X.12
me 375  cmk
Example 2
The coupled electromechanical equations for an electric motor (ignoring armature
inductance and armature damping) are given by:
J
!
!
=
K
T
i
a
"
#
L
e
i
t
( ) =
Ri
a
+
K
T
where
is the rotation rate of the motor,
is the mass moment of inertia of the
armature,
K
T
is the motor constant,
i
a
is the armature current,
L
is the applied motor
torque,
e
i
t
( )
is the input voltage applied to the armature and
is the armature
resistance.
An electric motor governed by the above equations is used to propel a fan boat along a
smooth surface of ice. In this application, the fan exerts a resistive load torque of
L
=
K
L
"
on the output shaft of the motor, and the rotation of the fan creates a
propulsive force
f
P
=
K
P
on the boat (where
K
L
and
K
P
are constants). In addition,
the fan boat experiences of drag force of
f
D
=
K
D
v
where
is the speed of the boat and
K
D
is a constant. Let
m
represent to total mass of the boat, motor and fan.
For this problem,
develop the transfer function relating the input voltage to the boat
speed,
G s
( ) =
V s
( )
E
i
s
( )
.
Determine the steadystate speed of the boat for a step input
voltage
e
i
t
( ) =
e
( )
.
J
R
v
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 Fall '10
 Meckle
 Electric motor, KT Vi, X. Electromechanical systems

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