Topic: Control Systems
Which of the following is the error transfer function for negative feedback?
- A. $\frac{1}{1+GH}$
- B. $\frac{G}{1+GH}$
- C. $\frac{GH}{1+GH}$
- D. $\frac{-1}{1+GH}$
Answer: A. $\frac{1}{1+GH}$
Explanation: In a standard closed-loop control system with negative feedback, the error signal $E(s)$ is the difference between the reference input $R(s)$ and the feedback signal $B(s)$.
$E(s) = R(s) - B(s) = R(s) - E(s)G(s)H(s)$.
$E(s)[1 + G(s)H(s)] = R(s)$.
The error transfer function is $\frac{E(s)}{R(s)} = \frac{1}{1+G(s)H(s)}$.