How to get a close loop transfer function from an open loop one?

Hi all

The transfer function for my open loop system is

13.11 s^3 + 30.28 s^2 - 17650 s - 692.3

-------------------------------------------------

s^5 + 19.97 s^4 + 150.1 s^3 + 12.95 s^2 + 26.24 s

I wanted to know how to get the close loop equivalent of that transfer function above on MATLAB?

Kind regards

Answer 1

[Sam Chak]

Hi @Maaz Madha

Assuming that the sensor measures perfectly (), then this is one of the ways:

s = tf('s');
G = (13.11*s^3 + 30.28*s^2 - 17650*s - 692.3)/(s^5 + 19.97*s^4 + 150.1*s^3 + 12.95*s^2 + 26.24*s)
H = 1;
Gcl = G/(1 + G*H)   % closed-loop transfer function
Gcl = minreal(Gcl)  % minimal order of Gcl
pole(Gcl)           % find the poles of  Gcl

ans =

-14.6294 + 0i

-6.1635 + 11.5538i

-6.1635 - 11.5538i

7.0258 + 0i

-0.0393 + 0i

Since one of the poles is in the right-half s plane, then the system is unstable. You will need to design a compensator to stabilize it.

[Sam Chak]

Here is the second approach:

G = tf([13.11 30.28 -17650 -692.3], [1 19.97 150.1 12.95 26.24 0])
Gcl = feedback(G, 1)
pole(Gcl)

For more details, I suggest you to check these links:

https://www.mathworks.com/help/control/ref/tf.html

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