Leonardo is having trouble drawing two root-locus plots for the following familiar feedback system: P(s) where is a real number. He has applied the "basic" rules he learned in class but is still unsure about some of the details of the plots. Help him by drawing the root-locus plot for one of the following transfer functions. If the last digit in your uOttawa student ID number is in the set (0, 1, 2, 3, 4), then use 5 +45 +5 s + 4s +5 P(S) = + +125 +595 +138s +130 (+3-2j) (s +3+2j) (s+3j) (s +3+j) P(s) = Otherwise, the last digit of your ID number must be in the set (5, 6, 7, 8, 9), and you should use s +65 +13 s + 6s +13 54+1053 +39s+70s +50 (s+3-j) (s +3+j) (s+2-1)(+2+1) (a) Write down the transfer function corresponding to the last digit in your uOttawa student ID number and list the open-loop poles and zeros. (b) For the positive (20) root-locus, find the angle of departure for each pole and the angle of arrival for each zero, either through calculation or by providing a logical argument. (c) Draw (by hand) the positive (20) root-locus plot. Fully label the plot. (d) For the complementary (K 0) root-locus, find the angle of departure for each pole and the angle of arrival for each zero, either through calculation or by providing a logical argument. (e) Draw (by hand) the complementary ( 0) root-locus plot. Fully label the plot. (f) Use any method to determine all values of K (if any exist) that result in a stable closed-loop system.