北京交通大学自动控制原理考试试题(含答案)

-1-北京交通大学2011-2012学年第一学期考试试题课程名称：自动控制理论班级：出题人：题号一二三四五总分满分2020202020100得分签字1.Theschematicdiagramofatemperaturecontrolsystemofanelectricfurnaceisshowninfigure1.Applyingbasicconceptsofcontroltheory,(20points)1)blockthediagramofthetemperaturecontrolsystem.(6points)2)Pointoutinput,plant,feedbackvariable,output,error,controller(s),actuator(s),andsensorofthesystem.Pleaseshowthemonthediagram.(6points)3)Tellhowthetemperaturecontrolsystemwork.(8points)Figure1.答：1）和2）的解答如图所示。（给分标准：画错两个环节扣一分，包括节点和比较节点和6个方框。2）中8个量，错一个扣1分。）3)假设电炉炉温低于给定的炉温，给定电压ui，经过Ri分压获得给定电压ug，其对应希望的电炉炉温（假定是300ºC），经过热电偶检测电炉内实际的炉温（假定是285ºC）并变换为电压值，反馈到输入端与给定电压ug比较获得炉温对应电压的偏差Δu，此时Δu〉0，经过电压放大和功率放大，得到使可逆电机旋转的电压ua，经过减速装置驱动调压器触头使其向上滑动，提高电炉内电加热器两端的电压，从而使炉内温度升高，当炉内温度达到300ºC时，电炉内电加热器停止加热。反之亦然。（给分标准：错两个环节叙述扣一分。）θºHeaterVoltageamplifierK1~220VVoltageregulatoruguf+--++--ReducerReversiblemotoruiThermometerRiΔuPoweramplifierK2学院班级学号姓名------------------------------------装-------------------------------------------------------------------订--------------------------------------线------------------2-DesiredTemperatureθdºCFeedbackTemperatureθfºCRiuiugufΔuVoltageamplifierK1PoweramplifierK2ReversiblemotorReducerVoltageregulatorHeaterActualTemperatureθ0ºCThermometerControllerActuatorSensorInputOutputErrorFeedbackvariablePlant-3-2.ObtainthetransferfunctionC(s)/R(s)oftheop-ampcircuitshowninfigure2,anddeterminetheoutputsteady-statevaluecss(t)andthesteady-stateerroress(t).Assumethat1,0.1,()5sin5RMCFrtt(20points)Figure2答：222211()10.010.11CssRssCRsCRss(6points)22222110.1()0.010.1110.01(10.01)(0.1)jarctgj424(5)33.731313jarctg20sin533.7,013sscttt(10points)205sin5sin533.7,013ssssetrtctttt(4points)3.Considerthesystemshowninfigure3,(20points)Figure3-4-1)Writetheopen-looptransferfunctionofthesystem;(5points)2)Writetheclosed-looptransferfunctionofthetransfer;（5points）3)IftheMaximumovershoot(Mp)ofthesystemis16.3%,Peaktime(tp)is1s,DeterminethegainKandvelocity-feedbackconstantτ（5points）4)If)/(5.1)(sttr,determinethesteady-stateerroress.(5points)答：（1）)110(10)1(101)1(10)(ssKsssssKsG5points（2）2222210)110(10)(1)()(nnnssKssKsGsGs5points（3）由113.16212npoooote联立解出263.063.35.0n由（2）18.1363.31022nK，得出318.1K。5points（4）63.31263.01018.1311010)(lim0KssGKsv3points413.063.35.1vssKAe5points4.Considerthesystemshowninfigure4,determinetherangeofKforstability.(20points)Figure4答：由结构图，系统开环传递函数为：-5-)4()124()(232sssssKsG(4分)0244)(2345KKsKsssssD(3分)Routh：S5142KS414KKS3)1(4KK1KS2)1(4)1615(KKKK067.11516KS)1(41647322KKK933.0536.0KS0K0K使系统稳定的K值范围是：933.0536.0K。(13分)5.Considerthesystemwhichopen-looptransferfunctionis,(20points)1)Sketchtherootlociforthesystem.(5points)2)DeterminetherangeofgainKcorrespondingtounderdampedsystemforclosed–loopsystem.(5points)3)GivingK=1,determinetheclosed–looppolesofthesystem,andcalculatethedampingration,maximumovershootMpandsettlingtimets.(5points)4)GivingK=1,designacompensatortomakedampingration=0.5,undampednaturalfrequencyn=1rad/sec.CalculatethemaximumovershootMpandsettlingtimetsofcompensatedsystem.Determinewhatkindofthecompensatorisusedbyyou.(5points)答：0K)1()2()()(sssKsHsG-6-1)如图.2)计算分离点.N(s)D’(s)-N’(s)D(s)=0(s+2)(2s+1)-(s*s+s)=0s*s+4s+2=0s12=(-22,-22)或者(-3.41,-0.59)闭环特征方程:s*s+s+ks+2k=0s=-0.59时,k=172.041.159.059.0222ssss=-3.41时,k=83.541.141.341.3222sss0.172K5.83时处于欠阻尼状态3)k=1,闭环特征方程:s*s+2s+2=0,闭环极点是-1+j,-1-j.2,222nn;2,22n;%,5.4pM02.0,4.44.405.0,5.35.3nsnstt4)对消法.-7-闭环特征方程:s*s+as+s+k=0,2,122nna,41.0,2,5.0an%,5.16pM02.0,22.64.405.0,9.45.3nsnstt滞后网络。