AN1931D Freescale Semiconductor / Motorola, AN1931D Datasheet - Page 13

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

MOTOROLA
3.3.3.2 Transformation from
To transfer the graphical representation into mathematical language:
In most cases, the 3-phase system is symmetrical, which means that the sum of the phase quantities is
always zero.
The constant “K” can be freely chosen and equalizing the
recommended. Then:
We can fully define the Park-Clarke transformation:
Vector Control is performed entirely in the d-q coordinate system to make the control of PM
synchronous motors elegant and easy; see
Of course, this requires transformation in both directions and the control action must be transformed
back to the motor side.
First, establish the d-q coordinate system:
Then transform from
=
2
-- -
3
0
=
------ -
–
1
1
-- -
3
3
K a
Freescale Semiconductor, Inc.
–
3-Phase PM Synchronous Motor Vector Control
–
to d-q coordinates:
------ -
d
q
For More Information On This Product,
1
-- -
3
1
–
3
1
-- - b
2
=
a
b
c
=
–
–
M
cos
sin
cos
1
-- - c
2
=
K
sin
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to d-q Coordinates and Backwards
=
=
a
Field
Field
=
1
0
Field
a
Field
+ +
Section
M
b
------ -
a
=
–
=
2
K
cos
1
-- -
2
sin
3
+ +
---------- -
+
-----------
c
=
b
M
Md
M
–
Md
3.3.2.
=
–
------ -
2
-- -
3
Field
M
Field
1
-- -
2
2
0
c
3
=
a
b
c
0
=
=
1
0
K
-quantity and a-phase quantity is
3
-- - a
2
------ -
0
1
3
–
------ -
0
1
3
Target Motor Theory
a
b
c
(EQ 3-22.)
(EQ 3-23.)
(EQ 3-24.)
(EQ 3-25.)
(EQ 3-26.)
(EQ 3-27.)
(EQ 3-28.)
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