$G(s)=\frac{32000}{s(s+8)(s+40)}$

$($a$)$ Use Bode plot sketches to design a compensator so that $PM>45$ and ${}_{Bw}>15ra\frac{d}{sec},$ where PM stands for phase margin and ${}_{BW}$ is the closed$-$loop bandwidth $(25\%).($b$)$ Verify your design by drawing compensated Bode plots. Refine and verify your design again if necessary $(15\%).$