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