GA Algorithm for PID tuning

I have a second order transfer function which I want to control using PID controller. I want Kp, Ki, Kd values using GA toolbox in matlab. My question is if I want suppose 5% overshoot or 0.1s settling time, how can I specify it in fitness function/app?

Here is my fitness function

function J = pidtest(x)
s = tf('s');
G = 49/(s^2+7*s+49);
Kp=x(1); Ki=x(2); Kd=x(3);
controller = Kp + Ki/s + Kd*s;
Loop = series(controller,G);
ClosedLoop = feedback(Loop,1);
dt = 0.1;
t = 0:dt:30;
y = step(ClosedLoop,t);
J = sum(t'.*abs(1-y)*dt); %ITAE

[krishna]

thanks surbhi for this code . can you help me , if my plant is quadcopter(drone) whose output is position(x, y , z) and angle(phi, theta, psi) so how i can tune PID controller using Genetic algorithm?

Answer 1

[Sam Chak]

Hi @SURBHI GOEL

Sometimes you can let GA randomly search during the initial run to observe if the performance requirements are satisfied.

s  = tf('s');
Gp  = 49/(s^2 + 7*s + 49)

Gp =
 
        49
  --------------
  s^2 + 7 s + 49
 
Continuous-time transfer function.

step(Gp, 2), grid on

nvars     = 3;
[K, fval] = ga(@pidtest, nvars)

ga stopped because the average change in the fitness value is less than options.FunctionTolerance.

K = 1×3

13.8153 96.6499 1.9877

fval = 3.5202e-05

Gc = K(1) + K(2)/s + K(3)*s;  % ideal type
Gcl = feedback(Gc*Gp, 1);
step(Gcl, 2), grid on

S = stepinfo(Gcl)

S = struct with fields:
         RiseTime: 0.0226
    TransientTime: 0.0404
     SettlingTime: 0.0404
      SettlingMin: 0.9040
      SettlingMax: 0.9989
        Overshoot: 0
       Undershoot: 0
             Peak: 0.9989
         PeakTime: 0.0751

function J = pidtest(K)
    s  = tf('s');
    
    % plant
    G  = 49/(s^2 + 7*s + 49);
    
    % pid controller
    Kp = K(1); 
    Ki = K(2); 
    Kd = K(3);
    controller = Kp + Ki/s + Kd*s;  % ideal type
    
    % closed-loop tf
    Loop = series(controller, G);
    ClosedLoop = feedback(Loop, 1);
    
    % cost
    dt = 0.1;
    t  = 0:dt:3;
    y  = step(ClosedLoop, t);
    J  = sum(t'.*abs(1-y)*dt);  % ITAE
end