Answer Happy

Leonardo is having trouble drawing two root-locus plots for the
following familiar feedback system:
a) Write down the transfer function 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.
(f) Use any method to determine all values of 𝐾 (if any
exist) that result in a stable closed-loop system.
r K P(S) у
P(S) = S2 + 6s + 13 54 + 1083 + 39s2 + 70s + 50 = S2 + 6s + 13 (s +3-j)(s +3+j)(s + 2 - )(s + 2 +j)