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GATE 2016 EC (EC3) – Question 56

Control Systems · Routh-Hurwitz and Nyquist Stability Criteria · 2 marks · Multiple choice

The first two rows of a cubic system's Routh table are
$$\begin{array}{c|cc}s^3&1&2K+3\\s^2&2K&4\end{array}.$$
The stable range of K is

  1. $-2<K<0.5$
  2. $0<K<0.5$
  3. $0<K<\infty$
  4. $0.5<K<\infty$

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Correct answer: (D) $0.5<K<\infty$

Explanation

The first-column entries are $1$, $2K$, $[2K(2K+3)-4]/(2K)$ and 4. All must be positive for strict stability.

First K>0. The numerator condition reduces to $4K^2+6K-4=2(2K-1)(K+2)>0$. With K positive, this requires K>1/2.

Thus the stable range is **0.5<K<∞, D**; equality places roots on the imaginary axis.

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