In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
11, N
o.
1, Mar
ch 20
20,
p
p.
496~
5
0
4
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
4
96-
50
4
496
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Improvemen
t of adapti
v
e fuzzy c
ontrol to adju
st speed
fo
r
a
doubly fed induction motor drive (D
FIM)
Da
hh
o
u
Bra
h
i
m
1
,
Bend
j
e
bb
ar
M
o
k
h
t
ar
2
,
L
a
ch
tar
Salah
3
1,
2
D
epart
e
m
e
nt of
Elect
ri
cal E
ngin
eering
,
O
r
an U
nive
rsity
o
f S
c
ienc
e a
nd Tec
h
n
o
l
o
g
y
-M
oha
m
e
d
Boud
iaf
,
Alg
e
r
i
a
3
Cent
re de D
é
ve
l
opp
em
ent des
En
ergi
es Reno
u
v
e
lab
l
es, A
l
g
eria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
Ju
n
3
,
2019
Re
vise
d Ju
l 2
6
,
201
9
A
c
c
e
pte
d
A
ug 9,
201
9
Th
is
p
aper
p
rese
n
t
s
t
h
e
do
ub
ly
f
ed
i
ndu
cti
o
n
m
o
tor
(DF
I
M
)
s
p
eed
c
on
trol
us
in
g
ad
aptiv
e
f
u
zzy
l
o
g
i
c
P
I
(A
FLP
I)
con
t
roll
er
t
o
give
b
et
ter
d
y
n
a
m
i
c
perf
o
r
man
ces.
Bef
o
re
t
he
a
dv
e
n
t
of
m
odern
t
echno
lo
gy
,
i
n
t
e
gral
p
r
op
ortion
a
l
bas
e
d
cu
rr
ent
c
o
nt
roller
i
s
u
sua
lly
u
sed
due
to
i
t
s
s
i
m
p
lici
t
y
.
B
u
t
,
t
h
e
ef
f
ecti
v
enes
s
o
f
c
l
o
s
e
d-lo
op
c
o
n
tro
l
i
s
w
i
del
y
a
ffec
t
ed
b
y
app
l
ie
d
th
is
t
yp
e
of
con
t
ro
ls,
t
a
kin
g
i
n
t
o
accou
n
t
t
h
at
t
h
e
P
I
co
nt
rollers
h
av
e
t
u
n
i
n
g
p
r
o
b
l
e
m
s
.
T
o
ov
ercom
e
t
he
p
ro
blem
,
a
n
e
w
tech
niq
u
e
AFL
P
I
bas
e
d
sp
ee
d
co
n
t
rol
le
r
fo
r
di
rect
f
i
e
ld
o
ri
e
n
ted
con
t
ro
l
f
e
d
DF
IM
t
o
g
e
t
fas
t
s
peed
r
esp
o
n
s
e
a
n
d
t
o
m
i
nim
i
ze
th
e
t
o
rq
ue
r
ip
ple.
T
he
a
ppl
icat
io
n
o
f
t
hi
s
ty
pe
o
f
con
t
r
ol
i
s
very
sat
i
sf
actory
to
r
epl
ace
th
e
conv
ent
i
o
n
al
P
I
co
n
t
rol
l
er
a
n
d
,
ev
e
n
t
h
e
f
u
zzy
lo
gi
c
P
I
(
FLP
I
)
con
t
ro
ll
er.
Th
e
perf
orm
a
n
ces
o
f
DF
IM
d
ri
v
i
n
g
u
n
de
r
the
fiel
d-o
r
i
e
n
t
ed
a
p
p
l
i
cati
o
n
are
sim
u
la
t
e
d
u
n
d
e
r
diff
eren
t
o
p
erat
in
g
c
o
nd
it
ion
s
us
in
g
th
e
AFLP
I
con
t
ro
ll
er.
The
s
i
m
u
l
a
ti
on
r
es
u
l
ts
obt
ain
e
d
wit
h
A
F
LP
I
are
com
p
are
d
w
i
t
h
th
ose
o
b
t
a
in
ed
i
n
th
e
case
o
f
t
he
F
L
P
I
cont
ro
ller
a
n
d
t
h
e
conventional
PI
c
ontroller.
A
ccord
ingl
y
,
a
n
improvement
i
n
d
yna
mi
c
and
rob
u
s
t
nes
s
i
s
clearl
y
a
pp
ears
in
A
FLP
I
c
o
n
tro
l
l
e
r
sim
u
lati
on
r
e
su
lt
s
com
p
are
d
t
o
t
h
e
ot
hers
a
f
o
rem
e
n
t
i
oned
c
o
nt
ro
l
l
ers
.
S
im
u
l
atio
n
R
esults
a
re
pres
ent
e
d
f
o
r
th
e
th
ree
tech
ni
qu
es
u
si
ng
M
a
tl
ab/Sim
ulink
t
o
p
ro
ve
t
he
dy
nam
i
c
perf
orm
a
n
ces
a
n
d
r
o
bus
tn
ess.
K
eyw
ord
s
:
A
F
LP
I
contr
o
l
l
e
r
DF
I
M
FLPI
c
o
n
t
roll
e
r
P
I
contro
l
l
er
Sp
ee
d
t
r
ac
ki
ng
Torque
t
racking
T
h
i
s
is an
op
en
a
ccess
ar
ticl
e under
th
e
CC
BY-
SA
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
D
a
hh
ou
Bra
h
im
,
D
e
pa
rtem
ent o
f
E
lectr
i
c
a
l E
n
gi
nee
r
in
g,
O
r
a
n
U
niversi
t
y
of
S
c
i
e
nce
an
d
Tech
no
l
o
g
y
-
M
oh
am
ed Bo
u
d
i
a
f
,
El M
nao
u
ar
,
BP
1505,
B
ir
E
l D
jir 31
0
00,
O
ra
n,
A
l
g
e
r
ia.
Em
ail:
alida
h
h
o
u
@
gma
i
l.
co
m
1.
I
N
TR
OD
U
C
TI
O
N
D
o
u
b
l
y
f
e
d
i
n
duc
t
i
o
n
m
o
t
or
(
DF
IM)
has
a
key
r
o
l
e
i
n
the
in
dustr
ial
fie
l
d
be
ca
use
o
f
i
t
s
l
ow
c
o
s
t,
ri
gi
d
i
t
y
,
re
as
on
abl
e
d
i
m
en
s
i
o
n
,
l
o
w
m
ai
n
t
en
an
c
e
a
nd
i
t'
s
on
e
of
t
he
m
ost
large
l
y
e
l
ectr
i
c
mo
tors
u
se
d
to
con
v
er
t
e
l
ec
t
r
ic
al
e
nergy
t
o
m
ec
han
i
cal
e
ner
gy.
I
n
ad
d
iti
on,
T
h
e
D
F
IMs
ha
ve
b
e
e
n
s
how
n
pr
o
m
ising
pros
pec
t
s
as
a
m
ac
hine
i
n
the
va
riab
le
s
pe
e
d
a
p
p
l
i
c
a
t
ions
[
1
–
3
]
.
The
con
t
ro
l
t
e
c
h
n
i
que
s
a
pplie
d
to
e
le
ctric
motors
b
ec
om
e
effec
tiv
e
tha
n
ks t
o adva
nces
i
n sem
i
c
o
n
d
u
ct
or c
om
p
o
n
e
nt
s a
n
d
d
i
gi
t
a
l
t
e
ch
nol
ogi
e
s
[4
, 5].
Th
e
DF
IM
c
o
n
t
r
ol
f
l
e
xi
bil
i
t
y
is
v
e
r
y
h
i
gh
er
d
u
e
t
o
i
n
d
e
p
e
nde
n
t
o
f
f
lu
x,
t
or
que,
s
l
ip
a
nd
p
ow
er
f
a
c
t
or
[6].
T
he
D
F
I
M
struc
t
u
r
e
m
a
ke
s
it
poss
i
ble
t
o
m
easur
e
t
h
e
qua
n
t
i
ti
e
s
o
f
ro
t
o
r
c
u
rr
e
n
ts
,
w
h
i
c
h
m
a
k
e
s
the
ac
quis
i
tio
n
of
t
he
f
l
ux
ve
c
t
or
n
ec
essar
y
f
or
v
e
c
t
or
c
on
tro
l
p
ur
p
o
ses
d
e
pen
d
onl
y
on
t
h
e
k
no
wl
edg
e
o
f
the
motor
re
actanc
e
.
The
D
F
IM
s
truct
u
re
m
a
k
es
i
t
pos
si
ble
to
a
dj
us
t
the
i
n
p
u
t
and
o
u
t
p
ut
r
oto
r
w
i
ndin
g
s
f
l
u
x
in
o
rd
e
r
t
o
ob
ta
in
b
o
t
h
a
va
ria
b
le
s
pee
d
i
n
su
per
-
sy
nc
hro
n
o
u
s
or
s
u
b
-sy
n
chr
on
o
u
s
mode
s
c
h
a
r
ac
terize
d.
H
ow
eve
r
,
the
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Im
prove
m
en
t
o
f
ad
a
p
t
i
ve f
u
zz
y
cont
ro
l
t
o
ad
j
u
s
t
speed for a do
u
b
ly
fe
d i
n
d
u
c
t
i
on … (D
ahho
u
Bra
h
i
m
)
49
7
ma
jor
o
b
s
t
ac
le
t
ha
t
m
a
kes
t
h
e
D
F
IM
c
on
trol
c
om
plica
t
e
d
,
is
t
he
d
i
ffic
u
l
t
y
t
o
obta
i
n
t
h
e
dec
o
u
p
l
in
g
of
t
he
tor
que
a
nd
the
flu
x
.
To
o
ver
c
om
e
t
h
is
o
b
s
ta
c
l
e,
a
n
al
gor
it
h
m
w
i
th
h
i
gh
pe
rform
a
nc
es
w
as
d
eve
l
ope
d
to
a
l
l
ow
ea
si
ly t
o t
h
e
D
F
IM contro
l [7
,
8].
C
o
n
v
e
n
t
i
ona
l
P
I
c
ontr
o
l
l
ers
c
a
n
o
n
l
y
b
e
tu
ne
d
a
t
a
s
peci
fic
o
p
e
ra
tin
g
p
o
i
n
t,
a
nd
t
h
e
c
h
an
ge
o
f
t
h
is
opera
tin
g
p
o
i
nt
m
aks
the
s
e
t
y
pe
s
of
c
ontro
l
l
ers
ac
t
i
n
a
n
u
n
sa
t
isfac
t
ory
m
a
nner
.
To
s
olv
e
t
hi
s
p
r
ob
l
e
m,
f
u
z
z
y
lo
gic
c
o
n
t
ro
lle
rs
c
a
n
b
e
re
p
l
a
c
e
d
t
he
c
on
ve
n
t
i
o
nal
P
I
c
on
tr
ol
l
e
rs.
H
o
w
e
ve
r,
t
his ty
pe of
c
o
n
t
r
o
ller
ha
s
a
m
a
jor
draw
back,
w
h
e
n
s
pec
i
a
lize
d
k
no
w
l
e
d
ge
i
s
r
e
qu
ired
t
o
de
term
ine
t
h
e
m
e
m
b
e
rshi
p
fun
c
tion
s
a
n
d
t
h
e
ru
l
e
s.
T
o
elimi
n
a
t
e
the a
f
or
em
ent
i
on
e
d
dra
wback,
i
t
m
us
t
be
u
sin
g
th
e
com
bi
na
ti
on
of
bot
h co
n
t
ro
lle
rs na
m
e
l
y ad
apt
i
v
e
f
u
zzy logic cont
r
oller
[9].
The
per
f
orm
a
n
c
e
sa
tisfa
ct
ion
for
a
n
e
le
ctro
m
e
c
h
ani
cal
c
l
o
se
d-l
o
op
c
on
t
r
o
l
a
ppl
i
c
a
t
i
o
n
i
s
g
e
n
e
r
a
l
l
y
requ
ire
d
c
o
n
t
rol
l
i
n
g
t
he
s
pee
d
b
y
a
P
I
c
ontr
o
ller
to
e
l
i
mi
nate
t
h
e
sta
t
ic
e
rror
and
re
du
ce
t
h
e
s
p
ee
d
resp
ons
e
ti
m
e
.
M
a
ny
tec
h
n
i
que
s
ha
ve
b
e
e
n
ap
p
lie
d
t
o
a
dj
ust
the
P
I
c
on
tro
l
l
er
i
n
ord
e
r
t
o
e
lim
ina
t
e
the
spee
d
ove
r
s
hoo
t
w
h
en
s
t
a
rt
ing
the
m
o
tor w
h
ic
h
is
r
e
l
a
t
e
d
t
o t
h
e
con
t
ro
l
l
er
a
nd
t
h
e
ma
chi
n
e
para
me
t
e
rs [10, 11]
.
Th
e
c
o
mbi
n
atio
n
of
P
I
c
ont
rol
l
ers
and
AF
L
tec
h
nol
ogy
i
s
ex
p
r
e
s
s
e
d
a
m
o
ng
re
cen
t
rese
arc
h
t
op
ics
i
n
the
c
o
n
t
ro
l
of
e
lectr
i
ca
l
ma
chi
n
es
[
1
2
–
1
4
].
R
e
c
e
n
tl
y,
t
he
c
om
b
i
ne
d
AFLP
I
con
t
rol
l
er
h
as
l
ar
ge
ly
u
sed
in
in
dus
trial
a
p
plica
t
ion
s
t
o
impr
o
v
e
t
h
e
r
e
sults
o
f
no
nl
i
n
ear
a
nd
c
omplex
p
r
o
cesses.
A
m
o
ng
the
AFL
P
I
con
t
ro
l
l
er
p
erf
o
rm
ance
s
is
r
o
b
us
t
n
ess,
d
o
not
n
eed
a
p
re
cise
m
a
t
h
e
m
a
t
i
c
al
e
l
e
c
t
ric
m
achi
n
e
m
o
d
e
l
a
nd
the
in
se
ns
iti
v
ity
t
o
p
a
ram
e
t
e
r
v
a
ria
tio
ns.
In
r
e
c
e
n
t
de
c
a
de
s,
m
ode
r
n
tec
h
no
l
o
g
y
a
l
l
ow
e
d
t
he
f
as
t
inc
r
ea
si
n
g
deve
l
opm
en
t
o
f
a
p
p
rox
i
ma
ti
o
n
t
heor
y,
a
s
an
a
dap
t
i
v
e
c
o
n
t
rol
m
e
t
ho
d
w
a
s
in
tro
duce
d
t
o
deal
w
i
t
h
n
o
n
l
i
n
ea
r
para
me
tric
u
nc
er
t
a
int
y
s
yste
ms
b
ase
d
o
n
a
fu
zz
y
lo
g
i
c
syst
e
m
[
1
5,
16].
Th
e
m
a
in
t
w
o
d
r
a
w
b
ac
ks
o
f
t
h
e
F
L
P
I
con
t
ro
l
l
er
d
es
i
gn
ar
e
r
e
spec
t
i
vel
y
,
ge
t
t
i
ng
a
n
a
deq
u
a
t
e
ru
l
e
f
o
r
t
h
e
a
p
p
l
i
c
a
tio
n
a
n
d
se
le
cti
ng
sca
lin
g
fact
ors
pri
o
r
to
f
u
z
z
i
fi
ca
t
i
o
n
a
n
d
d
e
f
uz
zi
fica
ti
on,
a
s
e
x
pe
dit
i
n
g
t
he
d
e
s
ig
n
de
t
e
rmina
t
i
o
n
p
a
ram
e
te
rs
a
nd
red
u
c
e
the
com
p
u
t
a
t
i
o
n
ti
m
e
a
re
the
a
pp
ropria
te
so
l
ut
io
n to o
ve
rcom
e
t
h
e
s
e
dr
a
wbacks.
S
e
ve
ral
ada
p
ti
ve
t
e
c
h
niq
u
e
s
h
ave
be
e
n
p
ro
pos
ed
a
s
s
o
lu
ti
ons
t
o
o
v
e
r
c
o
m
e
t
h
e
s
e
p
r
o
b
l
e
m
s
.
I
n
[
1
7
]
,
the
au
t
h
ors
pr
esen
t
a
n
o
n
l
i
n
e
m
e
t
h
o
d
f
or
a
dap
t
i
n
g
t
h
e
s
cali
n
g
f
a
c
t
o
r
s
o
f
t
h
e
F
L
c
o
n
t
r
o
l
l
e
r
,
t
h
i
s
m
e
t
h
o
d
i
s
c
o
nsid
e
r
ed
a
s
a
so
lu
ti
on
t
o
d
e
si
g
n
an
a
d
a
pt
iv
e
f
u
zzy
c
ont
rol
l
er
.
The
aim
of the pro
p
o
sed
te
chn
i
que
i
s to
a
da
p
t
on
line
sc
al
i
n
g
fact
ors
a
ccor
d
i
ng
t
o
a
p
er
for
m
ance
m
e
a
sure
,
and
the
p
u
rp
ose
of
t
h
a
t
is
t
o
r
e
fine
t
h
e
co
ntr
o
l
l
er
and
i
m
pr
ove
t
h
e
dr
i
ve
sys
tem
per
f
orm
a
nce
.
In
t
hi
s
pa
per,
A
F
L
P
I
c
ont
r
o
ller
perf
orm
a
nce
s
i
nve
st
i
g
at
i
o
n
t
o
i
m
p
rov
e
D
FIM
FLP
I
s
p
e
ed
c
ontro
ller
gai
n
s.
T
h
e
p
ap
e
r
i
s
orga
n
i
ze
d
a
s
f
o
l
l
o
w
s
.
I
n
s
ecti
o
n
2,
t
he
D
F
I
M
m
odel,
f
ie
ld-
o
rien
te
d
con
t
ro
l
an
d
in
ve
rter
are
de
ve
l
ope
d.
T
he
m
eth
o
d
o
l
og
y
a
p
proa
c
h
e
s
o
f
the
A
F
LP
I
con
t
ro
ll
e
r
a
n
d
F
L
P
I
c
o
n
t
r
o
l
l
e
r
a
re
p
rese
nted,
in
sect
io
n
3.
T
he
s
im
ula
t
i
o
n
res
u
l
t
s
an
d
the
i
r
di
scuss
i
o
n
a
r
e
p
r
e
s
en
ted
in
s
ec
t
i
o
n
4
.
F
i
na
l
l
y,
t
he
c
onc
l
u
sio
n
i
s
prese
n
t
e
d i
n
t
h
e
l
a
s
t
sec
t
i
on.
2.
DESCRIPTIO
N
O
F
TH
E
S
Y
S
TEM
The
cl
ose
d
-
l
oo
p
sys
t
em
i
s
i
l
l
u
s
t
ra
t
e
d
in
F
ig
ur
e
1
bel
o
w
,
t
w
o
c
o
n
v
er
t
e
rs
(
rec
t
ifie
r
a
n
d
i
nver
t
er)
ar
e
prese
n
t
e
d re
sp
ecti
v
e
l
y,
t
he
fir
st
i
s
co
nnec
t
e
d
to t
h
e
st
a
t
or
an
d
th
e
o
t
her
is con
ne
c
t
ed
t
o
the
rotor
[1
8].
F
i
gure
1.
G
loba
l sche
me
of
th
e
stu
d
i
e
d sys
t
e
m
w
ith ad
j
us
t
m
e
n
t
s
pee
d
c
o
n
tr
ol
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
496
–
50
4
49
8
The
D
F
IM
m
athem
a
tica
l
m
od
e
l
m
ust
be
t
a
k
e
n
i
n
t
o
ac
c
o
u
n
t
s
om
e
s
i
m
pl
i
f
y
hy
p
o
th
e
s
e
s
t
o
ge
t
a
dy
nam
i
c
m
ode
l m
a
ke
it p
o
ss
ible
t
o co
ntr
o
l t
h
e
ele
c
t
rical
s
y
s
tem
.
[19].
3.
MODELING S
YSTE
M
S
i
mplifying
as
sumptions
a
re
n
ece
ssary
t
o
av
oi
d
th
e
D
F
IM
s
t
r
u
c
tu
re
c
om
pl
e
x
i
t
y
a
nd
ge
t
t
i
ng
a
dy
nam
i
c
m
o
d
e
l
[20]:
C
ons
ide
r
in
g
t
h
at t
he
r
o
t
or
i
s
s
y
m
m
e
t
rical
w
ith
a
u
n
i
form
a
i
r
-gap,
th
e
m
a
gnet
i
c
circ
ui
t
is
perfec
t
l
y
l
am
i
n
ate
d
a
nd
n
o
t
sa
tura
ted,
w
it
h
sort
o
f
t
h
e
ir
o
n
l
o
sses
an
d
hy
st
e
r
es
i
s
a
re
n
eg
l
i
g
i
bl
e
and
on
ly
t
h
e
w
i
n
d
in
gs
a
re
t
hr
ou
g
h
b
y
cu
r
r
ents;
sta
t
or
a
nd
ro
t
o
r
p
h
a
s
e
s
a
re
c
re
ated
t
he
M
MFs
c
o
n
s
i
d
er
ed
p
er
fec
t
l
y
sinus
o
i
da
l
d
i
s
t
rib
u
t
i
ons
a
lo
n
g
t
he
g
a
p
.
Th
e
r
efore,
t
he
D
F
I
M
m
a
t
hem
a
tica
l
d
y
n
am
ic
m
odel
i
s
d
e
s
c
r
ibe
d
a
s
fo
l
l
ow
:
(
1
)
wher
e,
i
i
i
i
:
is
t
he stat
e
v
e
c
t
or
:
i
s
i
n
put
v
ec
tor
⎣
⎢
⎢
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎥
⎥
⎤
(2)
⎣
⎢
⎢
⎢
⎡
0
0
0
0
0
0
0
0
⎦
⎥
⎥
⎥
⎤
(
3
)
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
(4)
The
overall D
F
IM dy
n
am
ic m
o
d
el
in
t
h
e
d-q
plan
c
an
b
e
repo
rted
as followi
n
g
[21]
:
⎣
⎢
⎢
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎡
0
0
0
0
0
0
0
0
⎦
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎡
⎦
⎥
⎥
⎤
(5)
The
me
chan
ica
l
equa
tio
n is g
i
v
en
a
s
fo
llow
:
J
(6)
The
elec
t
r
oma
g
ne
t
i
c
tor
que
e
xpre
ssi
on is g
i
v
en
a
s fo
llow
:
(7)
Whe
r
e
,
:
S
ta
to
r
a
n
d
r
o
t
o
r el
e
c
t
ri
cal
a
ng
l
e
s
;
Ω
:
R
otor
m
echa
n
i
c
a
l
p
os
it
ion
a
nd sp
ee
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
I
m
prov
em
e
n
t
o
f
ad
a
p
tiv
e
f
u
zz
y cont
rol to ad
jus
t
spe
e
d
f
o
r
a
do
ubly
fe
d in
d
u
ct
i
on … (
D
ahho
u
Bra
h
i
m
)
49
9
,
,
:
El
e
c
t
r
i
ca
l
fr
e
que
nc
ie
s
of
s
ta
tor
,
r
ot
or
a
nd
s
h
af
t
,
:
Loa
d
a
nd
ele
c
t
r
o
m
a
g
n
et
ic
t
or
qu
e
1
:
L
eaka
g
e c
o
effic
i
e
n
t
,
,
,
:
S
t
ator
a
n
d
r
otor
d
-
q
a
xes
vol
tage
s
,
,
,
:
S
t
ator
a
n
d
r
otor
d
-
q
a
xes
cur
r
e
nts
,
:
S
tator
an
d r
o
tor
re
sistanc
e
:
Fri
c
t
i
o
n
co
ef
fi
ci
ent
The p
u
r
p
o
s
e of
v
e
c
t
or
c
o
n
tr
ol
i
s
t
o
e
nsur
e de
c
o
u
p
le
d
c
o
n
t
r
o
l of
f
l
o
w
a
n
d
t
o
r
q
u
e
[
2
2]
.
I
n
t
he
F
i
gur
e
2
cl
ea
rly
sho
w
s
t
h
e
v
ect
o
r
r
ep
rese
nt
a
tio
n
of
v
ec
t
o
r
con
t
ro
l
in
t
h
e
s
ync
hr
o
n
o
u
s
fr
am
e
of
r
e
f
er
e
n
ce
w
hose
a
x
is
d
is
a
lig
ne
d
w
ith
t
he
r
o
t
or
f
l
u
x
v
e
ctor
∗
an
d
0
.
F
i
gur
e
2.
R
otor
o
r
i
en
tat
i
on
d
i
a
g
r
a
m
I
n
o
r
d
e
r
t
o
ob
ta
i
n
a
goo
d
dec
oup
li
n
g
b
e
t
w
e
en the
a
xes d
a
n
d
q,
t
he
i
nter
me
di
a
t
e
v
olt
a
ge
s
a
r
e
d
e
fi
ned
by
the
f
o
l
l
o
w
i
n
g
e
qua
tio
ns
:
⎩
⎪
⎪
⎨
⎪
⎪
⎧
V
V
.V
V
V
.V
V
V
.V
V
V
.V
(8
)
The
tr
a
n
sf
er
f
u
n
ct
i
o
n
s
c
on
ne
c
tin
g
t
h
e
s
t
at
or
a
nd
r
o
t
o
r
com
p
one
n
ts of
ea
ch
a
xis
are
:
.
.
(
9
)
4.
ADAPTIVE FU
ZZY CONT
R
O
L
DES
I
G
N
FO
R DFIM
Re
gar
d
in
g
the
a
d
ap
t
i
v
e
fuzz
y
co
n
t
ro
ller
w
h
ic
h
is
b
ase
d
on
the
t
he
or
y
of
t
he
y
a
p
un
ov,
w
e
pr
oce
e
d
a
ccor
d
i
n
g
t
o
t
w
o
p
hases,
a
t
t
h
e
be
g
i
nn
ing
w
e
s
t
a
r
t
b
y
de
sign
i
n
g
a
f
uzz
y
P
I
co
ntro
l
l
er,
wher
eas
l
a
t
e
r
a
n
d
se
co
nd
ly,
w
e
d
ecide t
o
the
m
e
th
o
d
o
f deter
m
in
i
ng
t
h
e gai
n
s
of
a
f
uz
zy
r
e
g
ula
t
or
b
ase
d
on
the
a
f
or
em
ent
i
one
d
the
o
r
y
.
T
h
i
s
c
on
t
r
ol
ler
t
h
at
w
e
app
l
ied
to
D
F
I
M
i
s
unde
r
t
h
e
as
s
u
ra
n
c
e
of
a
c
o
n
t
rol
l
er
o
f
t
h
e
FLPI
ty
pe
[
2
3
,
2
4
]
.
I
n
this
w
or
k,
w
e
im
p
l
em
ente
d
a
n
o
t
he
r
str
a
t
e
g
y
,
com
p
l
et
e
l
y
n
e
w
whi
c
h
e
n
su
re
s
ad
apt
i
v
e
fu
zzy
co
nt
r
o
l
b
a
sed
o
n
th
e
t
h
e
o
ry
o
f
t
h
e
y
a
p
unov
t
o
d
e
li
mit
t
h
e
g
a
in
s
a
nd
(
nor
m
a
l
i
z
e
d)
,
bein
g
a
b
l
e
t
o
b
e
im
pl
e
m
e
n
te
d
i
n
a
v
a
s
t
cla
s
s
of
n
on
l
i
n
ear
s
yste
ms
i
t
is
a
r
gue
d
t
h
a
t
t
h
e
a
d
vant
a
g
e
s
o
f
t
w
o
t
ech
niq
u
e
s
a
r
e
a
s
se
mble
d
a
n
d
ar
e
bot
h
k
now
n
to
b
e
ver
y
s
o
lid,
i
n
t
h
i
s
cas
e
,
t
h
e
co
n
t
r
o
l
b
y
f
uzz
y
l
og
ic
a
nd
t
h
e
a
d
a
p
ti
ve
o
ne
[
2
5
]
.
I
t
is
how
e
v
e
r
poss
i
ble t
o
hi
g
hli
g
h
t
w
ha
t
cha
r
ac
ter
i
ze
s
t
h
e
a
p
p
l
i
ca
ti
o
n
o
f
t
h
e
co
n
t
ro
ll
er
on
a
DFIM
s
o
t
h
a
t
it f
o
ll
ows the
re
fere
nce
spee
d.
Stato
r
a
xis
Rot
o
r
axis
d
i
i
i
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
496
–
50
4
50
0
5.
S
T
U
DY
OF THE ADAP
T
A
T
I
ON
M
ECHANIS
M
There
a
r
e ma
ny no
t
i
ons
o
f sta
b
i
l
i
ty
f
o
r
d
y
n
am
i
c
s
y
s
t
e
m
s
.
W
e
w
i
l
l st
ud
y
t
h
e fo
llow
i
n
g
n
ot
i
on:
A
s
ym
pt
otic
s
t
a
bil
i
t
y
:
Lya
p
u
n
ov s
t
ab
i
lit
y
an
d tra
j
e
c
t
or
ies t
e
nd
as
ym
pto
tic
a
l
l
y
t
o
0.
We
con
si
der
a no
n
l
i
n
ea
r sys
t
e
m
w
hose
m
echa
n
i
c
a
l
e
q
u
a
tio
n
of D
F
I
M is
d
e
s
cribe
d
i
n t
h
e f
o
ll
ow
i
ng f
o
rm:
Ω
Ω
(10)
The
prev
io
us
ly
e
quat
i
on c
a
n
refor
mula
te
d
as foll
o
w
:
Ω
Ω
Ω
(11)
By
r
epla
ci
n
g
equa
tio
n (
43) in
e
quat
i
on (4
4),
w
e
obta
i
n t
h
e
fol
l
ow
ing
form
:
Ω
Ω
∗
1
(12)
The
error
e
(t)
an
d
i
t
s
de
r
i
v
a
t
i
v
e
a
r
e
u
sed
to
b
u
i
ld
t
h
e
b
ase
of
t
he
a
dapta
t
ion
m
e
c
h
an
ism
of
t
he
ada
p
t
i
ve
f
uz
zy
l
o
g
i
c
co
ntr
o
ll
e
r
.
Ea
ch
s
ize
o
f
t
he
a
da
p
t
at
i
o
n
m
echa
n
i
s
m
i
s
o
f
the
fo
llow
i
n
g
f
or
m:
T
h
e
s
p
eed
err
o
r noted
e
(
t) is de
fi
ned
by
:
Ω
é
Ω
(
13)
The
deri
va
ti
ve
o
f t
h
e
spee
d
err
o
r note
d
b
y
:
Ω
é
Ω
(14)
S
o
,
w
e
g
e
t
a
s
f
o
l
l
o
w
s
:
Ω
∗
1
(15)
Sin
c
e
Ω
é
0
a
n
al
y
s
i
s
o
f
t
h
e st
ab
ili
t
y
o
f th
e
p
r
op
os
e
d
o
rd
er.
6.
RE
S
U
L
T
S
A
ND DIS
CUSS
I
ON
A
f
ter
t
h
e
c
o
n
t
rib
u
ti
on
a
n
d
i
m
plem
en
tat
i
on
o
f
the
m
ach
i
n
e
mo
de
l
w
i
t
h
d
i
f
f
e
r
e
n
t
t
y
p
e
s
o
f
s
p
e
e
d
-
adj
u
s
t
a
b
le
c
o
n
t
r
o
l
in
t
he
Ma
t
l
a
b/S
i
m
u
l
i
nk
en
vir
onme
n
t, t
he
tor
q
u
e
a
nd
s
p
eed
s
i
m
ul
at
io
n
re
sul
t
i
s
sho
wn i
n
th
e
F
i
gure
3.
The m
a
c
h
i
n
e
ope
ra
t
i
n
g
i
n i
t
s n
o
m
i
na
l
c
o
n
d
iti
on
w
i
t
h
a
refe
renc
e sp
e
e
d 1
5
0
ra
d
/ s,
a torque
l
oa
d
=
10 N
.
m
appl
ie
d a
t
(0.
7 s < t
<
1.7 s).
I
n
t
his
sect
i
o
n
,
t
he
p
er
form
anc
e
s
of
t
he
p
ro
pose
d
c
on
t
r
ol
s
c
h
e
m
e
a
r
e
i
llu
st
ra
t
e
d
by
n
u
m
eri
c
al
si
m
u
lat
i
on.
M
e
a
nw
hile,
the
pr
op
ose
d
c
o
n
t
rol
me
thod
c
o
mp
a
r
ed
w
it
h
F
L
P
I
c
ontro
l
l
er
i
n
term
s
of
r
e
s
ponse
to
spee
d
varia
t
i
o
n
,
s
e
n
si
t
i
v
i
t
y
t
o
exter
n
a
l
l
oa
d d
i
s
t
urba
nc
es a
n
d
rob
u
st
ness a
g
a
i
ns
t pa
ram
e
t
e
r va
riatio
ns.
N
o
te
t
h
a
t
a
ll
t
h
e
des
i
g
n
p
ar
am
eter
s
in
t
h
o
s
e
c
on
tro
l
s
y
s
te
m
s
a
r
e
c
hosen
t
o
ac
hie
v
e
a
sat
i
sfac
tor
y
t
ra
nsien
t
con
t
ro
l pe
rform
anc
e
c
ons
i
d
e
r
in
g the
requ
ir
em
ent
of sta
b
i
l
i
t
y
.
Com
p
ar
ative
p
e
rform
ance
s
o
f
A
FLPI
c
on
t
r
oller
,
F
LPI
c
ontr
o
lle
r
a
n
d
P
I
c
o
n
t
r
o
l
l
e
r
f
o
r
t
e
s
t
s
p
e
r
f
o
r
m
e
d
u
n
d
e
r
the
sa
me
c
o
n
d
iti
o
n
s
a
r
e
stud
ie
d.
T
he
r
esp
onse
of
D
F
I
M
is
o
bse
r
v
ed
und
e
r
d
if
f
e
ren
t
o
p
e
rat
i
ng
c
ond
i
t
i
o
n
s
s
u
c
h
as a
step
chan
g
e
in the
co
n
t
ro
l
spee
d or
a
sud
de
n cha
n
ge in
t
h
e
loa
d.
Res
u
l
t
s
o
f
a
s
e
t
o
f
tes
t
s
o
f
s
te
p
cha
nge
s
in
s
peed
r
efe
r
enc
e
a
r
e
show
n
i
n
F
i
gur
e
3
(
c
),
F
ig
ure
4
(c)
,
F
i
gure
5
(
c
)
a
nd
F
i
g
u
re
6
(
c
)
f
or
t
he
D
F
I
M.
V
aria
t
i
on
i
n
t
he
r
e
f
e
re
n
ce
sp
e
e
d
at
:
0.25
1
,
Ω
1
5
0
/
,
1
2
,
Ω
150
/
a
nd
2
,
Ω
0
/
,
and
a
tor
que
l
oa
d
= 10
N
.
m a
pplie
d
at (
0.7 s
<
t < 1.7
s) .
In
t
h
e
se
t
es
ts
t
he
p
erform
anc
e
of
t
he
t
hre
e
c
on
tro
l
l
e
rs
i
s
e
v
a
l
u
a
t
e
d
i
n
t
e
r
m
s
o
f
s
p
e
e
d
r
e
s
p
o
n
s
e
.
I
t
c
a
n
be
s
e
e
n
t
hat
th
e
am
pl
i
t
u
d
e
of
t
ra
nsie
nt
o
sc
i
llat
i
on
s
of
s
pe
e
d
i
s
low
e
r
w
i
t
h
A
F
L
P
I
c
ontr
o
l
l
e
r
w
hic
h
a
ls
o
has
bet
t
er
r
ejec
t
i
o
n
o
f
per
t
ur
ba
tions.
The
resu
l
t
s
dem
o
n
s
tra
t
e
tha
t
t
he
A
F
L
P
I
c
ontr
o
lle
r
show
s
im
pr
ove
m
e
nt,
albe
i
t
sm
a
ll, in
performa
n
ce
com
p
ar
ed wit
h t
h
e
FLPI c
ontro
ll
e
r
a
n
d con
v
e
n
ti
ona
l P
I
c
ont
rol
l
e
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Im
prove
m
en
t
o
f
ad
a
p
t
i
ve f
u
zz
y
cont
ro
l
t
o
ad
j
u
s
t
speed for a do
u
b
ly
fe
d i
n
d
u
c
t
i
on … (D
ahho
u
Bra
h
i
m
)
50
1
Th
e
e
s
t
i
m
at
e
d
s
p
eed
s
d
e
vi
a
t
e
f
r
o
m
t
h
e
s
p
e
ed
r
e
f
ere
n
ce
s
wh
en
t
h
e
c
ond
it
io
n
s
o
f
th
e
ea
ch
D
FIM
a
r
e
di
ffe
re
nt. S
t
ea
dy-s
t
ate err
o
rs
i
n
s
p
e
e
d a
nd
e
l
e
c
trom
ag
net
i
c to
r
que var
iat
i
o
ns ar
e
i
nt
er
relate
d due to
t
h
e motors
bei
n
g c
onne
c
t
e
d
i
n
para
ll
e
l
a
n
d
t
he
re
b
e
i
n
g
cou
p
l
i
n
g ter
m
s be
tw
ee
n
the d-
q
axe
s
o
f
eac
h
m
o
t
o
r
.
F
i
nal
l
y,
t
he
s
im
ulat
i
on
re
sul
t
s
o
f
t
he
D
F
I
M
us
ing
A
F
LP
I
contr
o
l
l
e
r,
F
L
P
I
controll
er
a
nd
P
I
con
t
ro
l
l
er
w
e
r
e
a
l
so
a
na
l
y
ze
d
r
e
gar
d
ing
l
o
ad
t
orq
u
es
a
nd
s
p
e
e
d
var
i
a
tio
ns.
Th
e
s
e
re
su
lts
c
o
n
fir
m
that
t
he
AFLPI
control
l
er
d
emons
t
rates
a
sl
igh
t
ly
b
et
ter
perfor
m
a
n
ce
u
n
d
er
c
han
g
i
n
g
o
per
a
tin
g
co
nd
it
io
ns
a
n
d
prese
n
t
s
s
a
t
i
s
fa
ctor
y
perfor
ma
nce.
a
b
c
d
F
i
gure
3
.
Ro
tat
i
o
n
spee
d
an
d
e
lec
t
r
o
ma
gne
t
i
c
torq
ue
e
vo
l
u
tio
n
unde
r n
o
m
i
n
al pa
r
am
eter
s
con
d
i
t
i
on
s.
(a)
Rota
ti
on sp
e
e
d for a
stead
y-
sta
t
e
re
fer
e
nce
spee
d c
ond
i
t
i
o
n
s.
(b)
Elec
t
r
o
ma
gne
tic t
or
que
c
or
resp
o
n
d
i
n
g
t
o
the
ro
tor spe
e
d
c
ondi
ti
o
n
s.
(
c)
R
o
t
at
i
on spe
e
d
for
an
a
lter
n
a
t
e
re
fer
e
nce
sp
ee
d con
d
i
t
i
ons.
(d) Elec
t
r
o
ma
gne
t
i
c
tor
que
c
orre
sp
o
n
d
i
n
g
t
o
t
h
e
rot
o
r
sp
e
e
d
co
n
d
i
tio
ns.
T
e
st wi
t
h D
F
I
M
with
p
erturbation
par
amet
ers
Te
s
t
1
:
the
m
o
tor
i
s
o
pera
ti
ng
a
t
t
h
e
sam
e
c
o
n
d
i
tio
ns
a
forem
e
nt
i
o
n
e
d
(n
om
ina
l
c
o
n
d
i
t
io
ns)
.
T
o
s
t
u
d
y
t
h
e
effec
t
o
f p
a
ra
me
t
e
rs va
r
ia
tio
n
on the
perf
orma
nce
o
f
the
d
iff
e
r
en
t
c
ont
rol
l
ers, a
n
i
n
cre
a
se w
i
t
h R
r
=
1.5Rr, the
perform
ance
of
DFI
M
drive
i
s
grea
tl
y
affec
t
e
d
by the
varia
t
i
on
of t
his
para
me
ter
espec
i
a
l
l
y
a
t low
spe
e
d a
t
t
0.7
1
.7
.
But
the
c
o
n
v
e
nt
i
ona
l
P
I
a
nd
F
L
P
I
c
ontr
o
l
l
ers
respo
n
ses
a
r
e
la
rg
er
t
h
a
n
t
h
e
ma
rg
in
val
u
e
of
A
F
L
P
I
c
ont
r
o
l
l
er
a
re
s
how
n
o
n
s
pe
ed
r
esp
onse
i
n
F
igure
4
(
a
)
,
on
t
o
rque
r
e
s
p
ons
e
i
n
F
igur
e
4
(
b
)
,
als
o
o
n
the
spe
e
d
a
n
d
t
orque
r
espo
nses
w
he
n
ap
p
l
y
i
n
g
a
n
alter
n
a
te
s
pee
d
r
efere
n
ce
resp
ec
tive
l
y
i
n
F
i
gur
e
4
(c) a
nd F
i
gure
4
(d).
Te
s
t
2
:
an
i
nc
r
e
a
s
i
n
g
o
f
t
he
s
t
a
tor
re
s
i
s
t
anc
e
Rs
=
1
.5
Rs.
F
r
om
F
igure
5,
w
e
ca
n
s
e
e
th
a
t
a
t
st
a
r
ting
u
p
with
n
o
loa
d
o
r
i
n
c
a
s
e
of
n
om
i
n
al
l
oa
d,
t
he
A
F
L
P
I
c
on
t
r
oller
r
eac
hes
i
ts
s
pe
ed
r
efere
n
ce
ra
pid
l
y
wi
th
a
l
i
t
t
l
e
overs
ho
o
t
c
om
pare
d
t
o
t
he
F
LP
I
or
c
onve
nt
io
na
l
P
I
c
ont
r
o
l
l
e
r
.
A
s
conse
q
ue
nce,
t
he
A
F
L
P
I
c
ontro
ll
e
r
h
as
a
n
e
x
c
e
l
l
en
t
d
y
n
am
i
c
p
e
r
f
o
rm
ance
o
f
s
p
eed
and
torque
c
ont
r
o
l
is
e
v
i
d
en
t
d
e
sp
ite
t
he
s
t
a
to
r
resista
n
ce
v
a
r
iat
i
o
n
,
eve
n
o
n t
h
e
al
t
e
rna
tin
g spe
e
d
te
s
t a
s
show
n i
n
F
igure
5 (c
) and
F
i
g
ur
e 5
(d).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
496
–
50
4
50
2
(a)
(b)
c
d
F
i
gure
4
.
R
o
t
at
io
n spee
d an
d
elec
t
r
o
m
a
g
ne
ti
c
torq
ue
e
vo
l
u
tio
n
in
p
e
r
tu
r
b
ed
c
as
e
d
u
r
in
g
R
r
=
1
.
5
R
r
.
(a)
Rota
ti
on sp
e
e
d for a
stead
y-
sta
t
e
re
fer
e
nce
spee
d c
ond
i
t
i
o
n
s.
(b)
Elec
t
r
o
ma
gne
tic t
or
que
c
or
resp
o
n
d
i
n
g
t
o
the
ro
tor spe
e
d
c
ondi
ti
o
n
s.
(
c)
R
o
t
at
i
on spe
e
d
for
an
a
lter
n
a
t
e
re
fer
e
nce
sp
ee
d con
d
i
t
i
ons.
(d) Elec
t
r
oma
gne
t
i
c
tor
que
c
orre
sp
o
n
d
i
n
g
t
o
t
h
e
rot
o
r
sp
e
e
d
co
n
d
i
tio
ns.
(a)
(b)
(d)
(d)
F
i
gure
5
.
R
o
t
a
tio
n
spe
e
d
a
n
d
e
l
e
ctr
o
m
a
gne
t
i
c
t
o
r
que
e
vol
ut
io
n
i
n
per
tur
b
e
d
c
ase
duri
ng
Rs
=
1
.5
Rs.
a
)
R
o
t
a
t
i
o
n
s
p
e
e
d
f
o
r a st
e
a
dy
-st
a
t
e
re
f
ere
n
ce sp
ee
d
con
d
i
t
i
on
s
.
b)
E
l
e
ctrom
a
g
n
et
ic
t
or
q
u
e c
o
rre
spon
d
i
n
g
t
o the
ro
tor
spe
e
d
c
ond
iti
o
n
s.
c)
Rot
a
t
i
o
n spe
e
d
for a
n
alt
er
n
a
te r
efe
r
enc
e
s
pe
ed
c
o
n
d
it
i
o
n
s
.
d)
E
l
e
ctrom
a
g
n
et
ic
t
or
q
u
e c
o
rre
spon
d
i
n
g
t
o the
ro
tor
spe
e
d
c
ond
iti
o
n
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Im
prove
m
en
t
o
f
ad
a
p
t
i
ve f
u
zz
y
cont
ro
l
t
o
ad
j
u
s
t
speed for a do
u
b
ly
fe
d i
n
d
u
c
t
i
on … (D
ahho
u
Bra
h
i
m
)
50
3
Te
s
t
3
:
an
i
nc
rea
s
i
n
g
o
f
t
he
i
ner
tia
J
=
1
.5J.
T
he
s
peed
a
n
d
e
l
e
c
tr
om
agne
t
i
c
tor
q
ue
t
ra
ck
in
g
ar
e
respec
tive
l
y
show
n
i
n
F
i
g
u
r
e
6
(a
)
and
F
i
gur
e
6
(b).
T
h
e
p
ro
pose
d
A
F
L
P
I
c
ont
ro
l
l
e
r
s
how
s
a
si
g
n
ific
ant
impr
ove
me
nt
i
n
t
h
e
ti
me
i
nt
e
r
v
a
l
c
o
rre
s
pon
din
g
to
t
h
e
p
e
r
i
o
d
of
r
api
d
ly
c
h
a
ngi
n
g
l
oa
d
c
o
n
d
iti
on
s
i
n
t
e
r
m
of
r
espo
ns
e
t
i
m
e
a
n
d
ov
e
r
shoo
t
.
T
h
e
i
n
e
rti
a
v
ari
a
ti
on
h
as
a
l
it
t
l
e
in
fl
u
e
n
c
e
on
t
h
e
A
F
LP
I
c
o
nt
r
o
ller
a
n
d
sh
ow
s
a
n
e
xc
elle
n
t
dy
nam
i
c
perf
or
ma
nce
in
case
of
a
l
t
e
r
na
ti
n
g
s
pe
e
d
(
F
i
gure
6
(
c
)
and
F
i
gur
e
6
(
d
))
com
p
a
r
ed
w
it
h
the
F
L
P
I
o
r
con
v
e
n
t
i
ona
l P
I
c
ont
r
o
l
l
e
r
s.
F
i
gure
6
.
R
o
t
at
io
n spee
d an
d
elec
t
r
oma
gne
t
i
c
torq
ue
e
vo
l
u
tio
n
in
p
ert
u
rbe
d
c
a
s
e
duri
ng
J
=
1.5J.
(a)
Rota
ti
on sp
e
e
d for a
stead
y-
sta
t
e
re
fer
e
nce
spee
d c
ond
i
t
i
o
n
s.
(b)
Elec
t
r
o
ma
gne
tic t
or
que
c
or
resp
o
n
d
i
n
g
t
o
the
ro
tor spe
e
d
c
ondi
ti
o
n
s.
(
c)
R
o
t
at
i
on spe
e
d
for
an
a
lter
n
a
t
e
re
fer
e
nce
sp
ee
d con
d
i
t
i
ons.
(d) Elec
t
r
oma
gne
t
i
c
tor
que
c
orre
sp
o
n
d
i
n
g
t
o
t
h
e
rot
o
r
sp
e
e
d
co
n
d
i
tio
ns.
7.
CO
NC
L
U
S
I
O
N
The
m
a
in
p
urp
o
se
o
f
t
h
i
s
w
or
k
is
t
o
t
a
ke
c
a
r
e
of
t
he
t
or
q
u
e
as
w
e
ll
a
s
t
he
s
pee
d
o
f
a
D
F
IM
u
si
ng
a
n
appr
opr
i
a
t
e
v
e
c
tor
co
ntr
o
l
di
agr
a
m
.
T
he
s
ta
bil
ity
o
f
t
h
e
co
ntr
o
l
s
y
stem
i
s
e
n
sur
e
d
b
y
a
w
a
y
o
f
c
onc
e
i
ving th
is
sam
e
c
on
tro
l
.
T
h
e
de
ve
l
o
ped
m
ode
l
is
p
r
e
sen
t
ed
u
nli
k
e
the
c
o
n
t
r
ol
lers
p
roposed
for
DFI
M
b
ecaus
e
n
ot
requ
irin
g a
ny m
a
them
at
ica
l
m
ode
l o
f
the
D
F
I
M ty
pe fo
llo
w
i
n
g
a s
im
ul
a
t
i
o
n a
nd t
h
e re
ader
of
the
r
e
su
lts the
re
of,
i
t
h
as
b
e
e
n
p
r
o
v
e
d
t
h
a
t
t
h
e
a
dap
t
i
v
e
fuz
z
y
co
ntr
o
l
l
er
i
s
fa
r
m
o
r
e
e
f
f
e
c
t
i
v
e
i
n
t
e
r
m
s
o
f
a
b
i
l
i
t
y
t
o
a
c
h
i
e
v
e
mor
e
f
ocuse
d
t
r
ack
in
g
a
n
d
b
e
tter
m
o
n
itor
i
n
g
o
f
tor
que
a
n
d
s
pe
e
d
a
n
d
a
t
the
sam
e
t
im
e
a
m
o
re
a
pp
r
o
pria
te
leve
l
o
f
f
l
o
w
c
ontr
o
l
i
n
t
h
e
p
rese
nce
o
f
unstr
uc
t
u
r
e
d
mode
l
and
l
oa
d
u
n
c
e
rtai
n
t
i
e
s
no
t
k
n
o
w
n
i
n
a
l
l
ca
se
s,
a
nd
e
s
p
e
c
i
a
l
l
y
t
h
i
s
f
u
zzy
a
d
a
pt
iv
e
co
nt
ro
l
sy
st
em
w
h
i
c
h
w
e
a
r
e
t
a
lk
i
n
g
ab
ou
t
has
prove
n
to
b
e
m
o
re
e
ffic
i
e
n
t
in
ca
rryin
g
o
u
t
t
h
e
fol
l
ow
-up
c
o
m
m
a
nd
tha
n
t
he
l
inea
ri
zat
i
o
n
vec
t
o
r
s
y
s
t
e
m
oper
a
t
i
ng
b
y
fe
ed
bac
k
u
lt
i
m
ate
l
y
and
in pers
p
e
c
t
i
ve
o
f
future res
earch
and
wo
rk wil
l
t
a
rget the
pu
t
t
i
n
g i
n
to p
ra
ctice
(i
n e
x
p
e
rim
e
nta
t
i
o
n) o
f t
h
is
con
t
ro
l
l
er
s
ub
j
e
c
t
of
th
is w
o
r
k.
REFE
RENCES
[1]
D
e
tt
ori
S
,
I
annino
V,
C
o
l
l
a
V
,
Sig
nori
n
i
A.
"
A
Fuzzy
L
ogi
c-
bas
e
d
Tunin
g
A
p
p
roach
o
f
P
I
D
Contro
l
f
o
r
S
t
eam
T
u
rb
ines f
o
r
S
o
l
ar
A
p
p
li
cati
ons,"
Energy
Pr
oced
ia
;
Vol.
1
0
5
,
pp.
48
0
–
5
,
201
7.
[2]
Z
e
mm
i
t
A
,
Mes
s
al
t
i
S
,
Harrag
A.
"
A
new
im
proved
D
T
C
o
f
doub
l
y
f
ed
i
ndu
ction
mach
in
e
u
s
i
n
g
G
A
-b
ased
P
I
cont
roller,”
Ain
Sh
ams
En
g
J,
V
o
l
.
9
,
pp
.
18
77
–85,
2
01
8.
doi:1
0
.
1
0
1
6
/
j
.
a
s
e
j.
201
6.
10.
011
.
[3]
P
a
y
a
m
AF.
"An
Ad
apt
i
v
e
I
nput-O
ut
put
F
eedb
ack
L
in
earizati
o
n
Con
t
roller
f
o
r
Do
ub
ly
-F
ed
I
nd
uct
i
on
M
achi
n
e
Dr
ive
s
,”
J
Elect
r
E
n
g
, Vo
l
5
, pp
. 1
39
–
5
4
,
2
00
8
.
[4]
Bel
f
ort
C.
"
Field
Ori
e
nt
ed
C
on
tro
l
o
f
a
Do
ub
le
F
ed
Asy
nch
r
o
n
ous
M
achi
n
e:
M
o
d
el
li
ng
a
nd
I
m
p
lem
e
n
t
at
ion,”
IFAC
P
ro
c
Vo
l
1
9
9
7
;3
0:11
01
–6
.
do
i:10
.
10
16
/S
1
4
7
4
-
66
70
(1
7)4
3
5
1
0
-
5
.
[
5
]
T
i
r
Z
,
M
a
l
i
k
O
P
,
"
E
l
t
a
m
a
l
y
A
M
.
F
u
z
z
y
l
o
g
i
c
b
a
s
e
d
s
p
e
e
d
c
o
n
t
rol
o
f
i
ndirect
f
i
e
ld
o
ri
en
ted
contr
o
lled
Double
Sta
r
I
nd
uc
tio
n
Motor
s
c
o
n
n
e
c
t
e
d
i
n
pa
ra
lle
l
t
o
a
sing
le
s
ix-p
h
a
se
i
nverter
supply,
”
El
ectr P
o
wer
Syst
R
e
s
;
V
o
l.
1
3
4
,
p
p.
1
26
–3
3,
2
01
6.
doi:1
0.
10
1
6
/
j
.
e
p
s
r.
2
0
1
6
.
01.
013
.
d
c
d
b
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
496
–
50
4
50
4
[6]
Ch
erifi
D,
M
iloud
Y
.
"
P
erf
o
rm
an
ce
an
alys
is
o
f
a
d
apt
i
v
e
f
u
z
z
y
sli
d
in
g
mod
e
f
o
r
n
on
line
a
r
c
o
n
trol
o
f
the
do
ub
ly
f
e
d
in
du
cti
on
moto
r,
”
In
don
es
J
El
ectr
En
g Informa
ti
cs
,
V
o
l
.
6
,
p
p
.
4
36
–47
,
2
0
1
8
.
d
o
i:1
0.
1
1
5
91/ijeei.
v6i
1.
6
05.
[7]
A
r
oussi
HA,
Z
iani
E
,
Bo
s
s
ou
fi
B
.
"
C
ontri
bution
to
t
he
e
nha
n
cem
e
n
t
of
d
ua
l
dtc
ap
plicat
io
n
:
D
o
u
b
l
y
f
e
d
in
du
c
tio
n
mo
to
r,”
Pro
c
- 3rd
Int Co
nf Ad
v
Te
c
h
no
l S
i
gn
al Imag
e
Pro
c
e
s
s AT
SIP
20
17
,
2
017
.
d
o
i
:
1
0
.
1
10
9/A
T
S
I
P
.
2
0
1
7
.
8
07
5608.
[8]
Bab
o
u
r
i
R,
A
ouzell
a
g
D
,
G
h
e
dam
s
i
K
.
"
In
tro
ductio
n
o
f
d
oub
ly
f
ed
i
nd
uctio
n
machi
n
e
in
a
n
el
e
c
t
r
ic
v
ehi
c
le,”
E
n
er
gy Pro
c
ed
ia
,
V
o
l
36,
pp.
1
076–
84,
2
0
1
3
.
doi:10
.
10
16
/j
.
e
gy
pro.
20
13.
07.
12
3
.
[9]
W
a
ng
Y
,
Chen
H
,
W
a
n
g
W
,
X
i
ao
T
.
"Ad
a
ptiv
e
con
t
ro
l
f
o
r
a
c
l
a
s
s
o
f
n
o
n
l
i
n
e
a
r
s
y
s
t
e
m
s
v
i
a
T
-
S
f
u
z
z
y
l
o
g
i
c
s
y
s
t
e
m
s
with
nonl
in
e
a
r rul
e
c
on
seq
u
ent
s
.
'
P
r
o
c
2
0
15
27
th
Chinese Con
t
r
o
l
Deci
s Co
nf
CCDC
2015
,
pp
.
3
7
6
–81,
2
0
1
5
.
do
i
:
1
0
.
1
109/
CCDC.
2
015
.
7161
72
1.
[1
0]
C
ha
o
u
i
H,
S
ic
a
r
d
P.
"
Ad
a
p
tiv
e
f
u
z
z
y
l
og
ic
c
on
trol
o
f
pe
rma
nent
m
agn
e
t
sy
nch
r
o
n
o
u
s
mach
in
es
w
ith
non
li
near
fr
ic
t
i
o
n
,”
I
EEE Tr
ans
Ind E
l
ectr
o
n,
V
o
l
.
5
9
,
p
p.
1
1
23–
33
,
2
012
. d
oi
:1
0
.
1
1
0
9
/T
IE.
201
1.
2
1
4
8
6
7
8
.
[11
]
T
rip
a
th
i
SM
,
Mish
ra
A
,
P
a
nd
ey
AK.
"
Hi
gh
perf
orm
a
n
ce
sp
eed
tracki
n
g
of
C
S
I-f
ed
S
CIM
d
r
ive
em
pl
oyi
ng
a
variable-gai
n
proporti
o
na
l-inte
g
r
al
(
VG
P
I
)
s
p
eed
c
ont
roller,”
J El
ectr
Syst
In
f T
e
ch
no
l,
V
o
l
.
5,
p
p,
6
35
–52,
2
0
1
8
.
do
i
:
1
0
.
1
016/
j.j
e
sit.
2
0
1
7
.
0
8.0
0
1
.
[12
]
B
o
u
n
a
r
N,
B
o
u
lk
rou
n
e
A
,
B
ou
d
j
em
a
F,
M
’S
aad
M
,
F
a
rza
M.
"
A
d
ap
tiv
e
f
u
zzy
v
ecto
r
c
on
trol
f
or
a
d
ou
bly
-
f
e
d
in
du
c
tio
n
mo
to
r
,
”
Neuro
c
om
pu
tin
g
,
V
ol.
1
5
1
,
p
p.
756
–6
9,
201
5
.
d
o
i
:
1
0
.
10
16/j.
neuco
m
.
2
0
1
4
.
10.
026.
[13
]
R
am
ad
an
E
A,
E
l
-
Bardi
n
i
M
,
F
k
i
ri
n
MA.
"Desi
g
n
an
d
F
P
G
A
-impl
em
en
tation
of
a
n
i
m
prov
ed
a
dap
tiv
e
f
u
zzy
l
o
g
i
c
con
t
roll
er
f
o
r
D
C
m
o
tor
sp
eed
c
on
tro
l
,”
Ai
n
Sh
a
m
s
En
g J
,
Vo
l
5,
p
p.
8
0
3
–1
6,
2
014
.
d
o
i
:
1
0
.
1
01
6/j.
asej.
2
01
4.
0
4
.
0
02
.
[14
]
Z
aki
AM,
El-Ba
r
di
ni
M
,
S
o
lim
a
n
F
A
S
,
S
h
araf
M
M
.
"
Em
bed
d
ed
t
w
o
l
ev
el
d
irect
a
d
a
pt
iv
e
fu
zzy
c
o
n
t
r
o
l
l
e
r
f
o
r
D
C
m
ot
or
s
peed
con
trol
,
”
Ain
Sham
s
E
ng
J
,
Vol.
9,
pp
.
65
–7
5,
2018.
doi:
10.
10
16
/j.
a
sej.
20
15.
10.
0
0
3.
[
1
5
]
L
i
n
T
C
,
L
i
u
H
L
,
K
u
o
M
J
.
"
D
i
re
ct
a
dapt
iv
e
in
terval
t
ype-2
f
uzzy
c
ontrol
o
f
mult
ivaria
ble
no
nl
in
e
a
r
s
yste
ms,”
E
n
g Appl Artif
I
n
tell
,
V
o
l
.
2
2,
p
p
.
4
2
0
–
30,
2
0
0
9
. d
oi:
10.
10
16
/j.
e
ng
app
a
i.
2
008
.
1
0.0
2
4
.
[16
]
L
i
Y,
T
o
n
g
S
.
"
Co
m
m
an
d-fi
lt
ered-bas
ed
f
uzzy
a
dap
tiv
e
con
t
r
ol
d
es
ig
n
f
o
r
M
I
M
O
-s
w
itch
e
d
n
o
n
s
t
ri
ct-f
eedb
ack
no
nlin
e
a
r
sy
s
te
m
s
,”
I
E
EE
Trans Fuzz
y
Syst
,
Vo
l.
2
5,
p
p
.
6
6
8
–
8
1
, 2
017
.
d
o
i
:10.
1
109/TF
UZ
Z.
2
0
1
6
.2
57
491
3.
[17
]
S
at
hishk
u
m
a
r
H,
P
arthas
arath
y
S
S
.
"
A
nov
el
f
uzzy
l
o
g
i
c
c
o
n
tro
l
l
e
r
f
o
r
vect
or
c
ont
rol
l
ed
i
n
d
u
c
ti
on
m
ot
or
d
ri
ve,
”
E
n
er
gy Pro
c
ed
ia
,
V
o
l
.
1
3
8
:
6
8
6–91,
2
0
17.
doi:
10.
1
0
16
/j.
egy
p
ro.
2017.
10.
20
1.
[18
]
K
elt
oum
L
,
L
e
ila
B
,
A
b
d
e
rrah
m
e
n
B.
"
S
p
eed
c
o
n
t
r
ol
o
f
a
D
o
u
bly
-
F
e
d
in
du
ctio
n
m
o
t
o
r
(DF
I
M
)
b
as
ed
o
n
f
u
zzy
s
l
i
d
i
ng m
o
d
e
c
on
troller,
”
Int
J I
n
t
e
ll
E
n
g S
y
st
,
vo
l
10,
pp.
2
0–9,
2
0
1
7.
d
o
i
:1
0
.
2
2
2
66/ijies
2
0
1
7
.
06
30.03
.
[19
]
L
ou
kal
K
,
B
enali
a
L
.
"Int
erval
ty
pe-2
f
uzzy
g
ai
n-adap
ti
ve
co
nt
roll
er
o
f
a
Do
ub
ly
F
ed
I
nducti
on
M
achi
n
e
(D
FIM),
”
J
F
u
nd
a
m
A
p
pl
S
c
i
,
Vo
l.
8
,
pp
.
47
0,
2016
.
doi:
10.
43
14
/jfas
.
v8i2
.
20.
[20]
G
eorges
S
,
Rita
M
,
Mari
a
P,
"
Anal
ysis
A
H
M
i
xed
Sens
itivit
y
H
’
Con
t
ro
l
of
D
ou
bl
y
F
e
d
In
d
u
cti
o
n
M
o
t
o
r,
"
2
0
0
7
:
130
0–
4.
[21
]
H
asn
i
M
,
M
a
ncer
Z
,
M
e
kh
tou
b
S
,
Bacha
S.
"
Pa
ram
e
t
r
ic
i
den
t
i
fi
cati
o
n
o
f
t
he
d
ou
bl
y
fed
i
ndu
cti
o
n
M
achi
n
e,
”
En
e
r
g
y
Proc
edia
,
V
o
l
.
1
8
,
p
p.
1
7
7
–8
6,
201
2.
doi:10
.
10
16/j.
egyp
ro.
2
01
2.
0
5
.
0
29.
[22
]
E
l
Ou
anjli
N,
M
o
t
ahh
i
r
S,
D
erou
ich
A
,
E
l
G
h
zizal
A
,
Ch
eba
b
hi
A
,
Ta
ou
ssi
M
.
"
I
m
p
ro
ve
d
DTC
s
t
ra
te
gy
o
f
d
o
u
b
l
y
f
ed
i
nducti
on
m
oto
r
u
s
i
ng
f
uzzy
l
og
ic
c
o
n
tro
l
l
e
r,
”
Ener
gy
R
e
por
ts,
vo
l.
5
,
pp.
2
7
1
–
9
,
2
019
.
d
o
i
:
1
0
.
1
01
6/j.
eg
yr.
2
019
.
0
2.
0
01.
[23
]
B
en
A
tt
ou
s
D,
B
ek
akra
Y
.
"S
peed
c
o
n
tro
l
o
f
a
do
ub
ly
f
ed
i
n
d
u
ct
ion
m
o
to
r
using
f
u
zzy
l
og
ic
t
echn
i
q
u
es
,”
In
t
J
El
e
c
t
r
En
g
I
n
fo
r
m
a
t
i
c
s
,
Vo
l. 2
, p
p. 17
9
–
9
1
,
20
1
0
.
[24
]
K
ar
B
N,
M
o
h
an
ty
K
B,
M
em
ber
S
,
S
ing
h
M
.
"
I
n
d
i
r
ect
V
ect
or
C
o
ntro
l
of
I
nd
u
c
t
i
on
M
ot
or
U
sing
F
u
zzy
L
ogic
Co
nt
roller"
2
0
11:
6–
9.
[
2
5
]
T
a
o
u
s
s
i
M
,
K
a
r
i
m
M
,
B
o
s
s
o
u
f
i
B
,
H
a
m
m
o
u
m
i
D
,
L
a
g
r
i
o
u
i
A
,
D
e
ro
uich
A
.
"S
peed
v
ariabl
e
adap
ti
ve
b
acks
t
epp
i
n
g
c
o
n
t
r
ol
o
f
th
e
do
ub
ly-fed
in
du
cti
o
n
mach
in
e
driv
e,
”
Int
J Autom
Contro
l
,
V
o
l
.
1
0
,
p
p
.
1
2
,
2
0
1
6
.
d
o
i
:
1
0
.
1
50
4/IJ
AA
C.
20
16
.
0
7
5
1
4
0.
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