fig128.m

realize analysis and design for computer-controlled system

% Generates Fig 12.8 (lqvar)
% 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=[1.7 1;-0.7 0];
B=[0.9; 1];
Q=[1 0;0 0];
N=50;
%
rho=logspace(-5,5,N);
yvar=zeros(1,N);
uvar=zeros(1,N);

for kk=1:N, 
[L,S,E]=dlqr(A,B,Q,rho(kk));
P=poly(E);
s0=(1+P(2)+P(3))/1.9;
r1=s0-P(3);
R=[1 r1 0];
S=[s0 -0.7*s0 0];
yvar(kk)=dcovar(R,P,1);
uvar(kk)=dcovar(-S,P,1);
end;

subplot(2,1,1)
semilogx(rho,yvar,'k-',rho,uvar,'k--','Linew',lw)
axis([0.001,1000,0 10]);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.001 1 1000]);
set(gca,'ytick',[0 5 10]);
xlabel('Weighting \rho','Fontname','NewCenturySchlbk','Fontsize',9)
ylabel('Variance','Fontname','NewCenturySchlbk','Fontsize',9)