F-4 ANGLES OF ASYMPTOTES OF THE R

 F-4 ANGLES OF ASYMPTOTES OF THE ROOT LOCI AND
BEHAVIOR OF THE ROOT LOCI AT |s|  
As shown by the root loci in Figs. F-2 and F-3, when n, the order of P(s) is not equal to
m, the order of Q(s), of the loci will approach infinity in the s-plane. The properties
of the root loci near infinity in the s-plane are described by the asymptotes of the
loci when The angles of the asymptotes and their intersect with the real axis of
the s-plane are described as follows.
For large values of s, the root loci for K  0 (RL) are asymptotic to asymptotes
with angles given by
(F-9)
where i  0, 1, 2, … , and n and m are the number of finite poles
and zeros of G(s)H(s), respectively.
n  m  1;
ui  12i  12
0n  m0  180° n m
0s 0 S .
2 0n  m0
• Asymptotes of root loci
refers to behavior of root
loci at sS .