For a differentiating (D) control element with gain K_D, the transfer function is:

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Mechanical Engineering QUESTION #2378

Question 1

For a differentiating (D) control element with gain \(K_D\), the transfer function is:

\(Y(s) = K_D / s\)
\(Y(s) = K_D\)
\(Y(s) = K_D s\)✔️
\(Y(s) = K_D s^2\)

Correct Answer Explanation

A differentiating element: \(x_o(t)=K_D \dot{x}_i(t)\), so \(X_o(s)=K_D s X_i(s)\), giving \(Y(s)=K_D s\). Differentiation in time corresponds to multiplication by \(s\) in the Laplace domain.

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