控制系统的MATLAB仿真与设计课后答案.docx

1、控制系统的MATLAB仿真与设计课后答案控制系统的MATLAB仿真与设计 课后答案第二章lx=15 22 33 94 85 77 60xx(l 3 5)x (4: end)x (find(x70)2T=1 -2 3 -4 2 -3;n=length (T);TT=T,;for k=n-l：-l:0B(:,n-k)=TT. k;endBtest=vander(T)3A=zeros(2, 5);A(:)=-4:5L=abs(A)3islogical (L)X=A(L)4A=4,15, -45,10, 6; 56, 0,17, -45, 0find(A=10&Acq二商多项式为；cr二余多项式为；d

2、isp(cq, poly2str (q, s ), disp(cr, poly2str (r, s)6A=11 12 13;14 15 16;17 18 19;PA=poly(A)PPA=poly2str (PA, s)第三章y=abs(n);plot (n, y, r., MarkerSize*, 20)axis equalgrid onxlabel ( n)2x=0:pi/100:2*pi；y=2*exp(0. 5*x). *sin(2*pi*x);plot (x, y), grid on;3t=0:pi/50:2*pi；x=8*cos(t);y=4*sqrt (2) *sin(t);z=

3、-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;4theta=0:0.01:2*pi;rho=sin(2*theta).*cos(2*theta);polar(theta,rho, k );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

4、);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1for m=100:999m1=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) endendM文件:2function s,p=fcircle(r)s=pi*r*r;p=2*pi*r; 主程序： s,p=fcircle(10) 3y=0;n=100;for

5、 i=1:ny=y+1/i/i;endy4 M 文件：function f=factor(n)if ns=0;for i=1:5s=s+factor(i);ends5sum=0;i=1;while sumn=i-26 for 循环 M 文件：function k=jcsum(n)k=0;for i=0:nk=k+2Ai;end 主程序： jcsum(63)While循环M文件：function k=jcsum1(n)k=0;i=0;while ijcsum1(63) 第五章 1A=2,1,-5,1;1,-5,0,7;0,2,1,-1;1,6,-1,-4; b=13,-9,6,0;x=Ab2M文

6、件：function f=fxyz(u)x=u(1);y=u(2);z=u(3);f=x+y42./x/4+z42./y+2./z;主程序：U,fmi n=fmi nsearch( fxyz ,0.5,0.5,0.5)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, -* )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

7、.5:10;hi=0:10:60;temps=interp2(x,h,T,xi,hi, cubic );mesh(xi,hi,temps);第六章1syms xy=finverse(1/tan(x)2syms x yf=1/(1+xA2); g=s in (y);fg=compose(f,g)3syms xg=(exp(x)+x*sin(x)A(1/2);dg=diff(g)4F=int(int( x*exp(-x*y) ,x ), y )5syms xF=ztrans(x*exp(-x*10)6a=0 1;-2 -3;syms sinv(s*eye(2)-a);7f=solve( a*xA2

8、+b*x+c )8f=solve( x+y+z=1 , x-y+z=2 , 2*x-y-z=1 )9y=dsolve( D2y+2*Dy+2*y=0 ,y(0)=1 ,Dy(0)=0 )ezplot(y),grid on 10a=maple(simplify(sin(x)A2+cos(x)A2); )1 1 f=maple( laplace(exp(-3*t)*sin(t) ,t,s) ; )12syms t xF=sin(x*t+2*t); L=laplace(F) 第七章1第八章1-1h=tf(5,0,1,2,2)1-2s = tf( s );H = 5/(sH+2*s+2);H.inpu

9、tdelay =21-3h=tf(0.5,0,1,-0.5,0.5,0.1)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)3num=1,5; den=1,6,5,1; ts=0.1; sysc=tf(num,den);sysd=c2d(sysc,ts, tustin )4r1=1;r2=2;c1=3;c2=4;A,B,C,D=linmod( x84 );num,den=ss2tf(A,B,C,D);sys=tf(num,de

10、n)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( 系统完全能控 );elsedisp( 系统不完全能控 );end第九章1num=2,5,1;den=1,2,3;bode(num,den);grid on ;figure;nyquist(num,den);2num=5*1,5,6;den=1,6,10,8;step(num,den);grid on ;figure;impulse(num,den);grid on ;3kosi=0.7;wn=6;n um=w n2;de n=1,2*ko

11、si*w n,wn A2;step(num,den);grid on ;figure;impulse(num,den);grid on ;4M 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; 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)=rta

12、b(k,i+1)-alpha(k)*rtab(k+1,i+1);endif sum(abs(a3)=0a3=polyder(vec2);info=info, All elements in row , .int2str(k+2) are zeros; ;elseif abs(a3(1)den=1,2,8,12,20,16,16;rtab,info=routh(den)a=rtab(:,1)if all(a0)disp( 系统是稳定的 );elsedisp( 系统是不稳定的 );end5num=7*1,5;den=conv(1,0,0,conv(1,10,1,1);gm,pm,wg,wc=mar

13、gin(num,den)第十章1M 文件：function varargout=rg_lead(ng0,dg0,s1)if nargout=1ngv=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=2ngv=polyval(ng0,s1); dgv=polyval(dg0,s1);g=ngv/dgv; theta=angle(g); phi=angle(s1);if the

14、ta0phi_c=pi-theta;endif theta0;phi_c=-thetaendtheta_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 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

15、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2M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bet

16、a=k/KK;kosi1,wn1=s2kw(s1);zc=-w n1*si n(a*pi/180)/si n(pi-ata n( sqrt(1-kosi1A2)/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=1ng0=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

17、=feedback(g0c,1);step(b1, r- ,b2, b );grid on3M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=-w n1*si n(a*pi/180)/si n(pi-ata n( sqrt(1-kosi1A2)/kosi1)-(a*pi/180); %利用正弦定理pc=beta*zc; ngc=beta*1

18、,-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);figure,step(b1, r- ,b2, b );grid on4M文件：function ngc,dgc=lead4(ng0,dg0,KK,Pm,w)mu,pu

19、=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), ngc=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,

20、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(magwb=w(a(1) max(mag) b=find(mag=max(mag) wr=w(b)5ngc,dgc=fg_lead_pm(ng0,dg0,Pm,w)%计算原系统的对数频率响应数M

21、文件： function mu,pu=bode(ng0,dg0,w);据%求取原系统的相角裕度和剪切%计算控制器提供的最大超前角%将最大超前角转换为弧度单位%+算a值%系统的对数幅值%w处的控制器对数幅值%差值求取wm认为wmr wc%+算Tgm,pm,wcg,wcp=margin(mu,pu,w); 频率alf=ceil(Pm-pm+5);度，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);ngc=a

22、*T,1; dgc=T,1; 主程序：KK=40; Pm=50;ng0= KK *1; dg0=conv(1,0,conv(1,1,1,4); g0=tf(ng0,dg0) ;w=logspace(-2,4); ngc,dgc=fg_lead_pm(ng0,dg0,Pm,w) gc=tf(ngc,dgc),g0c=tf(g0*gc);on,b1=feedback(g0,1); b2=feedback(g0c,1); step(b1, r- , b2, b ); grid on figure, bode(g0, r- ,g0c, b ,w), grid gm,pm,wcg,wcp=margin(g0c), Km=20*log10(gm)