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GATE 2022 EE – Question 17

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 1 mark · Multiple choice

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is $-180^\circ$. This system has

Diagram for GATE 2022 EE question 17
  1. one LHP pole and one RHP zero at the same frequency.
  2. one LHP pole and one LHP zero at the same frequency.
  3. two LHP poles and one RHP zero.
  4. two RHP poles and one LHP zero.

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Show answer and explanation

Correct answer: (A) one LHP pole and one RHP zero at the same frequency.

Explanation

A constant magnitude means the pole and zero are at the same frequency (an all-pass system). Stability needs the pole in the left half plane. The phase of $\frac{a-s}{a+s}$ is $0^\circ$ at DC and falls to $-180^\circ$ at high frequency, which requires the zero in the right half plane.