GATE EE 2023 Set 1 — Question 38
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Control Systems → Compensators & Controllers → Bode Plots
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Question
Consider a lead compensator of the formThe frequency at which this compensator produces maximum phase lead is 4 rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bode-magnitude plot of , is 6 dB. The values of , respectively, are
Correct answer
(B) 2, 4
Solution
1.The transfer function of the lead compensator is given as . The corner frequencies are and .
2.The frequency of maximum phase lead () is the geometric mean of the corner frequencies:
Given rad/s, we have .3.In the asymptotic Bode magnitude plot, the gain is 0 dB for . For , the gain increases at a slope of +20 dB/decade. The gain at any frequency in this range is:
4.At , the gain is:
5.Given the gain at is 6 dB:
6.Substituting into the equation for :
7.Thus, and , which corresponds to option (B).
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