I have two root locus of two closed loop transfer fuctions, which differ just by a different value of the gain. I have that the one with a larger gain has a reasonance peak bigger in the frequency responce and the one with the smaller gain as almost no overshoot. I also plotted the root locus to see this:

for the transfer function with a larger gain I have

enter image description here

while for the one with smaller gain:

enter image description here

I can see that the upper one has two poles complex conjugate, so I guess this is the reason for the reasonance peak.

My question is: Why the transfer fuction with smaller gain has only poles on the real axis, while the one with the larger gain has two conjugate poles?

I have also tried tuning values of the gain, and what I get is that as I increase the gain the distance between the conjugate poles increases.

Can somebody please explain this behaviour? And what is the relationship between complex conjugate poles and resonance peak?

Thanks in advance.


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