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1
MANE4050 – Modeling and Control
Homework Assignment #3
1.
Given a transfer function
)
9
9
.
0
)(
4
(
5
.
22
)
(
2
+
+
+
=
s
s
s
s
G
a.
Show the Bode or normalized form of the transfer function.
b.
Sketch on the attached log paper on page #3 the magnitude and phase
asymptotes for each term and the composite asymptotes for the transfer
function as well. Clearly label each slope and corner frequency.
c.
Determine the magnitude corner correction for the quadratic term.
Solution:
a. The Bode form of the transfer function
G
(
j
!
)
=
22.5
4(
j
+
1)
"
9(
#
+
0.1
j
+
=
0.625
(
j
+
1)(
#
2
+
0.1
j
+
b. See attached sheet for the magnitude and phase asymptotes.
c. From the quadratic term, we get the natural frequency
3
9
=
=
n
rad/second
and
15
.
0
3
2
9
.
0
2
9
.
0
9
.
0
2
=
!
=
=
"
=
n
n
#
$
$#
So, the magnitude corner correction for the quadratic term is
)
15
.
0
2
log(
20
)
2
log(
20
!
"
=
!
"
=10.4576
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2.
Evaluate gain margin and phase margin from the Bode plots shown below.
Solution:
Gain margin = 26.8 dB
Phase margin = 70.8 degree
3.
Given the unit feedback system shown below.
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 Spring '08
 Li

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