unit step disturbance at a time of 40 seconds

How do I generate a unit step disturbance at a time of 40 seconds for my PID controller

clear all;
s=tf('s');
load time.dat;
load response.dat;
K = 2;
Tau = 3;
dt = 0.9;
g = ((2/(3*s + 1))*(exp(-dt*s)))
[gy,tg]=step(g,20)
plot(time, response,'k',tg,gy,'r','LineWidth',2)
hold on
% 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)));
P = Kc;
I = Kc/Tau_1;
cont = ((s*P + I)/s);
gol = cont*g
gcl = feedback(gol,1)
step(gcl,20)
hold on
grid on

Thanks

Answer 1

[Sam Chak]

Hi @MUHAMED SIDIBEH

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