Biomedical Engineering Reference
In-Depth Information
FIGURE 4-32
DC
motor block
diagram.
The transfer function that relates the input voltage to the output speed, as shown in Figure 4-32,
can be written as
(
s
)
K
m
T
(
s
)
=
)
=
(4.86)
V
i
(
s
(
Js
+
b
)(
Ls
+
R
)
+
K
e
K
m
An alternative is to consider the two governing equations separately, with the back
EMF applied as feedback.
The current drawn by the motor can be obtained by rewriting equation (4.84)
I
r
(
s
)(
Ls
+
R
)
=
V
i
(
s
)
−
K
e
(
s
)
1
Ls
+
R
(
I
r
(
s
)
=
V
i
(
s
)
−
K
e
(
s
))
(4.87)
The equation for the mechanical portion con be obtained by rewriting equation (4.85) in
terms of the input current:
(
s
)(
Js
+
b
)
=
K
m
I
r
(
s
)
K
m
Js
+
b
I
r
(
(
s
)
=
s
)
(4.88)
A block diagram can be constructed that is equivalent to that shown in Figure 4-32 but
includes the two individual transfer functions as well the back EMF feedback. This is
shown in Figure 4-33.
The advantage of using this form to describe the open-loop motor model is that each
of the first-order systems can be rewritten in a form that is easy to interpret in the time
domain. In addition, it gives access to the torque node (just after the
K
m
block), which
then allows for the introduction of an external torque requirement or disturbance.
From the table of Laplace transforms (Table 4-6), it would be convenient to write the
first-order blocks in the form
1
F
(
s
)
=
τ
s
+
1
FIGURE 4-33
Alternative form for
DC motor block
diagram.
