2) The transfer function of a process between its controlled variable and its setpoint is G(s) = 5(s-4) (s+1)(s+8s+20) All other devices to implement closed-loop feedback control for this process except the controller that must be designed are assumed to have fast dynamics and unity gain. a) Use the first 4 rules for drawing root locus by hand and draw the approximate root locus plot when the process is controlled by a proportional feedback controller. State explicitly your work for each rule. b) Determine the critical frequency of the closed-loop system (if any) from the approximate root locus plot. Show your work in determining it. c) Assess the stability of the system as Kc is increased and describe the nature of the response to a step change in the input, i.e., whether the system response is (i) overdamped or underdamped, (ii) stable or unstable for various ranges of Kc. d) Draw the root locus by using Matlab. Record the values of the maximum gain and critical frequency from the plot and compare with your result in Part (b). e) Sketch semi-qualitatively the response to a step increase of magnitude 2 in the set-point when Kc has a value leading to stable response. Show the critical features and state your reason(s) for each critical feature in the response. For the Kc value that you selected, is the response overdamped or underdamped?