4 Chopper-Controlled DC Motor Drive
4 Chopper-Controlled DC Motor Drive
4 Chopper-Controlled DC Motor Drive
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• The armature current is expressed as<br />
i<br />
a<br />
A<br />
(t) = I<br />
n<br />
av +<br />
∞<br />
∑n<br />
= 1 sin(nωct<br />
+ θn<br />
− φ<br />
Zn<br />
Va<br />
− E<br />
Iav<br />
Zn<br />
= R<br />
Ra<br />
−1<br />
R<br />
φ cos {<br />
a<br />
n =<br />
}<br />
2 2 2<br />
R + n ω L<br />
where<br />
= a c a<br />
a<br />
c<br />
2<br />
a<br />
n<br />
)<br />
+<br />
jnω<br />
L<br />
• The input power is<br />
P<br />
i<br />
=<br />
V<br />
a<br />
⎧V aI<br />
⎪<br />
= ⎨<br />
⎪+<br />
V<br />
⎩<br />
a<br />
(t)i<br />
av<br />
a<br />
+ I<br />
(t)<br />
av<br />
∑<br />
∞<br />
n = 1<br />
sin(nω<br />
t + θ<br />
∞ An<br />
∑ = ω + θ − φ +<br />
∞<br />
n 1 sin(n ct<br />
n n)<br />
∑n<br />
=<br />
Z<br />
n<br />
A<br />
n<br />
c<br />
n<br />
)<br />
1<br />
A<br />
(<br />
Z<br />
2<br />
n<br />
n<br />
sin(nω<br />
c<br />
t + θ<br />
n<br />
)sin(nω<br />
c<br />
t + θ<br />
n<br />
− φ<br />
n<br />
⎫<br />
⎪<br />
⎬<br />
)) ⎪<br />
⎭