An improved approximation for settling time of second-order linear systems

An improved approximate expression is developed for the settling time of a second-order linear system subjected to a step input. The new expression is more accurate than several existing approximate expressions. Furthermore, although it is slightly more complicated than one of the existing approximations, it is much more convenient to use than the other, which requires iteration for design application. Finally, it is noted that explicit results in dimensionless graphical form are given for the first time for the exact settling time versus damping ratio.