For the third$-$order servo system

$G(s)=\frac{50,000}{s(s+10)(s+50)}$

use MATLAB Bode plot sketches to design a lead compensator so $PM50$ and crossover frequency ${}_{\text{m}\text{a}\text{x}}20ra\frac{d}{sec}.($Note: $1)$ Solving this problem requires the maximum phase lead vs$.\frac{1}{},$ shown below. $2)$ Referring to the example shown in Lecture $16$ will help solve this problem.$)$