Gain Margin, Open or Closed Loop?

AI Thread Summary
To determine the gain margin of a system with a closed loop transfer function, the open loop transfer function K.H should be used. The process involves finding the frequency where the phase reaches -180 degrees and then determining the gain at that frequency. The gain margin is calculated as the reciprocal of this gain. The closed loop transfer function KH/(1+KH) is not applicable for this calculation. Therefore, for gain margin analysis, always utilize the open loop transfer function.
saad87
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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)?
 
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saad87 said:
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.
 

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