Gain Margin, Open or Closed Loop?

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SUMMARY

The discussion centers on calculating the gain margin of a closed loop system with a gain of K=1 and a plant H(s). To determine the gain margin, the correct approach is to utilize the open loop transfer function, represented as K.H. The steps outlined include finding the frequency where the phase is -180 degrees, determining the gain at that frequency, and calculating the gain margin as 1/a, where 'a' is the gain at the specified frequency.

PREREQUISITES
  • Understanding of control systems and transfer functions
  • Familiarity with gain margin and phase margin concepts
  • Knowledge of frequency response analysis
  • Proficiency in using Bode plots for stability analysis
NEXT STEPS
  • Study the calculation of gain margin using Bode plots
  • Learn about the implications of phase margin on system stability
  • Explore the differences between open loop and closed loop transfer functions
  • Investigate the effects of varying gain K on system performance
USEFUL FOR

Control engineers, system analysts, and students studying control theory who need to understand gain margin calculations in closed loop systems.

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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