Assume the transfer function g(s) has the form: g(s) = k /(s + 1)^2*(s + 10) the system operates with a damping ratio of 0.6. design a pi controller to drive the step response error to zero. 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 pi 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). create a simulink model of the closed loop system (which includes the pi controller) and determine the step response.