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UM0324 Datasheet(PDF) 62 Page - STMicroelectronics

Part # UM0324
Description  This user manual describes
PDF  105 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

UM0324 Datasheet(HTML) 62 Page - STMicroelectronics

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Library functions
UM0324
62/105
With this choice, the electromagnetic torque can be written as:
i.e. as a product of a flux and a current component (P= number of stator poles).
Let’s investigate further on the rotor flux
λdrλr.
Considering the d-axis rotor flux equation:
then, the equation for idrλ
r is:
Combining the latter with the d-axis rotor voltage equation, leads to:
where
τ r is the rotor time constant, τ r = Lr / rr.
Therefore, a lag in flux response is caused to this first order transfer function between idsλ
r
and
λdrλr.
The CalcIm routine performs a numerical integration using Euler’s method which, for a first
order ODE written as
may be summarized in this way:
where t is the sampling time.
Putting the equation above in the explicit form, we have:
()r
r
qs
dr
r
m
e
i
L
L
p
T
λ
λ
λ
2
2
3
=
)
(
r
dr
r
ds
m
r
dr
lr
r
dr
i
i
L
i
L
λ
λ
λ
λ
λ
+
+
=
r
r
ds
m
r
dr
r
dr
L
i
L
i
λ
λ
λ
λ
−
=
0
)
(
=
−
+
r
ds
m
r
dr
r
r
r
dr
i
L
L
r
dt
d
λ
λ
λ
λ
λ
r
r
r
ds
r
m
dr
r
m
dr
i
L
L
dt
d
λ
τ
λ
τ
λ
λ
λ
1
1
=
⎟⎟⎠
⎞
⎜⎜⎝
⎛
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
)
,
( y
t
f
y
=
′
)
,
(
1
n
n
n
n
y
t
f
t
y
y
⋅
Δ
+
=
+
⎟⎟⎠
⎞
⎜⎜⎝
⎛
−
=
′
⎟⎟⎠
⎞
⎜⎜⎝
⎛
m
dr
ds
r
m
dr
L
i
L
r
r
r
λ
λ
λ
τ
λ
λ
1



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