Renesas YROTATE-IT-RX62T, User Manual

Page: 21 / 54

RX62T YROTATE-IT-RX62T Motor Control Kit
UM-YROTATE-IT-RX62T Rev.1.00 Page 21 of 51
Jan 15, 2014
dt
d
i R v
dt
d
i R v
S
S
β
β β
α
α α
λ
λ
+ =
+ =
These equations show that magnetic flux can be obtained from applied voltages and measured currents simply by
integration:
d i R v
dt i R v
S
t
S
t
) (
) (
0
0
0
0
β β β β
α α α α
λ λ
λ λ
∫
∫
− + =
− + =
Furthermore:
β β
α α
λ ϑ
λ ϑ
Li
Li
m
m
− = Λ
− = Λ
) sin(
) cos(
If the synchronous inductance L is small, the current terms can be neglected, if not they have to be considered. In
general:
β β β β β β
α α α α α α
λ λ ϑ
λ λ ϑ
Li dt i R v Li y
Li dt i R v Li x
S
t
m
S
t
m
− − + = − = Λ =
− − + = − = Λ =
∫
∫
) ( ) sin(
) ( ) cos(
0
0
0
0
So in the (
α
,
β
) system phase we obtain from the flux components:
) arctan(
y
x
=
ϑ
The system speed
ω
can be obtained as the derivative of the angle
ϑ
.
) (t
dt
d
ϑ ω
=
Based on this, a sensorless control algorithm was developed to give the imposed phase voltages, to measure phase
currents, to estimate the angular position
ϑ
and finally the system speed.