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GATE 2023 IN – Question 43

Control Systems · Stability and frequency response · 2 marks · Multiple choice

Which transfer function matches the magnitude and phase plots shown?

Diagram for GATE 2023 IN question 43
  1. $\dfrac{10000}{s^2+2s+10000}$
  2. $\dfrac{10000e^{-0.05s}}{s^2+2s+10000}$
  3. $\dfrac{10000e^{-0.5\times10^{-12}s}}{s^2+2s+10000}$
  4. $\dfrac{100}{s^2+2s+100}$

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Show answer and explanation

Correct answer: (B) $\dfrac{10000e^{-0.05s}}{s^2+2s+10000}$

Explanation

The resonance near 100 rad/s selects denominator $s^2+2s+10000$. A second-order system alone approaches −180°, whereas the plotted phase continues far below it. A 0.05 s delay adds phase $-0.05\omega$ radians: at 200 rad/s, about −573°, consistent with the plot. Answer: **B**.