GATE EC 2014 Set 1 — Question 57
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Control Systems → Frequency-Domain Analysis → Bode Plots
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Question
The phase margin in degrees of calculated using the asymptotic Bode plot is ________.
Correct answer
42 to 48
Solution
To calculate the phase margin using the asymptotic Bode plot, we first express the transfer function in the standard time-constant form:The corner frequencies are rad/s, rad/s, and rad/s.1. Asymptotic Magnitude Plot to find Gain Crossover Frequency ():
Using the standard asymptotic phase approximation for a pole at :
- For : Magnitude dB. The slope is 0 dB/dec.
- For : The pole at introduces a slope of dB/dec.
- At rad/s: dB.
Using the standard asymptotic phase approximation for a pole at :
- for
- at
- for
- Phase due to pole at : Since , .
- Phase due to pole at : Since , .
- Phase due to pole at : Since , .
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