P$4.(40$ points$)$ For the unity feedback control system shown below, use the frequency response design method using the analytical method explained in the lectures to design a phase lead controller that has:

$-$ a phase margin of $($exactly or at least$)60,$ and

$-$ the velocity error constant K$\_\{$v$\}=250$

$-$ Present Bode plots and step and ramp simulation responses with and without compensation. Compare your compensated and uncompensated system results $($the two conditions above plus gain margin and phase cross$-$over frequency and other time response specifications we learned in class$)$ in a tabular fashion.

$-$ Draw Matlab root locus plots of the compensated and uncompensated systems.

$-$ Draw Matlab Nyquist plots of the compensated and uncompensated systems.