UM-YROTATE-IT-RX62T Datasheet, PDF (18/54 Pages) Renesas Technology Corp – Low Cost Motor Control Kit based on RX62T

RX62T
YROTATE-IT-RX62T Motor Control Kit
v_a
=
R_S i_a
+
dλ_a
dt
v_b
=
R_S i_b
+
dλ_b
dt
v_c
=
R_S i_c
+
dλ_c
dt
- λ_i is the magnetic flux linkage with the i-th stator winding
- R_S is the stator phase resistance (the resistance of one of the stator windings)
The magnetic flux linkages λ_i are composed by two items, one due to the stator currents, one to the permanent
magnets.
c axis
β axis
a
b’
c’
a axis
α
β’
Λ_m
ϑ
β’
α axis
c
b
α’
a’
b axis
Real axes (a, b, c) and equivalent ones (α, β); a fixed amplitude vector can be completely determined by its
position respect the (α, β) system (angle ϑ)
The permanent magnet creates a magnetic field that is constant in amplitude and fixed in position in respect to the
rotor. This magnetic field can be represented by vector Λ_m whose position in respect to the stator is determined by
the angle ϑ between the vector direction and the stator reference frame.
The contribution of the permanent magnets in the flux linkages depends on the relative position of the rotor and the
stator represented by the mechanical-electric angle ϑ.
It is, in every axis, the projection of the constant flux vector Λ_m in the direction of the axis:
λ_a = Li_a + Λ_m cos(ϑ)
λ_b = Li_b + Λ_m cos(ϑ − ^2π ₃₎
λ_c = Li_c + Λ_m cos(ϑ − ^4π ₃₎
UM-YROTATE-IT-RX62T Rev.1.00
Jan 15, 2014
Page 18 of 51