fig137.m

realize analysis and design for computer-controlled system

% Generates Fig 13.7 (feedback)
% Using the System Identification Toolbox
% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-08-04
% 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 8])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))

lw=0.9;

N=10000;
a1=-0.8;
b1=0.5;
sig=0.5;
P0=0.01;
k=0.2;


model=poly2th([1 a1+b1*k],[0 0]);
u=zeros(N,1);
randn('seed',217);
e=sig*randn(N,1);
y=idsim([u e],model);
u=-k*y;
ts=[1:N];
mydata=[y u];

th0=[0.5 0.5];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);
hold on
axis([-2.3 1.3 -1.2 1.2]);
axis('equal');
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[-2 -1 0 1],'ytick',[-1 0 1]);
xlabel('Parameter estimate \it{b}','Fontsize',9,'Fontname','NewCenturySchlbk')
ylabel('Parameter estimate \it{a}','Fontsize',9,'Fontname','NewCenturySchlbk')
a=hex2dec('d9');
text(0.01,-1.325,setstr(a),'fontname','symbol','fontsize',7)
text(-2.62,0.51,setstr(a),'fontname','symbol','fontsize',7,'rotation',90)
th0=[0.35 1.22];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);

th0=[0.7 -0.39];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);

th0=[-1.56 -1.1];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);

th0=[-1.71 -0.24];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);

th0=[-1.84 0.53];
[thm,yh,P]=rarx(mydata,[1 1 1],'ff',1,th0,P0*eye(2));
plot(thm(:,1),thm(:,2),'k-','Linew',lw);

plot([-0.4 -1],[-1.5 1.5],'k--','Linew',lw)
plot(-0.8,0.5,'k.','Markers',12)

arrow2([-1.6051 0.5753],13*pi/180)
arrow2([-1.4646 -0.1916],13*pi/180)
arrow2([-1.3203 -1.052],13*pi/180)
arrow2([-0.2987 1.088],193*pi/180)
arrow2([-0.1544 0.368],193*pi/180)
arrow2([0.0278 -0.525],193*pi/180)