GATE EC 2016 Set 2 — Question 56
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Control Systems → Stability Analysis → Gain & Phase Margin
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Question
In the feedback system shown below .
The positive value of for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is ________
Correct answer
59.5 to 60.5
Solution
The open-loop transfer function is .
The characteristic equation is .
Expanding the terms: .
For the gain margin to be 0 dB and phase margin to be 0 degrees, the system must be marginally stable.
Using the Routh-Hurwitz criterion:
.
The characteristic equation is .
Expanding the terms: .
For the gain margin to be 0 dB and phase margin to be 0 degrees, the system must be marginally stable.
Using the Routh-Hurwitz criterion:
- : 1, 11
- : 6,
- :
- :
.
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