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GATE 2020 IN – Question 16

Control Systems · Controllers and compensators: On-off, P, PI, PID, cascade, feed forward and ratio controllers, tuning of PID controllers, lead, lag and lead-lag compensators, actuators (control valves, servo valves, servo motors, stepper motors), supervisory control, DCS and PLC · 1 mark · Multiple choice

A phase-lead network has $G(s)=(1+0.2s)/(1+0.05s)$. Its maximum phase shift occurs at angular frequency

  1. 10 rad/s
  2. 20 rad/s
  3. 100 rad/s
  4. 200 rad/s

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Show answer and explanation

Correct answer: (A) 10 rad/s

Explanation

The phase is $\phi(\omega)=\tan^{-1}(0.2\omega)-\tan^{-1}(0.05\omega)$. Setting its derivative to zero gives $\omega_m=1/\sqrt{0.2(0.05)}=10$ rad/s, the geometric mean of its zero and pole frequencies, 5 and 20 rad/s. Select A.

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