what is the code to implement a disturbance of 0.2 in the system at 400 sec that would test the disturbance rejection of the controller and allow the system to return to 1?

Hi All,

Can anyone help me with MATLAB code for a disturbace of 0.2 at 400 seconds that would test the disturbance rejection of the PID controller and allow the system to return to 1?

I need to test the tuning by applying a disturbance at 400 seconds to see how the controller responds in that case in MATLAB code.

Help very much appreiciated!!

Thanking you

Answer 1

[Sam Chak]

Hi @sabavath jayaram

Since your system is not provided, here is a simple example to demonstrate the disturbance rejection capability of a PID controller for a Double Integrator system.

s   = tf('s');
m   = 5;
Gp  = 1/(m*s^2)         % Plant

Gp =
 
    1
  -----
  5 s^2
 
Continuous-time transfer function.

% PID controller
Kp  = 2.460;            % proportional gain
Ki  = 0.324;            % integral gain
Kd  = 4.650;            % derivative gain
N   = 114.29;           % 1st-order derivative filter coefficient
Gc  = pid(Kp, Ki, Kd, 1/N)

Gc =
 
             1            s    
  Kp + Ki * --- + Kd * --------
             s          Tf*s+1 

  with Kp = 2.46, Ki = 0.324, Kd = 4.65, Tf = 0.00875
 
Continuous-time PIDF controller in parallel form.

margin(Gc*Gp)

% closed-loop transfer function from Disturbance R(s) to Output Y(s)
Gcd = feedback(Gp, Gc)

Gcd =
 
                   s^2 + 114.3 s
  -----------------------------------------------
  5 s^4 + 571.5 s^3 + 533.9 s^2 + 281.5 s + 37.03
 
Continuous-time transfer function.

step(Gcd), grid on      % Response to a Unit step disturbance

If the output response to a unit step disturbance D(s) = 1 goes to zero in 50 seconds, then rest assured that the output will track the unit step reference R(s) = 1.

% closed-loop transfer function from Reference R(s) to Output Y(s)
Gcl = feedback(Gc*Gp, 1)

Gcl =
 
            533.9 s^2 + 281.5 s + 37.03
  -----------------------------------------------
  5 s^4 + 571.5 s^3 + 533.9 s^2 + 281.5 s + 37.03
 
Continuous-time transfer function.

step(Gcl, 60), grid on  % Step Response