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Root Locus
Q
UESTION
16
For the system shown in Figure 16 with
(
29
1
C
G
s
=
,
(
29
2
5
2
8
s
G s
s
s
+
=
+
+
, and
(
29
7
H s
s
β
=
+
,
sketch the Root Locus Diagram by hand and using Matlab.
Note:
the free parameter is
β
. 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)
G
C
(s)
R(s)
+

Y(s)
H(s)
Figure 16
The closed–loop transfer function is
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
3
2
2
3
2
2
3
2
7
5
7
5
2
15
35
2
8
1
2
15
35
2
8
1
2
15
35
C
C
s
G
s G s H s
s
s
s
s
T s
s
s
G
s G s H s
s
s
s
s
s
s
s
s
+
+
+
+
+
=
=
=
+
+
+
+
+
+
+
+
+
+
+
+
+
.
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 Spring '11
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