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AT32UC3B0256-A2UT 其他数据使用手册 - Microchip（微芯）
制造商:
Microchip（微芯）
分类:
微控制器
封装:
TQFP-64
描述:
AT32 系列 66 MHz 256 kB 闪存 32 kB SRAM AVR® 微控制器 - TQFP-64
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AT32UC3B0256-A2UT数据手册
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AVR32723
32126A-AVR32-06/09
4 Motor Control Theory
4.1 General Model.
The mathematical model in a constant domain linked to the stator is linked to
differential equation with constant coefficients defining the motor behavior.
Applying the Lenz-Faraday model, we have:
[]
[
]
[
]
abcabcabc
dt
d
IRV Φ+=
With:
[]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
c
b
a
abc
v
v
v
V
,
[]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
c
abc
i
i
i
I
b
a
and
[]
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
Φ
Φ
Φ
=Φ
c
b
a
abc
R is the statoric resistance,
[
]
t
cba
vvv are the statoric voltages,
[]
t
cba
iii are
the statoric current and
[
]
t
cba
ΦΦΦ are the global fields in the statoric solenoid.
[]
[
]
[
]
[
]
sfabcabc IL
Φ
+
=Φ
We can write :
Ls (constant) is the inductance in a statoric gyres.
M (constant) is the mutual inductance between the 2 statoric gyres
θ is the electrical position of the rotor (θ= θ
élec
)
Ф
sf
is the max value (constant) of the flux create by the permanents magnet through
the statoric gyres.
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+Φ
−Φ
Φ
+
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
)
3
2
cos(
)
3
2
cos(
)cos(
π
θ
π
θ
θ
sf
sf
sf
c
b
a
c
b
a
c
b
a
dt
d
i
i
i
LsMM
MLsM
MMLs
dt
d
i
i
i
R
v
v
v
In order to simplify the mathematical resolution of this system, some mathematical
transformations are used.
Using the Park P1(θ), the instantaneous power is kept and it allows to have a
mathematical expression of the torque still acceptable for the real motor.
[]
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
+Φ
−Φ
Φ
+
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=Φ
)
3
2
cos(
)
3
2
cos(
)cos(
π
θ
π
θ
θ
sf
sf
sf
c
b
a
abc
i
i
i
LsMM
MLsM
MMLs
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