AN1931D Freescale Semiconductor / Motorola, AN1931D Datasheet - Page 5

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

MOTOROLA
3.2 Mathematical Description of PM Synchronous Motor
3.2.1 Space Vector Definition
In this respect, the PM synchronous motor is equivalent to an induction motor, where the air gap
magnetic field is produced by a permanent magnet, so the rotor magnetic field is constant. PM
synchronous motors offer a number of advantages in designing modern motion control systems. The
use of a permanent magnet to generate substantial air gap magnetic flux makes it possible to design
highly efficient PM motors.
The model used for vector control design can be understood by using space vector theory. The
three-phase motor quantities (such as voltages, currents, magnetic flux, etc.) are expressed in terms of
complex space vectors. Such a model is valid for any instantaneous variation of voltage and current
and adequately describes the performance of the machine under both steady-state and transient
operation. The complex space vectors can be described using only two orthogonal axes. We can look
at the motor as a two-phase machine. Using a two-phase motor model reduces the number of equations
and simplifies the control design.
Assume i
Then we can define the stator current space vector as follows:
where a and a
chosen as k=2/3.
sa
, i
sb
2
, i
are the spatial operators, a = e
sc
Figure 3-2
Figure 3-1. PM Synchronous Motor - Cross Section
are the instantaneous balanced three-phase stator currents:
Freescale Semiconductor, Inc.
3-Phase PM Synchronous Motor Vector Control
For More Information On This Product,
shows the stator current space vector projection:
i
s
=
i
sa
Go to: www.freescale.com
k
+
i
sa
i
sb
+
+
ai
i
sb
j2 /3 , a
sc
+
=
a
0
2
i
2
sc
= e
j4 /3 and k is the transformation constant,
Stator
Stator winding
(in slots)
Shaft
Rotor
Air gap
Permanent magnets
Target Motor Theory
(EQ 3-1.)
(EQ 3-2.)
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