1
A design of the DC motor control circuit
Abstract:
The phase compensation method is applied in the control system design, the speed of DC
motor is controlled by using the feedback of both armature current and tachometer voltage.
1. Modeling a DC motor
The symbols used in the modeling is defined as follows:
L
: armature inductance
]
[
H
a
R
: armature resistance
]
[
Ω
i
:
armature current
]
[
A
e
: applied armature voltage
]
[
V
e
K
: back electromotive force constant
]
sec/
[
rad
V
t
K
: torque constant
[
A
Nm
/
]
m
J
: rotor momentum of inertia
[
2
kgm
]
w
: rotor speed
sec]
/
[
rad
l
J
: load momentum of inertia
[
2
kgm
]
l
B
: viscous friction coefficient
sec]
/
/
[
rad
Nm
f
t
: disturbance torque
]
[
Nm
.
In this case the electrical equation is given as
w
e
a
K
e
i
R
dt
di
L

=
+
(1.1)
and for the mechanical part of the system the torque equation is described as follows:
(
29
f
m
i
K
B
dt
d
J
J
t
w
w
t

=
+
+
l
l
.
(1.2)
It is often possible to neglect them on the design of a DC motor control system, because the effect of both the
inductance
L
of Eq. (1.1) and the viscous torque
w
l
B
of Eq. (1.2) is very slight. The following block diagram
for the design of a DC motor control system can be obtained.
e
i
t


1
R
K
t
f
t
1
Js
K
e
w
Fig. 1
The block diagram for the design of a DC motor control system.
The transfer function to the motor speed
w
from the applied armature voltage
e
in Fig. 1 is described as
s
T
K
s
e
s
m
+
=
1
)
(
)
(
w
,
(1.3)
where the time constant
m
T
and the gain
K
are the following formulation:
e
a
m
m
K
K
R
J
J
T
t
)
(
l
+
=
e
K
K
1
=
.
(1.4)
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