The settling time is the time from the application of an ideal instantaneous step input to the time at which the system output has entered and remained within a specified tolerance (also known as the error band).
This tool calculates the settling time for a second order system with a damping ratio ζ less than 1.
- Tolerance T% (this is the level to which a signal is considered as settled)
- Damping Ratio ζ
- Natural frequency fn (Hz)
TS = -Loge(0.01*T%* √(1-ζ2))/( ζ*2*π*fn)
For a tolerance of 2%, damping ratio of 0.5 and natural frequency 100 Hz, the settling time is 13 ms. As the tolerance decreases to 1%, the settling time increases to 15 ms.