Prob.1. (pts) The root-locus plot of
KG(s)H(s) = K \frac{(s+3-jl)(s+3+jl)}{s(s+3)(s+2)}
and the desired region (PO ?5% (? ? 0.7) and t ? 4 sec, are given below.
a. (pts) Label the gain K (such as K?, K?, ..., etc.) at each point where the root-
locus intersects the borders of the desired region but do not calculate the gai
K at these points. Find the range of the gain K in terms of K?, K?, ... such
that all characteristic roots (closed-loop poles) lie inside the desired region.
K
s-plane
Desired
Region
-3
-2
0
# of Characteristic Roots(Closed-Loop Poles)
Inside Desired Region Outside Desired Region
(Note that # of rows in the table above might be more than # of intervals.)