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GATE 2014 EC (EC1) – Question 31

Control Systems · Routh-Hurwitz and Nyquist Stability Criteria · 1 mark · Multiple choice

The feedback system and Nyquist plot of G(s) are shown. Which conclusion is correct?

Diagram for GATE 2014 EC (EC1) question 31
  1. G(s) is an all-pass filter
  2. G(s) is strictly proper
  3. G(s) is stable and minimum-phase
  4. The closed-loop system is unstable for sufficiently large positive k

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Show answer and explanation

Correct answer: (D) The closed-loop system is unstable for sufficiently large positive k

Explanation

The circular locus has a negative-real intersection between−1 and0 and the indicated clockwise traversal. Increasing positive k scales the locus about the origin. For sufficiently large k it surrounds−1 clockwise, producing a positive number of unstable closed-loop poles by the Nyquist criterion. Therefore **D**. A circle not centred at the origin does not establish an all-pass response.