fig519.m

realize analysis and design for computer-controlled system

% Generates Fig 5.19
% Computer Controlled Systems (3rd ed)
% Author: B. Wittenmark
% Last edit: 1997-07-04
% 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 10])
set(gcf,'Units','centimeters','position',get(gcf,'PaperPosition'))

hnoise=0.2;

block518;

lw=0.9;
td=15;
tn=30;
l0=-0.5;
h=0.2;
omo=4;
zeta=0.7;
zetao=0.7;
om=1.5;
omp=1;  
%
% Calculation of desired closed loop characteristic polynomial AmAo  
a=exp(-zeta*om*h);   
b=om*h*sqrt(1-zeta*zeta);
re=a*cos(b); 
am1=-2*re;   
am2=a*a; 
ams=1+am1+am2;   
ao=exp(-zetao*omo*h);
bo=omo*h*sqrt(1-zetao*zetao);
reo=ao*cos(bo);  
ao1=-2*reo;  
ao2=ao*ao;   
aos=1+ao1+ao2;   

% Sampling the oscillator giving B/A 
be=cos(omp*h);   

% Solution of the polynomial identity AR+BS=P=AmAo   
p1=ao1+am1;  
p2=ao2+am2+am1*ao1;  
p3=am2*ao1+am1*ao2;  
p4=am2*ao2;  
pm1=1-p1+p2-p3+p4;   
r=1-pm1/(4*(1+be));  
r1=r-1;  
r2=-r;   
s0=(p1-r+1+2*be)/(1-be); 
s1=(p2-p1-2*be+2*(1+be)*(r-1))/(1-be);   
s2=(p4+r)/(1-be);
t0=ams/(2*(1-be));   
t1=t0*ao1;   
t2=t0*ao2;   
%
clf;
%
[t,x,y]=sim('block518',[0, 40]);
subplot(3,2,1);
plot(t,y(:,3),'k--',t,y(:,1),'k','Linew',lw);
axis([0,40,0,1.3]);
set(gca,'FontSize',9,'Fontname','NewCenturySchlbk')
set(gca,'xtick',[0 20 40]);
set(gca,'ytick',[0 1]);
ylabel('Output','Fontname','NewCenturySchlbk','Fontsize',9)
text(-8,1.3,'(a)','Fontname','NewCenturySchlbk','Fontsize',9)
%title('Fig 5.19','fontname','NewCenturySchlbk','FontSize',9);
drawnow;
%
subplot(3,2,3);
[ts,ys]=stairs(t,y(:,2));
plot(ts,ys,'m','Linew',lw);
axis([0,40,-0.5,3.5]);
set(gca,'FontSize',9,'Fontname','NewCenturySchlbk')
set(gca,'xtick',[0 20 40]);
set(gca,'ytick',[0 2]);
ylabel('Input','Fontname','NewCenturySchlbk','Fontsize',9)
xlabel('Time','Fontname','NewCenturySchlbk','Fontsize',9)
drawnow;
%
omo=8;
%
% Calculation of desired closed loop characteristic polynomial AmAo  
a=exp(-zeta*om*h);   
b=om*h*sqrt(1-zeta*zeta);
re=a*cos(b); 
am1=-2*re;   
am2=a*a; 
ams=1+am1+am2;   
ao=exp(-zetao*omo*h);
bo=omo*h*sqrt(1-zetao*zetao);
reo=ao*cos(bo);  
ao1=-2*reo;  
ao2=ao*ao;   
aos=1+ao1+ao2;   

% Sampling the oscillator giving B/A 
be=cos(omp*h);   

% Solution of the polynomial identity AR+BS=P=AmAo   
p1=ao1+am1;  
p2=ao2+am2+am1*ao1;  
p3=am2*ao1+am1*ao2;  
p4=am2*ao2;  
pm1=1-p1+p2-p3+p4;   
r=1-pm1/(4*(1+be));  
r1=r-1;  
r2=-r;   
s0=(p1-r+1+2*be)/(1-be); 
s1=(p2-p1-2*be+2*(1+be)*(r-1))/(1-be);   
s2=(p4+r)/(1-be);
t0=ams/(2*(1-be));   
t1=t0*ao1;   
t2=t0*ao2;   
%
%
[t,x,y]=sim('block518',[0, 40]);
subplot(3,2,2);
plot(t,y(:,3),'k--',t,y(:,1),'k','Linew',lw);
axis([0,40,0,1.3]);
set(gca,'FontSize',9,'Fontname','NewCenturySchlbk')
set(gca,'xtick',[0 20 40]);
set(gca,'ytick',[0 1]);
ylabel('Output','Fontname','NewCenturySchlbk','Fontsize',9)
text(-8,1.3,'(b)','Fontname','NewCenturySchlbk','Fontsize',9)
drawnow;
%
subplot(3,2,4);
[ts,ys]=stairs(t,y(:,2));
plot(ts,ys,'m','Linew',lw);
axis([0,40,-0.5,3.5]);
set(gca,'FontSize',9,'Fontname','NewCenturySchlbk')
set(gca,'xtick',[0 20 40]);
set(gca,'ytick',[0 2]);
ylabel('Input','Fontname','NewCenturySchlbk','Fontsize',9)
xlabel('Time','Fontname','NewCenturySchlbk','Fontsize',9)
drawnow;