Answer Happy

Leonardo is having trouble drawing two root-locus plots for the following familiar feedback system: r K P(s) y where K 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 P(s) s2 + 4s + 5 s+ + 12s3 + 59s2 + 138s + 130 s2 + 4s +5 (s +3-2(s +3+27(s + 3 - 1(s +3+)
(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 (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. (c) Draw (by hand) the positive (K > 0) 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 (K = 0) root-locus plot. Fully label the plot. () Use any method to determine all values of K (if any exist) that result in a stable closed-loop system