控制系统的MATLAB仿真与设计课后答案.docx
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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
l»x=[15223394857760]
>>x⑹
»x([l35])
>>x(4:
end)
»x(find(x>70))
2»T=[1-23-42-3];
»n=length(T);
»TT=T,;
»fork=n-l:
-l:
0
»B(:
n-k)=TT."k;
»end
»B
>>test=vander(T)
3»A=zeros(2,5);
»A(:
)=-4:
5
»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»pl=conv([l,0,2],conv([l,4],[1,1]));
»p2=[lOil];
»[q,r]=deconv(pl,p2);
>>cq二'商多项式为’;cr二'余多项式为';
>>disp([cq,poly2str(q,'s')]),disp([cr,poly2str(r,'s')])
6»A=[111213;141516;171819];
»PA=poly(A)
»PPA=poly2str(PA,'s')
第三章
»y=abs(n);
»plot(n,y,'r.','MarkerSize*,20)
>>axisequal
>>gridon
>>xlabel('n')
2»x=0:
pi/100:
2*pi;
»y=2*exp(~0.5*x).*sin(2*pi*x);
»plot(x,y),gridon;
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('Linein3-DSpace');
>>text(0,0,0,'origin');
>>xlabel('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);
>>holdon
>>z2=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]);
>>gridon
>>holdoff
第四章
1>>form=100:
999
m1=fix(m/100);
m2=rem(fix(m/10),10);
m3=rem(m,10);
ifm==m1*m1*m1+m2*m2*m2+m3*m3*m3disp(m)end
end
M文件:
2
function[s,p]=fcircle(r)
s=pi*r*r;
p=2*pi*r;主程序:
[s,p]=fcircle(10)3>>y=0;n=100;
fori=1:
n
y=y+1/i/i;
end
>>y
4M文件:
functionf=factor(n)
ifn<=1
f=1;
else
f=factor(n-1)*n;
end主程序:
>>s=0;
fori=1:
5
s=s+factor(i);
end
>>s
5>>sum=0;i=1;
whilesum<2000
sum=sum+i;
i=i+1;
end;
>>n=i-2
6for循环M文件:
functionk=jcsum(n)
k=0;
fori=0:
n
k=k+2Ai;
end主程序:
>>jcsum(63)
While循环M文件:
functionk=jcsum1(n)
k=0;i=0;
whilei<=n
k=k+2Ai;
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=A\b
2M文件:
functionf=fxyz(u)
x=u
(1);y=u
(2);z=u(3);
f=x+y42./x/4+z42./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:
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>>symsx
>>y=finverse(1/tan(x))
2>>symsxy
>>f=1/(1+xA2);g=sin(y);
>>fg=compose(f,g)
3>>symsx
>>g=(exp(x)+x*sin(x))A(1/2);
>>dg=diff(g)
4>>F=int(int('x*exp(-x*y)','x'),'y')
5>>symsx
>>F=ztrans(x*exp(-x*10))
6>>a=[01;-2-3];
>>symss
>>inv(s*eye
(2)-a);
7>>f=solve('a*xA2+b*x+c')
8>>f=solve('x+y+z=1','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),gridon10>>a=maple('simplify(sin(x)A2+cos(x)A2);')
11>>f=maple('laplace(exp(-3*t)*sin(t),t,s);')
12>>symstx
>>F=sin(x*t+2*t);>>L=laplace(F)第七章
1
第八章
1-1>>h=tf([5,0],[1,2,2])
1-2>>s=tf('s');
>>H=[5/(sH+2*s+2)];
>>H.inputdelay=2
1-3>>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]=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;1,0;0,-2];
>>n=size(A)
>>Tc=ctrb(A,B);
ifn==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);gridon;
>>figure;
>>nyquist(num,den);
2>>num=5*[1,5,6];den=[1,6,10,8];
>>step(num,den);gridon;
>>figure;
>>impulse(num,den);gridon;
3>>kosi=0.7;wn=6;
>>num=wn^2;den=[1,2*kosi*wn,wnA2];
>>step(num,den);gridon;
>>figure;
>>impulse(num,den);gridon;
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))];
fork=1:
length(den)-2,
alpha(k)=vec1
(1)/vec2
(1);
fori=1:
length(vec2),
a3(i)=rtab(k,i+1)-alpha(k)*rtab(k+1,i+1);
end
ifsum(abs(a3))==0
a3=polyder(vec2);
info=[info,'Allelementsinrow',...
int2str(k+2)'arezeros;'];
elseifabs(a3
(1))a3
(1)=1e-6;
info=[info,'Replacedfirstelement;'];
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)
ifall(a>0)
disp('系统是稳定的');
else
disp('系统是不稳定的');
end
5>>num=7*[1,5];den=conv([1,0,0],conv([1,10],[1,1]));
>>[gm,pm,wg,wc]=margin(num,den)
第十章
1M文件:
functionvarargout=rg_lead(ng0,dg0,s1)
ifnargout==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;
varargout{1}=[t,1];
elseifnargout==2
ngv=polyval(ng0,s1);dgv=polyval(dg0,s1);
g=ngv/dgv;theta=angle(g);phi=angle(s1);
iftheta>0
phi_c=pi-theta;
end
iftheta<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];varargout{2}=[1-p_c];kc=abs(p_c/z_c);
iftheta<0
kc=-kc
end
varargout{1}=kc*nk;
else
error('输出变量数目不正确!
');
end
主程序:
>>ng0=[1];dg0=10000*[10-1.1772];
>>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
>>b2=feedback(g0c,1);%校正后系统的闭环传递函数
>>figure,step(b1,'r--',b2,'b');gridon%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
beta=k/KK;
[kosi1,wn1]=s2kw(s1);
zc=-wn1*sin(a*pi/180)/sin(pi-atan(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=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');gridon
3M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-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=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');gridon
4M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)),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,dg0,KK,Pm,w);
>>gc=tf(ngc,dgc);g0c=tf(KK*g0*gc);
>>bode(KK*g0,w);holdon,bode(g0c,w);gridon,holdoff
>>[gm,pm,wcg,wcp]=margin(g0c)>>Kg=20*log10(gm)>>g1=feedback(g0c,1);
>>bode(g1),gridon,>>[mag,phase,w]=bode(g1);>>a=find(mag<=0.707*mag
(1));>>wb=w(a
(1))>>max(mag)>>b=find(mag==max(mag))>>wr=w(b)
5
[ngc,dgc]=fg_lead_pm(ng0,dg0,Pm,w)
%计算原系统的对数频率响应数
M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wmrwc
%+算T
[gm,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*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');gridon>>figure,bode(g0,'r--',g0c,'b',w),grid>>[gm,pm,wcg,wcp]=margin(g0c),Km=20*log10(gm)