Question

The open-loop DC gain of a unity negative feedback system with closed-loop transfer function is given by \( \frac{5}{4 + 5s + 13s^2} \), what is the open-loop DC gain?

• A. \( \frac{4}{13} \)
• B. 4
• C. \( \frac{4}{9} \)
• D. 13

Hint:

For unity feedback systems, remember that the open-loop DC gain is evaluated by substituting \( s = 0 \) in the transfer function denominator.

Answer 1

The Correct Option is A

For unity feedback systems, the open-loop DC gain is calculated as the inverse of the value of the denominator evaluated at \( s = 0 \). For the given system, the open-loop gain is calculated as: \[ \frac{5}{4 + 5(0) + 13(0)^2} = \frac{5}{4}. \] This gives the open-loop DC gain of \( \frac{4}{13} \).