I need cost function for tuning PID controller help me
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Yazeed Ali on 22 Nov 2022
I have to apply some algorithms for tuning PID controller parameters (Kp,Ki,Kd) so for any algorithm i have to get separate cost function file or called objective function so if anyone has p;ease send me the file thanks
Sam Chak on 23 Nov 2022
Edited: Sam Chak on 25 Dec 2022
Hi @Yazeed Ali
Not sure what your system is, but I think you can try the one of the simplest cost function probably looks like this:
Tuning the gains is probably simpler by manual calculations (follow formulas in textbooks) or with the pidtune() command.
function J = costfun(Kp, Ki, Kd)
[t, x] = ode45(@(t, x) myode(t, y), tspan, ic, opts);
error = x - x_ref;
J = trapz(t, error.^2); % ISE
% J = trapz(t, t.*abs(error)); % ITAE
function dxdt = myode(t, x)
% Insert your system and the PID controller
dxdt = A.*x + B*u;
Edit: An example is included.
Example: Consider the system described by
The cost function J is given by
A full state-feedback controller is used:
The optimal feedback gain matrix is found using fmincon().
costfun = @objfun;
nvars = 2;
A = -eye(nvars);
b = zeros(nvars, 1);
Aeq = ;
beq = ;
lb = [0 0]; % lower bound
ub = [2 2]; % upper bound
k0 = [0.5, 1.5]; % initial guess
[k, fval, exitflag, output] = fmincon(costfun, k0, A, b, Aeq, beq, lb, ub)
function J = objfun(k)
tspan = linspace(0, 30, 3001);
ic = [1 0];
[t, x] = ode45(@(t, x) myode(t, x, k), tspan, ic);
Q = eye(2);
R = 1;
ifcn = Q(1,1)*x(:,1).^2 + Q(2,2)*x(:,2).^2 + R*(- k(1)*x(:,1) - k(2)*x(:,2)).^2;
J = trapz(t, ifcn); % ISE
function dxdt = myode(t, x, k)
dxdt = zeros(2, 1);
% my controller
u = - k(1)*x(1) - k(2)*x(2);
% my system
dxdt(1) = x(2);
dxdt(2) = - x(2) + u;
Sam Chak on 27 Dec 2022
Edited: Sam Chak on 27 Dec 2022
Hi @Yazeed Ali,
I'm familiar with Grey Wolf. Why not consider posting the GWO code and the error message in a new Question? GWO was published by Seyedali Mirjalili in 2014. Optimization experts in MATLAB would be able to advise you.
I'm not sure if the proposed Cost function is helpful or not. Most likely it is because you cannot test with the GWO. However, it works with other optimizers such GA, PSO, ABC, etc., then we can safely assure that the proposed "Cost Function template" maybe effective.
I only verified it using fmincon. It does not guarantee to work with other optimizers. Let me know it doesn't work because I may consider removing it as I don't want other users to be misguided by the 'flawed' Cost Function. Thanks!
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