Question
Download Solution PDFAssertion: Gain margin is the factor by which the system gain can be decreased to drive it to the verge of instability.Reason:
Gain margin is the reciprocal of the gain at a frequency at which the phase angle becomes 180°
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGain margin (GM):
The gain margin of the system defines by how much the system gain can be increased so that the system moves on the edge of stability
∴ Assertion Statement is incorrect.
It is determined from the gain at the phase cross over frequency, i.e.
Phase crossover frequency (ωpc) is the frequency at which phase angle of G(s) H(s) is -180°, i.e.
The Reason is therefore correct.
NOTES:
Phase margin (PM):
The phase margin of the system defines by how much the phase of the system can increase to make the system unstable.
It is determined from the phase at the gain cross over frequency.
Gain crossover frequency (ωgc): It is the frequency at which the magnitude of G(s) H(s) is unity.
- If both GM and PM are positive, the system is stable (ωgc < ωpc)
- If both GM and PM are negative, the system is unstable (ωgc > ωpc)
- If both GM and PM are zero, the system is just stable (ωgc = ωpc)
Last updated on Jul 4, 2025
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