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// Copyright INRIA
exec(SCI+'/demos/control/scheme.dem');
s=poly(0,'s');z=poly(0,'z');
x_message('Example of PID Design ')
n=x_choose(['Continuous time';'Discrete time'],'Select time domain');
select n
case 0
warning('Demo stops!');return;
case 1
mode(1)
dom='c';
s=poly(0,'s');
str='[(s-1)/(s^2+5*s+1)]';
rep=x_dialog('Nominal plant?',str);
if rep==[] then return,end
Plant=evstr(rep);
Plant=syslin('c',Plant);
mode(-1)
case 2
mode(1)
dom='d'
z=poly(0,'z');
str='(z+1)/(z^2-5*z+2)'
rep=x_dialog('Nominal plant?',str);
if rep==[] then return,end
Plant=evstr(rep)
Plant=syslin('d',Plant);
mode(-1)
end
//Nominal Plant
P22=tf2ss(Plant); //...in state-space form
[ny,nu,nx]=size(P22);
defv=['-1.2','1','0.1'];
if dom=='d' then defv=['-10','1','0.1'];end
while %t
mode(1)
if dom=='c' then
title='Enter your PID controller K(s)=Kp*(1+T0/s+T1*s)';
end
if dom=='d' then
title='Enter your PID controller K(z)=Kp*(1+T0/z+T1*z)';
end
defv=x_mdialog(title,['Kp=';'T0=';'T1='],defv);
if defv==[] then warning('Demo stops!');return;end
Kp=evstr(defv(1));T0=evstr(defv(2));T1=evstr(defv(3));
if dom=='c' then
Kpid=tf2ss(Kp*(1+T0/s+T1*s));
end
if dom=='d' then
Kpid=tf2ss(Kp*(1+T0/z+T1*z));
end
W=[1, -P22;
Kpid,1];Winv=inv(W);
disp(spec(Winv(2)),'closed loop eigenvalues');//Check internal stability
if maxi(real(spec(Winv(2)))) > 0 then
x_message('You loose: closed-loop is UNSTABLE!!!');
else
x_message('Congratulations: closed-loop is STABLE !!!');
break;
end
mode(-1)
end
mode(1)
[Spid,Rpid,Tpid]=sensi(P22,Kpid); //Sensitivity functions
Tpid(5)=clean(Tpid(5));
disp(clean(ss2tf(Spid)),'Sensitivity function');
disp(clean(ss2tf(Tpid)),'Complementary sensitivity function');
resp=['Frequency response';'Time response'];
while %t do
n=x_choose(resp,'Select response(s)');
if degree(Tpid(5))>0 then
warning('Improper transfer function! D(s) set to D(0)')
Tpid(5)=coeff(Tpid(5),0);
end
Tpid(5)=coeff(Tpid(5));
select n
case 0
break
case 1
mode(1)
xbasc(1);xset("window",1);xselect();bode(Tpid);
mode(-1)
case 2
if Plant(4)=='c' then
mode(1)
defv=['0.1','50'];
title='Enter Sampling period and Tmax';
rep=x_mdialog(title,['Sampling period?';'Tmax?'],defv);
if rep==[] then break,end
dttmax=evstr(rep);
dt=evstr(dttmax(1));tmax=evstr(dttmax(2));
t=0:dt/5:tmax;
n1=x_choose(['Step response?';'Impulse response?'],'Simulation:');
if n1==0 then
warning('Demo stops!');return;
end
if n1==1 then
xbasc(1);xset("window",1);xselect();
plot2d([t',t'],[(csim('step',t,Tpid))',ones(t')])
end
if n1==2 then
xbasc(1);xset("window",1);xselect();
plot2d([t',t'],[(csim('impul',t,Tpid))',0*t'])
end
mode(-1)
elseif Plant(4)=='d' then
mode(1)
defv=['100'];
title='Tmax?'
rep=x_mdialog(title,['Tmax='],defv);
if rep==[] then break,end
Tmax=evstr(rep);
mode(-1)
while %t do
n=x_choose(['Step response?';'Impulse response?'],'Simulation:');
select n
case 0 then
break
case 1 then
mode(1)
u=ones(1,Tmax);u(1)=0;
xbasc(1);xset("window",1);xselect();
plot2d([(1:Tmax)',(1:Tmax)'],[(dsimul(Tpid,u))',(ones(1:Tmax)')])
mode(-1)
case 2 then
mode(1)
u=zeros(1,Tmax);u(1)=1;
xbasc(1);xset("window",1);xselect();
plot2d((1:Tmax)',(dsimul(Tpid,u))')
mode(-1)
end
end
end
end
end
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