The closed-loop transfer function for Y(s)/D(s) is given by
The following shows how to compute the comparison between the step responses for 40 seconds. Let us know if this is the technical answer that you are looking for.
s = tf('s');
% Parameters
K = 2;
Tau = 3;
dt = 0.9;
% Plant
Gp = ((2/(3*s + 1))*(exp(-dt*s)));
% Cohen - Coon PI tuning
Kc = (1/K)*(Tau/dt)*(0.9 + (dt/(12*Tau)));
Tau_1 = (dt)*((30 + 3*(dt/Tau))/(9 + 20*(dt/Tau)));
Kp = Kc;
Ki = Kc/Tau_1;
Gc = ((Kp*s + Ki)/s);
% Response to the Unit Step Reference
Gol = Gc*Gp;
Gcl = feedback(Gol, 1); % closed-loop transfer function Y(s)/R(s)
step(Gcl, 40)
hold on
% Response to the Unit Step Disturbance
Gcd = feedback(Gp, Gc); % closed-loop transfer function Y(s)/D(s)
step(Gcd, 40)
legend('Step Reference Response', 'Step Disturbance Response')
hold off, grid on
