控制系统数字仿真与CAD实验答案.doc

程序及仿真结果1.1 G（s）= den=1,20,70,100,48;num=1,14,48,48;A,B,C,D=tf2ss(num,den)z,p,k=ss2zp(A,B,C,D)R,P,H=residue(num,den)A = -20 -70 -100 -48 1 0 0 0 0 1 0 0 0 0 1 0B = 1 0 0 0C = 1 14 48 48D = 0z = -9.4641 -2.5359 -2.0000p = -16.0051 -1.5269 + 0.9247i -1.5269 - 0.9247i -0.9412 k = 1.0000R = 0.3892 -0.0932 - 0.3754i -0.0932 + 0.3754i 0.7973 P = -16.0051 -1.5269 + 0.9247i -1.5269 - 0.9247i -0.9412 H = 1.2 =y=0 2 0 2 XA=2.25,-5,-1.25,-0.5;2.25,-4.25,-1.25,-0.25;0.25,-0.5,-1.25,-1;1.25,-1.75,-0.25,-0.75;B=4;2;2;0;C=0,2,0,2; num,den=ss2tf(A,B,C,D)z,p,k=ss2zp(A,B,C,D)R,P,H=residue(num,den)G=tf(num,den)num = 0 4.0000 14.0000 22.0000 15.0000den = 1.0000 4.0000 6.2500 5.2500 2.2500z = -1.0000 + 1.2247i -1.0000 - 1.2247i -1.5000 p = -0.5000 + 0.8660i -0.5000 - 0.8660i -1.5000 -1.5000 k = 4.0000R = 4.0000 -0.0000 0.0000 - 2.3094i 0.0000 + 2.3094iP = -1.5000 -1.5000 -0.5000 + 0.8660i -0.5000 - 0.8660iH = Transfer function: 4 s3 + 14 s2 + 22 s + 15-s4 + 4 s3 + 6.25 s2 + 5.25 s + 2.252已知元件的实验数据如下，拟合这一数据，并尝试给出其特性方程。 X 0.0100 1.0100 2.0100 3.0100 4.0100 Y 2.5437 7.8884 9.6242 11.6071 11.9727 X 5.0100 6.0100 7.0100 8.0100 9.0100 y 13.2189 14.2679 14.6134 15.4045 15.0805 x=0.01:1:9.01; y=2.5437 7.8884 9.6242 11.6071 11.9727 13.2189 14.2679 14.6134 15.4045 15.0805; p=polyfit(x,y,3); xi=0:0.01:9.01; yi=polyval(p,xi); plot(x,y,xi,yi) Grid 实验2的1分别用欧拉法、二阶龙格-库塔法、四阶龙格-库塔法求下面系统的输出响应y(t)在0t1上，h=0.1时的数值解。 要求保留4位小数，并将三种方法的结果与真解进行比较。2. 若为如何编程计算？第一题：程序h=0.1;disp(欧拉法求函数的数值解为);disp(y=);y=1;for t=0:h:1 m=y; disp(y); y=m-2*m*h;end运行结果为 欧拉法求函数的数值解为y= 1 0.8000 0.6400 0.5120 0.4096 0.3277 0.2621 0.2097 0.1678 0.1342 0.1074程序：h=0.1;disp(二阶龙格库塔法函数的数值解为);disp(y=);y=1;for t=0:h:1 disp(y); k1=-2*y; k2=-2*(y+k1*h); y=y+(k1+k2)*h/2;end运行结果： 二阶龙格库塔法函数的数值解为y= 1 0.8200 0.6724 0.5514 0.4521 0.3707 0.3040 0.2493 0.2044 0.1676 0.1374程序：h=0.1;disp(四阶龙格库塔法求解函数数值解为);disp(y=);y=1;for t=0:h:1 disp(y); k1=-2*y; k2=-2*(y+k1*h/2); k3=-2*(y+k2*h/2); k4=-2*(y+k3*h); y=y+(k1+2*k2+2*k3+k4)*h/6;end运行结果： 四阶龙格库塔法求解函数数值解为y= 1 0.8187 0.6703 0.5488 0.4493 0.3679 0.3012 0.2466 0.2019 0.1653 0.1353真解程序：h=0.1;disp(函数的离散时刻解为);disp(y=);y=1;for t=0:h:1 y=exp(-2*t); disp(y);end运行结果： 函数的离散时刻解为y= 1 0.8187 0.6703 0.5488 0.4493 0.3679 0.3012 0.2466 0.2019 0.1653 0.1353第二题：程序：h=0.1;disp(欧拉法求函数的数值解为);disp(y=);y=1;for t=0:h:1 m=y; disp(y); y=m+m*m*h;end运行结果： 欧拉法求函数的数值解为y= 1 1.1000 1.2210 1.3701 1.5578 1.8005 2.1246 2.5760 3.2397 4.2892 6.1289h=0.1;disp(二阶龙格库塔法函数的数值解为);disp(y=);y=1;for t=0:h:1 disp(y); k1=y*y; k2=(y+k1*h)2; y=y+(k1+k2)*h/2;end运行结果： 二阶龙格库塔法函数的数值解为y= 1 1.1105 1.2483 1.4248 1.6587 1.9833 2.4624 3.2364 4.6777 8.1288 22.2908程序：h=0.1;disp(四阶龙格库塔法求解函数数值解为);disp(y=);y=1;for t=0:h:1 disp(y); k1=y*y; k2=(y+k1*h/2)2; k3=(y+k2*h/2)2; k4=(y+k3*h)2; y=y+(k1+2*k2+2*k3+k4)*h/6;end运行结果： 四阶龙格库塔法求解函数数值解为y= 1 1.1111 1.2500 1.4286 1.6667 2.0000 2.4999 3.3328 4.9966 9.9291 81.9964真解程序：h=0.1;disp(函数的离散时刻解为);disp(y=);y=1;for t=0:h:0.99 y=(1-t)(-1); disp(y);end运行结果： 函数的离散时刻解为y= 1 1.1111 1.2500 1.4286 1.6667 2 2.5000 3.3333 5.0000 10.00001分别使用解微分方程方法、控制工具箱、Simulink求解具有如下闭环传递函数的系统的阶跃响应。微分：Num=10;den=1 8 36 40 10;A,B,C,D=tf2ss(num,den);t,x=ode45(wffc,0,8,0,0,0,0);y=10*x(:,4);plot(t,y);gridefunction dx=wffc(t,x)u=1;dx=-8*x(1)-36*x(2)-40*x(3)-10*x(4)+u;x(1);x(2);x(3);结果控制工具箱：num=10;den=1 8 36 40 10;sys=tf(num,den);step(sys);Grid结果2 某小功率随动系统动态结构如图所示，已知：， ，。若系统输入分别为，试用Simulink分析系统的输出分别如何？题目习题3-2设典型闭环结构控制系统如下图所示，当阶跃输入幅值R=20时，用面向系统结构图的数字仿真法sp3-1.m求取系统的输出响应。五实验要求：1列出复杂连接闭环系统的仿真程序框图；2列出MATLAB程序实现的主要程序，包括输入数据、形成闭环各系统阵、数值积分求解、以及输出结果。先建立sp3_1.m文件程序如下：b=b/a(1);a=a/a(1);A=a(2:n+1);A=rot90(rot90(eye(n-1,n);-fliplr(A);B=zeros(1,n-1),1;m1=length(b);C=fliplr(b),zeros(1,n-m1);Ab=A-B*C*V;X=X0;y=0;t=T0;N=round(Tf-T0)/h);for i=1:N K1=Ab*X+B*R; K2=Ab*(X+h*K1/2)+B*R; K3=Ab*(X+h*K2/2)+B*R; K4=Ab*(X+h*K3)+B*R;X=X+h*(K1+2*K2+2*K3+K4)/6; y=y,C*X; t=t,t(i)+h;end在命令窗口输入如下指令： a=0.016 0.864 3.27 3.42 1; b=30 25; X0=0 0 0 0; V=2; n=4; T0=0; Tf=10; R=20; h=0.05; sp3_1 t,y plot(t,y) title(四阶龙格法); xlabel(t); ylabel(y); grid输出结果如下：ans = 0 0 0.0500 0.2620 0.1000 2.1262 0.1500 5.1509 0.2000 8.7225 0.2500 12.1775 0.3000 14.9240 0.3500 16.5403 0.4000 16.8356 0.4500 15.8658 0.5000 13.9036 0.5500 11.3739 0.6000 8.7669 0.6500 6.5472 0.7000 5.0739 0.7500 4.5465 0.8000 4.9823 0.8500 6.2280 0.9000 8.0006 0.9500 9.9467 1.0000 11.7111 1.0500 12.9986 1.1000 13.6213 1.1500 13.5230 1.2000 12.7786 1.2500 11.5705 1.3000 10.1478 1.3500 8.7775 1.4000 7.6959 1.4500 7.0701 1.5000 6.9734 1.5500 7.3806 1.6000 8.1801 1.6500 9.2001 1.7000 10.2440 1.7500 11.1267 1.8000 11.7061 1.8500 11.9048 1.9000 11.7182 1.9500 11.2099 2.0000 10.4948 2.0500 9.7152 2.1000 9.0128 2.1500 8.5051 2.2000 8.2654 2.2500 8.3146 2.3000 8.6210 2.3500 9.1102 2.4000 9.6817 2.4500 10.2288 2.5000 10.6572 2.5500 10.9013 2.6000 10.9330 2.6500 10.7636 2.7000 10.4390 2.7500 10.0285 2.8000 9.6112 2.8500 9.2608 2.9000 9.0334 2.9500 8.9593 3.0000 9.0391 3.0500 9.2467 3.1000 9.5353 3.1500 9.8478 3.2000 10.1275 3.2500 10.3278 3.3000 10.4201 3.3500 10.3966 3.4000 10.2708 3.4500 10.0729 3.5000 9.8435 3.5500 9.6253 3.6000 9.4557 3.6500 9.3607 3.7000 9.3510 3.7500 9.4215 3.8000 9.5533 3.8500 9.7185 3.9000 9.8854 3.9500 10.0246 4.0000 10.1138 4.0500 10.1414 4.1000 10.1075 4.1500 10.0229 4.2000 9.9065 4.2500 9.7813 4.3000 9.6701 4.3500 9.5911 4.4000 9.5557 4.4500 9.5667 4.5000 9.6184 4.5500 9.6984 4.6000 9.7906 4.6500 9.8776 4.7000 9.9448 4.7500 9.9817 4.8000 9.9845 4.8500 9.9553 4.9000 9.9018 4.9500 9.8354 5.0000 9.7687 5.0500 9.7134 5.1000 9.6785 5.1500 9.6683 5.2000 9.6827 5.2500 9.7172 5.3000 9.7641 5.3500 9.8143 5.4000 9.8586 5.4500 9.8897 5.5000 9.9033 5.5500 9.8983 5.6000 9.8771 5.6500 9.8447 5.7000 9.8078 5.7500 9.7731 5.8000 9.7465 5.8500 9.7321 5.9000 9.7315 5.9500 9.7436 6.0000 9.7653 6.0500 9.7921 6.1000 9.8187 6.1500 9.8407 6.2000 9.8544 6.2500 9.8581 6.3000 9.8520 6.3500 9.8380 6.4000 9.8190 6.4500 9.7990 6.5000 9.7814 6.5500 9.7691 6.6000 9.7639 6.6500 9.7662 6.7000 9.7749 6.7500 9.7879 6.8000 9.8028 6.8500 9.8166 6.9000 9.8271 6.9500 9.8327 7.0000 9.8328 7.0500 9.8278 7.1000 9.8190 7.1500 9.8082 7.2000 9.7976 7.2500 9.7889 7.3000 9.7835 7.3500 9.7822 7.4000 9.7847 7.4500 9.7904 7.5000 9.7981 7.5500 9.8061 7.6000 9.8131 7.6500 9.8180 7.7000 9.8199 7.7500 9.8189 7.8000 9.8154 7.8500 9.8101 7.9000 9.8041 7.9500 9.7986 8.0000 9.7945 8.0500 9.7923 8.1000 9.7924 8.1500 9.7944 8.2000 9.7980 8.2500 9.8023 8.3000 9.8066 8.3500 9.8100 8.4000 9.8121 8.4500 9.8126 8.5000 9.8115 8.5500 9.8092 8.6000 9.8061 8.6500 9.8029 8.7000 9.8001 8.7500 9.7982 8.8000 9.7975 8.8500