Question

Time delay in control systems is usually represented as

• A. \(sT\)
• B. \(\dfrac{1}{sT}\)
• C. \(e^{-sT}\)
• D. \(\dfrac{T}{s}\)

Hint:

A pure transport delay (dead time) in the Laplace domain is \[ \boxed{ G(s)=e^{-sT} } \] where \(T\) is the delay time.

Answer 1

The Correct Option is C

Step 1: Recall the Laplace transform property of a time delay. If a signal is delayed by \(T\) seconds, \[ f(t-T)u(t-T), \] its Laplace transform is \[ e^{-sT}F(s). \]

Step 2: Identify the transfer function of a pure delay. Thus, a pure time delay is represented by \[ \boxed{e^{-sT}}. \] Therefore, \[ \boxed{(C)} \] is the correct answer.