I understand the physical significance of gain and phase margin. However, I would like some clarification regarding the mathematical aspects. Videos such as the following:
https://www.youtube.com/watch?v=ThoA4amCAX4 (time: 6:28)
https://www.youtube.com/watch?v=ThoA4amCAX4 (time: 7:12)
define phase margin and gain margin for unity feedback. Even in Matlab when we plot bode of any transfer function, it assumes unity feedback. What's so special about unity feedback?
My next question is, if I want to find gain and phase margin of system with gain G(s) and feedback H(s), whose gain and phase should I plot among the following:
G(s)/(1+G(s)) ? (unity feedback transfer function)
G(s)/(1+G(s)H(s)) ? (closed loop transfer function)
G(s)H(s) ? (loop gain)
I feel it should be option 4 but I would like to confirm since nothing seems to mention which bode plot they are checking to obtain PM and GM, and unity gain feedback seems to be extremely popular for some reason.