I
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t
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at
ion
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Jou
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t
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ical
an
d
Com
p
u
t
e
r
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n
gin
e
e
r
in
g
(
I
JE
CE
)
Vol.
15
,
No.
1,
F
e
br
ua
r
y
20
25
,
pp.
1
14
~1
28
I
S
S
N:
2088
-
8708,
DO
I
:
10
.
11591/i
jec
e
.
v
15
i1
.
pp1
14
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1
28
114
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K
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s
:
Ada
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ve
int
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gr
a
l
s
li
ding
mode
c
ontr
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r
B
idi
r
e
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ti
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DC
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onve
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ter
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oos
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uc
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I
ntegr
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s
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mode
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ontr
ol
P
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s
wa
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m
opti
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ti
on
R
obus
t
c
ontr
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Th
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s
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s
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n
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s
a
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l
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u
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d
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t
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CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
J
uli
us
De
r
ghe
C
ha
m
T
e
c
hnology
a
nd
Applied
S
c
ienc
e
s
L
a
bor
a
tor
y,
Uni
ve
r
s
it
y
of
Doua
la
P
.
O.
B
ox,
7236
Doua
la,
C
a
mer
oon
E
mail:
jul
ius
.
c
ha
m@yahoo.
c
om
1.
I
NT
RODU
C
T
I
ON
B
idi
r
e
c
ti
ona
l
DC
-
D
C
c
onve
r
ter
s
ha
ve
be
e
n
e
s
s
e
nt
ial
in
r
e
c
e
nt
ti
mes
f
or
c
ontr
oll
ing
a
nd
s
tabili
z
ing
DC
bus
volt
a
ge
in
a
r
a
nge
o
f
a
ppli
c
a
ti
ons
,
incl
uding
mi
c
r
ogr
ids
,
dis
tr
ibut
e
d
ge
ne
r
a
ti
ng
s
ys
tems
,
e
ne
r
gy
s
tor
a
ge
s
ys
tem
s
,
e
lec
tr
ic
c
a
r
s
,
powe
r
f
il
ter
s
,
a
nd
s
olar
or
wind
e
ne
r
gy
s
ys
tems
[
1]
,
[
2]
.
I
n
DC
mi
c
r
ogr
ids
,
DC
-
D
C
c
onve
r
ter
s
a
r
e
us
e
d
to
r
a
is
e
o
r
lowe
r
t
he
e
ne
r
gy
pr
oduc
e
d,
whic
h
typi
c
a
ll
y
doe
s
not
matc
h
the
de
mands
of
the
load
[
3
]
,
[
4]
.
A
DC
-
DC
c
onve
r
ter
f
unc
ti
oning
in
bid
ir
e
c
ti
ona
l
mode
e
nha
nc
e
s
the
e
f
f
icie
nc
y
a
nd
pe
r
f
o
r
manc
e
o
f
DC
mi
c
r
og
r
ids
by
s
e
r
ving
a
s
a
n
int
e
r
f
a
c
e
be
twe
e
n
a
powe
r
s
our
c
e
a
nd
a
s
tor
a
ge
unit
[
5]
.
Notwiths
tanding
the
s
igni
f
ica
nt
r
ole
that
two
-
wa
y
DC
-
DC
c
onve
r
ter
s
play
in
the
a
f
or
e
m
e
nti
one
d
a
ppli
c
a
ti
ons
,
a
nu
mber
of
r
e
s
e
a
r
c
he
r
s
ha
ve
f
oc
us
e
d
on
their
c
ontr
ol
due
to
va
r
ious
is
s
ue
s
,
including
volt
a
ge
r
ippl
e
,
output
-
tr
a
c
king
pe
r
f
o
r
manc
e
that
is
s
us
c
e
pti
ble
to
ti
me
-
va
r
ying
s
ys
tem
pa
r
a
metr
ic
unc
e
r
tainti
e
s
,
nonli
ne
a
r
pr
ope
r
ti
e
s
,
a
nd
mi
s
matc
he
d
a
nd
matc
he
d
dis
tur
ba
nc
e
s
that
r
e
quir
e
a
tt
e
nti
on
[
6]
.
A
s
uit
a
ble
c
ontr
ol
s
tr
a
tegy
will
he
lp
s
olve
s
ome
of
thes
e
c
ha
ll
e
nge
s
a
nd
e
ns
ur
e
the
e
f
f
icie
nt
pe
r
f
or
manc
e
o
f
the
s
y
s
tem
[
3]
.
B
e
c
a
us
e
of
their
ve
r
s
a
ti
li
ty
a
nd
e
a
s
e
of
us
e
,
pr
o
por
ti
ona
l
-
int
e
gr
a
l
(
P
I
)
a
nd
pr
opor
ti
ona
l
-
int
e
gr
a
l
-
de
r
ivative
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
R
obus
t
adapti
v
e
int
e
gr
al
s
li
ding
mode
c
ontr
ol
of
a
half
-
br
idge
…
(
J
uli
us
De
r
ghe
C
ham
)
115
(
P
I
D)
c
ontr
o
ll
e
r
s
a
r
e
f
r
e
que
ntl
y
uti
li
z
e
d
in
the
c
o
ntr
ol
of
DC
-
DC
c
onve
r
ter
s
wor
king
in
bidi
r
e
c
ti
ona
l
mode.
T
he
y
a
r
e
li
mi
ted
whe
n
it
c
omes
to
wor
king
with
nonli
ne
a
r
s
ys
tems
.
How
e
ve
r
,
lengthy
s
e
tt
li
n
g
ti
mes
,
s
igni
f
ica
nt
ove
r
s
hoot,
a
nd
a
lac
k
o
f
r
obus
tnes
s
in
the
f
a
c
e
o
f
pa
r
a
mete
r
va
r
iations
a
r
e
typi
c
a
ll
y
t
he
main
f
e
a
tur
e
s
of
r
e
s
ult
s
obtaine
d
with
s
uc
h
c
ontr
ol
ler
s
[
2]
,
[
7
]
–
[
11]
.
P
a
ny
e
t
al.
[
12
]
a
nd
C
he
ng
e
t
al.
[
13]
ha
ve
done
s
ome
wor
k
on
the
li
ne
a
r
c
ontr
ol
o
f
bid
i
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
s
.
Al
though
thes
e
s
ugge
s
ted
c
ontr
oll
e
r
s
a
c
hieve
d
their
de
s
ign
goa
ls
,
they
s
ti
ll
ha
ve
c
e
r
tain
s
hor
tcomings
,
including
poor
pe
r
f
or
manc
e
dur
ing
pa
r
a
mete
r
f
luctua
ti
ons
,
e
xtende
d
s
e
tt
li
ng
a
nd
r
is
ing
pe
r
iods
,
ove
r
s
hoot,
a
nd
r
e
s
il
ienc
e
.
DC
-
DC
c
onve
r
ter
s
wor
king
in
bidi
r
e
c
ti
ona
l
mode
a
r
e
be
t
ter
whe
n
us
ing
nonli
ne
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r
c
ontr
oll
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s
.
M
a
ny
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tudi
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s
ha
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n
done
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li
ding
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ontr
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(
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M
C
)
of
DC
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D
C
c
onve
r
ter
s
r
unn
ing
in
b
idi
r
e
c
ti
ona
l
mode,
a
nd
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r
e
s
ult
s
obtaine
d
met
the
objec
ti
ve
s
f
or
whic
h
they
we
r
e
de
s
igned.
How
e
ve
r
,
numer
ous
wor
ks
a
r
e
pr
e
s
e
nted
in
the
li
ter
a
tur
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to
a
ddr
e
s
s
s
ome
of
the
pr
oblems
pos
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d
by
the
nonli
ne
a
r
it
y
of
the
ha
lf
-
br
idge
bidi
r
e
c
ti
o
na
l
DC
-
DC
c
onve
r
ter
s
s
tudi
e
d
in
thes
e
pa
pe
r
s
.
One
o
f
the
mos
t
e
xploi
ted
c
ontr
o
ll
e
r
s
is
the
S
M
C
,
de
s
pit
e
the
pr
oblem
of
c
ha
tt
e
r
ing
wi
th
it
.
T
he
e
f
f
ica
c
y
of
thi
s
a
ppr
oa
c
h
c
a
n
be
a
tt
r
ibu
ted
to
it
s
nonli
ne
a
r
f
e
a
tur
e
s
,
g
r
e
a
t
s
tabili
ty,
e
a
s
e
of
im
pleme
ntation,
r
e
s
il
ienc
e
,
a
nd
ins
e
ns
it
ivi
ty
to
pe
r
tur
ba
ti
ons
[
14
]
a
nd
[
15]
.
M
or
e
ove
r
,
d
ue
to
the
nonli
ne
a
r
it
y
p
r
ope
r
ty
of
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
s
,
l
inea
r
c
ont
r
ol
tec
hniques
c
a
nnot
c
ope
with
thi
s
type
of
s
ys
tem,
lea
ding
to
s
ome
li
mi
tations
,
s
uc
h
a
s
l
a
r
ge
volt
a
ge
dis
tur
ba
nc
e
s
[
16
]
.
De
s
pit
e
the
good
c
ontr
ol
qua
li
ti
e
s
of
S
M
C
,
ther
e
a
r
e
s
ti
ll
s
ome
is
s
ue
s
w
it
h
thi
s
c
ontr
ol
tec
hnique
that
ne
e
d
to
be
ha
ndl
e
d.
T
he
c
ha
tt
e
r
ing
e
f
f
e
c
t,
poor
pe
r
f
or
manc
e
unde
r
s
igni
f
i
c
a
nt
load
a
nd
pa
r
a
mete
r
f
luctua
ti
ons
,
a
nd
the
e
xi
s
tenc
e
of
s
tea
dy
-
s
tate
f
law
s
in
the
r
e
gulation
a
r
e
a
f
e
w
of
thes
e
dif
f
iculti
e
s
[
1]
.
R
e
s
e
a
r
c
he
r
s
ha
ve
s
ugge
s
ted
va
r
ious
c
ontr
ol
s
tr
a
tegie
s
to
mana
ge
the
bidi
r
e
c
ti
ona
l
ha
lf
-
br
idge
DC
-
DC
c
onve
r
ter
s
in
a
n
e
f
f
or
t
to
a
ddr
e
s
s
s
ome
of
thes
e
is
s
ue
s
.
Nume
r
ous
s
olut
ions
a
r
e
a
va
il
a
ble
in
the
li
ter
a
tur
e
to
a
ddr
e
s
s
s
ome
o
f
the
p
r
oblems
w
it
h
S
M
C
that
a
r
e
s
hown
in
[
7
]
,
[
15]
,
[
17]
–
[
20
]
.
I
n
o
r
de
r
to
gua
r
a
ntee
s
tabili
ty,
quick
r
e
a
c
ti
on
ti
mes
,
a
nd
s
tea
dy
s
tate
pr
ope
r
ti
e
s
,
[
2]
,
[
13
]
c
r
e
a
ted
a
f
e
w
c
ontr
ol
s
tr
a
tegie
s
with
a
c
c
e
ptable
outcome
s
.
I
n
their
s
im
ulate
d
r
e
s
ult
s
,
it
is
e
vident
that
the
pr
opos
e
d
c
ont
r
oll
e
r
s
pe
r
f
or
med
be
tt
e
r
than
the
e
xis
ti
ng
one
s
in
ter
ms
of
s
tabili
z
a
ti
on
a
nd
r
e
f
e
r
e
nc
e
t
r
a
c
king
unde
r
load
r
e
s
is
tanc
e
va
r
iations
,
input
volt
a
ge
va
r
iation
,
a
nd
B
uc
k
-
boos
t
mode
s
witching
of
a
DC
-
DC
c
onve
r
ter
wor
king
in
bidi
r
e
c
ti
ona
l
mode.
How
e
ve
r
,
ther
e
a
r
e
s
ti
ll
s
e
ve
r
a
l
pr
ob
lems
with
the
a
f
or
e
mentioned
c
ontr
ol
s
tr
a
tegie
s
,
including
the
c
ompl
e
xit
y
of
the
de
s
ign,
the
ne
c
e
s
s
it
y
f
o
r
p
r
e
c
is
e
s
e
lec
ti
on
of
the
a
da
pti
ve
ga
ins
,
a
nd
the
ne
e
d
f
or
f
u
r
ther
s
tea
dy
s
tate
e
r
r
or
r
e
duc
ti
on.
T
he
pa
pe
r
a
ddr
e
s
s
e
s
the
s
igni
f
ica
nt
c
ha
ll
e
nge
s
in
c
ontr
oll
ing
ha
lf
-
br
idge
DC
-
DC
c
onve
r
ter
s
wor
king
in
bidi
r
e
c
ti
ona
l
mode
,
whic
h
a
r
e
c
r
uc
ial
in
a
ppli
c
a
ti
ons
s
uc
h
a
s
DC
mi
c
r
ogr
ids
,
e
ne
r
gy
s
tor
a
ge
s
ys
tems
,
a
nd
e
lec
tr
ic
ve
hicle
s
.
T
he
s
e
c
onve
r
ter
s
mana
ge
the
bi
dir
e
c
ti
ona
l
f
low
o
f
e
ne
r
gy,
s
tepping
up
o
r
s
tepping
down
volt
a
ge
s
a
s
ne
e
de
d.
How
e
ve
r
,
their
nonli
ne
a
r
be
ha
vior
a
nd
s
e
ns
it
ivi
ty
to
dis
tur
ba
nc
e
s
,
s
uc
h
a
s
inpu
t
volt
a
ge
f
luctua
ti
ons
a
nd
load
va
r
iations
,
c
r
e
a
te
s
ubs
tantial
c
ontr
ol
dif
f
iculti
e
s
.
T
r
a
dit
ional
c
ont
r
oll
e
r
s
,
li
ke
P
I
a
nd
P
I
D
c
ontr
oll
e
r
s
,
a
r
e
c
omm
only
us
e
d
due
to
their
s
im
pli
c
it
y
but
ha
ve
notable
li
mi
tations
whe
n
a
ppli
e
d
to
thes
e
c
onve
r
ter
s
.
P
I
a
nd
P
I
D
c
ont
r
oll
e
r
s
o
f
ten
s
tr
uggle
with
s
low
s
e
tt
li
ng
ti
mes
,
whe
r
e
the
s
ys
tem
take
s
l
onge
r
to
s
tabili
z
e
a
f
ter
a
dis
tur
ba
nc
e
.
T
he
y
a
r
e
a
ls
o
pr
one
to
ove
r
s
hoot,
whe
r
e
the
output
e
xc
e
e
ds
the
de
s
ir
e
d
va
lue
be
f
or
e
s
e
tt
li
ng
,
a
nd
lac
k
r
obus
tnes
s
a
ga
ins
t
p
a
r
a
mete
r
va
r
iations
,
mea
ning
s
mall
c
ha
nge
s
in
s
ys
tem
pa
r
a
mete
r
s
c
a
n
lea
d
to
de
gr
a
de
d
pe
r
f
or
manc
e
or
ins
tabili
ty.
T
he
s
e
is
s
ue
s
r
e
s
ult
in
s
ubopti
mal
pe
r
f
or
manc
e
,
manif
e
s
ti
ng
a
s
volt
a
ge
r
ippl
e
,
poo
r
output
tr
a
c
kin
g,
a
nd
ove
r
a
ll
ins
tabili
ty
,
whic
h
unde
r
mi
ne
the
e
f
f
icie
nc
y
a
nd
r
e
li
a
bil
it
y
o
f
the
c
onve
r
ter
s
in
dyna
mi
c
e
nvi
r
onments
.
I
n
high
-
de
mand
a
ppli
c
a
ti
ons
li
ke
e
ne
r
g
y
s
tor
a
ge
a
nd
e
lec
tr
ic
ve
hicle
s
,
thes
e
pe
r
f
or
manc
e
s
hor
tcom
ings
c
a
n
lea
d
to
e
ne
r
gy
los
s
e
s
,
r
e
duc
e
d
s
y
s
tem
e
f
f
icie
nc
y,
a
nd
e
ve
n
s
ys
tem
f
a
il
ur
e
s
.
T
he
pa
pe
r
highl
ight
s
the
ne
e
d
f
or
mo
r
e
a
dva
nc
e
d
c
ontr
ol
s
tr
a
tegie
s
that
c
a
n
ove
r
c
ome
the
li
mi
tations
of
tr
a
dit
ional
methods
,
e
ns
ur
ing
higher
e
f
f
icie
nc
y,
r
e
li
a
bil
it
y
,
a
nd
s
tabili
ty
in
mana
ging
the
c
ompl
e
x
dyna
mi
c
s
of
ha
lf
-
br
idge
bi
dir
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
s
.
T
o
a
ddr
e
s
s
thes
e
c
ha
ll
e
nge
s
,
the
pa
pe
r
p
r
opos
e
s
a
r
obus
t
a
da
pti
ve
int
e
g
r
a
l
s
li
ding
mode
c
ontr
o
l
(
AI
S
M
C
)
a
ppr
oa
c
h
e
nha
nc
e
d
by
pa
r
ti
c
le
s
wa
r
m
opti
mi
z
a
ti
on
(
P
S
O
)
.
T
his
c
ont
r
ol
s
tr
a
tegy
c
om
bines
the
a
dva
ntage
s
of
a
da
pti
ve
s
li
ding
mode
c
ontr
ol
with
the
r
obus
t
na
tur
e
of
int
e
gr
a
l
s
li
ding
mode
c
ont
r
o
l,
while
P
S
O
is
uti
li
z
e
d
to
opti
mi
z
e
the
s
li
ding
c
oe
f
f
icie
nts
dyna
mi
c
a
ll
y.
T
he
AI
S
M
C
is
de
s
igned
to
a
da
pt
to
c
ha
nge
s
in
s
ys
tem
dyna
mi
c
s
,
includ
ing
load
r
e
s
is
tanc
e
va
r
iations
a
nd
e
xter
na
l
dis
tur
ba
nc
e
s
,
ther
e
by
im
p
r
o
ving
the
ove
r
a
ll
s
tabili
ty,
a
c
c
ur
a
c
y,
a
nd
pe
r
f
o
r
manc
e
of
the
DC
-
DC
c
onve
r
ter
f
unc
ti
oning
in
bidi
r
e
c
ti
ona
l
mo
de
.
T
he
pr
opos
e
d
c
ontr
oll
e
r
is
va
li
da
ted
thr
ough
numer
ica
l
s
im
ulations
in
a
M
AT
L
AB
/S
im
uli
nk
e
nvi
r
onment,
whic
h
de
mons
tr
a
te
it
s
e
f
f
e
c
ti
ve
ne
s
s
in
maintaining
output
volt
a
ge
s
tabili
ty,
r
e
duc
ing
c
ha
tt
e
r
ing
phe
nome
na
,
a
nd
mi
nim
izing
s
tea
dy
-
s
tate
e
r
r
or
s
c
ompar
e
d
to
t
r
a
dit
i
ona
l
c
ontr
ol
methods
.
T
he
r
e
s
ult
s
f
r
om
the
M
AT
L
AB
/S
im
uli
nk
s
im
ulati
ons
r
e
ve
a
l
that
the
pr
opos
e
d
AI
S
M
C
ou
tper
f
or
ms
c
onve
nti
ona
l
P
I
a
nd
s
tanda
r
d
int
e
gr
a
l
s
li
ding
mo
de
c
ontr
oll
e
r
s
(
I
S
M
C
)
a
c
r
os
s
va
r
ious
s
c
e
na
r
ios
,
including
input
volt
a
ge
d
is
tur
ba
nc
e
s
,
r
e
f
e
r
e
nc
e
vo
lt
a
ge
c
ha
nge
s
,
a
nd
load
r
e
s
is
tanc
e
va
r
iations
.
Nota
bly
,
the
AI
S
M
C
a
c
hieve
s
a
s
igni
f
ica
nt
r
e
duc
ti
on
in
the
s
e
tt
li
ng
ti
m
e
,
r
is
e
ti
me,
a
nd
unde
r
s
hoot
in
both
s
tep
-
up
a
nd
s
tep
-
down
modes
of
ope
r
a
ti
on.
F
o
r
ins
tanc
e
,
in
buc
k
mode,
t
he
AI
S
M
C
r
e
duc
e
d
the
s
e
tt
li
ng
ti
me
to
2.
6
ms
c
ompar
e
d
to
8.
4
ms
with
the
P
I
c
ontr
ol
ler
a
nd
mi
nim
ize
d
unde
r
s
hoot
to
0.
083%
c
ompar
e
d
to
1
.
83%
with
the
P
I
c
ontr
oll
e
r
.
I
n
boos
t
mode,
the
A
I
S
M
C
de
mons
tr
a
ted
s
im
il
a
r
i
mpr
ove
ments
,
with
a
s
e
tt
li
ng
ti
me
of
0.
3
ms
a
nd
a
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
1
14
-
1
28
116
unde
r
s
hoot
of
0.
041
%
.
T
he
s
e
r
e
s
ult
s
unde
r
s
c
or
e
th
e
pr
opos
e
d
c
ont
r
oll
e
r
's
s
upe
r
io
r
pe
r
f
or
manc
e
in
e
n
ha
nc
ing
the
e
f
f
icie
nc
y
a
nd
r
e
li
a
bil
it
y
of
ha
lf
-
br
idge
bid
ir
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
s
in
dyna
mi
c
a
nd
unc
e
r
tain
e
nvir
onments
.
As
a
r
e
s
ult
,
the
f
oll
owing
c
a
n
be
us
e
d
to
s
umm
a
r
ize
thi
s
pa
pe
r
's
p
r
im
a
r
y
c
ontr
ibut
ions
:
−
De
ve
lopm
e
nt
of
a
r
obus
t
AI
S
M
C
s
tr
a
tegy
:
I
n
thi
s
r
e
s
e
a
r
c
h,
a
nove
l
c
ontr
ol
tec
hnique
a
ugmente
d
by
P
S
O
that
c
ombi
ne
s
int
e
gr
a
l
s
li
ding
mode
c
ontr
ol
a
nd
a
d
a
pti
ve
s
li
ding
mode
c
ontr
ol
is
pr
e
s
e
nted.
B
y
a
ddr
e
s
s
ing
nonli
ne
a
r
dyna
mi
c
s
a
nd
dis
tur
ba
nc
e
s
in
ha
lf
-
br
idge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
s
,
thi
s
s
olut
ion
of
f
e
r
s
e
nha
nc
e
d
s
tabili
ty,
pr
e
c
is
ion,
a
nd
r
obus
tnes
s
in
c
ompar
is
on
to
c
onve
nti
ona
l
c
ont
r
ol
tec
hniques
.
−
Optim
iza
ti
on
of
s
li
ding
mode
c
ontr
oll
e
r
pa
r
a
mete
r
s
:
the
us
e
of
P
S
O
to
dyna
mi
c
a
ll
y
opti
mi
z
e
the
s
l
idi
ng
c
oe
f
f
icie
nts
in
the
AI
S
M
C
f
r
a
mew
or
k
is
a
s
igni
f
ica
nt
c
ontr
ibut
ion
.
T
his
opti
m
iza
ti
on
e
ns
ur
e
s
that
the
c
ontr
oll
e
r
c
a
n
a
da
pt
to
va
r
ying
s
ys
tem
c
ondit
ions
,
s
uc
h
a
s
c
ha
nge
s
in
load
r
e
s
is
tanc
e
a
nd
input
volt
a
ge
,
ther
e
by
maintaining
opti
mal
pe
r
f
o
r
manc
e
.
−
I
mpr
ove
ment
in
s
ys
tem
e
f
f
icie
nc
y
a
nd
r
e
li
a
bil
it
y:
T
he
pr
opos
e
d
AI
S
M
C
s
igni
f
ica
ntl
y
e
nha
nc
e
s
the
e
f
f
icie
nc
y
a
nd
r
e
li
a
bil
it
y
o
f
ha
lf
-
br
idge
bid
ir
e
c
ti
o
na
l
DC
-
DC
c
onve
r
ter
s
,
making
them
mor
e
s
uit
a
ble
f
or
dyna
mi
c
a
nd
unc
e
r
tain
e
nvir
onments
,
s
uc
h
a
s
thos
e
f
ound
in
DC
mi
c
r
ogr
ids
,
e
ne
r
gy
s
tor
a
ge
s
ys
tems
,
a
nd
e
lec
tr
ic
ve
hicle
s
.
−
R
e
duc
ti
on
of
c
ha
tt
e
r
ing
phe
nomena
:
T
he
pa
pe
r
a
d
dr
e
s
s
e
s
the
c
omm
on
is
s
ue
of
c
ha
tt
e
r
ing
in
s
li
ding
mode
c
ontr
oll
e
r
s
by
int
e
gr
a
ti
ng
a
n
a
da
pti
ve
mec
ha
nis
m
that
r
e
duc
e
s
os
c
il
lations
a
nd
im
p
r
ove
s
the
s
moot
hne
s
s
of
the
c
ont
r
ol
r
e
s
pons
e
,
c
ontr
ibut
ing
to
mor
e
s
table
a
nd
r
e
li
a
ble
c
onve
r
te
r
ope
r
a
ti
on
.
2.
M
E
T
HO
D
T
h
is
pa
pe
r
e
mp
lo
ys
a
c
o
mp
r
e
he
ns
i
ve
a
n
d
s
ys
te
ma
t
ic
a
pp
r
oa
c
h
t
o
im
pl
e
m
e
n
ti
ng
a
n
op
t
im
a
l
c
o
nt
r
o
l
s
ol
ut
io
n
f
o
r
a
b
id
i
r
e
c
t
io
na
l
h
a
l
f
-
b
r
id
ge
DC
-
DC
c
on
ve
r
te
r
.
T
he
me
th
od
ol
og
y
is
me
t
ic
ul
ous
ly
s
t
r
u
c
t
u
r
e
d
a
nd
is
v
is
ua
ll
y
r
e
p
r
e
s
e
nt
e
d
i
n
a
b
lo
c
k
d
iag
r
a
m
i
n
F
i
gu
r
e
1
,
o
f
f
e
r
i
ng
a
c
l
e
a
r
a
nd
c
onc
is
e
o
ve
r
v
ie
w
of
t
he
e
n
t
ir
e
p
r
oc
e
s
s
.
T
o
e
ns
u
r
e
t
he
r
ob
us
t
ne
s
s
a
n
d
e
f
f
e
c
ti
ve
n
e
s
s
o
f
t
he
pr
o
pos
e
d
c
o
nt
r
ol
s
o
lu
t
io
ns
,
w
e
ut
il
iz
e
n
u
me
r
i
c
a
l
s
im
u
la
t
io
ns
a
nd
i
mp
le
me
nt
a
t
io
ns
w
i
th
in
t
he
M
A
T
L
AB
/S
i
mu
li
nk
e
nv
i
r
o
nme
n
t
.
T
h
is
s
im
u
lat
i
on
pl
a
t
f
o
r
m
p
r
o
vi
de
s
a
v
e
r
s
a
ti
le
a
nd
p
ow
e
r
f
ul
to
ols
e
t
f
o
r
m
od
e
l
in
g
,
a
na
l
yz
i
ng
,
a
n
d
o
pt
im
iz
in
g
c
o
mp
le
x
c
o
nt
r
ol
s
ys
te
ms
,
a
ll
ow
ing
us
to
r
i
go
r
ous
ly
e
va
l
ua
te
t
he
pe
r
f
o
r
man
c
e
o
f
ou
r
p
r
op
os
e
d
s
o
lu
t
io
ns
u
nde
r
a
va
r
ie
ty
o
f
op
e
r
a
t
in
g
c
on
di
t
io
ns
.
T
he
p
r
oc
e
s
s
b
e
g
ins
w
it
h
a
d
e
ta
i
led
m
a
t
he
ma
ti
c
a
l
m
ode
l
in
g
o
f
t
he
ha
l
f
-
b
r
i
dg
e
c
on
ve
r
te
r
,
tak
i
ng
i
nt
o
a
c
c
ou
nt
i
ts
d
is
ti
nc
t
m
od
e
s
o
f
op
e
r
a
t
i
on
-
b
uc
k
a
nd
bo
os
t
mo
de
s
.
T
h
is
mo
de
li
ng
ph
a
s
e
is
c
r
it
ica
l
,
a
s
i
t
l
a
ys
t
he
f
o
un
da
t
io
n
f
o
r
u
n
de
r
s
t
a
n
di
ng
th
e
s
ys
te
m's
dy
na
mi
c
be
ha
vi
o
r
a
n
d
id
e
n
t
if
yi
ng
t
he
k
e
y
pa
r
a
me
te
r
s
t
ha
t
i
n
f
l
ue
nc
e
i
ts
pe
r
f
o
r
ma
nc
e
.
F
o
ll
ow
in
g
the
m
ode
l
in
g
p
ha
s
e
,
we
p
r
oc
e
e
d
t
o
de
s
ig
n
the
c
o
nt
r
ol
le
r
s
f
o
r
e
a
c
h
mo
de
o
f
o
pe
r
a
ti
on
.
T
he
s
e
c
on
t
r
o
ll
e
r
s
a
r
e
me
ti
c
u
lo
us
l
y
c
r
a
f
ted
to
a
d
d
r
e
s
s
t
he
s
p
e
c
i
f
ic
c
h
a
l
le
nge
s
c
o
nne
c
t
e
d
wi
th
th
e
n
on
li
ne
a
r
dy
na
m
ics
o
f
t
he
c
on
ve
r
t
e
r
.
T
he
n
e
x
t
s
tep
a
f
t
e
r
d
e
s
i
gn
is
o
pt
im
i
z
a
t
i
on
,
wh
e
n
s
op
hi
s
t
ica
te
d
me
th
ods
l
ike
pa
r
t
icle
s
wa
r
m
o
p
ti
mi
z
a
ti
on
a
r
e
us
e
d
to
a
d
j
us
t
t
he
c
o
nt
r
ol
le
r
pa
r
a
m
e
te
r
s
f
o
r
be
s
t
r
e
s
u
lt
s
.
I
n
t
he
e
n
d
,
the
r
e
g
ul
a
t
e
d
s
y
s
te
m
is
i
m
pl
e
m
e
n
ted
in
th
e
M
A
T
L
A
B
/
S
i
m
ul
in
k
e
n
v
ir
on
men
t
w
he
r
e
it
is
t
e
s
t
e
d
e
xt
e
ns
iv
e
l
y
u
nd
e
r
a
r
a
n
ge
o
f
c
on
d
it
io
ns
.
T
h
e
s
e
t
e
s
ts
i
nc
lu
de
v
a
r
ia
t
io
ns
in
i
np
u
t
vo
lt
a
g
e
,
lo
a
d
r
e
s
is
ta
nc
e
,
a
nd
r
e
f
e
r
e
nc
e
vo
lt
a
ge
,
a
l
low
i
ng
us
t
o
t
ho
r
ou
gh
ly
i
n
ve
s
ti
ga
te
t
he
s
y
s
te
m
's
s
ta
bi
l
it
y
,
r
ob
us
tnes
s
,
a
n
d
o
ve
r
a
l
l
pe
r
f
or
ma
nc
e
a
c
r
os
s
a
wi
de
r
a
n
ge
of
s
c
e
n
a
r
i
os
.
T
h
is
m
e
th
od
ica
l
a
pp
r
oa
c
h
e
ns
ur
e
s
tha
t
th
e
pr
op
os
e
d
c
o
n
tr
o
l
s
o
l
ut
io
ns
a
r
e
n
ot
o
nl
y
the
o
r
e
ti
c
a
ll
y
s
ou
nd
b
u
t
a
ls
o
p
r
a
c
ti
c
a
l
l
y
v
iab
le
,
c
a
p
a
b
le
o
f
de
l
ive
r
in
g
s
u
pe
r
io
r
pe
r
f
o
r
ma
nc
e
in
r
e
a
l
-
wo
r
ld
a
pp
l
ica
ti
on
s
.
M
o
d
e
l
i
n
g
H
a
l
f
-
B
r
i
dg
e
s
y
s
t
e
m
C
onv
e
r
t
e
r
m
o
d
e
l
i
n
g
a
c
c
o
r
d
i
n
g
t
o
m
o
d
e
s
B
uc
k M
ode
l
B
o
o
s
t
M
o
d
e
l
C
o
n
t
r
o
l
de
s
i
gn
C
o
n
t
r
o
l
O
p
t
i
m
i
z
a
t
i
o
n
C
ont
r
ol
l
e
d
S
y
s
t
e
m
I
m
p
l
e
m
e
n
t
a
t
i
o
n
I
n
v
e
s
t
i
g
a
t
i
o
n
s
a
n
s
i
m
u
l
a
t
i
o
n
s
F
igur
e
1.
C
ompr
e
he
ns
ive
de
s
c
r
ipt
ion
of
the
s
tudy’
s
methodology
F
igur
e
2
pr
ov
ides
a
de
tailed
il
lus
tr
a
ti
on
of
the
s
ys
tem
unde
r
c
ons
ider
a
ti
on,
whic
h
c
ompr
is
e
s
a
bidi
r
e
c
ti
ona
l
ha
l
f
-
br
idge
DC
-
DC
c
onve
r
ter
.
T
his
c
onve
r
ter
ope
r
a
tes
with
a
n
input
volt
a
ge
Vi
a
nd
in
c
ludes
a
ba
tt
e
r
y
that
is
modele
d
a
s
a
n
int
e
r
na
l
r
e
s
is
tanc
e
,
de
noted
a
s
.
I
n
thi
s
r
e
s
e
a
r
c
h,
is
c
ons
ider
e
d
a
s
the
l
oa
d
whe
n
the
c
onve
r
ter
is
f
unc
ti
oning
in
buc
k
mo
de
.
T
he
c
hoice
of
the
bidi
r
e
c
ti
ona
l
ha
l
f
-
br
idge
DC
-
DC
c
onve
r
ter
is
s
tr
a
tegic
due
to
it
s
c
a
pa
bil
it
y
to
e
f
f
ic
iently
mana
ge
the
bidi
r
e
c
ti
ona
l
f
low
of
e
ne
r
gy,
making
it
idea
l
f
or
a
ppl
ica
ti
ons
s
uc
h
a
s
DC
mi
c
r
ogr
ids
a
nd
e
ne
r
gy
s
tor
a
ge
s
ys
tems
.
T
he
c
ont
r
ol
s
tr
a
tegy
a
d
opted
f
or
thi
s
c
onve
r
ter
is
a
c
ombi
na
ti
on
of
a
da
pti
ve
s
li
din
g
mode
c
ontr
ol
a
nd
P
S
O
.
T
his
hybr
id
a
ppr
oa
c
h
p
r
ovides
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
R
obus
t
adapti
v
e
int
e
gr
al
s
li
ding
mode
c
ontr
ol
of
a
half
-
br
idge
…
(
J
uli
us
De
r
ghe
C
ham
)
117
r
obus
t,
e
f
f
icie
nt
,
a
nd
f
lexible
c
ontr
ol
s
olut
ion
c
a
pa
ble
of
ha
ndli
ng
dyna
mi
c
c
ha
nge
s
withi
n
the
s
ys
tem
a
nd
mi
ti
ga
ti
ng
e
xter
na
l
dis
tur
ba
nc
e
s
.
T
he
a
da
pti
ve
s
li
d
ing
mode
c
ontr
ol
e
ns
ur
e
s
that
the
c
ontr
ol
ler
c
a
n
r
e
s
pond
to
a
br
upt
va
r
iations
in
load
r
e
s
is
tanc
e
by
dyna
mi
c
a
ll
y
a
djus
ti
ng
the
c
ontr
ol
pa
r
a
mete
r
s
.
T
he
P
S
O
a
l
gor
it
hm
f
ur
ther
e
nha
nc
e
s
thi
s
a
da
ptabili
ty
by
opti
mi
z
in
g
the
s
li
ding
mode
c
ontr
oll
e
r
's
pa
r
a
mete
r
s
in
r
e
a
l
-
ti
me,
a
ll
owing
the
s
ys
tem
to
c
onti
nuous
ly
a
dju
s
t
to
s
hi
f
ts
in
ope
r
a
ti
ng
c
ondit
ions
or
e
nvir
onmenta
l
f
a
c
t
or
s
.
T
he
AI
S
M
C
is
de
s
igned
to
maintain
opti
mal
pe
r
f
or
manc
e
by
c
onti
nuous
ly
tuni
ng
thes
e
pa
r
a
mete
r
s
,
r
e
s
ult
ing
in
incr
e
a
s
e
d
s
ys
tem
e
f
f
icie
nc
y
a
nd
r
e
duc
e
d
os
c
il
latio
ns
,
e
ve
n
unde
r
va
r
ying
c
ondit
ions
.
T
h
is
a
ppr
oa
c
h
e
ns
ur
e
s
that
the
c
onve
r
ter
ope
r
a
tes
s
moot
hly
a
c
r
os
s
it
s
e
nti
r
e
r
a
nge
of
f
unc
ti
ons
,
pr
ovidi
ng
r
e
li
a
ble
pe
r
f
or
manc
e
in
both
s
tea
dy
-
s
tate
a
nd
tr
a
ns
ient
c
ondit
ions
.
F
igur
e
s
2(
a
)
a
nd
2
(
b)
s
how
the
s
c
he
matic
diagr
a
m
of
the
s
ys
tem
de
s
c
r
ipt
ion
a
nd
c
onve
r
ter
's
topol
ogy
that
wa
s
c
hos
e
n
r
e
s
pe
c
ti
ve
ly.
T
he
two
modes
that
gove
r
n
thi
s
c
o
nve
r
ter
's
ope
r
a
ti
on
a
r
e
s
tep
-
up,
or
boos
t
mode,
a
nd
s
tep
-
d
own,
or
buc
k
mode.
T
he
ha
lf
-
br
idge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
(
B
DC
)
topol
ogy
c
ons
is
ts
of
a
DC
bus
volt
a
ge
on
the
DC
mi
c
r
ogr
id
s
ide,
is
the
output
vo
lt
a
ge
on
the
e
ne
r
gy
s
tor
a
ge
unit
s
ide,
a
nd
a
r
e
c
a
pa
c
it
o
r
s
on
the
DC
mi
c
r
og
r
id
s
ide
a
nd
e
ne
r
gy
s
tor
a
ge
u
nit
s
ide
r
e
s
pe
c
ti
ve
ly,
1
a
nd
2
a
r
e
the
uppe
r
a
nd
lowe
r
s
witche
s
of
the
c
onve
r
ter
r
e
s
pe
c
ti
ve
ly.
1
a
nd
2
a
r
e
the
diodes
of
the
uppe
r
a
nd
lowe
r
s
witche
s
of
the
c
onve
r
ter
,
a
nd
r
e
pr
e
s
e
nts
the
inducto
r
.
T
he
s
ophi
s
ti
c
a
ted
c
ontr
ol
tec
hnique
a
nd
e
xtens
ive
s
ys
tem
de
s
ign
gu
a
r
a
ntee
that
the
bid
ir
e
c
ti
ona
l
ha
lf
-
br
idge
DC
-
DC
c
onve
r
ter
pe
r
f
or
ms
we
ll
in
a
va
r
iety
of
s
e
tt
ings
,
of
f
e
r
ing
e
xc
e
ll
e
nt
pe
r
f
or
manc
e
a
nd
de
pe
nda
bil
it
y
in
it
s
int
e
nde
d
us
e
.
(
a
)
(
b)
F
igur
e
2
.
S
c
he
matic
diagr
a
m
of
the
s
ys
tem
de
s
c
r
ipt
ion
(
a
)
ge
ne
r
a
l
s
c
he
matic
diagr
a
m
a
nd
(
b)
ha
lf
-
br
i
dge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
2.
1
.
B
u
c
k
m
od
e
o
f
op
e
r
at
ion
T
he
topol
ogy
of
a
bidi
r
e
c
ti
ona
l
ha
lf
-
br
idge
DC
-
DC
c
onve
r
ter
is
c
hos
e
n
f
or
thi
s
s
tudy
be
c
a
us
e
of
the
s
mall
c
ur
r
e
nt
a
nd
volt
a
ge
s
tr
e
s
s
e
s
of
diodes
a
nd
s
witching
e
leme
nts
.
M
or
e
ove
r
,
the
e
xis
tenc
e
of
a
c
ti
ve
c
omponents
of
s
mall
c
onduc
ti
on
los
s
a
s
c
ompar
e
d
to
other
non
-
is
olate
d
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
t
e
r
s
[
21]
.
T
he
s
e
lec
ted
c
onve
r
ter
c
a
n
be
f
ound
in
[
21
]
,
[
22
]
.
T
his
c
onve
r
ter
ope
r
a
tes
in
two
modes
,
i.
e
.
buc
k
a
n
d
boos
t.
T
he
c
onve
r
ter
is
made
up
o
f
a
DC
bus
volt
a
ge
on
the
DC
mi
c
r
ogr
id
s
ide
a
nd
a
n
output
volt
a
ge
on
t
he
ba
tt
e
r
y
s
ide
de
pe
nding
on
the
ope
r
a
ti
ng
mode.
a
nd
r
e
pr
e
s
e
nt
the
c
a
pa
c
it
a
nc
e
s
of
the
c
a
pa
c
it
or
s
c
onne
c
ted
in
pa
r
a
ll
e
l
to
the
gr
id
a
nd
the
ba
tt
e
r
y
r
e
s
pe
c
ti
ve
ly.
1
a
nd
2
de
note
the
c
onve
r
ter
’
s
uppe
r
a
nd
lowe
r
s
witche
s
r
e
s
pe
c
ti
ve
ly.
1
a
nd
2
r
e
pr
e
s
e
nt
the
di
ode
s
in
pa
r
a
ll
e
l
to
the
uppe
r
a
nd
lowe
r
s
witche
s
of
the
c
onve
r
ter
r
e
s
pe
c
ti
ve
ly,
a
nd
L
de
notes
the
induct
or
.
I
n
the
buc
k
mode
of
ope
r
a
ti
on
,
powe
r
f
lows
f
r
om
the
mi
c
r
ogr
id
s
ide
to
the
load
s
ide.
Dur
ing
thi
s
mode
of
ope
r
a
ti
on,
s
witch
1
a
nd
Diode
2
c
onduc
t
while
2
a
nd
1
a
r
e
in
OFF
pos
it
ions
.
W
it
hin
thi
s
int
e
r
va
l
,
1
is
ON
while
2
,
1
a
nd
2
a
r
e
tu
r
ne
d
OFF
.
T
he
inductor
L
a
nd
C
a
pa
c
it
or
a
r
e
c
ha
r
ge
d.
2
be
ha
ve
s
a
s
a
f
r
e
e
whe
e
li
ng
diode
whe
n
1
a
nd
2
a
r
e
tur
ne
d
OFF
.
T
o
e
a
s
e
modeling,
the
ba
tt
e
r
y
is
c
ons
ider
e
d
a
s
a
n
int
e
r
n
a
l
r
e
s
is
tanc
e
.
E
qua
ti
ons
(
1)
a
nd
(
2)
a
r
e
de
r
ived
f
r
om
the
a
ppli
c
a
ti
on
of
Kir
c
hho
f
f
’
s
c
ur
r
e
nt
a
nd
volt
a
ge
law
s
.
T
he
e
quivale
nt
c
ir
c
uit
o
f
a
ha
l
f
-
br
idge
bidi
r
e
c
ti
o
na
l
DC
-
DC
c
onve
r
ter
ope
r
a
ti
ng
in
s
tep
-
down
i
s
il
lus
tr
a
ted
in
F
igur
e
3.
F
igu
r
e
s
3(
a
)
a
nd
3
(
b)
r
e
p
r
e
s
e
nt
the
e
quivale
nt
c
ir
c
uit
of
the
c
onve
r
ter
whe
n
the
uppe
r
s
witch
is
o
n
a
nd
of
f
,
r
e
s
pe
c
ti
ve
ly.
−
Output
e
qua
ti
on
whe
n
the
uppe
r
s
witch
is
ON
:
{
=
−
=
−
2
=
−
1
−
(
1)
B
u
c
k
m
od
e
B
oos
t
m
od
e
S
1
D
1
L
V
i
S
2
C
B
C
A
D
2
V
B
at
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
1
14
-
1
28
118
−
Output
e
qua
ti
on
whe
n
the
lowe
r
s
witch
is
ON
:
{
=
−
=
−
=
−
1
(
2)
(
a
)
(
b)
F
igur
e
3.
E
qu
ivale
nt
c
ir
c
uit
of
ha
l
f
-
br
idge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
ope
r
a
ti
ng
in
buc
k
mode
(
a
)
on
s
tate
a
nd
(
b)
of
f
s
tate
2.
2
.
B
oos
t
m
o
d
e
of
op
e
r
at
ion
I
n
the
s
tep
-
up
mode
of
ope
r
a
ti
on,
2
is
tur
ne
d
ON
a
nd
1
r
e
mains
OFF
.
T
he
ba
tt
e
r
y
d
is
c
ha
r
ge
s
ther
e
by
s
upplyi
ng
the
load
wi
th
2
a
nd
1
c
onduc
ti
n
g
while
1
a
nd
2
a
r
e
tur
ne
d
OFF
.
Du
r
ing
the
f
ir
s
t
int
e
r
va
l,
2
is
tu
r
ne
d
ON
with
1
,
1
,
a
nd
2
maintaine
d
a
t
O
F
F
pos
it
ion
.
T
he
inductor
L
a
nd
a
r
e
c
ha
r
ge
d
a
nd
no
c
ur
r
e
nt
f
lows
thr
ough
1
.
Dur
ing
the
s
e
c
ond
int
e
r
va
l,
2
a
nd
1
a
r
e
tur
ne
d
OFF
,
the
c
ir
c
uit
be
c
omes
a
n
ope
n
c
ir
c
uit
.
T
he
volt
a
ge
a
c
r
os
s
the
inductor
c
ha
nge
s
dir
e
c
ti
on.
1
be
c
omes
f
or
wa
r
d
b
ias
e
d
a
nd
is
c
ha
r
ge
d
on
a
higher
volt
a
ge
than
the
input
volt
a
ge
.
T
he
c
i
r
c
uit
then
ope
r
a
tes
in
s
tep
-
up
mode.
T
he
f
oll
owing
mathe
matica
l
e
qua
ti
ons
f
or
the
uppe
r
s
witch
a
nd
l
owe
r
s
witch
on
,
r
e
s
pe
c
ti
ve
ly,
may
then
be
de
r
ived
by
us
ing
Kir
c
hhof
f
's
volt
a
ge
law
(
KV
L
)
a
nd
Kir
c
hhof
f
's
c
ur
r
e
nt
law
(
KC
L
)
in
F
igur
e
4.
T
his
lea
ds
us
to
(
3)
a
nd
(
4)
.
T
he
c
or
r
e
s
ponding
c
ir
c
uit
of
the
c
onve
r
ter
is
s
hown
in
F
igur
e
s
4(
a
)
a
nd
4
(
b
)
whe
n
the
uppe
r
s
witch
is
tur
ne
d
on
a
nd
of
f
,
r
e
s
pe
c
ti
ve
ly.
(
a
)
(
b)
F
igur
e
4.
E
qu
ivale
nt
c
ir
c
uit
of
a
ha
lf
-
br
idge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
ope
r
a
ti
ng
in
boos
t
mode;
(
a
)
of
f
s
tate
a
nd
(
b)
on
s
tate
−
Output
e
qua
ti
on
whe
n
the
uppe
r
s
witch
is
ON
{
=
−
+
=
−
=
−
2
−
(
3)
−
Output
e
qua
ti
on
whe
n
the
lowe
r
s
witch
is
ON
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
R
obus
t
adapti
v
e
int
e
gr
al
s
li
ding
mode
c
ontr
ol
of
a
half
-
br
idge
…
(
J
uli
us
De
r
ghe
C
ham
)
119
{
=
=
−
=
−
2
−
(
4)
3.
DE
S
I
GN
OF
NONL
I
NE
AR
CONT
ROL
L
E
RS
3.
1
.
De
s
ign
of
in
t
e
gr
al
s
li
d
in
g
m
od
e
c
on
t
r
oll
e
r
I
n
de
s
igni
ng
a
s
li
ding
mode
c
ontr
o
ll
e
r
,
one
mus
t
f
ir
s
t
de
ve
lop
a
s
tate
s
pa
c
e
e
qua
ti
on
f
or
the
s
ys
tem
to
be
c
ontr
oll
e
d
a
s
a
f
unc
ti
on
of
the
c
ont
r
ol
va
r
iab
les
[
23]
.
I
t
is
then
f
oll
owe
d
by
de
s
igni
ng
a
s
li
ding
s
ur
f
a
c
e
,
whic
h
lea
ds
to
the
de
r
ivation
of
a
c
ont
r
ol
law
a
nd
e
nds
by
de
r
ivi
ng
the
e
xis
ti
ng
c
ondit
ion
of
the
s
li
di
ng
mode
c
ontr
oll
e
r
[
24
]
.
T
o
de
s
ign
the
p
r
opos
e
d
c
ontr
oll
e
r
f
or
thi
s
s
ys
tem,
we
be
gin
by
de
s
igni
ng
a
n
in
tegr
a
l
s
li
ding
mode
c
ontr
oll
e
r
with
the
c
onve
r
ter
ope
r
a
ti
ng
in
c
onti
nuous
c
onduc
ti
ng
mode
(
C
C
M
)
.
T
he
int
e
gr
a
l
s
li
ding
mode
c
ontr
ol
take
s
int
o
c
ons
ider
a
ti
on
a
n
a
ddit
io
na
l
volt
a
ge
int
e
gr
a
l
e
r
r
or
ter
m
,
whic
h
r
e
duc
e
s
the
s
tea
dy
-
s
tate
e
r
r
or
o
f
the
c
onve
nti
ona
l
s
li
ding
mode
c
ontr
o
ll
e
r
[
22
]
.
3.
1.
1.
B
u
c
k
m
od
e
T
he
I
S
M
C
de
s
ign
is
quit
e
dif
f
e
r
e
nt
f
r
o
m
the
c
onve
nti
ona
l
S
M
C
be
c
a
us
e
it
ha
s
th
r
e
e
c
ont
r
ol
pa
r
a
mete
r
s
,
whic
h
a
r
e
the
output
volt
a
ge
e
r
r
or
1
,
the
r
a
te
of
c
ha
nge
of
the
ou
tput
vo
lt
a
ge
e
r
r
o
r
2
,
a
nd
3
is
the
int
e
gr
a
l
of
the
outpu
t
volt
a
ge
e
r
r
or
[
25
]
.
I
n
e
a
c
h
mode
of
ope
r
a
ti
on
,
the
c
ontr
ol
va
r
iable
us
e
d
is
t
he
output
volt
a
ge
a
nd
s
igni
f
ies
the
de
s
ir
e
d
va
lue
of
the
outp
ut
volt
a
ge
.
L
e
t
1
=
−
,
2
=
−
∫
(
−
)
,
a
nd
3
=
∫
1
dt.
T
he
s
tate
s
pa
c
e
e
qua
ti
on
with
th
r
e
e
c
ontr
ol
pa
r
a
mete
r
s
(
1
,
2
,
3
)
c
a
n
be
e
xpr
e
s
s
e
d
a
s
in
(
5
)
;
[
y
̇
1
y
̇
2
y
̇
3
]
=
[
0
1
0
0
1
C
B
0
1
0
0
]
[
y
1
y
2
y
3
]
+
[
−
0
V
i
L
C
B
0
]
+
[
0
V
L
C
B
0
]
(
5)
=
{
1
,
ℎ
≥
0
0
,
ℎ
<
0
(
6)
whe
r
e
de
notes
the
s
witch's
s
witching
s
tate
a
nd
is
the
c
onve
r
ter
's
input
vo
lt
a
ge
.
T
he
ge
ne
r
a
l
c
ontr
ol
law
that
is
s
uit
a
ble
f
or
thi
s
s
ys
tem
a
s
a
dopted
f
r
o
m
r
e
f
e
r
e
nc
e
[
24]
is
given
in
(
6)
.
T
he
s
li
ding
s
ur
f
a
c
e
c
a
n
be
de
f
ined
in
(
7
)
a
s
f
ound
i
n
the
f
oll
owing
r
e
f
e
r
e
nc
e
[
25]
,
=
1
1
+
2
2
+
3
3
(7
)
̇
=
1
1
̇
+
2
2
̇
+
3
3
̇
(8
)
whe
r
e
1
,
2
,
3
a
r
e
the
s
li
ding
c
oe
f
f
icie
nts
.
T
he
ti
me
de
r
ivative
of
is
:
T
o
e
ns
ur
e
the
e
xis
tenc
e
of
s
li
ding
mode,
the
f
oll
owing
inequa
li
ty
mus
t
be
f
ul
f
il
led:
.
̇
<
0
(
9)
F
r
om
s
li
ding
mode’
s
pr
inciple
,
whe
n
<
0,
̇
>
0
=
0
.
W
he
n
>
0
,
̇
<
0
=1
(
10)
0
<
(
1
−
1
2
)
+
3
2
(
−
)
+
<
(
11)
B
y
s
olvi
ng
̇
=
0,
the
e
quivale
nt
c
ontr
ol
is
obtaine
d
that
is
given
in
(
12)
,
=
(
1
−
1
2
)
+
3
2
(
−
)
+
(1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
1
14
-
1
28
120
0<
d
=
−
−
ℎ
=
<1
(1
3
)
w
h
ere
s
i
g
n
i
f
i
es
t
h
e
co
n
t
r
o
l
s
i
g
n
a
l
g
i
v
en
i
n
(1
4
)
=
(
1
−
1
2
)
+
3
2
(
−
)
2
+
(1
4
)
3.
1.
2.
B
oos
t
m
o
d
e
I
n
thi
s
mode
of
ope
r
a
ti
on,
a
c
ur
r
e
nt
-
c
ontr
oll
e
d
s
li
ding
mode
c
ontr
oll
e
r
is
a
dopted
f
r
om
a
s
s
tate
d
in
r
e
f
e
r
e
nc
e
[
19]
.
B
y
letti
ng
1
be
the
inductor
c
ur
r
e
nt
e
r
r
or
,
2
be
the
output
volt
a
ge
e
r
r
o
r
,
a
nd
3
be
t
he
int
e
gr
a
l
o
f
the
s
um
of
the
inducto
r
c
ur
r
e
nt
a
nd
output
volt
a
ge
e
r
r
o
r
s
.
C
ons
ider
ing
that
the
c
on
ve
r
ter
is
ope
r
a
ti
ng
in
c
onti
nuous
c
onduc
ti
on
mode,
the
va
r
i
a
bles
1
,
2
,
a
nd
3
c
a
n
be
e
xpr
e
s
s
e
d
a
s
(
15)
;
{
1
=
−
−
2
=
−
3
=
∫
(
1
+
2
)
dt
(1
5
)
T
he
ins
tanta
ne
ous
inductor
’
s
r
e
f
e
r
e
nc
e
c
ur
r
e
nt,
−
=
(
−
)
(
16)
whe
r
e
is
the
volt
a
ge
e
r
r
or
a
mpl
if
ica
ti
on
ga
in,
be
ing
the
r
e
f
e
r
e
nc
e
output
volt
a
ge
a
nd
the
volt
a
ge
a
c
r
os
s
the
c
a
pa
c
it
or
.
T
he
ti
me
de
r
ivative
of
1
,
2
,
a
nd
3
c
a
n
be
f
ound
a
s
(
17)
-
(
19)
.
1
̇
=
−
-
−
̅
(
17)
2
̇
=
−
1
(
18)
3
̇
=
1
+
2
=
(
+
1)
(
−
)
−
(
19)
whe
r
e
,
̅
is
the
inver
s
e
logi
c
of
a
nd
de
notes
a
s
̅
=1
−
u
.
Give
n
that
(
6)
r
e
pr
e
s
e
nts
the
ove
r
a
ll
s
witching
f
un
c
ti
on
of
a
s
li
ding
mode
c
ontr
oll
e
r
f
or
thi
s
s
ys
tem,
the
s
li
ding
s
ur
f
a
c
e
c
a
n
be
c
hos
e
n
a
s
(
20
)
.
=
1
1
+
2
2
+
3
3
(
20)
with
=
[
1
,
2
,
3
]
(
21
)
B
y
f
indi
ng
the
ti
me
de
r
ivative
of
a
nd
s
olvi
ng
it
s
e
qua
l
to
z
e
r
o,
the
e
quivale
nt
c
ontr
ol
law
be
c
omes
.
=
−
2
+
1
(
−
)
−
3
−
(
22)
T
he
de
tailed
de
s
ign
o
f
the
c
ont
r
ol
law
a
nd
the
c
a
lcula
ti
on
of
it
s
s
li
ding
c
oe
f
f
icie
nts
c
a
n
f
u
r
ther
be
s
e
e
n
in
r
e
f
e
r
e
nc
e
s
[
14]
,
[
22]
.
I
n
the
boos
t
mode
o
f
ope
r
a
ti
on
,
the
s
li
ding
mode
c
ontr
oll
e
r
ne
e
ds
to
f
ulf
il
l
the
e
xis
tenc
e
c
ondit
ion,
whic
h
is
given
by
:
l
im
→
0
.
̇
<
0,
he
nc
e
,
we
c
a
n
obtain
the
f
oll
owing
inequa
li
ti
e
s
0
<
−
2
+
1
(
−
)
−
3
−
<1
(
23)
=
−
2
+
1
(
−
)
−
3
−
(
24)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
R
obus
t
adapti
v
e
int
e
gr
al
s
li
ding
mode
c
ontr
ol
of
a
half
-
br
idge
…
(
J
uli
us
De
r
ghe
C
ham
)
121
=
(
25)
{
1
=
3
(
+
1
)
1
2
=
(
+
2
1
)
3
=
3
1
(
26)
3.
2.
Adap
t
ive
in
t
e
gr
al
s
li
d
in
g
m
od
e
c
on
t
r
oll
e
r
T
he
goa
l
of
a
da
pti
ve
c
ontr
ol
is
to
modi
f
y
the
s
ys
tem's
be
ha
vior
in
r
e
s
pons
e
to
modi
f
ica
ti
ons
in
the
dyna
mi
c
s
of
the
p
r
oc
e
s
s
[
26]
.
W
e
thus
incor
po
r
a
t
e
a
n
a
da
pti
ve
pr
ope
r
ty
int
o
the
t
r
a
dit
ional
int
e
gr
a
l
s
li
ding
mode
c
ontr
ol,
s
ince
non
-
a
da
pti
ve
s
li
ding
mode
c
o
ntr
ol
is
ine
f
f
e
c
ti
ve
whe
n
it
c
omes
to
a
b
r
upt
c
ha
nge
s
in
load
r
e
s
is
tanc
e
.
I
n
th
is
wor
k
,
the
a
da
pti
ve
s
li
ding
mode
is
us
e
d
to
f
ur
ther
les
s
e
n
the
c
ha
tt
e
r
ing
im
pa
c
t
in
a
ddit
ion
to
r
e
s
olvi
ng
the
is
s
ue
of
the
non
-
a
da
pti
ve
s
li
ding
mode
c
ontr
ol's
poor
pe
r
f
o
r
manc
e
r
e
ga
r
ding
f
a
s
t
c
ha
nge
s
in
load.
B
y
im
pleme
nti
ng
the
a
da
pti
ve
s
li
ding
f
a
c
tor
de
s
c
r
ibed
in
[
27]
,
[
28
]
the
de
s
ign
is
c
a
r
r
ied
out.
T
he
de
f
ini
ti
ons
of
the
a
da
pti
ve
s
li
ding
c
oe
f
f
icie
nt
a
nd
s
li
ding
s
ur
f
a
c
e
o
f
the
a
da
pti
ve
s
li
ding
mode
a
r
e
given
in
(
27)
a
nd
(
28)
a
c
c
or
dingl
y.
=
1
+
2
2
+
3
3
(
27)
whe
r
e
2
a
nd
3
a
r
e
the
s
li
ding
c
oe
f
f
icie
nts
.
=
1
(
28)
whe
r
e
≠
0
=
,
with
≠
0
whe
r
e
is
the
nomi
na
l
load
r
e
s
is
tanc
e
,
1
is
the
s
li
di
ng
c
oe
f
f
icie
nt
o
f
the
c
ontr
oll
e
r
.
is
the
ins
tanta
ne
ous
load
r
e
s
is
tanc
e
.
De
tail
s
tudy
of
the
a
dopted
a
da
p
ti
ve
c
ontr
ol
law
c
a
n
be
s
e
e
n
in
[
28]
,
[
29]
.
T
he
a
da
pti
ve
mec
ha
nis
m
f
or
the
boos
t
mode
of
ope
r
a
ti
on
is
de
s
igned
a
s
in
r
e
f
e
r
e
nc
e
[
30]
a
s
de
f
ined
in
(
29)
,
(
30)
a
nd
(
31)
.
=
+
(
29)
=
ℎ
(
)
(
30)
=
(
31)
3
.
3.
P
ar
t
icle
s
war
m
op
t
im
izat
io
n
P
a
r
ti
c
le
s
wa
r
m
opti
mi
z
a
ti
on
(
P
S
O
)
is
a
n
opti
mi
z
a
ti
on
a
lgor
it
hm
de
ve
loped
in
1995
by
Dr
.
E
be
r
ha
r
t
a
nd
Dr
.
Ke
nne
dy
that
is
ba
s
e
d
on
the
s
oc
ial
be
ha
v
ior
of
f
is
h
s
c
hooli
ng
or
bir
d
f
locking
[
31]
.
I
n
r
e
c
e
nt
ye
a
r
s
,
r
e
s
e
a
r
c
he
r
s
in
a
va
r
iety
of
powe
r
e
lec
tr
onics
c
onve
r
ter
a
ppli
c
a
ti
ons
ha
ve
s
uc
c
e
s
s
f
ull
y
us
e
d
t
he
P
S
O
tec
hnique.
T
his
opti
mi
z
a
ti
on
s
tr
a
tegy
e
ns
ur
e
s
the
s
ys
tem
will
f
unc
ti
on
we
ll
in
a
s
hor
ter
length
of
ti
me
than
pr
ior
one
s
[
32]
.
T
h
is
tec
hnique
e
ns
ur
e
s
good
pe
r
f
or
manc
e
of
the
s
ys
tem
withi
n
a
s
hor
t
ti
me
a
s
c
om
pa
r
e
d
to
other
opti
mi
z
a
ti
on
tec
hniques
[
31]
.
As
s
tate
d
in
r
e
f
e
r
e
nc
e
[
33]
,
the
AI
S
M
C
de
s
ign
is
now
e
xpr
e
s
s
e
d
a
s
a
n
opti
mi
z
a
ti
on
pr
oblem
de
f
ined
in
(
32
)
.
(
)
=
∑
(
(
)
)
2
=
0
(
32)
S
ubjec
t
to
<
<
lb
.
W
it
h
a
nd
be
ing
the
lowe
r
a
nd
uppe
r
bounds
o
f
va
r
iable
s
=
(
1
,
2
,
3
)
a
nd
r
e
pr
e
s
e
nts
th
e
s
tar
t
-
up
ti
me
f
or
t
r
a
ns
ient
r
e
s
pons
e
.
T
he
pa
r
a
mete
r
s
that
ne
e
d
to
be
a
djus
ted
in
thi
s
s
tudy
a
r
e
the
g
a
ins
a
nd
c
oe
f
f
icie
nts
of
the
s
li
ding
mode
c
ontr
ol
ler
.
P
S
O's
objec
ti
ve
is
to
maximi
z
e
ga
ins
f
o
r
im
pr
ove
d
pe
r
f
or
manc
e
by
opti
mi
z
ing
the
s
li
ding
mode
c
ontr
o
ll
e
r
's
pa
r
a
mete
r
va
lues
[
34]
,
the
ini
ti
a
l
f
i
tnes
s
of
e
a
c
h
pa
r
ti
c
le
in
the
population
s
ize
wa
s
a
s
c
e
r
taine
d
us
ing
the
pe
r
f
or
manc
e
index,
a
nd
the
a
nd
,
a
s
f
ound
in
r
e
f
e
r
e
nc
e
[
35]
,
[
36]
we
r
e
then
c
a
lcula
ted.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
1
14
-
1
28
122
=
∫
|
|
∞
0
(
33)
T
a
ble
1
a
nd
2
pr
ovide
the
pa
r
a
mete
r
s
of
the
opti
m
um
va
lues
of
s
li
ding
c
oe
f
f
icie
nts
(
1
,
2
,
3
)
f
or
the
buc
k
mode
a
nd
s
li
ding
mode
c
ontr
ol
ler
ga
ins
(
1
,
2
,
3
)
f
or
the
boos
t
mode,
r
e
s
pe
c
ti
ve
ly,
wi
th
15
be
ing
the
s
wa
r
m
s
ize
.
T
o
de
ter
mi
ne
e
a
c
h
pa
r
t
icle
's
po
s
it
ion
a
nd
ve
locity
in
P
S
O
,
a
3
-
x
S
wa
r
m
s
ize
matr
ix
is
uti
li
z
e
d.
T
he
r
e
c
a
n
be
up
to
100
it
e
r
a
ti
ons
in
to
tal.
T
he
a
c
c
e
ler
a
ti
on
c
oe
f
f
icie
nts
f
or
s
oc
ial
a
nd
pe
r
s
ona
l
f
a
c
tor
s
a
r
e
r
e
ga
r
de
d
a
s
1
=
2
=
2.
S
im
ulating
us
ing
M
AT
L
AB
-
S
im
uli
nk,
the
pe
r
f
or
manc
e
of
the
opti
mal
pr
oc
e
s
s
is
given
in
F
igur
e
5
.
T
a
ble
2
pr
e
s
e
nts
the
p
a
r
a
mete
r
s
of
the
c
onve
nti
ona
l
I
S
M
C
c
ont
r
ol
tec
hni
que
a
nd
the
s
ugge
s
ted
c
ontr
oll
e
r
.
T
a
ble
1
.
P
a
r
a
mete
r
s
of
s
li
ding
c
oe
f
f
icie
nts
in
B
uc
k
mode
C
ont
r
ol
s
tr
a
te
gy
1
2
3
I
S
M
C
90.1
0.000286
177366
A
I
S
M
C
P
S
O
2.4840
4.1120e
-
8
1.8236e
4
F
igur
e
5.
I
te
r
a
ti
on
of
the
P
S
O
a
lgor
it
hm
T
a
ble
2
.
P
a
r
a
mete
r
s
of
s
li
ding
mode
c
ontr
oll
e
r
ga
i
ns
in
B
oos
t
mode
C
ont
r
ol
s
tr
a
te
gy
1
2
2
I
S
M
C
750
30
4
A
I
S
M
C
P
S
O
896.01
36.203
16.032
4.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
his
s
e
c
ti
on
dis
c
us
s
e
s
s
im
ulation
f
indi
ngs
us
ing
M
AT
L
AB
/S
im
uli
nk
to
s
uppor
t
the
viabili
ty
of
the
s
ugge
s
ted
a
da
pti
ve
int
e
gr
a
l
s
li
ding
mode
c
ont
r
ol
a
ugmente
d
by
pa
r
ti
c
le
s
wa
r
m
opti
mi
z
a
ti
on
f
or
a
DC
-
D
C
c
onve
r
ter
wor
king
in
bidi
r
e
c
ti
ona
l
mode
.
T
he
s
ugge
s
ted
c
ontr
oll
e
r
f
or
the
buc
k
a
nd
boos
t
mo
de
s
of
a
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
is
de
picte
d
in
F
ig
u
r
e
2
(
a
)
o
f
the
s
c
he
matic
diagr
a
m
o
f
the
s
ys
tem
de
s
c
r
ipt
ion.
T
he
r
e
is
only
one
s
witching
f
r
e
que
nc
y,
whic
h
is
20
kHz
.
F
or
the
s
tep
-
down
a
nd
s
tep
-
up
modes
,
the
output
volt
a
ge
s
a
r
e
12
a
nd
24
V
,
r
e
s
pe
c
ti
ve
ly,
while
s
im
u
lating
the
c
onve
r
te
r
a
t
4
ohms
f
or
buc
k
mode
a
nd
60
Ω
f
o
r
boos
t
mode.
L
ow
volt
a
ge
s
,
high
volt
a
ge
s
,
a
nd
loa
d
r
e
s
is
tanc
e
R
a
r
e
va
r
ied
dur
ing
the
s
im
ulation
to
c
onf
ir
m
that
the
s
ugge
s
ted
c
ontr
oll
e
r
ope
r
a
tes
a
s
int
e
nde
d
ba
s
e
d
on
tr
a
ns
ient
r
e
s
pons
e
s
.
T
hr
e
e
s
c
e
na
r
ios
a
r
e
de
r
ived
f
r
om
the
s
im
ulation
f
indi
ngs
.
T
he
tr
a
ns
ient
r
e
s
pons
e
s
of
the
c
ur
r
e
nts
a
nd
volt
a
ge
s
o
f
the
c
onve
r
te
r
to
s
tep
c
ha
nge
s
a
r
e
e
xa
mi
ne
d
in
thes
e
c
ir
c
ums
tanc
e
s
.
T
he
s
pe
c
if
ica
ti
ons
of
the
bid
ir
e
c
ti
ona
l
ha
lf
-
br
idge
DC
-
DC
c
onve
r
ter
a
r
e
li
s
ted
in
T
a
ble
3
a
nd
we
r
e
s
our
c
e
d
f
r
om
[
22]
,
[
25]
.
T
a
ble
3
.
S
im
ulation
pa
r
a
mete
r
s
of
ha
lf
-
br
idge
bidi
r
e
c
ti
ona
l
DC
-
DC
c
onve
r
ter
P
a
r
a
me
te
r
s
S
ymbol
V
a
lu
e
I
nput
vol
ta
ge
24
V
R
e
f
e
r
e
nc
e
vol
ta
ge
12
V
I
nduc
ta
nc
e
L
100
H
C
a
pa
c
it
a
nc
e
=
5
mF
S
w
it
c
hi
ng f
r
e
que
nc
y
20
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
R
obus
t
adapti
v
e
int
e
gr
al
s
li
ding
mode
c
ontr
ol
of
a
half
-
br
idge
…
(
J
uli
us
De
r
ghe
C
ham
)
123
4.
1.
S
i
m
u
lat
io
n
r
e
s
u
lt
s
in
b
u
c
k
m
od
e
o
f
o
p
e
r
at
i
on
S
c
e
na
r
io
1:
I
n
thi
s
s
c
e
na
r
io,
the
s
ys
tem
a
dmi
ts
a
dis
tur
ba
nc
e
c
a
us
e
d
by
a
n
a
br
upt
s
hif
t
in
input
volt
a
ge
f
r
om
24
to
40
V
with
=
0.
5
s
a
nd
f
r
om
4
0
to
15
V
with
=
0.
2
s
,
r
e
s
pe
c
ti
ve
ly.
T
he
r
e
f
e
r
e
nc
e
volt
a
ge
is
ke
pt
c
ons
tant
a
t
12
volt
s
.
T
he
f
indi
n
gs
de
mons
tr
a
te
that
a
ll
th
r
e
e
c
ont
r
ol
s
tr
a
tegie
s
f
unc
ti
on
s
a
ti
s
f
a
c
tor
il
y
in
ter
ms
of
r
obus
tnes
s
,
wi
th
the
s
ugg
e
s
ted
c
ontr
oll
e
r
outper
f
o
r
mi
ng
the
two
tr
a
dit
ional
methods
in
ter
ms
of
s
pe
e
d,
a
s
s
e
e
n
in
F
igu
r
e
6
.
F
igur
e
s
6(
a
)
a
nd
6
(
b)
il
lus
tr
a
te
the
output
vo
lt
a
ge
a
nd
c
ur
r
e
nt
,
r
e
s
pe
c
ti
ve
ly.
T
he
wa
ve
f
or
m
of
the
output
volt
a
ge
of
the
s
ugge
s
ted
c
ontr
oll
e
r
dur
ing
input
vo
lt
a
ge
dis
tur
ba
nc
e
r
e
jec
ti
on
is
s
igni
f
ica
ntl
y
im
pr
ove
d
upon
than
that
of
P
I
c
ontr
ol
a
nd
tr
a
dit
ional
int
e
gr
a
l
s
li
ding
mode
c
ontr
ol
,
pe
r
the
s
im
ulation
r
e
s
ult
s
.
(
a
)
(
b)
F
igur
e
6.
S
im
ulation
r
e
s
ult
s
of
bidi
r
e
c
ti
ona
l
B
DC
in
buc
k
mode,
s
c
e
na
r
io
1
(
a
)
output
volt
a
ge
a
nd
(
b)
load
c
ur
r
e
nt
S
c
e
na
r
io
2:
T
he
r
e
f
e
r
e
nc
e
volt
a
ge
in
thi
s
c
a
s
e
is
a
djus
ted
by
de
c
r
e
a
s
ing
it
f
r
om
12
to
8
a
nd
10
V
a
t
int
e
r
va
ls
of
0.
1
a
nd
0
.
2
s
,
r
e
s
pe
c
ti
ve
ly,
while
the
input
volt
a
ge
is
s
e
t
a
t
24
V
.
P
I
,
I
S
M
C
,
a
nd
the
s
ugge
s
ted
c
ontr
oll
e
r
c
ontr
ol
the
c
onve
r
ter
;
F
igur
e
5
dis
plays
the
output
volt
a
ge
a
nd
load
c
ur
r
e
nt
r
e
s
ult
s
.
I
t
is
de
t
e
r
mi
ne
d
that
a
ll
thr
e
e
c
ontr
ol
tec
hniques
ha
ve
pe
r
f
or
med
s
a
ti
s
f
a
c
tor
il
y
in
ter
ms
of
mon
it
or
ing
the
r
e
f
e
r
e
nc
e
volt
a
ge
.
F
igur
e
7
make
s
it
c
lea
r
that
the
s
ugge
s
ted
c
ontr
oll
e
r
ha
s
a
quicke
r
dyna
mi
c
r
e
a
c
ti
on
in
r
e
tur
ning
the
DC
-
DC
c
onve
r
ter
's
output
vo
lt
a
ge
to
it
s
matc
hing
r
e
f
e
r
e
nc
e
va
lues
,
e
ve
n
in
s
pit
e
of
the
s
udde
n
s
hif
t
in
the
r
e
f
e
r
e
nc
e
volt
a
ge
.
As
a
r
e
s
ult
,
the
s
ugge
s
ted
c
ontr
oll
e
r
maximi
z
e
s
c
ontr
ol
-
tr
a
c
king
a
c
c
ur
a
c
y
c
omp
a
r
e
d
to
it
s
c
onve
nti
ona
l
c
ounter
pa
r
ts
.
T
he
r
e
c
omm
e
nde
d
c
ontr
oll
e
r
outper
f
or
med
the
c
onve
nti
ona
l
one
s
in
t
e
r
ms
of
s
pe
e
d,
e
ve
n
though
bo
th
c
ont
r
oll
e
r
s
did
a
good
j
ob
of
r
e
jec
ti
ng
the
dis
tur
ba
nc
e
,
a
s
s
e
e
n
in
F
igur
e
7(
a
)
a
nd
F
igur
e
7
(
b
)
.
I
t
is
s
e
e
n
that
the
P
I
c
ont
r
oll
e
r
is
ove
r
s
hooti
ng.
(
a
)
(
b)
F
igur
e
7.
S
im
ulation
r
e
s
ult
s
of
B
DC
in
buc
k
mode,
s
c
e
na
r
io
2
(
a
)
output
volt
a
ge
a
nd
(
b)
load
c
ur
r
e
nt
S
c
e
na
r
io
3:
I
n
the
load
r
e
s
is
tanc
e
tes
t,
the
load
is
r
e
duc
e
d
f
r
om
4
Ω
to
2
Ω
a
t
0.
1
s
a
nd
then
incr
e
a
s
e
d
to
8
Ω
a
t
0.
2
s
,
with
a
s
im
ulation
pe
r
io
d
of
0.
3
s
.
F
igur
e
s
8(
a
)
a
nd
8
(
b)
dis
play
the
outpu
t
volt
a
ge
a
nd
load
c
ur
r
e
nt
wa
ve
f
or
m
diagr
a
ms
whe
n
the
c
onve
r
ter
is
unde
r
the
c
ontr
ol
of
P
I
,
I
S
M
C
,
a
nd
the
pr
opos
e
d
c
ontr
oll
e
r
.
F
r
o
m
the
r
e
s
ult
s
,
it
is
obs
e
r
ve
d
that
the
P
I
c
ontr
ol
r
e
gis
ter
s
a
n
ove
r
s
hoot
whe
n
th
e
load
is
incr
e
a
s
e
d
to
8
Ω
a
nd
a
n
unde
r
s
hoot
whe
n
the
load
is
de
c
r
e
a
s
e
d
to
2
Ω
.
T
he
I
S
M
C
c
ontr
oll
e
r
unde
r
s
hoots
the
Evaluation Warning : The document was created with Spire.PDF for Python.