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4 Chopper-Controlled DC Motor Drive

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• The normalized torque is<br />

T<br />

en<br />

=<br />

T<br />

T<br />

av<br />

b<br />

/ V<br />

/ V<br />

b<br />

b<br />

=<br />

K<br />

b<br />

(dV<br />

K<br />

s<br />

b<br />

− K<br />

I R<br />

b<br />

a<br />

b<br />

ωm<br />

) /<br />

/ V<br />

b<br />

V<br />

b<br />

=<br />

dVn<br />

− ω<br />

R<br />

an<br />

mn<br />

,<br />

p.u.<br />

I<br />

R<br />

where R<br />

b a<br />

an = , p.u. V<br />

s<br />

V<br />

n = , p.u. ω<br />

m<br />

mn = , p.u.<br />

b<br />

Vb<br />

ωb<br />

• 4.9.2 Instantaneous steady-state computation<br />

(including harmonics)<br />

• The equations of the motor for on and off times<br />

(continuous current conduction)<br />

di<br />

V E R i L<br />

a<br />

s = + a a + a<br />

dt<br />

di<br />

0 = E + R i L<br />

a<br />

a a + a ,<br />

dt<br />

,<br />

0<br />

dT<br />

≤<br />

≤<br />

t<br />

t<br />

V<br />

≤<br />

≤<br />

dT<br />

T<br />

ω

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