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GATE 2017 EC – Question 29

Control Systems · Frequency Response · 1 mark · Multiple choice

Consider a stable system with transfer function

$$G(s) = \frac{s^p + b_1 s^{p-1} + \cdots + b_p}{s^q + a_1 s^{q-1} + \cdots + a_q}$$

where $b_1, \ldots, b_p$ and $a_1, \ldots, a_q$ are real valued constants. The slope of the Bode log magnitude curve of $G(s)$ converges to $-60$ dB/decade as $\omega \to \infty$. A possible pair of values for $p$ and $q$ is

  1. $p = 0$ and $q = 3$
  2. $p = 1$ and $q = 7$
  3. $p = 2$ and $q = 3$
  4. $p = 3$ and $q = 5$

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Correct answer: (A) $p = 0$ and $q = 3$

Explanation

At high frequency the slope of the Bode magnitude plot is $-20(q - p)$ dB/decade. For $-60$ dB/decade we need $q - p = 3$. Only $p = 0$, $q = 3$ gives that difference.