控制系统的MATLAB仿真与设计课后答案

1、第二章1>>x=15 22 33 94 85 77 60>>x(6)>>x(1 3 5)>>x(4:end)>>x(find(x>70)2>>T=1 -2 3 -4 2 -3 ;>>n=length(T); >>TT=T' >>for k=n-1:-1:0 >>B(:,n-k)=TT.k; >>end >>B >>test=vander(T) 3>>A=zeros(2,5); >>A(:)=-4:5 &

2、gt;>L=abs(A)>3 >>islogical(L) >>X=A(L) 4>>A=4,15,-45,10,6;56,0,17,-45,0>>find(A>=10&A<=20)5>>p1=conv(1,0,2,conv(1,4,1,1); >>p2=1 0 1 1; >>q,r=deconv(p1,p2);>>cq='商多项式为 ' cr='余多项式为 '>>disp(cq,poly2str(q,'s')

3、,disp(cr,poly2str(r,'s') 6>>A=11 12 13;14 15 16;17 18 19;>>PA=poly(A) >>PPA=poly2str(PA,'s') 第三章1>>n=(-10:10)'>>y=abs(n);>>plot(n,y,'r.','MarkerSize',20)>>axis equal>>grid on>>xlabel('n')2>>x=0:pi

4、/100:2*pi;>>y=2*exp(-0.5*x).*sin(2*pi*x);>>plot(x,y),grid on;3>>t=0:pi/50:2*pi;>>x=8*cos(t);>>y=4*sqrt(2)*sin(t);>>z=-4*sqrt(2)*sin(t);>>plot3(x,y,z,'p');>>title('Line in 3-D Space');>>text(0,0,0,'origin');>>xlabel(&

5、#39;X'),ylable('Y'),zlable('Z');grid;4>>theta=0:0.01:2*pi;>>rho=sin(2*theta).*cos(2*theta);>>polar(theta,rho,'k');5>>x,y,z=sphere(20);>>z1=z;>>z1(:,1:4)=NaN;>>c1=ones(size(z1);>>surf(3*x,3*y,3*z1,c1);>>hold on>>z

6、2=z;>>c2=2*ones(size(z2);>>c2(:,1:4)=3*ones(size(c2(:,1:4);>>surf(1.5*x,1.5*y,1.5*z2,c2);>>colormap(0,1,0;0.5,0,0;1,0,0);>>grid on>>hold off第四章1>>for m=100:999 m1=fix(m/100); m2=rem(fix(m/10),10); m3=rem(m,10); if m=m1*m1*m1+m2*m2*m2+m3*m3*m3 disp(m) endend2

7、 M文件：functions,p=fcircle(r)s=pi*r*r;p=2*pi*r;主程序：s,p=fcircle(10)3>>y=0;n=100;for i=1:n y=y+1/i/i;end>>y4 M文件：function f=factor(n)if n<=1 f=1;else f=factor(n-1)*n;end主程序：>>s=0;for i=1:5 s=s+factor(i);end>>s5>>sum=0;i=1;while sum<2000 sum=sum+i; i=i+1;end;>>n=

8、i-26 for循环M文件：function k=jcsum(n)k=0;for i=0:n k=k+2i;end主程序：>>jcsum(63) While循环M文件：function k=jcsum1(n)k=0;i=0;while i<=n k=k+2i; i=i+1;end主程序：>>jcsum1(63)第五章1>>A=2,1,-5,1;1,-5,0,7;0,2,1,-1;1,6,-1,-4;>>b=13,-9,6,0'>>x=Ab2 M文件：function f=fxyz(u)x=u(1);y=u(2);z=u(

9、3);f=x+y.2./x/4+z.2./y+2./z;主程序：U,fmin=fminsearch('fxyz',0.5,0.5,0.5)3>>X=linspace(0,2*pi,50);>>Y=sin(X);>>P=polyfit(X,Y,3)>>AX=linspace(0,2*pi,50);>>Y=sin(X);>>Y1=polyval(P,X)>>plot(X,Y,':O',X,Y1,'-*')4>>x=0:2.5:10;>>h=0:

10、30:60'>>T=95,14,0,0,0;88,48,32,12,6;67,64,54,48,41;>>xi=0:0.5:10;>>hi=0:10:60'>>temps=interp2(x,h,T,xi,hi,'cubic');>>mesh(xi,hi,temps);第六章1>>syms x>>y=finverse(1/tan(x)2>>syms x y>>f=1/(1+x2); g=sin(y);>>fg=compose(f,g)3>

11、>syms x>>g=(exp(x)+x*sin(x)(1/2);>>dg=diff(g)4>>F=int(int('x*exp(-x*y)','x'),'y')5>>syms x>>F=ztrans(x*exp(-x*10)6>>a=0 1;-2 -3;>>syms s>>inv(s*eye(2)-a);7>>f=solve('a*x2+b*x+c') 8>>f=solve('x+y+z=1

12、9;,'x-y+z=2','2*x-y-z=1')9>>y=dsolve('D2y+2*Dy+2*y=0','y(0)=1','Dy(0)=0')>>ezplot(y),grid on 10>>a=maple('simplify(sin(x)2+cos(x)2);')11>>f=maple('laplace(exp(-3*t)*sin(t),t,s);')12>>syms t x >>F=sin(x*t+2*t)

13、; >>L=laplace(F)第七章1234567第八章1-1>>h=tf(5,0,1,2,2)1-2>>s = tf('s');>>H = 5/(s2+2*s+2) ; >>H.inputdelay =21-3>>h=tf(0.5,0,1,-0.5,0.5,0.1)2>>num=2*1,0.5;den=1,0.2,1.01;>>sys=tf(num,den)>>z,p,k=tf2zp(num,den);>>zpk(z,p,k)>>A,B,C,D

14、=tf2ss(num,den);>>ss(A,B,C,D)3 >>num=1,5; den=1,6,5,1; ts=0.1; >>sysc=tf(num,den); >>sysd=c2d(sysc,ts,'tustin') 4>>r1=1;r2=2;c1=3;c2=4;>>A,B,C,D=linmod('x84');>>num,den=ss2tf(A,B,C,D);>>sys=tf(num,den)5>>A=1,1,0;0,1,0;0,0,2;B=0,0;

15、1,0;0,-2;>>n=size(A)>>Tc=ctrb(A,B);if n=rank(Tc) disp('系统完全能控');else disp('系统不完全能控');end第九章1>>num=2,5,1;den=1,2,3;>>bode(num,den);grid on ;>>figure;>>nyquist(num,den);2>>num=5*1,5,6;den=1,6,10,8;>>step(num,den);grid on ;>>figure;&

16、gt;>impulse(num,den);grid on ;3>>kosi=0.7;wn=6;>>num=wn2;den=1,2*kosi*wn,wn2;>>step(num,den);grid on ;>>figure;>>impulse(num,den);grid on ;4 M文件：function rtab,info=routh(den)info=; vec1=den(1:2:length(den); nrT=length(vec1);vec2=den(2:2:length(den)-1); rtab=vec1; vec

17、2, zeros(1,nrT-length(vec2);for k=1:length(den)-2, alpha(k)=vec1(1)/vec2(1); for i=1:length(vec2), a3(i)=rtab(k,i+1)-alpha(k)*rtab(k+1,i+1); end if sum(abs(a3)=0 a3=polyder(vec2); info=info,'All elements in row ',. int2str(k+2) ' are zeros;' elseif abs(a3(1)<eps a3(1)=1e-6; info=i

18、nfo,'Replaced first element;' end rtab=rtab; a3, zeros(1,nrT-length(a3); vec1=vec2; vec2=a3;end主程序：>>den=1,2,8,12,20,16,16;>>rtab,info=routh(den) >>a=rtab(:,1) if all(a>0) disp('系统是稳定的'); else disp('系统是不稳定的'); end5>>num=7*1,5;den=conv(1,0,0,conv(1,1

19、0,1,1);>>gm,pm,wg,wc=margin(num,den)第十章1 M文件：function varargout=rg_lead(ng0,dg0,s1)if nargout=1 ngv=polyval(ng0,s1); dgv=polyval(dg0,s1); g=ngv/dgv; thetal=pi-angle(g); zc=real(s1)-imag(s1)/tan(thetal); t=-1/zc; varargout1=t,1;elseif nargout=2 ngv=polyval(ng0,s1); dgv=polyval(dg0,s1); g=ngv/dg

20、v; theta=angle(g); phi=angle(s1); if theta>0 phi_c=pi-theta; end if theta<0; phi_c=-theta end theta_z=(phi+phi_c)/2; theta_p=(phi-phi_c)/2; z_c=real(s1)-imag(s1)/tan(theta_z); p_c=real(s1)-imag(s1)/tan(theta_p); nk=1 -z_c; varargout2=1 -p_c; kc=abs(p_c/z_c); if theta<0 kc=-kc end varargout1

21、=kc*nk;else error('输出变量数目不正确！');end主程序：>> ng0=1; dg0=10000*1 0 -1.1772;>>g0=tf(ng0,dg0); %满足开环增益的为校正系统的传递函数>>s=kw2s(0.7,0.5) %期望的闭环主导极点>>ngc=rg_lead(ng0,dg0,s); >>gc=tf(ngc,1)>>g0c=tf(g0*gc);>>rlocus(g0,g0c);>>b1=feedback(g0,1); %未校正系统的闭环传递函数&g

22、t;>b2=feedback(g0c,1); %校正后系统的闭环传递函数>>figure,step(b1,'r-',b2,'b'); grid on %绘2 M文件：function ngc,dgc,k=rg_lag(ng0,dg0,KK,s1,a)ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);g=dgv/ngv; k=abs(g); %期望主导极点处的根轨迹增益beta=k/KK;kosi1,wn1=s2kw(s1);zc=-wn1*sin(a*pi/180)/sin(pi-atan(sqrt(1-kosi1

23、2)/kosi1)-(a*pi/180); %利用正弦定理pc=beta*zc;ngc=beta*1,-zc;dgc=1,-pc;主程序：>>KK=20;s1=-2+i*sqrt(6);a=1 >>ng0=10;dg0=conv(1,0,1,4);>>g0=tf(ng0,dg0); >>ngc,dgc,k=rg_lag(ng0,dg0,KK,s1,a); >>gc=tf(ngc,dgc) >>g0c=tf(KK*g0*gc);>>b1=feedback(k*g0,1); >>b2=feedback(

24、g0c,1); >>step(b1,'r-',b2,'b');grid on3 M文件：function ngc,dgc,k=rg_lag(ng0,dg0,KK,s1,a)ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);g=dgv/ngv; k=abs(g); %期望主导极点处的根轨迹增益beta=k/KK;kosi1,wn1=s2kw(s1);zc=-wn1*sin(a*pi/180)/sin(pi-atan(sqrt(1-kosi12)/kosi1)-(a*pi/180); %利用正弦定理pc=beta*zc;ng

25、c=beta*1,-zc;dgc=1,-pc;主程序：>>KK=128;s1=-2+i*2*sqrt(3);a=2 >>ng0=10;dg0=conv(1,0,conv(1,2,1,8);>>g0=tf(ng0,dg0); >>ngc,dgc,k=rg_lag(ng0,dg0,KK,s1,a); >>gc=tf(ngc,dgc) >>g0c=tf(KK*g0*gc);>>rlocus(g0,g0c);>>b1=feedback(k*g0,1); >>b2=feedback(g0c,1);

26、 >>figure,step(b1,'r-',b2,'b');grid on4 M文件：function ngc,dgc=lead4(ng0,dg0,KK,Pm,w)mu,pu=bode(KK*ng0,dg0,w); gm,pm,wcg,wcp=margin(mu,pu,w);alf=ceil(Pm-pm+5); phi=(alf)*pi/180;a=(1+sin(phi)/(1-sin(phi), dbmu=20*log10(mu);mm=-10*log10(a);wgc=spline(dbmu,w,mm), T=1/(wgc*sqrt(a),ng

27、c=a*T,1; dgc=T,1;主程序：>>ng0=1;dg0=conv(1,0,0,1,5);>>g0=tf(ng0,dg0);>>w=logspace(-3,3);>>KK=1;Pm=50;>>ngc,dgc=lead4(ng0,dg0,KK,Pm,w);>>gc=tf(ngc,dgc);g0c=tf(KK*g0*gc);>>bode(KK*g0,w);hold on,bode(g0c,w);grid on,hold off>>gm,pm,wcg,wcp=margin(g0c) >>Kg=20*log10(gm)>>g1=feedback(g0c,1);>>bode(g1),grid on,>>mag,p