The GATE Grind

GATE 2017 EE – Question 21

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

A closed loop system has the characteristic equation given by $s^3 + Ks^2 + (K + 2)s + 3 = 0$. For this system to be stable, which one of the following conditions should be satisfied?

  1. $0 < K < 0.5$
  2. $0.5 < K < 1$
  3. $0 < K < 1$
  4. $K > 1$

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Correct answer: (D) $K > 1$

Explanation

In the Routh array the first column is $1$, $K$, $\frac{K(K + 2) - 3}{K}$ and $3$. For stability $K > 0$ and $K^2 + 2K - 3 > 0$, which factors as $(K + 3)(K - 1) > 0$. So $K > 1$.