Question:
The transfer function of the following system is
The transfer function of the following system is
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Use block diagram reduction: simplify feedback first, then combine with forward paths.
Updated On: May 23, 2025
- \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 + GH_2}\)
- \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 - GH_2}\)
- \(\frac{C(s)}{R(s)} = \frac{G + H_1}{1 + GH_2}\)
- \(\frac{C(s)}{R(s)} = \frac{G - H_1}{1 - GH_2}\)
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The Correct Option is C
Solution and Explanation
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:
\[
\frac{G + H_1}{1 + GH_2}
\]
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