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GATE 2015 EE – Question 34

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 1 mark · Multiple choice

A Bode magnitude plot for the transfer function $G(s)$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

A Bode magnitude plot against frequency in Hz. The gain is flat at 20 dB at low frequency, falls from about 10 Hz down to -20 dB at about 1 kHz, and then stays flat at -20 dB.
  1. $\frac{1000(s + 10)}{s + 1000}$
  2. $\frac{10(s + 10)}{s(s + 1000)}$
  3. $\frac{s + 1000}{10s(s + 10)}$
  4. $\frac{s + 1000}{10(s + 10)}$

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Correct answer: (D) $\frac{s + 1000}{10(s + 10)}$

Explanation

The low-frequency gain is 20 dB, which is 10, and the high-frequency gain is $-20$ dB, which is 0.1. Option D at $s \to 0$ gives $\frac{1000}{100} = 10$ and at $s \to \infty$ gives $\frac{1}{10} = 0.1$. Its pole at 10 starts the drop and its zero at 1000 ends it, which matches the plot.