Design Considerations

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Design Considerations
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Traditional Design Considerations

Pole placement.png
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}}