Question:

A unity feedback system has open loop transfer function \( \frac{1}{(s^2 + 5)} \), then the closed loop transfer function is

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For unity feedback: \( T(s) = \frac{G(s)}{1 + G(s)} \)
Updated On: May 23, 2025
  • \( \frac{1}{s^2 + 5} \)
  • \( \frac{1}{(5^2 + s)} \)
  • \( \frac{1}{(s^2 + 5s + 1)} \)
  • \( \frac{s}{(s^2 + 5)} \)
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The Correct Option is C

Solution and Explanation

Closed-loop transfer function for unity feedback is: \[ T(s) = \frac{G(s)}{1 + G(s)} = \frac{1 / (s^2 + 5)}{1 + 1 / (s^2 + 5)} = \frac{1}{s^2 + 5 + 1} = \frac{1}{s^2 + 5s + 1} \]
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