GATE 2016 EE (EE2) – Question 31

Control Systems · Lag, Lead and Lead-Lag compensators; P, PI and PID controllers · 1 mark · Numerical answer

For the shown RC network, the angular frequency in rad/s at which maximum phase lag occurs is ________.

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Correct answer: 0.30 to 0.33

Explanation

The lower branch impedance is $1+1/s$, giving transfer $H(s)=(1+s)/(1+10s)$. The zero is at −1 and pole at −0.1 rad/s.

For this first-order lag network, maximum lag occurs at the geometric mean of pole and zero frequencies: $\omega_m=\sqrt{0.1\cdot1}=$ **0.316228 rad/s**, in 0.30–0.33.

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