MATLAB project

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.

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