Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
(I
J
PE
D
S
)
Vo
l.
11
,
No.
3
,
Septem
be
r
2020
, pp.
12
59
~
1267
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v
1
1
.i
3
.
pp
1259
-
1267
1259
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
A study
of
s
ens
orless vec
t
or co
ntr
ol of IM
using ne
ural n
etwork
luenber
ger o
bse
rver
Tahar B
el
bek
ri
, Bo
us
ma
ha
Bouchib
a, Is
mail Kh
alil
Bou
sser
hane,
H
ou
ci
ne Bec
her
i
Depa
rtment
o
f
E
le
c
tri
c
al E
ngin
eering,
Ta
hr
i
Moh
am
ed
Univer
sity
Béc
h
ar,
Alger
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
26
, 201
9
Re
vised
Feb
15
, 2
0
20
Accepte
d
M
a
y
4
, 2
0
20
After
th
e
dev
elopment
of
elec
t
ronic
com
ponen
ts,
the
e
li
mi
n
ati
on
of
the
sensors
has
become
a
ne
ce
ss
ar
y
subjec
t
to
g
et
good
result
s
in
the
f
ie
ld
of
spee
d
cont
ro
l,
b
ec
ause
of
the
pri
ce
of
the
sensors
,
the
str
enuous
c
hoic
e
of
i
ts
positi
on
and
th
e
disturba
nc
e
o
f
me
asure
me
nt
which
aff
e
ct
s
th
e
robustness
of
cont
rol
.
Th
e
luenberge
r
observ
e
r
show
ed
to
be
one
of
th
e
mo
st
exc
e
ll
en
t
me
thods
suggest
ed
by
th
e
r
ese
ar
che
rs;
th
is
is
du
e
to
the
b
est
p
er
forma
nc
e,
it
offe
rs
in
t
erm
s
o
f
stabilit
y
,
reliab
il
it
y
and
l
ess
co
unti
ng
eff
ort
.
In
thi
s
ar
ticle
,
a
study
of
lue
nb
erg
er
observe
r
b
ase
d
on
neur
al
n
et
work
-
base
d
wa
s
discussed.
Thi
s
artificia
l
in
te
lligen
ce
me
tho
d
ma
kes
i
t
poss
i
ble
to
d
ec
r
ea
se
t
he
err
or
of
esti
mated
spee
d
for
IRFO
C
cont
r
ol
of
the
inducti
on
mot
or
.
Sim
ul
at
ion
result
s
are
ob
ta
in
ed to
s
how t
he
rob
ustness a
nd
stab
il
i
ty of t
he
sys
te
m
.
Ke
yw
or
d
s
:
Ar
ti
fici
al
intel
li
gen
ce
Async
hro
nous
mo
to
r
Lue
nb
e
rg
e
r
Neural
netw
ork
Vecto
r
c
on
tr
ol
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Tahar B
el
be
kr
i
,
Dep
a
rtme
nt of
Ele
ct
rical
En
gi
neer
i
ng,
Tahr
i
Mo
hame
d Un
i
ver
sit
y,
M
oha
mme
d
Ta
hr
i
U
niv
er
sit
y B
échar, B.P
41
7,
Ke
nadsa
r
oa
d.
0800
0
Bé
c
ha
r,
Alge
ria.
Emai
l:
taharm
oh87@
ya
hoo.f
r
1.
INTROD
U
CTION
Ow
i
ng
to
the
a
dv
a
nce
of
pow
er
el
ect
r
on
ic
s
i
n
la
te
st
year
s
,
the
c
on
t
ro
l
of
var
ia
ble
s
peed
mo
to
rs
has
increase
d
nota
bly
.
T
he
asy
nc
hro
nous
m
oto
r
is
t
he
mo
st
util
iz
ed
i
n
t
he
en
gin
ee
rin
g
fiel
d
beca
us
e
of
it
s
rob
us
tness
,
l
ow
pr
ic
e
an
d
simpli
ci
ty
of
us
age
mainte
n
a
nc
e.
But
it
has
a
dif
ficult
,
it
s
con
t
ro
l
is
not
simple
because
of
sta
tor
f
ie
ld a
nd t
he
rotor cu
rr
e
nt i
s
not meas
urab
le
without i
nter
mediar
y
[1,
2].
The
FO
C
is
f
ounded
on
e
ff
i
ci
ent
co
ntr
ol
of
the
ma
gn
et
ic
va
riable.
It
ha
s
bee
n
i
n
la
te
st
years
the
essenti
al
resea
rch
wa
y
an
d
be
tt
er
ada
pted
t
o
i
ndus
tria
l
e
xi
gen
c
y.
H
owe
ver,
this
c
onfigurati
on
requir
es,
in
gen
e
ral,
the
in
sta
ll
ment
of
se
ns
or
on
the
r
ot
or
f
or
t
he
knowin
g
of
a
mec
han
ic
al
meas
ure
[
3].
The
go
al
of
this
con
t
ro
l
is
to
be
able
to
c
om
man
d
t
he
as
yn
chro
nou
s
m
otor
as
a
direct
cu
rr
e
nt
m
otor
wi
th
se
par
at
e
exc
it
at
ion
wh
e
re
t
her
e
is
a
nor
mal
dec
ouplin
g
am
ong
the
flu
x
quantit
y,
the
excit
at
io
n
c
urre
nt,
a
nd
t
hat
ass
ociat
ed
to
the
tor
qu
e
, th
e
stat
or cu
rr
e
nt.
T
hi
s d
ec
ouplin
g re
nd
e
rs
it
possibl
e to
hav
e
a s
o r
apid
t
or
que re
s
pons
e
[4, 5
].
The
pr
ob
le
mat
ic
of
our
pa
per
is
to
el
imi
nate
the
sp
ee
d
sen
s
or
a
nd
c
ha
ng
e
it
with
ano
t
her
te
chn
iq
ue
to
obta
in
it
s
va
lue.
In
our
stu
dy,
we
c
ho
se
ve
ct
or
c
ontrol
by
or
ie
ntati
on
of
the
r
otor
fl
ow
wh
ic
h
re
quires
the
instal
lment
of
a
sens
or
t
o
m
easur
e
the
sp
e
ed
or
posit
ion
of
the
r
otor
f
low
.
T
he
inte
grat
ion
of
this
sens
or
boos
ts
the
m
as
s
and
t
he
pri
ce
wh
ic
h
can
be
big
tha
n
that
of
the
m
otor
f
or
the
low
powe
r
.
It
is
too
esse
nt
ia
l
to
reserve
a
s
uppl
ementar
y
loca
ti
on
f
or
the
i
nst
al
lment
of
the
se
nsor.
B
ut
that
is
not
c
on
sta
ntly
wan
t
ed
or
avail
able.
Last
ly,
t
he
reli
abili
ty
of
the
str
uct
ur
e
re
duces
be
cause
of
this
c
risp
instr
ume
nt
that
nee
ds
part
ic
ular
at
te
ntion
for
it
sel
f
an
d
f
or
it
s
associat
ion.
It
is
from
these
r
emar
ks
t
hat
th
e
idea
of
re
movin
g
th
e
s
peed
sens
or
was
bor
n.
To
s
olv
e
t
his p
r
oble
mati
c,
seve
ral
stu
di
es h
ave
c
on
ce
ntrate
d
in
the
la
st
fe
w
ye
ars
on
the
de
ve
lop
in
g
of
di
ver
se
a
ppr
oach
e
s
to
est
i
mate
spe
ed
.
F
or
that
pu
rpose
,
rem
ov
i
ng
a
spe
ed
se
nsor
in
t
he
IRF
OC
ma
kes
us
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
1259
–
1267
1260
of
it
s
e
valuati
on
f
rom
the
el
ect
rical
var
ia
bles
of
t
he
sta
to
r
(
vo
lt
age
,
c
urrent
)
[6,
7]
.
I
n
the
obser
ver
s
,
we
sel
ect
the
lue
nber
ge
r
obse
rv
e
r,
wh
i
ch
offe
rs
t
he
possibil
it
y
of
re
const
ru
ct
in
g
th
e
sta
te
s
of
a
n
ob
s
er
vab
le
str
uctu
re
from
t
he
quant
it
ie
s
of
i
nputs
and
out
pu
ts.
It
’s
us
e
d
in
sta
te
fee
db
ac
k
co
nt
ro
ls
w
hen
al
l
or
par
t
of
the
va
riabl
e
canno
t
be
e
val
uated.
T
his
est
imat
or
ca
n
be
util
iz
ed,
f
or
e
xa
mp
le
t
o
ob
ta
i
n
the
fl
ux
of
t
he
m
otor
knowle
dge
that t
hese
meas
ur
es
are
f
a
r
f
r
om bei
ng sim
ply
determi
nate [
8].
The
go
al
of
ou
r
pa
per
is
t
o
a
meli
or
at
e
the
r
esults
at
ta
ined
by
t
he
lue
nber
ger
obser
ver
w
hic
h
is
base
d
on
the
P
I
re
gu
l
at
or
.
F
or
this
,
we
c
hose
to
use
arti
fici
al
intel
li
gen
ce
te
ch
niques
.
I
n
in
ou
r
l
ast
pu
blished
a
rtic
le
,
we
a
ppli
ed
t
he
f
uzz
y
te
c
hn
i
que,
an
d
we
f
ou
nd
e
d
go
od
r
es
ults
c
ompare
d
to
the
old
te
ch
niques.
F
or
the
same
reasons
, we
de
ci
ded
t
o
a
pp
l
y ano
t
her met
ho
d of arti
fici
al
intel
li
gen
ce i
n
t
his ar
ti
cl
e.
Neural
netw
ork
is
one
of
th
e
te
ch
niques
of
a
rtific
ia
l
intel
li
gen
ce,
t
his
t
echn
i
qu
e
has
pro
ved
their
eff
ect
ive
ness
i
n
s
eve
ral
a
rea
s:
su
c
h
as
sig
nal
processi
ng,
par
a
metri
c
i
den
ti
ficat
io
n,
con
t
ro
l
of
non
-
li
near
processes
, esti
mati
on
a
nd
faul
t detec
ti
on
[19
, 24, 25
].
In
our
pa
per
,
we
will
util
iz
e
the
ne
ur
al
net
work
to
upgra
de
the
est
imat
i
on
of
spe
ed
a
nd
to
obta
in
a
gr
eat
performa
nce
an
d
e
ff
ect
ive
co
ntr
ol.
T
his
arti
cl
e
is
struc
ture
d
li
ke
this
.
Sec
ti
on
2
pr
e
sents
the
in
duc
ti
on
mo
to
r
model.
Sect
ion
3
de
s
cribes
the
te
c
hn
i
qu
e
of
t
he
ind
i
rect
vector
co
ntr
ol.
Se
ct
ion
4
disc
usse
s
the
luen
berger
ob
serv
e
r
an
d
his
structu
re.
T
he
ne
xt
sect
ion
desc
ribes
the
luen
be
rg
e
r
ob
se
r
ver
te
c
hn
i
qu
e
connecte
d
to
neural
net
w
ork.
The
res
ults
of
sim
ulati
on
an
d
discussi
on
a
re
offer
e
d
in
sect
io
n
6
a
nd
7,
resp
ect
ivel
y. T
he
la
st sect
io
n pr
ese
nts t
he
c
oncl
us
i
on of the
artic
le
.
2.
THE
M
O
DEL
OF
I
N
DUCT
ION
M
OTOR
The
modeli
ng
of
t
he
as
ynch
r
onous
mo
t
or
i
s
f
ounded
on
t
he
Pa
r
k
c
onve
rsion,
w
hich
c
onnects
t
he
ro
t
or
a
nd
sta
tor
el
ect
rical
s
ta
te
s
equ
at
io
ns
to
perpendic
ular
a
xes,
el
ect
rical
ly
te
rme
d
d
(
direct)
,
and
q,
(qua
dr
at
ure)
.
The
i
nductio
n
machi
ne
ca
n
be
def
i
ned
by
ne
xt
sta
te
s
e
qu
at
io
ns
in
t
he
ci
rcli
ng
fiel
d’
s
re
fer
e
nce
fr
ame
w
ork [9,
16].
{
̇
=
.
+
.
=
.
(1)
With:
−
−
−
−
−
−
−
−
−
=
5
4
5
4
2
3
1
3
2
1
)
(
0
)
(
0
.
.
a
w
w
a
w
w
a
a
a
w
a
a
w
w
a
a
w
a
A
r
s
r
s
r
s
r
s
;
=
0
0
1
0
0
0
0
1
s
s
L
L
B
;
=
r
r
s
s
i
i
X
;
=
s
s
V
V
U
=
s
s
i
i
Y
;
=
0
0
0
0
1
0
0
1
C
.
And:
r
r
r
R
L
T
=
,
2
2
1
r
s
m
r
s
s
L
L
L
R
L
R
a
+
=
,
r
r
s
m
T
L
L
L
a
=
2
,
r
s
m
L
L
L
a
=
3
,
r
m
T
L
a
=
4
,
r
T
a
1
5
=
.
3.
INDIRE
CT F
IEL
D
-
O
RIE
N
TE
D
C
ONT
R
OL
The
in
de
pe
nd
e
nt
excit
at
ion
di
rect
curre
nt
m
otor
is
ve
r
y
a
da
pted
for
t
orq
ue
c
on
tr
ol,
bec
ause
it
just
necessit
ie
s
to
c
on
t
ro
ll
er
it
s
in
du
ce
d
c
urren
t.
The
obje
ct
ive
i
s
to
make
t
he
s
imi
la
r
thing
wi
th
the
asy
nc
hrono
us
mo
to
r. This
is
exactl
y
t
he of
t
he vect
or c
on
t
r
ol [1
1]
.
In
I
RF
OC
,
the
flu
x
is
no
t
c
ontr
olled;
s
o,
t
he
flo
w
sen
sors
are
not
requir
ed
i
n
the
est
i
mators
a
nd
ob
s
er
ver
s
,
but
the
qua
ntit
y
of
the
r
otor
l
oc
al
it
y
is
need
e
d.
This
met
hod
is
ve
r
y
sim
ple
bu
t
evi
dent
ly
hi
s
performa
nce
is
lowe
r
tha
n
to
the
RFOC,
t
his
is
ow
in
g
to
t
he
sensibili
ty
of
this
ge
nr
e
of
c
on
t
ro
l
to
t
he
c
hange
of
t
he
r
otor
ti
me
co
ns
ta
nt
.
The
ben
e
fit
of
this
te
ch
nique
is
to
util
iz
e
just
re
fer
e
nce
measu
reme
nt
wh
ic
h
by
def
i
niti
on
is
not
distu
rb
e
d.
I
n
ef
fect,
fro
m
an
el
ect
romag
netic
sit
uation
torque
∗
and
t
he
re
fer
e
nce
r
otor
flo
w
∗
, th
e
ref
e
r
ence c
urren
ts
∗
and
∗
can
be
ass
um
e
d direct
ly
f
rom the
stat
e e
qu
at
io
ns.
∗
=
1
⋅
(
⋅
̇
∗
+
)
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A stu
dy of se
nsorless
vect
or
c
on
tr
ol
of I
M
u
s
ing
ne
ural net
work lue
nber
ge
r observer
(
T
ahar
Bel
bekri
)
1261
∗
=
⋅
⋅
∗
(
3)
The
IRF
OC
te
chn
i
qu
e
is
bas
ed
on
the
ge
ne
rati
on
of
t
he
s
upply
volt
ages
in
order
to
fin
d
a
wa
nted
flo
w
a
nd
tor
qu
e
.
By
us
in
g
the
volt
age s
uppl
y o
f
the
async
hro
nous
mac
hin
e,
the contr
ol stat
es are t
he vo
lt
a
ge
an
d
.
ds
s
s
r
r
m
r
qs
s
qs
s
qs
qs
s
s
r
r
m
ds
s
ds
s
ds
i
L
L
L
dt
di
L
i
R
v
i
L
dt
d
L
L
dt
di
L
i
R
v
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
+
+
+
=
−
+
+
=
(4)
The
Co
up
li
ng
is
am
ong
the
two
sta
te
s
(
qs
ds
v
v
,
),
c
an
be
ave
rted
by
util
iz
ing
m
any
c
ompen
sat
ion
meth
od
s
[10].
3.1. Dec
ou
pli
n
g
by c
onven
ti
onal co
mpens
at
i
on
This
te
c
hn
i
qu
e
co
ns
ist
s
i
n
a
da
ptati
on
of
the
cu
rr
e
nts
by
el
imi
nation
of
the
c
onju
nction
va
riables
.
These
are
tote
d
t
o
t
he
ou
t
p
ut
of
the
cu
rrent
re
gula
tor
s
to
fin
d
the
r
efere
nce
volt
ages
re
qu
ire
d
f
or
the
regulat
ion
(
fig
ur
e
1).
T
he
s
uppleme
ntar
y
te
rms
a
re
fi
xe
d
in
wh
ic
h
the
re
sidu
al
vo
lt
a
ges
are
relat
e
d
wi
th
the
corres
pondin
g cur
ren
ts
[10].
The
e
xpressi
on of the
volt
ages
at the
ou
t
put o
f
c
orrector
s is:
dt
di
L
i
R
v
dt
di
L
i
R
v
qs
s
qs
s
r
qs
ds
s
ds
s
r
ds
.
.
.
.
.
+
=
+
=
(5)
The
e
xpressi
on of the
cou
plin
g vo
lt
age
s ar
e:
ds
s
s
r
r
m
s
c
qs
qs
s
s
r
r
m
c
ds
i
L
L
L
v
i
L
dt
d
L
L
v
.
.
.
.
.
.
.
.
+
=
−
=
(6)
The
te
rm
dt
r
d
L
L
r
m
is
e
qu
al
s
ze
ro
,
see
ing
the
sta
ble
sta
te
.
T
her
e
for
e
,
th
e
ref
e
re
nc
e
volt
ages
desi
red
f
or
t
he
con
t
ro
l
:
r
qs
c
qs
qs
r
ds
c
ds
ds
v
v
v
v
v
v
+
=
+
=
*
*
(7)
The
pulsa
ti
on
*
s
is
esse
ntial
f
or
t
he
op
po
sit
e
conve
rsion
of
park
in
order,
to
obta
in
t
he
r
eal
re
fer
e
nce
vo
lt
age
s,
is
f
ound by t
he next
equ
at
io
n:
qs
r
r
r
m
r
s
i
L
R
L
+
=
*
(
8)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
1259
–
1267
1262
Figure
1.
Dec
ouplin
g b
y
cl
ass
ic
co
m
pensat
io
n
The
gra
ph
ic
diagr
a
m
of
the
s
peed
c
ontrol
of
the
asy
nc
hro
nous
m
otor
by
the
IRFO
C
te
chn
i
qu
e
is
giv
e
n
in
f
i
gure
2.
Figure
2.
Dia
gram of t
he
IR
F
OC of i
nductio
n
m
otor
3.2. R
otor spe
ed contr
oller
The
s
pee
d
c
ontrolle
r
giv
es
t
he
ref
e
rence
to
r
qu
e
,
a
go
al
of
pr
ese
r
ving
the
corres
pondin
g
sp
ee
d.
F
or
the
te
ch
nique
t
o
be
justi
fie
d,
it
is
essenti
al
that
the
i
nter
na
l
loop
is
s
o
ra
pid
t
han
the
l
oop
of
the
s
pee
d.
T
he
mecha
nical
expressi
on is
:
s
J
f
P
C
c
em
r
+
=
(9)
The
cl
os
ed
lo
op tra
nsfer
f
un
ct
ion
is
g
i
ven by
:
(
)
(
)
s
ρ
J
P
K
s
K
i
p
r
r
+
=
*
(10)
The
c
ontrolle
r
PI
par
a
mete
rs
i
s g
i
ven by: [
10
, 11]
−
=
=
P
f
J
K
P
ρ
J
K
c
p
i
2
2
2
(11)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A stu
dy of se
nsorless
vect
or
c
on
tr
ol
of I
M
u
s
ing
ne
ural net
work lue
nber
ge
r observer
(
T
ahar
Bel
bekri
)
1263
4.
LUENBE
R
G
ER OBSE
RVE
R
This
t
yp
e
is
on
e
of
t
he
deter
minist
ic
obse
r
ver
s
wh
ic
h
bel
ong
to
the
gro
up
of
cl
os
e
d
lo
op
ob
se
r
ver
s
[12].
4.1. Desi
gn
of
Luenber
ger
obser
ver
The ne
xt f
ig
ur
e re
pr
ese
nts th
e sche
mati
c d
i
agr
a
m
of
l
uenb
erg
e
r obser
ver
Figure
3. Sc
he
mati
c d
ia
gram
of Lu
e
nbe
r
ger
ob
s
er
ver
The
est
imat
ed
sta
te
s
are
re
pre
sented
by
th
e
ci
rcu
m
flex
acc
ent
a
nd
k
is
t
he
gai
n
of
the
obser
ve
r,
his
sta
te
model
is
giv
e
n by
:
[
5,
6, 8].
=
−
+
+
=
X
C
Y
Y
Y
K
U
B
X
A
X
.
)
.(
.
.
(12)
With
:
=
r
r
s
s
i
i
X
,
=
s
s
i
i
Y
,
−
−
=
3
4
4
3
1
2
2
1
K
K
K
K
K
K
K
K
K
−
−
−
−
−
−
=
5
4
5
4
2
3
1
3
2
1
0
0
.
0
.
0
a
w
a
w
a
a
a
w
a
a
w
a
a
a
A
r
r
r
r
We
will
u
se t
he
pole place
me
nt meth
ods a
nd
the L
ya
punov
appr
oach to cal
culat
e the
obse
rv
e
r gain
−
=
−
+
−
+
−
+
−
=
−
=
+
−
−
=
r
r
m
s
r
s
r
m
s
r
m
r
m
s
r
s
r
r
s
w
L
L
L
k
K
T
T
k
L
L
L
T
L
L
L
L
T
T
k
K
w
k
K
T
T
k
K
.
).
1
(
1
1
)
1
(
1
1
).
1
(
).
1
(
)
1
1
)
.(
1
(
4
2
3
2
1
(13)
The
pole
s
of
the
obser
ve
r
a
r
e
ch
os
e
n
to
ha
ve
a
rap
i
d
co
nver
ge
nce
t
o
th
e
dy
namics
of
the
open
-
lo
op
sy
ste
m.
T
he ga
in K is
gen
e
rall
y
sel
ect
ed
smal
l
[12, 1
4, 15
,
23]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
1259
–
1267
1264
4.2.
Adap
tatio
n mech
an
ism
of Luenber
ger
The
obje
ct
ive
of
this
sect
ion
is
to
lo
ok
f
or
a
n
a
dap
ta
ti
on
la
w
to
est
imat
e
the
s
pee
d.
We
us
e L
ya
punov
t
heor
y
to
re
du
ce
the
ada
pt
ive sp
ee
d mec
han
is
m.
This
obser
ver
is
co
ns
ti
tuted
by
the
e
sti
mati
on
er
ror
on
th
e
sta
tor
cu
rr
e
nt
and
the
r
otor
flu
x.
The
difference
betwee
n
this
observe
r
a
nd the
MAS mo
del is
d
esc
ri
be
d by
:
X
A
e
KC
A
e
)
(
)
(
+
−
=
(14)
With:
−
−
−
−
=
−
=
5
5
3
3
0
0
0
0
0
.
0
0
.
0
0
0
)
(
)
(
a
w
w
a
w
a
w
a
w
A
w
A
A
r
r
r
r
r
r
(15)
we give t
he
la
w of
ada
ptati
on
of the esti
ma
te
d
s
peed
:
[10,
12, 13].
dt
e
e
a
w
r
i
r
i
t
r
s
s
)
(
0
3
−
=
(16)
by u
si
ng
of
PI
con
t
ro
ll
er,
the
est
imat
ed
s
pee
d
is
giv
e
n b
y
[
14, 15].
dt
e
e
k
e
e
k
w
r
i
r
i
i
r
i
r
i
p
r
s
s
s
s
)
(
)
(
−
+
−
=
(17)
With
:
p
k
an
d
i
k
:
posit
ive
s
consta
nts [
23]
.
5.
NEU
RA
L
N
E
TWOR
K LU
ENBE
RGE
R OB
SER
VER
Ar
ti
fici
al
ne
ural
netw
orks
(
A
NN
s
)
a
re
a
gro
up
of
meas
ur
a
ble
le
arn
i
ng
al
gorithms
w
hic
h
use
the
data
to lear
n
f
or a
pur
pose
of cal
cu
la
ti
ng
val
ues fr
om
t
he
in
puts [
17].
The
res
ult
of
s
ci
entifi
c
w
orks
giv
e
s
a
l
ot
of
cases
of
suc
c
eeded
c
on
tr
ol
execu
ti
ons
util
iz
ing
ne
ur
al
sy
ste
ms
.
The
bi
g
pro
blem
on this
way
is
th
e
decisi
on
of
a
s
uitable
ne
ur
al
s
ys
te
m
de
sig
n
f
or
u
se
in
th
e
con
t
ro
l.
Howe
ver,
som
e
con
t
ro
l
str
uc
tures
a
re
fir
mly
ide
ntifie
d
with
their
ne
uro
nal
par
t
ners,
w
hich
e
nc
oura
ges
neur
on
al
us
a
ge
[
18, 19,
20].
(a)
(b)
Figure
4, (a
)
B
lock diag
ram
of
neural ne
t
wor
k
lue
nber
ger o
bs
er
ve
r,
(b)
Bl
ock d
ia
gr
a
m
of n
e
ur
al
netw
ork
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A stu
dy of se
nsorless
vect
or
c
on
tr
ol
of I
M
u
s
ing
ne
ural net
work lue
nber
ge
r observer
(
T
ahar
Bel
bekri
)
1265
As
the
sim
ulati
on
res
ults
will
sh
ow,
Fig
ur
es
4
sho
ws
the
s
c
hemati
c
dia
gr
a
m
of
the
le
ar
ni
ng
of
sp
ee
d
by
ne
ur
al
netw
orks
le
ar
ning
offli
ne.
T
he
ou
tpu
t
of
th
e
in
duct
ion
m
oto
r
pl
ays
the
ro
le
of
the
s
uper
visor
an
d
pro
vid
es
the
de
sired
in
f
or
mat
ion
.
This
in
f
ormat
ion
is
c
ompare
d
wit
h
the
ou
t
pu
t
of
th
e
obser
ve
r
de
velo
ped
by
the
ne
ur
al
net
work.
Th
e
a
da
ptati
on
al
gorit
hm
us
es
the
e
rror
gen
e
rated
to
a
dju
st
the
weig
hts
of
t
he
ne
ural
netw
ork
[21, 2
2]
.
6.
RESU
LT
S
A
ND
DI
SCUS
S
ION
In
this
sect
io
n,
we
us
e
M
at
la
b
softwa
re
to
s
how
the
sim
ul
at
ion
of
se
ns
or
le
ss
ind
irect
ve
ct
or
c
on
tr
ol
us
in
g
t
he
lue
nb
erg
e
r obser
ver
with a
n
a
dap
ta
t
ion
mecha
nism
b
ase
d o
n
the
neural
net
w
ork
t
echn
i
qu
e
.
(a)
(b)
Figure
5, (a
)
E
sti
mate
d
an
d
a
ct
ual sp
ee
d res
pons
e
w
it
h Lu
enb
e
r
ger
obser
ver
, (b
)
E
rror o
f
est
imat
ed
and
actual
sp
ee
d
re
spo
ns
e
Figure
6, To
r
que
of I
RF
OC
Af
te
r
usi
ng
th
e
ne
ur
al
netw
ork
te
c
hn
i
qu
e
in
the
l
ue
nb
e
r
ger
obse
rv
e
r,
we
no
ti
ce
t
hat
the
resu
lt
s
ob
ta
ine
d
a
re
gr
eat
an
d i
m
proved c
ompare
d
t
o
the
pre
vious
researc
hes.
The
sim
ulati
on
resu
lt
s
s
how
n
in
Fig
ures
5
a
nd
6
pr
e
sent
t
he
com
par
is
on
amo
ng
est
imat
ed
a
nd
real
sp
ee
d
by
us
in
g
Neural
net
wor
k
lue
nber
ger
obser
ve
r,
we
ap
plied
10
N.m
load
distu
r
ban
c
e
at
t
equ
al
s
t
o
2
a
nd
4
sec
r
es
pecti
ve
ly.
The
co
ntr
ol
of
mo
to
r
by
us
in
g
the
se
nsor
or
t
he
est
imat
or
gi
ves
the
same
dyna
mic
perf
ormance
e
ven
if torq
ue resi
sta
nt is a
pp
li
ed
.
An
est
imat
ion
error
of
19
(r
a
d
/
sec
)
was
ob
ta
ined
at
t
he
st
arti
ng,
a
nd
dec
reases
t
o
a
val
ue
near
to
0
at
the
ti
me
t
=
0.3
sec
,
it
give
s
a
n
overs
hoot
of
12.
66
%
.
T
he
c
omman
d
was
able
to
rej
ect
the
l
oa
d
c
ouple
r.
Wh
e
n
t
he
s
pe
ed
ref
e
ren
ce
ha
s
bee
n
i
nv
e
rt
ed,
t
he
est
ima
ti
on
e
rror
val
ue
cha
ng
e
s
to
-
26
(r
a
d
/
sec
)
a
nd
decr
ease
s to
a
value nea
r
to
0 after
6.4 se
c.
At
the
ti
me
of
sta
rting
,
the
to
r
qu
e
i
ncr
ea
ses
r
apidly
to
the
va
lue
of
51.12
N.
m
,
a
nd
quic
kly
retu
rn
s
t
o
it
s
init
ia
l
value;
afterwa
r
d
it
fo
ll
ows
the
t
raject
ory
of
th
e
resist
ant
t
orqu
e
.
Wh
e
n
re
ver
si
ng
the
s
pe
ed,
it
decr
ease
s to
th
e v
al
ue
of
-
64
Nm
a
nd
retur
ns t
o
it
s
or
i
gin
al
v
al
ue
In
al
l
the
res
ults,
we
hav
e
a
sign
ific
a
nt
est
imat
ion
of
the
sp
ee
d.
T
he
est
imat
ed
spe
ed
f
ollo
w
s
perfect
ly t
he
tr
aj
ect
or
ie
s
of
t
he
r
efe
re
nces; th
e esti
mate
d
e
rror o
f
s
pee
d
ra
pi
dly
c
onve
rg
es
to the n
ull val
ue
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
1
1
, N
o.
3
,
Se
ptembe
r
2020
:
1259
–
1267
1266
7.
CONCL
US
I
O
N
In
t
his
ar
ti
cl
e,
we
ha
ve
ma
de
a
the
or
et
ic
al
study
of
the
ind
i
rect
vect
or
con
t
ro
l,
with
out
the
s
pee
d
sens
or
of
t
he
i
nductio
n
mo
t
or
by
the
us
e
of
the
sp
ee
d
est
imat
ion
te
ch
nique,
w
hich
base
d
on
t
he
lue
nb
erg
e
r
ob
s
er
ver
wit
h
an
a
da
ptati
on
mecha
nism
de
velo
ped
by
int
egr
at
i
on
of
t
he
ne
ur
al
net
wor
k
te
c
hn
i
qu
e
.
t
he
res
ults
wer
e
obtai
ne
d by a sim
ulati
on s
of
t
war
e
.
By
us
i
ng
t
he
ne
ur
al
netw
ork
Lue
nb
e
rg
e
r
observ
e
r,
t
he
sim
ulati
on
resu
lt
s
com
par
is
on
of
est
imat
ed
and
act
ual
sp
e
ed
res
ponse
,
f
or
dif
fer
e
nt
op
erati
ng
re
gime
s
of
t
he
mac
hi
n
e
al
lows
us
to
co
nf
ir
m
the
best
performa
nces
o
f
fer
e
d,
faste
r
respo
ns
e w
it
h a
minimi
ze
d
over
run
duri
ng
s
ta
rt
up
a
nd
s
pe
ed
rev
e
rsal.
O
bt
ai
nin
g
high
perf
or
ma
nce
with
a
n
asy
nchron
ous
machine
nece
ssit
at
es
com
plex
c
omman
ds
,
w
hich
re
qu
i
r
e
i
n
par
ti
cula
r
the
knowle
dge
of th
e p
a
rameters
a
nd the
r
oto
r
sta
te
s.
Gen
e
rall
y,
t
his
study
has
s
how
n
very
e
ff
e
ct
ive
co
ntr
ol
and
sat
isfyi
ng
for
the
in
du
s
tria
l
need
s
,
because
of
the
minimi
zat
io
n
of
the
est
imat
ion
e
rror
on
th
e
one
ha
nd,
th
e
r
obus
t
ness
a
nd
the
sta
bili
ty
of
t
he
sy
ste
m
i
n op
e
r
at
ion
unde
r
a
ny c
onditi
ons
of u
se
on t
he oth
er
hand.
ACKN
OWLE
DGE
MENTS
We
a
re
grat
ef
ul
to
al
l
the
rev
ie
wer
s
f
or
their
ca
reful
r
eadin
g
of
t
he
pa
pe
r
a
nd
t
he
ir
helpful
comme
nts.
REFERE
NCE
S
[1]
R.
Mini
,
C.
Sara
nya,
B
.
H.
Satheesh,
M.
N
.
Dine
sh,
“L
ow
spe
ed
esti
mation
in
se
nsorless
dire
c
t
t
orque
con
trol
l
ed
induc
ti
on
mot
or
drive
usi
ng
ext
e
nded
kalman
f
il
t
er,
”
Inte
rnat
iona
l
Journal
of
Pow
er
El
e
ct
roni
cs
and
Dr
iv
e
Syst
em
(IJ
PE
DS)
,
vol
.
6
,
no
.
4
,
pp
.
819
-
830
,
2018
.
[2]
H.
Naye
e
m,
H.
Iqba
l
“A
Lue
nb
erg
er
–
Slid
ing
Mode
Obs
erv
er
fo
r
Online
Par
am
e
te
r
Est
im
a
ti
on
a
nd
Adapta
t
ion
i
n
High
-
Perform
an
ce
Induc
ti
on
Motor
Driv
es,
”
Tr
ansacti
ons
on
I
ndustry
App
li
ca
t
ions
,
Vol
.
45,
n
o.
2
,
pp.
772
-
78
1
2009.
[3]
M.
Benamour,
“Cont
rol
by
DT
C
of
th
e
indu
ction
machin
e
wi
thout
sensor
.
Us
e
of
KA
LMAN
fil
t
er
for
sp
e
ed
esti
mation
,
”
the
s
is of
Magist
er,
Mus
ta
pha
Benbo
ula
ïd
,
Ba
tna (Al
ger
ia
)
,
2012
.
[4]
P.
J.
Shaija,
D.
As
ha
Eliza
b
et
h
“
An
intelligent
sp
ee
d
cont
ro
ller
d
e
sign
for
indi
r
ect
vec
tor
con
trol
l
ed
indu
ct
ion
mo
tor
drive
sys
teme
,
”
Proce
dia
te
chno
logy
S
ci
en
ce di
r
ec
t
,
vo
l
25
,
pp
.
8
01
-
807
2016.
[5]
Y.
Beddi
y
af,
“S
tudy
and
Simul
at
ion
of
esti
m
ators
and
robust
observe
rs
of
f
lu
x
and
spe
ed
fo
r
the
async
hrono
us
ma
ch
ine
,
” the
sis
of
Magist
er,
Mu
stapha
B
enboul
a
ïd,
B
at
na
,
2016
.
[6]
S.
DA
MK
HI,
“S
ensorle
ss
spe
ed
con
trol
of
indu
ction
mot
or
by
th
e
SIG
NA
L
FLO
W
GRA
PH
S
(SF
G)
of
HO
LTZ,
”
the
sis of
Mag
ist
er,
Mus
ta
ph
a
B
e
nboula
ïd
,
2007
.
[7]
H.
Naye
e
m,
H.
Iqba
l,
“Robust
sensorle
ss
vec
tor
cont
rol
of
an
i
nduct
ion
m
ac
h
in
e
using
mul
t
iobjective
ad
aptati
v
e
fuz
zy lue
nb
erg
er
observe
r
,
”
I
SA T
rans
act
ions E
lsev
i
er
,
Vol
.
74
,
p
p.
144
-
154
,
201
8.
[8]
A.
Chebbi
,
“Backste
pping
command
of
a
mac
hine
async
hron
ous
without
spee
d
sensor,
”
th
esis
of
Magister,
Mus
ta
pha
Benbo
ula
ïd
,
Ba
tna
,
20
11.
[9]
S.
Maiti,
C.
Cha
kra
borty,
“A
ne
w
insta
nt
ane
ous
rea
c
ti
ve
power
b
ase
d
MRA
S
for
sensorle
ss
induction
mot
or
drive,
”
Simulat
ion
mode
ll
ing
pra
ct
i
ce an
d
the
ory
,
vo
l.
18
,
pp
.
1314
-
1326
,
2010.
[10]
I.
K.
Bouss
erh
a
ne,
“Fuzz
y
Con
trol
lers
Optimiz
ed
by
the
Gen
e
ti
c
Algorit
h
m
f
or
Controlling
an
As
ynchr
onou
s
Mac
hine,”,
Doc
t
ora
l
the
sis,
US
TO,
2008.
[11]
B.
Bouch
iba
,
A.
Haz
z
ab,
H.
Gl
a
oui,
M.
K.
Fe
ll
a
h,
I.
K.
Bouss
er
hane
,
P.
Si
ca
rd
,
“Ba
ckst
eppi
ng
c
ontrol
for
multi
-
ma
ch
ine
w
eb
wi
nding
sys
te
m
,
”
J
ournal
of el
e
ct
ri
cal
engi
ne
ering and t
e
chnol
ogy
,
vol.
6
,
no
.
1
,
pp
.
59
-
66
,
2011
.
[12]
D.
Cher
ifi,
Y.
M
il
oud,
A.
T
ahr
i,
“Sim
ultaneous
e
stim
ation
of
ro
to
r
spee
d
and
sta
to
r
resist
anc
e
in
se
nsorless
indi
r
ec
t
vec
tor
cont
ro
l
o
f
induc
t
ion
motor
drive
s
using
a
lue
nb
erg
er
obs
erv
er,”
Int
ernational
Journal
of
compute
r
scie
n
c
e
issues
,
vol.
9,
no
.
2
,
pp
.
325
-
335
,
201
2.
[13]
M.
Jouil
i,
M.
Ja
rra
y,
Y.
Kouba
a
,
M
.
Bouss
ak,
“
A
Lunbe
rg
er
sta
te
observe
r
for
s
im
ultaneous
estimat
ion
spe
ed
an
d
rotor
resist
ance
i
n
sensorle
ss
indirec
t
stat
or
flux
o
rie
nt
at
ion
cont
ro
l
of
induc
t
ion
m
otor
driv
e”
,
Int
e
rnational
journa
l
of
comput
er
sci
e
nce
i
ss
ues
,
Vol
.
8,
no
.
3,
pp
.
116
-
125
,
2011
.
[14]
M.
Mess
aoudi
,
L.
Sbi
ta,
M.
B
enha
m
ed,
H.
K
rai
e
m,
“MRAS
and
lu
enbe
rg
er
observe
r
b
ase
d
sensorle
ss
vecto
r
cont
rol
of induct
ion
mot
o
rs”,
Asi
an
journal
o
f
in
f
orm
ati
on
techno
logy
,
vol
.
6,
no
.
4,
pp
.
232
-
239
,
2008.
[15]
A.
Benna
ss
ar,
A
.
Abbou,
A.
Ak
her
az,
M.
B
ara
r
a,
“Sensor
le
ss
slidi
ng
mod
e
control
of
induction
mot
or
base
d
on
lue
nber
g
er
obse
rve
r
using
fu
zzy
logi
c
ad
apt
a
tion
me
c
hani
sm
,
”
Journal
of
theor
et
ic
al
and
ap
pli
ed
inf
orm
ati
o
n
te
chno
logy
,
vol
.
65,
no
.
1
,
pp
.
13
0
-
136
,
2014
.
[16]
C.
Ben
r
ega
ya
,
C.
Z
aa
four
i,
A.
Chaa
ri
,
“E
l
ectric
drive
cont
rol
wi
th
rotor
r
esista
nc
e
and
ro
tor
spe
e
d
observe
rs
base
d
on
fuz
zy
log
ic,”
Mathe
mati
cal
Proble
ms
in
Engi
n
ee
ring
,
pp.
1
-
9
,
2014.
[17]
M.
Zol
f
agha
r
i,
T.
Sey
ed
abba
s,
D.
Vind
el
mu
nuz,
M
.
B
ara
r
a,
“Ne
ur
al
n
et
wo
rk
-
base
d
sensorl
ess
dire
c
t
powe
r
cont
rol
of
p
erm
a
nent
ma
gne
t
syn
chr
onous m
otor
,
”
A
in
sham
s e
ngi
nee
ring
journal
,
vol.
7
,
pp
.
729
-
7
40
,
2016
.
[18]
A.
Medve
d
ev,
G.
Hillerstrom
,
“Per
iod
ic
distu
rba
nce
re
jecti
on
:
A
n
eur
al
ne
t
work
appr
oa
ch,”
Springer
-
V
erla
g
London
L
im
i
te
d
,
pp.
814
-
817
,
19
93.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
A stu
dy of se
nsorless
vect
or
c
on
tr
ol
of I
M
u
s
ing
ne
ural net
work lue
nber
ge
r observer
(
T
ahar
Bel
bekri
)
1267
[19]
J.
Ghouili,
“Sen
sorless
cont
rol
o
f
an
async
hrono
us
ma
ch
ine
with
Esti
-
m
ing
spe
ed
by
neur
a
l
n
etw
ork
”,
Doc
tora
l
the
sis,
Québ
ec Unive
rsity
,
(2005)
.
[20]
N.
Thuy
Pham
,
D.
Phu
Nguyen,
K.
Huu
Nguyen,
N.
Van
Nguyen
“Ne
w
Version
o
f
Adapti
v
e
Spee
d
Obs
erv
er
base
d
on
Neura
l
Ne
twork
for
SP
IM,
”
,
Inte
rnat
ional
J
ournal
of
Powe
r
Elec
tronic
s
and
Dr
iv
e
Syst
em
(I
JP
EDS
)
,
Vol
.
9
,
No.
4,
pp.
1486
-
1502,
2018
.
[21]
A.
Mishra,
P.
C
houdhar
y
“Art
ificial
Neur
al
Ne
t
work
Based
Co
ntrol
ler
for
Spee
d
Control
of
a
n
Induc
t
ion
Moto
r
using
Indirect
V
ec
tor
Control
Method
,”
Int
ernational
Journal
o
f
Powe
r
Elec
troni
cs
and
Dr
iv
e
Sy
stem
(IJ
P
EDS
)
,
Vol.
2
,
No.
4,
pp
.
402
-
408
,
2012
.
[22]
B.
Purw
ahyudi,
Soebagi
o
,
M.
As
har
i
“RNN
Based
Roto
r
Fl
ux
and
Speed
Esti
mation
of
I
nduct
ion
Moto
r,”,
Inte
rnational
Jo
urnal
of Powe
r
El
e
ct
ronics
and
Dr
iv
e
Syst
em
(I
J
PE
DS)
,
Vol
.
1,
No.
1,
pp.
58
-
64,
2011.
[23]
T.
Bel
b
ekr
i
,
B
.
Bouchi
ba
,
I
.
K.
Bouss
erh
ane
,
H.
Be
che
ri
“Spe
ed
Sensorless
Fie
l
d
-
Orien
te
d
Cont
rol
of
Induc
ti
o
n
Motor
with
fu
zzy
lue
nb
erg
er
ob
serve
r,”
E
le
c
trot
ehni
ca
Elec
troni
ca
Au
tomati
ca
(
EE
A
)
,
Vol
.
66
,
No.
4,
pp.
22
-
28
,
2018
.
[24]
S.
Yi,
W
.
M
.
Ut
omo,
G
.
H.
Hw
a
ng,
C
.
S.
Kai
,
A
.
J.
Li
m
Meng
Si
ang,
N.
A
.
Za
mb
ri,
Y.
M.
Y.
Busw
ig,
K.
H.
L
aw,
S.
G.
Yi
“
Loss
mi
nimization
D
TC
elec
tri
c
motor
drive
sys
tem
Based
on
a
daptive
AN
N
strat
e
gy,
”
In
te
rnation
a
l
Journal
of
Power
El
e
ct
ronics
an
d
Dr
iv
e
S
yste
m
(
IJP
EDS)
,
Vol.
1
1,
No.
2,
pp.
618
-
624,
2020
.
[25]
H.
Araba
c
i
“An arti
f
ic
i
al
neu
ral
net
work a
pproa
c
h
for
sensorle
ss
spee
d
estimation
via
rotor
slo
t
ha
rmoni
cs,
”
Tur
ki
sh
Journal
of
Elec
t
rical
Engi
ne
erin
g
&
Comput
er
S
ci
en
ce
s
,
vol.
22
,
pp.
1076
-
1084
,
2014.
BIOGR
AP
HI
ES OF
A
UTH
ORS
Tah
ar
BELBEKRI
borne
d
in
1987
in
Béc
h
ar
(Alge
ria
)
.
He
o
bta
in
ed
the
elec
t
ric
a
l
engi
n
ee
r
in
g
dipl
oma
fro
m
B
éc
har
Univ
ersit
y
,
(Alge
ri
a)
in
20
10.
The
ma
gist
er
degr
ee
in
Elec
tr
ic
a
l
Engi
n
ee
ring
from
univ
ersit
y
of
Ta
hr
i moha
m
ed,
(Alg
eria), i
n
2014.
He’s
cur
re
ntl
y
pr
epa
ring
hi
s Ph.d.
d
egr
e
e.
e
-
mail addre
ss
:
t
aha
rmoh87@y
a
hoo.
fr
Bou
smah
a
BOUCHIBA
,
borne
d
in
Bé
cha
r
(
Alger
ia
)
,
in
19
77,
h
e
obt
ai
n
e
d
his
el
e
ct
ri
cal
engi
ne
eri
ng
dip
l
oma
from
B
éc
h
ar
Univ
ersit
y
,
(
Alger
ia
)
in
199
9.
And
a
Maste
r
deg
ree
fro
m
t
he
Univer
sity
Al
ex
andr
ia
Egypt
in
2006.
He
ac
hi
ev
ed
the
doc
tora
l
degr
ee
in
el
e
ct
r
i
ca
l
engi
n
ee
ring
from
the
Univer
sity
of
SD
B
(Al
ger
ia
)
,
in
2011.
Curre
ntl
y
,
He
is
Profess
or
at
th
e
Univ
ersit
y
of
Ta
hri
Moham
ed Béc
har
(Alge
r
ia
)
.
e
-
mail addre
ss
:
bouchi
ba_bous
ma
ha@ya
hoo
.
fr
Ismai
l
kh
al
i
l
B
OU
SS
ERH
AN
E
borne
d
in
197
6
in
Béc
h
ar
(Al
ger
ia
)
.
He
obt
ained
the
elec
tr
ical
engi
ne
eri
ng
di
pl
oma
from
Béc
h
ar
Univer
sity
,
(
Alger
ia
)
in
200
0.
Magiste
r
deg
ree
in
Elec
t
ric
al
Engi
ne
eri
ng
fro
m
the
Univ
ersity
US
TO
of
Or
an
in
2003
and
the
Doctor
ate
degr
ee
f
rom
th
e
El
e
ct
ri
ca
l
Engi
n
ee
ring
the
Unive
rsity
US
TO
of
Oran
in
2008
,
A
lge
ri
a.
Curr
ent
l
y
,
He
is
profe
ss
or
of
elec
t
rical
enginee
ring
at Univers
it
y
T
ahr
i
Moha
me
d
of
Bé
cha
r
,
Alger
ia.
e
-
mail addre
ss
: bou_isma@ya
ho
o.
fr
Houci
ne
BECHERI
borne
d
in
1987
in
Bé
cha
r
(Alge
ria
)
.
He
ob
ta
in
ed
the
e
lectr
ic
a
l
engi
n
ee
ring
dipl
oma
from
B
éc
har
Univ
ersit
y
,
(Alge
ri
a)
in
20
10.
The
ma
g
iste
r
degr
ee
in
E
lectr
ic
a
l
Engi
n
ee
r
ing
from
Univ
ersit
y
of
T
ahr
i
moha
m
ed
in
Bé
cha
r
(Al
ger
ia
)
,
in
2014
.
He
r
ec
e
ive
d
the
doct
ora
te
degr
ee
in
e
le
c
trica
l
eng
i
nee
ring
from
the Unive
rsity
of T
ahr
i
Moha
me
d
o
f
Béc
h
ar
(Alg
eria),
in
2018
.
e
-
mail addre
ss
: houci
ne
.
be
che
ri
@gma
il.c
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.