In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
4, D
e
c
e
m
ber
201
9,
pp.
1806~
18
14
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1806-1814
1806
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
High performance DC/
D
C b
u
ck c
onverter using sli
d
ing m
o
de
controller
Mu
staf
a A
. Fad
el A
l-Qaisi,
Moh
an
ad
A. S
h
e
h
a
b, A
m
m
ar
A
l-Giz
i
,
M
o
ha
mmed
Al-
S
a
a
d
i
Coll
ege
of
En
g
ineeri
ng,
M
ustansiri
y
ah
U
niv
e
rsity
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
31,
2
0
1
9
Re
vise
d A
p
r
20,
201
9
A
c
c
e
pte
d
J
u
l
22,
201
9
Th
is
p
ap
er
i
nv
est
i
g
a
ted
the
p
e
rf
orm
a
nce
o
f
t
h
e
s
lidi
n
g
m
o
d
e
c
on
trol
tech
ni
que
f
or
D
C/DC
c
onv
erter
u
s
i
n
g
f
r
equ
e
ncy
respo
n
s
e
m
eth
o
d
.
The
app
l
i
catio
n
s
o
f
the
s
t
ep
d
o
w
n
type
s
witchi
ng
r
eg
u
l
ato
r)
bu
ck
c
o
nverter
(ar
e
f
o
u
n
d
in
t
he
d
evi
ces
t
hat
u
s
e
b
a
tt
eri
e
s
as
p
o
w
er
s
o
u
rce
lik
e
l
a
pt
op,
cell
ph
on
es,
elect
ric
veh
i
cle,
a
n
d
r
ec
ent
l
y,
it
has
also
b
een
u
sed
i
n
the
ren
e
wabl
e
energ
y
p
ro
ces
si
ng,
a
s
a
m
a
x
i
m
u
m
ou
tp
u
t
p
o
w
er
can
b
e
a
c
h
i
eved
a
t
h
i
g
h
e
r
ef
fici
ency.
In
o
rd
e
r
t
o
o
p
ti
miz
e
t
he
e
f
f
i
c
ien
c
y
a
n
d
f
o
r
co
nv
e
n
i
en
t
pow
er
m
a
nag
e
men
t
,
the
i
s
s
u
es
lik
e
power
o
n
t
r
ansients,
th
e
eff
ect
o
f
load
v
a
r
i
a
ti
on,
S
w
itch
i
ng
a
n
d
E
lect
rom
a
gn
eti
c
i
n
t
erf
e
rence
(EM
I)
l
o
ss
es
h
as
t
o
be
o
ve
rc
o
m
e
f
o
r
which
c
o
ntrol
l
ers
are
us
ed.
In
t
he
p
ro
p
o
sed
m
e
t
h
o
d
,
p
u
ls
e
w
idth
mo
du
la
tion
(
P
WM)
ba
se
d
on
p
rop
o
r
tio
na
l
-
integral
-deri
v
ati
v
e
s
l
id
in
g
m
ode
vo
lt
age
con
t
roller
(P
ID
S
MVC)
i
s
des
i
gn
ed
f
o
r
a
b
uck
con
v
erter
an
d
th
e
resp
on
se
f
o
r
a
pp
rop
r
iate
c
on
trol
p
aramet
ers
has
been
o
b
t
ai
ned.
The
syst
e
m
st
abili
t
y
has
been
e
x
a
mi
ned
and
an
alyze
d
f
ro
m
th
e
perf
o
r
man
ce
chara
c
t
e
ri
stics
,
w
hi
ch
s
ho
w
s
c
le
arl
y
t
hat
t
h
e
buck
co
nv
ert
e
r
co
nt
ro
ll
ed
by
th
e
slid
in
g
m
o
d
e
c
ont
roller
has
fast
d
yn
ami
c
r
espo
nse
and
i
t
’s
v
ery
e
ffici
ent
f
o
r
vari
ou
s
ap
plication
s
.
K
eyw
ord
s
:
DC/
D
C co
nv
er
t
e
r
N
on-l
i
n
ear
con
tro
l
sys
tem
S
lid
ing
mode
c
ontro
l
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
M.
A
. Fadel Al-Qai
s
i,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
Mu
sta
n
s
i
ri
yah
U
n
i
v
e
r
si
t
y
,
Iraq
,
B
agh
d
a
d
, B
a
b
Al
mu
ad
am.
Em
ail:
mustafa
_
1
9
88a
b
b
as@
uom
u
s
ta
ns
iri
y
a
h
.
e
du.i
q
1.
I
N
TR
OD
U
C
TI
O
N
The
sl
idi
n
g
m
ode
c
on
t
r
o
lle
r
(S
MC
)
is
a
n
o
n
-
linea
r
c
o
n
t
r
o
l
me
t
h
o
d
tha
t
c
han
g
e
s
t
he
d
y
n
am
ics
o
f
a
no
n-l
i
ne
ar syst
e
m w
h
ich forc
e
s
t
he s
y
s
tem
t
o
s
li
de.
The
S
M
C w
e
l
l
know
n
b
y
i
ts ro
bus
t
n
ess, h
i
g
h s
t
a
b
i
l
i
t
y an
d
si
m
p
le
i
mp
le
me
nt
a
tio
n
[1-5]
.
O
ne
a
p
p
lica
tio
n
o
f
S
MC
i
s
th
e
c
o
n
t
rol
of
e
l
e
c
t
ri
c
d
r
i
v
e
s
o
p
e
ra
t
e
d
by
s
wit
c
hi
ng
pow
er
c
o
n
v
e
r
t
e
rs.
The
D
C
/
D
C
c
o
n
v
erter
s
m
ust
w
o
rk
w
i
t
h
su
i
t
a
b
le
con
t
ro
l
t
e
ch
ni
qu
e
in
o
rder
t
o
cope
w
i
t
h
the
i
r
i
n
tr
ins
i
c
no
n
l
i
n
ear
it
y,
s
ud
de
n
loa
d
c
h
a
nge
s,
w
ide
range
o
f
in
put
v
olta
ge
,
and
t
o
guara
nt
e
e
s
ta
bili
t
y
a
t
any
opera
ti
n
g
c
on
d
i
t
i
on w
h
i
l
e
pr
o
v
i
di
n
g
q
ui
ck trans
ie
nt r
es
po
ns
e
[
6
-8]. The SMC techn
i
que
ca
n
be
a
p
o
s
s
i
b
l
e
op
tio
n
to
c
on
tro
l
t
hese
t
y
p
e
o
f
c
i
r
c
ui
t
s
,
since
the
sw
i
t
c
h
i
n
g
c
onve
rt
e
r
s
mo
d
e
l
a
ca
se
o
f
v
a
ri
a
b
l
e
c
o
nst
r
u
c
ti
on
syst
e
ms [
9
]
.
The
l
iter
a
ture
r
eview
sh
ow
s
t
h
at
t
he
a
ut
h
o
rs
s
ugge
s
t
v
a
r
i
o
us
m
e
t
hod
s
to
d
e
s
i
g
n
SM
C
co
nt
roll
e
r
.
In
[1
0]
t
he
a
u
t
h
o
r
d
e
s
ig
ne
d
an
d
a
n
al
yze
d
a
r
ob
u
s
t
S
M
C
fo
r
the
c
o
nt
ro
l
o
f
D
C/
DC
buc
k
c
o
nv
e
r
t
e
r,
a
b
u
c
k
con
v
er
t
e
r
w
ith
t
w
o
l
o
o
p
c
o
n
tr
ol
i
s
em
p
l
oye
d.
T
he
s
ys
tem
con
t
ro
l
led
usi
n
g
S
M
C
is
t
este
d
a
nd
gi
ve
s
rob
u
st
n
e
ss
un
de
r
i
n
put
v
o
l
t
a
ge
v
a
r
ia
t
i
o
n
s
a
nd
ste
p
l
oa
d
c
h
a
nges
.
T
h
e
t
h
e
o
ret
i
ca
l
pr
ed
ict
i
o
n
r
e
s
u
l
t
s
ar
e
val
i
d
at
ed
by
m
eans
of
s
im
u
l
a
t
ion
s
u
s
i
ng
p
r
ogram
M
a
tla
b
.
I
n
[11]
t
h
e
a
u
t
h
o
r
u
s
e
s
a
f
i
x
e
d
f
r
e
q
u
e
n
c
y
P
W
M
base
d
o
n
S
M
C
f
or
D
C/D
C
c
o
nver
t
er
s
o
p
e
r
at
in
g
in
t
he
c
o
n
t
i
n
u
o
u
s
c
ondu
c
t
i
o
n
mod
e
(
CCM
)
.
A
p
r
o
t
ot
y
p
e
f
o
r
the
sys
t
em
i
s
deve
lope
d
a
n
d
the
e
xpe
rime
nta
l
r
esu
l
t
s
v
a
l
i
d
a
t
e
t
h
e
d
es
ign
m
e
t
h
od
olo
gy.
I
n
th
is
p
a
p
e
r
a
fre
que
nc
y
resp
ons
e
m
e
th
o
d
i
s
use
d
t
o
inve
s
t
i
g
a
t
e
the
S
M
C
used
t
o
c
o
nt
ro
l
DC/
D
C
buc
k
co
nv
e
r
t
e
r,
a
n
d
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
H
i
g
h
pe
rform
a
nce
D
C
/D
C
bu
ck
conve
r
t
e
r us
in
g
sli
d
i
n
g m
ode
con
t
r
o
ll
e
r
(Mus
ta
f
a
A.
Fadel A
l
-Q
ai
s
i
)
1
807
perform
ance
o
f
the
co
n
t
ro
ller
is
a
ssess
by
u
s
i
n
g
t
h
e
gra
p
h
s
p
re
sen
t
e
d
b
y
the
po
lar
p
l
ot
,
root
l
ocus,
N
y
q
u
i
st
pl
ot
a
nd
b
o
d
e
p
l
o
t,
w
hic
h
o
bta
i
n
e
d
b
y
u
sin
g
t
he
M
a
tla
b
pr
o
g
ra
m
.
T
h
e
o
r
g
a
n
i
z
a
t
i
o
n
o
f
t
h
e
p
a
p
e
r
i
s
a
s
f
o
l
l
o
w
s
:
sect
io
n 1
the
in
tro
duc
t
i
on.
Se
ct
i
o
n
2
d
e
scri
b
e
s
t
h
e
mat
h
emat
i
cal
a
nd
s
ta
t
e
s
p
a
ce
m
od
el
i
n
g
o
f
D
C
/D
C
buc
k
c
o
nver
t
e
r
,
w
h
i
c
h
i
s
f
o
ll
o
w
ed
b
y
se
c
t
i
o
n
3
th
a
t
s
ho
ws
t
h
e
d
esign
of
t
he
S
M
C
f
or
t
h
e
DC/
D
C
bu
c
k
c
o
n
v
e
rt
e
r
.
S
e
ct
i
on
4
sh
ows
th
e
syste
m
m
ode
li
ng.
S
ect
io
n
5
t
h
e
s
i
mul
a
t
i
on
and
e
x
perim
e
n
t
al
r
e
s
u
l
t
s
a
r
e
p
r
es
ent
e
d
.
C
onc
l
u
si
on
s
are
re
p
o
r
ted
in sec
t
i
on 5.
2.
MATHE
M
A
T
ICAL AND
ST
ATE
SPACE
M
ODELING OF BUCK
C
ONVERT
ER
The
t
o
po
l
o
g
y
s
how
n
in
F
i
g
ur
e
b
e
l
o
w
,
i
s
use
d
i
n
or
der
to
g
e
t
t
he
d
if
f
e
re
nti
a
l
equ
a
tio
n
s
th
a
t
d
esc
r
ib
e
s
t
h
e
D
C
/
D
C
b
u
c
k
c
o
n
v
e
r
t
e
r
,
t
h
e
c
i
r
c
u
i
t
c
o
n
s
i
s
t
s
o
f
s
w
i
t
c
h
(
I
G
B
T
)
,
o
u
t
pu
t
fi
lt
er,
dio
d
e
a
nd
o
utpu
t
lo
ad
prese
n
t
e
d
by
r
e
sisti
v
e
lo
ad
(
r
L
),
t
he
d
ire
c
t
a
pp
l
i
c
a
t
i
on
o
f
t
he
K
i
r
ch
h
o
ff's
curr
ent
a
n
d
v
o
ltag
e
l
a
w
s
a
r
e
u
s
e
d
t
o
proc
ur
e
the
e
qua
tio
ns
t
hat
de
scri
be
t
he
d
y
n
am
ics
of
t
he
c
o
n
v
ert
er
f
o
r
e
a
c
h
p
o
s
si
bl
e
ci
rc
ui
t
top
o
l
ogy
(diffe
ren
t
i
a
l
e
q
uat
i
o
n
s
),
t
he
t
o
p
o
l
og
ies
ar
e
sh
ow
n
from
t
he
p
a
r
t
i
cu
lar
assu
m
e
d
sw
it
c
h
p
o
s
i
tio
n
func
tio
n
val
u
e
(
u
)
[12].
Th
us,
as
s
h
o
w
n
i
n
F
i
gure
1(b),
w
h
en
t
he
s
w
i
tc
h
pos
iti
on
e
xh
ib
i
t
a
t
u
=1
(
T
ON
),
t
h
e
t
op
ol
o
gy
congruous
to
t
he
non-
conducting
m
o
de
f
or
t
he
d
iode
g
ained
and
c
urre
nt
w
il
l
fl
ow
t
o
t
h
e
l
o
a
d
a
n
d
t
he
in
duc
ta
nce
L
w
il
l
s
t
art
to
s
t
o
re
m
a
gne
tic
e
ner
gy.
A
l
t
er
na
t
i
ve
l
y
,
a
s
s
h
o
w
n
i
n
Fi
gu
re
1
(c),
w
h
e
n
swit
ch
p
o
s
i
t
i
on
is
a
t
u
=0
(
T
OF
F
)
,
t
he
i
n
p
u
t
v
o
lta
ge
s
ource
w
i
l
l
be
d
i
s
c
onne
c
t
ed
a
n
d
t
he
i
nd
uc
t
or
w
i
ll
be
h
a
ve
a
s
a
s
ource
a
n
d
passes
the
st
ored
e
ner
gy
in i
t to t
he
l
oa
d [1
3]
.
F
i
gure
1.
(
a) Buck
co
n
v
erte
r c
i
r
c
u
i
t
str
u
ct
ur
e;
(
b) c
onverte
r
e
qu
i
v
a
l
e
n
t
c
irc
u
it d
u
r
i
ng
u
=1
(
T
ON
);
(c
)
conver
t
e
r
e
qui
va
l
e
n
t
c
irc
u
it d
u
r
i
n
g
u
=0
(
T
OFF
)
Th
e
ci
rc
uit
di
gram
s
h
o
w
n
i
n
u
pp
e
r
f
i
g
u
r
e
c
a
n
ma
th
e
m
a
t
i
c
al
ly
r
e
p
re
sen
t
ed
b
y
t
h
e
fo
l
l
ow
i
ng
gr
ou
p
o
f
equa
t
i
o
n
s [14]
:
V
uV
dt
di
L
i
L
(
1
)
i
i
dt
dv
C
L
O
(
2
)
Where
L
a
nd
C
i
s
the
i
n
d
u
c
t
a
n
ce
a
n
d
t
he
c
a
p
aci
ta
nce
of
t
he
o
u
t
p
u
t
f
i
l
te
r,
i
L
i
s
t
h
e
c
u
rrent
p
asses
t
h
ro
ugh
t
h
e
i
nd
u
c
to
r,
V
o
i
s
t
h
e
o
u
tp
ut
v
o
lta
g
e
(
i.
e.
s
am
e
as
c
a
p
aci
t
o
r
v
o
lta
ge
),
V
i
i
s
the
in
pu
t
v
o
l
t
a
g
e
pro
v
i
d
e
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
0
6
– 1
814
1
808
from
e
xt
e
r
na
l
vo
l
t
age
s
o
urc
e
(
D
C
volta
ge
s
ource
),
a
nd
u
i
s
the
sw
itc
h
p
o
s
iti
on
a
nd
pr
esen
ts
(
O
N
-
O
F
F
)
t
hat
con
t
ro
l
l
ed t
he
i
npu
t
si
gna
l
b
y
tak
i
ng d
i
scre
t
e
va
l
ue
s
o
f
1
(
swi
tc
h is O
N
)
a
nd 0
(sw
i
tc
h is O
F
F
)
[15].
L
o
o
r
V
i
(3
)
B
y
s
u
b
s
t
itu
ti
n
g
e
q
u
a
t
i
on
(
3
)
in
e
qua
tio
n
(2) and
r
e
w
r
ite
e
q
u
a
t
i
on
s
(
1
),
(
2)
i
n
t
h
e
s
t
a
t
e
e
q
uat
i
on
s
form
by ta
ke
i
L
a
nd
V
o as
t
he
sys
te
m
states,
the n
e
xt
s
t
a
te e
q
u
a
tions
a
re
gi
v
en
:
L
o
V
u
L
i
V
dt
L
di
(
4
)
C
L
r
o
V
C
L
i
dt
o
dV
(
5
)
By
u
sin
g
t
he
s
t
a
te
e
qua
t
i
ons (4)
a
nd
(5),
buck
con
v
er
t
e
r bl
o
c
k
dia
g
ram
c
a
n
be bui
l
d
a
s
show
n i
n
F
i
gur
e 2.
F
i
gure
2.
B
uc
k
conver
t
e
r
blo
c
k
d
ia
gra
m
u
sin
g
t
he
s
tate
e
q
u
a
ti
o
n
[
11]
3.
SLIDING
M
O
DE CONTRO
L
(
SMC)
H
e
nce
,
the
S
M
C
c
on
t
r
ol
ler
is des
ig
n in
t
w
o
p
arts, t
he firs
t
p
ar
t c
o
n
t
a
i
n t
h
e des
i
gn
of a s
l
i
d
i
ng
su
r
fac
e
in
o
rder
t
o
m
a
ke
t
he
s
l
i
d
i
n
g
m
o
ti
on
t
o
b
e
c
o
n
t
e
n
t
w
i
t
h
t
h
e
d
es
i
g
n
f
ea
tur
e
s.
T
he
s
ec
on
d
part
i
s
t
h
e
part
t
ha
t
dea
l
s
w
i
t
h
t
he
c
hose
n
o
f
a
c
o
n
t
ro
l
r
u
l
e
m
a
k
es
t
he
s
w
i
tc
h
i
n
g
s
ur
fac
e
en
ga
gi
ng
t
o
sta
t
e
o
f
t
he
s
ystem
.
T
he
w
o
rki
n
g
pr
in
c
i
pl
e
o
f
S
M
C
i
s
to
i
mp
ose
t
h
e
s
t
ate
o
f
t
he
s
ys
te
m
t
o
be
s
t
a
b
l
e
for
a
n
y
val
u
es
o
f
i
n
itia
l
c
o
nd
it
ion
b
y
d
r
iv
ing
th
e
st
at
es
o
f
t
h
e
s
y
st
e
m
u
pon
a
s
p
e
c
i
al
s
u
r
f
ace
i
n
t
he
s
ta
te
s
pa
ce,
w
hic
h
know
n
a
s
t
he
s
l
i
di
ng
s
u
r
f
a
c
e
i
.
e
.
f
o
r
a
n
y
d
i
s
t
u
r
b
a
n
c
e
s
i
n
t
h
e
s
y
s
t
e
m
f
o
r
a
n
y
r
e
a
s
o
n
,
t
he
s
ta
tes
of
t
he
s
ys
t
e
m
i
s
c
oe
rci
v
e
to
g
o
b
a
c
k
t
o
lin
e
(
S
=
0
)
an
d
ho
l
d
ing
t
h
e sl
i
d
in
g
mo
d
e
f
u
n
c
ti
on
(
S
)
t
o
z
ero.
A
t the
t
i
m
e
tha
t
t
he
s
l
i
di
n
g
sur
fac
e
is
a
t
t
a
ine
d
,
the c
o
ntr
o
lle
r
r
e
tai
n
the sta
tes
on t
h
e
c
l
ose
p
r
ox
im
i
t
y of the
sli
d
in
g
su
rfa
ce,
t
h
e
s
l
i
di
ng
s
urf
a
c
e
i
s
d
e
s
cri
b
ed
by
(
S
=0) [16
]
.
F
o
r
i
n
f
i
n
i
t
e
r
a
p
i
d
s
w
i
t
c
h
i
n
g
s
t
a
t
e
,
t
h
e
s
y
s
t
e
m
w
i
l
l
m
a
k
e
m
o
v
e
m
e
n
t
ove
r
the
line
a
f
ter
se
ve
ral
r
e
s
t
r
i
c
t
e
d
t
i
m
e
,
t
h
i
s
m
o
v
e
m
e
n
t
k
n
o
w
n
a
s
s
l
i
d
i
n
g
m
o
d
e
a
n
d
t
h
i
s
p
re
se
nt
e
d
t
he
i
dea
l
m
o
tio
n
of
t
he
s
ys
te
m
.
T
he
sy
st
em
s
t
a
t
e
i
s
ON
&
O
F
F
st
at
e
of
s
wit
c
h
of
t
h
e
b
u
c
k
conv
ert
e
r.
F
igure
3
sh
ow
s
t
h
e
b
l
ock
di
agra
m
o
f
S
MC
con
t
ro
l
l
ed
buc
k
c
o
n
v
erter
.
I
f
the
sw
itch
is
i
n
O
N
c
o
n
d
it
io
n,
t
h
e
s
l
i
d
i
n
g
f
u
n
c
t
i
o
n
w
i
l
l
b
e
g
r
e
a
t
e
r
t
h
a
n
z
e
r
o
(
S
>
0)
a
nd
t
h
e
sw
it
c
h
i
s
in
O
F
F
c
on
dit
i
o
n
(
S
<
0
)
[17,
18].
The
sl
i
d
i
n
g
m
o
d
e
s
ca
n
be
t
heor
e
t
ic
a
l
ly
d
e
s
cri
b
e
d
by
the
sys
t
em
s
t
a
ys
c
l
o
se
d
t
o
t
h
e
s
lid
in
g
sur
f
a
c
e
a
nd
nee
d
o
n
l
y
be
v
iew
e
d
a
s
s
l
i
d
i
ng
a
l
on
g
the
s
u
rfa
ce.
I
n
sli
d
in
g
con
t
ro
l
m
ode,
there
are
tw
o
m
odes
t
h
e
rea
c
hi
n
g
m
ode
a
n
d
t
he
e
xi
s
t
ing
mode
.
D
u
r
i
ng
t
h
e
be
gi
n
n
i
n
g
(in
itia
l
pha
se)
the
s
y
s
t
e
m
canno
t
g
o
e
s
t
o
the
sw
itc
h
i
n
g
s
urfa
ce
(
i.e
.
a
t
S
=
0
),
b
e
c
a
u
s
e
of
t
h
a
t
a
c
o
nt
rol
ai
me
d
ac
ro
ss
the s
l
id
ing s
u
rfac
e
i
s k
n
o
w
n
a
s the r
eac
h
i
ng
mode
. A
fter
th
a
t t
he s
yst
e
m g
a
in
ing
t
h
e r
eac
hin
g
mode
it m
u
s
t
be
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
H
i
g
h
pe
rform
a
nce
D
C
/D
C
bu
ck
conve
r
t
e
r us
in
g
sli
d
i
n
g m
ode
con
t
r
o
ll
e
r
(Mus
ta
f
a
A.
Fadel A
l
-Q
ai
s
i
)
1
809
st
a
b
le i
n tha
t
c
on
d
iti
on
(
S
=
0) th
i
s na
me
d as
the
e
xi
s
t
in
g m
o
de,
t
hi
s
mode
i
s ca
lle
d
sl
idi
n
g
m
ode
[
1
8
].
F
igure
4
show
s t
h
e tw
o
mode
s of
v
ar
ia
ble
co
ns
truc
t
i
o
n
con
tro
l
sys
te
m
.
F
i
gur
e 3.
Bl
o
c
k
sc
h
e
m
e
of bu
c
k
con
v
er
t
e
r
F
i
gure
4.
T
he
m
ode
s
of
S
MC
s
ys
tem
controll
ed by
SMC [
1
0
]
.
A
s
a
n
exa
m
p
l
e
F
i
gur
e
4
d
i
s
p
la
y
t
h
e
tra
j
e
c
t
or
y
o
f
a
s
yste
m
under
S
M
C
.
Aft
e
r
t
h
e
in
iti
al
r
e
a
c
h
i
ng
pha
se,
t
h
e s
y
st
em
sta
t
e
s
"sl
id
e
s
"
al
on
g t
h
e
line
(
S
=
0
)
.
The
c
e
r
tai
n
(
S
=
0
) sur
f
ac
e
i
s
c
ho
se
n due
t
o h
i
s c
a
p
ab
i
lit
y
to
m
in
i
m
ize
or
de
r
dy
n
a
m
i
c
s
w
he
n
c
o
mpe
l
e
d
t
o
i
t
.
I
n
t
h
i
s
sit
u
a
t
i
on
,
S=x
1
+x
֗
1
w
il
l
be
e
q
u
al
t
o
ze
ro,
the
su
r
f
ac
e
tha
t
m
atche
s
t
o
the
firs
t
order
sys
t
em
x
֗
1
=
(
-
x
1
), w
hic
h
has
a
n e
x
p
o
n
en
t
i
a
l
l
y
s
ta
ble
ori
g
i
n
.
4.
SYS
T
E
M
M
ODELLING
F
i
gure
5
s
h
ow
s
the
sc
hem
a
t
i
c
d
iagra
m
o
f
t
h
e
P
W
M
base
d
P
I
D
S
M
V
C
co
nve
r
t
ers,
a
s
me
ntio
n
e
d
befor
e
a
m
a
t
he
ma
ti
c
a
l
m
ode
l
of
t
he
buc
k
c
onve
r
t
er
i
s
de
ri
ve
d
in
p
re
vio
u
s
s
ec
ti
on
o
f
th
i
s
p
a
p
e
r
u
si
ng
t
he
l
a
w
s
of
c
ircu
it
a
na
lys
i
s.
T
he
buc
k
con
v
er
ter
is
l
oa
d
e
d
w
i
t
h
r
e
s
i
s
ti
v
e
loa
d
(
r
L
)
,
a
nd
t
h
e
ou
t
p
ut
v
ol
t
a
ge
(
V
o
)
of
t
he
con
v
er
t
e
r
co
n
t
rol
l
ed
by
S
M
C.
A
ssum
ed
t
hat
t
h
e
c
o
nver
t
er
t
o
be
o
per
a
ted
in
C
CM.
F
o
r
the
ca
se
o
f
PWM
base
d
on P
I
D S
M
V
C
c
on
ver
t
e
r
s,
t
he c
on
t
r
o
l
v
aria
ble
x
c
a
n
be
prese
n
t
e
d i
n
the
f
orm
:
o
V
ref
V
x
1
(
6
)
dt
LC
u
V
V
C
r
V
x
x
i
o
L
o
)
(
1
2
(
7
)
dt
V
V
dt
x
x
o
ref
)
(
1
3
(
8
)
F
i
gure
5.
Comple
t
e
schem
a
t
i
c
di
a
g
ram
of t
h
e
S
MV
C conv
e
r
ters
[
10
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
0
6
– 1
814
1
810
Wh
e
r
e
t
h
e
v
a
ria
b
l
e
s
x
1
,
x
2
a
n
d
x
3
r
e
p
r
e
sen
t
t
he
v
o
lta
ge
e
rr
or
,
the
ra
te
o
f
c
h
a
nge
o
f
t
h
e
vol
ta
ge
e
rror
,
and the
i
n
tegra
l
o
f v
o
ltage
e
rror [1
9].
Where
β=
R
2
/(
R
1
+
R
2
),
i
s the
vo
l
t
a
g
e div
i
der
ra
tio [1
1
].
T
he des
i
gn of th
e
buc
k c
o
nver
t
er
c
o
n
tr
ol
ler
nee
d
s
sta
t
e spa
ce
descr
i
pt
i
o
n
s
, w
h
i
c
h
a
s
fo
llow
[2
0]
:
0
0
0
0
0
0
1
0
1
0
0
1
0
3
2
3
2
1
1
LC
o
V
u
LC
i
V
x
x
x
C
L
r
x
x
x
(
9
)
Aft
e
r
h
a
vi
ng
t
h
e
s
t
a
te
s
p
a
ce
c
h
a
ra
c
t
e
r
i
zati
o
n
,
n
o
w
t
h
e
f
ollo
wi
n
g
sta
g
e
is
t
he
c
on
t
r
oller
des
i
g
n
.
F
o
r
th
i
s
s
ys
t
e
m,
i
t
’
s
sui
t
a
b
le
t
o
ha
ve
a
u
nive
rsal
S
MC
co
n
t
ro
l
rule
t
h
a
t
e
m
b
r
ace
a
s
wi
t
c
h
ing
f
un
ct
ion
(
S
)
such
a
s
u
=0
(
w
h
e
n
S
<0
)
and
u
=1(w
he
n
S
>0
), W
h
e
re
S
is t
h
e
i
m
m
e
diate
sta
t
e
va
r
i
a
b
le’s r
ou
t
e
,
and c
a
n
be w
r
i
tte
n
as
:
x
J
x
x
x
S
T
3
3
2
2
1
1
(
1
0
)
3
2
1
T
J
(
1
1
)
Wh
ere
α
1
,
α
2
and
α
3
r
ep
re
se
n
tin
g
t
h
e
c
o
n
t
ro
l
p
a
ra
me
t
e
rs
t
e
r
me
d
a
s
s
l
i
din
g
co
ef
fi
c
i
en
t
s
.
Ho
we
v
e
r,
w
h
en
t
he
s
ys
te
m
r
eac
hes
t
h
e
s
tea
d
y
s
t
a
t
e,
act
ua
ll
y
it
be
c
o
me
s
a
f
ix
ed
poi
nt
,
t
h
a
t
’s
l
ea
d
s
t
o
re
mo
vi
ng
th
e
in
t
e
gral
c
on
tro
l
.
The
co
n
t
ro
l
si
gna
l
(
v
C
)
the
n
r
e
duce
d
t
o
P
W
M
P
D
l
i
n
e
a
r
con
t
ro
l
l
er
f
or
m
,
a
nd
the
for
m
ul
a
bec
a
m
e
:
)
(
2
1
o
ref
c
c
V
V
K
i
K
v
(
1
2
)
Whe
r
e
K
1
a
nd
K
2
c
an
b
e
f
ound
f
ro
m:
C
r
L
K
L
1
2
1
1
(
1
3
)
2
3
2
LC
K
(
1
4
)
K
1
,
K
2
a
re
t
he gai
n
c
o
nsta
n
t
f
or
t
he fee
db
a
c
k
s
igna
l
s
,
a
n
d
t
h
eir va
lu
es
can
b
e
d
e
t
e
rmi
n
ed
i
n
t
h
e
t
e
rms
of
c
onve
r
t
er
c
ompo
ne
nt
L
,
C
a
n
d
r
L
a
n
d
v
a
lu
e
s
o
f
s
lid
ing
p
aramet
ers
α
1
,
α
2
,
and
α
3
.
The
sl
id
ing
c
o
e
f
fic
i
e
n
ts
ca
n be
f
o
u
nd b
y
put
ti
n
g
S
=0
,
a
nd com
p
ar
e t
h
i
s
e
qu
a
t
i
o
n
w
ith
s
ta
n
d
a
r
d
se
c
o
n
d
or
d
er
s
ys
te
m
form [21,
22
]
:
0
1
3
2
2
1
1
x
dt
dx
x
(
1
5
)
0
1
3
2
2
1
1
x
dt
dx
x
(
1
6
)
W
h
ere:
2
3
n
w
,
is
t
he un
d
a
m
pe
d na
tu
ra
l
fre
que
ncy,
3
2
1
2
, is the
dam
p
in
g
ra
t
i
o,
2
3
2
n
Bw
w
f
, is
t
h
e
con
t
ro
ll
er’
s
re
s
ponse
b
a
ndw
id
t
h
.
Bw
f
4
2
1
,
and
2
2
2
3
4
Bw
f
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
H
i
g
h
pe
rform
a
nce
D
C
/D
C
bu
ck
conve
r
t
e
r us
in
g
sli
d
i
n
g m
ode
con
t
r
o
ll
e
r
(Mus
ta
f
a
A.
Fadel A
l
-Q
ai
s
i
)
1
811
Usi
n
g
f
Bw
=2
K
H
z
,
c
onseq
u
e
nt
l
y
t
he
d
es
ign
o
f
t
he
s
lid
in
g
c
o
ef
ficie
n
t
is
n
ow
c
ou
n
t
on
o
n
t
he
ban
d
w
i
d
t
h
o
f
t
he
r
e
q
u
i
red
fre
qu
e
n
cy
r
es
p
onse
o
n
c
oup
l
i
n
g
w
i
t
h
t
he
s
ta
bi
lit
y
pro
v
i
s
ion
[2
3].
N
o
w
by
su
bs
tit
ut
i
n
g
th
e v
a
l
u
e
of
f
Bw
we
g
e
t
:
25120
=
)
10
*
(2
4
3
2
1
a
nd
157753600
=
)
10
*
(2
4
2
3
2
2
3
The
refere
nce
vo
lta
g
e
i
s se
t
as
V
re
f
=5V,
and
V
o
=
2
4
V
c
o
rre
s
p
ondi
n
g
to
V
in
=4
8
V
wh
i
ch
g
iv
es:
2083334
.
0
o
ref
V
V
Th
e
st
at
e
of
t
he
c
on
v
e
rt
er
i
n
wh
i
c
h
t
h
e
i
L
n
ev
e
r
r
ea
c
h
es
zero
fo
r
a
n
y
p
e
ri
od
o
f
t
i
me
i
s
c
a
l
l
e
d
th
e
CCM.
There
f
o
r
e
the filter
L
a
nd
C
t
akes
a
p
p
r
ox
ima
t
el
y t
h
e
fo
llow
i
n
g
va
l
u
e
s:
f
r
D
L
L
2
)
1
(
.)
(min
(
1
7
)
2
.)
(min
8
)
1
(
Lf
V
V
D
C
r
o
(
1
8
)
Where
D
i
s
t
h
e
du
ty
c
yc
l
e
a
nd
e
qua
l
t
o
D
=
0
.
5
,
r
L
=
1
0
Ω
(
m
a
xim
u
m
loa
d
r
esis
ta
nce
)
,
f
=
2
0
k
H
z
,
(
V
r
/
V
o
)
=
1%
. The bo
u
ndar
y
(
L
(
mi
n
.
)
= 125µH).
F
or
(
L
>
L
(min.)
), the c
on
verte
r
o
per
a
tes
in
t
h
e
(C
C
M
)
. A
va
l
ue
of
(14
0
µ
H
)
is
c
hose
n
,
the
c
u
rrent
p
a
s
s
i
n
g
i
n
t
h
e
i
n
d
u
c
t
or
f
i
l
t
e
r
(
i
L
)
is
i
n
the
CCM
a
nd
hav
i
n
g
t
w
o
c
om
p
one
n
t
s
the
first
is
D
C
c
o
mpo
n
e
n
t
(
I
o
)
w
ith
a
n
ac
c
o
m
pone
n
t
f
l
o
w
s
t
hr
ou
g
h
t
he
f
i
l
t
er
c
a
p
ac
i
t
or
C
a
s
ca
p
aci
t
o
r
c
u
rren
t
I
c
c
om
pose
of
a
t
ria
n
g
u
l
ar,
t
h
i
s
c
ur
rent
i
s
t
h
e
re
as
on
o
f
t
h
e
ri
p
pl
e
a
ppe
a
r
s
in
t
he
o
u
t
p
u
t
vo
l
t
age
fr
o
m
t
he
con
v
er
t
e
r.
T
o r
e
duc
e
t
h
e
pea
k
-to-pea
k
ri
p
p
l
e
va
lue be
low
a
ce
rt
ai
n
va
lue
(
V
r
),
t
he
c
apacitor
of
f
i
l
ter
s
h
ould be
mor
e
t
ha
n t
h
e
minimum
c
a
pa
c
i
t
a
nce
is
e
q
u
a
l
t
o
(1
25µ
F
)
.
In th
i
s
pa
per
a
value
o
f
(
25
0
µ
F
)
is c
hosen [
24]
.
A
c
c
o
rdi
n
g
to t
he
a
bo
ve
v
a
l
u
e
s,
t
he
im
p
l
e
me
nte
d
c
o
n
tr
ol
s
i
gna
l
(
v
C
) e
quat
i
o
n
i
s
:
V
V
V
i
v
o
ref
c
c
)
(
4.9298
-0.6433
5.
SIMU
L
A
TION
R
ESULT
S
AN
D
DIS
CUSS
ION
The
fo
llow
i
n
g
ste
p
s
i
llus
t
ra
t
e
d
t
h
e
sim
u
la
t
i
o
n
p
roce
dur
e
t
h
at
e
xe
cute
d
us
i
ng
t
h
e
s
o
ftw
a
re
(Mat
lab
/
S
i
m
u
li
nk
2
0
1
6
-b)
pr
ogram
m
a
ble
a
nd
the
d
i
sc
ussio
n
f
or
t
h
e
r
e
sults
i
s
s
how
n,
T
a
b
l
e
1
s
ho
w
s
t
he
val
u
es
o
f
t
h
e
c
o
m
p
o
n
e
n
t
s
a
nd
par
a
m
e
ters
o
f
buc
k
c
o
nve
rt
er
b
ase
d
o
n
S
M
C
c
ont
rol
l
e
r.
F
i
g
u
r
e
6
shows
t
h
e
Ma
tla
b
/
S
i
mul
i
nk
pro
g
ram
for
the
mode
li
n
g
of
D
C
/
D
C
b
u
c
k
c
o
nver
t
e
r
b
a
sed
o
n
S
M
C
;
the
pr
ogr
am
s
truc
t
u
re
c
o
nsi
s
t
s
o
f
the
e
q
u
a
ti
on
on
e
a
c
h
of
t
h
r
ee
p
o
ssi
bl
e
ope
rat
i
n
g
st
a
g
es.
The
defa
ult
va
l
u
es
o
f
c
o
n
v
er
ter
para
me
ters; the
inpu
t
vol
ta
ge
(
V
in
)
,
t
he
in
d
u
ct
anc
e
va
l
ue
,
t
h
e
ca
pac
itor
val
u
e,
and
t
h
e
lo
ad
v
al
u
e
r
L
.
Tabl
e
2
sho
w
s
t
h
e
out
put
v
o
l
t
a
g
e
(
V
o
)
a
nd
out
pu
t
cur
r
en
t
(I
o
)
results
o
f
the
DC
/
DC
b
uc
k
co
nve
r
t
e
r
f
o
r
di
ffe
rent
v
al
u
e
s
of
o
u
t
pu
t
l
o
ad
(
r
L
),
w
hic
h
c
o
n
form
ed
t
ha
t
the
s
y
s
t
em
unde
r
S
M
C
n
o
t
o
r
l
ess
a
f
fec
t
e
d
by
the
c
h
a
n
gi
ng
o
n
t
he
o
u
t
p
u
t
l
o
a
d
r
e
sista
n
c
e
.
F
i
gure
7
a
n
d
8
sh
ow
s
t
h
e
P
W
M
sig
n
a
l
a
t
the
ga
te
o
f
t
h
e
IG
B
T
sw
it
c
h
an
d
t
he
c
urrent
p
ass t
h
rou
gh t
h
e
ca
p
a
cit
o
r
I
c
w
hen
the
sys
t
em
cont
rol
l
ed
b
y
S
M
C
.
Tabl
e 1. S
pecificati
o
n
s
of
th
e propo
sed
sy
s
t
em
P
a
r
a
m
e
t
e
r
D
e
s
c
ription
N
o
m
i
n
a
l Va
lu
e
V
in
I
n
p
u
t volt
a
ge
48 V
V
o
De
sir
e
d output vol
t
a
g
e
12 V
f
S
w
i
t
c
h
ing F
r
e
que
n
c
y for B
u
c
k
C
on
ve
rte
r
20 kH
z
L
Ind
u
c
t
a
n
ce
140 µH
C
C
a
p
a
c
i
t
a
n
c
e
250 µF
r
Lm
i
n
M
i
n
i
mu
m
l
o
ad
r
es
i
s
t
a
n
c
e
1
Ω
r
Lmax
Ma
xim
u
m
lo
a
d
re
s
i
s
ta
n
c
e
10 Ω
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
0
6
– 1
814
1
812
F
i
g
u
r
e
6.
Mo
d
e
li
n
g
of
D
C
/
D
C b
u
c
k
c
on
ve
rt
er
b
ased
on S
M
C usi
n
g m
a
t
la
b
/
s
i
m
u
lin
k
Tab
l
e
2.
S
imula
t
i
o
n r
e
sul
t
s
of the
s
yste
m
r
L
(O
h
m
)
V
o
(V
olt)
I
o
(A
m
p
e
r
)
1
22.96
22.97
2
23.59
11.86
3
23.61
6
.947
4
23.61
5
.122
5
23.61
4
.64
6
23.61
3
.956
7
23.61
3
.39
8
23.61
2
.967
9
23.58
2
.629
10
23.46
2
.44
F
i
gure
7.
IG
B
T
gate si
gna
l
o
f
t
he
D
C
/
D
C
b
uck
co
nv
e
r
t
e
r
F
i
gure
8.
Capa
c
i
t
o
r
curr
ent si
gna
l
I
c
F
i
gures
9
a
n
d
10
s
h
ow
s
t
h
e
out
pu
t
vo
l
t
age
si
g
n
a
l
V
o
a
nd
cu
rren
t
I
o
f
or
t
he
b
uc
k
c
o
nv
e
r
ter
sy
stem
con
t
ro
l
l
ed
b
y
S
M
C
w
i
t
h
i
n
put
v
ol
t
a
ge
V
in
=
48V
a
nd
r
L
=
6
Ω
of
o
u
t
p
u
t
l
o
ad
r
esista
nc
e
(r
esisti
ve
l
oa
d)
,
whic
h
gi
ves o
u
t
p
u
t
v
olta
ge
V
o
=
23.
61 V
(w
ith ver
y low
v
o
l
t
a
g
e
rip
p
l
e
)
a
nd o
u
t
p
ut cur
ren
t
I
o
=
3.95
A
.
The
sys
t
e
m
s
te
p
respo
n
se
u
nde
r
S
M
C
c
o
nt
r
o
l
i
s
s
h
o
w
n
i
n
F
i
gure
1
1
.
T
he
c
o
n
t
r
ol
l
e
r
in
t
hi
s
sy
st
em
elimi
n
a
t
e
d
o
ve
rsho
o
t
,
stea
d
y
s
ta
te
e
rror
a
n
d
de
cre
a
si
ng
t
he
s
e
t
tl
i
n
g
t
i
me
(
i
.
e.
t
he
s
ys
tem
rea
c
h
to
t
he
s
ta
bi
l
i
t
y
fa
ste
r
w
i
t
h
se
ttli
n
g
t
im
e
e
qua
l
t
o
(
0.98
4
S
e
c
)
.
F
i
gure
1
2
s
h
o
ws
t
he
N
y
q
u
i
s
t
di
a
g
ram
of
t
he
p
r
o
p
o
se
d
s
y
ste
m
wi
t
h
S
MC
c
ont
rol
l
e
r.
A
s
sh
own
in
t
h
e
f
i
gure,
t
h
e
p
oin
t
(-1+
0
j
)
ou
ts
i
d
e
t
h
e
reg
i
on
e
nc
l
o
se
d
by
t
he
N
yq
u
i
st
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
H
i
g
h
pe
rform
a
nce
D
C
/D
C
bu
ck
conve
r
t
e
r us
in
g
sli
d
i
n
g m
ode
con
t
r
o
ll
e
r
(Mus
ta
f
a
A.
Fadel A
l
-Q
ai
s
i
)
1
813
pl
ot,
w
h
ic
h
i
n
di
c
a
t
es
t
ha
t
the
sys
t
e
m
i
s
s
t
ab
le.
F
i
g
u
re
1
3
s
how
s
th
e
root
l
o
c
u
s
o
f
t
h
e
syst
e
m
w
it
h
cont
ro
l
l
e
r.
N
o
p
ole
s
o
r
ze
ros
o
f
t
he
s
ys
te
m
lies
on
r
i
g
h
t
-ha
l
f
of
S
-p
la
ne
,
a
l
s
o
t
he
b
e
h
a
v
ior
of
t
he
R
oo
ts
L
oc
us
i
nd
i
c
a
t
es
tha
t
t
he
s
y
s
te
m
i
s
s
t
a
b
l
e.
F
igure
14
sh
ow
s
the
b
o
d
e
-
plo
t
o
f
t
h
e
s
yst
e
m
w
i
t
h
S
MC
c
o
n
t
r
o
l
l
e
r
t
he
p
ha
se
a
n
d
ma
gni
tude
g
ra
p
h
s
i
n
d
i
ca
tes
t
h
at t
he
sys
t
e
m
is
s
t
a
ble.
F
i
gure
9.
B
uc
k
conve
r
t
er
outp
u
t v
o
lta
ge
V
o
F
i
gure
1
0
.
Buc
k
con
ve
rter
o
u
t
pu
t c
u
rre
nt
I
o
F
i
gure
11.
S
t
e
p r
e
sponse o
f
th
e
system
w
ith t
he
S
MC
F
igure
1
2
.
N
yquist
d
ia
g
r
am
of
the sys
t
em
w
ith S
MC
F
i
gure
1
3
.
Roo
t
loc
us
o
f the
s
y
ste
m
w
i
t
h
S
M
C
F
i
gure
1
4
. The
bod
e
p
l
o
t
o
f t
h
e
syste
m
w
it
h
SMC
6.
CONCL
U
S
IONS
The
pr
esen
t
w
o
rk
i
nve
s
tig
ate
d
t
he
p
er
form
ance
o
f
SM
C
con
t
ro
l
l
er
f
or
D
C/D
C
buc
k
c
o
n
v
erter
b
y
tu
nin
g
t
he
va
l
u
e
s of th
e
ga
i
n vec
t
or
K
a
s
s
h
ow
n in t
a
b
l
e
1.
Rega
r
d
in
g t
h
e
sim
u
l
a
tio
n res
u
l
t
s ob
ta
ine
d
from
the
sy
st
em
o
f
bu
ck
c
onv
e
r
t
e
r
(
t
a
b
l
e
2
)
c
o
n
f
i
r
m
e
d
t
h
a
t
t
h
e
S
M
C
c
o
n
t
r
o
lle
r
is
a
r
ob
us
t
c
o
n
t
ro
l
l
e
r
a
ga
inst
l
oa
d
cha
nge
s
a
n
d
it
s
tro
n
g
l
y
less
sens
iti
ve
t
o
d
i
stur
bance
s
l
i
k
e
pow
er
s
up
p
l
y
var
i
a
t
i
o
ns.
S
m
oot
h
o
u
t
p
ut
v
o
l
tag
e
respo
n
se
o
bser
ved
w
i
th
z
ero
e
rror
stea
dy
s
t
a
te
a
n
d
goe
s
to
s
ta
b
i
l
i
t
y
f
a
s
t
e
r
.
T
h
e
s
t
e
p
r
e
s
p
o
n
s
e
,
r
o
o
t
l
o
c
u
s
,
ny
q
u
ist d
i
a
g
r
a
m
and
bode
p
l
o
t f
i
gur
es c
onf
ir
me
d the
sta
b
il
ity
o
f
t
h
e syst
e
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
1
8
0
6
– 1
814
1
814
ACKNOW
LEDG
M
E
N
T
The
au
t
hors
w
o
u
l
d
l
i
k
e
t
o
tha
n
k
t
h
e
I
r
aqi
g
over
n
me
n
t
r
epre
sente
d
by
t
h
e
m
i
n
i
stry
o
f
h
i
gher
educ
a
t
i
o
n
a
n
d
scie
nt
ific
r
esea
rch,
M
us
ta
ns
iriya
h
U
nive
rsi
t
y
(w
w
w
.
uomusta
nsir
iya
h
.
e
d
u
.
iq)
Ba
g
hda
d
–
I
r
aq
for
its
s
up
p
o
rt
i
n
the pr
ese
n
t wor
k
.
REFE
RENCES
[1]
G.
R
a
m
,
et
a
l
.
,
"Revi
e
w
o
f
S
li
d
i
ng
Mo
de
O
bs
ervers
f
o
r
S
ens
o
rless
Cont
ro
l
o
f
P
erm
a
n
e
nt
M
ag
net
S
y
n
c
h
r
on
ou
s
Motor
Dr
ives",
Inter
n
a
t
i
onal Jo
urn
a
l
o
f
Po
wer El
ectr
o
n
i
cs an
d Dr
ive Sys
t
em
(
I
JPEDS)
,
vol.
9,
n
o
.
1
,
p
p
.
4
6
-5
4,
20
18
.
[2]
A.
O
ma
r
i
,
et
al.
,
"
d
SP
ACE
DS
11
04
B
a
s
e
d
R
ea
l
Time
I
m
p
lement
ati
o
n
of
S
lidin
g
M
o
d
e
C
on
trol
o
f
In
du
c
tion
Motor"
,
In
t
e
rna
t
i
o
n
a
l Jou
r
na
l
o
f
Po
wer
El
ectr
o
n
i
cs
an
d Drive
Sys
t
em (IJPED
S
)
,
vol
.
9
,
n
o.
2
,
p
p
.
5
4
6-55
8,
201
8.
[3]
A
.
O
m
a
ri
,
et
a
l
.
,
"Ad
a
pti
v
e
fu
zzy sli
d
i
ng
m
od
e
b
a
sed M
PPT
c
o
n
tro
l
l
e
r
f
o
r a
ph
ot
o
v
ol
ta
ic water pum
pin
g
system
"
,
In
ter
n
a
t
io
nal Jour
na
l o
f
P
o
wer
El
ectr
o
n
i
cs
and
Dr
ive S
y
st
em
(
I
JP
EDS)
,
v
o
l.
10,
n
o.
1
,
p
p
.
4
1
4
-422,
2
0
1
9
.
[4]
Z.
B
ou
dr
ie
s,
et al
.
,
"S
tu
dy
o
n
sli
d
in
g
mo
de
v
i
r
tual
f
l
ux
ori
e
nte
d
c
o
n
tro
l
f
or
t
hre
e-ph
ase
PW
M
recti
f
iers",
Rev.
R
o
u
m
.
Sci.
T
echn
.
– É
l
ect
rotechn
.
et
Én
erg,
vol.
6
1
,
n
o
.
2
,
p
p
.
153-15
8,
201
6.
[5]
N.
M
oh
se
ni
fa
r
,
et
a
l
.
, "Imp
r
ov
ed cas
cad
e s
l
i
d
in
g m
ode f
or p
o
w
er con
trol
i
n
a mi
crog
r
id
"
,
R
ev.
R
oum.
S
c
i.
T
echn.
–
É
l
ect
rotechn
.
e
t
Én
erg
,
vo
l.
61,
no.
4
,
p
p
.
430
-435,
201
6.
[6]
Y.
L
i,
et
a
l
.
,
"
S
lid
i
ng
M
od
e
Co
ntro
lle
r
De
sig
n
f
or
N
o
n
line
a
r
S
y
s
te
m
s
w
i
t
h
Ma
t
c
hi
ng
P
e
rtu
r
bati
on
ss
"
,
Th
e
9
t
h
Internat
ional Conf
erenc
e
on Modelling,
Ident
i
fica
tion
and
Contro
l
(
I
C
M
IC
)
,
p
p
.
506-5
10,
2
0
1
7
.
[7]
A
.
B
ou
cheta,
et
al.
,
"
F
u
zzy-sl
i
din
g
m
od
e
co
nt
roller
f
o
r
li
near
i
n
d
u
c
tio
n
m
o
t
o
r
con
trol",
Rev.
R
oum.
Sci.
T
echn.
–
É
l
ect
rotechn
.
e
t
Én
erg
,
v
o
l
.
54,
no.
4
,
p
p
.
405
-414,
200
9.
[8]
M
.
A
djo
udj,
et a
l
.
,
"
S
liding
m
o
de
c
ont
rol
of
a
d
o
u
bl
y
f
e
d
ind
u
c
t
io
n
generat
o
r
fo
r
w
ind
tur
b
ines",
Rev. Rou
m
. Sci.
T
ech
n. –
É
l
ectro
t
echn
.
et Én
e
r
g
,
vo
l.
56,
n
o
.
1
,
pp.
1
5-2
4
,
201
1.
[9]
A
.
K
erbo
ua,
M.
A
b
i
d
,
"
Hy
bri
d
f
uzzy
s
lidin
g
m
o
d
e
c
o
n
tro
l
o
f
a
do
u
b
l
y
f
ed
i
nd
uctio
n
gen
e
ra
t
o
r
in
w
ind
turbines",
R
ev. R
o
u
m
. S
c
i. T
e
c
h
n.
–Électr
o
techn
.
et Éner
g
,
v
o
l.
57
, n
o.
4,
p
p
.
4
1
2
-4
2
1
, 20
1
2
.
[10]
H
.
G
u
l
demi
r,
"
S
t
u
dy
of
s
liding
m
o
de
c
o
n
t
r
ol
o
f
DC-DC
bu
ck
c
o
n
v
e
rter
"
,
Ener
gy
an
d P
o
wer
En
gi
neeri
n
g
,
vo
l
.
3
,
p
p
.
40
1-40
6,
2011
.
[11]
S
.
T
a
n
,
Y
.
M
.
L
a
i
,
"
A
u
n
i
f
i
e
d
a
p
p
r
o
a
c
h
t
o
t
h
e
d
e
s
i
g
n
o
f
P
W
M
-
b
a
s
ed
s
l
i
di
ng
-mod
e
vol
tag
e
c
on
t
r
ol
lers
f
o
r
b
as
ic
D
C
-DC
co
nv
erters
i
n
cont
in
uo
u
s
c
on
du
ctio
n
mo
de",
IEEE Tra
n
s
ac
tio
n
s
on
c
i
r
c
uits an
d sy
ste
m
,
vo
l.
53,
n
o.
8
,
20
06
.
[12]
C.
A
nd
re
s,
R
.
L
e
yv
a
,
"
M
a
t
la
b:
a
s
yste
m
s
t
o
o
l
fo
r
de
sig
n
o
f
f
uz
z
y
L
M
I
c
o
n
t
r
o
l
l
e
r
i
n
D
C
-
D
C
c
o
n
v
e
r
t
e
r
s
"
,
Rovira I
V
i
r
g
ili
univer
sit
y
T
a
rra
go
na
,
20
1
1
.
[13]
K
.
S
aad,
et a
l
.
,
"
S
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
a
n
d
f
u
z
z
y
s
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
f
o
r
D
C
-
D
C
conv
e
r
ter",
National
E
n
g
i
n
e
e
r
i
n
g
S
c
ho
o
l
of
T
u
n
i
s
(
E
NI
T
)
,
T
unisia,
2011.
[14]
C.
S
he
kh
e
r
,
et al.
,
"P
erf
o
rm
ance
a
naly
sis
o
f
D
C/DC
b
i
d
irect
io
na
l
co
nvert
er
w
it
h
s
lidi
ng
m
o
de
a
n
d
p
i
controller",
In
ter
n
a
t
io
nal Jour
na
l o
f
P
o
wer
El
ectro
n
i
cs
a
n
d
Dr
ive S
y
s
t
em
(
I
JP
EDS)
,
v
o
l.
10,
n
o.
1
,
p
p
.
3
5
7
-365,
2
0
1
9
.
[15]
M
.
D
eshm
u
kh,
M
.
K
.
N
a
m
bo
othi
rip
a
d
,
"DS
P
B
as
edS
eco
nd
O
r
d
e
r
S
l
idin
g
M
o
d
e
C
o
n
tro
l
l
e
r
f
o
r
Bu
ck
C
on
vert
er
"
,
T
h
e 3r
d Inter
nati
ona
l
Co
n
f
eren
ce fo
r
Co
nverg
e
nce i
n
Tech
no
lo
g
y
(
I
2CT)
,
India, p
p.
1
-5
,
20
18
.
[16]
K
.
B
e
l
gacem
,
et
a
l
.
,
"Des
ign
an
d
Anal
ysis
o
f
Ad
a
p
ti
v
e
S
l
i
d
i
ng
M
o
d
e
with
E
xp
on
e
n
tia
l
Reach
ing
L
a
w
Co
nt
ro
l
f
o
r
Do
ub
le
-F
e
d
I
nd
uc
tion
Ge
n
e
ra
to
r
Ba
se
d
Wind
T
urb
i
n
e
"
,
In
tern
atio
na
l Jo
ur
nal o
f
Po
wer E
l
ectronics
a
n
d
Dr
ive
S
y
st
em (
I
JPEDS)
,
v
o
l
.
9
,
n
o
.
4
,
pp.
1
53
4-1
544
,
201
8.
[17]
L
.
L
ak
hd
ari
,
a
n
d
B
.
Bo
uch
i
b
a
,
"
F
u
zzy
S
li
din
g
M
od
e
Cont
ro
l
l
e
r
f
o
r
Ind
u
c
t
io
n
M
achi
n
e
F
eed
b
y
T
h
ree
Lev
e
l
Invert
er"
,
Inter
n
a
t
i
onal
Jour
na
l of Power
El
ectron
i
cs
and D
r
ive Syst
em (IJPED
S
)
,
v
o
l
.
9
,
no
.
1
,
pp.
55-6
3
,
2
0
18.
[18]
T.
C
h
i
n
t
hu
,
P
.
S
h
i
vk
uma
r
,
"
N
on
-l
inear
c
ontroller
f
o
r
DC-DC
buck
c
onv
erter",
D
e
pa
rt
men
t
of EEE,
So
na
Co
lla
ge
o
f
Tech
no
lo
gy
, S
al
em,
Tamil
Nad
u
, In
d
i
a,
2
01
2
.
[19]
M
.
D
e
s
hm
u
kh,
"
A
Con
s
t
a
nt
F
requ
ency
S
eco
nd
O
rd
er
S
lidi
ng
M
o
de
C
o
nt
ro
l
l
e
r
f
or
B
uck
Convert
er",
Th
e
2
n
d
In
ter
n
a
t
io
nal Conf
eren
c
e
on
El
ectr
i
cal
,
Com
puter an
d Co
mm
uni
c
a
t
i
o
n
T
ech
nol
ogies
(
I
CECCT
)
,
F
e
b
20
18
.
[20]
V.
J
.
S
i
va
n
a
ga
pp
a
l
,
et al.
,
"
V
ol
ta
g
e
c
on
trol
o
f
AC-DC
c
o
nv
e
r
te
r
u
s
in
g
slid
ing
mod
e
c
on
tro
l",
Interna
t
ional
Jo
ur
na
l of
E
m
ergi
ng T
e
c
h
no
lo
gy a
n
d
Ad
vanced
En
gi
neer
ing
,
v
o
l
. 3
,
n
o
.
4
,
2
013
.
[21]
K
.
R
.
Jo
shi1,
H.
V
.
K
a
nnad
,
"
D
esig
n
of
s
li
ding
m
o
d
e
c
ont
rol
fo
r
buck
conv
e
r
te
r
",
International Journal of
A
d
va
nced
Resea
r
ch
in El
ectrica
l, Elect
ro
n
i
cs
a
n
d
Ins
t
rumen
t
atio
n
Eng
i
n
eeri
n
g
,
vol.
4,
no.
5
,
2
0
15.
[22]
S.
C
.
Ta
n
,
et al.
,
"A
f
ixed
-f
requ
ency
p
u
l
se
w
i
d
th
m
o
d
u
l
ati
on
bas
e
d
quas
i
-slidin
g
-m
o
d
e
co
ntroll
er
f
o
r
b
u
c
k
co
nv
erters",
IE
EE
T
r
a
n
s
a
c
t
i
ons on
Power El
ectron
i
cs
, v
ol
.
2
0
,
n
o
. 6,
2
0
0
5
.
[23]
S.
C
.
Ta
n,
et
al.
,
"Ind
irect
s
l
i
ding
m
o
d
e
c
on
tro
l
o
f
po
wer
co
nv
e
r
t
e
rs
v
ia
d
ou
bl
e
i
n
t
egral
slid
in
g
surf
ace",
IEE
E
T
r
an
sa
ctio
ns
on
Po
wer E
l
ectro
nic
s
,
vo
l
.
23
,
no
. 2
,
2
0
0
8
.
[24]
M
.
H.
Ra
s
h
i
d
,
P
h.
D
.
,
"
P
o
w
e
r
e
l
ect
ron
i
cs
h
and
book
d
ev
ices,
c
i
rcu
its, an
d ap
plicat
ion
s
", T
h
i
rd E
d
i
tion.
Evaluation Warning : The document was created with Spire.PDF for Python.