Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
5, N
o
. 4
,
A
p
r
il
201
5, p
p
.
45
3
~
46
3
I
S
SN
: 208
8-8
6
9
4
4
53
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
Three-L
e
vel DT
C B
a
sed on Fuzzy L
ogi
c and Neu
r
al
Network of
Sensorless DSSM Using Ex
tende Kalman Filter
Ela
khda
r
Beny
oussef
*
, Abdelkader Mer
o
ufel
*
, S
a
id B
a
rkat
**
*
Faculty
of
Science and Engineering,
Dep
a
rtm
e
n
t
of El
ectr
i
ca
l En
gineer
ing,
Unive
r
sit
y
of Dj
ila
li
Li
abes, Sid
i
B
e
l A
bbes
22000, BP 89
Algeria, In
telligen
t Control Elec
tro
n
ic Power S
y
stem laborator
y
(I
.C.E.P.S)
**
Faculty
of Technolog
y
,
Dep
a
rtment
of El
ectrical Engineering
,
University
of
M’
sila, Ichb
ilia Street, M’sila 28000
, BP
166 Algeria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 7, 2014
Rev
i
sed
Jan 15, 201
5
Accepte
d
Ja
n 28, 2015
This paper presents a direct torq
ue
control is ap
plied for salient-
pole double
star s
y
n
c
hronou
s machine witho
u
t mechan
ical s
p
eed
and stator
flux link
a
ge
sensors. The
esti
m
a
tion is per
f
or
m
e
d
using the
ex
tended K
a
lm
an f
ilter
known
b
y
it is abi
lit
y to process nois
y
discrete measurements. Two control
approach
es usin
g fuzzy
logic D
T
C,
and neur
al
network DTC ar
e proposed
and compared.
The validity
of
the propos
ed co
ntrols scheme is verified
b
y
simulation tests of a doub
le star s
y
n
c
hronous machine. Th
e
stator flu
x
,
torque,
and speed are determin
ed and
compared in the above
techn
i
ques
.
Sim
u
lation r
e
sults presen
ted
i
n
this
pap
e
r h
i
ghlight the improvements
produced b
y
the proposed con
t
r
o
l method b
a
sed on th
e ex
tend
ed Kalman
filter under
var
i
o
u
s operat
i
on
con
d
itions.
Keyword:
Di
rect
T
o
r
q
ue
C
ont
r
o
l
D
oub
le Star
Ex
tend
ed
Kalman
Filter
Fuzzy L
o
gic Cont
rol
Mu
ltilev
e
l Inverter
Neu
r
al Netw
or
k
Syn
c
hro
nou
s Mach
in
e
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
:
El
akh
d
ar
B
e
ny
ous
sef,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Dj
ilali Liab
es
Un
i
v
ersity,
Si
di
B
e
l
A
b
bes
2
2
0
0
0
, B
P
89
Al
ge
ri
a.
Em
ail: lakhdarbeny
o
ussef@yahoo.c
o
m
1.
INTRODUCTION
A m
u
l
t
i
phase dri
v
e has m
o
re
t
h
an t
h
ree
pha
ses i
n
t
h
e st
at
o
r
an
d t
h
e sam
e
num
ber
of i
n
v
e
rt
er l
e
gs i
s
i
n
t
h
e i
n
vert
er
si
de. T
h
e m
a
i
n
adva
nt
age
s
o
f
m
u
l
t
i
phase
dr
iv
es ov
er
conv
en
tio
n
a
l
thr
e
e-
ph
a
s
e
d
r
iv
es
in
clu
d
e
i
n
creasi
n
g t
h
e
i
nvert
e
r
o
u
t
p
ut
po
we
r, re
d
u
ci
n
g
t
h
e am
pl
i
t
ude of t
o
r
q
u
e
ri
ppl
e a
nd l
o
we
ri
n
g
t
h
e D
C
l
i
n
k
cu
rren
t
h
a
rm
o
n
i
cs.
Furth
e
rmo
r
e, th
e m
u
ltip
h
a
se
d
r
i
v
e syst
e
m
is ab
le to im
p
r
o
v
e
t
h
e
reliab
ility. In
d
e
ed
, t
h
e
m
o
t
o
r can st
art
and ru
n si
nc
e t
h
e l
o
ss of o
n
e or m
a
ny
ph
ases [1]
.
Last
t
w
o deca
des
,
t
h
e m
u
l
t
i
phase dri
v
e
sy
st
em
s have
been
use
d
i
n
m
a
ny
appl
i
cat
i
ons
, s
u
ch a
s
t
r
act
i
on, el
ect
ri
c
/
hy
bri
d
ve
hi
cl
es, an
d s
h
i
p
pr
o
pul
si
on
[2]
.
In
m
u
ltip
h
a
se
mach
in
e driv
e
syste
m
s,
m
o
re th
an
t
h
reep
h
a
se wind
ing
s
are i
m
p
l
e
m
en
ted
in
th
e sam
e
stator
of t
h
e el
ectric m
achine. One c
o
mm
on exam
ple of
such structure is
the doubl
e star
synchronous m
o
tor
(DS
S
M
)
. T
h
i
s
m
o
t
o
r has t
w
o
set
s
of t
h
ree-
p
h
ase wi
ndi
ng
s spat
i
a
l
l
y
phase
shi
f
t
e
d
by
3
0
el
ect
ri
cal
degr
ees an
d
each
set of
thre
e-phase stator windings
is fe
d
by a t
h
ree
-
pha
s
e voltage s
o
urce inve
rter [3].
The fee
d
i
n
g
o
f
t
h
e
DSSM
i
s
gene
ral
l
y
assure
d
by
t
w
o t
w
ol
e
v
el
i
n
v
e
rt
ers.
Ho
we
ver
,
fo
r t
h
e
hi
g
h
p
o
wer; m
u
lti
le
v
e
l inv
e
rters are
o
f
ten requ
ired
.
Sin
c
e
th
e ad
v
a
n
t
ag
es o
f
m
u
l
tilev
e
l
in
v
e
rters
and
m
u
lti
p
h
a
se
machines com
p
lem
e
nt each othe
r, it appe
a
r
s to be logi
ca
l to try to comb
ine them
by realizing a m
u
ltilevel
m
u
l
tip
h
a
se driv
e [4
]. In
t
h
e o
t
h
e
r h
a
n
d
, mu
ltilev
e
l in
v
e
rt
er fed
electric mach
in
e system
s
are co
n
s
i
d
ered
as a
p
r
o
m
isin
g
appro
a
ch
in ach
iev
i
ng
h
i
gh
power/h
igh
v
o
ltage ratin
gs. M
o
reo
v
e
r, m
u
ltile
v
e
l inv
e
rters hav
e
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
45
3
–
46
3
45
4
ad
v
a
n
t
ag
es of
o
v
e
rco
m
in
g
vo
ltag
e
limit ca
p
a
b
ility o
f
semico
n
d
u
c
tor switch
e
s, and
i
m
p
r
o
v
i
ng
2
h
a
rm
o
n
i
c
pr
ofi
l
e
s
of
ou
t
put
wa
ve
fo
rm
s [5]
.
T
h
e
ou
t
put
v
o
l
t
a
ge
wave
f
o
rm
app
r
oac
h
es a si
n
e
wave
, t
h
us h
a
vi
n
g
pract
i
cal
l
y
no
com
m
on-m
ode vol
t
a
ge a
n
d n
o
v
o
l
t
a
ge s
u
r
g
e to
th
e m
o
to
r wind
ing
s
. Furth
e
rm
o
r
e, th
e
red
u
c
ti
on
in
dv
/
dt
ca
n
pr
event
m
o
t
o
r
wi
ndi
ng
s a
n
d
bea
r
i
n
gs
fr
om
fai
l
ure
.
In
t
h
e
o
t
h
e
r han
d
, th
e m
u
ltil
ev
el d
i
rect to
rq
u
e
con
t
ro
l (DTC)
of electrical d
r
i
v
es
h
a
s b
e
co
m
e
an
at
t
r
act
i
ng t
o
pi
c
i
n
re
searc
h
a
n
d aca
dem
i
c com
m
uni
t
y
over
t
h
e pa
st
deca
d
e
. Li
ke
an
eve
r
y
cont
rol
m
e
t
hod
has
som
e
advant
ag
es and di
sa
d
v
a
n
t
a
ges
,
DTC
m
e
t
hod ha
s t
oo. S
o
m
e
of t
h
e adva
nt
ages ar
e prese
n
t
e
d i
n
[6]
.
Th
e
basi
c
di
sad
v
a
n
t
a
ges
of
DTC
schem
e
usi
n
g
hy
st
eresi
s
c
o
nt
rol
l
e
rs
are
t
h
e
va
ri
abl
e
s
w
i
t
c
hi
n
g
fre
q
u
enc
y
, t
h
e
cur
r
ent
an
d t
o
r
que ri
ppl
e
.
In t
h
e aim
t
o
im
pr
ove t
h
e
pe
rformance of the electrical
dri
v
es
based o
n
t
r
a
d
i
t
i
onal
DTC,
fuzzy logic direct torque cont
rol (FL
D
TC) a
n
d arti
ficial neural ne
t
w
o
r
k
di
rect
t
o
r
q
ue co
nt
r
o
l
(DTC
-
ANN) attracts
m
o
re an
d
m
o
re th
e atten
tio
n
o
f
m
a
n
y
scie
n
tists [7
], [8
]. Th
is p
a
p
e
r is
d
e
v
o
t
ed
to
FLDTC and
DTC-ANN of sen
s
o
r
less DSSM
u
s
i
n
g
ex
ten
d
e
d
Kalm
an
f
ilter fed
b
y
two
three-lev
e
l
dio
d
e
clam
p
e
d
i
n
v
e
rter
(DCI
).
In
t
h
is con
t
ex
t
,
sev
e
ral sp
eed
ob
serv
ers
h
a
v
e
b
e
en
sug
g
e
sted
in
literature, su
ch
as slid
ing
m
o
d
e
o
b
s
erv
e
r
[9
], ad
ap
tiv
e
ob
server, m
o
d
e
l referen
ce ad
ap
tiv
e
syste
m
, an
d
Ex
tend
e Kalm
a
n
filter [1
0
]
.
Kal
m
an
filter is a s
t
o
c
hastic state
o
b
s
erv
e
r wh
ere non
lin
ear eq
u
a
tion
s
are lin
earized
in
ev
ery sam
p
l
i
n
g
p
e
ri
od
. It h
a
s
t
h
e ad
vant
a
g
e
of
pr
o
v
i
d
i
n
g
b
o
t
h
fl
u
x
an
d s
p
eed e
s
t
i
m
a
t
e
s, an
d t
h
us av
oi
ds l
i
m
i
t
a
ti
ons
of t
h
e o
p
en l
o
op
p
u
re
in
teg
r
ation
m
e
t
h
od
.
Th
e
p
r
esen
t p
a
p
e
r
st
r
u
ct
u
r
e is as f
o
llow
s
. Firstly, th
e
m
o
d
e
l o
f
t
h
e DSSM
is p
r
esen
ted
i
n
th
e second
sectio
n
.
In
th
e
th
ird
section
,
t
h
e th
ree-lev
e
l in
v
e
rter
m
odel
i
ng i
s
des
c
ri
be
d
.
In t
h
e
fo
urt
h
sect
i
on, t
h
e F
L
DTC
strateg
y
is app
lied
to g
e
t
deco
up
led con
t
ro
l of th
e
st
at
o
r
fl
ux
an
d el
e
c
t
r
om
agnet
i
c
t
o
r
q
ue.
Next
,
a
bri
e
f
in
trodu
ctio
n
on
th
e EKF algo
rith
m
is p
r
esen
ted
in
th
e
fi
fth
sectio
n. The six
t
h
sectio
n in
trod
u
ces th
e DTC-
AN
N a
p
pr
oac
h
.
The
se
vent
h
sect
i
o
n
i
s
dev
o
t
e
d t
o
t
h
e c
o
m
p
arat
i
v
e st
ud
y
bet
w
ee
n t
h
re
e-l
e
vel
F
L
DT
C
an
d
th
ree-lev
e
l DTC-ANN
of
se
n
s
orl
e
ss
D
SSM
.
Fi
nal
l
y
, co
ncl
u
si
o
n
s a
r
e
dra
w
n in t
h
e last s
ection.
2.
MODELING OF
THE DOUBLE
ST
AR SYNCHRONOUS
MACHINE
The
st
at
o
r
v
o
l
t
a
ges
e
q
uat
i
ons
are gi
ve
n by
:
1
11
2
22
s
ss
s
s
ss
s
d
vR
i
dt
d
vR
i
dt
(1)
Wi
t
h
12
,
s
s
vv
: Stato
r
vo
ltag
e
s
.
12
,
s
s
ii
: S
t
a
t
o
r
cu
rr
en
ts
.
12
,
s
s
: Stato
r
flux
.
The
rot
o
r
v
o
l
t
a
ge e
quat
i
o
n i
s
gi
ve
n
by
:
f
ff
f
d
vR
i
dt
(2)
Wi
t
h
:
f
: Flux
o
f
ro
tor
ex
citatio
n
.
,
ff
vi
: Vo
ltag
e
and
cu
rren
t
of ro
tor ex
citatio
n.
Th
e tran
sform
a
tio
n
o
f
th
e syst
e
m
six
ph
ases to
th
e system
(,
)
i
s
gi
ve
n
by
:
12
ss
XX
A
X
X
(3)
Whe
r
e:
X
s1
and
X
s2
can re
prese
n
t the
s
t
ator c
u
rrents,
st
ato
r
f
l
ux
,
and
stato
r
vo
ltag
e
s.
Th
e tran
sform
a
tio
n
m
a
trix
A
i
s
gi
ven
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Three
-
Level
DTC Bas
e
d on F
u
zzy
Logic
and Neur
al
Network of
Se
nsorless DSSM
… (Elakhdar
Beny
ous
s
ef)
45
5
11
3
3
10
22
2
2
33
1
1
01
22
2
2
1
11
3
3
10
3
222
2
33
1
1
01
22
2
2
11
1
0
0
0
00
0
1
1
1
A
(4)
To e
x
pres
s t
h
e
st
at
or
eq
uat
i
o
ns i
n
t
h
e
sam
e
refe
re
n
c
e frame, th
e fo
llowing
ro
tation
tran
sform
a
t
i
o
n
i
s
ad
op
ted.
co
s
(
)
s
i
n
(
)
()
sin(
)
c
os(
)
P
(5)
Wi
t
h
:
is th
e ro
t
o
r po
sitio
n.
W
i
t
h
t
h
i
s
t
r
a
n
s
f
o
r
m
a
ti
on, t
h
e
com
pone
nt
s
of
t
h
e
-
plane
can
be e
x
presse
d i
n
the
d
-
q
plane
as:
The electrical
equations
d
ds
d
q
q
qs
q
d
d
vR
i
dt
d
vR
i
dt
(6
)
Whe
r
e:
,
dq
vv
: Stato
r
vo
ltag
e
s
dq
c
o
m
pone
n
t
s.
,
dq
ii
: Stator c
u
r
r
e
n
ts
dq
co
m
p
onen
t
s.
,
dq
: Stator fl
ux
dq
c
o
m
pone
nt
s.
The fl
u
x
e
quat
i
ons
dd
d
f
d
f
qq
q
f
ff
f
d
d
L
iM
i
Li
L
iM
i
(7)
The m
echanica
l
equation
em
L
d
JT
T
f
dt
(8)
Wi
t
h
:
,
em
L
TT
:
El
ect
rom
a
gne
t
i
c
and l
o
a
d
t
o
r
que
.
: R
o
to
r sp
eed.
The electrom
a
gnetic torque
em
d
q
q
d
Tp
i
i
(9)
3.
MODELING
OF THE TH
REE-LEVEL INVE
RTER
Figure
1 s
h
ows the ci
rcuit
of a three-le
vel
diode
clam
ped inve
rter and t
h
e
s
w
itching
s
t
ates of each
leg of t
h
e inve
rter.
Each leg
is com
posed
of two
up
p
e
r an
d lower switch
e
s
with
a
n
t
i
-
paral
l
e
l
di
ode
s
.
T
w
o
series DC-link
cap
acito
rs sp
lit th
e DC-b
us voltag
e
in
h
a
lf, an
d
si
x
clam
p
i
n
g
d
i
o
d
e
s con
f
i
n
e th
e vo
ltag
e
acro
s
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
45
3
–
46
3
45
6
th
e switch
e
s with
in
th
e vo
ltag
e
of th
e cap
acito
rs, each
leg
of th
e in
v
e
rt
er can
h
a
v
e
three p
o
ssi
b
l
e switch
i
n
g
st
at
es;
2,
1
or
0
[
11]
.
ck
v
c
2
ck
s
1
ck
s
4
ck
s
3
ck
s
b
2
bk
s
1
bk
s
4
bk
s
3
bk
s
a
2
ak
s
1
ak
s
4
ak
s
3
ak
s
2
c
v
1
c
v
dc
v
bk
v
ak
v
n
ok
Fi
gu
re
1.
Sc
he
m
a
t
i
c
di
agram
of
a t
h
ree-l
e
vel
i
nve
rt
er
(
k
=1
f
o
r
fi
rst
i
nve
rt
er
an
d
k=2
f
o
r
se
con
d
i
nve
rt
er
)
The re
pr
esent
a
t
i
on o
f
t
h
e s
p
a
ce vol
t
a
ge
vec
t
ors
of
a three-lev
e
l inv
e
rter
for all switch
i
n
g
states is
gi
ve
n
by
Fi
g
u
r
e 2.
Acc
o
rdi
n
g
t
o
t
h
e
m
a
gni
t
ude
o
f
t
h
e
vol
t
a
ge
vect
o
r
s,
t
h
e v
o
l
t
a
ge
vect
ors
can
be
p
a
rt
i
t
i
oned
in
to
fo
ur gro
u
p
s
: th
e zero
voltag
e
v
ectors
v
0
, the large
vol
tage vectors (
v
1L
,
v
3L
,
v
5L
,
v
7L
,
v
9L
,
v
11L
), t
h
e m
i
ddl
e
vol
t
a
ge
ve
ct
or
s
(
v
2L
,
v
4L
,
v
6L
,
v
8L
,
v
10L
,
v
12L
), an
d th
e
sm
al
l v
o
ltag
e
v
ect
o
r
s (
v
1S
,
v
2S
,
v
3S
,
v
4S
,
v
5S
,
v
6S
).
1
(
200)
L
v
0
v
3
(
220)
L
v
2
(2
1
0
)
L
v
5
(0
2
0
)
L
v
4
(
120)
L
v
9
(
002)
L
v
10
(
102)
L
v
11
(
202
)
L
v
12
(2
0
1
)
L
v
(
211
)
(
100)
(
221
)
(
110)
(
121
)
(010)
(
122)
(011
)
(
112)
(001
)
(
212)
(
101
)
1
S
v
2
S
v
6
S
v
5
S
v
4
S
v
3
S
v
(
2
22)
(1
1
1
)
(0
0
0
)
7
(022)
L
v
6
(0
2
1
)
L
v
8
(
012
)
L
v
1
Z
2
Z
3
Z
4
Z
5
Z
6
Z
7
Z
8
Z
9
Z
10
Z
11
Z
12
Z
Fi
gu
re
2.
S
p
ac
e vect
o
r
di
ag
ra
m
of t
h
ree
-
l
e
ve
l
i
nve
rt
er
4.
DIRE
CT TO
RQ
UE C
O
NT
ROL B
A
SED
ON
FUZ
Z
Y
LOGI
C ST
RA
TEGY
The
pri
n
ci
pl
e
of
fuz
z
y
l
ogi
c
di
rect
t
o
rq
ue
cont
rol
i
s
si
m
i
l
a
r t
o
t
r
adi
t
i
onal
DTC
.
H
o
we
ve
r, t
h
e
hysteresis controllers are repl
aced by fuz
z
y cont
roller an
d
the out
put vect
or of the fuzzy controller is led to a
swi
t
c
hi
n
g
t
a
bl
e
t
o
deci
de w
h
i
c
h vect
o
r
s
h
o
u
l
d
be
ap
pl
i
e
d.
Thi
s
m
e
t
hod b
a
sed on
f
u
zzy
cl
assi
fi
cat
i
on h
a
s
t
h
e
adva
nt
age
o
f
si
m
p
li
ci
t
y
and e
a
sy
im
pl
em
entat
i
on
[8]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Three
-
Level
DTC Bas
e
d on F
u
zzy
Logic
and Neur
al
Network of
Se
nsorless DSSM
… (Elakhdar
Beny
ous
s
ef)
45
7
The c
o
m
pone
n
t
s of
st
at
or
fl
ux
can
be e
s
t
i
m
a
ted
by
:
0
0
ˆˆ
ˆ
0
ˆˆ
ˆ
0
t
s
t
s
tv
R
i
d
tv
R
i
d
(10)
The
st
at
o
r
fl
u
x
am
pl
i
t
ude
i
s
gi
ven
by
:
22
ˆˆ
ˆ
s
(11)
The stator
flux
angle is
calcul
a
ted by:
1
ˆ
ˆ
ta
n
2
ˆ
s
(12)
El
ect
rom
a
gnet
i
c
t
o
r
q
ue e
quat
i
on
i
s
gi
ve
n
by
:
ˆˆ
ˆ
em
Tp
i
i
(1
3)
The fuzzy c
o
ntroller is de
signed t
o
have t
h
ree fu
zzy state varia
b
les and one
control variable for
achi
e
vi
n
g
c
o
ns
t
a
nt
t
o
r
que a
n
d fl
ux c
o
nt
r
o
l
.
The
fi
rst
va
ri
abl
e
*
ˆ
()
s
s
E
is th
e
d
i
fferen
ce
b
e
tween
the
com
m
a
nd st
at
or
fl
u
x
*
s
an
d t
h
e
est
i
m
a
t
e
d st
ator
fl
u
x
m
a
gni
t
ude
ˆ
s
. The s
econd
varia
b
le
*
ˆ
()
Te
m
e
m
ET
T
is
the differe
n
ce
betwee
n the c
o
mmand electric torque
*
em
T
and
estim
a
ted electric torque
ˆ
em
T
. The third
fuzzy
state variable is the stator fl
ux phase
ˆ
()
s
. Fi
g
u
r
e
3 gi
ve
s t
h
e m
e
m
b
ershi
p
f
u
n
c
t
i
ons f
o
r i
n
p
u
t
vari
abl
e
s
,
T
EE
and
ˆ
s
.
Wb
E
P
Z
N
Nm
E
T
P
L
Z
a
P
S
NS
NL
b
ˆ
s
s1
ˆ
s2
ˆ
s1
2
ˆ
s1
1
ˆ
s10
ˆ
s9
ˆ
s8
ˆ
s7
ˆ
s6
ˆ
s5
ˆ
s4
ˆ
s3
ˆ
0
2
c
Fi
gu
re
3.
M
e
m
b
ers
h
i
p
f
u
nct
i
o
ns
of
i
n
put
va
ri
abl
e
s:
a)
St
at
or
fl
u
x
e
r
r
o
r
,
b)
Tor
q
ue e
r
r
o
r
,
c
)
St
at
o
r
fl
u
x
a
n
gl
e
The s
w
i
t
c
hi
n
g
t
a
bl
es of t
h
e p
r
o
p
o
sed t
h
ree
-
l
e
vel
FLD
T
C
are use
d
t
o
sel
e
ct
t
h
e best
o
u
t
put
vol
t
a
g
e
d
e
p
e
nd
ing
on
th
e p
o
s
ition
o
f
th
e
stat
o
r
flux
an
d d
e
sired
actio
n
on
th
e
t
o
rqu
e
an
d
stato
r
flux
.
Th
e op
ti
m
a
l
vol
t
a
ge
vect
o
r
sel
ect
i
on, f
o
r
cont
r
o
l
l
i
ng
b
o
t
h
t
h
e am
pl
i
t
ude a
nd
rot
a
t
i
ng
di
rect
i
o
n o
f
t
h
e st
at
or fl
ux
, i
s
in
d
i
cated
i
n
Tab
l
e 1,
2
.
Th
e lin
gu
istic term
s u
s
ed
fo
r stator flux
error
are N
(ne
g
ative),
Z (zero), and P
(po
s
itiv
e). For th
e to
rq
u
e
error, th
e term
s u
s
ed
are NL
(n
eg
ativ
e larg
e),
NS (n
eg
ati
v
e small), ZE (zero
)
, PS
(po
s
itiv
e sm
all
)
, and
PL (po
s
itiv
e larg
e).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
45
3
–
46
3
45
8
Tabl
e 1.
R
u
l
e
s of
f
u
zzy
co
ntr
o
l fo
r
first star
1
ˆ
s
2
ˆ
s
3
ˆ
s
T
EE
P
Z
N
T
EE
P
Z
N
T
EE
P
Z
N
PL
3
L
v
2
S
v
5
L
v
PL
3
L
v
2
S
v
5
L
v
PL
5
L
v
3
S
v
7
L
v
PS
2
L
v
2
S
v
4
L
v
PS
4
L
v
3
S
v
6
L
v
PS
4
L
v
3
S
v
6
L
v
Z
E
0
0
0
Z
E
0 0 0
Z
E
0
0
0
NS
12
L
v
0
10
L
v
NS
12
L
v
0
10
L
v
NS
2
L
v
0
12
L
v
NL
11
L
v
5
S
v
9
L
v
NL
1
L
v
6
S
v
11
L
v
NL
1
L
v
6
S
v
11
L
v
4
ˆ
s
5
ˆ
s
6
ˆ
s
T
EE
P
Z
N
T
EE
P
Z
N
T
EE
P
Z
N
PL
5
L
v
3
S
v
7
L
v
PL
7
L
v
4
S
v
9
L
v
PL
7
L
v
4
S
v
9
L
v
PS
6
L
v
4
S
v
8
L
v
PS
6
L
v
4
S
v
8
L
v
PS
8
L
v
5
S
v
10
L
v
Z
E
0
0
0
Z
E
0
0
0
Z
E
0
0
0
NS
2
L
v
0
12
L
v
NS
4
L
v
0
2
L
v
NS
4
L
v
0
2
L
v
NL
10
L
v
1
S
v
1
L
v
NL
3
L
v
1
S
v
1
L
v
NL
5
L
v
2
S
v
3
L
v
7
ˆ
s
8
ˆ
s
9
ˆ
s
T
EE
P
Z
N
T
EE
P
Z
N
T
EE
P
Z
N
PL
9
L
v
5
S
v
11
L
v
PL
9
L
v
5
S
v
11
L
v
PL
11
L
v
6
S
v
1
L
v
PS
8
L
v
5
S
v
10
L
v
PS
10
L
v
6
S
v
12
L
v
PS
10
L
v
6
S
v
12
L
v
Z
E
0
0
0
Z
E
0
0
0
Z
E
0
0
0
NS
6
L
v
0
4
L
v
NS
6
L
v
0
4
L
v
NS
8
L
v
0
6
L
v
NL
5
L
v
2
S
v
3
L
v
NL
7
L
v
3
S
v
5
L
v
NL
7
L
v
3
S
v
5
L
v
10
ˆ
s
11
ˆ
s
12
ˆ
s
T
EE
P
Z
N
T
EE
P
Z
N
T
EE
P
Z
N
PL
11
L
v
6
S
v
1
L
v
PL
1
L
v
1
S
v
3
L
v
PL
1
L
v
1
S
v
3
L
v
PS
12
L
v
1
S
v
2
L
v
PS
12
L
v
1
S
v
2
L
v
PS
2
L
v
2
S
v
4
L
v
Z
E
0
0
0
Z
E
0
0
0
Z
E
0
0
0
NS
8
L
v
0
6
L
v
NS
10
L
v
0
8
L
v
NS
10
L
v
0
8
L
v
NL
9
L
v
4
S
v
7
L
v
NL
9
L
v
4
S
v
7
L
v
NL
11
L
v
5
S
v
9
L
v
Tabl
e
2. R
u
l
e
s
of
f
u
zzy
co
nt
r
o
l
fo
r sec
o
nd
st
ar
1
st
a
r
12
ˆ
s
1
ˆ
s
2
ˆ
s
3
ˆ
s
4
ˆ
s
5
ˆ
s
6
ˆ
s
7
ˆ
s
8
ˆ
s
9
ˆ
s
10
ˆ
s
11
ˆ
s
2
st
a
r
1
ˆ
s
2
ˆ
s
3
ˆ
s
4
ˆ
s
5
ˆ
s
6
ˆ
s
7
ˆ
s
8
ˆ
s
9
ˆ
s
10
ˆ
s
11
ˆ
s
12
ˆ
s
5.
SPEED ESTIMATION BASED ON
E
X
T
E
NDE
D KAL
M
AN
FILTER
Kalm
an
filter is a state o
b
s
erv
e
r th
at establish
e
s th
e
b
e
st ap
pro
x
i
m
a
tio
n
b
y
m
i
n
i
m
i
za
tio
n
of the
squ
a
re er
ro
r f
o
r t
h
e st
at
e vari
abl
e
s of a sy
st
em
, sub
j
ect
ed
at
bot
h i
t
s
i
n
p
u
t
and o
u
t
p
ut
t
o
ran
dom
di
st
ur
bance
s
.
If the d
y
n
a
m
i
c
syste
m
o
f
wh
i
c
h
th
e state is
b
e
ing
o
b
s
erv
e
d
is non
lin
ear, th
en
t
h
e Kal
m
an
filter is called
an
ex
tend
ed on
e
(EKF) [10
]
. The d
e
v
e
lop
m
en
t
o
f
t
h
e
Kalm
a
n
filter is closely lin
k
e
d
to the sto
c
h
a
stic syste
m
s.
The linea
r st
oc
hastic system
s
are
descri
bed by:
()
()
()
()
,
(
)
()
()
()
oo
x
tA
x
t
B
u
t
w
t
x
t
x
yt
C
x
t
v
t
(14)
Whe
r
e:
w
an
d
v
are t
h
e syste
m
and m
easurement noise
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Three
-
Level
DTC Bas
e
d on F
u
zzy
Logic
and Neur
al
Network of
Se
nsorless DSSM
… (Elakhdar
Beny
ous
s
ef)
45
9
Esti
m
a
tio
n
o
f
an
erro
r cov
a
rian
ce m
a
trix
:
(1
)
(
)
T
dd
Pk
A
P
k
A
Q
(15)
Co
m
p
u
t
atio
n
s
o
f
a
Kalm
an
filter g
a
i
n
:
1
(1
)
(
1
)
(1
)
TT
K
kP
k
C
C
P
k
C
R
(16)
Upd
a
te
o
f
an erro
r cov
a
rian
ce m
a
trix
:
(1
)
(
1
)
(
1
)
Pk
I
K
k
C
P
k
(17)
State estim
a
tion:
ˆˆ
ˆ
(1
)
(
)
(
1
)
(1
)
.
(1
)
xk
xk
K
k
y
k
C
x
k
(18)
Whe
r
e:
(1
)
Pk
: is a priori erro
r cov
a
rian
ce
matrix
Q
and
R
res
p
ectively.
Th
e ex
tend
ed
Kalm
an
filter im
p
l
e
m
en
tatio
n
fo
r a DSSM
req
u
i
res three
b
a
sic step
s:
a)
C
ont
i
n
u
ous
D
S
SM
m
odel
b)
Discretizatio
n o
f
th
e DSSM m
o
d
e
l
c)
Si
m
u
latio
n
5.
1. Contin
uous
DSS
M
Model
The m
odel
of
DSSM
i
n
t
h
e
-
referen
ce can
be written
in
t
h
e fo
llo
wi
n
g
from:
()
()
()
()
(
)
x
tA
x
t
B
u
t
yt
C
x
t
(19)
Wi
t
h
:
()
xt
i
i
,
yi
i
u
v
v
00
0
1
0
0
00
0
0
1
0
00
0
0
0
1
0
0
,
00
0
0
0
0
1
0
00
0
0
0
00
0
0
0
0
0
0
sq
q
qs
q
s
s
Rp
L
p
L
pL
R
p
L
R
AB
R
p
Jp
J
f
J
f
J
p
Wi
t
h
:
co
s
(
)
si
n
(
)
qf
qf
Li
Li
5.2. Discretiz
ation
of the DSSM Model
The c
o
r
r
es
po
n
d
i
n
g
di
scret
e
t
i
m
e
m
odel
i
s
gi
ven
by
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
45
3
–
46
3
46
0
(1
)
(
)
(
)
(1
)
(
)
kd
k
d
k
kd
k
x
Ax
B
u
yC
x
(20)
The c
o
nve
rsi
o
n i
s
d
one
by
t
h
e f
o
l
l
o
wi
ng
ap
pr
o
x
i
m
at
i
on:
0
At
ds
t
A
ds
d
A
eI
A
T
Be
B
d
B
T
CC
(21)
5.
3. Si
mul
a
ti
o
n
Based
on
th
e
prev
i
o
u
s
elem
en
ts, th
e EKF can
n
o
w b
e
bu
ilt
an
d ap
p
lied to
th
e
DSSM. By d
e
riv
a
tion
o
f
th
e
v
ector
fun
c
tio
n in
relatio
n to
t
h
e state
v
ector, m
a
trix
A
d
,
B
d
an
d C
d
a
r
e gi
ve
n by
:
10
0
0
00
10
0
0
00
00
0
0
0
0
0
1
0000
,
,
01
0
0
0
0
0
0
1
000
01
0
00
00
0
0
1
00
0
ss
q
s
q
s
sq
sq
s
s
q
s
sq
ss
s
d
dd
ss
s
ss
s
s
s
TR
L
T
p
L
T
p
TL
Tp
L
T
R
L
Tp
TL
TR
T
AB
C
TR
T
Tp
J
T
p
J
T
f
J
Tf
J
Tp
The st
ruct
ure
o
f
D
T
C
based
o
n
fuzzy
l
ogi
c c
ont
rol
of
D
S
S
M
i
s
sh
ow
n i
n
Fi
gu
re
4.
ˆ
1
xj
S
2
xj
S
*
*
s
1
s
i
2
s
i
ˆ
s
ˆ
em
T
ˆ
s
ˆ
v
i
1,
2
ab
c
dc
v
T
E
E
1
ˆ
s
v
2
ˆ
s
v
*
em
T
1
22
ˆˆ
ˆ
ˆˆ
()
ˆˆ
ˆ
ta
n
2
(
)
ˆˆ
ˆ
em
s
s
Tp
i
i
ˆ
i
ˆ
S
f
i
*
f
i
f
v
Fi
gu
re
4.
Th
re
e-l
e
vel
FL
DTC
schem
e
fo
r se
nso
r
l
e
ss
DS
S
M
(wi
t
h
j=1
,
2,
3
or
4
)
6.
DIRE
CT TO
RQ
UE C
O
NT
ROL B
A
SED
ON
NEU
R
A
L
NETWO
R
K
STRATEG
Y
Th
e ANN
h
a
s
man
y
m
o
d
e
ls;
b
u
t
th
e usu
a
l
m
o
d
e
l is
th
e
mu
ltilayer feed
fo
rward
n
e
t work
using
th
e
er
ro
r b
a
ck
pr
op
ag
ation algo
r
i
th
m
[
9
]. Su
ch
a n
e
u
r
al
n
e
t
w
or
k con
t
ain
s
three layer
s
: inp
u
t layer
s
,
h
i
dd
en
layer
s
and
o
u
t
p
ut
l
a
y
e
rs
(Fi
g
ure
5).
Each
l
a
y
e
r i
s
com
posed
o
f
s
e
veral
ne
ur
o
n
s
.
T
h
e
num
ber
of
t
h
e
ne
ur
o
n
s
i
n
t
h
e
i
n
p
u
t
an
d
out
p
u
t
l
a
y
e
rs de
pe
nds
o
n
t
h
e
n
u
m
ber of t
h
e
se
l
ect
ed i
n
p
u
t
an
d o
u
t
p
ut
vari
a
b
l
e
s. T
h
e
num
ber
of
hi
d
d
en
l
a
y
e
rs a
n
d
t
h
e
n
u
m
b
er
of
ne
ur
o
n
s i
n
e
ach
depe
n
d
on
t
h
e de
si
red
de
g
r
ee
of acc
u
r
acy
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Three
-
Level
DTC Bas
e
d on F
u
zzy
Logic
and Neur
al
Network of
Se
nsorless DSSM
… (Elakhdar
Beny
ous
s
ef)
46
1
N
I
1
I
2
I
K
Y
Fig
u
re
5
.
Arch
i
t
ectu
r
e
o
f
M
u
ltilayer Neural
Netwo
r
k
The structure of the
neural net
w
or
k
t
o
p
e
rform th
e DTC app
lied
to
DSSM
satisfacto
r
ily was a neural
net
w
or
k
wi
t
h
3 l
i
n
ea
r i
n
p
u
t
no
des
,
12
ne
u
r
o
n
s i
n
t
h
e
hi
dde
n l
a
y
e
r
,
a
n
d
6
ne
ur
on
s i
n
t
h
e
out
put
l
a
y
e
r, a
s
sho
w
n i
n
Fi
gu
r
e
6.
1
ak
S
2
ak
S
1
bk
S
2
bk
S
1
ck
S
2
ck
S
Te
m
i
Z
Fi
gu
re
6.
Ne
ur
al
net
w
or
k st
ru
ct
ure
fo
r t
h
ree
-
l
e
vel
DTC
The gene
ral
struct
ure of
t
h
e
DSSM with DTC-ANN
usi
ng a t
h
ree
-
level inverter i
n
each star is
rep
r
ese
n
t
e
d by
Fi
gu
re 7.
ˆ
1
xj
S
2
xj
S
*
*
s
1
s
i
2
s
i
i
Z
ˆ
em
T
ˆ
s
ˆ
v
i
1,
2
ab
c
dc
v
T
1
ˆ
s
v
2
ˆ
s
v
*
em
T
1
22
ˆˆ
ˆ
ˆˆ
()
ˆˆ
ˆ
ta
n
2
(
)
ˆˆ
ˆ
em
s
s
Tp
i
i
ˆ
i
ˆ
S
f
i
*
f
i
f
v
Fi
gu
re
7.
Th
re
e-l
e
vel
DTC
-
A
N
N
schem
e
fo
r
sens
orl
e
ss
D
S
SM
(
w
i
t
h
j
=
1,
2, 3
or
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 4
,
Ap
r
il 2
015
:
45
3
–
46
3
46
2
7.
SIMULATION RESULTS
The p
r
o
p
o
se
d cont
rol
s
ba
sed
on E
K
F o
b
se
rv
er are t
e
st
ed by
som
e
num
eri
c
al
sim
u
l
a
ti
ons t
o
veri
fy
i
t
s
effectiv
en
ess in
t
h
e stead
y
-st
a
te and
d
y
n
a
mic. Param
e
ters
o
f
EKF are cho
s
en
as fo
llo
wi
n
g
to en
sure
filter no
t
di
ve
rge
n
t
.
5
5
5
100
0
0
0
0
0
0
.1
0
0
0
0
0
0
1
0
0
00
00
0
0
.
1
0
0
0
0
0
0
0
.
1
0
00
00
1
0
0
0
0
0
.
1
2
0
, ,
0
0
0
0
.
1
00
00
0
1
0
0
0
0
0
.
1
2
0
0
00
0
.
1
0
00
0
0
1
0
0
0
0
00
0
0
.
1
00
0
0
0
0
.
1
s
QP
R
Th
e sim
u
latio
n
resu
lts
o
f
t
h
ree-lev
e
l DTC-ANN
of
se
nsorle
ss DSSM are c
o
m
p
ared
with t
h
ree
-
level
FLDTC
.
For th
is en
d, th
e co
n
t
ro
ls system was tested
un
der de
fere
nt
o
p
erat
i
n
g co
n
d
i
t
i
ons suc
h
as sud
d
e
n
chan
ge
o
f
l
o
a
d
t
o
r
que
an
d st
e
p
cha
nge
i
n
ref
e
rence
spee
d.
Fi
gu
re
8.
Dy
na
m
i
c respo
n
ses
of
t
h
ree
-
l
e
vel
FLDTC
fo
r se
ns
orless
DSSM
Fi
gu
re
9.
Dy
na
m
i
c respo
n
ses
of
t
h
ree
-
l
e
vel
DTC
-
ANN
for se
ns
orless DSSM
0
0.
5
1
1.
5
2
2.
5
3
0
1
2,
15
3
Ti
me
(
s
)
St
at
o
r
f
l
u
x
(
W
b
)
0
0.
5
1
1.
5
2
2.
5
3
0
1
2,
15
3
Sta
t
o
r
f
l
u
x
(
W
b
)
Tim
e
(
s)
Evaluation Warning : The document was created with Spire.PDF for Python.