QUESTION 2 [10 marks] Michelangelo wants to draw two Nyquist plots for the following familiar feedback system: K P(s) y where K is a real number. He tried using Maple but the plot that appeared was incomplete. Help him by drawing the rest of the Nyquist plot for one of the following transfer functions. If the last digit in your uOttawa student ID number is in the set (0,2,4,6,8}, then use P(s) = (s+2)(s + 4) (s + 5)(s + 6) 54(5-3) Otherwise, the last digit of your ID number must be in the set {1,3,5,7,9), and you should use P(s) = (s+1)(s+3)(s+4)(s-5) s (5-2)(5-3) The incomplete plots are provided on the next page. (a) Write down the transfer function corresponding to the last digit in your uOttawa student ID number. (b) Draw (by hand) the Nyquist path. (c) Calculate the expressions corresponding to "Part C" and "Part D" of the Nyquist plot. (d) Draw (by hand) the Nyquist plot for K = 1. Fully label the plot. (e) Draw (by hand) the Nyquist plot for K = -1. Fully label the plot. (f) Determine all values of K (if any) for which the closed-loop system is stable. Partial Nyquist plot for P(s) (s+2)(s+4)(s+5)(s+6) = s4 (5-3) 1. x 10 5.x 107 -8.x 10 -6.x 10" -4. x 10" -1.x 10 -5.x 107 -1.x 10% Partial Nyquist plot for P(s) = 5.x 10 -5.x 10% (s+1)(s+3)(s+4)(s-5) s (5-2)(5-3) $4000 100000 150000 200000