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 />
Finally, the discrete transfer function <strong>of</strong> controlled plant G ( z ) can be written as:<br />
M<br />
Where:<br />
C<br />
M _ d<br />
⎛ A ⎞<br />
Md<br />
GM<br />
( z) = ( z−1) ⎜ 2<br />
⎟<br />
⎝ z − BMd<br />
z+<br />
CMd<br />
⎠<br />
2<br />
A<br />
BM<br />
A = e sin( T C − ) ,<br />
4<br />
BM<br />
− T<br />
M<br />
s<br />
2<br />
M _ d<br />
2<br />
s M<br />
BM<br />
CM<br />
−<br />
4<br />
BM<br />
Ts<br />
= e − and T<br />
s<br />
is sampling time.<br />
(5.78)<br />
BM<br />
2<br />
− Ts<br />
B<br />
2<br />
M<br />
BM _ d<br />
= 2e cos( Ts CM<br />
− )<br />
4<br />
Hence, the transfer function <strong>of</strong> closed torque control loop is obtained as:<br />
G<br />
M _ closed<br />
( z)<br />
M ( z) C ( z) G ( z) D( z)<br />
M ( z) 1 + C ( z) G ( z) D( z)<br />
e_<br />
ref M M<br />
= = =<br />
e M M<br />
K<br />
A ( K + K )( z−<br />
)<br />
pM<br />
M _ d pM iM<br />
KpM<br />
+ KiM<br />
3 2<br />
−<br />
M _ d<br />
+ [<br />
M _ d( pM<br />
+<br />
iM) +<br />
M _ d]<br />
−<br />
M _ d pM<br />
=<br />
z B z A K K C z A K<br />
(5.79)<br />
Selecting<br />
K Ψ<br />
, K Ψ<br />
will influence poles placement <strong>of</strong> closed torque control loop and as a<br />
p<br />
i<br />
consequence also torque step responses can be selected.<br />
The transfer function <strong>of</strong> closed torque control loop is more complicated than flux control loop<br />
(see design <strong>of</strong> PI-flux controller – section 5.3.1). One possibility is use to the SISO tools from<br />
Matlab package to tune parameters <strong>of</strong> PI torque controller [106].<br />
a) b)<br />
Figure 5.37. a) <strong>Torque</strong> step response for sampling time T = 200µ<br />
s, b) <strong>with</strong> denoted rise time,<br />
overshoot and settling time.<br />
As can be observed the response is characterized by overshoot about 40%, rise time 4 samples<br />
and settling time 17 samples.<br />
s<br />
103