<P> Tay, Mareels and Moore (1997) defined settling time as "the time required for the response curve to reach and stay within a range of certain percentage (usually 5% or 2%) of the final value ." </P> <P> Settling time depends on the system response and natural frequency . </P> <P> The settling time for a second order, underdamped system responding to a step response can be approximated if the damping ratio ζ ≪ 1 (\ displaystyle \ zeta \ ll 1) by </P> <P> T s = − ln ⁡ (tolerance fraction) damping ratio × natural freq (\ displaystyle T_ (s) = - (\ frac (\ ln ((\ text (tolerance fraction)))) ((\ text (damping ratio)) \ times (\ text (natural freq))))) </P>

Rise time and settling time in control system