AN1914 Freescale Semiconductor / Motorola, AN1914 Datasheet - Page 9

• Manufacturer Part Number: AN1914
• Description: 3-Phase BLDC Motor Control with Sensorless Back EMF Zero Crossing Detection Using DSP56F80x
• Manufacturer: Freescale Semiconductor / Motorola

3.4.1 Mathematical Model
The following set of equations is valid for the presented topology:
where:
The equations (EQ 3-1.) can be written taking into account the motor phase resistance and the
inductance. The mutual inductance between the two motor phase windings can be neglected because it
is very small and has no significant effect for our abstraction level.
where:
R,L
u
u
u
i
u
A
A
iA
O
VA
i
u
C
u
C
u
iC
VC
-
is the voltage between the central point of the star of motor winding and the power stage
natural zero
are “branch” voltages; the voltages between one power stage output and its virtual zero.
are motor phase winding voltages.
are phase Back-EMF voltages induced in the stator winding.
are phase currents
motor phase resistance, inductance
DSP56F80x MC PWM Module in Motor Control Applications
u
u
u
Freescale Semiconductor, Inc.
VC
VA
VB
For More Information On This Product,
–
–
–
u
u
u
u
u
u
u
C
O
iC
A
B
0
iA
iB
=
=
=
=
=
–
–
–
1
-- -
3
1
-- -
3
1
-- -
3
1
-- - 2u
3
1
-- - 2u
3
1
-- - 2u
3
1
-- -
3
i
A
x
x
x
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x
+
=
=
=
C
C
C
C
=
i
A
A
A
VA
VB
VC
B
A
u
u
u
u
+
Vx
Vx
Vx
–
–
–
Vx
i
C
u
u
u
–
–
–
–
VB
VC
VA
x
x
x
x
C
=
C
=
C
=
–
C
=
–
–
A
A
A
A
u
u
u
u
u
u
VC
u
VA
VB
ix
ix
ix
ix
+
+
+
=
=
=
x
x
x
=
=
=
C
C
C
R i
R i
R i
A
A
A
u
u
u
ix
ix
ix
A
B
C
+
+
+
L
L
L
di
t d
di
t d
di
t d
A
B
C
Target Motor Theory
(EQ 3-1.)
(EQ 3-2.)
9