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EE 428
PROBLEM SET 2
DUE: 10 SEP 2007
Reading assignment: Ch 1, Ch 2, and Ch 3 sections 3.1 and 3.2.
The goals of the Frst problem set are to:
1. Review basic concepts and mathematical tools from EE 350.
2. Obtain an ODE model of a physical system from Frst principles.
3. Convert from one method of representing a dynamic system to another method of representation. ±or example,
given an ODE representation, Fnd a corresponding statespace representation.
Problem 1:
(30 points)
A SISO system with input
u
(
t
) and output
y
(
t
) has the ODE representation
˙
y
+
y
=˙
u
+ 100
u.
1. (5 points) Determine the transfer function representation of the system. Express your answer in the standard
form
Y
(
s
)
U
(
s
)
=
b
m
s
m
+
b
m
−
1
s
m
−
1
+
···
+
b
1
s
+
b
0
s
n
+
a
n
−
1
s
n
−
1
+
+
a
1
s
+
a
0
,
and specify the poles and zeros of the transfer function, as well as the DC gain of the system.
2. (5 points) Express the frequency response function in a form suitable for sketching a Bode magnitude and
phase plot, that is,
Y
(
jω
)
U
(
jω
)
=
K
jω/ω
1
+1
jω/ω
2
,
and specify the numeric value of the parameters
K
,
ω
1
,and
ω
2
. What is the signiFcance of the parameter
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This note was uploaded on 07/23/2008 for the course EE 428 taught by Professor Schiano during the Fall '07 term at Pennsylvania State University, University Park.
 Fall '07
 SCHIANO

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