Question: Define Gain margin and Phase margin. Explain how these margin are used for stability analysis.
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Mumbai University > Electronics Engineering > Sem 4 > Linear Control Systems

Topic: Stability Analysis in Frequency Domain

Difficulty : Medium

Marks : 5M

lcs(43) • 245 views
 modified 6 months ago by written 7 months ago by
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Gain Margin =>

i) The gain margin, Kg is defined as the value of gain to be added to system, in order to bring the system,to the verge of instability

ii) The gain margin, kg is given by the Reciprocol of the magnitude of open loop transfer function at phase cross over frequency. The frequency at which the phase of open loop Transfer function is 180 is called the phase cross-over frequency, $w_{pe}$

iii) Gain margin, Kg = $\frac{1}{|G(jw_{pc})|}$

In db,

Kg in db = 20 log kg = 20log $\frac{1}{|G(jw_{pc})|}$

iv) The gain margin indicates the additional gain that can be provided to system without affecting the stability of the system.

Phase marging=>

i) The phase margin Y is defined as the additional phase log to be added at the gain cross over frequency in order to bring the system to the verge of instability.

ii) The gain cross over frequency $w_{gc}$ is the frequency at which the magnitude of the loop transfer function in unity.

iii) The phase margin Y is obtained by adding 180 to the phase angle 0 of the open lop tranfer function at the gain cross over frequency,

phase margin Y = 180 + $\phi_{gc}$ , where $\phi_{gc} = \lt G(jw_{gc})$

iv) The phase margin indicates the additional phase log that can be provided to the system without affecting stability.

Note => For definition of gain and phase margin write only 1st point and formulae.