Q $-2$ For the system shown in Figure $Q-2,G{P}_P=\frac{1}{5(s)+1},G_f=\frac{1}{2(s)+1},G_m=\frac{1}{(s)+a},$ and

$G_c=K_c$ are given.

$($a$)$ Determine the transfer function, $Y\frac{s}{R}(s)$ and the characteristic equation, writing it in the form, $(s)=0.$

$[16$ pts$.\}$

b$)$ Determine the values of the controller gain, Kc by using Routh criteria, so that the feedback control system becomes stable.

$[24$

pts$.]$

note: this is control system course please explain it with formulas and take your time to solve it $.$