Inter
national
J
our
nal
of
P
o
wer
Electr
onics
and
Dri
v
e
Systems(IJPEDS)
V
ol.
7,
No.
3,
September
2016,
pp.
759
–
768
ISSN:
2088-8694
759
A
new
Backstepping
Sliding
Mode
Contr
oller
applied
to
a
DC-DC
Boost
Con
v
erter
Y
osra
Massaoudi
*
,
Dorsaf
Elleuch
*
,
J
ean
P
aul
Gaubert
**
,
Driss
Mehdi
**
,
and
T
arak
Damak
*
*
Uni
v
ersity
of
Sf
ax,
National
School
of
Engineering
of
Sf
ax,
Lab-ST
A,
PB
1173,
3038
Sf
ax,
T
unisia
**
Uni
v
ersity
of
Poitiers,
LIAS-ENSIP
,
Bat.B25-2,
Rue
Pierre
Brousse-
BP633,
86
022
Poitiers
Cede
x,
France
Article
Inf
o
Article
history:
Recei
v
ed
Feb
07,
2016
Re
vised
Jul
26,
2016
Accepted
Aug
8,
2016
K
eyw
ord:
Boost
con
v
erter
non
minimum
phase
chattering
phenomenon
super
twisting
SMC
backstepping
SMC.
ABSTRA
CT
In
order
to
deal
with
the
boost
con
v
erter
non
minimum
phase
property
and
to
solv
e
the
Slid-
ing
Mode
Control
(SMC)
major
problem
(
the
chattering
phenomenon),
a
ne
w
backstepping
Sliding
Mode
Controller
is
de
v
eloped.
In
this
paper
,
a
comparati
v
e
study
betw
een
the
pro-
posed
controller
and
the
(2-SMC)super
twisting
and
the
classica
l
SMC
is
pro
vided
in
order
to
e
v
aluate
each
controller
.
Simulations
and
e
xperimental
results
sho
w
the
ef
fecti
v
eness
and
the
rob
ustness
of
the
proposed
controller
with
respect
to
load
v
ariation.
Copyright
c
2016
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Y
osra
Massaoudi,
Uni
v
ersity
of
Sf
ax,
National
School
of
Engineering
of
Sf
ax,
Lab-ST
A,
PB
1173,
3038
Sf
ax,
T
unisia,
yosra.massaoudi1@gmail.com
1.
INTR
ODUCTION
The
boost
con
v
erter
is
widely
used
in
rene
w
able
ener
gy
area
and
in
particular
solar
ener
gy
([1,
2,
12,
15])
since
it
allo
ws
to
maintain
a
desired
output
v
oltage
despite
the
fluctuation
of
the
input
v
oltage
produced
by
the
rene
w-
able
ener
gy
s
ource.
Ho
we
v
er
,
the
output
v
oltage,
which
is
the
v
ariable
to
be
re
gulated,
is
a
non
minimum
phase
output
(due
to
the
boost
con
v
erter
inherent
Right
Half
Plane-zero).
Man
y
approaches
and
techniques,
such
as,
t
he
P
arallel
Damped
P
assi
vity
Based
Controller
[17],
the
Backstepping
Controller
(BC)
[5]
and
the
Sliding
Mode
Controller
(SMC)
[10],
ha
v
e
been
proposed
to
deal
with
the
non-minimum
phase
beha
vior
.
The
y
pro
vide
a
f
ast
transient
response
and
cope
with
the
boost
con
v
erter
parameter
v
ariations.
Pre
vious
w
ork
by
the
authors,
[10],
sho
w
that
the
Backstepping
Controller
and
the
P
arallel
Damped
P
assi
vity
Based
Controller
ha
v
e
a
good
tracking
and
rob
ustness
performance
b
ut
in
the
same
time
f
ail
to
solv
e
the
boost
non
minimum
phase
problem.
Moreo
v
er
,
despite
the
well
admitted
ef
fecti
v
eness
and
rob
ustness
of
SMC
strate
gies,
[18],
the
chatter
-
ing
phenomenon
remains
the
major
dra
wback
of
the
approach,
[18].
Man
y
solutions
ha
v
e
been
propos
ed
to
o
v
ercome
the
chattering
problem
and
to
mitig
ate
the
non
minimum
phase
boost
problem.
F
or
instance
[7]
proposes
a
ne
w
sliding
surf
ace
gi
ving
rise
to
an
inte
gral
SMC
or
a
double
inte
gral
SMC.
The
obtained
controller
reduces
the
chattering
phenomenon
b
ut
f
ails
to
suppress
it.
The
second
order
SMC
(2-SMC)
has
been
pro
v
ed
to
be
a
good
solution
for
the
chattering
problem.
Indeed,
for
dif
fer
-
ent
v
ariant
of
the
2-SMC,
that
is,
with
the
twisting
algorithm,
with
the
terminal
algorithm
or
with
the
quasi
continuous
algorithm,
the
chattering
is
eliminated.
No
w
adays,
the
(2-SMC)
with
super
-twist
ing
algorithm
is
preferable
since
it
reduces
the
chat
tering
phenomenon
in
man
y
applications.
Moreo
v
er
,
in
the
case
of
a
boost
con
v
erter
,
it
is
able
to
mitig
ate
the
non
mini
mum
phase
beha
vior
[4].
In
addition,
combining
the
SMC
with
others
approaches
g
a
v
e
rise
to
man
y
ne
w
approaches
such
as
a
PI
controller
in
[16],
a
fuzzy
controller
in
[19]
and
a
backstepping
controller
in
[14].
Through
the
backstepping
Sliding
Mode
Controller
(BSMC),
one
can
tak
e
the
adv
antages
of
both
methods
by
impro
v-
ing
the
Backstepping
rob
ustness
and
eliminating
the
Sliding
Mode
Controller
chattering
phenomenon
[6].
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJPEDS
Evaluation Warning : The document was created with Spire.PDF for Python.
760
ISSN:
2088-8694
In
this
paper
,
a
comparati
v
e
study
between
the
super
twisting
(2-SMC)
and
the
backstepping
SMC
with
the
classical
SMC
is
pro
vided
in
order
to
sho
w
the
adv
antages
of
each
controller
especially
in
terms
of
chattering
phenomenon
reduction
and
non
minimum
phase
beha
vior
mitig
ation.
The
paper
is
or
g
anized
as
follo
ws:
Section
2
present
s
the
modeling
of
the
boost
con
v
erter
.
In
section
3,
the
proposed
backstepping
Sliding
Mode
Controller
is
presented.Section
4
is
de
v
oted
to
recall
the
classical
SMC
and
the
(2-SMC)
with
super
twisting
controller
.
The
ef
fecti
v
eness
and
the
rob
ustness
of
the
proposed
approaches
are
v
erified
through
simulation
in
section
5
and
e
xperimentally
v
erified
in
section
6.
Some
conclusions
end
the
paper
in
section
7.
2.
BOOST
CONVER
TER
MODELLING
The
ideal
boost
con
v
erter
gi
v
en
by
Figure
1
contains
a
MOSFET
(an
acti
v
e
switch),
a
diode,
an
inductor
L
,
a
capacitor
C
,
a
load
resistance
R
.
W
e
notice
that
E
is
the
input
v
oltage,
V
s
is
the
output
v
oltage
and
is
the
duty
c
ycle:
Figure
1.
Boost
con
v
erter
The
a
v
erage
Boost
con
v
erter
model
is
gi
v
en
by
the
follo
wing
equations:
L
dx
1
(
t
)
dt
=
(1
u
(
t
))
x
2
(
t
)
+
E
C
dx
2
(
t
)
dt
=
(1
u
(
t
))
x
1
(
t
)
x
2
(
t
)
R
(1)
where:
x
1
is
the
input
current
a
v
erage
v
alue,
x
2
is
the
output
v
oltage
a
v
erage
v
alue
and
u
is
the
duty
ratio.
Let
X
1
r
be
the
input
current
reference
v
alue
(
constant),
then
the
equilibrium
v
alues
of
x
1
1
=
X
1
r
,
x
2
1
=
X
2
r
and
u
1
=
U
(
0
<
U
<
1
)
satisfy
the
follo
wing
equations:
X
1
r
=
E
R
(1
U
)
2
(2)
X
2
r
=
E
1
U
(3)
The
relation
between
X
1
r
and
X
2
r
is
gi
v
en
by:
X
1
r
=
X
2
2
r
R
E
(4)
3.
THE
PR
OPOSED
B
A
CKSTEPPING
SLIDING
MODE
CONTR
OLLER
The
backstepping
sli
ding
mode
controller
is
composed
of
the
backstepping
control
la
w
u
B
C
and
a
discontin-
uous
sliding
mode
control
la
w
u
dis
.
3.1.
The
backstepping
contr
ol
law
The
backstepping
design
control
is
a
recursi
v
e
Methodology
.
It
In
v
olv
es
a
systematic
b
uilding
of
both
feed-
back
control
la
w
and
the
associate
L
yapuno
v
function
([5,
9]).
The
backstepping
controller
will
be
designed
in
tw
o
steps
since
the
boost
con
v
erter
is
a
second
order
system.
The
first
step
:
The
output
error
is
defined
by:
e
1
=
x
1
X
1
r
(5)
IJPEDS
V
ol.
7,
No.
3,
September
2016:
759
–
768
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
761
The
output
error
deri
v
ati
v
e
is:
_
e
1
=
_
x
1
=
(1
u
)
L
(1
u
)
x
2
+
E
L
(6)
W
e
will
suppose
that
x
2
is
defined
as
follo
ws:
x
2
=
L
(1
u
)
(
c
1
e
1
+
1
L
E
)
(7)
Thus:
_
e
1
=
c
1
e
1
and
we
deduce
that
x
2
L
beha
v
es
as
a
control
v
ariable
of
e
1
and
its
virtual
e
xpression
is
gi
v
en
by:
1
=
1
(1
u
)
(
c
1
e
1
+
1
L
E
)
(8)
The
second
step
Considering
that
e
2
=
x
2
L
1
the
error
between
the
real
and
the
virtual
controllers.
The
deri
v
ati
v
e
of
e
1
can
be
re
written
as
follo
ws:
_
e
1
=
(1
u
)(
e
2
+
1
)
+
E
L
=
(1
u
)
e
2
c
1
e
1
(9)
In
order
to
kno
w
the
beha
vior
of
e
2
,
we
calculate
its
deri
v
ati
v
e:
_
e
2
=
_
x
2
L
_
1
(10)
_
1
=
_
u
(1
u
)
2
(
c
1
e
1
+
E
L
)
+
c
1
(1
u
)
_
e
1
=
_
u
(1
u
)
2
c
1
(1
u
)
((1
u
)
e
2
+
c
1
e
1
)
(11)
Then,
the
deri
v
ati
v
e
of
e
2
is:
_
e
2
=
(1
u
(
t
))
x
1
(
t
)
LC
x
2
(
t
)
R
LC
+
_
u
(1
u
)
2
+
c
1
(1
u
)
((1
u
)
e
2
+
c
1
e
1
)
(12)
W
e
will
consider
the
follo
wing
L
yapuno
v
function:
V
=
1
2
e
2
1
+
1
2
e
2
2
(13)
The
deri
v
ati
v
e
of
V
is
gi
v
en
by:
_
V
=
e
1
_
e
1
+
e
2
_
e
2
=
c
1
e
2
1
+
e
2
(
_
e
2
(1
u
)
e
1
)
(14)
Assuming
that
c
2
e
2
=
_
e
2
(1
u
)
e
1
,
we
deduce
that
_
V
=
c
1
e
2
1
c
2
e
2
2
:
(15)
The
control
la
w
must
satisfy
the
follo
wing
condition:
(1
u
)
2
e
1
c
2
(1
u
)
e
2
=
1
R
LC
(1
u
)
x
2
+
1
LC
x
1
(1
u
)
2
_
u
(1
u
)
1
+
c
1
((1
u
)
e
2
+
c
1
e
1
)
(16)
which
yields
_
u
=
(1
u
)
2
(
c
1
e
1
+
E
L
)
1
(((1
u
)
2
c
2
1
)
e
1
+
(
c
1
+
c
2
)(1
u
)
e
2
+
1
R
LC
(1
u
)
x
2
1
LC
x
1
(1
u
)
2
)
:
(17)
A
ne
w
BSMC
applied
to
a
Boost
Con
verter
(Y
osr
a
Massaoudi)
Evaluation Warning : The document was created with Spire.PDF for Python.
762
ISSN:
2088-8694
3.2.
The
discontinuous
sliding
mode
contr
ol
law
The
sliding
surf
ace
is
gi
v
en
by:
S
=
K
1
e
1
+
K
2
e
2
:
(18)
The
discontinuous
sliding
mode
control
la
w
can
be
written
as
follo
ws
[13]:
u
dis
=
k
S
j
S
j
+
:
(19)
3.3.
The
backstepping
sliding
mode
contr
ol
law
The
proposed
backstepping
sliding
mode
control
la
w
is
gi
v
en
by:
u
=
u
B
C
+
u
dis
(20)
_
u
B
C
=
(1
u
)
2
(
c
1
e
1
+
E
L
)
1
(((1
u
)
2
c
2
1
)
e
1
+
(
c
1
+
c
2
)(1
u
)
e
2
+
1
R
LC
(1
u
)
x
2
1
LC
x
1
(1
u
)
2
)
:
(21)
4.
RECALL
OF
THE
CLASSICAL
SMC
AND
THE
SECOND
ORDER
SMC
WITH
SUPER
TWISTING
4.1.
The
classical
sliding
mode
contr
oller
In
[8],
a
classical
sliding
mode
controller
is
gi
v
en
as
follo
ws:
u
=
1
for
S
<
0
,
0
for
S
>
0
.
The
sliding
surf
ace
is:
S
=
K
1
(
x
1
X
1
d
)
+
K
2
(
x
2
X
2
r
)
(22)
with:
X
1
d
=
X
2
r
x
2
R
E
:
the
input
current
reference
v
alue.
The
sliding
surf
ace
can
be
re
written
as
follo
ws:
S
=
K
1
(
x
1
X
1
r
)
+
K
0
2
(
x
2
X
2
r
)
=
K
1
e
1
+
K
0
2
e
2
(23)
with:
K
0
2
=
K
2
K
1
X
2
r
R
E
:
(24)
The
e
xistence
and
stability
conditions
are
v
erified
if
K
0
2
K
1
<
R
C
E
X
2
r
L
where
K
1
and
K
2
are
positi
v
e
scalars
[8].
4.2.
Second
order
sliding
mode
contr
oller
with
super
twisting
The
super
twisting
control
algorithm
is
gi
v
en
by
[11]:
u
=
u
1
+
u
2
(25)
_
u
1
=
sign
(
S
)
(26)
u
2
=
j
S
j
sign
(
S
)
(27)
with:
>
0
,
>
0
and
=
0
:
5
IJPEDS
V
ol.
7,
No.
3,
September
2016:
759
–
768
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
763
5.
SIMULA
TION
RESUL
TS
In
order
to
test
the
ef
fecti
v
eness
and
the
rob
ustness
of
each
controller
,
the
a
v
erage
model
of
the
DC-DC
con-
v
erter
has
been
simulated
using
the
Matab/Simulink
softw
are.
The
simulations
were
performed
with
the
follo
wing
parameter’
s
v
alues
and
the
initial
v
alues
are:
R
=
30
;
L
=
10
mH
;
C
=
100
F
;
E
=
15
V
;
T
e
=
50
s;
X
2
r
=
30
V
x
1
(0)
=
0
:
6
A;
x
2
(0)
=
16
V
;
u
(0)
=
0
:
1
:
CSMC
parameters:
K
1
=
0
:
01
,
K
2
=
0
:
5
(2-SMC)ST
parameters:
K
1
=
0
:
01
,
K
2
=
5
=
0
:
1
,
=
0
:
1
BSMC
parameters:
c
1
=
700
,
c
2
=
7000
,
K
1
=
50
,
K
2
=
1
,
k
=
0
:
01
,
=
0
:
5
.
5.1.
Refer
ence
v
ariation:
In
this
e
xperiment,
the
current
reference
v
ariation
switches
from
2
A
to
3
A
at
0
:
05
s
.
The
desired
v
alues
of
the
output
v
oltage
and
the
duty
ratio
are
gi
v
en
by
T
able
1.
T
able
1.
Desired
v
alues
of
the
output
v
oltage
and
the
duty
ratio
CSMC
(2-SMC)ST
BSMC
X
1
r
(
A
)
2
3
X
2
r
(
V
)
30
36
:
74
U
0
:
5
0
:
6
0
0.02
0.04
0.06
0.08
0.1
0
20
40
O
u
t
p
u
t
V
o
l
t
a
g
e
[
V]
0
0.02
0.04
0.06
0.08
0.1
0
2
4
I
n
p
u
t
C
u
r
r
e
n
t
[
A]
0
0.02
0.04
0.06
0.08
0.1
0
0.5
1
D
u
t
y
r
a
t
i
o
0
0.02
0.04
0.06
0.08
0.1
−1
0
1
T
i
m
e
[
s
]
S
l
i
d
i
n
g
s
u
r
f
a
c
e
(a)
CSMC
0
0.02
0.04
0.06
0.08
0.1
0
0.5
1
D
u
t
y
r
a
t
i
o
0
0.02
0.04
0.06
0.08
0.1
10
20
30
40
O
u
t
p
u
t
v
o
l
t
a
g
e
[
V]
0
0.02
0.04
0.06
0.08
0.1
0
2
4
I
n
p
u
t
c
u
r
r
e
n
t
[
A]
0
0.02
0.04
0.06
0.08
0.1
−10
−5
0
5
T
i
m
e
[
s
]
S
l
i
d
i
n
g
s
u
r
f
a
c
e
BSMC
ref
(2−SMC)ST
(b)
BSMC
and
(2-S
MC)ST
Figure
2.
Simulation
results
with
reference
v
ariation
.
T
able
2.
Performances
of
the
CSMC,
(2-SMC)ST
and
the
BSMC.
Rise
time
5%(
ms
)
0
:
7157
3
:
2
2
:
9
Settling
time
(
ms
)
2
:
05
2
:
35
3
:
5
Ov
ershoot
(
A
)
26
:
5254
6
:
7929
0
Peak
(
A
)
2
:
4571
2
:
0769
2
A
ne
w
BSMC
applied
to
a
Boost
Con
verter
(Y
osr
a
Massaoudi)
Evaluation Warning : The document was created with Spire.PDF for Python.
764
ISSN:
2088-8694
W
e
notice
from
Figure
2,
that
the
input
current
and
the
output
v
oltage
tracking
are
ef
fecti
v
e
in
all
cases.
Ho
we
v
er
,
we
can
say
from
T
able
2
that
the
BSMC
approach
outperforms
the
other
approaches
s
ince
it
reaches
its
desired
v
alue
with
no
o
v
ershoot
and
no
peak
v
alue
and
with
a
relati
v
e
sm
all
settling
time.
The
zoomed
parts
in
Figure
2
sho
w
that
the
chattering
phenomenon
presented
in
the
case
of
the
CSMC
is
reduced
by
the
(2-SMC)ST
and
totally
eliminated
by
the
BSMC
and
non-minimum
phase
beha
vior
seen
plainly
in
the
CSMC
output
v
oltage
is
mitig
ated
by
the
BSMC
and
well
impro
v
ed
by
the
(2-SMC)ST
.
5.2.
Load
r
esistor
v
ariation
In
order
to
e
v
aluate
the
rob
ustness
of
the
proposed
controllers,
a
load
resistor
v
ariation
is
applied
from
R
=
30
to
R
=
15
at
t
=
0
:
5
s
in
the
cas
e
of
CSMC
and
B
SMC
and
at
t
=
2
s
in
the
case
of
(2-SMC)ST
(in
or
d
e
r
to
see
clearly
the
response).
The
desired
v
alues
of
the
output
v
oltage
and
the
duty
ratio
are
gi
v
en
by
T
able
3.
T
able
3.
Desired
v
alues
of
the
output
v
oltage
and
the
duty
ratio.
CSMC
(2-SMC)ST
BSMC
R
()
30
15
X
1
r
(
A
)
2
2
X
2
r
(
V
)
30
21
:
21
0
0.02
0.04
0.06
0.08
0.1
0
1
2
3
I
n
p
u
t
C
u
r
r
e
n
t
[
A]
0
0.02
0.04
0.06
0.08
0.1
10
20
30
40
O
u
t
p
u
t
V
o
l
t
a
g
e
[
V]
0
0.02
0.04
0.06
0.08
0.1
0
0.5
1
D
u
t
y
r
a
t
i
o
0
0.02
0.04
0.06
0.08
0.1
−1
−0.5
0
0.5
T
i
m
e
[
s
]
S
l
i
d
i
n
g
s
u
r
f
a
c
e
(a)
CSMC
0
0.5
1
1.5
2
2.5
3
10
20
30
40
O
u
t
p
u
t
v
o
l
t
a
g
e
[
V]
0
0.5
1
1.5
2
2.5
3
0
2
4
I
n
p
u
t
c
u
r
r
e
n
t
[
A]
0
0.5
1
1.5
2
2.5
3
0
0.5
1
D
u
t
y
r
a
t
i
o
0
0.5
1
1.5
2
2.5
3
−10
−5
0
5
T
i
m
e
[
s
]
S
l
i
d
i
n
g
s
u
r
f
a
c
e
BSMC
ref
(2−SMC)ST
(b)
BSM
C
and
(2-SMC)ST
Figure
3.
Simulation
results
with
load
resistor
v
ariation
.
It
can
be
seen
from
Figure
3
that
all
controllers
are
rob
ust.
Ho
we
v
er
,
the
BSMC
beha
vior
ag
ainst
a
load
v
ariation
is
better
than
the
CSMC
(elimination
of
chattering)
and
f
aster
than
the
(2-SMC)ST
.
This
is
e
xplained
by
the
f
act
that
the
(2-SMC)ST
control
la
w
contains
an
inte
gral
term
which
slo
w
do
wn
the
system.
6.
EXPERIMENT
AL
RESUL
TS
These
controllers
were
e
xperimentally
e
v
aluated
on
the
real
system
a
v
ailable
in
the
LIAS
laboratory
.
IJPEDS
V
ol.
7,
No.
3,
September
2016:
759
–
768
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
765
6.1.
Experiments
in
open
loop
Experiments
in
open
loop
presented
by
Figure
4
sho
w
a
dif
ference
between
the
theoretical
output
v
oltage
v
alue
and
the
e
xperimental
output
v
oltage
v
alue.
The
same
phenomenon
is
noticed
for
the
input
current.
The
ne
glected
internal
resistor
of
the
inductor
and
the
MOSFET
in
the
on-state
and
the
threshold
v
oltage
with
the
dynamic
resistance
of
the
diode
could
be
a
source
of
these
errors
[3].
0.1
0.2
0.3
0.4
0.5
0.6
15
20
25
30
35
40
D
u
t
y
R
a
t
i
o
O
u
t
p
u
t
V
o
l
t
a
g
e
[
V]
V
s
e
x
p
V
s
t
h
(a)
Output
v
oltage.
0.1
0.2
0.3
0.4
0.5
0.6
0.5
1
1.5
2
2.5
3
3.5
D
u
t
y
R
a
t
i
o
I
n
p
u
t
C
u
r
r
e
n
t
[
A]
i
L
e
x
p
i
L
t
h
(b)
Input
current.
Figure
4.
Experimental
curv
es
in
open
loop.
6.2.
Experiments
in
closed
loop
The
controllers
implementation
w
as
carried
out
using
the
DSP-based
system
DS1104
de
v
eloped
by
DSpace.
Refer
ence
V
ariation:
(a)
CSMC
(b)
(2-SMC)ST
(c)
BS
MC
Figure
5.
Experimental
results
with
r
eference
v
ariation:
1-
The
input
current
i
L
(
t
)
;
2-
The
output
v
oltage
V
s
(
t
)
;
3-
The
duty
c
ycle
u
(
t
)
;
4-
The
sliding
surf
ace.
.
Figure
5
sho
ws
that
the
e
xperimental
results
are
similar
to
the
simulation
results
and
the
state
error
i
s
justified
by
ne
glecting
the
internal
resistors
of
the
inductance,
the
MOSFET
and
the
diode
as
well
as
the
diode
threshold
v
oltage
and
the
switching
transient
beha
vior
for
semiconductors
as
sho
wn
in
Figure
4.
The
BSMC
and
the
(2-SMC)ST
are
able
to
eliminate
the
chattering
phenomenon
which
appears
in
the
case
of
CSMC
and
which
is
undesirable
for
po
wer
con
v
erters.
Ho
we
v
er
,
the
BSMC
is
f
aster
than
the
(2-SMC)ST
.
Load
r
esistor
V
ariation:
A
ne
w
BSMC
applied
to
a
Boost
Con
verter
(Y
osr
a
Massaoudi)
Evaluation Warning : The document was created with Spire.PDF for Python.
766
ISSN:
2088-8694
(a)
CSMC
(b)
(2-SMC)ST
(c)
BSMC
Figure
6.
Experimental
results
with
load
resistor
v
ariation:
1-
The
input
current
i
L
(
t
)
;
2-
The
output
v
oltage
V
s
(
t
)
;
3-
The
duty
c
ycle
u
(
t
)
;
4-
The
sliding
surf
ace.
.
It
is
observ
able
from
Figure
6
that
the
BSMC
is
more
rob
ust
than
the
CSMC
and
the
(2-SMC)S
T
and
it
is
insensiti
v
e
to
a
load
resistor
v
ariation.
Ho
we
v
er
,
the
(2-SMC)ST
tak
es
its
time
to
reach
the
desired
v
alue
under
a
load
resistor
v
ariation.
A
similar
beha
vior
is
reported
in
[20].
7.
CONCLUSION
In
this
paper
,
we
de
v
eloped
a
ne
w
backstepping
sliding
mode
controller
(BSMC
applied
to
a
DC-DC
Boost
con
v
erter
.
In
order
to
v
erify
the
ef
fecti
v
eness
and
the
rob
ustness
of
this
controller
,
a
comparati
v
e
study
with
the
classical
Sliding
Mode
Controller
and
the
Super
twisting
Sliding
Mode
Controller
(2-SMC)ST)
w
as
presented.
W
e
conclude
that
the
chattering
phenomenon
which
is
the
major
problem
of
classical
SMC
is
reduced
by
the
(2-SMC)ST
and
totally
eliminated
by
the
BSMC.
Ho
we
v
er
,
the
non
minimum
phase
beha
vior
is
mitig
ated
by
the
BSM
C
and
well
impro
v
ed
by
the
(2-SMC)ST
.
REFERENCES
[1]
A
L
L
A
H
,
B
.
A
.
,
A
N
D
D
J
A
M
E
L
,
L
.
Control
of
po
wer
and
v
oltage
of
solar
grid
connected.
Bulletin
of
Electrical
Engineering
and
Informatics
5
,
1
(2016),
37–44.
[2]
A
N
U
S
U
Y
A
D
E
V
I
,
R
.
,
P
A
N
D
I
A
R
A
J
A
N
,
P
.
S
.
,
A
N
D
B
H
A
R
A
T
H
I
,
J
.
M
.
Sliding
mode
controller
based
maximum
po
wer
point
tracking
of
dc
to
dc
boost
con
v
erter
.
International
J
ournal
of
P
ower
Electr
onics
and
Drive
System
(IJPEDS)
3
,
3
(2013),
321–327.
[3]
A
R
J
U
N
,
M
.
,
A
N
D
P
A
T
I
L
,
V
.
Steady
state
and
a
v
eraged
state
space
modelling
of
non-ideal
boost
con
v
erter
.
International
J
ournal
of
P
ower
Electr
onics
7
,
1/2
(2015),
109–133.
[4]
A
S
H
O
K
,
R
.
,
A
N
D
S
H
T
E
S
S
E
L
,
Y
.
Sliding
mode
control
of
electric
po
wer
system
comprised
of
fuel
cell
and
multiple-modular
dc-dc
boost
con
v
erters.
In
V
ariable
Structur
e
Systems
(VSS),
2014
13th
International
W
orkshop
on
(June
2014),
pp.
1–7.
[5]
E
L
F
A
D
I
L
,
H
.
,
A
N
D
G
I
R
I
,
F
.
Backstepping
based
control
of
pwm
dc-dc
boost
po
wer
con
v
erters.
In
Industrial
Electr
onics,
2007.
ISIE
2007.
IEEE
International
Symposium
on
(June
2007),
pp.
395–400.
[6]
E
L
L
E
U
C
H
,
D
.
,
A
N
D
D
A
M
A
K
,
T
.
Backstepping
sliding
mode
controller
coup
l
ed
to
adapti
v
e
sliding
mode
ob-
serv
er
for
interconnected
fractional
nonlinear
system.
W
orld
Academy
of
Science
,
Engineering
and
T
ec
hnolo
gy
(2013).
[7]
H
A
R
I
R
C
H
I
,
F
.
,
R
A
H
M
A
T
I
,
A
.
,
A
N
D
A
B
R
I
S
H
A
M
I
F
A
R
,
A
.
Boost
pfc
con
v
erters
with
inte
gral
and
double
inte
gral
sliding
mode
control.
19th
Ir
anian
Confer
ence
on
Electrical
Engineering
(ICEE)
(2011),
1–6.
[8]
H
I
J
A
Z
I
,
A
.
,
D
I
L
O
R
E
T
O
,
M
.
,
B
I
D
E
A
U
X
,
E
.
,
V
E
N
E
T
,
P
.
A
N
D
C
L
E
R
C
,
G
.
,
A
N
D
R
O
J
A
T
,
G
.
Sliding
mode
control
of
boost
con
v
erter:
Application
to
ener
gy
storage
system
via
supercapacitors.
In
EPE
(2009).
IJPEDS
V
ol.
7,
No.
3,
September
2016:
759
–
768
Evaluation Warning : The document was created with Spire.PDF for Python.
IJPEDS
ISSN:
2088-8694
767
[9]
M
A
S
S
A
O
U
D
I
,
Y
.
,
D
A
M
A
K
,
T
.
,
G
H
A
M
G
U
I
,
M
.
,
A
N
D
M
E
H
D
I
,
D
.
Comparison
between
a
backstepping
mode
control
and
a
sliding
mode
control
for
a
boost
dc-dc
con
v
erter
of
a
photo
v
oltaic
panel.
In
Systems,
Signals
De
vices
(SSD),
2013
10th
International
Multi-Confer
ence
on
(March
2013),
pp.
1–7.
[10]
M
A
S
S
A
O
U
D
I
,
Y
.
,
E
L
L
E
U
C
H
,
D
.
,
M
E
H
D
I
,
D
.
,
D
A
M
A
K
,
T
.
,
A
N
D
H
A
S
H
I
M
,
G
.
Comparison
between
non
linear
controllers
applied
to
a
dc-dc
boost
con
v
erter
.
International
J
ournal
of
Inno
vati
ve
Computing
,
Information
and
Contr
ol
11
,
3
(2015),
935–947.
[11]
M
E
F
O
U
E
D
,
S
.
,
M
O
H
A
M
M
E
D
,
S
.
,
A
N
D
A
M
I
R
A
T
,
Y
.
T
o
w
ard
mo
v
ement
restoration
of
knee
joint
using
rob
ust
control
of
po
wered
orthosis.
Contr
ol
Systems
T
ec
hnolo
gy
,
IEEE
T
r
ansactions
on
21
,
6
(No
v
2013),
2156–2168.
[12]
O
L
A
D
I
M
E
J
I
,
I
.
,
Y
A
H
A
Y
A
,
Y
.
N
.
Z
.
,
A
N
D
N
O
R
D
I
N
,
S
.
State-space
modelling
and
digital
controller
design
for
dc-dc
con
v
erter
.
T
elecommunication,
Computing
,
Electr
onics
and
Contr
ol
14
,
2
(2016).
[13]
R
I
O
S
-
B
O
L
I
V
A
R
,
M
.
A
N
D
Z
I
N
O
B
E
R
,
A
.
,
A
N
D
S
I
R
A
-
R
A
M
I
R
E
Z
,
H
.
Dynamical
sliding
mode
control
via
adapti
v
e
input-output
linearization:
A
backstepping
approach.
In
Rob
ust
Contr
ol
via
V
ariable
Structur
e
and
L
yapuno
v
T
ec
hniques
,
F
.
Garof
alo
and
L.
Glielmo,
Eds.,
v
ol.
217
of
Lectur
e
Notes
in
Contr
ol
and
Information
Sciences
.
Springer
Berlin
Heidelber
g,
1996,
pp.
15–35.
[14]
R
I
O
S
-
B
O
L
I
V
A
R
,
M
.
,
Z
I
N
O
B
E
R
,
A
.
S
.
I
.
,
A
N
D
S
I
R
A
-
R
A
M
I
R
E
Z
,
H
.
Adapti
v
e
sliding
mode
output
tracking
via
backstepping
for
uncertain
nonlinear
systems.
In
Pr
oceedings
of
3r
d
Eur
opean
Contr
ol
Confer
ence
(1995).
[15]
S
I
D
D
I
K
,
A
.
A
.
,
A
N
D
S
H
A
N
G
E
E
T
H
A
,
M
.
Implementation
of
fuzzy
logic
controller
in
photo
v
oltaic
po
wer
gen-
eration
using
boost
con
v
erter
and
boost
in
v
erter
.
International
J
ournal
of
P
ower
Electr
onics
and
Drive
Systems
(IJPEDS)
2
,
3
(2012),
249–256.
[16]
S
I
R
A
-
R
A
M
I
R
E
Z
,
H
.
,
M
A
R
Q
U
E
Z
,
R
.
,
A
N
D
F
L
I
E
S
S
,
M
.
Generalized
pid
sliding
mode
control
of
dc
to
dc
po
wer
con
v
erters.
IF
A
C/IEEE:
Symposium
on
system
structur
e
and
contr
ol,
Czec
k
Republic,
Pr
a
gue
(29-31
August
2001).
[17]
S
O
N
,
Y
.
I
.
,
A
N
D
K
I
M
,
I
.
H
.
Complementary
pid
controller
to
passi
vity-based
nonlinear
control
of
boost
con-
v
erters
with
inductor
resistance.
IEEE
T
r
ansactions
On
Contr
ol
Systems
T
ec
hnolo
gy
20
(2012).
[18]
V
E
R
M
A
,
S
.
,
S
I
N
G
H
,
S
.
K
.
,
A
N
D
R
A
O
,
A
.
G
.
Ov
ervie
w
of
control
techniques
for
dc-dc
con
v
erters.
Resear
c
h
J
ournal
of
Engineering
Sciences
V
ol.
2(8)
(2013),
18–21.
[19]
Y
A
N
G
,
Y
.
-
N
.
,
W
U
,
J
.
,
A
N
D
Z
H
E
N
G
,
W
.
T
rajectory
tracking
for
an
autonomous
airship
using
fuzzy
adapti
v
e
sliding
mode
control.
J
ournal
of
Zhejiang
Univer
sity
SCIENCE
C
13
,
7
(2012),
534–543.
[20]
Z
A
I
D
I
,
N
.
,
J
E
M
L
I
,
M
.
,
B
E
N
A
Z
Z
A
,
H
.
,
A
N
D
B
O
U
S
S
A
K
,
M
.
A
time-v
arying
g
ain
super
-twisting
algorithm
to
dri
v
e
a
spim.
J
ournal
of
P
ower
Electr
onics
6
,
6
(2013).
BIOGRAPHY
OF
A
UTHORS
Y
osra
Massaoudi
recei
v
ed
her
diploma
in
Electrical
Engineering
from
the
National
School
of
En-
gineers
of
Sf
ax,
T
unisia,
in
2010.
From
the
same
school,
she
recei
v
ed
her
M.
S.
de
gree
in
Automatic
and
Industrial
Informatics
and
the
Ph.
D.
in
Electrical
Engineering,
in
2011
and
2015
respecti
v
ely
.
She
is
currently
a
doctor
in
the
Laboratory
of
Sciences
and
T
echniques
of
Automatic
and
Com-
puter
Engineering
Lab-ST
A,
Uni
v
ersity
of
Sf
ax.
Her
research
interests
include
boost
con
v
erters
modelling
and
control,
nonlinear
control
and
especialy
sliding
mode
control.
A
ne
w
BSMC
applied
to
a
Boost
Con
verter
(Y
osr
a
Massaoudi)
Evaluation Warning : The document was created with Spire.PDF for Python.
768
ISSN:
2088-8694
Dorsaf
Elleuch
recei
v
ed,
from
the
Higher
School
of
Sciences
and
T
echnique
of
T
unisia,
her
M.
S
de
gree
in
Electri
cal
Engineering
in
2005
and
her
M.
S
de
gree
in
Automatic-Product
in
2007.
She
had
the
PHD
de
gree
in
Automatic
and
Industrial
Informatics
in
2011
from
the
National
School
of
Engineers
of
Sf
ax
T
unisia.
She
is
currently
an
assistant
Professor
in
ISSA
T
Gafsa
,
T
unisia.
Her
current
research
interests
are
in
the
fields
of
rob
ust
sliding
mode
control
and
observ
ers,
Robots
control,
photo
v
oltaque
systems.
J
ean
P
aul
Gaubert
w
as
born
in
France
in
1965.
He
recei
v
ed
the
Engineer’
s
de
gree
in
electrical
engineering
from
the
Uni
v
ersity
of
Clermont-Ferrand,
France,
in
1988,
and
the
M.Sc.
and
Ph.D.
de
grees
in
electrical
engineering
from
the
Uni
v
ersity
of
Science
and
T
echnology
of
Lille,
Lille,
France,
in
1990
and
1992,
respecti
v
ely
.
He
is
currently
an
Associate
Professor
with
the
Automatic
Control
and
Industrial
Data
Processing
Laboratory
(LAII),
Poitiers
National
School
of
Engineering
(ESIP),
Uni
v
ersity
of
Poitiers,
Poitiers,
France.
His
current
research
interests
are
the
modeling
and
adv
anced
control
of
po
wer
con
v
erters
and
po
wer
electronics
systems
and
their
digital
control
tech-
niques.
The
deri
v
ed
topics
deal
with
po
wer
quality
,
such
as
acti
v
e
filters,
pulse
width
modulation
rectifiers,
or
rene
w
able
ener
gy
systems.
Driss
Mehdi
recei
v
ed
an
engineer
de
gree
from
Mohammadia
Engineering
School,
Rabat,
Morocco
in
1979
and
a
Ph.
D.
de
gree
in
automatic
control
from
Nanc
y
Uni
v
ersity
in
1986.
He
w
as
a
senior
lecturer
from
1988
to
1992
at
Louis
P
asteur
Uni
v
ersity
in
Strasbour
g
and
since
1992
he
has
been
professor
at
the
Uni
v
ersity
of
Poitiers.
His
research
interests
include
automatic
control,
rob
ust
control,
delay
and
descriptor
systems.
T
arak
Damak
recei
v
ed
his
diploma
in
Electrical
Engineering
from
the
National
School
of
Engi-
neers
of
Sf
ax,
T
unisia,
in
1989
and
his
D.E.A
de
gree
in
Automatic
Control
from
the
Institut
National
des
Sciences
Appliques
de
T
oulouse,
France,
in
1990.
He
recei
v
ed
his
Ph.D.
from
the
Uni
v
ersit
P
aul
Sabatier
de
T
oulouse,
France,
in
1994.
I
n
2006.
He
then
obtained
the
Uni
v
ersity
Habilitation
from
the
National
School
of
Engineers
of
Sf
ax.
He
is
currently
a
professor
in
the
Department
of
Mechan-
ical
Engineering
of
the
National
School
of
Engineers
of
Sf
ax,T
unisia.
His
current
research
interests
are
in
the
fields
of
distrib
uted
parameter
systems,
sliding
mode
control
and
observ
ers,
adapti
v
e
nonlinear
control.
IJPEDS
V
ol.
7,
No.
3,
September
2016:
759
–
768
Evaluation Warning : The document was created with Spire.PDF for Python.