$4\mathrm{.}13$ Consider the second$-$order system

$1$

G$($s$)=$

$$2+255+1$

We would like to add a transfer function of the form Dc$($s$)=$ series with G$($s$)$ in a unity feedback structure.

$$Ignoring stability for the moment, what are the constraints on K$,$ a$,$ and b so the system is Type $1?$

$$What are the constraints placed on K$,$ a$,$ and b so the system is both stable and Type $1?$

$$What are the constraints on a and b so the system