Question

The transfer function of the following system is

• A. \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 + GH_2}\)
• B. \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 - GH_2}\)
• C. \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 + GH_2}\)
• D. \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 - GH_2}\)

Hint:

Use block diagram reduction: simplify feedback first, then combine with forward paths.

Answer 1

The Correct Option is C

The inner feedback loop with \(H_2\) has transfer function: \[ \frac{G}{1 + GH_2} \] This is then added with \(H_1\) in feedforward path, giving overall transfer function: \[ \frac{G + H_1}{1 + GH_2} \]