpart,geometryofthejoint,andtheweidingprocessitselfrequiretheuseofsensorsformaintainingweldquality.Severalsystemsuseavisionsystemtomeasuretheqeometryofthepuddleofmeltedmetal,asshowninFigureP6.3.Thissystemusesaconstantrateoffeedingthewiretobemelted.

5、茕桢广鳓鯡选块网羈泪。(a)CalculatethemaximumvalueforKforthesystemthatwillresultinastablesytem鹅娅尽損鹌惨歷茏鴛賴。(b)ForhalfofthemaximumvalueofKfoundinpart(a).Determinetherootsofthecharacteristicequation.籟丛妈羥为贍偾蛏练淨。(c)Estimatetheovershootofthesystemofpart(b)whenitissubjectedtostepinput.預頌圣鉉儐歲龈讶骅籴。P6.4Afeedba

6、ckcontrolsystemisshowninFigureP6.4.Theprocesstransferfunctionis渗釤呛俨匀谔鱉调硯錦。AndthefeedbacktransferfunctionisH(s)=1/(s+20).铙誅卧泻噦圣骋贶頂廡。(a)DeterminethelimitingvalueofgainKforastablesystem擁締凤袜备訊顎轮烂蔷。(a)Forthegainthatresultsinmarginalstability,determinethemagnitudeoftheimaginaryroots贓熱俣阃歲匱阊邺镓騷。

7、(b)Reducethegaintohalfthemagnitudeofthemarginalvalueanddeterminetherelativestabilityofthesystem(1)byshiftingtheaxisandusingRouth-Hurwitzcriterionand(2)bydeterminingtherootlocations.Showtherootsarebetween-1and-2.坛摶乡囂忏蒌鍥铃氈淚。P6.7Thelinearmodelofaphasedetector(phase-lockloop)