GATE 2014 EC (EC4) – Question 58
A unity negative-feedback system has characteristic equation $1+KG(s)=0$. G(s) has one pole at 0 and two at −1. The root locus is shown. The constant-damping line ξ = 0.5 intersects it at A, whose distance from the origin is 0.5. Find K at A.
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Correct answer: 0.32 to 0.41
Explanation
With ζ=0.5and distance|s|=0.5, the point is s=−0.25+j√3/4. For the intended normalized G(s)=1/[s(s+1)²], the magnitude condition gives K=|s||s+1|²=0.5×(0.75²+3/16)=**0.375**. An additional gain constant in G would rescale K; the source specifies only the pole locations and implicitly assumes unit numerator.