GATE EC 2018 Set 1 — Question 52
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Control Systems → Frequency-Domain Analysis → Bode Plots
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Question
The figure below shows the Bode magnitude and phase plots of a stable transfer function .
Consider the negative unity feedback configuration with gain in the feedforward path. The closed loop is stable for . The maximum value of is ______.
Correct answer
0.1 to 0.1
Solution
From the Bode plot, the phase crossover frequency is the frequency where the phase is .
At this frequency, the magnitude of is read from the magnitude plot as .
.For the closed-loop system with gain to be stable, the loop gain at the phase crossover frequency must be less than 1:
.
Thus, the maximum value of for stability is .
At this frequency, the magnitude of is read from the magnitude plot as .
.For the closed-loop system with gain to be stable, the loop gain at the phase crossover frequency must be less than 1:
.
Thus, the maximum value of for stability is .
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