5.8.1.39
For the system of Figure 1 let For the system of Figure 1
G
H
C
R
+
-
Figure 1: Standard Closed Loop Conguration
G(s)H(s)=
K(s +2)
s
2
(s +3)(s +10)
:
The pole/zero excess (pze) is 5;2=3,sothere will be three asympotes
at
=60
;;180
;; and 300
:
The asymptotes intersect at
i
=
P
polesofGH ;
P
zeros of GH
pze
=
(;1;20;40);(;2;3)
3
= ;18:67:
The root locus, shown in Figure 2, is generated bytheMATLAB program:
K=linspace(0,1000,1000);;
gh = zpk([-2 -3],[0 0 -1 -30 -40],10)
[R,K] = rlocus(gh,K)
plot(R,'k.')
print -deps rl58139.eps
1
-50 -40 -30 -20 -10 0 10
8
6
4
2
0
2
4
6
8
Figure 2: Accurate root locus
2