fig516.m

realize analysis and design for computer-controlled system

% Generates Fig 5.16
% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-07-02
% Copyright (c) 1996 by K. J. 舠tr鰉, B. Wittenmark and
% Department of Automatic Control, Lund Institute of
% Technology, Lund, Sweden

newplot;clf;
lw=0.9;
set(gcf,'PaperUnits','centimeters','PaperPosition',[2 2 13 9.5])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))

a=2;
z=0.707;

h=0.2;
w=0.2;
%
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;

apol=[1 -2 1];
bpol=h*h/2*[1 1];
rpol=[1 r1 r2];
spol=[s0 s1 s2];
alg=conv(apol,rpol);
blg=conv(bpol,spol);
wrad1=logspace(-3,pi,100)/h;
[mag1,ph1,wrad1]=dbode(blg,alg,h,wrad1);

h=1;
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;

apol=[1 -2 1];
bpol=h*h/2*[1 1];
rpol=[1 r1 r2];
spol=[s0 s1 s2];
alg=conv(apol,rpol);
blg=conv(bpol,spol);
wrad2=logspace(-3,pi,100)/h;
[mag2,ph2,wrad2]=dbode(blg,alg,h,wrad2);

subplot(2,1,1)
loglog(wrad1,mag1,'m--',wrad2(1:98),mag2(1:98),'k-','Linew',lw)
axis([0.01 100 0.01 10000])
hold on
plot([0.01 100],[1 1],'k:','Linew',lw)
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'ytick',[0.01 1 100 10000]);
set(gca,'xtick',[0.1 1 10]);
ylabel('Gain','Fontname','NewCenturySchlbk','Fontsize',9)

subplot(2,1,2)
semilogx(wrad1,ph1,'m--',wrad2,ph2,'k-','Linew',lw)
axis([0.01 100 -300  -100]);
hold on
plot([0.01 100],[-180 -180],'k:','Linew',lw)
set(gca,'Fontsize',9,'Fontname','NewCenturySchlbk');
set(gca,'xtick',[0.1 1 10]);
set(gca,'ytick',[-300 -200 -100]);
xlabel('Frequency, rad/s','Fontname','NewCenturySchlbk','Fontsize',9)
ylabel('Phase','Fontname','NewCenturySchlbk','Fontsize',9)
ylblalgn