Consider a system with the following plant transfer function

(where the controller gain K = 1).

G(s)- s2+s+a

- s(s + l)(s2 + s + 1.25)(s2 + s + 4.25)

{a) Plot the root locus for the plant as a varies from 1.25 to 4.25.

{b) Find the exact value of a for which the pair of poles which asymptotically approach zero changes.

Problem