Int
ern
at
i
onal
Journ
al of
R
obot
ic
s
and
Autom
ati
on
(I
J
RA
)
Vo
l.
7
, No
.
3
,
Septem
ber
201
8
, p
p.
197
~
204
IS
S
N:
20
89
-
4856, DO
I: 10
.11
591/ij
ra.
v7
i
3.p
p197
-
204
197
Journ
al h
om
e
page
:
http:
//
ia
escore.c
om/j
ourn
als/i
ndex.
ph
p/IJRA/i
ndex
Modellin
g and Pa
ssivity
-
b
ased C
on
tro
l
of
a Non Is
olated
DC
-
DC
Convert
er in a F
uel Cell
System
Mout
ab
ir
Ahm
ed, Abdelm
ou
nim
El
h
as
s
an
e,
Abo
ulfat
ah
M
ohamed
L.
A.
S.
T.
I
.
Un
ive
rsit
y
H
asa
n
1
st,
Facu
lty
of
Sci
enc
es
and Techn
olog
y
of
Se
tt
a
t,
Sett
at
,
Moro
cc
o
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
18
, 201
8
Re
vised
Jun
27
, 201
8
Accepte
d
J
ul
11
, 2
01
8
Thi
s
pap
er
pre
se
nts
the
m
odel
of
a
fue
l
ce
l
l
and
t
he
d
esign
and
si
m
ula
ti
on
of
a
c
asc
ad
e
of
two
DC
-
DC
conve
rt
ers.
First,
a
de
ta
i
le
d
m
at
h
ematica
l
m
od
el
of
fue
l
c
el
l
is
pre
s
ent
ed
and
sim
ul
at
ed
.
The
n
,
a
no
nli
ne
ar
m
ode
l
o
f
th
e
whole
cont
rolled
s
y
ste
m
is
deve
lop
ed
and
a
robust
no
nli
ne
ar
con
trol
l
e
r
of
cur
r
ent
s
is
s
y
n
the
si
ze
d
u
sing
a
passivi
t
y
-
base
d
cont
rol
.
A
form
al
anal
y
s
is
base
d
on
L
y
apunov
st
abi
l
ity
and
ave
rag
e
the
or
y
is
dev
el
o
ped
to
desc
r
ibe
the
cont
rol
cur
ren
ts
loops
p
erf
orm
anc
es.
A
cl
assic
al
PI
controlle
r
is
used
fo
r
the
voltages
loops.
The
sim
ula
ti
on
m
odel
s
hav
e
b
ee
n
d
e
vel
oped
and
tes
te
d
in
the
Matl
ab
/
Sim
uli
nk
.
Sim
ula
t
ed
r
esult
s
ar
e
displ
a
y
ed
to
v
al
id
at
e
th
e
fea
sibi
li
t
y
and
th
e effect
iv
e
ness of
the prop
osed
strateg
y
.
Ke
yw
or
d:
Ca
scaded b
oos
t
Euler L
ag
ra
nge
Fu
el
cell
Ly
apun
ov
Passivit
y
-
base
d
c
on
t
ro
l
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Mou
ta
bir Ah
m
ed,
Hassa
n 1
er
U
ni
ver
sit
y FS
T Se
tt
at
, Mo
ro
cc
o
.
Em
a
il
:
m
ou
ta
bir_
a
hm
ed@
ho
t
m
ai
l.co
m
1.
INTROD
U
CTION
In
rece
nt
ye
ar
s,
a
ra
pid
i
ncrea
se
of
t
he
popu
la
ti
on
of
the
w
or
l
d
a
nd
a
s
ign
ific
a
nt
de
ve
lop
m
ent
of
industries
are
the
or
i
gin
e
of
increase
of
the
dem
and
of
el
ect
rici
ty
.
The
us
e
of
re
ne
wa
ble
ene
rg
ie
s
s
uch
as
so
la
r,
wind
or
fu
el
cel
l
can
be
a
s
olu
ti
on
to
this
pro
blem
.
To
m
eet
a
par
t
of
his
ene
rg
y
needs,
m
orocc
o
has
dev
el
oppe
d
se
ver
al
so
la
r
[
1]
an
d
wind
[
2]
sit
es
in
diff
e
re
nt
re
gions
.
It
al
so
ha
s
a
n
op
portu
nity
to
de
velo
p
hydro
ge
n
pro
duct
ion.
T
he
f
ue
l
cel
l
is
one
of
the
m
os
t
pro
m
isi
ng
s
ources
of
ren
e
wa
ble
energy.
They
c
an
be
consi
der
e
d
as
gr
ee
n
powe
r
be
cause
t
hey
ar
e
en
vir
on
m
ental
ly
cl
ean
an
d
ha
ve
l
ow
em
i
ssion
of
gr
ee
nhouse
gases,
they
ca
n
operat
e
with
a
ver
y
lo
w
le
vel
of
noise
.
I
n
a
ddit
ion
,
the
y
can
pro
vide
energy
i
n
a
co
ntr
olle
d
way with
h
i
gher effici
ency th
an
c
onve
ntio
na
l powe
r plants.
Fu
el
cel
ls
a
re
e
le
ct
ro
chem
ic
al
de
vices
w
hich
co
nvert
c
hem
i
cal
ene
rg
y
i
nto
el
ect
rical
ene
r
gy
directl
y
by
ox
i
di
zi
ng
fu
el
(
hydro
ge
n)
without
i
nterm
ediat
e
ther
m
al
or
m
echan
ic
al
pr
ocesse
s
[
3],
[
4].
T
he
y
are
eff
ic
ie
nt
a
nd
si
le
nt
dev
ic
es
t
ha
t
can
pro
vid
e
powe
r
to
a
wi
de
var
ie
ty
of
util
it
ie
s,
fr
om
po
r
ta
ble
el
ect
ro
ni
cs
to
veh
ic
le
s,
t
o
el
e
ct
ric
gr
i
ds
.
T
he
y
are
cat
eg
or
i
zed
m
ai
nly
on
the
ty
pe
of
el
e
ct
ro
ly
te
us
e
d,
op
e
rati
ng
co
nd
it
ion
s
or
f
uel.
I
n
thi
s
w
ork,
the
t
ype
of
f
uel
c
el
l
con
si
der
e
d
is
the
P
oly
m
er
E
xc
hange
Mem
br
ane
F
ue
l
Ce
ll
(P
EMFC
)
.
O
btaining
a
high
vo
lt
age
is
nee
ded
in
so
m
e
app
li
cat
io
ns
us
i
ng
a
fu
el
c
el
l.
The
pr
ob
le
m
can
be
handled
ei
ther
by
us
i
ng
a
si
m
ple
ste
p
-
up
conve
rter
with
high
du
ty
cy
c
le
or
by
us
i
ng
casca
de
d
c
onver
te
r
s.
In
this
w
ork,
a
casca
de
d
bo
os
t
DC
-
DC
co
nv
e
rter
is
us
e
d
a
nd
desi
gned
by
a
nonlinea
r
co
ntr
ol
strat
egy
s
uch
as
a p
assi
vity
-
bas
ed
c
on
t
ro
l.
Passivit
y
-
base
d
c
ontrol
is
ess
entia
ll
y
the
co
ntr
ol
of
e
ne
rg
y
.
It
has
been
util
iz
ed
in
s
om
e
app
li
cat
io
ns
s
uc
h
as
the
D
C
-
DC
c
onver
t
ers
[
5
]
-
[
6],
act
ive
powe
r
filt
e
rs
[
7
]
-
[
8]
an
d
con
t
ro
ll
ed
rect
ifie
rs
[
9
]
-
[
10]
.
Using
the p
assi
vity
-
ba
sed
co
ntr
ol ca
n
bri
ng abo
ut good
c
on
tr
ol eff
ect
s o
n powe
r
el
ect
ro
nic c
onve
rters b
e
cause
it
can
acce
le
rate
the
conve
rg
e
nce
of
t
he
ene
rg
y
f
un
ct
io
n
to
th
e
desire
d
ene
rg
y
f
unct
ion
unde
r
t
he
preco
ndit
ion
of
syst
e
m
sta
bili
t
y
by
pro
pe
rly
inj
ect
in
g
da
m
pin
g
[
11
]
.
S
om
e
pr
evi
ou
s
works
hav
e
pr
esented
a
stu
di
es
of
casca
de
d DC
-
DC c
onver
te
rs i
n
a
fu
el
cell
sy
stem
co
ntr
olled
by a
sli
di
ng
m
od
e strate
gy
[12]
-
[
14]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2089
-
4856
IJ
RA
V
ol.
7
,
No.
3
,
Se
ptem
ber
201
8
:
197
–
204
198
The
pap
e
r
is
orga
nized
as
f
ollows:
in
Sec
ti
on
2,
the
f
ue
l
cel
l
m
od
el
is
de
velo
ped
;
i
n
sect
io
n
3
the
casca
de
d
boos
t
c
onve
rter
is
descr
i
be
d
a
nd
m
od
el
e
d,
S
ect
ion
4
is
de
vo
te
d
to
desi
gnin
g
the
i
nn
e
r
loop,
us
in
g
the
pas
sivit
y
co
ntr
ol,
a
nd
the
sy
nth
es
is
of
t
he
oute
r
lo
op.
The
c
ontrolle
r
pe
rfor
m
ances
are
il
lus
trat
ed
by sim
ulati
on
s in
Sect
io
n 5
,
a
con
cl
us
io
n
a
nd
a re
fer
e
nce list
end the
p
a
pe
r
.
2.
FUEL CELL
MO
DEL
Gen
e
rall
y,
the
el
ect
ro
chem
ic
a
l
operati
on
pr
i
nciple
of
a
PE
M
fu
el
cel
l
is
descr
i
bed
by
two
ch
em
ic
a
l
reacti
on
s
and
m
ay
b
e su
m
m
a
rized as
foll
ow
s:
-
I
n
a
node
, th
e
ox
i
dation react
ion
is
g
i
ven b
y
:
H2 →
2 H+ +
2
e
-
-
I
n
t
he
cat
ho
de
, th
e
re
du
ct
io
n react
ion
is
giv
en
b
y:
½O2 +
2 H+ +
2
e
-
→
H2
O
-
T
he ov
e
rall
re
act
ion
is:
H2 + ½
O2 →
H2 O
The
m
od
el
of
PEM
f
uel
cel
l
pro
po
se
d
in
Re
fer
e
nce
[
15]
is
co
ns
ide
red
i
n
this
pap
e
r.
T
he
outp
ut
vo
lt
age
of
a stac
k
is
give
n by
(1)
:
=
(
1
+
(
ℎ
)
(1)
V_Nis
the
ope
n
sta
ck
volt
age
, V
_FC
a
nd
i
_FC
are
r
esp
ect
ively
the
v
oltag
e
an
d
c
urren
t
of f
uel
cel
l, σ
and
I
_h
are
t
w
o
par
am
et
ers
exp
e
rim
ental
l
y
def
i
ned.
U
sin
g
the
val
ues
i
n
Table
1,
the
sim
ula
ti
on
of
th
e
PEM
fu
el
cell
m
od
el
h
as
b
ee
n usin
g M
at
l
ab
softwa
re
giv
es a
gra
ph
of volt
age
ve
rsu
s
curr
ent
as
sh
ow
n
in
Fi
gur
e 1
.
Figure
1.
T
he
fuel cel
l v
oltage
v
e
rsu
s
c
urren
t
Fo
r
t
he
rest
of
stud
y,
it
was
c
on
si
der
e
d
that
the
e
nergy
pro
vid
e
d
by
the
f
ue
l
cel
l
is
i
n
the
li
near
z
one
“oh
m
ic
r
egio
n”
, whe
re t
he
fu
el
cell
d
el
iver
a
stable
power.
3.
DC
-
D
C CO
N
VERTER
MO
DELL
ING
The
ci
rcu
it
t
opol
og
y
of
t
he
casca
de
d
bo
ost
DC
-
DC
c
onve
rter
is
s
hown
in
Fig
ure
2
.
The
us
ed
par
am
et
er v
al
ue
s of the
prese
nt con
ver
te
r
ar
e d
e
picte
d
i
n
T
able 1.
Figure
2. the c
ascade
d boost
DC
-
DC con
vert
er s
chem
e
Table
1.
T
he
U
sed
P
aram
et
er V
al
ues
f
or the
Syst
e
m
Para
m
eter
Valu
e
Pra
m
e
ter
Valu
e
Pra
m
e
ter
Valu
e
Pra
m
e
ter
Valu
e
0
,33
5
Nu
m
b
e
r
o
f
cell
22
Ind
u
cto
rs
1
=
35
2
=
100
Fuel cell
vo
lta
g
e
=
12
ℎ
4
8
3
,2
26V
Ca
p
a
cito
rs
1
=
4
2
=
600
Lo
a
d
res
isto
r
=
10
1
,2k
W
Freq
u
en
cy
10
S
wich
es
IGBT
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
IS
S
N:
20
89
-
4856
Mo
delli
ng
and
Pass
iv
it
y
-
B
as
e
d
C
on
tr
ol o
f
a N
on I
s
ola
te
d D
C
-
DC C
on
ve
rte
r in
… (
Mo
ut
ab
ir
Ahme
d
)
199
3.1.
Swi
tche
d
mo
del
The
casca
de
d B
oo
st c
onve
rte
r
ca
n be r
e
pres
ented by t
he
fo
ll
ow
in
g diff
e
re
ntial
eq
ua
ti
on
s
(2
-
5)
.
1
1
=
−
1
1
−
(
1
−
1
)
1
(2)
1
1
=
(
1
−
1
)
1
−
2
(3)
2
2
=
1
−
1
2
−
(
1
−
2
)
(4)
2
=
(
1
−
2
)
2
−
0
(5)
Wh
e
re
i
_1
a
nd
i
_2
are
,
res
pecti
vely
,
the
currents
in
in
du
ct
or
s
L
_1
a
nd
L
_2,
r_1a
nd
r_2a
re
resp
e
ct
ively
the
se
ries
re
sist
or
of
i
nducto
rs
L_
1
an
d
L_
2,
V_
c
1
de
note
s
t
he
volt
age
in
c
apacit
or
C_
1a
nd
V
_O
is
the
outp
ut
vo
lt
age
. μ_
1
a
nd μ_
2
a
re
denoted
t
he du
ti
es
rati
o
f
unct
io
ns
def
i
ned b
y
(6
-
7):
1
=
{
1
1
0
1
(6)
2
=
{
1
2
0
2
(7)
The
a
ver
a
ge
d m
od
el
is def
i
ne
d
as
f
ollows
(
8
-
11)
:
(8
)
(9)
(10)
(
11)
In
the
a
bove
m
od
el
x1,
x2,
x3,
x4
are
de
note
d,
res
pecti
ve
ly
,
the
a
ver
a
ge
s
cu
rr
e
nts
a
nd
vo
lt
a
ges
i1
,
VC1
,
i2
,
VO
a
nd (u
1,u2)
repr
esents the
av
e
r
ages
duti
es r
at
io
functi
on (μ
1,µ2).
3.2.
Est
ab
li
sh
ment o
f
eule
r
lag
r
ange m
odel
fo
r
DC
-
D
C
conve
rt
er
These e
quat
io
ns ca
n be
r
e
wr
it
te
n
in
E
uler
-
La
gr
a
nge (
EL)
fo
rm
as
sh
ow
n
in
(12)
:
̇
+
ℑ
+
ℛ
=
ℰ
(
12
)
w
he
re
x
is
the
syst
e
m
sta
te
va
riable
vect
or
,
D
is
th
e
posit
iv
e
def
init
e
dia
gonal
m
at
rix,
ℑ
is
the
a
nt
i
-
sym
metri
c
m
at
rix
ℑ
=
−
ℑ
wh
ic
h
ref
le
ct
s
the
syst
e
m
internal
interc
onnecti
on
struct
ur
e;
R
i
s
the
syst
em
dissipati
on
el
e
m
ent
m
at
rix
w
hich reflect
s
the syst
em
d
issi
pation
c
ha
racteri
sti
cs an
d
ℰ
is t
he
syst
em
ex
te
rn
al
i
nput
vec
tor.
The det
ai
le
d
e
xpressi
on
s
o
f
t
hese m
at
rices are li
ste
d
as
sho
wn in (
13
-
17)
:
=
(
1
2
3
4
)
(13)
ℰ
=
(
0
0
0
)
(14)
=
(
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
)
(15)
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No.
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,
Se
ptem
ber
201
8
:
197
–
204
200
ℑ
=
(
0
1
−
1
−
(
1
−
1
)
0
0
0
1
0
0
−
1
0
0
0
1
−
2
−
(
1
−
2
)
0
)
(16)
ℛ
=
(
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
/
)
(17)
3.2.
Equi
li
brium
p
oint
s
The
e
quil
ibrium
po
int
can
be
obta
in
e
d
by
f
or
ci
ng
the
ti
m
e
der
ivati
ve
of
the
sta
te
var
ia
bles
of
the
re
duce
d
order
m
od
el
to
be
null
wh
il
e
le
t
ti
ng
t
he
a
ve
rages
co
ntr
ols
i
nputs
u1
a
nd
u2
t
o
a
dopt
res
pect
ively
the
co
ns
ta
nt
va
lues
U10
a
nd
U
20.
As
a
res
ult,
we
obta
in
a
sim
ple
li
near
syst
e
m
of
e
qu
a
ti
on
s
for
t
he
ste
ady
sta
te
eq
uili
bri
um
v
al
ues
of the
av
e
rag
e
stat
e
var
ia
bles [1
6].
Using
t
he
a
ve
rag
e
sta
te
repr
esentat
ion
where
we
ta
ke
i
nto
acco
unt
th
at
:
r_1=r_
2=0
an
d
so
l
vin
g
the
syst
e
m
of
equ
at
io
ns
for
the
unkn
own
s
x10,
x2
0,
x30
a
nd
x4
0,
we
obta
in
th
e
equ
il
ib
rium
sta
te
of
the syst
em
as
sh
ow
n
in
(1
8)
:
̇
=
0
⟹
{
1
0
=
1
(
1
−
1
0
)
2
(
1
−
2
0
)
2
2
0
=
1
−
1
0
3
0
=
(
1
−
1
0
)
(
1
−
2
0
)
2
4
0
=
1
(
1
−
1
0
)
(
1
−
2
0
)
(1
8
)
The
e
quil
ibrium
p
oin
t i
s note
d by
(19
-
20)
0
=
(
1
0
2
0
3
0
4
0
)
=
(
100
70
14
140
)
(19)
0
=
(
1
0
2
0
)
=
(
0
.
83
0
.
5
)
(20)
Fr
om
the
e
quil
ibriu
m
po
i
nt,
t
he
outp
ut
po
w
er
is
e
qual
to
the
i
nput
powe
r
an
d
t
hat
the
i
nput
volt
age
in a
boos
t c
onve
rter is less
tha
n
it
s
ou
t
pu
t
volt
age.
4.
CONTR
OL D
ESIGN
Ther
e
are
two
op
e
rati
onal
contr
ol ob
j
ect
ive
s:
a.
Re
gula
ti
ng the
ou
t
pu
t
volt
age
4
to a
desire
d value
4
∗
.
b.
Ensu
re th
e
gl
ob
al
sta
bili
ty
of the syst
em
.
c.
E
ns
ure t
he
r
obus
t
ness of t
he
syst
e
m
.
The
c
ontrol la
ws
a
re ill
us
tre
d by the
Fig
ure
3.
Figure
3.
Co
ntr
ollers
base
d
str
uctu
re
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delli
ng
and
Pass
iv
it
y
-
B
as
e
d
C
on
tr
ol o
f
a N
on I
s
ola
te
d D
C
-
DC C
on
ve
rte
r in
… (
Mo
ut
ab
ir
Ahme
d
)
201
4.1
.
Inne
r
loo
p
Let
z=x
-
x^*
de
no
te
s
t
he
tra
ckin
g
er
r
or
m
at
rix
an
d
c
ons
ider
the
desi
re
d
er
ror
dissipa
ti
on
m
at
rix
def
i
ned b
y
(
21
-
22)
:
ℛ
=
ℛ
+
ℛ
(
21
)
ℛ
=
(
1
,
2
,
3
,
4
)
(22)
w
he
re
ℛ
de
no
te
s
the in
j
ect
ed
d
a
m
pin
g
an
d
1
,
2
,
3
a
nd
4
are
posit
ive c
on
st
ants.
P
erfo
rm
ing
a
dam
pin
g
i
nj
e
c
ti
on
e
nsure
s
t
he
desire
d
as
ym
pto
ti
c
beha
vior
of
the
outp
ut
e
rror
dynam
ic
s.
Usin
g
the
e
quat
io
ns
(3)
a
nd
(
5)
,
an
d
re
placi
ng
by
(
+
∗
)
the
e
rror
dy
nam
ic
s
with
desire
d
dam
pin
g bec
om
e
(23)
:
̇
+
ℑ
+
ℛ
=
ℰ
−
(
∗
̇
+
ℑ
∗
+
ℛ
∗
−
ℛ
)
(
23
)
The
c
ontrol la
ws wil
l be
def
i
ne by t
he f
ollo
wing e
xpressi
on
(24)
:
ℰ
−
(
∗
̇
+
ℑ
∗
+
ℛ
∗
−
ℛ
)
=
0
(24
)
In this case
the
erro
r dynam
ics
is de
fine
d by
(25)
:
̇
+
ℑ
+
ℛ
=
0
(
25
)
We
def
i
ne
the
total
en
e
rg
y as
a Lya
puno
v
f
unct
ion f
or eq
ua
ti
on
(
25
)
as
fo
l
lows
(
26):
=
1
2
(
26
)
To get a sta
bili
zi
ng
c
on
tr
ol laws,
t
he
ti
m
e
-
der
ivat
ive
H
̇
m
us
t be a
n
e
gativ
e d
e
finite
fu
nction o
f
z.
The
n H
̇
is c
ho
sen
as
sho
wn i
n (27)
:
̇
=
−
ℛ
<
0
,
f
or
z
≠ 0
(27)
Con
si
der the e
xpressi
on
(
24
)
as sho
wn in (
28):
ℰ
=
∗
̇
+
ℑ
∗
+
ℛ
∗
−
ℛ
(
28
)
w
hic
h
c
orres
pond
s
to
th
e
fo
ll
owin
g
scal
ar
d
i
f
fer
e
ntial
equati
on
s
(
29)
:
{
1
̇
1
∗
+
(
1
−
1
)
2
∗
+
1
1
∗
−
1
1
=
2
̇
3
∗
−
2
∗
+
(
1
−
2
)
4
∗
+
2
3
∗
−
3
3
=
0
(
29
)
The
n,
t
he
c
on
t
r
ol laws
to
sat
is
fy a stabil
iz
at
ion
are
d
e
fine
d by
(
30)
:
{
1
=
1
+
1
2
∗
(
1
̇
1
∗
+
1
1
∗
−
1
1
−
)
2
=
1
+
1
4
∗
(
2
̇
3
∗
+
2
3
∗
−
3
3
−
2
∗
)
(
30
)
4.2
.
V
olt
age
outer l
oop c
on
t
rol
The
ai
m
is
to
desi
gn
tu
n
i
ng
la
w
s
f
or
the
x
1
*
a
nd
x
3
*
.
We
c
onsid
er:
2
=
2
2
an
d
4
=
4
2
.
Using t
he
e
qu
a
ti
on
s
(
8
-
11
) we
can
e
sta
blish
the
fo
ll
owin
g re
la
ti
on
s
as
sho
w
n
in
(3
1
-
32):
̇
2
=
2
1
1
∗
+
2
1
1
1
1
∗
−
1
1
(
1
∗
2
)
−
2
1
1
̇
1
∗
+
(
,
)
(31
)
̇
4
=
2
2
[
(
3
3
+
2
−
2
̇
3
∗
)
(
3
2
+
3
∗
)
−
2
4
]
(32)
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ol.
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,
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,
Se
ptem
ber
201
8
:
197
–
204
202
We
m
us
t
us
e
a
low
pass
filt
er
for
the
first
de
rivati
ve
1
∗
̇
(r
es
pe
ct
ively
3
∗
̇
)
of
t
he
ref
e
ren
ce
1
∗
(r
es
pecti
vely
3
∗
)
exists,
we ob
ta
in f
i
nally
(33
-
34)
:
1
∗
=
+
(
2
2
+
2
22
)
(
33
)
3
∗
=
′
+
′
(
4
4
+
4
44
)
(34)
W
it
h
(35
-
37)
:
(
,
)
=
1
1
(
−
2
√
2
3
∗
+
2
1
1
1
2
+
2
1
1
−
2
3
2
√
2
)
(
35
)
{
2
=
2
∗
−
2
22
=
∫
2
(36)
{
4
=
4
∗
−
4
44
=
∫
4
(37)
5.
RESU
LT
S
AND A
N
ALYSIS
In
this
sect
io
n,
t
he
perf
orm
an
ces
of
t
he
co
ntr
oller
will
be
il
lust
rated
by
sim
ulati
on
s
in
t
he
Ma
tl
ab/Sim
ul
ink
e
nv
ir
onm
ent.
The
c
on
t
ro
ll
ed
DC/
DC
co
nverter
has
the
f
ollow
i
ng
c
ha
racteri
sti
cs:
r_
a
1=r_a
2=40
Ω;
b=
b’
=
3;
k_p2=k
_p4=
2;
k_i2=
k_i4=
4.
T
he
c
onve
r
te
r
ha
s
been
sim
ulate
d
to
chec
k
the
pr
e
vious
st
abili
ty
conditi
on
s
.
Th
e
F
ig
ure
4
s
how
s
t
he
fu
el
cel
l
vo
lt
a
ge.
T
he
outp
ut
volt
age
of
c
onve
rter
and
his
re
fer
e
nc
e
that
hav
i
ng
two
value
s:
70
V
a
nd
14
0V
ar
e
sho
wn
in
F
ig
ur
e
5.
We
ob
s
e
rv
e
that
the
tra
ckin
g
is sat
isfie
d
a
nd the sta
bili
ty
is g
ua
ra
nteed.
To
analy
ze
t
he
r
obus
tne
ss
capa
bili
ty
of
the
pr
opos
e
d
co
ntr
oller,
a
ne
w
ex
pe
rim
ent
will
be
perform
ed.
It
c
on
sist
s
in
c
ha
ngin
g
the
f
uel
c
el
l
vo
lt
age
acc
ordin
g
t
o
Fi
gur
e
6.
E
xcep
t
f
or
this
c
hange,
th
e
rest
of
the
c
onve
rt
er
cha
racteri
sti
cs
are
the
sam
e
as
pr
e
v
io
us
l
y.
The
F
ig
ure
7
sho
ws
that
t
he
ef
fect
of
f
ue
l
cell
vo
lt
age
cha
nge
is w
el
l c
om
pen
sa
te
d
by t
he
c
on
t
ro
ll
er
.
Figure
4. F
uel
cel
l vo
lt
age
v
e
rsu
s
ti
m
e
Figure
5. O
utput v
oltage
with
trak
i
ng
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Mo
delli
ng
and
Pass
iv
it
y
-
B
as
e
d
C
on
tr
ol o
f
a N
on I
s
ola
te
d D
C
-
DC C
on
ve
rte
r in
… (
Mo
ut
ab
ir
Ahme
d
)
203
Figure
6. F
uel
cel
l vo
lt
age
v
e
rsu
s
ti
m
e
Figure
7
.
O
utput v
oltage
with
d
ist
urba
nce
6.
CONCL
US
I
O
N
The
a
naly
sis
a
nd
stu
dy
of
the
inse
rtion
of
f
ue
l
cel
l
in
powe
r
syst
em
is
i
m
portant
i
n
orde
r
to
inc
reas
e
the
com
petit
iveness
of
t
his
source
.
A
nonlin
ear
co
ntr
oller
is
pro
po
s
ed
for
DC/DC
casca
de
d
bo
os
t
co
nve
rter
to
achieve
volt
ag
e
outp
ut
re
gu
l
at
ion
.
It
is
de
ve
lop
e
d
in
t
wo
ste
ps
.
Fi
rst,
a
n
inn
e
r
-
l
oop
is
desig
ne
d,
base
d
on
the
passivity
t
echn
i
qu
e
.
The
in
ner
-
lo
op
re
gu
la
to
r
ge
ne
ra
te
s
the
duti
es
cy
cl
e
1
a
nd
2
.
The
seco
nd
ste
p
consi
sts
in
de
ve
lop
in
g
a
n
ou
t
er
-
loo
p
that
ge
ner
at
es
t
he
re
f
eren
ce
c
urre
nts
so
that
t
he
s
quare
d
ou
t
pu
t
volt
ages
1
(
2
)
an
d
(
4
)
f
ollo
ws
a
giv
e
n
ref
e
ren
ce
sig
nals
2
∗
a
nd
4
∗
.
T
he
sy
nth
es
is
of
this
lo
op
i
nvolv
es
a
li
near
iz
in
g
va
riable
c
ha
ng
e
,
a
si
gn
al
filt
eri
ng
to
c
op
e
w
it
h
m
od
el
ti
m
e
-
var
yi
ng
a
nd
c
ontrolla
bili
ty
issu
es
an
d
a
lo
op
m
od
e
se
par
at
io
n.
A
f
orm
al
analy
sis
a
nd
a
sim
ulati
on
stu
dy
pro
ve
that
t
he
pro
pose
d
co
ntr
ollers
a
ct
ually
m
eet
i
ts
obj
ect
ives:
trackin
g,
sta
bili
ty
and
robu
st
ness
gu
a
ra
ntied.
T
he
re
sul
ts
ob
t
ai
ne
d
ar
e
si
m
il
ar
to
tho
se
o
f
the sli
ding m
od
e c
on
t
ro
ll
er
.
REFERE
NCE
S
[1]
F.
Outfe
rdin
e,
L.
Bouhouch
,
M.
Kourch
i,
M.
Aj
aa
m
oum
,
A.
Moudde
n,
“
Feasibi
l
ity
of
Subs
ti
tu
ti
o
n
of
the
Conv
ent
ion
al
Str
ee
t
L
ight
i
ng
Installation
b
y
the
Photovo
lt
aic
C
ase
Stud
y
on
a
Muni
ci
p
al
ity
in
Agadir
i
n
Morocc
o” IJECE
Vol.
7,
No.
5,
Octobe
r
2017
,
p
p.
2287
-
2299
[2]
A.
Ezza
id
i,
M
.
Ely
aqouti,
L.
B
ouhouch,
A.
Ihl
al
“
Evaluation
o
f
the
Ene
rg
y
Per
form
anc
e
of
the
Am
ougdoul
W
ind
Farm
,
Morocc
o”
IJECE
Vol
.
7
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705
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J.
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C
orre
a
,
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A.
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el,
L.
N.
Canha,
M.
G.
Sim
oes
"A
n
El
e
ct
roc
h
emica
l
b
a
sed
Fuel
Cell
Model
Suit
abl
e
for
El
e
ct
ri
ca
l
Engi
n
ee
ring
Aut
om
at
i
on
Approac
h,
"
I
EE
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nsa
ct
io
ns
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offe
n,
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"A
d
vanc
ed
Con
trol
for
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Cells
Connec
t
ed
to
a
DC
-
DC
Convert
er
and
an
Elec
tr
i
c
Motor" Computers
and
Chemical
Eng
ine
er
ing
(2
010).
[5]
Sira
-
Ramirez
H.
,
Per
ez
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Moreno
R.
A.
,
Ot
ega
R.
et
a
l.,
"P
assivity
-
bas
ed
C
ontro
llers
for
the
S
ta
bi
li
z
at
ion
of
DC
t
o
DC
Pow
er
Convert
ers
,
"
Aut
om
atica 33(4): 499
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5
13
(1997).
[6]
W
u
Le
i
-
ta
o
,
Y
ang
Zha
o
-
hu
a,
Xu
Bu
-
gong,
"
Inve
stigation
of
Pass
ivi
t
y
-
b
ase
d
Control
of
D
C/DC
Converte
r".
Tra
nsac
ti
ons of
China
El
e
ct
ro
-
technical
Soc
iet
y
19(4):
66
-
69
(20
04)
(in
Ch
ine
se)
.
[7]
Xue
Hua,
Jian
g
Jian
-
guo,
"S
t
ud
y
on
Adapt
i
ve
Pass
ivi
t
y
-
b
ase
d
Contro
l
Stra
te
gi
es
of
Shunt
Acti
v
e
Fil
te
rs
"
.
Proce
edi
ngs of
t
he
CS
EE 27(25)
:
114
-
118
(2007
)
(in
Ch
ine
se)
.
[8]
Tz
ann
-
Shin
L
ee,
"L
agr
angian
Modeli
ng
and
Pass
ivi
t
y
-
b
ase
d
C
ontrol
of
T
hre
e
-
phase
AC/
DC
Volta
gesou
rce
Convert
ers
".
Ind
ustria
l
Elec
t
ro
ni
cs
51(4):
89
2
-
90
2
(2004).
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2089
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4856
IJ
RA
V
ol.
7
,
No.
3
,
Se
ptem
ber
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8
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204
204
[9]
W
ang
Jiu
-
he
,
"
Pass
ivi
t
y
-
b
ase
d
Control
The
or
y
and
i
ts
Appl
icati
on
,
"
B
ei
j
ing:
Publishing
Ho
use
of
E
le
c
tron
ic
s
Industr
y
(2010) (in Chi
n
ese
).
[10]
Qiao
Shu
-
tong,
W
u
Xiao
-
ji
e
,
Ji
ang
Jian
-
guo,
"
Applic
a
ti
on
of
Pass
ivi
t
y
-
ba
sed
Slidi
ng
Mode
C
o
ntrol
in
DC/
D
C
Convert
ers".
Tr
a
nsac
ti
ons of
Chi
na
E
le
c
tro
-
t
ec
hn
ic
a
l
Soci
ety
18(4
):
41
-
45
(20
03).
[11]
LI
HU
A
-
W
U
and
al
"A
n
E
L
Mo
del
Based
Pass
ivi
t
y
Contro
l
of
F
our
Phase
Inte
r
l
ea
ved
PF
C"
Archi
ves
of
E
le
c
tric
al
Engi
ne
eri
ng
V
.
62
pp
.
613
-
628
(
2013).
[12]
Bin.
HU
AN
G
"
Co
nver
ti
ss
eur
s
Conti
nu
–
Conti
n
u
à
Rapport
de
Tra
nsform
at
ion
El
ev
é
pour
Appl
ic
a
ti
ons
PA
C"
Thè
se
soutenue
le 14
m
ai
2009
.
156
p
ag
es.
[13]
A.
M.
Shah
in"Contri
buti
on
à
l’O
pti
m
isat
ion
d
es
Struct
ure
s
d
e
Co
nver
sion
DC
-
DC
Non
Isolés"
Th
è
se
soutenue
l
e
0
8
jui
llet
2011.
162
p
age
s.
[14]
R.
Saidi "Conve
rti
ss
eur
Basse
T
ension
(42V,
54
0V) Appli
cation S
ourc
e
H
y
bride
Util
isant une
PA
C" T
hèse
sout
en
ue
le
11
m
ars
2015.
147
page
s.
[15]
M.
Hina
je,
D
.
Ngu
y
en
,
S.
R
ae
l
and
B.
Dav
at,
"M
odel
ing
of
th
e
Proton
Ex
change
Mem
bra
n
e
Fuel
C
el
l
in
Ste
a
d
y
Stat
e
",
Pow
er
E
l
ec
tron
ic
s Spe
ci
a
l
ists Confe
ren
ce, P
ESC 2008.
[16]
H.
Sira
-
Ramire
z
,
R.
Silva
-
Ort
igo
za
.
Control
Desi
gn
Techni
ques
i
n
Pow
er
El
e
ct
ro
nic
s
Devi
ce
s.
20
06,
XV
III,
424p
,
Hardc
over
.
Spri
nger
.
ISBN
:
978
-
1
-
84628
-
458
-
8
.
BIOGR
AP
H
I
ES
OF
A
UTH
ORS
Moutabir
Ah
me
d
was
born
in
1
965
in
C
asa
bla
n
ca
,
Morocc
o
.
He
recei
ved
th
e
En
gine
er
degr
e
e
in
e
le
c
trica
l
E
ngine
er
ing
fro
m
High
Institute
of
T
ec
hni
ca
l
Educat
ion
(ENSET)
of
Moham
m
edi
a
i
n
1989.
In
199
6,
h
e
suc
ce
ss
fu
lly
p
assed
the
ext
ern
al
aggr
eg
at
ion
con
te
st.
He
obt
ai
ned
hi
s
M
aste
r
in
Autom
at
ic,
Sign
al
Proce
ss
ing
an
d
Industri
al
Co
m
puti
ng
from
Facul
t
y
of
Sc
ience
s
and
T
ec
hn
ic
s,
Univ
ersity
Hass
an
First,
S
et
t
at
,
Morocc
o
.
Since
1995,
he
jo
ine
d
the
t
e
chni
c
al
school
Alkhaoua
rim
y
o
f
Casablanc
a
wh
ere
h
e
teac
h
es
i
n
class
es
BTS
"Te
chnici
a
n
Cer
ti
ficat
e
Superior
s"
in
Casablanc
a,
Morocc
o
and
pursues
his
do
ct
ora
l
studie
s
at
the
Univer
si
t
y
H
assan
f
irst
Sett
at.
His
m
ain
rese
arc
h
in
te
r
ests
and
exp
erienc
e
in
cl
ud
e
ana
l
y
sis,
design
,
and cont
ro
l
of
p
ower
conv
ert
ers
and
ren
ewa
bl
e e
ner
g
y
app
li
c
atio
ns.
Elhas
san
e
Ab
d
el
moun
im
r
ecei
ved
h
is
Ph
.
D
in
appl
i
ed
Spect
r
al
an
aly
sis
from
Li
m
oges
Univer
sit
y
at
sc
i
enc
e
and
techni
ca
l
Facult
y
,
Fra
nce
in
1994
.
I
n
1996,
he
jo
ine
d,
as
Profess
or,
appl
i
ed
ph
y
si
cs
dep
art
m
ent
of
sci
enc
e
and
technical
fa
cul
t
y
,
Hass
an
1st
Un
ive
rsit
y
,
Se
tt
a
t,
Morocc
o.
His
c
urre
nt
rese
arc
h
i
nte
rests
include
digi
tal
signal
pr
oce
ss
ing
and
m
ac
hine
l
ea
rn
ing.
He
is
cur
r
ent
l
y
coor
dinator
of
a
Bac
he
lor
of
Sc
ie
nc
e
in
elec
tr
ica
l
eng
ineeri
ng
a
nd
rese
ar
che
r
in
“
AS
TI”
S
y
st
em
Anal
y
sis
an
d
Inform
at
ion
T
ec
hnolog
y
La
bo
rat
or
y
at
sci
ence
and
technical
fac
ul
t
y
,
Hass
an 1s
t
Univer
sit
y
,
S
et
t
at
,
Morocc
o
.
Mohame
d
A
bou
lfatah
was
born
in
C
asa
bla
n
c
a
Morocc
o
in
1967,
he
re
ce
iv
ed
his
Ph
.
D
in
Me
asure
s
and
Instrum
ent
a
ti
on
from
Bord
ea
ux
Univer
sit
y
,
Fran
ce
in
1994.
Fro
m
1993
to
1995
he
was
associa
t
ed
profe
ss
or
at
the
Te
c
hnologic
al
Inst
it
ut
e
of
Bordea
ux
Univ
e
rsit
y
.
I
n
1996,
he
jo
ine
d
,
as
per
m
ane
nt
Profess
or,
appl
i
ed
ph
y
si
c
s
depa
rtmen
t
of
scie
nc
e
and
te
ch
nic
a
l
f
ac
ul
t
y
,
Hass
an
1st
Univ
ersity
,
Se
tt
a
t,
M
oroc
co.
He
is
cu
r
ren
tly
h
ea
d
of
Applie
d
Ph
y
si
cs
dep
art
m
ent
and
coor
dinator
of
“
Autom
at
ic
,
Sig
nal
Proce
ss
ing
and
Industrial
Com
puti
ng”
Ma
ster.
His
m
ai
n
rese
arc
h
intere
st
s
and
expe
r
ie
nc
e
include
Instru
m
ent
at
ion
,
Sign
al
Proce
ss
ing.
a
s
a
rese
ar
che
r
m
ember
of
AS
TI
La
bor
at
or
y
in
Hass
an
1st Uni
v
ersity
.
Evaluation Warning : The document was created with Spire.PDF for Python.