AN1913D Freescale Semiconductor / Motorola, AN1913D Datasheet - Page 8

• Manufacturer Part Number: AN1913D
• Description: 3-phase BLDC Motor Control with Sensorless Back-EMF ADC Zero Crossing Detection using DSP 56F80x
• Manufacturer: Freescale Semiconductor / Motorola

Target Motor Theory
3.4.1 Mathematical Model
8
The following set of equations is valid for the presented topology:
where:
The equations (EQ 3-1.) can be rewritten 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
-
winding and the power stage natural zero
are “branch” voltages between one power stage output and its natural zero.
are motor phase winding voltages.
are phase Back-EMF induced in the stator winding.
is the differential voltage between the central point of the star connection of motor
are phase currents
motor phase resistance, inductance
u
BLDC control with BEMF Zero Crossing using ADC
u
u
Freescale Semiconductor, Inc.
VC
VA
VB
For More Information On This Product,
–
–
–
u
u
u
u
u
u
u
O
C
0
iC
A
B
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
u
VC
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
(EQ 3-1.)
(EQ 3-2.)