c$)(50$ pts$.)$ Consider a PID controller for transfer function $G_1(s)=\frac{s}{u}(s)$ in the form

$C(s)=K\frac{(s+a)(s+b)}{s}$

Adjust parameters $a,b$ such that the root locus passes through points $s=-1+-j0\mathrm{.}5($Hint: use angle condition$).$ Now, determine the value of gain $K$ to ensure conjugate poles placed on points $s=-1+-j0\mathrm{.}5$ as well $($Hint: use magnitude condition$).$

G$1=$

Continuous$-$time transfer function. i want the sloution in detail