Conversion to double from pid2 is not possible-optimization app

I have written the following code for optimizing ki, kp and kd values for pid controller using genatic algorithm. but the error come" conversion to double from pid2 is not possible".

code is:

function[j]= pid2(x)

s=tf('s');

plant= 1/ (s^2 + 3*s + 11);

kp=x(1)

ki= x(2)

kd=x(3)

cont= kp+ ki/s + kd*s

step(feedback(plant*cont,1));

dt=0.01;

t=0:dt:1;

err=1-step(feedback(plant*cont,1),t);

j=sum(t'.*abs(err)*dt)

end

please guide me, i am new in matlab.

Answer 1

[Sam Chak]

Hi @Ihsan Ullah Khalil

I ran your code using the ga() tool, and it produced a set of PID gains that enable the controller to track the reference signal. It seems that there might have been a syntax error in the input argument of the ga() command in your previous attempt.

%% Tune PID controller via Genatic Algorithm
lb        = [75 300 25];        % lower bound
ub        = 2*lb;               % upper bound
[k, fval] = ga(@pid2, 3, [], [], [], [], lb, ub)

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

k = 1×3

144.3332 529.2219 48.1111

fval = 4.2379e-04

s   = tf('s');
P   = 1/(s^2 + 3*s + 11);
kp  = k(1);
ki  = k(2);
kd  = k(3);
C   = pid(kp, ki, kd)

C =
 
             1          
  Kp + Ki * --- + Kd * s
             s          

  with Kp = 144, Ki = 529, Kd = 48.1
 
Continuous-time PID controller in parallel form.

G   = feedback(C*P, 1);
step(P), hold on
step(G), grid on
legend('Original Plant', 'Compensated System', 'location', 'East')

%% Maybe your previous attempt
[k, fval] = ga(@(k) @pid2, 3, [], [], [], [], lb, ub)

Conversion to double from function_handle is not possible.

Error in fcnvectorizer (line 19)
y(i,:) = feval(fun,(pop(i,:)));

Error in makeState (line 69)
Score = fcnvectorizer(state.Population(initScoreProvided+2:end,:),FitnessFcn,1,...

Error in galincon (line 24)
state = makeState(GenomeLength,FitnessFcn,Iterate,output.problemtype,options);

Error in ga (line 420)
[x,fval,exitFlag,output,population,scores] = galincon(FitnessFcn,nvars, ...

Caused by:
Failure in user-supplied fitness function evaluation. GA cannot continue.

%% Cost function: Integral Time-weighted Absolute Error (ITAE)
function J = pid2(k)            % I usually choose J = costfun(k)
    s   = tf('s');
    P   = 1/(s^2 + 3*s + 11);   % Plant
    kp  = k(1);
    ki  = k(2);
    kd  = k(3);
    C   = kp + ki/s + kd*s;     % Classical PID Controller
    dt  = 0.01;
    t   = 0:dt:1;
    err = 1 - step(feedback(C*P, 1), t);    % Error
    J   = sum(t'.*abs(err)*dt);             % ITAE
end