A Bode magnitude plot for the transfer function \( G(s) \) of a plant is shown below. Which one of the following transfer functions best describes the plant?
- \( \frac{100}{s (s + 10)} \)
- \( \frac{s + 1000}{s^2 (s + 10)} \)
- \( \frac{10 (s + 10)}{s^2 + 1000} \)
- \( \frac{10 (s + 10)}{s (s + 1000)} \)
The Correct Option is A
Solution and Explanation
Based on the Bode plot characteristics, we observe a slope change at break frequencies. The transfer function \[ \frac{100}{s(s+10)} \] fits the magnitude plot due to a pole at the origin and another pole at \( s = 10 \).
\(\text{Conclusion:}\) The correct transfer function is given by option (a).
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