Root Locus
Q
UESTION
11
For the system shown in Figure 11 with
(
29
1
C
G
s
=
and
(
29
2
2
4
1
s
G s
s
+
=
+
, sketch the Root Locus
Diagram by hand and using Matlab. How many zeros does the system contain and what are their
values? How many poles does the system contain and what are their values? What are the total
number of branches and how many branches will go to infinity? Where is the Root Locus on the
real axis? If necessary, calculate the asymptote angles and real axis intercept, imaginary axis
crossing, and the value of
K
at the imaginary axis crossing.
G(s)
KG
C
(s)
R(s)
+

Y(s)
Figure 11
There are
m
= 2 zeros located at –2
j
and 2
j
.
There are
n
= 2 poles located at –
j
and
j
.
There are
n
= 2 branches and
n
–
m
= 0 branches go to infinity.
The Root Locus is not on the real axis.
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 Spring '11
 LANDERS
 Root Locus, Complex number

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