控制系统的Matlab仿真与设计课后答案.doc

MATLAB课后习题答案2.1x=15 22 33 94 85 77 60x(6)x(1 3 5)x(4:end)x(find(x70)2.3A=zeros(2,5);A(:)=-4:5L=abs(A)3islogical(L)X=A(L)2.4A=4,15,-45,10,6;56,0,17,-45,0find(A=10&A=20)2.5p1=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),disp(cr,poly2str(r,s)2.6A=11 12 13;14 15 16;17 18 19;PA=poly(A) PPA=poly2str(PA,s) 3.1n=(-10:10);y=abs(n);plot(n,y,r.,MarkerSize,20)axis equalgrid onxlabel(n)3.2x=0:pi/100:2*pi;y=2*exp(-0.5*x).*sin(2*pi*x);plot(x,y),grid on;3.3t=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(X),ylable(Y),zlable(Z);grid;3.4theta=0:0.01:2*pi;rho=sin(2*theta).*cos(2*theta);polar(theta,rho,k);3.5x,y,z=sphere(20);z1=z;z1(:,1:4)=NaN;c1=ones(size(z1);surf(3*x,3*y,3*z1,c1);hold onz2=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 onhold off第四章function f=factor(n)if n=1 f=1;else f=factor(n-1)*n;endfunctions,p=fcircle(r)s=pi*r*r;p=2*pi*r;function k=jcsum1(n)k=0;i=0;while i=n k=k+2i; i=i+1;endfunction k=jcsum(n)k=0;for i=0:n k=k+2i;end4.1for 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) endend4.2s,p=fcircle(10)4.3y=0;n=100;for i=1:n y=y+1/i/i;endy4.4s=0;for i=1:5 s=s+factor(i);ends4.5sum=0;i=1;while sum2000 sum=sum+i; i=i+1;end;n=i-24.6jcsum(63)jcsum1(63)4.1for 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) endend4.3y=0;n=100;for i=1:n y=y+1/i/i;endy4.4s=0;for i=1:5 s=s+factor(i);ends4.5sum=0;i=1;while sum2000 sum=sum+i; i=i+1;end;n=i-24.6i=0;k=0;while i=63 k=k+2i; i=i+1;endkii=0;k=0;for i=0:63 k=k+2i;endik第五章function f=fxyz(u)x=u(1);y=u(2);z=u(3);f=x+y.2./x/4+z.2./y+2./z;5.1A=2,1,-5,1;1,-5,0,7;0,2,1,-1;1,6,-1,-4;b=13,-9,6,0;x=Ab5.2U,fmin=fminsearch(fxyz,0.5,0.5,0.5)5.3X=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,-*)5.4x=0:2.5:10;h=0:30:60;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);5.1A=2,1,-5,1;1,-5,0,7;0,2,1,-1;1,6,-1,-4;b=13,-9,6,0;x=Ab5.3X=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,-*)6.1syms xy=finverse(1/tan(x)6.2syms x yf=1/(1+x2); g=sin(y);fg=compose(f,g)6.3syms xg=(exp(x)+x*sin(x)(1/2);dg=diff(g)6.4F=int(int(x*exp(-x*y),x),y)6.5syms xF=ztrans(x*exp(-x*10)6.6a=0 1;-2 -3;syms sinv(s*eye(2)-a);6.7 f=solve(a*x2+b*x+c) 6.8 f=solve(x+y+z=1,x-y+z=2,2*x-y-z=1)6.9y=dsolve(D2y+2*Dy+2*y=0,y(0)=1,Dy(0)=0)ezplot(y),grid on 6.10a=maple(simplify(sin(x)2+cos(x)2);)6.11f=maple(laplace(exp(-3*t)*sin(t),t,s);)6.12 syms t x F=sin(x*t+2*t); L=laplace(F)第七章function sys,x0,str,ts=ww(t,x,u,flag)%SA=0,1;-0.4,-0.2;B=0;0.2;C=1,0;D=0;switch flag,case 0, sys,x0,str,ts=mdlInitializeSizes(A,B,C,D);case 1, sys=mdlDerivatives(t,x,u,A,B,C,D);case 2, sys=mdlUpdate(t,x,u);case 3, sys=mdlOutputs(t,x,u,A,B,C,D);case 4, sys=mdlGetTimeOfNextVarHit(t,x,u);case 9, sys=mdlTerminate(t,x,u);otherwise error(Unhandled flag = ,num2str(flag);end%=function sys,x0,str,ts=mdlInitializeSizes(A,B,C,D)sizes = simsizes;sizes.NumContStates = 2;sizes.NumDiscStates = 0;sizes.NumOutputs = 1;sizes.NumInputs = 1;sizes.DirFeedthrough = 1;sizes.NumSampleTimes = 1; sys = simsizes(sizes);x0 = 0;0;str = ;ts = 0 0; %=function sys=mdlDerivatives(t,x,u,A,B,C,D)sys = A*x+B*u;%=function sys=mdlUpdate(t,x,u)sys = ;%=function sys=mdlOutputs(t,x,u,A,B,C,D)sys = C*x+D*u;%=function sys=mdlGetTimeOfNextVarHit(t,x,u) sampleTime = 1; sys = t + sampleTime;%=function sys=mdlTerminate(t,x,u)sys = ;7.17.27.37.47.57.67.7第八章8.1num=5; den=1,2,2;sys=tf(num,den) 8.1.2s = tf(s);H = 5/(s2+2*s+2) ; H.inputdelay =28.1.3h=tf(0.5,0,1,-0.5,0.5,0.1)8.2num=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=tf2ss(num,den);ss(A,B,C,D)8.3 num=1,5; den=1,6,5,1; ts=0.1; sysc=tf(num,den); sysd=c2d(sysc,ts,tustin) 8.4.08.4.1%,8,r1=1;r2=2;c1=3;c2=4;G1=r1;G2=tf(1,c1,0);G3=1;%,1G4=-1;G5=1/r2;G6=tf(1,c2,0);G7=-1;G8=-1;%G=append(G1,G2,G3,G4,G5,G6,G7,G8)%Q=1 4 0 %14 2 1 7 %21,7 3 2 0 4 2 0 5 3 8 6 5 0 7 5 0 8 6 0;%inputs=1;outputs=6;%sys=connect(G,Q,inputs,outputs)8.4.2r1=1;r2=2;c1=3;c2=4;A,B,C,D=linmod(x84);num,den=ss2tf(A,B,C,D);sys=tf(num,den)8.5A=1,1,0;0,1,0;0,0,2;B=0,0;1,0;0,-2;n=size(A)Tc=ctrb(A,B);if n=rank(Tc) disp();else disp();end第九章function rtab,info=routh(den)info=; vec1=den(1:2:length(den); nrT=length(vec1);vec2=den(2:2:length(den)-1); rtab=vec1; vec2, 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)0) disp(); else disp(); end9.5num=7*1,5;den=conv(1,0,0,conv(1,10,1,1);gm,pm,wg,wc=margin(num,den)9.1 sys=tf(2,5,1,1,2,3) Transfer function:2 s2 + 5 s + 1- s2 + 2 s + 3 rlocus(sys) nyquist(sys) bode(sys)9.2 G=tf(conv(5,1,5,6),1,6,10,8); step(G) impulse(G)sys=tf( 5,25,30,1,6,10,8); step(sys) impulse(sys)9.4 GH=tf(conv(7,1,5),conv(1,0,0,conv(1,10,1,1); Gm,Pm,Wcg,Wcp=margin(GH)Gm = 0Pm = -47.2870Wcg = 0Wcp =1.4354 GH=tf(conv(7,1,5),conv(1,0,0,conv(1,10,1,1); Gm,Pm,Wcg,Wcp=margin(GH)GH_close=feedback(GH,1)step(GH_close),grid onGm = 0Pm = -47.2870Wcg = 0Wcp =1.4354第十章function s=bpts2s(bp,ts,delta)kosi=sqrt(1-1./(1+(1./pi).*log(1./bp).2);wn=-log(delta.*sqrt(1-kosi.2)/(kosi.*ts);s=-kosi.*wn+j.*wn.*sqrt(1-kosi.2);function ngc,dgc=fa_lead(ng0,dg0,Pm,wc,w)ngv=polyval(ng0,j*wc); dgv=polyval(dg0,j*wc); g=ngv/dgv;thetag=angle(g); mg=abs(g); thetar=Pm*pi/180;tz=(1+mg*cos(thetar-thetag)/(-wc*mg*sin(thetar-thetag);tp=(cos(thetar-thetag)+mg)/(wc*sin(thetar-thetag);ngc=tz,1;dgc=tp,1;function ngc,dgc=fg_lag_pm(ng0,dg0,w,Pm)mu,pu=bode(ng0,dg0,w); wgc=spline(pu,w,Pm+5-180); %ngv=polyval(ng0,j*wgc); dgv=polyval(dg0,j*wgc); g=ngv/dgv;alph=abs(1/g);T=10/alph*wgc,ngc=alph*T,1; dgc=T,1;function ngc,dgc=fg_lag_wc(ng0,dg0,w,wc)ngv=polyval(ng0,j*wc);dgv=polyval(dg0,j*wc); g=ngv/dgv;alph=abs(1/g); T=10/(alph*wc);ngc=alph*T,1;dgc=T,1;function ngc,dgc=fg_lead_pd(ng0,dg0,wc)ngv=polyval(ng0,j*wc); dgv=polyval(dg0,j*wc);g=ngv/dgv; mg0=abs(g); t=sqrt(1/mg0)2-1)/(wc2); %ngc=t,1;dgc=1; %Gc(s)=1+Tsfunction ngc,dgc=fg_lead_pm(ng0,dg0,Pm,w)mu,pu=bode(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); %adbmu=20*log10(mu); %mm=-10*log10(a); %wmwgc=spline(dbmu,w,mm); %wmwmwc T=1/(wgc*sqrt(a); %Tngc=a*T,1; dgc=T,1;function ngc,dgc=fg_lead_pm_wc(ng0,dg0,Pm,wc,w)mu,pu=bode(ng0,dg0,w);ngv=polyval(ng0,j*wc);dgv=polyval(dg0,j*wc);g=ngv/dgv; %G0(jwc) theta=180*angle(g)/pi; %alf=ceil(Pm-(theta+180)+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);function s=kw2s(kosi,wn)s=-kosi.*wn+j*wn.*sqrt(1-kosi.2);10.1ng0=1; dg0=10000*1 0 -1.1772; g0=tf(ng0,dg0); % s=kw2s(0.7,0.5) % ngc=rg_lead(ng0,dg0,s); gc=tf(ngc,1) g0c=tf(g0*gc); rlocus(g0,g0c); b1=feedback(g0,1); % b2=feedback(g0c,1); % figure,step(b1,r-,b2,b); grid on %102KK=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(g0c,1); step(b1,r-,b2,b);grid on103KK=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); figure,step(b1,r-,b2,b);grid on104ng0=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 offgm,pm,wcg,wcp=margin(g0c) Kg=20*log10(gm)g1=feedback(g0c,1);bode(g1),grid on,mag,phase,w=bode(g1);a=find(mag0 phi_c=pi-theta; end if theta0; 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 theta0 kc=-kc end varargout1=kc*nk;else error();endfunction bp,ts=s2bpts(s,delta)kosi,wn=s2kw(s);bp=exp(-kosi.*pi./sqrt(1-kosi.2);ts=-1./(kosi.*wn)*log(delta.*sqrt(1-kosi.2);function kosi,wn=s2kw(s)kosi=1./sqrt(1+(imag(s)/real(s).2);wn=-real(s)./kosi;%wnwnkosiiwn=(wn=1 tr=t(i); break; endend;for i=1:length(y) if y(i)=(1+delta)*yss ts=t(i); endend第十一章11.1a=0 1 0; 0 0 1;-1 -5 -6;b=0 0 1;p=-2+4j;-2-4j;-10;K=acker(a,b,p)eig(a-b*K)11.2a=0 1 0; 0 0 1;-6 -11 -6;b=1,0,0;p=-2+2*sqrt(3)*j;-2-2*sqrt(3)*j;-10;K=acker(a,b,p)eig(a-b*K)11.6A=-1 0 0;0 -2 -3;0 0 -3;B=1 0 ;2 3 ;-3 -3;C=1 0 0;1 1 1 ;G,K,L=decoupling(A,B,C)11.8A=0 20.6; 1 0;b=0 1;c=0 1;d=0;G=ss(A,b,c,d);Q=diag(1,0,0,0,0);R=1;p=-1.8+2.4j;-1.8-2.4j; k,P=lqr(A,b,Q,R);l=(acker(A,c,p)Gc=-reg(G,k,l);zpk(Gc),eig(Gc.a),t=0:0.05:2;G_1=feedback(G*Gc,1);a1=eig(G_1.a),y_1=step(G_1,t);第十二章function t,xx=diffstate(G,H,x0,u0,N,T)xk=x0;u=u0;t=0for k=1:N xk=G*xk+H*u; x(:,k)=xk; t=t,k*T;end;xx=x0,x;12.1function sys=M601(t,x)u=1;sys=x(2);x(3);-800*x(1)-80*x(2)-24*x(3)+u;function t,y=ode4(A,B,C,D,x0,h,r,v,t0,tf)Ab=A-B*v*C;B=B;C=C;x=x0;y=0;t=t0;N=round(tf-t0)/h);for i=1:N k1=Ab*x+B*r; k2=A