I
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n J
o
urna
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f
E
lect
rica
l En
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a
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Co
m
pu
t
er
Science
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
ar
y
20
2
5
,
p
p
.
749
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DOI
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Ana
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PI
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co
ntroller for
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ticle
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CC B
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C
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Dep
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U
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Vis
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(
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I
n
d
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m
ail:
s
ath
y
a.
k
@
u
v
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.
ac
.
in
1.
I
NT
RO
D
UCT
I
O
N
C
o
n
v
en
tio
n
al
f
o
s
s
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d
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s
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s
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m
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lp
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ter
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ts
o
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x
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f
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aso
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d
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ca
r
s
ar
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d
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tal
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b
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o
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b
u
s
in
ess
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d
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ic
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ec
to
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p
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ter
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co
m
b
u
s
tio
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g
in
e
v
eh
icle
s
(
I
C
Vs)
to
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icles
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E
Vs)
as
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r
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lt
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th
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th
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is
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alter
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ativ
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m
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in
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Vs
a
r
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s
tar
tin
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to
lead
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.
A
s
u
f
f
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u
an
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f
ch
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g
in
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tatio
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with
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to
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ch
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ick
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ar
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ca
p
ab
ilit
ies,
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d
in
cr
ea
s
ed
r
an
g
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ar
e
all
n
ec
ess
ar
y
f
o
r
th
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m
ain
s
tr
ea
m
ad
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tio
n
o
f
E
Vs.
Hig
h
-
p
o
wer
ch
ar
g
er
s
ar
e
n
ec
ess
ar
y
to
en
ab
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to
m
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d
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if
ican
tly
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cr
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r
d
r
iv
in
g
r
an
g
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T
h
e
r
eso
n
an
t
L
L
C
co
n
v
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ter
ar
ch
itectu
r
e
h
as
s
h
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wn
to
b
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a
s
u
cc
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f
u
l
m
eth
o
d
f
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g
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r
atin
g
th
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n
ec
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is
o
lated
DC
/D
C
co
n
v
er
ter
s
tag
e,
as
th
ese
h
ig
h
-
p
o
wer
ch
ar
g
er
s
n
o
w
n
ee
d
to
b
e
s
ep
ar
ated
f
r
o
m
th
e
g
r
id
.
L
L
C
r
eso
n
an
t
c
o
n
v
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r
ter
attr
ib
u
tes
s
u
ch
as
h
ig
h
-
p
o
w
er
d
en
s
ity
,
l
o
w
n
o
is
e
an
d
h
i
g
h
ef
f
icien
cy
,
it
is
u
tili
ze
d
in
wid
e
ap
p
licatio
n
s
,
in
clu
s
iv
e
o
f
elec
tr
ic
v
eh
icle
s
[
1
]
,
p
o
wer
elec
tr
o
n
ics
[
2
]
,
r
en
ewa
b
le
en
er
g
y
,
m
icr
o
g
r
i
d
s
[
3
]
,
u
n
i
n
ter
r
u
p
ted
p
o
wer
s
u
p
p
ly
,
DC
m
o
t
o
r
d
r
i
v
er
s
,
telec
o
m
m
u
n
icatio
n
s
,
b
at
ter
y
ch
ar
g
er
s
,
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
5
0
2
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4
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52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
4
9
-
7
5
7
750
s
witch
m
o
d
e
p
o
wer
s
u
p
p
lies
.
T
h
e
L
L
C
r
eso
n
a
n
t
co
n
v
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t
er
s
ar
e
o
f
ten
m
o
d
u
lated
u
s
in
g
p
u
ls
e
f
r
eq
u
en
c
y
m
o
d
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latio
n
(
PF
M)
an
d
a
wid
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o
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s
witch
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eq
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n
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ar
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ally
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eq
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r
ed
f
o
r
a
r
an
g
e
o
f
in
p
u
t
v
o
ltag
es
[
2
]
,
[
4
]
,
[
5
]
.
An
L
L
C
r
eso
n
an
t
co
n
v
e
r
ter
with
a
z
er
o
-
v
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lta
g
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s
witch
in
g
(
Z
VS)
s
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s
tem
ca
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ac
h
iev
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r
ea
ter
c
o
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v
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icien
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b
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allo
win
g
its
ac
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witch
es
to
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en
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s
e.
I
t
is
ch
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g
in
g
to
a
n
aly
ze
an
d
r
eg
u
late
th
is
r
eso
n
an
t
c
o
n
v
er
ter
o
p
tim
ally
,
wh
ich
r
esu
lts
in
lar
g
e
er
r
o
r
s
an
d
e
x
ten
d
e
d
p
r
o
ce
s
s
in
g
tim
es.
T
h
e
o
u
t
p
u
t
v
o
ltag
e
o
f
L
L
C
r
e
s
o
n
an
t
co
n
v
er
ter
is
c
o
n
tr
o
lled
u
s
in
g
s
ev
er
al
tr
ad
itio
n
al
m
et
h
o
d
s
in
clu
d
in
g
PID
,
PI,
an
d
PD.
an
d
h
av
e
th
e
b
en
ef
its
o
f
b
ein
g
in
ex
p
e
n
s
iv
e
as
well
as
s
im
p
le
to
u
s
e
[
6
]
.
B
u
t
th
ey
also
n
ee
d
a
s
o
p
h
is
ticated
m
ath
em
atica
l
m
o
d
el
a
n
d
a
r
e
u
n
ab
le
t
o
g
u
ar
an
tee
th
e
in
ten
d
e
d
p
e
r
f
o
r
m
an
ce
u
n
d
er
d
if
f
er
en
t
o
p
er
atin
g
s
itu
atio
n
s
[
7
]
,
[
8
]
.
F
u
r
th
er
m
o
r
e,
th
e
liter
atu
r
e
r
e
v
i
ew
in
d
icate
s
th
at
r
esear
ch
er
s
h
av
e
b
ee
n
d
r
awn
to
th
e
s
tab
ilit
y
an
aly
s
is
an
d
co
n
tr
o
ller
d
esig
n
is
s
u
es
o
f
L
L
C
r
es
o
n
an
t
co
n
v
er
ter
s
,
w
h
ich
h
as
le
d
to
im
p
r
o
v
em
e
n
ts
in
tr
an
s
ien
t d
o
m
ai
n
s
p
ec
if
icatio
n
s
ev
en
in
th
e
f
ac
e
o
f
m
u
ltip
le
u
n
ce
r
tain
ties
an
d
p
er
tu
r
b
atio
n
s
.
T
h
e
r
esear
ch
f
o
c
u
s
ed
o
n
c
o
n
t
r
o
ller
d
esig
n
in
th
is
p
ap
e
r
,
s
p
ec
if
ically
u
s
in
g
th
e
PID
D2
[
9
]
co
n
tr
o
l
d
esig
n
to
ad
d
r
ess
th
e
L
L
C
r
eso
n
an
t
co
n
v
e
r
ter
v
o
ltag
e
co
n
t
r
o
l
is
s
u
e.
Sev
er
al
co
n
tr
o
l
d
es
ig
n
tech
n
iq
u
es
f
o
r
L
L
C
r
eso
n
an
t
co
n
v
er
ter
s
h
av
e
b
ee
n
d
escr
ib
ed
b
y
r
esear
ch
er
s
in
th
e
liter
atu
r
e.
Ho
wev
er
,
it
is
d
ep
icted
f
r
o
m
th
e
s
u
r
v
ey
th
at
is
d
o
n
e
th
at
th
e
PID
D2
co
n
tr
o
ller
h
as
n
o
t
b
ee
n
in
v
esti
g
ated
f
o
r
L
L
C
r
eso
n
an
t
co
n
v
e
r
ter
v
o
ltag
e
r
e
g
u
latio
n
.
T
h
is
r
esear
ch
p
ap
e
r
p
r
esen
ts
th
e
p
r
o
p
o
s
e
d
PID
D2
ap
p
r
o
ac
h
to
ca
lib
r
at
e
th
e
L
L
C
r
eso
n
an
t
co
n
v
er
ter
o
u
tp
u
t
v
o
ltag
e
v
alu
e
to
t
h
e
r
e
f
er
en
ce
v
o
ltag
e
v
alu
e.
PID
D2
co
n
tr
o
ller
s
p
r
o
v
id
e
ac
cu
r
ate
co
n
tr
o
l
o
f
th
e
L
L
C
co
n
v
er
ter
u
s
in
g
m
i
n
im
al
r
is
e
tim
e,
o
v
er
s
h
o
o
t,
a
n
d
s
ettlin
g
tim
e.
Fo
llo
win
g
th
e
p
r
esen
tatio
n
o
f
PID
D2
an
d
PID
s
im
u
latio
n
r
e
s
u
lts
,
a
co
m
p
ar
is
o
n
an
al
y
s
is
o
f
th
e
two
co
n
tr
o
ller
s
u
n
d
er
c
o
n
s
id
er
atio
n
is
d
o
n
e.
Ad
d
itio
n
ally
,
with
s
u
d
d
e
n
ch
a
n
g
es
in
in
p
u
t
v
o
ltag
e
a
n
d
lo
a
d
,
th
e
ef
f
ec
tiv
e
n
ess
an
d
ef
f
ici
en
cy
o
f
t
h
e
PID
D2
co
n
tr
o
ller
ar
e
ex
am
in
e
d
.
T
h
e
f
in
d
in
g
s
f
r
o
m
th
e
s
im
u
latio
n
ar
e
co
m
p
ar
e
d
with
ea
ch
o
th
er
.
2.
M
O
DE
L
I
NG
AN
D
DE
SI
G
N
O
F
L
L
C
RE
SO
NAN
T
CO
N
VE
R
T
E
R
As
illu
s
tr
ated
in
th
e
Fig
u
r
e
1
,
L
L
C
r
eso
n
an
t
co
n
v
er
ter
is
co
m
p
o
s
ed
o
f
two
s
witch
es
(
MO
SF
E
T
)
,
f
o
u
r
d
io
d
es,
a
h
ig
h
f
r
e
q
u
en
c
y
tr
an
s
f
o
r
m
er
an
d
an
L
L
C
f
ilter
.
I
n
o
r
d
er
to
m
ain
tain
a
f
ix
ed
d
u
t
y
cy
cle
o
f
5
0
%,
th
e
co
m
p
lem
en
tar
y
p
o
wer
s
witch
es
Q1
an
d
Q2
f
r
e
q
u
en
c
y
is
m
an
ag
ed
b
y
th
e
f
r
eq
u
e
n
cy
c
o
n
tr
o
lled
s
witch
in
g
n
etwo
r
k
,
wh
ich
also
s
er
v
es
as
a
s
q
u
ar
e
wav
e
g
en
er
at
o
r
[
1
]
,
[
4
]
.
T
h
e
r
eso
n
an
t
tan
k
r
ec
eiv
e
s
th
is
s
q
u
ar
e
wav
e,
th
e
cu
r
r
e
n
t
p
ass
in
g
th
r
o
u
g
h
t
h
e
n
etwo
r
k
co
n
s
is
ts
o
f
tr
an
s
f
o
r
m
er
'
s
m
ag
n
etizin
g
in
d
u
ctan
ce
L
m
,
th
e
r
eso
n
an
t
ca
p
ac
itan
ce
C
r
,
an
d
th
e
s
er
ie
s
r
eso
n
an
t
in
d
u
ctan
ce
L
r
m
ak
e
u
p
t
h
e
r
eso
n
a
n
t
cir
cu
it
wit
h
a
tu
r
n
r
atio
o
f
n
s
u
p
p
ly
in
g
a
n
d
cir
c
u
latin
g
en
e
r
g
y
to
t
h
e
lo
ad
.
T
h
e
s
p
ec
if
ica
tio
n
s
o
f
in
d
u
cto
r
s
an
d
ca
p
ac
it
o
r
s
ar
e
esti
m
ated
,
wid
e
s
u
p
p
ly
v
o
ltag
e
r
a
n
g
e
an
d
s
witch
in
g
f
r
eq
u
e
n
cy
a
r
e
k
ey
c
o
m
p
o
n
en
ts
in
d
esig
n
[
1
0
]
,
[
1
1
]
.
Fig
u
r
e
1
.
L
L
C
r
eso
n
a
n
t
co
n
v
e
r
ter
s
ch
em
atic
C
ir
cu
it
p
ar
am
eter
s
ar
e
co
m
p
u
ted
u
s
in
g
th
e
p
e
r
tin
en
t
e
q
u
atio
n
s
f
o
r
d
ev
elo
p
i
n
g
L
L
C
r
eso
n
an
t
co
n
v
er
ter
s
[
1
2
]
.
T
h
e
c
o
n
v
e
r
ter
o
p
er
ates a
t 1
2
v
o
lts
,
with
a
s
witch
in
g
f
r
eq
u
e
n
cy
(
F
s
)
o
f
8
0
k
Hz
to
1
2
5
k
Hz
an
d
a
r
eso
n
an
ce
f
r
eq
u
e
n
cy
(
F
r
)
o
f
1
2
4
.
4
k
Hz.
T
h
e
co
n
n
ec
tio
n
b
e
twee
n
v
o
ltag
es o
f
in
p
u
t a
n
d
o
u
tp
u
t is tr
ad
itio
n
ally
b
e
r
ep
r
esen
ted
b
y
th
eir
r
atio
o
r
g
ain
.
T
h
e
o
u
t
p
u
t
v
o
ltag
e
i
s
s
im
p
ly
d
eter
m
in
ed
u
s
in
g
in
(
1
)
af
ter
th
e
in
p
u
t
v
o
ltag
e
V
i
,
g
ain
M
g
an
d
tu
r
n
s
r
atio
n
ar
e
k
n
o
w
n
[
1
3
]
.
Desig
n
in
g
a
co
n
v
er
ter
f
o
r
v
ar
iab
le
en
er
g
y
tr
a
n
s
f
er
an
d
o
u
tp
u
t
v
o
ltag
e
m
o
d
if
icatio
n
r
eq
u
ir
es
co
n
s
id
er
atio
n
o
f
v
o
lta
g
e
tr
an
s
f
er
f
u
n
ctio
n
.
T
h
e
c
h
a
r
ac
ter
is
tics
o
f
g
ain
an
d
its
f
o
r
m
u
la
is
d
escr
ib
ed
[
1
4
]
-
[
1
6
]
.
I
n
(
2
)
th
at
r
e
p
r
ese
n
ts
an
in
d
u
cta
n
ce
r
atio
is
u
s
ed
to
co
m
b
in
e
two
in
d
u
ctan
ce
s
in
to
o
n
e.
I
n
(
3
)
is
p
r
o
v
id
e
d
b
elo
w
d
ef
in
es th
e
q
u
ality
f
ac
to
r
"Q"
in
a
r
eso
n
an
t s
er
ies cir
cu
it.
0
=
∗
1
∗
2
(
1
)
=
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
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N:
2
5
0
2
-
4
7
52
A
n
a
lysi
s
o
f LLC
r
e
s
o
n
a
n
t c
o
n
ve
r
ter p
erfo
r
ma
n
ce
w
ith
P
I
D
D2
co
n
tr
o
ller
fo
r
…
(
S
a
th
y
a
K
.
)
751
=
√
(
3
)
T
h
e
g
r
ap
h
illu
s
tr
ates
th
e
r
elati
o
n
b
etwe
en
g
ai
n
(
M
)
an
d
i
n
p
u
t
v
o
ltag
e
(
V
i
)
o
v
e
r
a
r
an
g
e
o
f
n
v
alu
es
f
r
o
m
1
5
t
o
1
9
.
Dif
f
e
r
en
t
v
al
u
es
o
f
n
ar
e
r
e
p
r
esen
ted
b
y
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h
lin
e
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d
as
th
e
in
p
u
t
v
o
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e
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ea
s
es
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e
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ain
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ed
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ce
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ai
n
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ig
h
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9
an
d
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west
at
n
=1
5
.
T
h
e
i
n
p
u
t
v
o
ltag
e
(
V
i
)
b
etwe
en
3
7
0
an
d
4
1
0
v
o
lts
is
s
h
o
wn
b
y
th
e
x
-
ax
is
an
d
g
ai
n
(
M)
s
p
an
s
f
r
o
m
0
.
8
6
to
1
.
2
1
o
n
th
e
y
-
a
x
is
is
r
ep
r
esen
t
ed
in
F
ig
u
r
e
2
[
1
7
]
.
Fig
u
r
e
3
s
ig
n
if
ies
th
e
co
r
r
elatio
n
b
etwe
en
th
e
m
ag
n
etizi
n
g
in
d
u
cto
r
(
L
m
)
an
d
th
e
in
d
u
cto
r
r
atio
(
L
n
)
,
m
ag
n
etizin
g
in
d
u
cto
r
(
L
m
)
v
a
lu
e
elev
ates
f
r
o
m
2
5
0
µH
to
4
3
0
µH
as
th
e
in
d
u
cto
r
r
atio
g
o
es
f
r
o
m
3
.
5
to
7
,
s
y
s
tem
in
d
u
ctan
ce
in
cr
ea
s
es
as
th
e
in
d
u
cto
r
r
atio
im
p
r
o
v
es.
Qu
ality
f
ac
to
r
Q
v
ar
iatio
n
with
r
esp
ec
t
to
r
esis
tan
ce
in
o
h
m
(
Ω
)
is
o
b
s
er
v
ed
in
F
ig
u
r
e
4
.
Ob
tain
i
n
g
th
e
o
p
tim
u
m
v
alu
es
f
o
r
Q,
g
ain
,
n
an
d
L
n
in
o
r
d
er
to
en
h
an
ce
th
e
p
o
wer
co
n
v
er
ter
'
s
p
er
f
o
r
m
an
ce
is
th
e
aim
o
f
t
h
is
p
ap
er
.
T
h
u
s
,
th
is
p
ap
er
o
f
f
er
s
co
m
p
r
eh
en
s
iv
e
d
esig
n
co
m
p
u
tatio
n
s
a
n
d
a
co
n
tr
o
ller
c
o
m
p
ar
is
o
n
f
o
r
th
e
r
e
s
p
ec
tiv
e
d
esig
n
,
p
ar
ticu
lar
ly
b
etwe
en
PID
D2
an
d
PID
,
wh
ich
is
co
v
er
ed
in
s
ec
tio
n
3
.
T
h
e
p
e
r
f
o
r
m
an
ce
o
f
a
n
L
L
C
r
eso
n
an
t
co
n
v
er
ter
is
cr
itical
o
n
th
e
s
ize
o
f
th
e
in
d
u
ct
o
r
as
well
as
t
h
e
v
al
u
es
o
f
g
ain
,
L
n
an
d
n
.
Ach
iev
i
n
g
th
e
in
ten
d
e
d
o
u
tp
u
t
p
er
f
o
r
m
an
ce
,
co
n
tr
o
llin
g
v
o
ltag
e,
m
in
im
izin
g
s
witch
in
g
lo
s
s
es
an
d
m
ax
im
izin
g
p
o
wer
co
n
v
er
s
io
n
ef
f
icien
cy
ar
e
a
ll
m
ad
e
p
o
s
s
ib
le
b
y
ca
r
ef
u
lly
c
h
o
o
s
in
g
th
ese
p
ar
a
m
eter
s
.
T
h
e
r
eso
n
an
t
f
r
eq
u
e
n
c
y
is
in
f
lu
en
ce
d
b
y
th
e
s
ize
o
f
th
e
in
d
u
ct
o
r
,
wh
ile
th
e
s
tab
ilit
y
an
d
o
p
er
atin
g
r
a
n
g
e
o
f
th
e
co
n
v
er
ter
ar
e
d
eter
m
in
ed
b
y
g
ain
,
L
n
a
n
d
n
.
L
n
als
o
h
as
a
n
im
p
ac
t
o
n
th
e
tr
an
s
f
o
r
m
er
d
esig
n
,
p
ar
tic
u
lar
ly
th
e
tu
r
n
s
r
atio
,
w
h
ich
h
as
an
im
p
ac
t
o
n
v
o
ltag
e
is
o
latio
n
an
d
s
ca
lin
g
.
I
n
th
e
co
n
v
er
ter
,
o
p
tim
izin
g
L
n
aid
s
in
ac
h
iev
in
g
a
b
alan
ce
b
etwe
en
s
ize,
co
s
t
an
d
p
er
f
o
r
m
a
n
ce
tr
ad
e
o
f
f
s
.
T
h
e
L
L
C
co
n
v
er
ter
g
ai
n
estab
lis
h
es
th
e
co
n
n
ec
tio
n
b
etwe
en
th
e
in
p
u
t
an
d
o
u
tp
u
t
v
o
ltag
es.
T
h
e
co
n
v
e
r
ter
ca
n
co
n
tr
o
l
th
e
o
u
tp
u
t
v
o
ltag
e
o
v
er
a
v
ar
iety
o
f
i
n
p
u
t
v
o
ltag
es
an
d
lo
a
d
cir
cu
m
s
tan
ce
s
b
y
ad
ju
s
tin
g
th
e
g
ai
n
.
Selectin
g
an
ap
p
r
o
p
r
iate
g
ain
en
s
u
r
es
co
n
v
er
ter
o
p
er
at
es
well
th
r
o
u
g
h
o
u
t
all
k
in
d
s
o
f
o
p
e
r
atio
n
al
cir
cu
m
s
tan
ce
s
.
I
n
o
r
d
e
r
to
b
alan
ce
ef
f
icien
cy
,
th
er
m
al
p
e
r
f
o
r
m
a
n
ce
an
d
d
y
n
am
ic
r
esp
o
n
s
iv
en
ess
in
L
L
C
r
eso
n
an
t c
o
n
v
er
ter
s
,
it is
cr
u
ci
al
to
ch
o
o
s
e
th
ese
p
a
r
am
eter
s
as b
est as p
o
s
s
ib
le.
Fig
u
r
e
2
.
Dev
iatio
n
o
f
in
p
u
t
v
o
ltag
e
b
ased
o
n
g
ai
n
(
M)
Fig
u
r
e
3
.
Var
iatio
n
o
f
L
n
p
er
ta
in
in
g
to
L
m
Fig
u
r
e
4
.
Var
iatio
n
o
f
R
e
with
r
esp
ec
t to
Q
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
4
9
-
7
5
7
752
T
h
e
ex
ten
d
ed
d
escr
ib
i
n
g
f
u
n
c
tio
n
(
E
DF)
tech
n
iq
u
e
is
u
s
ed
to
co
n
s
tr
u
ct
th
e
g
ain
,
co
m
m
o
n
ly
k
n
o
wn
as
in
p
u
t
to
o
u
t
p
u
t
v
o
ltag
e
tr
a
n
s
f
er
f
u
n
ctio
n
[
1
8
]
.
A
co
n
v
e
n
tio
n
al
s
m
all
s
ig
n
al
m
o
d
el
o
f
co
n
v
e
r
ter
s
m
ay
b
e
cr
ea
ted
u
s
in
g
s
tate
s
p
ac
e
ap
p
r
o
x
im
atio
n
s
to
im
p
r
o
v
is
e
th
e
m
o
d
el
ac
cu
r
ac
y
f
o
r
t
h
e
L
L
C
r
eso
n
an
t
co
n
v
er
ter
,
th
e
s
m
all
s
ig
n
al
m
o
d
el
th
at
u
s
es a
n
E
DF [
1
9
]
h
as b
ee
n
c
o
n
s
id
er
ed
in
o
r
d
e
r
to
s
witch
h
ar
m
o
n
ics [
2
0
].
=
(
−
1
.
542
11
1.665
e
6
-
1.667
e
4
0
-
110.1 1
10.1
-
110
.1
110
.1
4
.
758
5
-
4.7
58
5
0
3.2
05
e
−
12
31.46
-
31.46 31
.46
-
31.46
3.663
e
7
0
0
0
0
0
0
0
0
0
0
-
2.08
5
e
4
-
10
-
10
-
10
-
10
2.643
e
4
-
2.643
e
4
0
-
4000
-
5998
1998
-
1998
-
2002
-
2.643
e
4
2.643
e
4
0
-
4000
1998
-
599
8
-
2002
-
1998
2.643
e
4
-
2.643
e
4
0
-
4000
-
1998
-
200
2
-
5998
1998
-
2.643
e
4
2.643
e
4
0
-
4000
-
2002
-
199
8
1
998
-
5998
)
=
(
1
.
667
4
0
0
0
0
0
0
0
)
=
(
0
0
0 1
0 0
0 0
)
=
(
0
)
=
∧
+
∧
∧
=
∧
+
∧
T
h
e
f
o
llo
win
g
m
atr
ices
r
ep
r
esen
t
s
tate
s
p
ac
e
o
f
th
e
L
L
C
r
eso
n
an
t
c
o
n
v
er
te
r
:
wh
er
e
,
s
tate
-
s
p
ac
e
s
y
s
tem
m
atr
ices
ar
e
A,
B
,
C
,
an
d
D,
x
̂
is
s
tate
v
ec
to
r
o
f
th
e
s
tate
s
p
ac
e
m
o
d
el,
ȗ
is
th
e
co
n
tr
o
l
v
ec
to
r
in
p
u
t,
ŷ
is
th
e
v
ec
to
r
o
u
tp
u
t,
th
e
s
y
s
tem
tr
an
s
f
er
f
u
n
ctio
n
is
g
iv
e
n
b
y
G
as in
(
4
)
.
=
−
1
.
174
−
6
5
−
0
.
1335
4
−
1
96
2
3
−
7
.
751
6
2
−
1
.
063
6
+
1
.
753
−
7
8
+
1
.
542
11
7
+
8
.
026
16
6
+
3
.
3
97
21
5
+
5
.
149
25
4
+
3
.
329
29
3
+
7
.
837
32
2
+
3
.
0
98
33
−
1
.
93
6
21
(
4
)
3.
CO
M
P
ARI
SO
N
O
F
P
I
D
AN
D
P
I
DD2
CO
NT
RO
L
L
E
R
T
h
is
s
ec
tio
n
p
r
esen
ts
two
m
e
th
o
d
s
f
o
r
c
o
n
tr
o
llin
g
th
e
v
o
lt
ag
e
o
u
tp
u
t
o
f
L
L
C
r
eso
n
an
t
co
n
v
er
ter
s
n
am
ely
PID
an
d
PID
D2
co
n
t
r
o
ller
.
Pre
s
er
v
in
g
th
e
ac
tu
al
v
o
ltag
e
at
th
e
r
ef
er
en
ce
v
alu
e
is
th
e
co
n
tr
o
ller
's
f
u
n
ctio
n
.
T
h
e
d
if
f
er
en
ce
b
etw
ee
n
th
e
r
ef
er
e
n
ce
a
n
d
ac
t
u
al
t
er
m
in
al
v
o
ltag
e
f
o
r
m
s
th
e
er
r
o
r
s
ig
n
al,
wh
ich
is
cr
ea
ted
wh
en
th
e
v
o
ltag
e
at
th
e
co
n
v
er
ter
is
d
etec
ted
u
s
in
g
t
h
e
s
en
s
o
r
.
T
h
e
co
n
tr
o
l
s
ig
n
al
is
p
r
o
d
u
ce
d
b
y
th
e
co
n
tr
o
ller
b
ased
o
n
th
e
er
r
o
r
s
ig
n
al,
m
u
s
t
p
ass
th
r
o
u
g
h
th
e
P
FM
s
o
as
to
allo
w
th
e
co
n
tr
o
ller
to
m
o
d
u
late
th
e
f
r
eq
u
e
n
cy
in
ter
m
s
o
f
th
e
in
p
u
t
v
o
ltag
e.
Ad
d
itio
n
all
y
,
th
e
s
ig
n
al
is
a
g
ate
d
r
iv
er
i
n
p
u
t
th
at
estab
lis
h
es
th
e
d
r
iv
in
g
v
o
ltag
e
f
o
r
th
e
co
n
v
er
t
er
'
s
s
witch
es a
s
r
ep
r
esen
ted
in
F
ig
u
r
e
5
.
3
.
1
.
P
r
o
po
rt
io
na
l int
eg
r
a
l der
iv
a
t
iv
e
co
ntr
o
ller
Mu
ltip
le
ar
ch
itectu
r
es
lik
e
s
er
ies,
p
ar
allel
o
r
h
y
b
r
id
ar
e
f
ea
s
ib
le.
T
h
e
m
o
s
t
tr
ad
itio
n
al
p
a
r
allel
PID
s
tr
u
ctu
r
e
in
th
is
s
tu
d
y
is
d
ep
icted
in
F
ig
u
r
e
6
[
2
1
]
,
[
2
2
].
T
h
e
er
r
o
r
s
ig
n
al
e(
t)
is
co
n
n
ec
ted
with
co
n
tr
o
l
s
ig
n
al
u
(
t)
th
r
o
u
g
h
PID
c
o
n
tr
o
ller
i
n
wh
ich
K
p
,
K
i
,
a
n
d
K
d
s
tan
d
s
f
o
r
t
h
e
p
r
o
p
o
r
tio
n
al
g
ain
,
in
teg
r
al
g
ain
an
d
d
er
iv
ativ
e
g
ain
r
esp
ec
tiv
ely
,
e(
t)
is
th
e
er
r
o
r
s
ig
n
al
an
d
u
(
t)
is
th
e
co
n
tr
o
ller
'
s
o
u
tp
u
t
[
2
3
]
,
[
2
4
]
,
th
r
o
u
g
h
Z
eig
ler
Nich
o
ls
tu
n
in
g
p
r
o
c
ed
u
r
e,
th
e
v
al
u
es
o
f
K
p
,
K
i
,
an
d
K
d
ar
e
d
eter
m
in
e
d
.
T
h
e
f
o
llo
win
g
is
th
e
ex
p
r
ess
io
n
as in
(
5
)
f
o
r
its
tem
p
o
r
al
d
escr
ip
tio
n
,
(
)
=
(
)
+
∫
(
′
)
0
′
+
(
)
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2
5
0
2
-
4
7
52
A
n
a
lysi
s
o
f LLC
r
e
s
o
n
a
n
t c
o
n
ve
r
ter p
erfo
r
ma
n
ce
w
ith
P
I
D
D2
co
n
tr
o
ller
fo
r
…
(
S
a
th
y
a
K
.
)
753
Fig
u
r
e
5
.
C
o
n
tr
o
ller
r
ep
r
esen
tatio
n
with
L
L
C
r
eso
n
an
t c
o
n
v
er
ter
s
ch
em
atic
Fig
u
r
e
6
.
PID
co
n
tr
o
ller
s
ch
e
m
atic
3
.
2
.
P
r
o
po
rt
io
na
l int
eg
r
a
l der
iv
a
t
iv
e
do
ub
le
deriv
a
t
iv
e
A
p
o
p
u
la
r
v
e
r
s
io
n
o
f
co
n
tr
o
lle
r
PID
is
PID
D2
o
r
PID
A
o
r
d
o
u
b
le
d
er
i
v
ativ
e
PID
co
n
tr
o
ller
.
I
t
d
if
f
er
s
f
r
o
m
co
n
v
en
tio
n
al
PID
co
n
tr
o
ller
s
b
y
in
clu
d
in
g
a
ter
m
o
f
d
er
iv
ativ
e
o
f
t
h
e
s
ec
o
n
d
o
r
d
er
an
d
s
ch
em
atic
PID
D2
is
r
ep
r
esen
ted
in
Fig
u
r
e
7
[
2
5
]
.
I
t
e
n
h
an
ce
s
t
h
e
p
la
n
t
s
tab
ilit
y
,
ac
cu
r
ac
y
i
n
s
tead
y
s
tate
an
d
p
h
ase
m
ar
g
in
.
B
o
th
th
e
v
ib
r
atio
n
in
ac
cu
r
ac
y
ca
u
s
ed
b
y
o
s
cillatio
n
an
d
th
e
r
ea
ctio
n
s
ettlin
g
tim
e
ar
e
d
ec
r
ea
s
ed
as
a
r
esu
lt.
T
h
e
co
n
tr
o
ller
PID
D2
i
s
r
ep
r
esen
ted
in
its
tr
an
s
f
er
f
u
n
ctio
n
f
o
r
m
as
in
(
6
)
an
d
p
r
ac
tical
f
o
r
m
as
in
(
7
)
as
f
o
llo
ws
,
wh
er
e
co
ef
f
icien
t
g
ain
s
o
f
PID
D2
ar
e
K
p
,
K
i
,
K
d
,
an
d
K
a
an
d
its
v
alu
es
ar
e
f
o
u
n
d
u
s
in
g
Z
eig
ler
Nich
o
ls
tu
n
in
g
m
eth
o
d
.
(
)
=
+
+
+
2
(
6
)
(
)
=
+
+
+
1
+
2
(
+
1
)
2
(
7
)
Fig
u
r
e
7
.
PID
D2
c
o
n
tr
o
ller
s
c
h
em
atic
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
52
In
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
3
7
,
No
.
2
,
Feb
r
u
a
r
y
20
2
5
:
7
4
9
-
7
5
7
754
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Per
f
o
r
m
an
ce
o
f
th
e
PID
D2
an
d
PID
co
n
tr
o
ller
with
th
e
ab
o
v
e
L
L
C
r
eso
n
an
t
co
n
v
er
ter
is
s
im
u
lated
to
d
em
o
n
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
m
o
d
if
ied
co
n
tr
o
ller
as
s
h
o
wn
in
F
ig
u
r
e
s
8
an
d
9
,
th
e
p
ar
am
eter
s
o
f
d
if
f
er
en
t
co
m
p
o
n
en
ts
o
f
th
e
c
o
n
v
er
ter
ar
e
c
o
n
s
id
er
ed
as
m
e
n
tio
n
ed
i
n
T
ab
le
1
.
MA
T
L
AB
/Si
m
u
lin
k
R
2
0
2
3
a
is
u
s
ed
to
co
n
d
u
ct
an
d
d
is
cu
s
s
th
e
s
im
u
latio
n
r
esu
lts
.
C
o
n
t
r
o
ller
s
PID
D2
a
n
d
PID
in
S
im
u
lin
k
ar
e
u
s
ed
to
co
n
s
tr
u
ct
clo
s
ed
lo
o
p
co
n
tr
o
l.
Ass
es
s
m
en
t is d
o
n
e
u
s
in
g
s
u
p
p
ly
v
o
ltag
e
d
is
tu
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I
SS
N
:
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7
52
In
d
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.
RE
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NC
E
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[
1
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y
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