
Filtering Techniques for Power Quality Improvement 38-41
As described in Figure 38.54, the peak value
i
s
is delivered by the outer regulator and is therefore con-
sidered
a
s
t
he
i
nput
si
gnal
o
f
t
he
o
uter
s
ubsystem.
e
n
ext
s
tep,
t
hen,
i
s
to
d
evelop
t
he
t
ransfer
f
unc-
tion
t
hat
r
elates
t
he
o
uter
c
ontrolled
v
ariable
to the input control variable
i
s
, on the basis of which
t
he
d
esign
o
f
t
he
l
inear
o
uter
r
egulator
w
ill
b
e
c
arried
o
ut.
U
sing
e
xpressions
(
38.52)
a
nd
(
38.54)
i
nto
E
quation 38.55 yields the steady-state time expression of the duty cycle
d t
v
v
L
d i i
dt
dc
s
c
L s
1
1
2
1
2
*
( )
= + +
−
*
(
38.55)
with
v
v t
s
s s
=
ˆ
sin ω
(38.56)
and
i i