Project Problem statement

Consider a plant having nominal model

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

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