BLDC Motor Control
Brushless DC Motor Control Theory
DRM028 — Rev 0
Designer Reference Manual
MOTOROLA
BLDC Motor Control
29
3.2.4.1 Stator Winding Equations
The BLDC motor is usually very symmetrical. All phase resistances,
phase and mutual inductances, flux-linkages can be thought of as equal
to, or as a function of the position
θ
with a 120° displacement.
The electrical BLDC motor model then consists of a set of the following
stator voltage equations
(EQ 3-1.)
.
(EQ 3-1.)
The task of this section is to explain the background of the back-EMF
sensing and to demonstrate how the zero crossing events can be
detected. Parasitic effects that negatively influence the back-EMF
detection are discussed and their nature analyzed.
3.2.4.2 Indirect Back EMF Sensing
Let us assume a usual situation, where the BLDC motor is driven in
six-step commutation mode using PWM technique, where both top and
bottom switches in the diagonal are controlled using the same signal (so
called “hard switching PWM” technique). The motor phases A and B are
powered, and phase C is free, having no current. So the phase C can be
used to sense the back-EMF voltage. This is described by the following
conditions:
(EQ 3-2.)
The branch voltage
u
Vc
can be calculated using the above conditions,
(EQ 3-3.)
u
Sa
u
Sb
u
Sc
R
S
i
Sa
i
Sb
i
Sc
t
d
d
Ψ
Sa
Ψ
Sb
Ψ
Sc
+
=
S
Ab
S
Bt
,
PWM
←
u
VA
1
2
---u
d
+−
=
u
VB
1
2
---
±
u
d
=
,
i
Sa
i
Sb
–
i
=
=
i
Sa
d
i
Sb
d
–
i
d
=
=
,
i
Sc
0
=
i
Sc
d
0
=
,
u
backEMF a
u
backEMF b
u
backEMF c
+
+
0
=
u
VC
u
Sc
1
3
---
u
backEMF x
x
a
=
c
∑
L
ac
L
bc
–
(
)
i
d
t
d
---- u
VC
–
+
–
=
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