What is Settling time?

The time from applying a step input until the output enters a specified band around its final value (such as ±2% or ±5%) and stays within it. It describes the speed and the settling of a response together; for a second-order system the ±2% settling time is estimated at about 4/(ζωn) and the ±5% one at about 3/(ζωn). The ±2% settling time of a first-order system is about 3.9T, where T is the time constant. In specifications for A/D converters and op-amps, the time for the output to settle to a specified accuracy is also called the settling time.

Japanese name: 整定時間

Settling time appears in 2 practice questions across 1 topic, including Control Engineering Basics.

Field: Control Engineering Basics

Try it: questions about Settling time

Which of the following is the settling time, until the step response of the system G(s) = 25/(s² + 4s + 25) stays within ±2% of its final value, estimated with the approximation ts ≈ 4/(ζωn)?

A0.5 s
B0.8 s
C2 s

Show answer and explanation

Answer: C. 2 s

This system has ωn = 5 rad/s and ζ = 0.4, so ζωn = 2 s⁻¹ and ts ≈ 4/2 = 2 s. The envelope of the oscillation shrinks as e^(−ζωn t), and e^(−4) ≈ 0.018 falls below 2%, which is where this approximation comes from. For a ±5% settling time, ts ≈ 3/(ζωn) is used. Because it is estimated from the envelope, it often comes out a little longer than the true value; computing this system numerically gives a ±2% settling time of about 1.7 s.

Settling time in the explanations

For a ±5% settling time, ts ≈ 3/(ζωn) is used.
Which of the following is the settling time, until the step…
The oscillation of the response decays within an envelope e^(−σt), so the settling time is set at roughly 4/σ and stays about the same if σ is unchanged.
A second-order system without zeros has its poles at s = −σ…