Topic: Control Systems
The open-loop DC gain of a unity negative feedback system with closed loop transfer function $(s+4)/(s^{2}+7s+13)$ is
- A. $4/13$
- B. 4
- C. $4/9$
- D. 13
Answer: C. $4/9$
Explanation: Closed loop T.F. $= \frac{G(s)}{1+G(s)} = \frac{s+4}{s^{2}+7s+13}$.
Open loop T.F. $G(s) = \frac{\text{Numerator}}{\text{Denominator} - \text{Numerator}} = \frac{s+4}{s^{2}+7s+13 - (s+4)} = \frac{s+4}{s^{2}+6s+9}$.
Open loop DC gain is obtained by putting $s=0$: $G(0) = \frac{4}{9}$.