Assignment: Task 1. Proportional compensation Assume GSC (s) is a proportional (P) controller, i.e., GSC (s) = KP. (a) Find the closed-loop system transfer function and determine the range of KP > 0 for stability. (b) For the uncompensated closed-loop system (i.e., with KP = KP1 = 1): · Simulate and plot the system unit-step response c(t). · Determine (from the plot) the P.O., peak time Tp, rise time Tr, settling time Ts, and steady-state error e step (∞) in % of the input. · Find also e ramp (∞) =? · Plot the Bode diagrams and indicate the bandwidth, and the phase and gain margins. (c) Find KP = KP2 that yields a steady-state error e step (∞) = 1%. · Repeat part (b) with the found KP2. (d) Plot the RL for KP and determine KP = KP3 that yields critically damped closed-loop response. · Repeat part (b) with the found KP3. (e) Compare the results from (b), (c) and (d), and make comments.