Three common specifications of the step response are percent overshoot, rise time, and settling time. We will consider these in the time domain, getting corresponding s plane regions, then map these to the z plane for design purposes. These will all be with reference to a continuous second-order underdamped system with no zeros, which has transfer function
An example step response plot for this kind of system is shown in Figure 1 (with $\zeta = 0.5$ and $\omega_n = 1$), where the percent overshoot, rise time, and settling time are marked on the plot
Use the controls below to change $\zeta$ and $\omega_n$ in Figure 1. Observe how they affect the percent overshoot PO, rise time $t_r$, and settling time $t_s$.