1
AE 383 SYSTEM DYNAMICS
Lecture Notes 3 (June 24
th
2006)
Transfer Function Representation of Dynamic Systems
Transfer function of a system is defined as the ratio of the Laplace transform of the output to the
Laplace transform of the input, with zero initial conditions.
Transfer Function =
[ ]
[ ]
conditions
initial
zero
)
(
)
(
)
(
input
L
output
L
s
u
s
x
s
G
=
=
•
Transfer functions are defined by only linear timeinvariant systems
•
Transfer function is a property of the system, it is independent of the magnitude and
nature of the input.
•
It does not contain any information about the physical structure of the system.
Let the equation of motion for a system be
(massspringdamper system)
)
(
t
u
kx
x
b
x
m
=
+
+
Taking the Laplace transform with zero initial conditions:
)
(
)
(
)
(
)
(
2
s
u
s
kx
s
bsx
s
x
ms
=
+
+
Transfer function
k
bs
ms
s
u
s
x
s
G
+
+
=
=
2
1
)
(
)
(
)
(
We will use Tranfer function blocks in our Simulink Simulations.
State Space Representation of Dynamical Systems
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 Spring '11
 Melin
 Force, Laplace

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