6. (15pts) Given the feedback system shown below,

RO-Σ

5

s(s+2)

1 + as

(a) (8pts) Put the characteristic equation in Roo-Locus form with respect to the parameter a and

identify the corresponding loop transfer function L(s).

(a) (7pts) Sketch the root locus diagram with respect to the parameter a as it varies from 0 to 0.