fig916.m

realize analysis and design for computer-controlled system

% Generates Fig 9.16
% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-07-09
% Copyright (c) 1996 by K. J. 舠tr鰉, B. Wittenmark and
% Department of Automatic Control, Lund Institute of
% Technology, Lund, Sweden

newplot;
set(gcf,'PaperUnits','centimeters','PaperPosition',[2 2 13 8])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))
 
lw=0.9;
m=400;
h=1;
w=0.2;
z=0.707;
d=0.01;
a=1;
%Regulator design pole placement with Am=z2+a1m*z+a2m and
%Ao=z2+a1o*z+a2m
wh=w*h;
z1=sqrt(1-z*z);
a1m=-2*exp(-z*wh)*cos(z1*wh);
a2m=exp(-2*z*wh);
ams=1+a1m+a2m;

ae=exp(-a*h);
a1o=-2*ae;
a2o=ae*ae;
aos=1+a1o+a2o;
amp=2+a1m;
aop=2+a1o;

p1=ams*aos;
pp=amp*aos+ams*aop;
p2p=2*(ams+amp*aop+aos);
h2=h*h;
s0=(p1/4-pp/2+p2p/2)/h2;
s1=(-p1+2*pp-p2p)/h2;
s2p=(7*p1/4-3*pp/2+p2p/2);
s2=s2p/h2;
r=s2p/2-a2m*a2o;
r1=r-1;
r2=-r;
t0=ams/h2;
t1=t0*a1o;
t2=t0*a2o;
Spol=[s0 s1 s2];
Rpol=[1 r1 r2];
Bpol=[h*h/2 h*h/2];
Apol=[1 -2 1];
clf;
%
wfre=logspace(-4,pi,m)/h;
i=sqrt(-1);
z=exp(i*wfre*h);
ac=conv(Apol,Rpol);
bc=conv(Bpol,Spol);
gz=polyval(bc,z)./polyval(ac,z);
ny1=gz.';
plot(ny1,'k-','Linew',lw)
hold on;
axis([-7,1,-2,2]);
axis('equal');
%title(['Fig 9.16']);
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
ylabel('Imaginary axis','Fontname','NewCenturySchlbk','Fontsize',9)
xlabel('Real axis','Fontname','NewCenturySchlbk','Fontsize',9)
set(gca,'xtick',[-6 -4 -2 0],'ytick',[-2 0 2]);
plot([0 0],[-3 3],'k:',[-10 5],[0 0],'k:','Linew',lw)
plot(-1,0,'k+','Linew',lw)
arrow2([-1.8016 -1.03],-0.05);