Root Locus
Q
UESTION
15
For the system shown in Figure 15 with
(
29
1
C
G
s
s
=
and
(
29
1
G s
s
α
=
+
, sketch the Root Locus
Diagram by hand and using Matlab.
Note:
the free parameter is
α
. 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
α
at the imaginary axis crossing.
G(s)
G
C
(s)
R(s)
+

Y(s)
Figure 15
The closed–loop transfer function is
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
2
2
2
1
1
1
1
1
1
1
C
C
s
G
s G s
T s
s
G
s G s
s
s
s
+
=
=
=
+
+
+
+
+
.
The effective open–loop transfer function with
α
as the free variable is
(
29
(
29
2
1
eff
s
G
s
s
=
+
There is
m
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 Spring '11
 LANDERS
 Root Locus, Complex number

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