User Manual

Power Stage - Motor System Model
3-Phase BLDC Motor Control with Sensorless Back-EMF, ADC, Zero Crossing, Rev. 3
Freescale Semiconductor 9
Preliminary
3.4.1 Mathematical Model
The following set of equations is valid for the presented topology:
u
A
1
3
---
2u
VA
u
VB
– u
VC
–
u
ix
xA=
C
∑
+
⎝⎠
⎜⎟
⎜⎟
⎛⎞
=
u
B
1
3
---
2u
VB
u
VC
– u
VA
– u
ix
xA=
C
∑
+
⎝⎠
⎜⎟
⎜⎟
⎛⎞
=
u
C
1
3
---
2u
VC
u
VA
– u
VB
– u
ix
xA=
C
∑
+
⎝⎠
⎜⎟
⎜⎟
⎛⎞
=
u
O
1
3
---
u
Vx
xA=
C
∑
u
ix
xA=
C
∑
–
⎝⎠
⎜⎟
⎜⎟
⎛⎞
=
0 i
A
i
B
i
C
++=
(EQ 3-1.)
where:
u
VA
…u
VC
are “branch” voltages between one power stage output and its natural zero.
u
A
…u
C
are motor phase winding voltages.
u
iA
…u
iC
are phase Back-EMF induced in the stator winding.
u
O
is the differential voltage between the central point of the star connection of motor winding and
the power stage natural zero
i
A
…i
C
are phase currents
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.
u
VA
u
iA
–
1
3
---
u
Vx
xA=
C
∑
u
ix
xA=
C
∑
–
⎝⎠
⎜⎟
⎜⎟
⎛⎞
– Ri
A
⋅ L
td
di
A
+=
u
VB
u
iB
–
1
3
---
u
Vx
xA=
C
∑
u
ix
xA=
C
∑
–
⎝⎠
⎜⎟
⎜⎟
⎛⎞
– Ri
B
⋅ L
td
di
B
+=
u
VC
u
iC
–
1
3
---
u
Vx
xA=
C
∑
u
ix
xA=
C
∑
–
⎝⎠
⎜⎟
⎜⎟
⎛⎞
– Ri
C
⋅ L
td
di
C
+=
(EQ 3-2.)
where:
R,L - motor phase resistance, inductance