RX62T YROTATE-IT-RX62T Motor Control Kit
UM-YROTATE-IT-RX62T Rev.1.00
Page 20 of 51
Jan 15, 2014
The reference frame transformations from the (
α
,
β
) system to the (d, q) system depends on the instantaneous
position angle
ϑ
ϑϑ
ϑ
So we obtain two inter-dependant equations in the (d, q) system:
m
d
q
q
S
q
q
d
d
S
d
Li
dt
di
L
i
R
v
Li
dt
di
L
i
R
v
Λ
+
+
+
=
−
+
=
ω
ω
ω
These two equations represent the mathematical motor model.
A control algorithm which wants to produce determined currents in the (d, q) system must impose voltages given
from the formulas above.
This is ensured by closed loop PI control on both axis “d” & “q” (Proportional Integral).
Since there is a mutual influence between the two axes, decoupling terms can be used.
In the block scheme the mechanic part is included, where “p” is the number of pole pairs, while “B” represents
friction, “J” the inertia, “
τ
load
“ the load torque and “
τ
” the motor torque.
Λ
×
×
=
p
2
3
τ
The angular speed
ω
is represented in the scheme as
ω
e
to distinguish the electrical speed from the mechanical one.
Let’s now consider the equations we have seen in (
α
,
β
) system:
1/(R+sL)
1/(R+sL)
(3/2)p
Λ
1/(B+sJ)
τ
load
p
Λ
pL
V
d
V
q
+
-
+
-
-
+
ω
mec
I
d
I
q
τ
+
L
ω
e
Λω
e
