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GATE 2014 EE (EE1) – Question 54

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Numerical answer

Find the minimum α for stability of the system shown.

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Correct answer: 0.61 to 0.63

Explanation

Adding the forward numerator under unity negative feedback gives characteristic polynomial s³+(1+α)s²+αs+1. The cubic Routh condition is α>0and α(1+α)>1. Thus αmust exceed(√5−1)/2=**0.618034**. This is the infimum or boundary; equality gives an imaginary-axis pair and is not strictly stable.