Settling time depends on the system response and
natural frequency. The settling time for a
second order,
underdamped system with natural frequency \omega_n responding to a
step response can be approximated if the damping ratio \zeta \ll 1 by T_s = -\frac{\ln (\text{tolerance fraction})}{\text{damping ratio} \times \text{natural freq}} A general form is T_s = -\frac{\ln (\text{tolerance fraction} \times \sqrt{1-\zeta^2} )}{\text{damping ratio} \times \text{natural freq}} Thus, if the damping ratio \zeta \ll 1, settling time to within 2% = 0.02 is: T_s = -\frac{\ln(0.02)}{\zeta \omega_n}\approx\frac{3.9}{\zeta \omega_n} ==See also==