TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6017 ~ 6026
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.576
3
6017
Re
cei
v
ed Fe
brua
ry 8, 201
4; Revi
se
d April 19, 201
4; Acce
pted Ma
y 6, 2014
Fuzzy Sliding Mode Control of PEM Fuel Cell System
for Residential Application
Mahdi Mans
ouri*
1
, Mohammad Ghadi
m
i
2
, Kamal Abbaspoor Sani
3
1
Departme
n
t of energ
y
, Islami
c Azad Univ
ers
i
t
y
of South T
ehran br
anc
h,
T
ehra
n
, Iran
2
Departme
n
t of energ
y
, Islami
c Azad Univ
ers
i
t
y
of Ro
ude
he
n, Iran
3
Departme
n
t of energ
y
, Islami
c Azad Univ
ers
i
t
y
of T
a
kestan, Iran
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: Mahdi.Ma
n
so
ri@gma
il.com
1
, m.Ghadimi@r
iau.ac.ir
2
,
k-Abasp
our@
m
erc.ac.ir
3
A
b
st
r
a
ct
Proton exc
h
a
n
ge
me
mbra
ne
fuel ce
lls (PE
M
F
C
s)
are rec
e
ivin
g
mor
e
at
tention c
o
mp
ar
ed w
i
th
other sources
of power
generation. Maintaining a
fuel cell system
r
e
quires
excellent system
control
to
receiv
e the be
st operatin
g.
T
herefor
e, in thi
s
paper
a dyn
a
mic mod
e
l of
a (PEMF
C
) for reside
ntial
po
w
e
r
gen
eratio
n is a
ppli
ed. T
he
mo
del pr
opos
ed i
n
clu
des t
he fu
el cell stack
mode
l, pow
er conditi
on un
ite th
at
consists of t
h
e
metha
nol
refo
rmer
mod
e
l
an
d DC-A
C
i
n
ver
t
er mode
l. Acc
o
rdi
ng to
pow
e
r
outp
u
t of (PE
M)
fuel ce
ll syste
m
, a fu
z
z
y
s
lid
ing
mode c
ont
roller w
h
ic
h
co
ntains th
e ch
a
r
acteristics of f
u
z
z
y
c
ontro
l a
n
d
slidi
ng
mo
de c
ontrol is a
ddr
e
ssed, in ord
e
r to mo
dify
the hy
drog
en flow
feedb
ack from th
e termi
n
a
l
loa
d
. In
add
ition, th
is c
o
mbi
ned c
ontr
o
ller
is us
ed t
o
i
m
pr
ove
sta
b
ility
by fu
zz
y
reaso
n
in
g to c
ontrol th
e o
u
tp
ut
variati
on th
at reduc
es ch
attering
and
incr
ea
se the sp
ee
d o
f
tracking by r
e
ason
ing
of sli
d
i
ng
mo
de c
ontr
o
l.
Cons
equ
ently,
the dy
na
mic
a
l
beh
avior
of sy
stem w
i
th
F
S
MC is
more
i
m
pr
oved
as c
o
mp
ared
to th
e F
L
C
and PI control
l
e
r in terms of
rate of hydrog
en flow
, output
AC voltage a
nd outp
u
t pow
er of F
C
and it is
show
n that the prop
osed
c
ontr
o
ller c
an ach
i
e
v
e better contr
o
l effect than o
t
her control
l
ers
.
Ke
y
w
ords
: PEM fuel cell, dynamic mo
d
e
l, fuzz
y
sli
d
in
g
mo
de contro
ller, r
e
sid
entia
l pow
er
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
No
wad
a
ys, the interest in
Fuel Cell
s h
a
s in
crea
sed
durin
g the pa
st de
cade
du
e to the
fact that the use of fossil
fuels for p
o
wer ha
s re
sult
ed in many n
egative co
nseque
nces. F
uel
cell
s are
sou
r
ce
s of energy that generat
e electri
c
al
e
nergy from
chemical rea
c
t
i
ons an
d are
set
to becom
e the power sou
r
ce of the future. The
r
e
are
many types of fuel cells t
hat are u
s
ed
in
many appli
c
a
t
ions
su
ch a
s
: stationary p
o
we
r, tr
an
sp
o
r
tation sy
ste
m
, portabl
e p
o
we
r, dist
ribu
ted
gene
rato
rs, a
l
ternative po
wer
and
appli
c
ation in
s
p
a
c
e [1-4], but (PEMFCs) a
r
e
the best
kind
of
FC
due
to lo
w o
perating t
e
mpe
r
ature
(l
ess th
a
n
1
00
degree
C), hi
gh p
o
wer
den
sity, quick
sta
r
t-
up capability
,
low wei
ght
, limited nu
mber
of
mo
ving part
s
, null polluta
nt emission
s,
low
electrolyte
co
rro
sio
n
a
nd l
ong life
-
time.
Thu
s
, a
ne
w p
o
wer sou
r
ce
i
s
n
eed
e
d
that i
s
ene
rgy
efficient, has l
o
w poll
u
tant emission
s an
d has u
n
limited su
pply of fuel [5-6].
There are
several re
se
a
r
ch
re
sults o
n
t
he desig
n
of PEMFC
controlle
rs th
at can
improve th
e
behavio
ur of
system. F
o
r this p
u
rp
os
e
,
an an
alytical detail
s
of
how
active a
n
d
rea
c
tive power outp
u
t of a stand
-alo
n
e
PEMFC
po
wer
plant ha
s bee
n prop
ose
d
in [5]. This
analysi
s
is b
a
se
d on an
integrate
d
dynamic mo
del
of the entire powe
r
pla
n
t includin
g
the
reform
er.
In
addition, a
d
y
namic mod
e
ling of
va
ri
ous compo
n
ents
of an
isolated
syste
m
is
pre
s
ente
d
in
[7] and
a PID co
ntrolle
r i
s
use
d
to
adju
s
t the fuel
cell
inlet an
d oxy
gen
pre
s
su
re
to
maintain a co
nstant sta
c
k output voltag
e. The ai
m of used PID type co
ntro
ller
is control of the
fuel cell voltage by varying the hydrogen
and oxygen
flow rate
s. Un
fortunately, the perfo
rman
ce
of a PEMFC i
s
very
difficult
to mod
e
ling
analytic
ally. S
o
, the mai
n
challen
ge of
controlle
r d
e
si
gn
in order to im
prove
perfo
rmance of PE
MFC
syst
em
is satisfying o
f
the
stability and rob
u
stn
e
ss
of cell
s [8]. On the
oth
e
r han
ds,
the
Perform
a
n
c
e
of PEMF
C
depe
nd
s o
n
existen
c
e
of
many
variable
s
su
ch as o
peratin
g temperatures, flow
rate
of hydroge
n
,
membra
ne
humidity, wat
e
r
manag
eme
n
t of the memb
rane, p
r
e
s
sure and oth
e
r
f
a
ctors. Th
ese
variable
s
infl
uen
ce on
ea
ch
other a
nd ma
king
nonlin
ea
rity in the performan
ce
m
o
dels th
at makes the
re
sea
r
ch o
n
PEMF
C
sy
st
em
s v
e
ry
dif
f
i
cult
,
so e
m
piri
cal mod
e
l hav
e
bee
n
used [9
-10].
Ho
wever,
co
ntrolling the
rate
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TELKOM
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Vol. 12, No. 8, August 2014: 601
7 –
6026
6018
of flow of hyd
r
oge
n is
more impo
rtan
ce
in ord
e
r to i
m
prove th
e p
e
rform
a
n
c
e o
f
a PEMFC st
ack
and to follow
the desi
r
ed o
u
tput power i
n
stand
-alo
ne
and grid
con
necte
d mode.
There a
r
e three
rea
s
on
s fo
r t
h
is
claim
such a
s
: 1. Protons ge
nerate
d
by hyd
r
og
e
n
oxidation
a
t
the an
ode
and
then a
r
e red
u
ce
d to hyd
r
ogen
at the
catho
de; 2.
l
a
ck of the
hydrog
en le
ad
s to drying
of
the
membrane a
nd failure of
chemi
c
al
rea
c
tion in the ce
ll; 3. Total pressu
re of F
C
is controll
e
d
by
the flow of hydroge
n. So for this pu
rpo
s
e,
re
se
arch
ers have
pro
posed
differe
nt method
s ([9],
[11-13]
).
In this pap
er
a Fuzzy slidi
n
g mode
cont
roller
(FSMC)
is propo
sed f
o
r the control
of flo
w
of hydro
gen
in PEMFC.
Sliding mo
de
cont
rol (S
M
C
) i
s
a type
of variabl
e
stru
cture con
t
rol
method that i
s
de
sig
ned t
o
co
nst
r
ain t
he state
va
ri
able
s
of sy
stem within
a
neigh
bou
rho
o
d
of
swit
chin
g fun
c
tion. The
ch
oice
of switching fun
c
tion
s can b
e
tun
ed the dyn
a
m
ical b
ehavi
our of
system. Also, SMC ha
s fast resp
on
se ch
ara
c
teri
stic
to
the fast load
cha
nge
s with
out sen
s
itive to
para
m
eter va
riation
s
and
external di
sturba
nces.
Howeve
r, in SM controll
er
one of the most
importa
nt disadvantag
es i
s
ch
attering
probl
em
and
anothe
r is th
at dynamic e
quation influe
nce
on co
ntrolle
r
desi
gn. In ad
dition, Fuzzy logic
c
ontrolle
r (FL
C
) p
o
sse
s
ses
seve
ral
advantag
es li
ke
robu
stne
ss, model
-free a
nd is de
sig
n
ed ba
sed o
n
human expe
rien
ce. Du
e to this advant
age,
FLC ha
s be
e
n
addresse
d for many ind
u
s
trial ap
plications [9].
The fu
zzy sli
d
ing m
ode
control
(FSM
C) meth
od,
wh
ich i
s
an i
n
te
gration
of S
M
C
and
FLC, provide
s
a sy
stemati
c
ally
de
sign f
o
r FL
C. In the term of de
signing of FS
MC, fuzzy rul
e
s
are
u
s
ed
for tuning of
sli
d
i
ng su
rface. More
over
, thi
s
m
e
thod
ca
n p
r
ovide
ro
b
u
stne
ss a
gai
nst
model un
ce
rtainties an
d e
x
ternal distu
r
ban
ce
s and a
l
so it is cap
a
b
le to minimize the ch
attering
phen
omen
on
while a
s
suri
n
g
slidin
g beh
aviour.
The pa
pe
r is
orga
nized a
s
follows: Sect
ion 2
introdu
ce
s a m
odel
for a fuel
cell
syste
m
con
s
i
s
ts of the FC sta
ck, the fuel pro
c
e
ssi
ng uni
t or t
he refo
rme
r
, and the invert
er. In Section
3,
Fuzzy logi
c
controlle
r d
e
si
gn is intro
d
u
c
ed for PEM
F
C
an
d the
n
F
u
zzy Sliding
Mode
co
ntroll
er i
s
addresse
d to regulate flo
w
rate of hydrog
en.
The
propo
se
d controlle
r mod
i
fies the rate
of
hydrog
en flo
w
for control
ling the
acti
ve po
we
r to
the lo
ad
chang
e. Finall
y
, in se
ction
4,
Simulation results and
di
scussi
ons are present
ed and an illustrative example confirms t
h
e
advantag
es o
f
our app
roa
c
h.
2. PEM Fuel
Cell Model
2.1. Fuel Cell Static Model
In [9] intro
d
u
c
ed
a
model
of PEMFC
system
for
resid
ential
po
wer ge
ne
rati
on. Th
e
chemi
c
al
rea
c
tion
s in PEMFC sy
stem are given as:
)
(
2
2
2
Anode
e
H
H
(
1
)
)
(
2
2
/
1
2
2
Cathode
O
H
e
H
O
(
2
)
The re
pre
s
e
n
t
ation of a PEMFC sy
stem i
s
sh
own in Figure 1.
Figure
1. Sch
e
matic Di
ag
ram of PEMFC
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TELKOM
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ISSN:
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046
Fuzzy Sliding
Mode Co
ntro
l of PEM Fuel Cell
System
for Re
side
ntial… (Ma
hdi
Mansou
ri)
6019
The output vo
ltage of a cell
can be d
e
fin
ed in the follo
wing term:
conc
ohm
act
Nerst
Fc
V
V
V
E
V
(3)
Whi
c
h
Nerst
E
is th
e thermodyn
a
mic
potenti
a
l of t
he
cel
l
that re
pre
s
ent reve
rsibl
e
voltage of cell
, with:
1
.229
0
.85
∗
10
298
.15
4
.31
∗
10
ln
ln
(4)
Whe
r
e
2
H
P
an
d
2
O
P
are
the
hydrogen
and
ox
ygen p
r
e
s
sures, a
nd
)
(
K
T
fc
is t
he o
perating
temperature of
cell.
act
V
is the voltage dro
p
of the anode
and the catho
de:
0
.9514
3
.12
∗
10
7
.
4
∗1
0
ln
1
.
8
7
∗1
0
ln
(5)
Whe
r
e
)
(
A
i
is the
elect
r
ical current a
nd
2
O
C
is t
he oxygen
concentratio
n
.
ohmic
V
is the
ohm
i
c
voltage dro
p
of proton
s through the
soli
d electrolyte and ele
c
tro
n
s:
)
(
C
M
ohmic
R
R
i
V
(
6
)
Whe
r
e
)
(
C
R
is the
conta
c
t re
si
stance
of electron flow, a
n
d
)
(
M
R
is
the re
sistance of
prot
on
transfe
r throu
gh the memb
rane.
A
l
R
M
M
(7)
fc
fc
fc
M
T
T
A
i
A
i
T
A
i
303
18
.
4
exp
3
634
.
0
303
062
.
0
03
.
0
1
6
.
181
5
.
2
2
(8)
W
h
er
e
)
.
(
cm
M
is th
e mem
b
ra
ne
sp
ec
ifi
c
resistivity,
)
(
cm
l
is th
e mem
b
ra
ne
thickne
s
s,
)
(
2
cm
A
is
the memb
rane
a
c
tive area, and
is a
sp
ecifi
c
co
efficient f
o
r eve
r
y type of
membrane.
conc
V
repre
s
e
n
ts the voltage drop of the mass tr
a
n
sporta
tion effects, whi
c
h affects the
con
c
e
n
tration
of the reactin
g
gases a
nd
can b
e
de
scri
bed in the foll
owin
g term:
)
1
ln(
max
i
i
B
V
conc
(
9
)
Whe
r
e
)
(
v
B
is a
para
m
etri
c
co
efficient which dep
end
s o
n
the
cell a
n
d
its op
eratio
n state
and
max
i
represent the curre
n
t of cell.
The stati
c
mo
del of the PEMFC is
sho
w
n in Figure 2.
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Vol. 12, No. 8, August 2014: 601
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6026
6020
Figure
2. PEMFC Static M
odel
2.2. Fuel Cell D
y
namic M
odel
The dynami
c
al model of cell is ba
sed o
n
simulatin
g
the relatio
n
shi
p
betwe
en th
e output
voltage and p
a
rtial pre
s
su
re of hydroge
n, oxygen,
and curre
n
t. This model of PEMFC is sho
w
n
in Figure 3.
Figure 3. PEMFC Dyn
a
mi
c Model
The PEMFC
dynamic m
o
d
e
l para
m
eters are de
scrib
e
d
as follo
w:
:
2
H
q
input mola
r flow of hydro
g
en (kmol/s),
:
2
O
q
input mola
r flow of oxygen
(kmol/
s),
:
2
H
K
hydroge
n valve molar con
s
tant (kmol/b
a
r/s)),
:
2
O
K
oxygen valve molar con
s
ta
nt (kmol/b
a
r/
s),
:
4
/
0
F
N
K
r
c
o
ns
tant, (kmol/s
/
A),
:
0
N
numbe
r of se
ries fuel
cell
s in the stack,
:
F
Fara
dy con
s
t
ant 9684
600
C/kmol.
2.3. Refo
rme
r
Model
A developed
model of PEMFC is g
e
n
e
rating
of hydrog
en throu
gh the meth
ane. Th
e
reform
er mod
e
l is
a
se
con
d
orde
r tra
n
sf
er fun
c
tion. T
he
math
emati
c
al
m
odel
of the
mod
e
l ca
n
be written as
follows
[15]:
1
)
(
2
1
2
2
1
2
s
s
CV
q
q
methane
H
(
1
0
)
Whe
r
e,
:
methane
q
methane flo
w
rate [kmol/s],
:
CV
conve
r
si
on fa
ctor [km
o
l of hydrog
en pe
r kmol of meth
ane],
:
,
2
1
reformer time c
o
ns
tants
[10].
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Fuzzy Sliding
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System
for Re
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hdi
Mansou
ri)
6021
2.4. DC/AC Inv
e
rter Model
The mo
del of
the inverte
r
i
s
given
in [14
]. DC/AC inv
e
rter i
s
used
to conve
r
t DC outp
u
t
voltage to A
C
. Fuel
cell
is
DC voltage
source
that
wh
en it
con
n
e
c
ted to th
e el
ectrical
load,
or
to
the electri
c
al
grid followe
d by a single
-
pha
se
o
r
three-p
h
a
s
e DC/AC inverter. Con
s
id
erin
g the
fuel cell a
s
a sou
r
ce of po
wer, the inve
rter
and loa
d
conne
ction i
s
shown in Figu
re 4.
Figure
4. Fue
l
cell, Inverter and Loa
d Co
nne
ction Di
ag
ram
The AC outp
u
t voltage as
a function of the modul
atio
n index
)
(
m
ca
n b
e
written a
s
:
cell
ac
mV
V
(
1
1
)
The AC outp
u
t powe
r
, rea
c
tive output p
o
we
r
and
L
I
can
be written a
s
:
X
V
mV
P
L
cell
ac
)
sin(
(12)
X
V
mV
mV
Q
L
cell
cell
ac
)
cos(
(13)
)
cos(
s
L
L
V
P
I
(14)
Whe
r
e,
:
m
inverter mo
du
lation index;
:
pha
se an
gle
of the AC voltage [rad];
:
ac
P
AC output po
wer from the i
n
verter [W];
:
ac
Q
reac
tive output power from
the inverter [VAR];
:
L
V
load termi
nal
voltage [V]; r
eacta
nce of the li
ne conn
e
c
ting the fuel
cell to the loa
d
;
:
L
I
load cu
rrent [A];
:
load pha
se angle [ra
d
];
:
L
P
load po
we
r [W]. and assu
ming a lossle
ss inve
rter:
stack
cell
dc
ac
I
V
P
P
(
1
5
)
)
cos(
L
stack
mI
I
(
1
6
)
PI controll
ers are u
s
e
d
to
cont
rol the
m
odulatio
n in
dex. The tra
n
sfer fun
c
tion of the
modulatio
n in
dex is:
),
(
6
5
ac
r
V
V
s
sK
K
m
(
1
7
)
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046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 601
7 –
6026
6022
We
re
5
K
and
6
K
are the PI gain,
and
r
V
is the
re
feren
c
e volta
ge si
gnal. T
h
e blo
ck
diag
ram of
the inverter
with the PI controlle
rs i
s
sh
o
w
ne
d in Figu
re 5.
A relation
ship
betwee
n
the
stack current
and
the mol
a
r flow of hydrogen
can b
e
written
as:
,
2
0
2
FU
I
N
q
stack
H
(
1
8
)
We
re U i
s
a u
t
ilization facto
r
. From (12),
(15
)
and (18
)
we obtai
n:
2
0
2
)
sin(
H
s
q
N
mV
FUX
(
1
9
)
Assu
ming
a
small
pha
se
angle. Eq
uati
on (18
)
de
scribe
s
the
rel
a
tionshi
p bet
ween th
e
output voltage phase angl
e and flow of hydroge
n. T
hese indicate
that the active powe
r
as
a
function of the voltage p
hase angl
e
can be co
ntro
lled by contro
lling the am
ount of flow of
hydrog
en.
Figure 5. The
DC/AC Inverter Model
The mod
e
l pa
ramete
rs a
r
e
as follo
ws:
:
ac
V
AC output voltage of the inverter (V
),
:
m
inverter mod
u
lation index
:
pha
se an
gle
of the AC voltage (rad
),
:
ac
P
AC output po
wer from the i
n
verter
(W),
:
ac
Q
reactive outp
u
t powe
r
from
the inverter (W),
:
L
V
load termin
al
voltage (V),
:
X
rea
c
tan
c
e of the line conn
e
c
ting the fuel
cell to the loa
d
,
:
L
I
load cu
rrent (A),
:
load ph
ase a
ngle (rad
),
:
L
P
load po
wer
(W),
:
stack
I
st
ac
k cu
rr
ent
(A
).
3. Contr
o
l Approac
h
A fuzzy slidi
n
g mode
controller is
de
sig
ned fo
r the P
E
MFC. The
structu
r
e of th
e fuzzy
slidin
g mode
control syste
m
is sh
own in
Figure 6.
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TELKOM
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ISSN:
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046
Fuzzy Sliding
Mode Co
ntro
l of PEM Fuel Cell
System
for Re
side
ntial… (Ma
hdi
Mansou
ri)
6023
e
e
e
FC
V
P
0
U
S
.
S
U
d
du
d
du
.
()
()
s
ce
k
e
k
.
()
(
)
ue
e
s
i
g
n
s
fu
z
z
y
con
t
r
o
l
l
er
P
EM
F
C
/
D
CA
C
con
vert
e
r
2.
Hb
q
Figure
6. Fuzzy Sliding Mo
de Co
ntrol System
3.1. Fuzzy
Logic Con
t
rol
l
er Design
The F
L
C
stud
ied in thi
s
se
ction ha
s two i
nputs:
the
error a
nd the
rat
e
of chan
ge o
f
erro
r
with:
b
H
ref
meth
H
q
q
q
e
,
2
2
,
(
2
0
)
Whi
c
h
2
H
q
is the hydroge
n flow from the current f
eedba
ck
signal p
r
o
portion
al to the terminal
load,
ref
meth
q
,
is the methane referen
c
e
sign
al
and
b
H
q
,
2
is the flow of hydro
gen feed
ba
ck
sign
al.
1
(
2
1
)
The o
u
tput o
f
the co
ntroll
er i
s
fed to
i
nput
of the
reforme
r
whi
c
h co
nvert
s
f
uel into
hydrog
en a
s
per loa
d
dem
and [13].
(
2
2
)
1
.
(
2
3
)
Each of
two inputs of
the
FLC have
fi
ve
lingui
stic
variable
s
a
n
d
the output
(U)
have
seven
varia
b
l
e
, namely,
“PB”, “PM”,
“PS”, “ZO
”
, “NB”, “NM
”
, “NS”,
wh
i
c
h
stand for “po
s
itive
large
”
, “po
s
itive
mediu
m
”, “positive sm
all”,
“ze
r
o”,
“n
eg
ative larg
e”,
“negat
ive med
i
um”, “ne
gative
small
”
. The ru
le base used
in the FLC is i
llustrate
d in T
able 1.
Table 1. Fu
zzy Rule Base
u
NB NS
ZO
PS
PB
s
NB NB
NB
NM
NM
ZO
NS NB
NS
NS
ZO
PM
ZO NB
NS
ZO
PS
PB
PS NM
ZO
PS
PS
PB
PB ZO
PM
PM
PB
PB
F
o
r
in
s
t
an
ce
, a
ru
le
in
th
e r
u
le b
a
s
e
ca
n
be
e
x
pr
ess
e
d b
y
: if e
rro
r
is
N
B
a
nd r
a
te
o
f
cha
nge
of e
rro
r i
s
NB, t
hen
output i
s
NB. In
fa
ct, in thi
s
section,
MIN-Max metho
d
i
s
impleme
n
ted.
Namely, the
output of ea
ch
rule
i
s
giv
en by the MI
N op
erato
r
,
while th
e total
output is give
n by the MAX operato
r
.
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ISSN: 23
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046
TELKOM
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KA
Vol. 12, No. 8, August 2014: 601
7 –
6026
6024
3.2. Sliding
Mode Co
ntr
o
ller Design
As previo
us
mentione
d; the output vol
t
age of
PEMFC an
d activ
e
power flo
w
from the
PEMFC to th
e loa
d
i
s
con
t
rolled th
oug
h controlli
ng
the flow of h
y
droge
n. Hen
c
e,
we
co
nsi
d
e
r
the error fun
c
tion as same
as (1
9).
For de
sign o
f
controlle
r, we a
s
sume
this pro
b
lem
is equal to
the tracki
ng
control
probl
em with
desi
r
ed traje
c
tory
)
(
,
2
ref
meth
H
d
q
q
x
and the tracking e
r
ror:
)
(
d
x
x
e
(
2
4
)
The model of
system with
assume
s
,
2
2
1
CV
is:
1
4
1
2
,
(25)
A sliding surf
ace for
se
con
d
orde
r sy
ste
m
s is d
e
termi
ned by:
0
),
)(
/
(
)
,
(
e
dt
d
t
x
s
(
2
6
)
To d
e
rive
a
control
law
su
ch th
at the
st
ate vari
able
remain
s o
n
th
e sli
d
ing
surf
ace,
we
define a Lyap
unov functio
n
:
,
2
/
1
2
s
V
(
2
7
)
Sufficient con
d
ition for the stability of the
system (2
1) i
n
the sen
s
e o
f
Lyapunov is:
,
0
,
)
(
/
2
/
1
2
s
s
dt
d
V
(
2
8
)
For the secon
d
orde
r sy
ste
m
(refo
rme
r
model
) we h
a
v
e:
e
e
s
(29)
e
e
s
(30)
With ass
u
me
1
we obtai
n:
),
4
/
1
2
/
1
)(
(
e
e
u
e
e
e
s
s
(
3
1
)
Definin
g
co
ntrolle
r sig
nal a
s
follow, we reach to con
d
i
t
ion (24
)
:
|
|
,
,
0
(
3
2
)
4. Simulation Resul
t
s an
d Discus
s
io
ns
The PEMF
C
model
which
is n
o
ted
in
section
2
is im
plemente
d
a
nd te
sted. T
h
e mo
del
para
m
eters a
r
e
given i
n
T
able
2. Thi
s
system
was t
e
sted
with
a
step
ch
ang
e
in the
loa
d
a
s
sho
w
n i
n
Fig
u
re
6. The
main g
oal in
this im
plem
entation i
s
to
investigate
the a
c
tive po
we
r
behavio
ur un
der effe
ct of termin
al load.
The reform
er controller
pa
ramete
rs
hav
e an imp
o
rta
n
t effect on the po
we
r co
ntrol. In
this pa
per, th
e fuzzy slidin
g mode
co
ntroller
wa
s abl
e to improve
the variation
of
and
flow
w
i
th
r
e
sp
ec
t to
lo
ad
c
h
an
ge
. T
h
e fu
zz
y
s
lid
ing
mod
e
c
o
n
t
ro
ller
ha
ve
a
fas
t
er
time
re
s
p
o
n
s
e
an
d
good tra
c
king
compa
r
ed to
the fuzzy an
d PI contro
lle
rs, as
sho
w
n
in Figure 7. T
he variation o
f
hydrog
en flo
w
is
sho
w
n i
n
Figu
re 8. A
s
note
d
abov
e, load chan
ge is a
refe
re
nce
sig
nal which
hydrog
en flo
w
sho
u
ld
be
cap
able
to track it
si
gnifi
cantly
with minimum error and
it obviou
s
ly
depi
cted in F
i
gure
8. Con
s
eq
uently, the fuzzy s
lidin
g mode
co
ntroller h
a
s b
e
tter pe
rforman
c
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Fuzzy Sliding
Mode Co
ntro
l of PEM Fuel Cell
System
for Re
side
ntial… (Ma
hdi
Mansou
ri)
6025
than othe
r ap
proa
ch. Th
e
error vari
atio
n is sho
w
n Fi
gure
9 and th
e absolute of
error i
s
sh
own in
Table 3. It is obvious that
erro
r variati
on with p
r
op
ose
d
app
roa
c
h con
s
ide
r
a
b
ly is lowe
r tha
n
other control method
s. Out
put voltage is sho
w
n Figu
re 10.
Table 2. Mod
e
l Paramete
rs
value
paramete
r
s
value
paramete
r
s
value
paramete
r
s
value
paramete
r
s
2S
7.716*
10
1.4251*
10
Kmo
l/sA
343K
T
2
CV
3.37S
0.8
U
9648460
0
C/Kmol
F
0.04777
B
6.74S
4.22*
10
Kmol/s
atm
8314.47
J/Kmol
K
R
0.0136V
C
18.418S
2.11*
10
Kmol/s atm
0.6 V
88
0.000015
0.05 ohm
X
0.2778
Rint
Figure 6. Loa
d Step
Figure 7. Power
Figure 8. Hyd
r
oge
n Flo
w
Figure 9. Erorr
Table 3. Absolut of Error
PI
Fuz
z
y
Fuzz
y
sliding mode
3.743*
10
6.961*
10
6.417*
10
0
10
20
30
40
50
60
70
80
90
100
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
ti
me
lo
a
d
l
oad
0
10
20
30
40
50
60
70
80
90
0
10
00
20
00
30
00
40
00
50
00
60
00
ti
m
e
pow
e
r
f
u
zzy
F
u
z
zy s
l
i
d
i
n
g
m
o
d
e
PI
0
10
20
30
40
50
60
70
80
90
10
0
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
x 1
0
-3
Ti
m
e
F
l
ow
H
y
d
r
oge
n
PI
F
u
zzy
F
u
zzy sl
i
d
i
n
g
0
10
20
30
40
50
60
70
80
90
10
0
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
2
2.
5
x 1
0
-3
Ti
m
e
E
rro
r
PI
Fu
z
z
y
F
u
z
z
y
s
lid
in
g
mo
d
e
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ISSN: 23
02-4
0
46
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 601
7 –
6026
6026
Figure 10. AC Voltage
5. Conclusio
n
In this
pape
r the PEM fu
el cell sy
ste
m
mod
e
l for
resi
dential
ge
neratio
n i
s
p
r
opo
s
ed.
This mo
del i
n
clu
d
e
s
a dy
namic fu
el cell model, a
methanol
ref
o
rme
r
mod
e
l, powe
r condi
tion
unit, and fuzzy sliding mode controller. The sim
u
lati
on results indi
cate that the DC-AC
converter
and fuel hav
e to be cont
rolled, an
d also indi
cate that the fuzzy sliding mo
de co
ntrolle
r is
effective to control the
flow for p
o
wer l
oad vari
ation.
PEMFCs
re
quire
goo
d control
syste
m
becau
se n
e
e
d
to ke
ep the
output po
we
r invari
able.
By using fu
zzy sliding m
o
d
e
co
ntrolle
r, fuel
cell
can fa
st
re
spon
se
chara
c
te
risti
c
, and h
a
ve
good
stea
dy-state
behavi
our a
n
d
stro
ng
robu
stne
ss.
Referen
ces
[1]
MA Laug
hton.
F
uel cel
l
s.
Pow
e
r Eng. J.,
vol.
16, no. 1, pp.
3
7–4
7, F
eb. 200
2.
[2]
P F
a
mour
i, R
G
e
mmen. PE
M fuel
cel
l
e
l
e
c
tric circuit m
o
del.
Pr
esent
ed
at the
Pow
e
r
Electron
ics fo
r
F
uel Ce
lls
. W
o
rkshop, Nat. F
uel C
e
lls R
e
s. Center, Un
iv. Califor
ni
a, Irvine, CA, Aug. 8–
9, 2002.
[3]
CJ Hatzia
do
ni,
U et al. A sim
p
l
i
fied
d
y
nam
ic
mode
l of gri
d
-c
onn
ected fu
el-
c
ell g
e
n
e
rators
.
IEEE Trans.
Pow
e
r Deliv
ery
.
2002; 17: 46
7
–47
3.
[4]
M Jeferson, A
Farret, N Canha,
G
Marce
l
o.
An El
ectroche
mical-Bas
ed F
uel-C
el
l Mod
e
l
Suitab
le fo
r
Electrical E
ngi
neer
ing A
u
tom
a
tion Ap
pro
a
ch
.
IEEE
T
r
ansac
tios on Ind
u
strial Electro
n
ics
. 200
4; 51(5).
[5]
F
r
umkin H, Hess J, V
i
ndi
gni
S. Energ
y
a
n
d
P
ublic Hea
l
th:
T
he Chall
e
n
g
e
of Peak Petrole
u
m.
Public
Healt
h
Rep
o
rts.
2009; 12
4(1): 5–1
9.
[6]
Peig
hamb
a
rd
o
u
st SJ, Ro
w
s
h
anzam
ir S,
Amjadi
M. Revi
e
w
of the pr
oton
exc
h
a
n
g
e
me
mbran
e
s for
fuel cel
l
ap
plic
ations.
Intern
ation
a
l Jour
na
l of Hydrog
en En
e
r
gy
.
2010; 35(
1
7
): 9349
–9
384.
[7]
Yued
on
g Z
han
, Jiang
uo Z
h
u, Youg
ua
ng G
u
o
,
Alex
Ro
drig
u
e
z.
An Intelligent Cont
roller for PEM Fuel
Cell P
o
w
e
r System Bas
e
d
on Dou
b
l
e
Close
d
-l
oop
Contro
l.
Australasian Univ
ersities Po
w
e
r
Engi
neer
in
g C
onfere
n
ce. 20
0
5
.
[8]
K Hauer. An
al
ysis T
ool for F
u
el Ce
ll Veh
i
cle
Hard
w
a
re a
nd
Soft
w
a
re (Co
n
trols) W
i
th an A
pplic
atio
n to
F
uel Eco
nom
y Comp
ariso
n
s
of Altern
ative
S
y
stem
Desi
gn
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