Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
5, N
o
. 4
,
A
ugu
st
2015
, pp
. 72
9
~
74
1
I
S
SN
: 208
8-8
7
0
8
7
29
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
/
IJECE
Contribution to the Artifical Ne
ural Network Speed Estimator
in a Degraded Mode for Sensor
-Less Fuzzy Direct Control of
Torque Application Using Du
al S
t
ars Ind
u
ction Machine
Hechelef Mohammed, Abde
lkader Mer
o
ufel
F
acult
y of Engin
eering
S
c
ien
ces
,
Ele
c
tri
cal
Eng
i
n
eering
Depar
t
m
e
nt
Djilla
li
Li
abes U
n
iversit
y
S
i
di B
e
l Abbes Alg
e
ria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 19, 2015
Rev
i
sed
Ap
r 4, 20
15
Accepted Apr 28, 2015
Recen
tl
y
on
e of the m
a
jor topic of research i
s
the involvem
e
nt of the
intel
ligen
ce
ar
tif
ici
a
l
in th
e
contr
o
l s
y
st
em
. Th
is
paper d
e
a
l
s with
appl
ica
tion
of a new combination b
e
tween
two-control str
a
teg
y
known
as fuzzy
dir
e
ct
control of torqu
e
and then an a
d
aptiv
e Neurona
l Speed estim
at
or utiliz
ing
dual star
ts indu
ction motor. Th
e resear
ch discu
ssed consist to
replace
the
switching table
used in th
e conv
ention
a
l dir
e
ct control method
and adaptive
m
echanis
m
of the cl
as
s
i
c M
R
AS
es
tim
ator wit
h
fuzz
y con
t
roll
er and ne
w
neural n
e
twork
accord
ingl
y, bo
t
h
s
t
rategi
es
can
m
a
nage the d
e
graded and
normal modes.
The n
e
ural netw
orks used are the back-prop
a
gatio
n
, to
reduce
the tr
aining p
a
t
t
e
rns
and in
creas
e the
exe
c
ution s
p
eed of th
e tr
ain
i
ng proces
s
.
As results we achiev
ed can be
summar
ised as
follows: 1) high
degree of
reli
abil
it
y of
speed
estim
ation
e
v
en with
using
onl
y one
start
v
o
ltag
e
s and
currents and p
a
r
a
meters; 2) Minimization
of th
e torque and flux r
i
pples; an
d
3) Minimization
of the curr
ent total h
a
rmonic d
i
stortion.
Keyword:
A
NN
de Se
ns
or
-Less
D
e
gr
ad
ed Mode
DSIM
DTC
Copyright ©
201
5 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
:
A
b
d
e
lk
ad
er
Me
r
o
u
f
e
l
,
Faculty of E
n
gineering
Sciences.
Electrical Engineeri
n
g
Departm
e
nt,
Dj
illali Liab
es
Un
i
v
ersity Sid
i
Bel Ab
b
e
s Al
g
e
ria.
Em
a
il: h
m
ed
1
4
@yaho
o
.fr
1.
INTRODUCTION
Mo
st recen
tly, th
e in
trod
u
c
ti
o
n
of an
artificial n
e
ur
al
net
w
or
k
has st
a
r
t
e
d
t
o
pl
ay
an i
n
c
r
easi
n
g r
o
l
e
i
n
m
odel
i
ng an
d co
nt
r
o
l
of s
p
eed est
i
m
a
t
o
rs.
For e
x
am
pl
e, whe
n
used
within a s
p
ecific railway application;
“Feedback
of t
h
e wheel spee
ds in high
-s
pee
d
traction system”. Whe
n
the
sp
ee
d sens
or is
defective
occupies a
large area
on the nowadays s
p
eed s
e
ns
o
r
-less app
licatio
n
researchs, wh
ich
raises th
e
fo
llo
wing
q
u
e
stion
how
can the
s
p
eed be estim
a
ted in
a de
gra
d
e
d
m
ode
?
The
desi
gn
o
f
AN
N e
s
t
i
m
a
t
o
r’s
sol
u
t
i
o
n
i
s
base
d
on
t
h
e
t
r
ai
ni
ng
of t
h
e
r
ecur
r
ent
an
d
f
eed
fo
rwa
r
d
neu
r
al
net
w
or
k
,
w
h
i
c
h
m
a
nages an
d c
o
nt
rol
s
b
o
t
h
t
h
e
no
rm
al
and
de
g
r
ade
d
m
odes.
Th
e
du
al start
in
du
ctio
n m
a
c
h
in
e
will prov
i
d
e th
e
en
d u
s
er m
o
re
o
p
tion
s
to
estim
ate th
e sp
eed
b
y
u
s
ing
th
e t
w
o-start wind
ing
s
o
u
t
p
u
t
s as t
h
e
cu
rren
ts and
vo
ltag
e
s in
no
rmal
m
o
d
e
, o
r
altern
ativ
ely on
ly o
n
e
start ou
tpu
t
s
wh
en th
e
ou
tpu
t
o
f
th
e secon
d
st
arts are
not available in a
de
grade
d
m
ode.
Add
itio
n
a
lly wh
en
t
h
ere is a
n
eed to
in
crease sy
st
em
perf
orm
a
nce, pa
rt
i
c
ul
arl
y
w
h
en
f
aci
ng l
i
m
it
s
on t
h
e
po
we
r r
a
t
i
ngs o
f
p
o
we
r su
ppl
i
e
s an
d
sem
i
cond
uct
o
r
s
l
e
vel
const
r
ai
nt
s, t
h
e d
u
al
st
art
i
n
d
u
ct
i
on m
achi
n
e
shall m
o
tivate the use
of phas
e num
b
er
ot
her
t
h
an
t
h
ree,
ne
w m
achi
n
e
des
i
gn c
r
i
t
e
ri
a a
n
d
t
h
e
use
o
f
har
m
oni
c
current a
n
d
flux c
o
m
pone
nts.
In a
m
u
lti-phas
e
system
, it
shall be ass
u
m
e
d a system
that
com
p
rises m
o
re tha
n
th
e con
v
e
n
tion
a
l th
ree
ph
ases; th
e m
achine o
u
t
p
ut
p
o
w
er ca
n
be di
vi
de
d i
n
t
o
t
w
o o
r
m
o
re sol
i
d-st
at
e
i
nve
rt
ers.
Accepting the
above c
o
mme
ntary and co
nc
lusion takes one to the
next
level to study
in this pa
pe
r
the ANN s
p
ee
d estim
ator when
only
one
sta
r
t data’s are
a
v
ailable.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
72
9
–
74
1
73
0
W
i
t
h
in t
h
e
pa
per, a
sm
all power dual start i
n
duc
tion
m
ach
in
e was
u
s
ed to
st
u
d
y
t
h
e com
b
in
atio
n
of
two
ty
p
e
s
o
f
artificial in
tellig
en
ce
wh
en a series
o
f
test
s sh
ows th
at t
h
e
h
i
gh
qu
ality o
f
th
e sp
eed
estimatio
n
an
d th
e effectiv
en
ess
o
f
th
e t
a
rg
eted
an
d pro
p
o
s
ed
so
lu
tion
.
The
pa
per i
s
o
r
gani
ze
d as
f
o
l
l
o
ws;
St
art
wi
t
h
m
o
d
e
l
of a DSIM
whi
c
h has bee
n
de
vel
o
ped
,
t
h
en a di
rect
t
o
rq
ue co
nt
r
o
l
(DTC
) t
h
e
o
r
y
al
go
ri
t
h
m
wi
ll
be i
n
t
r
od
uce
d
Next
a f
u
zzy
l
ogi
c t
ech
ni
q
u
e
shal
l
be use
d
i
n
t
h
e DTC
i
n
Sect
i
on
2. A
f
t
e
r t
h
at
,
p
r
op
o
s
ed
n
e
ural ro
to
r sp
eed
esti
m
a
t
i
o
n
u
s
e th
e v
o
ltag
e
a
n
d
cu
rren
t of th
e first star
t.
Th
is will b
e
in
clud
ed
with Secti
o
n 3, in t
h
e e
n
d of t
h
e sam
e
section
we
pr
es
ente
d a Sim
u
link Fuzzy DTC m
o
del.
W
ithi
n
Sect
ion
5,
a selectio
n
o
f
t
h
e sim
u
lat
i
o
n
resu
lts will b
e
in
tegrated
as sam
p
le rev
i
ew do
cu
m
e
n
t
atio
n
.
Th
e clo
s
i
n
g
sectio
n
shall enc
o
m
p
ass a set
of rem
a
rks a
n
d a c
o
nclusion statem
ent.
Th
is p
a
p
e
r is org
a
n
i
zed
as fo
llo
ws. First,
DTC th
eo
ry
al
g
o
rith
m
is in
trod
u
c
ed
in
Secti
o
n
2. Th
en
, t
h
e
fuzzy
l
ogi
c t
echni
que
used i
n
DTC
,
after that, a propos
ed
neural rot
o
r
s
p
eed estim
a
tion use the voltage and
current of
the first
start,
is presen
ted
in
Sectio
n
3. In
th
e Sectio
n
4, some si
m
u
la
tio
n resu
lts are presen
ted.
Fin
a
lly, so
m
e
co
n
c
l
u
d
i
n
g
rem
a
rk
s are stated
in
th
e last
Sectio
n.
2.
MODELING OF
THE DOUBLE
STAR INDUCTION MOTOR
The dual star asynchrono
us machine.
Whose Figure 1 express
e
s t
h
e wi
ndi
ng
s of t
h
e
do
u
b
l
e
st
ar
in
du
ctio
n m
a
c
h
in
e and
th
e
o
f
fset ang
l
e
b
e
tween
th
e two
stars
wind
ing
s
[1
]
.
Fi
gu
re
1.
S
h
o
w
s t
h
e
wi
n
d
i
n
g a
n
d
o
ffs
et
an
gl
e
s
-A
1, B
1
,
C
1
:
W
i
n
d
i
n
g
of
st
at
or
0
1
.
-A
2, B
2
,
C
2
:
W
i
n
d
i
n
g
of
st
at
or
0
2
-
α
:
of
fset
a
ngl
e
bet
w
ee
n t
w
o
s
t
at
ors.
-
θ
: offset ang
l
e b
e
tween
t
h
e
rotativ
e part
a
n
d
t
h
e st
at
or
s
01
&
0
2
.
The m
a
the
m
a
tical
m
odel
of the m
achine is
can be expresse
d
by the following set of
electrical/m
ech
anical equations
The first
star:
Va
b
c
,
s
1
Rs
ab
c,
s
d
φabc,
s
dt
(1
)
The sec
o
nd sta
r
t:
Va
b
c
,
s
2
Rs
ab
c,
s
d
φabc,
s
dt
2
Fo
r th
e ro
tative p
a
rt:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Co
n
t
ribu
tion
t
o
th
e Artifica
l
Neu
r
a
l
Network
Sp
eed Estimato
r
in a Deg
r
ad
ed Mo
d
e
fo
r
…
(A. Meroufe
l)
73
1
Va
b
c
,
r
Rr
ab
c,
r
d
φabc,
r
dt
(3
)
The m
echanica
l
equations:
J
dΩ
dt
T
e
m
T
r
k
f
Ω
(4
)
Wh
ere J is th
e
m
o
men
t
in
ertia o
f
th
e ro
tating p
a
rts, K
f
is th
e frictio
n
co
efficien
t related
t
o
th
e eng
i
ne
beari
ngs
, a
n
d
T
em
represen
ts th
e torq
u
e
lo
ad
ing
[2
].
The electrical state variables
in "
αβ
" syste
m
are the elec
trical flux,
and
th
e in
pu
t v
a
riab
le in
th
e
syste
m
"
αβ
" e
x
presse
d
by the vector
[U] then the
state sp
ace represe
n
tation
of the m
achine ca
n
be m
odele
d
and expresse
d
in the
form
:
X
dX
dt
A
X
B
U
(5
)
W
ith X
: state variables
A: system
ev
o
l
u
tio
n m
a
trix
A
A11
A
12
A13
A
14
A15
A
16
A21
A
22
A23
A
24
A25
A
26
A31
A
32
A33
A
34
A35
A
36
A41
A
42
A43
A
44
A45
A
46
A51
A
52
A53
A
54
A55
A
56
A61
A
62
A63
A
64
A65
A
66
(6
)
B
:
cont
r
o
l
Vec
t
or
B
10
000
0
01
000
0
00
100
0
00
010
0
00
000
0
00
000
0
(7
)
U
:
i
nput
vect
or
i
t
i
s
rep
r
ese
n
t
e
d
by
t
h
e t
e
nsi
o
n
vect
o
r
U
V
V
V
V
(8
)
3.
PRI
NCI
PLE
OF
DIRE
CT
E CO
NTR
O
L
OF TO
RQ
U
E
Di
rect
c
ont
r
o
l
of t
o
r
q
ue, i
s
a
n
a
p
p
r
oach
t
h
a
t
al
l
o
ws c
o
nt
r
o
l
o
f
t
h
e
di
rec
t
swi
t
c
h c
o
nve
rt
er
usi
n
g a
sim
p
l
e
al
go
ri
t
h
m
.
The DTC
(
D
i
r
ect
T
o
r
q
ue
cont
rol
)
ap
pea
r
ed
i
n
t
h
e
19
8
0
, a
f
t
e
r a
vari
e
t
y
of al
go
ri
t
h
m
s
has
been
p
r
op
ose
d
base
d
on
re
fi
ne
m
e
nt
s de
vel
o
p
e
d
fr
om
heuri
s
t
i
c swi
t
c
hi
n
g
c
h
oi
ces [
3
]
,
If we c
o
nsi
d
e
r
t
h
e fi
rst
st
art
and t
h
e e
q
ua
t
i
ons w
h
i
c
h a
r
e used
fo
r ve
ct
ori
a
l
rep
r
ese
n
t
a
t
i
on
of t
h
e
st
at
or
characte
r
istics of the m
achine
,
bi
nds to the st
ator
refe
rence.
V
R
I
d∅
dt
V
0
R
I
d∅
dt
j
w
∅
(9)
From
the electrical flux expre
ssion, th
e
rotor curre
nt can be
expres
sed as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
72
9
–
74
1
73
2
I
1
σ
∅
L
L
L
L
∅
(1
0)
W
i
th
th
e d
i
sp
er
s
i
on
co
e
f
f
i
c
i
e
n
t
1
The e
x
pressi
on
s (
1
0
)
bec
o
m
e
V
R
I
d∅
dt
d∅
dt
1
στ
j
w
∅
L
L
1
στ
∅
(1
1)
Relatio
n
(11
)
sh
ows t
h
at:
*It
i
s
p
o
ssi
bl
e t
o
c
ont
rol
t
h
e
fl
ux
vect
or
∅
by
a
c
t
i
ng
on
t
h
e
v
o
l
t
a
ge vect
or
a
s
we
can consi
d
er the t
h
e
vol
t
a
ge
d
r
op
|
Rs
I
s
|
so sm
all
if co
mp
ari
n
g with vo
l
t
age vect
or val
u
e
i
n
t
h
e
peri
od
[
0
T
e
]
*
T
h
e
ro
tor act
as a filter
with
(ti
m
e co
n
s
tan
t
)
bet
w
ee
n t
h
e
fl
ux
∅
and
∅
. M
o
re
ove
r,
∅
reach
his
steady state val
u
e as
follow:
∅
L
L
∅
1
j
wrστ
(1
2)
By p
u
tting
:
∅
∅
)
:
Th
e
r
e
pr
esen
tatio
n of
t
o
r
que
ex
pressi
o
n
beco
m
e
s:
Γ
p
L
σL
L
ϕ
∗ϕ
sin
γ
(1
3)
Th
e exp
r
essi
o
n
(1
3) sh
ows th
at:
*T
he t
o
rq
ues
v
a
l
u
e i
s
depe
n
d
e
nt
s
of t
h
e am
pl
i
t
ude o
f
t
w
o
v
ect
ors
ϕ
and
ϕ
wit
h
relativ
e po
sit
i
o
n
.
*
If
we m
a
n
a
ge well th
e con
t
ro
l
o
f
th
e
flux
v
ector
ϕ
by
act
i
ng
o
n
t
h
e
m
odul
e a
n
d t
h
e
v
o
l
t
a
ge
vect
o
r
p
o
s
ition
,
th
erefo
r
e it is po
ssib
l
e to
co
n
t
ro
l t
h
e am
p
l
i
t
u
d
e
and th
e
relativ
e positio
n
o
f
ϕ
,
*T
hi
s i
s
pos
si
b
l
e onl
y
i
f
t
h
e c
ont
rol
peri
od
T
e
o
f
t
h
e
v
o
l
t
a
g
e
satisfies th
is
co
nd
itio
n.
≪
3.
1. Set
t
i
n
g
o
f
the
S
t
at
or fl
u
x
The e
x
pressi
o
n
of
the
stator
flu
x
with t
h
e
refe
re
n
ce ass
o
ciated t
o
the
stator
is
ob
tain
ed fro
m
th
e
fo
llowing
equ
a
tio
n
∅
sj
Vs
j
R
s
j
I
s
j
dt
j
=
1,2 (
1
4
)
Using
in
terv
al
[0, Te] co
rrespo
nd
ing
to
a sam
p
l
i
n
g
p
e
riod
(Te), the s
w
itch state (Sa
Sb
Sc) are
fixe
d,
and i
f
we c
o
nsider
the val
u
e,
|
R
s
I
s
|
to
b
e
n
e
g
lig
i
b
le
wh
en
co
mp
ared
with
vo
ltag
e
|
|
weican
iassu
m
e
:
∅sj
t
∅
V
T
j
=
1,2 (
1
5
)
Wi
t
h
φ
bei
n
g the flux
vector at
Tim
e
t=0
Thi
s
rel
a
t
i
on s
h
o
w
s t
h
at
i
f
w
e
appl
y
a no
n-
zero
vol
t
a
ge
v
ect
or, t
h
e e
nd
of t
h
e st
at
o
r
fl
ux
vect
o
r
m
o
v
e
s o
n
a straig
h
t
lin
e
wh
ose d
i
rection
t
h
e app
lied
v
o
ltag
e
g
i
v
e
s
v
ect
or. Fi
g
u
re
2
illustrates th
is
p
r
i
n
cip
l
e,
taking as e
x
ample the
voltage
vector (V3).
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S
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7
0
8
Co
n
t
ribu
tion
t
o
th
e Artifica
l
Neu
r
a
l
Network
Sp
eed Estimato
r
in a Deg
r
ad
ed Mo
d
e
fo
r
…
(A. Meroufe
l)
73
3
Fi
gu
re
2.
Ev
ol
ut
i
o
n
o
f
t
h
e e
n
d
of
t
h
e
fl
u
x
i
.
e
(
=
)
3.
2. C
o
ntr
o
l
o
f
t
h
e
E
l
ectr
o
m
a
gnetic T
o
rque
In a stea
dy state, we
ca
n ass
u
me for
sim
p
lic
ity th
at th
e stato
r
flux
v
ect
o
r
∅
ro
tates with a
co
nstan
t
am
pl
i
t
ude
|
∅
|
, and with an a
v
era
g
e s
p
ee
d
s
. It
can als
o
be a
s
s
u
m
e
d that
th
e
ro
t
o
r flux v
ect
o
r
m
a
in
tain
s
co
nstan
t
am
p
lit
u
d
e
and
ro
tates with
sam
e
p
u
l
satio
n
ω
s0
as the vector
∅
.
W
e
put at
;
∅
∅
e
∅
∅
e
(1
6)
B
a
sed
on t
h
e f
l
ux,
cu
rre
nt
an
d el
ect
rom
a
gni
t
c
t
o
rq
ue m
e
nt
i
one
d a
b
o
v
e, t
h
e el
ect
rom
a
g
n
et
i
c
t
o
r
q
u
e
equat
i
o
n c
o
ul
d
be t
r
ans
f
orm
e
d t
o
a si
nus
oi
d
a
l
fo
rm
as fol
l
o
ws:
Γ
P
L
σL
L
∅
∅
sin
γ
(1
7)
whe
r
e
0
is the angle bet
w
een the stator
a
n
d t
h
e
fl
u
x
rot
o
r
vect
or
.
If
we
Ap
ply
at
a
n
a
d
e
qua
t
e
v
o
l
t
a
ge
vec
t
or
, and w
e
i
m
p
o
s
e alon
g
w
ith
a
p
u
l
se
Δ
as
ro
tation
a
l sp
eed
an
d Imm
e
d
i
a
t
ely after
, we
can
note t
h
at there is a c
h
a
n
ge
s on
stator and rotor fl
ux:
∅
∅
∆
∅
∅
∆
∅
∆
(1
8)
with
:
∆
∆
Fro
m
th
e fl
u
x
ro
tor (18
)
exp
r
essio
n
,
we can
ded
u
c
e th
e
v
a
l
u
e d
e
riv
a
tiv
e
of
th
is qu
an
tity:
∅
∆
∅
∆
∅
(1
9)
with
:
∆
∆
∆
W
i
t
h
th
e sam
e
way,
we can
p
r
o
v
e
th
at: th
e Ro
tor fl
u
x
v
ect
or
k
eep tu
rn
ing
with
th
e sam
e
p
u
l
sation
Δ
and
m
a
i
n
t
a
i
n
i
ng t
h
e sam
e
am
pl
it
ude
∅
[3]
.
So after
t
h
e t
o
rq
ue e
q
u
a
t
i
on ca
n
be e
x
press
e
d
as:
Γ
P
L
σL
L
∅
∅
sin
γ
∆
γ
(2
0)
3.
3.
Sel
ecti
o
n
of
the
V
o
l
t
a
g
e
Vec
t
or
Th
e
po
sitio
n of th
e fl
u
x
v
e
cto
r
can b
e
d
e
termin
ed
fro
m
its
co
m
p
on
en
ts
∅
and
∅
W
h
en
th
e
flux vector is located inside
sector i, the two vectors V
i
et V
i+3
have the
bigger flux
com
ponent . In a
ddition,
t
h
ei
r effect
on
t
h
e t
o
r
que
de
p
e
nd
s of t
h
e p
o
s
i
t
i
on of t
h
e fl
u
x
vect
or i
n
t
h
e
sam
e
sect
or. B
o
t
h
, t
h
e fl
u
x
a
nd t
h
e
t
o
r
que
co
nt
r
o
l
are e
n
su
re
d
by
sel
ect
i
ng
one
o
f
t
h
e
f
o
u
r
n
o
n
-
zero
vect
ors
o
r
o
n
e
of
t
h
e t
w
o
n
u
l
l
vect
o
r
s
[
3
]
β
α
θ
s
φ
s
(T
i
)
φ
s
(T
i+1
)
∗
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
72
9
–
74
1
73
4
If
Vi+1 is selected
: Th
e fl
u
x
a
m
p
litu
d
e
will in
crease and
t
h
e
to
rqu
e
will
in
crease
If
Vi-1
is selected
: Th
e fl
u
x
am
p
l
itu
d
e
will
decrease an
d th
e to
rqu
e
will
in
crease.
If
Vi+2 is selected
: Th
e fl
u
x
a
m
p
litu
d
e
will in
crease and
t
h
e to
rqu
e
will decrease.
If
Vi-2
is selected
: Th
e fl
u
x
am
p
l
itu
d
e
will
decrease an
d th
e to
rqu
e
will
d
e
crease.
If
V0
o
r
V7
is
selected
: Th
e
v
ector fl
u
x
wil
l
m
a
in
tain
its valu
e and
t
h
e t
o
rqu
e
will d
ecrease if th
e sp
eed
is po
sitiv
e and
will in
crease if sp
eed
is
n
e
g
a
tiv
e.
3
.
4
.
Dev
e
lo
pmentiofifuzzy
iswitching
ita
b
le
Today, Fuzzy logic is a technique
used
i
n
artificial in
telli
g
e
n
ce
and
with
wi
d
e
ly u
s
ed in
v
a
riou
s
areas i
n
cl
udi
ng
:
cont
rol
,
aut
o
m
a
t
i
on, r
o
bot
i
c
s ...
et
c.
In
dee
d
t
h
i
s
i
s
a
ne
w
m
e
t
hod
o
f
deal
i
ng
wi
t
h
pr
o
b
l
e
m
s
of
adj
u
st
m
e
nt
, co
nt
r
o
l
an
d
deci
s
i
on
-m
aki
ng.
Th
ose Er
ro
rs o
f
b
o
t
h
t
o
rq
ue a
nd t
h
e fl
u
x
are
di
rect
l
y
used,
t
o
sel
ect
t
h
e inve
rt
er
vol
t
a
ge
swi
t
c
he
’
s
st
at
e wi
t
h
no
di
st
i
n
ct
i
on
bet
w
een a
ver
y
b
i
g
err
o
r
or
rel
a
tively
small
in the classical direct control of
to
rq
u
e
, also
the switch
i
ng
st
ate selected in
case an
impor
t
ant error
o
c
cu
rs
wh
ile startin
g
or with
d
i
fferent
con
s
i
g
ns
of
t
o
rq
ue
or
fl
ux
i
s
t
h
e sam
e
as d
u
ri
ng
t
h
e
n
o
r
m
al
operat
i
o
n.
as co
nse
que
nc
e i
n
a t
r
ansi
e
n
t
re
gi
m
e
resp
o
n
se o
f
t
h
e sy
st
em
i
s
slowe
r
,
ho
we
ver
t
h
e vol
t
a
ge v
ect
or i
s
sel
ect
ed, a
nd
by
t
a
k
i
ng i
n
t
o
acco
u
n
t
t
h
e
mag
n
itu
d
e
(
a
m
p
litu
d
e
)
an
d sig
n
s
of
t
h
e erro
rs of
tor
q
u
e
and f
l
ux
an
d no
t
j
u
st th
eir
si
g
n
s
, t
h
en th
e
r
e
sp
onses of
t
h
e sy
st
em
duri
n
g
st
a
r
t
i
n
g
an
d
whe
n
c
h
a
ngi
ng
t
h
e
fl
u
x
c
o
n
t
rol
or t
o
r
q
ue c
a
n
be
great
l
y
i
m
prove
d
We p
r
op
ose i
n
t
h
i
s
sect
i
o
n
a st
udy
of
d
i
rect
cont
rol
o
f
t
o
r
q
ue a
ppl
i
cat
i
on
on t
h
e
do
u
b
l
e
st
ar
asynchronous
machine base
d on
fu
zzy logic.T
h
e standa
rd
fuzzy logi
c co
n
t
ro
ller is u
s
ing
m
e
m
b
ersh
i
p
fu
nct
i
o
ns t
o
de
fi
ne t
h
e i
n
p
u
t
v
a
ri
abl
e
or
va
ri
abl
e
s as
we
l
l
as
t
h
e o
u
t
p
ut
vari
abl
e
. T
h
ey
ca
n
be
of
di
ffe
rent
t
y
pe
but
t
h
e m
o
st
fr
eque
nt
l
y
use
d
i
s
t
h
e t
r
i
a
ng
ul
ar
m
e
m
b
ershi
p
f
unct
i
o
n
[
4
]
.
Th
ose
hy
st
ere
s
i
s
co
nt
r
o
l
l
e
rs
an
d s
w
i
t
c
hi
n
g
t
a
bl
e
of c
onventional
DT
C are
replace
d
by a
fuzzy
cont
roller. T
h
e
fuzzy control
l
er ha
s th
ree
variable state.
Inputs a
n
d a
fu
zzy control
va
riable as
output to
pr
o
duce a co
ns
t
a
nt
cont
r
o
l
o
f
t
o
r
que a
nd
fl
u
x
. A
s
i
s
sho
w
n
i
n
Fi
gu
re 3 t
h
e fi
rst
fuzzy
va
ri
abl
e
, co
nsi
s
t
i
n
g
o
f
three
fuzzy
sets, is a
differe
n
c
e
betwee
n t
h
e
a
m
plit
ude
of t
h
e flux
refe
renc
e and the
estimated fl
ux.
Figu
re
3.
M
u
m
b
er
shi
p
fu
nction
with
th
ree f
u
zzy
s
ubsets
f
o
r the
er
ro
r
flu
x
The sec
o
n
d
f
u
zzy
vari
abl
e
i
s
sl
owe
r
co
nsi
s
t
i
ng
of
fi
ve f
u
zz
y
set
s
. Fi
gure
4 i
s
t
h
e di
f
f
ere
n
ce bet
w
ee
n
the re
fere
nce t
o
rque a
n
d estimated torque
,
Fig
u
re
4
.
Mu
mb
er sh
i
p
fun
c
tio
n with fi
v
e
the fu
zzy sets
Th
e th
ird
fu
zzy v
a
riab
le is th
e an
gle between the flux st
ator and
the
r
e refe
rence a
x
is "angle", the
uni
verse
of
di
sco
u
rse
of t
h
e t
h
i
r
d f
u
zzy
vari
abl
e
i
s
d
i
vi
ded i
n
t
o
t
w
el
ve f
u
zzy
s
y
m
m
e
t
r
i
cal
set
s
. The
d
i
str
i
bu
tio
n fun
c
tio
n of
t
h
ese
me
m
b
er
sh
ip
fun
c
tio
ns is show
n in
Figu
r
e
5.
0.
2
∆
Ce
m
0.
4
1.
0
-3
-2
-1
0 1
2
0
NL
ZL
PL
NS
PS
3
0.
8
0.
6
0.
6
0.
8
N
Z
P
-4
-3
-2
-1
0
1
2
3
*
1
0
-3
∆φ
0
0.
2
0.
4
1.
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Co
n
t
ribu
tion
t
o
th
e Artifica
l
Neu
r
a
l
Network
Sp
eed Estimato
r
in a Deg
r
ad
ed Mo
d
e
fo
r
…
(A. Meroufe
l)
73
5
Fi
gu
re
5.
M
u
m
b
er
shi
p
fu
nct
i
o
n
f
o
r
t
h
e
p
o
si
t
i
on
o
f
t
h
e
st
at
o
r
fl
ux
The
out
put
of
fuzzy
c
ont
rol
l
er i
s
t
h
e p
r
o
p
er
v
o
ltage ve
ctor. T
h
ese
voltage vectors
are disc
rete
val
u
es
;
singletons
re
present t
h
em
as in Figure
6.
Fi
gu
re
6.
M
u
m
b
er
shi
p
fu
nct
i
o
n
o
f
t
h
e
vect
o
r
s t
e
n
s
i
o
ns
3.
5. Selection Table
fo
r the
Vol
t
age Vectors
Tabl
e 1 sh
o
w
s t
h
e or
der
of
vol
t
a
ge
vect
o
r
s use
d
i
n
t
h
e
fuzzy
di
rect
cont
rol
m
e
t
hod o
f
t
o
r
que
according
t
o
voltage vector po
sition and t
h
e
variation
of t
h
e
torque a
n
d flux e
r
rors
Tabl
e
1. T
h
e
o
r
de
r
of
v
o
l
t
a
ge
vect
o
r
s
use
d
i
n
t
h
e
fuzzy
di
re
ct
t
o
r
que
co
nt
r
o
l
m
e
t
hod
Θ
1
Θ
2
Θ
3
∆Г
∆φ
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
P
V6 V1 V0 V2 V2
V6
V6 V0
V1 V2 V5 V6 V0 V1
V1
Z
V6 V6 V0 V0 V3
V5
V5 V0
V0 V2 V5 V5 V0 V0
V2
N
V5 V5 V0 V4 V3
V5
V4 V0
V3 V3 V4 V4 V0 V3
V2
Θ
4
Θ
5
Θ
6
∆Г
∆φ
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
P
V5 V4 V0 V6 V1
V4
V5 V0
V6 V6 V4 V4 V0 V5
V6
Z
V4 V4 V0 V0 V1
V4
V4 V0
V0 V1 V3 V3 V0 V0
V5
N
V4 V3 V0 V2 V2
V3
V3 V0
V2 V1 V3 V2 V0 V1
V1
Θ
7
Θ
8
Θ
9
∆Г
∆φ
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
P
V3 V4 V0 V5 V5
V3
V3 V0
V4 V5 V2 V3 V0 V4
V4
Z
V3 V3 V0 V0 V6
V2
V2 V0
V0 V5 V2 V2 V0 V0
V5
N
V2 V2 V0 V1 V6
V2
V1 V0
V6 V6 V1 V1 V0 V6
V5
Θ
10
Θ
11
Θ
12
∆Г
∆φ
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
PL
PS
Z
NS
NL
P
V2 V2 V0 V3 V4
V1
V2 V0
V3 V3 V1 V1 V0 V2
V3
Z
V1 V1 V0 V0 V4
V1
V1 V0
V0 V4 V6 V6 V0 V0
V3
N
V1 V6 V0 V5 V5
V6
V6 V0
V5 V4 V6 V5 V0 V4
V4
Vect
6
0 1
2
3
5
7
0
0.
2
0.
4
1.
0
V0
V1
V3
V2
V4
V5
V6
0.
6
0.
8
4
An
gle
Θ
1
0
50
1
00 1
50
2
00
30
0
25
0
35
0
0
0.
2
0.
6
1.
0
Θ
2
Θ
3
Θ
4
Θ
5
Θ
6
Θ
7
Θ
8
Θ
9
Θ
10
Θ
11
Θ
12
Θ
1
0.
4
0.
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
72
9
–
74
1
73
6
4.
FIS ALGO
RI
THEM
Th
e
fis
u
s
ed
i
n
th
is stud
y is fu
zzy inference syste
m
is a syste
m
that uses fuzzy set t
h
eory to m
a
p
in
pu
ts an
d ou
t
p
u
t
s.
Ou
r inp
u
t are:
flux er
ro
rs ef
[N Z P]
, tor
q
u
e
erro
r cpl[
NS
NL ZE PS PL]
,
and the p
o
s
ition of the
vol
t
a
ge vect
o
r
N[
θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
θ
8
θ
9
θ
10
θ
11
θ
1
2
]
t
h
e
n
a
s
out
put
vari
a
b
l
e
s we
hav
e
put
si
x
m
e
m
b
ershi
p
si
ngl
et
o
n
S[E
1
E2 E
3
E4
E
5
E6]
.
T
h
e
fi
s t
y
pe
we
use
d
i
n
ou
r
pa
per i
s
M
a
m
d
ani
wi
t
h
i
f
–a
nd
–
and-the
n
rule s
t
ructure,
i.e
r
u
l
e
N
u
m
b
er 01
[
if cf is P and
cpl is PL an
d N is O1
then Etat is E1
]
.
5.
SPEED ESTIMAT
O
R
M
odel
R
e
fere
nce A
d
apt
i
v
e
Sy
st
em
s (M
RAS) t
e
c
hni
que
s ap
p
lied
in
o
r
d
e
r to
estim
ate
ro
tor sp
eed.
Th
is techn
i
qu
e is b
a
sed
on
th
e co
m
p
arison b
e
tween
t
h
e o
u
t
p
u
t
s
o
f
two
esti
m
a
to
rs. Th
e ou
tpu
t
s of two
esti
m
a
to
rs
m
a
y
b
e
(t
h
e
ro
tor fl
u
x
, b
a
ck
em
f, o
r
m
o
to
r
reactiv
e power). Th
e esti
m
a
to
r th
at d
o
e
s no
t inv
o
l
v
e
th
e
q
u
a
n
tity to
b
e
esti
m
a
ted
(Th
e
ro
t
o
r sp
eed
ω
r) is con
s
id
ered
as th
e ind
u
c
tion
m
o
to
r vo
ltage
m
o
d
e
l. Th
is
m
o
d
e
l
con
s
i
d
ere
d
t
o
be t
h
e
re
fere
n
ce m
odel
(R
M
)
. T
h
e
ot
he
r m
odel
i
s
t
h
e c
u
r
r
ent
m
odel
,
de
ri
ve
d f
r
o
m
t
h
e r
o
t
o
r
eq
u
a
tion
,
th
is
m
o
d
e
l co
n
s
id
ered
to
b
e
th
e ad
ju
stab
le
m
o
d
e
l (AM). Th
e error b
e
tween
the esti
m
a
ted
q
u
an
tities
b
y
th
e two
m
o
d
e
ls is used
t
o
driv
e a su
itab
l
e ad
ap
tatio
n
m
ech
an
ism
,
wh
ich
g
e
n
e
rat
e
s th
e esti
m
a
t
e
d
ro
tor
spee
d. T
h
e
Figure
7 shows t
h
e arc
h
itecture
of
MRAS tec
h
nique.
For s
p
ee
d estim
ator [5]
Fi
gu
re 7.
St
r
u
c
t
ure of
A
N
N
M
R
AS
S
p
ee
d Est
i
m
a
t
o
r
In
o
u
r
pa
pe
r t
h
e ne
ural
net
w
o
r
k
schem
a
use
d
as
spee
d e
s
t
i
m
at
or, t
a
ke
t
h
e
co
nve
nt
i
o
nal
M
R
AS as a
refe
rence
and
measurem
ent of the
spee
d
se
nsor as target
ve
ctor
for trai
ning.
5.
1. Neur
al
Ne
tw
ork Speed
E
s
ti
ma
tor
i
n
Degr
ade
d
Mo
de
Ou
r p
r
op
ose
d
st
ruct
u
r
e o
f
t
h
e neu
r
al
net
w
o
r
k t
o
per
f
o
rm
the ne
ural
net
w
or
k s
p
eed est
i
m
a
t
o
r whe
n
syste
m
sto
p
deliv
ering
a fu
ll d
a
te is a b
ack
-
p
r
op
ag
ation
con
t
ro
ller with
sev
e
n
inp
u
t n
o
d
e
s, three
h
i
dden
l
a
y
e
r, an
d
o
n
e
neu
r
ons
i
n
t
h
e
out
put
l
a
y
e
r
,
as
sh
ow
n i
n
Fi
g
u
r
e
8.
In
or
de
r t
o
si
m
u
l
a
t
e
t
h
e spe
e
d
est
i
m
a
ti
on i
n
deg
r
a
d
ed m
o
d
e
we are c
o
nsi
d
eri
ng i
n
o
u
r
st
udy
, t
h
at
o
n
e
start voltage a
nd c
u
rrent m
e
asurem
en
ts are n
o
t
av
ailab
l
e. Mo
reov
er, the ANN sp
eed
esti
m
a
to
r u
s
ing
on
ly
t
hose
cu
rre
nt
s
and
v
o
l
t
a
ges
m
eas
urem
ents of a single star.
The i
n
puts a
r
e
curre
nts,
voltages, spee
d (t-1) and
t
h
e esti
mated
to
rq
u
e
.
Th
e
d
e
tails of th
e
n
e
u
r
al
n
e
two
r
k
sp
eed
esti
m
a
to
r it is sh
owed
as in
t
h
e Figu
re 9.
ANN adaptive
me
c
h
a
n
i
s
m
Referen
c
e
Mod
e
l
+
-
Adaptive
model
C&
V
meas
ure
m
ent
of a
sin
g
le sta
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Co
n
t
ribu
tion
t
o
th
e Artifica
l
Neu
r
a
l
Network
Sp
eed Estimato
r
in a Deg
r
ad
ed Mo
d
e
fo
r
…
(A. Meroufe
l)
73
7
Fi
gu
re
8.
A
N
N
Spee
d
Est
i
m
a
tor
B
l
ock
1
y{
1
}
a{
4
}
a{
3
}
a{
2
}
a{
1
}
ay
Pr
oc
es
s
O
u
t
p
ut
1
xp
Pr
oc
es
s
I
n
p
u
t
1
a{4} a
{
5
}
La
y
e
r
5
a{3} a
{
4
}
La
y
e
r
4
a{2} a
{
3
}
La
y
e
r
3
a{1} a
{
2
}
La
y
e
r
2
p{1}
a
{
1
}
La
y
e
r
1
a{
4
}
a{
3
}
a{
2
}
a{
1
}
1
x{
1
}
Fig
u
re
9
.
Th
e
d
e
tails o
f
th
e ANN Sp
eed Estimato
r
5.
2. A
N
N
T
r
ai
ni
i
n
g
Th
e Fi
g
u
re
10
sh
ows th
e evo
l
u
tio
n of th
e ANN tr
aining
From
the converge
nce
curve we can
de
duc
e
th
at is wou
l
d still b
e
a ch
an
ce to
im
p
r
ove th
e netwo
r
k
p
a
ram
e
ters b
y
in
creasing
t
h
e
n
u
m
b
e
r
o
f
iteratio
n
s
(
e
po
ch
s) to
r
e
ach
eno
ugh
p
e
rf
or
m
a
n
ce
Fi
gu
re
1
0
. T
h
e
Ev
ol
ut
i
o
n
of
t
h
e
AN
N s
p
ee
d
est
i
m
a
t
o
r t
r
ai
ni
ng
0
50
10
0
150
20
0
25
0
300
350
40
0
450
50
0
10
-5
10
0
10
5
500
E
p
o
c
hs
T
r
ai
n
i
ng
-
B
l
ue
G
o
al
-
B
l
a
c
k
P
e
r
f
o
r
m
anc
e i
s
0.
0001
512
51,
G
o
al
i
s
5e-
005
6M
D
ata
acqu
i
s
i
t
i
o
n
ca
r
d&co
n
t
r
o
l
z
1
x{
1
}
y{
1
}
NN
T
_
S
d
.
E
s
t
I
s
a
l
f
a11
I
s
be
t
a11
vs
a
l
f
a
v
s
bet
a
E
_
V
i
t
e
s
s
e
(z
-1
)
Cp
l
(
z
-
1
)
1
Out
1
Da
t
a
s
b
l
o
c
k
PI
Wref
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 5
,
N
o
. 4
,
Au
gu
st 2
015
:
72
9
–
74
1
73
8
6.
FUZ
Z
Y
DIRECT
CO
N
T
ROL
OF
TOR
Q
UE
WITH
N
E
UR
AL
NE
TWOR
K S
P
EED
ESTIMAT
O
R
The m
odel
i
n
g
and
si
m
u
l
a
t
i
on of
t
h
e c
o
nt
r
o
l
m
e
t
hod
use
d
t
o
dri
v
e t
h
e
d
o
u
b
l
e st
ars i
n
duct
i
on
m
achi
n
e
i
n
t
h
i
s
pape
r c
ont
ai
n
t
h
e st
at
e-space
f
o
rm
ul
at
i
on i
n
M
A
T
L
AB
/
S
i
m
ul
i
nk ver
s
i
o
n
7.
10
.
The
pr
o
pose
d
m
e
t
h
o
d
has
bee
n
s
u
cce
ssful
l
y
i
m
pl
em
ent
e
d i
n
a
si
m
u
l
a
t
i
o
n
pac
k
a
g
e use
O
D
4
(
r
a
nge
-
kut
t
a
)
as s
o
l
v
e
r
.
A
n
d
NE
WFF
fu
nct
i
o
n t
o
de
vel
o
p t
h
e
A
N
N
s
p
ee
d est
i
m
at
or.
The
Fi
gu
re
11
sh
o
w
s t
h
e Si
m
u
l
i
nk
m
odel
of
o
u
r
cont
ro
l
pr
o
posal
.
Fi
gu
re
1
1
. M
o
del
o
f
t
h
e F
u
zz
y
Di
rect
C
o
nt
r
o
l
o
f
T
o
rq
ue
w
i
t
h
A
N
N
S
p
ee
d Est
i
m
at
or
6.
1. Si
mul
a
ti
o
n
& Resul
t
s A
n
al
ysi
s
Aft
e
r a se
ri
es of t
e
st
s wi
t
h
se
veral
o
r
der c
o
m
b
i
n
at
i
on of l
a
y
e
rs an
d n
ode
s, we achi
e
ve
d
a very
g
o
o
d
resul
t
s
by
usi
n
g t
h
e c
o
nfi
g
u
r
a
t
i
on m
e
nt
i
oned
i
n
1
1
.
The
Fi
g
u
re
1
2
dem
ons
t
r
at
es t
h
e dy
na
m
i
c perf
orm
a
nce of
th
e PI Con
t
ro
ller wh
ile startin
g
and
in
th
e even
t o
f
l
o
ad
di
st
ur
ba
nce. A
n
e
x
cess o
f
0
.
0
6
%
and a re
sp
o
n
s
e
t
i
m
e
of
0.66 sec
o
ndes cha
r
acterize
the starting ti
me. At t = 1.
5s
we a
p
ply 10n.m
as load on t
h
e m
o
tor, t
h
e c
l
assica
l
cont
rol
l
e
r
PI
re
ject
s t
h
e
di
st
ur
bance
wi
t
h
a s
p
eed
d
r
op
o
f
0.
01
5%
an
d a
re
j
ect
i
on t
i
m
e 0.0
02s
.
Th
e Fi
g
u
re
1
3
illu
strates m
o
to
r
b
e
h
a
v
i
or i
n
th
e ev
en
t of lo
ad
d
i
sturb
a
n
ce an
d
t
h
e en
larg
ed
v
i
ew
sho
w
s
t
h
e el
ec
t
r
om
agnet
i
c
t
o
rq
ue
ri
p
p
l
e
s e
n
cou
n
t
e
re
d
w
h
i
l
e
usi
n
g t
h
e
fuz
z
y
di
rect
m
e
t
hod
o
f
t
o
r
que
c
ont
rol
,
th
e tor
q
u
e
r
i
pple is r
e
du
ced
by 5
0
%
c
o
m
p
ared
with the
cla
ssical
m
e
thod
of
di
rect
c
o
nt
r
o
l
o
f
t
o
r
que
.
Fi
gu
re 1
4
sh
o
w
s t
h
e fo
rm
o
f
t
h
e el
ect
rom
a
gnet
i
c
fl
u
x
w
h
en
usi
n
g t
h
e
di
rect
m
e
t
hod of t
o
rq
ue
cont
rol, also the high quality
of the unc
o
upl
i
ng bet
w
een
fl
ux a
nd torque, it
also shown
the flux
reachi
ng the
refe
rence
valu
e with a ri
pple
rate of
0.
4
1
%.
In th
e sam
e
figu
re,
we ca
n s
ee t
h
e ev
ol
ut
i
o
n o
f
t
h
e
fl
u
x
a
nd t
h
e
uni
fo
rm
it
y
between
bot
h fl
ux
com
pone
nt
s,
whi
c
h ap
pr
o
v
e
t
h
at
t
h
e fl
ux
h
a
s a const
a
nt
d
i
st
ri
but
i
o
n i
n
si
de t
h
e
machine wi
nding.
ANN Speed Estimator
X
1
X
2
Xn
-
W
r
ef
C
ONV
02
FIS-Nª
01
D S I M
FIS
-
N
ª
01
ADAP
TATI
ON
Estim
ation
of th
e flux
,
torque
an
d the
position
D
e
te
ction
of
the
tension v
ector
(
Vs.
)
PI
CON
V
01
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