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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)

enter image description here

enter image description here

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.

enter image description here

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 :(

Brian1776
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  • A bode plot might help. – Andy aka Jul 11 '21 at 15:58
  • You have poles on the right hand side. – a concerned citizen Jul 11 '21 at 16:15
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    A PID controller places a pole at the origin - your root locus does not seem to show this. Also, a PID can contribute two left-plane zeros, so there are only two parameters that you can play with. – Chu Jul 11 '21 at 17:04
  • **1** In the siso design figure, it seems that you placed two more poles on the RHS to try to stabilize the system. So the controller is also unstable in that design. I don't know if that is a good strategy. **2** you have two poles on the RHS and a zero in between them. Is it even possible to bring both those open loop poles to LHS simultaneously since poles have a tendency to move towards the zero as gain increases. **3** what is this system physically? Perhaps the transfer function extraction went wrong somewhere. – AJN Jul 12 '21 at 01:20

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