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Freescale semiconductor, inc – Motorola M68HC08 User Manual

Page 29

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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

+

=

F

re

e

sc

a

le

S

e

m

ic

o

n

d

u

c

to

r,

I

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