E7.11 A robot force control system with unity feedback has a loop transfer function [6]

a. Find the gain K that results in dominant roots with a damping ratio of 0.707. Sketch the root locus.

b. Find the actual percent overshoot and peak time for the gain K of part (a).

L(s) = KG(s) = K(s+1) s(s + 6s+18) (2