自控原理习题.docx

习题一 1.Thedifferentialequationofasystemshownbelow, trytoestablishthedynamicstructurediagramof thesystemanddeterminethetransferfunction Y(s)/R(s),Y(s)/N1(s),Y(s)/N2(s). x1(t) r(t)y(t)n1(t) x2(t) 3x1(t) x3(t) x2(t)x5(t) 2dx4(t) x(t) dt 3 x5(t) x4(t)n2(t) 10x5(t) d2y(t) dy(t) dt2 dt 2.AFeedbackcontrolsystemhasthestructure showninfigure2.DeterminetheK1andK2sothat theunitstepresponsey(t)hasTp=and=2%. R(s) -  K1Y(s) s(s+1) K2s+1 Figure2 theinputsignalofthesystemisr(t)1(t)t, themeasuredoutputresponse 1 for y(t)(t0.9) 0.9e10t. (1) Determine thesystemtransfer function Y(s). R(s) (2) For aunit step inputandaunit ramp input ,calculate the steady-state error respectively. 4.Anegativefeedbacksystemhasalooptransfer function K 2. GH(s) s(s2) (1)Using theRouth-Hurwitzcriterion, findthe valueofthegainKwhentheclosed-loopsystemhastwopolesontheimaginaryaxis. FindthevalueofthegainKwhens=-3and otherrootsofthecharacteristicequation. unityfeedbacksystemhasaplant K(s 1) G(s) (s1)2 (1)Sketch therootlocus of theclosed-loopsystem. (2)DeterminetherangeofKforstability. (3)FindthegainKatthebreakawaypoint. amplitude frequency characteristic curveof 2 minimumphasesystemsshownbelow,writeoutthe systemtransferfunctionrespectively. L(w)dBL(w)dB -20dB/dec -20dB/dec 12 -40dB/dec 0 w 0 400 w 1 10 4 200 (a) (b) -40dB/dec L(w)dB L(w)dB -20dB/dec -40dB/dec -40dB/dec 10 -20dB/dec 0 0.1 0.2 w0 0.4 0.05 w 0.025 -20dB/dec -40dB/dec -40dB/dec (d) (c) 7.Aunityfeedbackcontrolsystemhasaplant G(s) 10(s 1) s s s( 1)( 1) 30 PlottheBodediagramofG(s). DeterminethephasemarginPMandgainmarginGM. PlotthepolarplotandMarkGM,PMonthethismap. 3 习题二 Aunitynegativefeedbackcontrolsystemhastheplant G(s)  K s(s2K) Determinethepercentovershootduetoaunitstepinput. ForwhatrangeofKisthesettlingtimelessthan1 second 2.Acontrolsystemisshowninfigure2. (1)whenr(t)=tandn(t)=t,determineallsteady-stateerrorofthesystem. (2)whenr(t)=1(t)andn(t)=0,determinetheandTs. Figure2 Acontrolsystemshowninfigurecontrolleristheproportionalcontroller,Gc(s)=Kp.