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GATE 2020 EE – Question 46

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

Consider a negative unity feedback system with the forward path transfer function $\dfrac{s^2+s+1}{s^3+2s^2+2s+K}$, where $K$ is a positive real number. The value of $K$ for which the system will have some of its poles on the imaginary axis is ________.

  1. 9
  2. 8
  3. 7
  4. 6

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Correct answer: (B) 8

Explanation

The closed-loop characteristic equation is $s^3+2s^2+2s+K+s^2+s+1=s^3+3s^2+3s+(K+1)=0$. The Routh array has a zero in the $s^1$ row when $3\times3=K+1$, so $K=8$, giving poles on the imaginary axis.