GATE 2014 EE (EE2) – Question 54
$G(s)=K/[s(s+2)(s^2+2s+2)]$ has unity negative feedback. Find K for marginal closed-loop stability.
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Correct answer: 5 to 5
Explanation
The characteristic polynomial is s(s+2)(s²+2s+2)+K=s⁴+4s³+6s²+4s+K. Its Routh first column is1,4,5,(20−4K)/5,K. For positive gain,the upper stability boundary is K=5. The auxiliary equation5s²+5=0gives the imaginary pair±j. Thus the requested nonzero boundary is **K=5**.