GA Algorithm for PID tuning

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SURBHI GOEL
SURBHI GOEL 2020-11-8
编辑： Sam Chak 2023-10-31
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
  1 个评论
krishna
krishna 2023-10-31
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?

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回答（1 个）

Sam Chak
Sam Chak 2023-10-31
编辑：Sam Chak 2023-10-31
Ran in:
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

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