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
% 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)
margin(Gc*Gp)
% closed-loop transfer function from Disturbance R(s) to Output Y(s)
Gcd = feedback(Gp, Gc)
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)
step(Gcl, 60), grid on % Step Response
