Lets say there is a system
H(s) = 3/s
which I want to control with a controller
G(s) = Kp·(1+10/s)
The Bode diagram of the open loop G(s)H(s) with Kp=1 is:
At the transit frequency the phase is about -150°, which gives a phase margin of 30°.
Decreasing K makes the phase reserve smaller and ringing is increased:
Q1: I understand this behavior, but usually it is said that by increasing Kp the system gets more unstable, but here the opposite is the case. So why is there a "discrepancy"?
Q2: (This is the main question): How is gain margin defined here? In my opinion, GM is infinite, because gain can be increased infinitely without making the system unstable.
EDIT: LTSpice simulation of the same system