why is my PID doing this

clc

clear all

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% original plant

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

s = tf('s');

% Delay = 0.5; % 1 sec pure time delay in the process

% Gp = exp(-Delay*s)/((s+1)^2); % second order system

Delay = 21.9; % 1 sec pure time delay in the process

g2 = 0.33*exp(-Delay*s)/(17.28*s + 1); % second order system

% determine settlingTime and use that to generate sufficient number of

kcu = 35;

tu = 21;

figure()

g2cl = feedback(g2,1);

step(g2,g2cl);

legend('open loop','close loop');

grid on;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% tuning

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%P Only

p1 = kcu/2;

figure()

g2p1 = g2*p1;

g2p1cl = feedback(g2p1,1);

step(g2p1,g2p1cl);

legend('open loop','close loop');

%pi

p2 = kcu/2.2;% proportional gain

i1 = tu/1.2;% integral time

con1 = p2*(1+(1/(i1*s)));

figure()

g2p2 = g2*con1;

g2p2cl = feedback(g2p2,1);

step(g2p2cl);

legend('close loop');

%PID

p3= kcu/1.7;

i2 = tu/2;

d1 = tu/8;

con2 = p3*(1+(1/(i2*s))+(d1*s));

figure()

g3p3 = g2*con2;

g3p3cl = feedback(g3p3,1);

step(g3p3cl);

legend('close loop');

%comparing the controllers

figure()

step(g3p3cl,g2p2cl,g2p1cl)

legend('PID','PI','P');

Answer 1

[Mathieu NOE]

hi

I found that you have too much loop gain and therefore your are unstable - maybe before closing the loop you should look at the opel loop gain first and check stability margins. I let you do this

For just the sake of the demo, I reduced the unity feedback gain to lower values so that it remains stable.

example : P regulator :

g2p1cl = feedback(g2p1,2/p1); instead of g2p1cl = feedback(g2p1,1);

same for PI and PID

I also tweaked a bit your PID coefficients. I do not pretend that this is optimal PID design but I just suggest a few ideas to test...

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% original plant
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
s = tf('s');
% Delay = 0.5; % 1 sec pure time delay in the process
% Gp = exp(-Delay*s)/((s+1)^2); % second order system
Delay = 21.9; % 1 sec pure time delay in the process
g2 = 0.33*exp(-Delay*s)/(17.28*s + 1); % second order system
% determine settlingTime and use that to generate sufficient number of
 kcu = 35;
 tu  = 21;
figure()
g2cl = feedback(g2,1); 
step(g2,g2cl);
legend('open loop','close loop');
grid on;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% tuning
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%P Only
p1 = kcu/2;
figure()
g2p1 = g2*p1;
g2p1cl = feedback(g2p1,2/p1);
step(g2p1,g2p1cl);
legend('open loop','close loop');
%pi
p2 = kcu/2.2;% proportional gain
i1 = tu/1.2;% integral time
con1 = p2*(1+(1/(i1*s)));
figure()
g2p2 = g2*con1;
g2p2cl = feedback(g2p2,2/p2);
step(g2p2cl);
legend('close loop');


%PID
% p3= kcu/1.7;
% i2 = tu/2;
% d1 = tu/8;

p3= kcu/1.7;
i2 = tu;
d1 = tu/6;

con2 = p3*(1+(1/(i2*s))+(d1*s));
figure()
g3p3 = g2*con2;
g3p3cl = feedback(g3p3,2/p3);
step(g3p3cl);
legend('close loop');
%comparing the controllers
figure()
step(g3p3cl,g2p2cl,g2p1cl)
legend('PID','PI','P');

[Aadarsh Biju]

thank you