Design Considerations
 Overshoot: $LaTeX: M_p=e^\left( \frac{-\pi \zeta}{\sqrt{1-\zeta^2}} \right)$ $LaTeX: \zeta=\sqrt{\frac{\left( \ln M_p \right)^2}{\pi^2+\left( \ln M_p \right)^2}}$ Rise Time: $LaTeX: t_r \approx \frac{1.8}{\omega_n}$ Settling Time: $LaTeX: t_s=\frac{4.6}{\zeta \omega_n}$ $LaTeX: \sigma=\zeta\omega_n$ $LaTeX: \tau=\frac{t_s}{5}$ Time Delay: $LaTeX: e^\left(-s\delta \right)=\left[ \frac{\frac{2}{\delta}-s}{\frac{2}{\delta}+s} \right]$ Peak Time: $LaTeX: t_p=\frac{\pi}{\omega_n \sqrt{1-\zeta^2}}$