The open loop transfer function of a unity gain negative feedback system is given by G(s)=ks2+4s-5. The range of k for which the system is stable, is

GATE 2022 EE – Question 19

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

The open loop transfer function of a unity gain negative feedback system is given by $G(s)=\dfrac{k}{s^2+4s-5}$. The range of $k$ for which the system is stable, is

$k>3$
$k<3$
$k>5$
$k<5$

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Correct answer: (C) $k>5$

Explanation

The characteristic equation is $s^2+4s-5+k=0$. For a second-order polynomial all coefficients must be positive, so $k-5>0$, i.e. $k>5$.