Code credit to Steve Brunton
close all; clear all; clc
dt = 0.001;
PopSize = 25;
MaxGenerations = 10;
s = tf('s');
G = 1/(s*(s*s+s+1));
options = optimoptions(@ga,'PopulationSize',PopSize,'MaxGenerations',MaxGenerations);
[x,fval] = ga(@(K)pidtest(G,dt,K),3,-eye(3),zeros(3,1))
function J = pidtest(G,dt,parms)
s = tf('s');
K = parms(1) + parms(2)/s + parms(3)*s/(1+.001*s);
Loop = series(K,G);
ClosedLoop = feedback(Loop,1);
t = 0:dt:20;
[y,t] = step(ClosedLoop,t);
CTRLtf = K/(1+K*G);
u = lsim(CTRLtf,1-y,t);
Q = 1;
R = .001;
J = dt*sum(Q*(1-y(:)).^2+R*u(:).^2)
[y,t] = step(ClosedLoop,t);
plot(t,y,'LineWidth',2,'color','r')
drawnow
end
