G(s) = k(s + 6) /(s + 2)(s + 3)(s + 5) the system is operating with a dominant pole damping ratio of 0.707. design a pd con- troller so that the settling time is reduced by a factor of 2. in the process of doing the design, prepare two hand sketches of the root locus - the first for the uncompensated system and the second for the system with the pd controller. in drawing these hand sketches, show the asymptotes and centroid of the root locus. (for numerical details of break-away/break-in points, j! -axis crossings and other intersection points, use matlab).