PID - Root Locus (Sisotool) for Transfer Function with Zeros and Poles

[Brian1776]

Hi everyone! I have a 8th order transfer function, you can see it in the first image:

% Transfer function
num = [2.091,0,203.3,0,-2151,0,-1.072e05];
den = [1,0,-830.4,0,-1.036e05,0,-5.767e05,0,2.412e07];
tf = tf(num, den)

I need to use a PID, so I'm trying to use a compensator, adding poles and zero with the sisotool in MatLab to turn it stable. But iI tried, I tried, and tried, without success. How you can see in picture bellow. But the zero on the right side always holds a pole.
Note: Red zeros and poles have been added, and blue ones belong to the original transfer function.

My question is:
Is it possible stable this function adding zeros and poles, or not ?

Any tips ?
Note: I must use a PID for this lesson :(

 

[Valkarie]

Yes, it is possible to stabilize the transfer function by adding zeros and poles. However, it may take some trial and error to find a configuration that works. You may want to experiment with different combinations of zeros and poles, as well as adjusting the parameters of the PID controller. Additionally, you may want to consider using a more advanced type of controller, such as an Adaptive Control, which is designed to automatically adjust itself based on feedback from the system.