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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 />

<strong>Control</strong> Plant<br />

P controller<br />

Ψ s_ref<br />

C<br />

Ψ<br />

() s<br />

U s<br />

G<br />

Ψ<br />

() s<br />

Ψ s<br />

Figure 5.7. Block diagram <strong>of</strong> flux controller in s domain.<br />

Hence the transfer function <strong>of</strong> the closed stator flux amplitude control loop is obtained as:<br />

G<br />

Ψ _ closed<br />

Ψ<br />

s<br />

() s<br />

_ ref CΨ() s GΨ()<br />

s<br />

() s = =<br />

Ψ () s 1 + C () s G () s<br />

s<br />

Ψ<br />

Ψ<br />

(5.12)<br />

Substituting transfer function for CΨ ( s)<br />

and GΨ ( s)<br />

one becomes:<br />

⎛1⎞ ⎛1⎞<br />

KpΨ⎜ ⎟ KpΨ⎜ ⎟<br />

s s K<br />

p<br />

GΨ _ closed<br />

() s =<br />

⎝ ⎠<br />

=<br />

⎝ ⎠<br />

=<br />

⎛1<br />

⎞ s+ KpΨ<br />

s+<br />

K<br />

1+ K<br />

pΨ<br />

⎜ ⎟<br />

⎝s<br />

⎠ s<br />

Ψ<br />

pΨ<br />

(5.13)<br />

Discrete design<br />

The transfer function for P controller in discrete system is expressed as:<br />

CΨ( z) = KpΨ<br />

(5.14)<br />

Ψ<br />

s_ ref( z)<br />

C<br />

Ψ<br />

( z)<br />

U<br />

= sα U<br />

s<br />

Dz ( )<br />

z −1<br />

GΨ<br />

( z)<br />

}<br />

ZOH<br />

1<br />

s<br />

Ψ<br />

s<br />

( z)<br />

Figure 5.8. Block diagram <strong>of</strong> flux controller in discrete domain.<br />

Where, CΨ ( z)<br />

is discrete transfer function for P controller, Dz ( )<br />

delay for voltage generation from PWM .<br />

1<br />

z −<br />

is for one sampling time<br />

71

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