Question

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

• A. \( \frac{1}{s^2 + 5} \)
• B. \( \frac{1}{(5^2 + s)} \)
• C. \( \frac{1}{(s^2 + 5s + 1)} \)
• D. \( \frac{s}{(s^2 + 5)} \)

Hint:

For unity feedback: \( T(s) = \frac{G(s)}{1 + G(s)} \)

Answer 1

The Correct Option is C

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