Gain Margin, Open or Closed Loop?

[saad87]

Homework Statement

I'm given a closed loop transfer function with a gain, K=1 and a plant H(s). I need to find the gain margin of the system.

Homework Equations

I know how to solve this problem:

a) I find the frequency where the phase is -180 degrees.
b) I find the gain at that frequency, let's called that a.
c) the gain margin is 1/a.

What I'm confused about is, to find the gain margin, do I use the open loop transfer function K.H or the closed loop transfer function KH/(1+KH)?

 

[overt26]

What I'm confused about is, to find the gain margin, do I use the open loop transfer function K.H or the closed loop transfer function KH/(1+KH)?

You use the open loop TF.

 

[Mene]

To find the gain margin of a system, you will need to use the closed loop transfer function. The open loop transfer function, K.H, does not take into account the feedback loop and therefore does not accurately represent the overall system. The closed loop transfer function, KH/(1+KH), takes into account the feedback loop and provides a more accurate representation of the system. Using this function, you can follow the steps outlined in the problem to find the gain margin. It is important to use the closed loop transfer function in order to accurately assess the stability and performance of the system.