Question

1. Obtain the response of the closed loop system using MATLAB:

C(s)/R(s) = 5 / (s^2 + s + 5) when the input is given by r(t) = 1 + t^2

Answer 1

1. If the given transfer function is closed loop system, use the below code to obtain the response with given input

sys = tf([5],[1 1 5])
%sys = feedback(sys,1)
t = 0:0.1:1;
u = 1+t.^2;
lsim(sys,u,t)

This gives the systems response for the input r(t).

The response obtained is

2. If the given Transfer function is closed loop system, then use the below code to obtain the system response fro given input

sys = tf([5],[1 1 5])
sys = feedback(sys,1)
t = 0:0.1:1;
u = 1+t.^2;
lsim(sys,u,t)

The resposne obtained is:

Here we can change the time for which we want the simulation to be run by updating 't' value range in the code.