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GATE 2019 EE – Question 40

Control Systems · Lag, Lead and Lead-Lag compensators; P, PI and PID controllers · 2 marks · Multiple choice

The transfer function of a phase lead compensator is given by

$$D(s)=\frac{3\left(s+\frac1{3T}\right)}{\left(s+\frac1T\right)}$$

The frequency (in rad/sec), at which $\angle D(j\omega)$ is maximum, is

  1. $\sqrt{\dfrac{3}{T^2}}$
  2. $\sqrt{\dfrac{1}{3T^2}}$
  3. $\sqrt3T$
  4. $\sqrt3T^2$

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Correct answer: (B) $\sqrt{\dfrac{1}{3T^2}}$

Explanation

The maximum phase lead occurs at the geometric mean of the zero and pole frequencies: $\omega_m=\sqrt{\frac{1}{3T}\cdot\frac1T}=\sqrt{\frac{1}{3T^2}}$.