Biomedical Engineering Reference
In-Depth Information
TABLE 4-2
Description of Electrical Blocks
Block
Describing Equation
Energy/Power
=
L
di
dt
1
L
1
2
Li
2
Inductor
V
i
=
Vdt
E
ind
=
1
C
i
=
C
dV
dt
1
2
CV
2
Capacitor
V
=
idt
E
cap
=
V
R
1
R
V
2
Resistor
V
=
Ri
i
=
P
res
=
WORKED EXAMPLE
Direct Current Motor Model
A simple model for an electric motor combines electrical and mechanical elements, as shown
in Figure 4-9 and described in the following section.
FIGURE 4-9
Block diagram of
elements of an
electric motor.
τ(
)
(Nm), generated by the motor is proportional to the current,
i
r
(
)
The torque,
t
t
(A), in
the rotor
τ(
)
=
K
m
i
r
(
)
t
t
(4.39)
where K
m
(Nm/A) is the motor torque constant and is related to the physical properties of the
motor, including the number of turns and the strength of the magnetic field.
The back EMF,
V
emf
(
t
)
(volts), is proportional to the motor speed,
ω(
t
)
(rad/s)
d
θ(
t
)
V
emf
(
t
)
=
K
e
ω(
t
)
=
K
e
(4.40)
dt
where
K
e
(V/rpm) is the back EMF constant, also known as the speed constant.
The equations that relate the motor output to the input current are described equations
for the electrical and for the mechanical sections of the circuit. A second-order differential
equation describes the mechanical section
d
2
θ(
t
)
b
d
θ(
t
)
(
J
r
+
J
L
)
+
=
K
m
i
r
(
t
)
(4.41)
dt
2
dt
where
J
r
(kgm
2
) and
J
L
(kgm
2
) are the moments of inertia of the rotor and the load respectively,
and
b
is the damping coefficient.
