AN1931D Freescale Semiconductor / Motorola, AN1931D Datasheet - Page 7

• Manufacturer Part Number: AN1931D
• Description: 3-Phase PM Synchronous Motor Vector Control
• Manufacturer: Freescale Semiconductor / Motorola

MOTOROLA
For a description of the PM synchronous motor, the symmetrical three-phase smooth-air-gap machine
with sinusoidally-distributed windings is considered. The voltage equations of stator in the
instantaneous form can then be expressed as:
where u
instantaneous values of stator currents, and
linkages, in phase SA, SB and SC.
Due to the large number of equations in the instantaneous form, the equations
and
transformation). The PM synchronous motor can be expressed as:
where:
The equations
stationary frame , fixed to the stator.
(EQ
u
i
R
L
p
J
T
SA
S
3-8.), it is more practical to rewrite the instantaneous equations using two axis theory (Clarke
S
S
L
S
r
, u
S
M
SB
F
(EQ 3-9.)
and u
d
t d
SC
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is the stator orthogonal coordinate system
is the stator voltage
is the stator current
is the stator magnetic flux
is the rotor magnetic flux
is the stator phase resistance
is the stator phase inductance
is the electrical rotor speed / fields speed
is the number of poles per phase
is the inertia
is the load torque
is the rotor position in
3-Phase PM Synchronous Motor Vector Control
through
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are the instantaneous values of stator voltages, i
=
S
S
p
-- -
J
u
u
u
u
u
=
S
S
3
-- - p
2
SC
SA
SB
=
(EQ 3-13.)
L
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=
S
L
=
=
=
=
i
S
S
R
i
S
R
R
R
R
S
S
+
S
S
S
S
i
i
i
i
i
i
S
S
+
S
SA
SB
SC
+
M
–
+
+
+
SA
+
represent the model of PM synchronous motor in the
M
sin
t d
d
t d
t d
t d
t d
,
d
d
d
d
cos
S
coordinate system
i
SB
S
SA
SB
SC
S
S
r
,
r
–
SC
T
L
are
instantaneous values of stator flux
SA
, i
(EQ
Target Motor Theory
SB
3-6.),
and i
(EQ 3-10.)
(EQ 3-11.)
(EQ 3-12.)
(EQ 3-13.)
SC
(EQ 3-7.)
(EQ 3-6.)
(EQ 3-7.)
(EQ 3-8.)
(EQ 3-9.)
are the
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