Assignment:? Task 1. ?Proportional compensation? Assume GSC (s) is a proportional (P) controller, i.e., GSC (

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.