$G_0(s)=\frac{B_0((s))}{A_0((s))}=\frac{s+3}{((s)+4)(s+6)}$

Assume a one degree of freedom control loop with controller, $C(s),$ of the form

$C(s)=\frac{P(s)}{L(s)}=\frac{P_{1}s+P_0}{L_{1}s+L_0}$

In our design we want to guaranty the stability just at the start with proper pole$-$zero placement. A parametric solution will enable us to make some ajustment on the speed of response and accuracy. To that end, we have decided to use a controller with several variables $(P_1,P_0,L_1$ and $L_0)$ that needs to be found in terms of parameter $"$a$",$ also representing a pole of the characteristic equation. In this project, a $4$th$-$order characteristic equation $)=1+C(s)G_o(s)=((s+a{)}^2((s)+5{)}^2$ is to be used. The one degree$-$of $-$freedom controller, with a second order plant model, however, is going to give a third order polynomial. So$,$ we need to upgrade the proposed controller from first order to second order in order to enable pole zero cancellation. After reading the introduction section that follows the problem statement, you are asked to follow a stepwise approach to complete and present the following controller design assignment.

#please find A with two questions and B and C and also explain which role you use to solve the project $($EACH RULE THAT YOU DID REALLY OBEY$)$