Gain Margin
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## 1 Introduction to Gain Margin[1]

The gain margin (GM) is the factor by which the gain is less than the neutral stability value. For the typical case it can be read directly from the open loop Bode plot.

The gain margin is is the factor by which the controller gain can be changed before the system goes unstable.

## 2 Determining the Gain Margin

The gain margin is determined from the open loop Bode plot by finding the frequency ω where

 $LaTeX: \angle G\left(j\omega \right) = -180^\circ$

At ω the magnitude is the gain margin.

The system is unstable when

 $LaTeX: \left | GM \right | < 1$ - not in dB

## 3 Gain Margin Guideline

A good gain margin is > 9 dB.

## 4 References

• Franklin, G. F., Emami-Naeini, A., and Powell, J. D. 1993 Feedback Control of Dynamic Systems. 3rd. Addison-Wesley Longman Publishing Co., Inc. ISBN 0201527472

### 4.1 Notes

1. Franklin, pg. 375