1. Consider a unity feedback control system as follows
Controller
Process
Eg(s)
R(s)
G$_c$(s)
G(s)
Y(s)
K
(a) Let G$_c$(s)G(s) = \frac{K}{s(s+3)(s^2+4s+7.84)}. Sketch the root locus. Determine angle and center
of asymptotes, j? axis crossings, break-in/break-away points, and angles of departure
from complex poles.
(b) Approximately locate two complex poles (on the root locus graph from part a) that are
nearest to j? axis and have a damping ratio (?) of 0.707. Then use the magnitude
condition to determine the value of K that generates the selected closed loop poles.
(c) Let G$_c$(s)G(s) = \frac{K(s+2)^2}{s(s^2+1)(s+8)}. Sketch the root locus and indicate all of its significant
features.
