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GATE 2014 EE (EE2) – Question 55

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

For $G(s)=5(s+4)/[s(s+0.25)(s^2+4s+25)]$, find normalized constant gain term and highest Bode corner frequency respectively.

  1. 3.2, 5.0
  2. 16.0, 4.0
  3. 3.2, 4.0
  4. 16.0, 5.0

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Correct answer: (A) 3.2, 5.0

Explanation

Normalize(s+4)=4(1+s/4),(s+0.25)=0.25(1+s/0.25),and(s²+4s+25)=25[1+(4/25)s+s²/25]. The constant coefficient is5×4/(0.25×25)=3.2. Corners are0.25,4and√25=5rad/s,the largest being5. Hence **3.2,5.0,A**. This constant factor is not a finite dc gain because an integrator remains.