Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol.
4, No. 4, Decem
ber
2014, pp. 481~
488
I
S
SN
: 208
8-8
6
9
4
4
81
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Sliding Mode Backstepping Control of Induction
Motor
Othmane B
o
ugh
a
z
i
,
Abde
lmadjid B
oume
dienne, Hac
h
e
m
i
Glaoui
Faculty
of Scien
ces and
technolo
g
y
, BEC
HAR U
n
iversity
B.P. 41
7 BECHAR, 080
00
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 30, 2014
Rev
i
sed
Sep
15
, 20
14
Accepte
d Oct 2, 2014
This work treats
the modeling and simu
lation of
non-linear s
y
stem behavior
of an indu
ction
motor using b
ackst
epp
i
ng slid
ing mode contr
o
l (BACK-
S
M
C). F
i
rs
t, the direct fi
eld ori
e
nted
contro
l IM is derived. Th
en, a sliding
for direct field o
r
iented control is pr
oposed to co
mpensate the un
certainties,
which occur
in
the contro
l. F
i
nally
,
th
e stud
y
of Backstepp
i
ng sliding
controls str
a
teg
y
of
th
e indu
ction motor drive. Our non linear
s
y
stem is
sim
u
lated in MATLAB SIMULINK environm
ent, the res
u
lts obtained
illustrate th
e eff
i
ci
ency
of th
e p
r
oposed control
with no overshoot, and
th
e
rising time is im
proved with goo
d disturba
nc
es re
jec
tions com
p
ari
ng with the
classic
a
l contro
l law.
Keyword:
Backstepping
I
ndu
ctio
n m
o
to
r
Propo
rtion
a
l-i
n
teg
r
al (PI)
Sl
i
d
i
n
g
m
ode c
ont
rol
Sl
i
d
i
n
g
m
ode c
ont
rol
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Hachem
i Glaoui
Faculty of Scie
nces a
n
d technology,
BECHAR Un
iv
ersity,
B.P.
4
17 BECH
A
R
, 080
00
Em
a
il: mek
k
a
60
@g
m
a
il.co
m
1.
INTRODUCTION
The
de
velopment of induction m
o
tor drives hasc
onside
rably acceler
ated in orde
r t
o
satisfy the
i
n
creasi
n
g nee
d
of
vari
ou
s i
n
dust
r
i
a
l
appl
i
c
at
i
ons i
n
l
o
w and m
e
di
um
po
wer ra
n
g
e. I
n
d
eed, i
n
duct
i
on
m
o
t
o
rs
have si
m
p
l
e
struct
ure,
hi
g
h
effi
ci
en
cy and
in
creased
to
rque/in
ertia ratio
. Howev
e
r, th
eir d
y
n
a
m
i
ca
l
m
o
d
e
l is
n
o
n
lin
ear, m
u
ltiv
ariab
l
e, coup
led
,
and
is sub
j
ect t
o
p
a
ram
e
ter un
certai
n
ties sin
ce t
h
e
p
hysical p
a
ram
e
t
e
rs are
t
i
m
e
-vari
a
nt
. T
h
e
desi
g
n
of
r
o
bust
co
nt
r
o
l
l
e
r
s
bec
o
m
e
s t
h
en
a rel
e
vant
c
h
al
l
e
nge
[
1
]
-
[
2
]
.
In
d
u
ct
i
on m
o
t
o
r
dri
v
es co
nt
rol
ha
s bee
n
a
n
act
i
v
er
esea
rch dom
a
in over the last years. Di
ffe
rent
cont
rol
t
ech
ni
q
u
es suc
h
as Fi
e
l
d-
Ori
e
nt
e
d
co
nt
r
o
l
(FOC
), fe
edbac
k
l
i
n
eari
z
at
i
on co
nt
r
o
l
,
s
l
i
d
i
ng m
ode co
nt
r
o
l
p
a
ssiv
ity ap
pro
ach, and
ad
ap
tiv
e con
t
ro
l h
a
v
e
b
e
en
reported
in
th
e liter
a
tu
re [3
]. Th
e FOC en
su
res p
a
rtial
deco
u
p
l
i
ng
of
t
h
e pl
ant
m
odel
usi
ng a sui
t
a
bl
e t
r
ans
f
o
r
m
a
t
i
on an
d t
h
en
PI co
nt
r
o
l
l
e
rs are use
d
f
o
r t
r
acki
n
g
reg
u
l
a
t
i
o
n
er
r
o
rs
. T
h
e
hi
g
h
per
f
o
r
m
a
nce o
f
s
u
c
h
st
ra
t
e
gy
m
a
y
be det
e
ri
orat
e
d
i
n
pract
i
ce
due
t
o
pl
ant
u
nce
r
t
a
i
n
t
i
e
s [4]
-
[
5]
. E
x
act
i
n
put
-
o
ut
put
feed
bac
k
l
i
n
eari
zat
i
on
o
f
i
n
duct
i
o
n m
o
t
o
rs m
odel
can
b
e
obt
ai
ne
d u
s
i
n
g
t
ool
s fr
om
di
ffere
nt
i
a
l
geom
et
ry
. Thi
s
m
e
tho
d
cancel
s t
h
e no
nl
i
n
ear t
e
r
m
s i
n
t
h
e pl
ant
m
odel
w
h
ich
f
a
ils when
th
e
p
h
y
sical p
a
r
a
m
e
ter
s
v
a
r
i
es [
6
]-[7
].
By co
n
t
r
a
st,
p
a
ssiv
ity-
b
ased
contr
o
l do
es
n
o
t
can
cel
all th
e n
o
n
lin
earities b
u
t
enfo
rce th
em
to
b
e
p
a
ssiv
e,
i.e. d
i
ssip
a
ting
en
erg
y
and
h
e
nce en
suring
track
ing
regi
m
e
[8]
-
[
1
0
]
. Sl
i
d
i
ng M
o
de C
o
nt
r
o
l
(S
M
C
) i
s
wi
d
e
l
y
ap
p
lied
b
e
cau
s
e of its easin
ess and
attractiv
e
r
obu
stn
e
ss prop
er
ties
[
1
1
]
-
[
12
].
Ot
he
rwi
s
e, t
h
e
con
v
e
n
t
i
onal
PI co
nt
r
o
l
l
e
rs
are t
h
e m
o
st
com
m
on al
gori
t
hm
s used i
n
i
n
dust
r
y
t
oday
.
Th
eirattractiv
en
ess is du
e to
th
eir stru
ct
u
r
e
si
m
p
licit
y an
d
th
e in
du
strial o
p
e
rators acquain
tan
ce with
t
h
em
.
Sev
e
ral PI con
t
ro
llers
h
a
v
e
b
een pro
p
o
s
ed in
th
e literatu
re fo
r lin
ear
an
d non
lin
ear
p
r
o
cesses [5
], [1
5
]
.
Nev
e
rth
e
less,
PI con
t
ro
llers
fu
nd
am
en
tal d
e
ficien
cy is th
e
lack
of asym
p
t
o
tic stab
ility a
n
d
robu
stn
e
ss
p
r
oo
fs
for a
give
n
nonlinear system
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
48
1 – 488
48
2
There
f
ore, t
h
i
s
pape
r p
r
o
p
o
s
e
s t
o
deal
wi
t
h
t
h
i
s
de
fi
ci
en
cy
by
pro
p
o
si
ng a r
o
bu
st
n
onl
i
n
ea
r P
I
co
n
t
ro
ller
fo
r an
indu
ctio
n mo
tor
d
r
iv
e with un
kno
wn
l
o
ad to
rqu
e
. Th
e co
n
t
ro
ller is d
e
riv
e
d
b
y
co
m
b
i
n
ing
a
back
st
ep
pi
n
g
p
r
oce
d
ure wi
t
h
a sl
i
d
i
ng m
ode. M
o
re p
r
eci
sel
y
, t
h
e cont
r
o
l
l
e
rs are det
e
rm
i
n
ed by
im
posi
n
g t
h
e
current
-
spee
d tracki
ng rec
u
rsively in
t
w
o st
eps an
d by
usi
n
g ap
pr
op
ri
at
e g
a
i
n
s t
h
at
are n
onl
i
n
ea
r f
unct
i
ons
of
th
e system
stat
e.Th
e adv
a
n
t
ag
e
o
f
Back
stepp
i
ng
slid
i
n
g mo
d
e
con
t
ro
l is
its rob
u
stn
e
ss
an
d ab
ility to
h
a
nd
l
e
t
h
e n
o
n
-l
i
n
ea
r
beha
vi
o
u
r
of t
h
e sy
st
em
.
The m
odel
of
t
h
e i
n
d
u
ct
i
o
n
m
o
t
o
r, an
d sh
ows t
h
e di
rect
fi
el
d-
ori
e
nt
ed
cont
rol
(
F
OC
)
of i
n
d
u
ct
i
o
n
m
o
t
o
r i
n
Sect
ion (
2
). Sect
i
o
n (3
) sh
o
w
st
h
e
devel
o
pm
ent
of sl
i
d
i
ng t
e
c
hni
que c
ont
rol
desi
gn
. Sect
i
on (
4
)
sho
w
s
t
h
e
de
ve
l
opm
ent
of
B
a
ckst
ep
pi
n
g
t
e
c
hni
que
co
nt
r
o
l
d
esi
g
n.
The
S
p
eed C
ont
r
o
l
ofi
n
d
u
ct
i
o
n m
achi
n
e by
B
ackst
ep
pi
n
g
sl
i
d
i
n
g
m
ode
cont
rol
l
e
rs
des
i
gn i
s
gi
ve
n i
n
sect
i
o
n
(5
).
Sim
u
l
a
t
i
on res
u
l
t
s
usi
n
g
M
A
TLA
B
SIMUL
I
NK
of differe
n
t studi
e
d cases
is de
fined in Sec
tio
n (6). Fin
a
lly,
the
con
c
lu
si
o
n
s
are
drawn
in
Sectio
n
(7
).
2.
MAT
H
EM
AT
ICAL
M
O
DE
OF I
M
Th
e used
m
o
to
r is a three
p
h
a
se ind
u
c
tion
m
o
to
r typ
e
(IM) sup
p
lied
b
y
an
inv
e
rter vo
ltag
e
cont
rol
l
e
d
wi
t
h
P
u
l
s
e M
o
d
u
l
a
t
i
on
W
i
dt
h (
P
WM
) t
ech
ni
q
u
e
s. A m
odel
b
a
sed o
n
ci
rc
ui
t
equi
val
e
nt
eq
uat
i
o
n
s
i
s
general
l
y
su
ffi
ci
ent
i
n
o
r
d
e
r t
o
m
a
ke cont
r
o
l
sy
nt
hesi
s
.
The dy
nam
i
c
m
odel
of t
h
re
e-p
h
ase,
Y-c
o
nnect
e
d
i
n
d
u
ct
i
o
n
m
o
t
o
r ca
n
be e
x
p
r
es
sed i
n
t
h
e
d
-
q
s
y
nch
r
o
n
ousl
y
r
o
t
a
t
i
ng
fram
e
as [
13]
:
r
m
dr
qs
m
dr
ds
dr
qs
m
dr
ds
s
qs
qs
ds
dr
qs
s
ds
ds
C
a
w
a
i
a
dt
dw
a
i
a
dt
d
V
b
w
a
i
w
i
a
dt
di
V
b
a
i
w
i
a
dt
di
.
.
.
.
.
.
.
.
.
.
.
8
7
6
5
4
3
1
2
1
(
1
)
Whe
r
e
i
s
t
h
e
c
o
ef
fi
ci
ent
of
di
spersi
o
n
a
n
d
i
s
gi
ve
n
by
:
r
s
m
L
L
L
2
1
,
s
L
sig
b
.
1
,
r
r
m
s
R
L
L
R
b
a
.
.
2
1
,
r
s
r
m
L
L
sig
R
L
a
2
2
.
.
.
,
r
m
L
L
b
a
3
r
r
m
L
R
L
a
.
4
,
r
r
L
R
a
5
,
r
m
L
J
L
P
a
.
.
2
6
,
J
f
a
c
7
,
J
p
a
8
(2
)
3.
SLIDI
N
G M
O
DE CO
NTR
O
L
A Slid
ing
Mode Co
n
t
ro
ller (SMC) is a Variab
le Stru
ctu
r
e
Co
n
t
ro
ller (VSC) [10
]
. Basically, a VSC
i
n
cl
ude
s seve
r
a
l
di
ffe
rent
c
ont
i
n
u
o
u
s
f
u
n
c
t
i
ons t
h
at
ca
n m
a
p plant state to a control surface
,
whe
r
eas
swi
t
c
hi
n
g
am
ong
di
ff
ere
n
t
fu
nct
i
o
n
s
i
s
det
e
rm
i
n
ed by
pl
ant
st
at
e repres
ent
e
d
by
a sw
i
t
c
hi
ng f
u
nct
i
o
n [
7
]
.
W
i
t
h
ou
t lo
st
of g
e
n
e
rality, co
n
s
i
d
er t
h
e desig
n
o
f
a
slid
in
g
m
o
d
e
co
n
t
ro
ller fo
r t
h
e fo
llo
wi
n
g
first-o
r
d
e
r
System
.
U
t
x
B
x
t
x
A
x
.
)
,
(
.
)
,
(
(3)
Whe
r
e
U
th
e i
n
pu
t to
th
e System
th
e fo
llo
wi
n
g
is a po
ssib
l
e cho
i
ce of th
e stru
ctu
r
e
o
f
a
slid
in
g
m
ode cont
rol
l
e
r
eq
U
U
t
x
s
Sign
K
,
.
(4)
Whe
r
e st
ands
fo
r e
q
ui
val
e
nt
c
ont
ro
l
used
whe
n
t
h
e Sy
st
em
st
at
e i
s
i
n
t
h
e Sl
i
d
i
ng m
ode [
2
]
,
K i
s
a
co
nstan
t
, b
e
i
n
g
th
e m
a
x
i
m
a
l
v
a
lu
e of th
e co
n
t
ro
ller ou
tput. S is switch
i
n
g
fun
c
tion
sin
ce th
e con
t
ro
l actio
n
switch
e
s its si
gn
o
n
th
e t
w
o si
d
e
s
o
f
th
e
swit
ch
ing
su
rface
0
)
(
x
S
,
S i
s
d
e
fi
ne
d a
s
[1
4]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
S
lid
ing
Mod
e
Ba
ckstepp
ing
Co
n
t
ro
l o
f
In
du
ctio
n Mo
to
r (
O
thman
e
Bough
a
z
i)
48
3
)
(
.
)
(
1
x
e
t
x
S
r
(5)
Whe
r
e:
x
x
*
x
e
,
*
x
B
e
i
ng t
h
e de
si
red st
at
e.
is a
co
nstan
t
.Con
cern
i
n
g
th
e
d
e
v
e
lo
p
m
en
t o
f
the co
n
t
ro
l law, it
is
divide
d into t
w
o
parts, the
equiva
le
nt cont
rol
U
eq a
n
d the attractiv
ely or reacha
b
ility control Us. The
equi
valent control is determ
ined
off-line
with a
m
odel th
at represe
n
ts the plant as accurately as possible. If
th
e p
l
an
t is exactly is ex
actly
id
en
tical to
t
h
e m
o
d
e
l
use
d
f
o
r
det
e
rm
i
n
i
n
g
Ue
q a
n
d
t
h
e
r
e
are
no
di
st
ur
b
a
nces,
t
h
ere w
o
ul
d be
no nee
d
t
o
ap
pl
y
an addi
t
i
o
n
a
l
cont
r
o
l
Us.
Ho
we
ver
,
i
n
pr
act
i
ce t
h
ere are a l
o
t
of di
ffe
renc
e
s
b
e
tween
th
e mo
d
e
l and
th
e actu
al p
l
an
t. Th
erefo
r
e, th
e con
t
ro
l co
m
p
on
en
t
Us is n
ecessary wh
ich
will always
gua
ra
ntee that
the state is attracted to t
h
e
switching
surface
by satisfy
ing
the
c
o
ndition [13], [14].
0
)
(
.
)
(
x
S
x
S
Th
erefo
r
e, th
e
b
a
sic switch
i
ng
law is
o
f
t
h
e
form
:
sw
eq
U
U
U
(6
)
eq
U
i
s
t
h
e eq
ui
val
e
nt
co
nt
r
o
l
,
a
n
d
sw
U
is th
e switchin
g
con
t
ro
l
.
Th
e fun
c
tion
of
eq
U
is to
m
a
in
tain
th
e
traj
ectory
o
n
the slid
ing
su
r
f
ac
e, an
d t
h
e
fu
nc
t
i
on
of
sw
U
is to
guid
e
th
e t
r
aj
ect
ory to
t
h
is su
rface.
The s
u
rface is
give
n
by:
m
md
w
w
z
S
*
1
1
(7)
The
deri
vative
of the s
u
rface i
s
:
m
md
w
w
z
S
*
1
1
(8)
In a c
o
nventional va
riable structure
con
t
ro
l,
Un
g
e
n
e
rates a h
i
gh
co
n
t
ro
l activ
ity. It was first tak
e
n
as
co
nstan
t
, a rel
a
y fun
c
tio
n, wh
ich
is
v
e
ry h
a
rm
fu
l to
th
e actu
ato
r
s and
m
a
y ex
cite th
em
o
d
el d
y
n
a
m
i
cs o
f
t
h
e
Syste
m
. This i
s
known a
s
a
cha
ttering phenom
enon. Ide
a
lly, to reac
h
the sliding surface, t
h
e c
h
attering
phe
n
o
m
e
non
s
h
o
u
l
d
be
el
i
m
inat
ed
[
13]
,
[
1
4
]
. Ho
we
ver
,
i
n
pract
i
ce, c
h
at
t
e
ri
n
g
ca
n
onl
y
b
e
re
duce
d
.
The fi
rst approach to
reduce c
h
attering wa
s to in
trod
u
ce a bo
und
ar
y layer
ar
oun
d
t
h
e slidin
g
su
rf
ace
and to
use
a s
m
ooth function to
replace t
h
e
discon
tinuous
part
of the c
o
nt
rol action as
follows:
)
(
)
(
))
(
sgn(
.
)
(
.
x
S
x
S
if
if
x
S
K
U
x
S
K
U
sw
sw
(9)
T
h
e c
onst
a
nt
K i
s
l
i
nke
d t
o
t
h
e s
p
e
e
d
of
co
n
v
er
ge
nce t
o
wa
rd
s t
h
e sl
i
d
i
n
g s
u
r
f
a
ce o
f
t
h
e
pr
oce
ss (t
he
reachi
n
g m
ode). C
o
m
p
rom
i
se
m
u
st be m
a
de when c
h
oosing
this
consta
nt, since
if
K is
very sm
all the tim
e
r
e
spon
se is imp
o
r
t
an
t and
th
e r
obu
stn
e
ss m
a
y b
e
lo
st
, wh
ereas wh
en
K is
to
o
b
i
g th
e ch
atter
i
n
g
ph
eno
m
enon
increases
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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94
I
J
PED
S
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l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
48
1 – 488
48
4
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
speed c
ont
rol
of
IM
I
ndi
rect
fi
el
d
-
ori
e
nt
ed c
o
nt
r
o
l
(IF
OC
)
o
f
i
n
d
u
ct
i
o
n
b
y
sl
i
d
i
n
g
m
ode
4.
BACK
STEPP
I
NG CO
NT
R
O
L
DESI
GN
In th
is section
,
we
u
s
e t
h
e Back
stepp
i
ng
al
g
o
rith
m
to
d
e
v
e
l
o
p
th
e sp
eed con
t
ro
l law
o
f
th
e in
du
ction
m
o
to
r Th
is sp
eed
will co
nv
erg
e
to th
e
referen
ce
v
a
lu
e
fro
m
a wi
d
e
set
o
f
in
itial co
nd
itio
ns.
Step 1:
Firstly we con
s
id
er t
h
e track
i
ng
objective of
the di
rect c
u
rrent
(
dr
)
.
A
tr
ack
i
ng
erro
r
m
md
w
w
z
1
i
s
defi
ned
,
a
n
d
t
h
e de
ri
vat
i
v
e
becom
e
s:
m
md
w
w
z
1
(10)
r
m
dr
qs
md
C
a
w
a
i
a
w
z
.
.
.
8
7
6
1
(11)
The pr
o
p
o
s
ed
vi
rt
ual
c
o
m
m
and
i
s
:
md
r
m
dr
qs
w
z
c
C
a
w
a
i
a
1
1
8
7
*
6
.
.
.
.
.
(12)
r
m
md
r
m
md
C
a
w
a
w
z
c
C
a
w
a
w
z
z
z
z
v
8
7
1
1
8
7
1
1
1
1
.
.
.
.
2
1
1
1
z
c
z
v
(13)
W
i
t
h
0
1
c
Step 2:
The
de
ri
vat
i
v
e
of
t
h
e
err
o
r
va
ri
abl
e
dr
qs
dr
qs
i
a
i
a
z
.
.
.
.
6
*
6
2
(14)
dr
qs
md
r
m
i
a
w
z
c
C
a
w
a
z
.
.
.
.
.
6
1
1
8
7
2
(15)
dr
ds
qs
qs
m
dr
ds
s
qs
dr
r
m
dr
qs
md
md
r
r
m
dr
qs
a
i
a
i
bv
w
a
i
w
i
a
a
C
a
w
a
i
a
w
c
w
C
a
C
a
w
a
i
a
a
z
5
4
3
1
6
8
7
6
1
8
8
7
6
7
2
.
.
.
.
qs
v
z
2
1
2
dr
ds
qs
m
dr
ds
s
qs
dr
r
m
dr
qs
r
md
md
a
i
a
i
w
a
i
w
i
a
a
C
a
w
a
i
a
a
c
C
a
w
c
w
5
4
3
1
6
8
7
6
7
1
8
1
1
.
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
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S
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8-8
6
9
4
S
lid
ing
Mod
e
Ba
ckstepp
ing
Co
n
t
ro
l o
f
In
du
ctio
n Mo
to
r (
O
thman
e
Bough
a
z
i)
48
5
dr
b
a
6
2
(16)
qs
v
z
z
z
z
v
2
1
2
2
2
2
.
(17)
2
2
2
1
z
c
v
qs
2
2
2
2
z
c
z
v
(18)
Wi
t
h
0
2
c
Step 3:
dr
dr
z
*
3
(19)
dr
ds
dr
dr
dr
a
i
a
z
5
4
*
*
3
(20)
The pr
o
p
o
s
ed
virtual
c
o
m
m
and
is:
3
3
*
5
*
4
z
c
a
i
a
dr
dr
ds
(21)
dr
dr
dr
dr
a
z
c
a
z
5
3
3
*
5
*
3
2
3
3
3
3
3
.
z
c
z
z
z
v
(22)
W
i
t
h
c
3
>0
Step 4:
ds
ds
i
a
i
a
z
4
*
4
4
(23)
ds
dr
dr
ds
ds
i
a
z
c
a
i
a
i
a
z
4
3
3
*
5
4
*
4
4
ds
v
z
4
3
4
(24)
Wi
t
h
,
dr
qs
s
ds
dr
ds
dr
dr
a
i
w
i
a
a
a
i
a
c
a
c
2
1
4
5
4
3
5
*
3
*
3
b
a
4
4
4
4
4
3
z
c
v
ds
(25)
4
4
4
4
3
3
4
z
c
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
4
,
No
.
4
,
D
ecem
b
er
2
014
:
48
1 – 488
48
6
2
4
4
4
4
4
.
z
c
z
z
z
v
(26)
W
i
t
h
c
4
>0
.
5.
ASS
O
CI
ATI
O
N B
A
CKST
EPPING
SLI
D
ING
MO
DE
CO
NTROL
The c
o
nt
rol
l
a
w
obt
ai
ne
d i
s
:
2
2
2
1
2
1
2
z
q
z
sig
n
q
v
z
qs
The
n
;
2
2
2
2
1
1
z
q
z
sign
q
v
qs
(
2
7
)
An
d,
4
4
4
3
4
3
4
z
q
z
si
g
n
q
v
z
ds
The
n
;
4
4
4
4
3
3
z
q
z
sign
q
v
ds
(
2
8
)
T
h
e Fi
gu
re
2 s
h
ows
t
h
e
back
st
ep
pi
n
g
sl
i
d
i
n
g
co
nt
r
o
l
st
rat
e
gy
sch
e
m
e
for
eac
h i
n
d
u
ct
i
o
n m
o
t
o
r
.
.
Fi
g
u
re
2
.
B
l
oc
k
di
ag
ram
s
peed c
ont
rol
of
IM
by
a c
o
m
b
i
n
at
i
on
o
f
t
h
e
B
A
C
K
-SM
C
c
o
m
m
a
nd
6.
SIMULATION RESULTS
Th
e t
h
r
e
e contr
o
ls ado
p
t
ed
as PI, slid
i
ng m
o
d
e
,
a
n
d B
ackstepping
sliding m
ode a
r
e tested
by
num
eri
cal
sim
u
l
a
t
i
on
f
o
r t
h
e
va
lues
of the
s
e
coe
fficients:
PI Rho
p
w
=10
Rho
iw
=10
Rho
d
=800
Rho
q
=800
SMC
L
d
=800
L
q
=500
Ep
s1
=1
0
-4
Ep
s2
=1
0
-4
Kvd=250
0
Kvq=150
0
Back
-SM
C
C1=100
C2=300
q1=100
q2=100
q3=100
q4=100
Ep
s1
=1
0
-6
Ep
s2
=1
0
-6
The si
m
u
l
a
t
i
o
n
res
u
l
t
s
are s
h
o
w
i
n
g Fi
gu
re
3-
Fi
gu
re
5.
Fi
g
u
r
e
3 s
h
ow
s t
h
e
spee
d wi
t
h
P
I
,
SM
C
A
n
d
B
ack-SM
C
,
Fi
gu
re
4 t
h
e t
o
rq
ue a
n
d
Fi
g
u
r
e
5 s
h
o
w
s
t
h
e c
u
rre
nt
I
a,b,c
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
S
SN:
208
8-8
6
9
4
Sliding
M
o
de Backstepping Control
of
Induction M
o
tor (
O
thmane
Boughazi)
48
7
Figu
re (
3
),
(4
) and (
5
) sh
ows
the evol
ution
o
f
elect
rical and
m
echanical param
e
ters of the IM ideal
voltage
s
u
p
p
lied to
a loa
d
vari
ation
betwee
n
0.
5 sec
o
nds
an
d
1 sec
o
n
d
,
an
d re
ve
rse s
p
ee
d set
poi
nt at tim
e 1
.
5
secon
d
200
-200
[
r
a
d
/ s].
The res
u
lts sh
ow a g
o
od
re
spo
n
se in
IM
alim
ented ide
a
l tension, c
o
ntinui
ng
with a very
low
response tim
e
and a static error to ze
ro
for
Backsteppi
n
g
cont
rol m
ode by
sliding t
h
e cont
rol in
put t
o
the PI
cont
roller, and controller wit
h
slidi
ng m
o
de. The couple
has a
pea
k
re
lated to the
st
art an
d
fade
s
du
rin
g
perm
anent re
gi
m
e
. The loa
d
c
h
ange
has als
o
allowed us
to c
oncl
ude
o
n
the
rejectio
n
of
th
e distu
r
ba
nce
whic
h
is satisfactory
Figu
re
3.
The
s
p
eed
o
f
IM
Figu
re
4.
The
tor
q
ue
Figu
re 5.
The
C
u
r
r
ent Ia,
b
,c
7.
CO
NCL
USI
O
N
The slidin
g m
ode contr
o
l of the field orie
nted in
duc
tion m
o
tor was pr
op
ose
d
.
To sh
o
w
th
e
effective
n
ess
a
n
d
pe
rf
o
r
m
a
nces o
f
the
de
ve
lope
d c
ont
rol schem
e
,
sim
u
lation
st
udy
wa
s
car
ried o
u
t. Go
o
d
results were obtained despite
the
si
m
p
licity of the chosen
sliding s
u
rfac
es. T
h
e
robust
ness a
n
d t
h
e tracking
qualities of t
h
e proposed cont
rol system
using
slidi
n
g m
ode controllers appear clearly.
Furt
herm
ore,
in
or
der
to
re
d
u
ce the
chatter
i
ng,
d
u
e t
o
th
e disc
ontin
u
o
u
s
nat
u
re
o
f
th
e co
ntr
o
ller
,
back
step
pin
g
c
ont
rollers
we
re
ad
ded
to t
h
e sl
iding
m
ode c
o
ntr
o
llers.
These
gave
good
results as well and sim
p
licity with
regards t
o
the ad
ju
stm
e
nt of pa
ra
m
e
ters. The
si
m
u
lations results show the efficien
cy
of
the slidin
g m
ode c
ontr
o
ller t
echni
que
,
ho
w
e
ver t
h
e strate
gy
o
f
back
step
pin
g
s
liding m
ode
co
ntr
o
ller b
r
in
gs
go
o
d
per
f
o
r
m
a
nces.
REFERE
NC
ES
[1]
PC Krause,
et al. Analy
s
is of
Electric Machiner
y
and Drive S
y
stem
s. John W
iley
& Sons: 2002.
[2]
PV Kokotovic, et al. Nonlinear
and Adap
tiv
e con
t
rol.
John
W
iley
& Sons: 1995.
[3]
Leonhard
W
.
Co
ntrol of
Electri
cal Drives. Springer-Verlag
, 1996
.
[4]
A Behal et al. An im
proved IFOC fo
r th
e
induction m
o
tor. I
EEE
Trans.
Con
t
rol Sy
stem
s Technolog
y
.
2003
11(2)
:
248-252.
[5]
D
Cas
a
dei, e
t
a
l
. F
O
C
and D
T
C: tw
o viable s
c
hem
e
s for induction m
o
tors torque control.
IE
EE T
r
ans. Power
Ele
ctr
onics
. 200
2; 17(5): 779-78
7.
0
0.
5
1
1.
5
2
2.
5
3
-4
0
0
-3
0
0
-2
0
0
-1
0
0
0
10
0
20
0
30
0
40
0
Ti
m
e
[
s
e
c
]
s
peed[
r
a
d/
s
]
PI
SM
C
BACK-
SM
C
0
0.
5
1
1.
5
2
2.
5
3
-100
-50
0
50
100
Ti
m
e
[
s
e
c
]
t
o
r
q
ue[
N
m
]
PI
SM
C
BACK-
SM
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0.
5
1
1.
5
2
2.
5
3
-6
0
-4
0
-2
0
0
20
40
60
T
i
me
[s
e
c
]
c
our
ant
s
i
a
s
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A
]
PI
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C
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
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BIOGRAP
HI
ES
OF AUTH
ORS
Oth
m
an
e BOUGHAZ
I
was b
o
rn in Bougtob
, El b
a
y
a
dh
, A
l
geria,
in 1977.
He receiv
ed
the Engin
eer d
e
gree in
Ele
c
tro
t
echn
i
cs
, and th
e M
a
gis
t
er deg
r
ee from
Bechar Univers
i
t
y
,
Bechar
, Algeria, in 2006 and 2010,
respectively
.
Wher
e he has been working toward the
Ph.D. degr
ee
in the Department of
Electr
i
c
and Electronics
Engineering sin
ce d
e
cember
2010. He is currently
a Resear
ch member La
borator
y
Contro
l, Analy
s
is and
Optimization
of Electroen
e
rg
y
S
y
s
t
ems Depart
ment of Electric a
nd Electronics Engin
e
ering, Bechar
Universit
y
. His m
a
in research activit
y is
focus
e
d on electri
c m
achine drive s
y
s
t
em
s
,
power
electronics and
process control.
Abelmadjid BOUM
ÉDIÈNE
was born
in
Béchar
,
Alegria,
in 1977
.
He receiv
e
d
the
Engineer degr
ee in
Electro
tec
hnics,
the Magister d
e
gree
and Doctor
at
d’Etat (Ph.D.)
degree in electric engineer
ing, from the
univers
ity
of bech
ar, Algeria, in 200
1, 2008 and
2012 respectiv
ely
.
Upon gr
ad
uation
,
he
joined
the Electr
ic Eng
i
neer
ing
Department of
Univers
i
t
y
of B
echar
. He was
a
n
as
s
o
ciat
e P
r
of
es
s
o
r, m
e
m
b
er of P
r
oces
s
Control Labor
ato
r
y
(ENP). Since
2012, he jo
ined the Electric
Engineering D
e
partment of
University
of
Tlem
cen
. He
i
s
an as
s
o
cia
t
e
P
r
ofes
s
o
r, m
e
m
b
er of Automatiqu
e
Labor
ator
y of
Tlem
c
e
n
(LAT). His
re
s
earch inter
e
s
t
s
include elec
tr
ic m
achine drives
, power electroni
cs
and
process
control.
Hach
emi GLA
O
UI
was born
i
n
Béchar, Alegr
i
a, in 1977. He received the Eng
i
neer degr
ee in
Ele
c
trot
echni
cs
,
the M
a
gis
t
er de
gree and Doctor
at d’Et
at (P
h.D.)
degree in el
ectr
i
c engin
eering
,
from the Univer
sity
o
f
Bech
ar,
Algeria, in
2001
, 2008 and 201
2 respectively
.
Currently
h
e
is
professor
in the Electric Engineering
Depar
t
m
e
nt
of Unive
r
s
i
t
y
at
Bechar
.
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