In a step-test procedure to identify a first-order plus dead-time model, which parameters define G(s) ≈ K e^{-Ls}/(τ s + 1)?

• A. L, K, τ
• B. τ, L, K
• C. L, τ, K
• D. K, L, τ

Answer: (C)

A step-test modeled by a first-order plus dead-time system is defined by three quantities: the gain, the dead-time, and the time constant. In the transfer function G(s) ≈ K e^{-Ls} /(τ s + 1), K is the steady-state gain (how large the final response is for a unit step), L is the dead time or transport delay (the time before the response begins), and τ is the time constant (how fast the system responds after the delay). So the parameters that define G(s) are L, τ, and K. In a practical step-test, you’d estimate L from when the output first starts to move after the step, τ from the time it takes to approach the final value (roughly the time to reach 63% of the final value after the delay), and K from the final value of the response. The correct option lists these three parameters, just in a different order, which still represents the same model components.