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GATE 2014 EE (EE1) – Question 28

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

Find the closed-loop transfer function C(s)/R(s) corresponding to the unity-feedback root locus shown.

Diagram for GATE 2014 EE (EE1) question 28
  1. $K/[(s+1)(s+2)]$
  2. $-K/[(s+1)(s+2)+K]$
  3. $K/[(s+1)(s+2)-K]$
  4. $K/[(s+1)(s+2)+K]$

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Correct answer: (C) $K/[(s+1)(s+2)-K]$

Explanation

The locus starts at−1and−2and moves outward along the real axis. This corresponds to(s+1)(s+2)−K=0, whose roots are[−3±√(1+4K)]/2, moving apart as K grows. Among the supplied closed-loop functions, **K/[(s+1)(s+2)−K],C** has this denominator. A plus-Kdenominator would move the roots together and then off the real axis.