$($a$)$ Consider a unity$-$feedback control system with the closed$-$loop transici funculit

$\frac{C(s)}{R(s)}=\frac{Ks+b}{s^2+as+b}$Determine the open$-$loop transfer function $G(s).$

Show that the steady$-$state error in the unit$-$ramp response is given by

$e_{ss}=\frac{1}{K_v}=\frac{a-K}{b}$

Where $e_{ss}$ is the steady$-$state error, and $K_v$ is the velocity error constant.

$($b$)$ Consider a unity$-$feedback control system whose open$-$loop transfer function is

$G(s)=\frac{K}{s(Js+B)}$

Discuss the effects that varying the values of $K$ and $B$ has on the steady$-$state error in unit$-$ramp response. Sketch typical unit$-$ramp response curves for a small value, medium value, and large value of $K,$ assuming that $B$ is constant.