5. (15pts) Consider a feedback system shown below.

K(s+a)

(s+b)

Controller Kisi

1

(²+255+8)

Plant G(s)

(a) (5pts) Ignoring stability for the moment, what are the constraints on K, a and b so that system is

type 1?

(b) (5pts) What are the constraints placed on K, a, and b so that the system is stable and type 1?

(c) (5pts) What are the constraints on a and b so that the system is type 1 and remains stable for

every positive value for K?