fig104.m

来自「realize analysis and design for computer」· M 代码 · 共 193 行

% Generates Fig 10.4
% Covariance function ,spectrum and realization for the systems
% H(z)=b/(z-a) a=0.8 and 0.4 
% H(z)=b/(z^2+a1*z+a2) with om=1 and zeta=0.5 and 0.1 sampled
% with h=1
% The output variance is one by adjusting b

% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-07-10
% Copyright (c) 1996 by K. J. 舠tr鰉, B. Wittenmark and
% Department of Automatic Control, Lund Institute of
% Technology, Lund, Sweden

newplot;clf
set(gcf,'PaperUnits','centimeters','PaperPosition',[2 2 13 13])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))
clear

lw=0.9;
n=10;
ns=100;
rl=-1;
ru=1;
su=20;
sl=0.02;
yu=4;
yl=-4;
Ms=6;
w=logspace(-2,pi,ns);

a=0.8;
for jj=1:n+1, t(jj)=jj-1; ry(jj)=a^(jj-1); end;
for jj=1:ns,
specy(jj)=(1+a*a)/(1+a*a-2*a*cos(w(jj)))/(2*pi);
end

subplot(4,3,1)
hpl=plot(t,ry,'k',t,ry,'m.','Linew',lw);
set(hpl,'Markersize',Ms)
hold on
plot([0 n],[0 0],'k--','Linew',lw)
axis([0 n rl ru]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 10]);
set(gca,'ytick',[-1 0 1]);
title('Covariance','Fontname','NewCenturySchlbk','Fontsize',9)

subplot(4,3,2)
loglog(w,specy,'k','Linew',lw)
axis([0.01 pi sl su]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.01 1]);
set(gca,'ytick',[0.1 10]);
title('Spectrum','Fontname','NewCenturySchlbk','Fontsize',9)

num=[sqrt(1-a*a)];
den=[1 -a];
[ts,x,y]=sim('blockcov',[0 50]);
subplot(4,3,3)
hpl=plot(ts,y,'k',ts,y,'m.','Linew',lw);
set(hpl,'Markersize',Ms);
axis([0 50 yl yu]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 50]);
set(gca,'ytick',[-2 0 2]);
title('Output','Fontname','NewCenturySchlbk','Fontsize',9)

a=0.4;
for jj=1:n+1, t(jj)=jj-1; ry(jj)=a^(jj-1); end;
for jj=1:ns,
specy(jj)=(1+a*a)/(1+a*a-2*a*cos(w(jj)))/(2*pi);
end

subplot(4,3,4)
hpl=plot(t,ry,'k',t,ry,'m.','Linew',lw);
set(hpl,'Markersize',Ms)
hold on
plot([0 n],[0 0],'k--','Linew',lw)
axis([0 n rl ru]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 10]);
set(gca,'ytick',[-1 0 1]);
subplot(4,3,5)
loglog(w,specy,'k','Linew',lw)
axis([0.01 pi sl su]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.01 1]);
set(gca,'ytick',[0.1 10]);

num=[sqrt(1-a*a)];
den=[1 -a];
[ts,x,y]=sim('blockcov',[0 50]);
subplot(4,3,6)
hpl=plot(ts,y,'k',ts,y,'m.','Linew',lw);
set(hpl,'Markersize',Ms);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 50]);
set(gca,'ytick',[-2 0 2]);
axis([0 50 yl yu]);

om=1;
zeta=0.5;
a1=-2*exp(-zeta*om)*cos(sqrt(1-zeta*zeta)*om);
a2=exp(-2*zeta*om);
phi=[-a1 -a2;1 0];
ga=[1;0];
c1=[0 1];
xl=dlyap(phi,ga*ga');
ry0=c1*xl*c1';
c=c1/sqrt(ry0);
for jj=1:n, t(jj)=jj-1; ry(jj)=c*phi^(jj-1)*xl*c'; end;
for jj=1:ns,
specy(jj)=abs(1/(exp(2*i*w(jj))+a1*exp(i*w(jj))+a2)...
/(exp(-2*i*w(jj))+a1*exp(-i*w(jj))+a2))/(2*pi);
end

subplot(4,3,7)
hpl=plot(t,ry,'k',t,ry,'m.','Linew',lw);
set(hpl,'Markersize',Ms)
hold on
plot([0 n],[0 0],'k--','Linew',lw)
axis([0 n rl ru]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 10]);
set(gca,'ytick',[-1 0 1]);
subplot(4,3,8)
loglog(w,specy,'k','Linew',lw)
axis([0.01 pi sl su]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.01 1]);
set(gca,'ytick',[0.1 10]);

num=[1];
den=[1 a1 a2];
[ts,x,y]=sim('blockcov',[0 50]);
subplot(4,3,9)
hpl=plot(ts,y,'k',ts,y,'m.','Linew',lw);
set(hpl,'Markersize',Ms);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
axis([0 50 yl yu]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 50]);
set(gca,'ytick',[-2 0 2]);

om=1;
zeta=0.1;
a1=-2*exp(-zeta*om)*cos(sqrt(1-zeta*zeta)*om);
a2=exp(-2*zeta*om);
phi=[-a1 -a2;1 0];
ga=[1;0];
c1=[0 1];
xl=dlyap(phi,ga*ga');
ry0=c1*xl*c1';
c=c1/sqrt(ry0);
for jj=1:n, t(jj)=jj-1; ry(jj)=c*phi^(jj-1)*xl*c'; end;
for jj=1:ns,
specy(jj)=abs(1/(exp(2*i*w(jj))+a1*exp(i*w(jj))+a2)...
/(exp(-2*i*w(jj))+a1*exp(-i*w(jj))+a2))/(2*pi);
end

subplot(4,3,10)
hpl=plot(t,ry,'k',t,ry,'m.','Linew',lw);
set(hpl,'Markersize',Ms)
hold on
plot([0 n],[0 0],'k--','Linew',lw)
axis([0 n rl ru]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 10]);
set(gca,'ytick',[-1 0 1]);
xlabel('\tau','Fontname','NewCenturySchlbk','Fontsize',9)

subplot(4,3,11)
loglog(w,specy,'k','Linew',lw)
axis([0.01 pi sl su]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.01 1]);
set(gca,'ytick',[0.1 10]);
xlabel('\omega','Fontname','NewCenturySchlbk','Fontsize',9)

num=[1];
den=[1 a1 a2];
[ts,x,y]=sim('blockcov',[0 50]);
subplot(4,3,12)
hpl=plot(ts,y,'k',ts,y,'m.','Linew',lw);
set(hpl,'Markersize',Ms);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
axis([0 50 yl yu]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0 50]);
set(gca,'ytick',[-2 0 2]);
xlabel('Time','Fontname','NewCenturySchlbk','Fontsize',9)