For a closed-loop (negative feedback) control system with forward path transfer function Y_1(s) and feedback path Y_2(s), the closed-loop transfer function is:

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Mechanical Engineering QUESTION #2380

Question 1

For a closed-loop (negative feedback) control system with forward path transfer function \(Y_1(s)\) and feedback path \(Y_2(s)\), the closed-loop transfer function is:

\(Y(s) = Y_1(s) \cdot Y_2(s)\)
\(Y(s) = \frac{Y_1(s)}{1 + Y_1(s) \cdot Y_2(s)}\)✔️
\(Y(s) = \frac{Y_1(s)}{1 - Y_1(s) \cdot Y_2(s)}\)
\(Y(s) = \frac{1}{1 + Y_1(s)}\)

Correct Answer Explanation

The closed-loop (negative feedback) transfer function: \(Y(s)=\frac{Y_1(s)}{1+Y_1(s)Y_2(s)}\). For unity feedback (\(Y_2=1\)): \(Y(s)=\frac{Y_1(s)}{1+Y_1(s)}\). This is the fundamental closed-loop formula.

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