How to plot the response of a closed loop system to a reference signal?

I would like to kindly ask how to plot the response of a closed loop system to a given reference signal.

A very simple closed loop system is provided below, time intervals, and specified 'w':

Many thanks in advance.

Answer 1

[Sarvesh Kale]

Hi Thomas,

I hope the following code snippet helps

% construct transfer function using tf 
g = tf(10*[1 4],[1 4 5 0]);
k=  tf([1 1],[1 3]);

% obtain the overall transfer function 
y_by_x = feedback(g*k,1);

% define input 
t = 0:0.01:10;
w=1.7;
r = sin(w*t);

%visualize result 
figure ;
lsim(y_by_x,r,t) % used to simulate response to input  

the gray line in input to system and the line is blue is the system output, since the input is sinusoidal, the output will also be sinusoidal in nature by definition of LTI systems, for more help on feedback, lsim, and tf refer the following documentation

transfer function, system resposnse, feedback.

I hope this helps, please accept the answer if query resolved.

Thank you

[Thomas]

This was very helpful, thank you for sharing you're knowledge.

[Thomas]

Is there any Matlab function which could estimate the Phase Shift that is present between the output and reference signal in closed loop systems such as this?