Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Direct Torque Control with Space Vector Modulation
∆Ψ = Ψ ∆ . (5.23b)
sβ
_ ref PM
δ Ψ
Stator voltage components using equations (2.23a-b) can be expressed as:
U α
= (5.24a)
s _ ref
0
U
= ∆Ψ K
(5.24b)
sβ _ ref sβ _ ref pΨ
And further because of U
β _
= U
_
s ref s ref
U
=Ψ ∆ δ K
(5.25)
s PM pΨ
So, the transfer function between stator voltage amplitude
angle ∆ δ Ψ
can be written as:
U
s
G
δ
() s = = K
ΨΨ
∆δ
M p PM
Ψ
U
s
and increment of torque
(5.26)
Where
K
p Ψ
is the gain of stator flux P controller.
For example for sampling time T = 200µ
s, calculated
s
0.2688
K = pΨ 1344
T
= (see
s
Table5.1.) and nominal value of Ψ
PM
= 0.264Wb
the calculated GMδ () s = 354,82V / rad .
The obtained transfer function between electromagnetic torque
amplitude
U
s
is (see equation 5.72):
M
e
and stator voltage
G
M
M () s A s
() s = =
U s s + B s+ C
(5.27)
e
M
2
s
()
M M
Where
A
M
2
3pbΨ
PM
RsΨ
3 Ψ
PM
s
ΨPM pb
= and BM
= CM
=
2L
Ψ L
2JL
s
Using the motor parameters (see Appendices), one obtains:
A = 198 and B = 115.3 C = 9065
M
M
M
s
s
s
Continuous s-domain
The torque control loop is shown in Fig. 5.16, where C ( s ) is a transfer function of the
PI controller given by [105]:
M
80