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UM-YROTATE-IT-RX62T Datasheet(PDF) 19 Page - Renesas Technology Corp

No. de pieza UM-YROTATE-IT-RX62T
Descripción Electrónicos  Low Cost Motor Control Kit based on RX62T
PDF  54 Pages
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Fabricante Electrónico  RENESAS [Renesas Technology Corp]
Página de inicio  http://www.renesas.com
Logo RENESAS - Renesas Technology Corp

UM-YROTATE-IT-RX62T Datasheet(HTML) 19 Page - Renesas Technology Corp

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RX62T
YROTATE-IT-RX62T Motor Control Kit
UM-YROTATE-IT-RX62T Rev.1.00
Page 19 of 51
Jan 15, 2014
Supposing that the rotor is rotating at constant speed
ω (that is: ϑ(t) = ωt) the flux linkages derivatives can be
calculated, and we obtain:
)
3
4
sin(
)
3
2
sin(
)
sin(
π
ϑ
ω
π
ϑ
ω
ϑ
ω
−
Λ
−
+
=
−
Λ
−
+
=
Λ
−
+
=
m
b
b
S
c
m
b
b
S
b
m
a
a
S
a
dt
di
L
i
R
v
dt
di
L
i
R
v
dt
di
L
i
R
v
A “three phases system” may be represented by an equivalent “two phases system”. So the by using specific
transformations, our three equations system is equivalent to a two equations system. It is basically a mathematical
representation in a new reference coordinates system.
In the two phases (
α,β) fixed system the above equations become:
dt
d
i
R
v
dt
d
i
R
v
S
S
β
β
β
α
α
α
λ
λ
+
=
+
=
For the magnetic field equations, we got:
)
sin(
)
cos(
ϑ
λ
λ
ϑ
λ
λ
β
β
β
β
α
α
α
α
m
m
m
m
Li
Li
Li
Li
Λ
+
=
+
=
Λ
+
=
+
=
After performing the derivation:
m
m
m
m
dt
di
L
dt
di
L
dt
d
dt
di
L
dt
di
L
dt
d
α
β
β
β
β
α
α
α
ωλ
ϑ
ω
λ
ωλ
ϑ
ω
λ
+
=
Λ
+
=
−
=
Λ
−
=
)
cos(
)
sin(
Finally, we obtain for the voltages in (
α,β) system:
m
S
m
S
dt
di
L
i
R
v
dt
di
L
i
R
v
α
β
β
β
β
α
α
α
ωλ
ωλ
+
+
=
−
+
=
A second reference frame is used to represent the equations as the frame is turning at the rotor speed. So the “d”
axis is chosen in the direction of the magnetic vector
Λ
m, and with the “q” axis orthogonal to the “d” axis. The new
reference system is (d, q).



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