Which of the following is the error transfer function for negative feedback?

Question

Question

This question was previously asked in

ISRO Scientist Electronics 2024 Official Paper

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Answer 1

Concept:

The error signal in a negative feedback control system is the difference between the input and the feedback signal.

The transfer function for error is given by:

\( \frac{E(s)}{R(s)} = \frac{1}{1 + GH} \)

Where:

R(s) = Reference Input,

E(s) = Error Signal,

G = Forward Path Gain,

H = Feedback Path Gain.

Calculation:

Given a negative feedback system, the output is fed back through H and compared with input R(s).

The error signal E(s) is: \( E(s) = R(s) - H \cdot C(s) \)

With unity feedback or feedback factor H, and forward gain G, the output becomes: \( C(s) = \frac{G}{1 + GH} R(s) \)

Hence, the error signal is: \( E(s) = R(s) - H \cdot C(s) = \frac{1}{1 + GH} R(s) \)

Answer:

\(\frac{1}{1+G H}\) is the correct error transfer function for a negative feedback system.