Let's take a look at the feedback control system C(s) K R(S) Here is a plot showing the root locus of the system: 2.5 2 1.5 1 0.5 -0.5 -1 -1.5 -2 -2.5 -6 Root Locus Real Axis (seconds) G(s) -1 Y(s) 1. Find the open loop transfer function. 2. Determine the range of values for the gain parameter, K, that ensures stability in the closed loop control system. 3. Determine the range of values for the gain parameter, K, that results in an overdamped control system. 4. Calculate the steady-state response (yss) of the feedback control system to a unit step input for K = 1 and K = 10. 5. Calculate the steady-state error (ess) of the feedback control system to a unit step input for K = 1 and K = 10. 6. Can the control system achieve zero steady-state error (perfect tracking) of a unit step input by adjusting only the gain, K? Please justify your answer. 7. Design a controller to replace the current proportional controller (C(s) = K) in order to achieve perfect tracking of a unit step input. Show your work by calculating either yss or ess. 8. Sketch a quick root locus of the closed loop system with the new controller designed in part 7. Please note that you do not need to calculate the angle of departure, break-in, or break-away points. Simply determine the locations where the asymptotes cross the real axis, as well as the overall shape of the root locus.