lqgclosed.m

realize analysis and design for computer-controlled system

% This is a scriptfile that simulates Fig 12:lqgclosed
% 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 10])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))

lw=0.9;

A=[1 -1.7 0.7];
As=[0.7 -1.7 1];
B=[0.9 1];
Bs=[1 0.9];
N=500;
den=conv(A,As);
num=[0 conv(B,Bs) 0];
%
rho=[0.000001:0.0001:0.1,0.1:0.01:1,1.1:0.1:10,logspace(1,4,N),1000000];
[m,n]=size(rho);
r=zeros(n,4);
for i=1:n,
  tot=num+rho(i)*den;
  r(i,:)=roots(tot)';
  end;
ro4=sort(r');
ro2=ro4(1:2,:)';
plot(ro2,'k','Linew',lw);
hold on
t=0:.1:6.3;
plot(sin(t),cos(t),'k-','Linew',lw)
axis([-1.5,1.2,-1.1,1.1]);
axis('equal');
plot(-0.9,0,'mo');
plot(0,0,'mo');
plot(1,0,'mx');
plot(0.7,0,'mx');
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'ytick',[-1 0 1]);
set(gca,'xtick',[-1 0 1]);
xlabel('Real axis','Fontsize',9,'Fontname','NewCenturySchlbk');
ylabel('Imaginary axis','Fontsize',9,'Fontname','NewCenturySchlbk');
plot([-3 3],[0 0],'k:','Linew',lw)
plot([0 0],[-2 2],'k:','Linew',lw)
rho=1;
po(1,:)=roots(num+rho*den)';
po4=sort(po');
po2=po4(1:2,:)';
plot(po2,'k*')
text(0.08,0.43,'\rho =1','Fontsize',9,'Fontname','NewCenturySchlbk')