For the following multi-loop feedback system, get closed loop transfer function and the corresponding pole-zero map of the system

i need help to solve this question on matlab. please help me how to solve it including the codes and everything .

Answer 1

[nick]

Hello osama,

I understand from your query that you need assistance with building the block diagram and obtaining the closed-loop transfer function of the multi-loop feedback system in MATLAB.

To achieve this, you can follow the steps mentioned below:

1. Use the “tf” function to define the transfer functions G1, G2, G3, G4, H1, H2, and H3.
2. Use the “series” function to connect the blocks in series and the “feedback” function to connect the systems with a feedback connection, as shown in the code snippet below:

%% Define the transfer functions 
G1 = tf([1],[1 10]) 
G2 = tf([1],[1 1]) 
G3 = tf([1 0 1],[1 4 4]) 
G4 = tf([1 1],[1 6]) 
H1 = tf([1 1],[1 6]) 
H2 = tf([2],[1 ]) 
H3 = tf([1],[1]) 
%% Connect the individual systems using feedback or series connection 
sys1 = H2/G4; 
sys2 = series(G3,G4); 
sys3 = feedback(sys2,H1,+1); 
sys4 = series(G2, sys3); 
sys5 = feedback(sys4,sys1); 
sys6 = series(G1,sys5); 
sys = feedback(sys6,H3) 

Here is the obtained output:

Figure 1 Output Transfer function of the multi-loop feedback system

Kindly refer the following documentations to learn more about “feedback” and “series” functions :

https://www.mathworks.com/help/control/ref/inputoutputmodel.feedback.html

https://www.mathworks.com/help/control/ref/inputoutputmodel.series.html

Hope this helps,

Regards,

Neelanshu