AN1931D Freescale Semiconductor / Motorola, AN1931D Datasheet - Page 8

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

Target Motor Theory
8
Besides the stationary reference frame attached to the stator, motor model voltage space vector
equations can be formulated in a general reference frame, which rotates at a general speed
general reference frame is used, with direct and quadrature axes x,y rotating at a general instantaneous
speed
stationary reference frame (
then
The stator voltage and flux-linkage space vectors can be similarly obtained in the general reference
frame.
Similar considerations hold for the space vectors of the rotor voltages, currents and flux linkages. The
real axis (r
reference frame by the rotor angle
general reference frame and the real axis of the reference frame rotating with the rotor (r
the general reference frame, the space vector of the rotor currents can be expressed as:
where
The space vectors of the rotor voltages and rotor flux linkages in the general reference frame can be
similarly expressed.
The motor model voltage equations in the general reference frame can be expressed by utilizing
introduced transformations of the motor quantities from one reference frame to the general reference
frame. The PM synchronous motor model is often used in vector control algorithms. The aim of vector
control is to implement control schemes which produce high dynamic performance and are similar to
those used to control DC machines. To achieve this, the reference frames may be aligned with the
(EQ 3-14.)
i
r
g
=d
is the space vector of the rotor current in the rotor reference frame.
g
of the reference frame attached to the rotor is displaced from the direct axis of the stator
/dt, as shown in
Figure 3-3. Application of the General Reference Frame
defines the stator current space vector in general reference frame:
y
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3-Phase PM Synchronous Motor Vector Control
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i
rg
i
attached to the stator and the real axis (x) of the general reference frame,
sg
=
Figure
=
i
r
r.
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e
i
Since it can be seen that the angle between the real axis (x) of the
–
s
j
e
–
3-3, where
j
g
–
g
=
r
i
=
sx
i
+
rx
ji
+
g
sy
ji
is the angle between the direct axis of the
ry
g
x
MOTOROLA
(EQ 3-14.)
(EQ 3-15.)
is
g
g
-
. If a
r
, in