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《控制系统仿真与CAD》实验课程报告一、实验教学目标与基本要求上机实验是本课程重要的实践教学环节。实验的目的不仅仅是验证理论知识，更重要的是通过上机加强学生的实验手段与实践技能，掌握应用MATLAB/Simulink求解控制问题的方法，培养学生分析问题、解决问题、应用知识的能力和创新精神，全面提高学生的综合素质。通过对MATLAB/Simulink进行求解，基本掌握常见控制问题的求解方法与命令调用，更深入地认识和了解MATLAB语言的强大的计算功能与其在控制领域的应用优势。上机实验最终以书面报告的形式提交，作为期末成绩的考核内容。二、题目及解答第一部分：MATLAB必备基础知识、控制系统模型与转换、线性控制系统的计算机辅助分析1.f=inline('[-x(2)-x(3);x(1)+a*x(2);b+(x(1)-c)*x(3)]','t','x','flag','a','b','c');[t,x]=ode45(f,[0,100],[0;0;0],[],0.2,0.2,5.7);plot3(x(:,1),x(:,2),x(:,3)),grid,figure,plot(x(:,1),x(:,2)),grid2.y=@(x)x(1)^2-2*x(1)+x(2);ff=optimset;ff.LargeScale='off';ff.TolFun=1e-30;ff.TolX=1e-15;ff.TolCon=1e-20;x0=[1;1;1];xm=[0;0;0];xM=[];A=[];B=[];Aeq=[];Beq=[];[x,f,c,d]=fmincon(y,x0,A,B,Aeq,Beq,xm,xM,@wzhfc1,ff)Warning:OptionsLargeScale='off'andAlgorithm='trust-region-reflective'conflict.IgnoringAlgorithmandrunningactive-setalgorithm.Toruntrust-region-reflective,setLargeScale='on'.Torunactive-setwithoutthiswarning,useAlgorithm='active-set'.Infminconat456Localminimumpossible.Constraintssatisfied.fminconstoppedbecausethesizeofthecurrentsearchdirectionislessthantwicetheselectedvalueofthestepsizetoleranceandconstraintsaresatisfiedtowithintheselectedvalueoftheconstrainttolerance.stoppingcriteriadetailsActiveinequalities(towithinoptions.TolCon=1e-20):lowerupperineqlinineqnonlin2x=1.000001.0000f=-1.0000c=4d=iterations:5funcCount:20lssteplength:1stepsize:3.9638e-26algorithm:'medium-scale:SQP,Quasi-Newton,line-search'firstorderopt:7.4506e-09constrviolation:0message:[1x766char]3.(a)s=tf('s');G=(s^3+4*s+2)/(s^3*(s^2+2)*((s^2+1)^3+2*s+5))G=s^3+4s+2------------------------------------------------------s^11+5s^9+9s^7+2s^6+12s^5+4s^4+12s^3Continuous-timetransferfunction.(b)z=tf('z',0.1);H=(z^2+0.568)/((z-1)*(z^2-0.2*z+0.99))H=z^2+0.568-----------------------------z^3-1.2z^2+1.19z-0.99Sampletime:0.1secondsDiscrete-timetransferfunction.4.A=[010;001;-15-4-13];B=[002]';C=[100];D=0;G=ss(A,B,C,D),Gs=tf(G),Gz=zpk(G)G=a=x1x2x3x1010x2001x3-15-4-13b=u1x10x20x32c=x1x2x3y1100d=u1y10Continuous-timestate-spacemodel.Gs=2-----------------------s^3+13s^2+4s+15Continuous-timetransferfunction.Gz=2---------------------------------(s+12.78)(s^2+0.2212s+1.174)Continuous-timezero/pole/gainmodel.5.设采样周期为0.01sz=tf('z',0.01);H=(z+2)/(z^2+z+0.16)H=z+2--------------z^2+z+0.16Sampletime:0.01secondsDiscrete-timetransferfunction.6.symsJKpKis;G=(s+1)/(J*s^2+2*s+5);Gc=(Kp*s+Ki)/s;GG=feedback(G*Gc,1)GG=((Ki+Kp*s)*(s+1))/(J*s^3+(Kp+2)*s^2+(Ki+Kp+5)*s+Ki)7.(a)s=tf('s');G=(211.87*s+317.64)/((s+20)*(s+94.34)*(s+0.1684));Gc=(169.6*s+400)/(s*(s+4));H=1/(0.01*s+1);GG=feedback(G*Gc,H),Gd=ss(GG),Gz=zpk(GG)GG=359.3s^3+3.732e04s^2+1.399e05s+127056----------------------------------------------------------------0.01s^6+2.185s^5+142.1s^4+2444s^3+4.389e04s^2+1.399e05s+127056Continuous-timetransferfunction.Gd=a=x1x2x3x4x5x6x1-218.5-111.1-29.83-16.74-6.671-3.029x212800000x30640000x40032000x5000800x6000020b=u1x14x20x30x40x50x60c=x1x2x3x4x5x6y1001.0973.5591.6680.7573d=u1y10Continuous-timestate-spacemodel.Gz=35933.152(s+100)(s+2.358)(s+1.499)----------------------------------------------------------------------(s^2+3.667s+3.501)(s^2+11.73s+339.1)(s^2+203.1s+1.07e04)Continuous-timezero/pole/gainmodel.(b)设采样周期为0.1sz=tf('z',0.1);G=(35786.7*z^2+108444*z^3)/((1+4*z)*(1+20*z)*(1+74.04*z));Gc=z/(1-z);H=z/(0.5-z);GG=feedback(G*Gc,H),Gd=ss(GG),Gz=zpk(GG)GG=-108444z^5+1.844e04z^4+1.789e04z^3----------------------------------------------------------------1.144e05z^5+2.876e04z^4+274.2z^3+782.4z^2+47.52z+0.5Sampletime:0.1secondsDiscrete-timetransferfunction.Gd=a=x1x2x3x4x5x1-0.2515-0.00959-0.1095-0.05318-0.01791x20.250000x300.25000x4000.12500x50000.031250b=u1x11x20x30x40x50c=x1x2x3x4x5y10.39960.63490.10380.050430.01698d=u1y1-0.9482Sampletime:0.1secondsDiscrete-timestate-spacemodel.Gz=-0.94821z^3(z-0.5)(z+0.33)----------------------------------------------------------(z+0.3035)(z+0.04438)(z+0.01355)(z^2-0.11z+0.02396)Sampletime:0.1secondsDiscrete-timezero/pole/gainmodel.8.s=tf('s');g1=1/(s+1);g2=s/(s^2+2);g3=1/s^2;g4=(4*s+2)/(s+1)^2;g5=50;g6=(s^2+2)/(s^3+14);G1=feedback(g1*g2,g4);G2=feedback(g3,g5);GG=3*feedback(G1*G2,g6)GG=3s^6+6s^5+3s^4+42s^3+84s^2+42s---------------------------------------------------------------------------s^10+3s^9+55s^8+175s^7+300s^6+1323s^5+2656s^4+3715s^3+7732s^2+5602s+1400Continuous-timetransferfunction.9.s=tf('s');T0=0.01;T1=0.1;T2=1;G=(s+1)^2*(s^2+2*s+400)/((s+5)^2*(s^2+3*s+100)*(s^2+3*s+2500));Gd1=c2d(G,T0),Gd2=c2d(G,T1),Gd3=c2d(G,T2),step(G),figure,step(Gd1),figure,step(Gd2),figure,step(Gd3)Gd1=4.716e-05z^5-0.0001396z^4+9.596e-05z^3+8.18e-05z^2-0.0001289z+4.355e-05----------------------------------------------------------------z^6-5.592z^5+13.26z^4-17.06z^3+12.58z^2-5.032z+0.8521Sampletime:0.01secondsDiscrete-timetransferfunction.Gd2=0.0003982z^5-0.0003919z^4-0.000336z^3+0.0007842z^2-0.000766z+0.0003214----------------------------------------------------------------z^6-2.644z^5+4.044z^4-3.94z^3+2.549z^2-1.056z+0.2019Sampletime:0.1seconds