Int
e
rna
t
i
o
na
l
J
o
u
r
na
l
of
Pow
e
r
El
ec
tro
n
i
c
s a
nd D
r
i
v
e
Sys
t
e
m
(
I
J
P
EDS
)
Vol
.
1
1
,
N
o
.
3
,
Se
pte
m
be
r 20
20
,
pp
.
11
6
5
~1
17
4
IS
SN
:
208
8-8
6
9
4
,
D
O
I
:
10.115
9
1
/ijp
e
d
s.v
11.
i3
.p
p
1
1
65-1
174
1
165
J
o
urna
l h
o
m
e
p
a
g
e
:
h
t
tp
:
//i
jpe
d
s.ia
esc
o
re
.co
m
Performance analy
s
is on direc
t torque controlled in
duction
motor drive with va
ryi
n
g hy
steresis controller bandwidth
S.
Al
l
i
r
a
ni
1
, N.
Subha
Lakshmi
2
, H.
V
i
dh
y
a
3
1
De
p
a
rt
me
nt
of
E
l
ec
t
r
ic
a
l
a
nd Ele
c
t
ro
nic
s
E
n
g
i
nee
r
i
n
g
,
Sri Ra
m
a
krish
n
a
En
gin
e
e
r
in
g
Co
lle
g
e
,
In
dia
2
Dep
a
rtm
e
nt
o
f
Ele
c
trical
and
El
ectro
n
i
cs Eng
i
ne
ering
,
S
r
i
Krishn
a Col
l
eg
e
of
Eng
i
n
eer
ing
an
d
T
ech
no
lo
gy
, Ind
i
a
3
De
p
a
rt
me
nt
of
E
l
ec
t
r
ic
a
l
a
nd Ele
c
t
ro
nic
s
E
n
g
i
nee
r
i
n
g, Sri Ra
m
a
krish
n
a
En
gin
e
e
r
in
g
Co
lle
g
e
,
In
dia
Ar
ti
cl
e Info
ABS
T
R
A
CT
Art
i
cl
e hi
sto
r
y
:
R
e
c
e
i
v
ed
A
ug 28
, 20
1
9
Re
v
i
se
d
F
e
b 4, 20
20
Ac
ce
pte
d
Mar
20
, 20
2
0
The
f
o
r
e
most
i
s
s
u
e in
DT
C
b
a
s
e
d in
du
ct
io
n
mo
t
o
r
d
r
iv
e
i
s
i
t
s
t
o
r
q
ue
r
i
pp
les
.
T
h
e
c
o
re ob
je
cti
v
e
of t
h
i
s
pa
pe
r is
t
o
re
d
u
c
e
t
h
e el
ec
tro
m
a
gne
t
i
c
torq
ue
r
i
p
p
l
e
s by va
ry
in
g
t
h
e
h
y
stere
s
i
s
c
o
n
t
rol
l
er ba
nd
wi
dt
h
.
S
p
a
c
e
Ve
ct
or
M
o
d
u
l
a
ti
on
(SVM) ba
se
d Di
rect Torque Con
t
roll
ed (DTC)
i
n
duct
i
o
n
m
o
t
o
r
dr
iv
e
is s
i
mu
l
a
t
e
d
i
n
M
A
T
L
A
B
/S
I
M
UL
I
NK en
vir
o
nm
e
n
t
and
i
t
s
performan
ce is
s
t
u
d
ied
with
ste
p
ch
an
ge
in
lo
ad
to
rqu
e
. Th
e i
n
fluen
c
e o
f
h
y
s
t
e
re
si
s c
o
n
t
rol
l
e
r
b
a
n
d
width on
the
pe
rfor
m
a
n
c
e
of
in
du
cti
on
m
o
t
o
r
dri
v
e
i
s
a
n
a
l
y
s
e
d
i
n
te
rm
s
of
st
at
or
flu
x
a
nd e
l
e
c
t
r
oma
g
n
e
ti
c t
o
rq
ue
ri
pp
le
s. T
h
e
e
l
ec
t
r
oma
g
n
e
ti
c
t
o
rq
ue
re
sp
on
se a
n
d t
h
e
st
a
t
or
f
l
u
x
t
r
aj
e
c
to
ry
for
di
ffe
re
nt
valu
es
o
f
hy
ster
es
is
con
t
roller b
a
ndw
id
th
are
o
b
tain
ed
and
th
e
resu
lts
ar
e
presen
ted
.
Ke
yw
o
r
d
s
:
Di
re
ct
t
o
rq
ue
c
ont
rol
F
l
u
x
vec
t
or
est
i
m
a
t
ion
Spac
e ve
ct
o
r
mo
dul
at
i
o
n
I
n
duc
t
i
on
Mot
o
r
Thi
s
i
s
an open
access
ar
t
i
cl
e under the
CC BY-SA
licens
e
.
C
o
rres
p
o
n
di
n
g
Au
t
h
or:
S.
A
l
lir
a
n
i
De
pa
rt
me
nt
o
f
El
ec
tr
ic
al
a
n
d
El
ec
tr
onic
s
E
n
gi
nee
r
in
g,
S
r
i
R
a
ma
kr
is
h
n
a E
n
gine
er
i
n
g
Col
l
e
ge,
Va
tt
a
m
a
l
a
i
pa
l
a
yam
,
Co
im
b
a
to
re,
Ind
i
a
.
Ema
il: a
l
l
i
ra
n
i
.
s
a
m
in
a
t
h
a
n@
sr
ec
.a
c
.
in
1.
IN
TRODUC
TI
ON
Var
i
a
b
le
spee
d
AC dr
i
v
e
s
are
wi
del
y
use
d
i
n
pr
od
uct
i
o
n pl
a
n
t
s
li
ke pa
per
,
ce
me
nt
, a
nd
te
xti
l
e
mi
ll
s
e
t
c
,
t
r
a
n
sp
or
ta
t
i
on syste
m
s,
fa
ns,
p
u
mps,
bl
o
w
e
r
s
,
wi
n
d
ge
ne
rat
i
o
n syst
e
m
s, d
o
mest
i
c
e
l
ec
t
r
i
cal
appl
i
a
nc
escs
e
t
c
.
El
ec
tr
ic
al
dri
v
es ca
n
be
c
l
assif
i
e
d
base
d
on it
s so
ur
ce
a
s
A
C
d
r
i
v
es a
nd
DC
d
r
i
v
es
and as c
o
nst
a
n
t
spe
e
d
a
n
d
va
r
i
abl
e
spe
e
d
dri
v
e
s
de
pe
n
d
i
n
g on
the
i
r
mec
h
a
n
i
cal
out
put
c
h
ar
act
e
r
i
s
t
i
c
s a
n
d
ap
pl
ic
at
i
ons.
A
C
mac
h
ine
s
a
r
e
b
a
s
ic
al
l
y
c
o
n
s
ta
nt spee
d a
nd
near
l
y
c
onst
a
n
t
speed
mac
h
i
n
e
s
a
nd he
nce
sui
t
a
bl
e f
o
r c
onst
a
nt
spee
d a
p
pli
c
at
i
ons
. DC
ma
c
h
i
n
es ca
n
be
us
ed i
n
va
ri
abl
e
spee
d a
p
pl
i
cat
ions
a
s
t
h
ei
r s
p
ee
ds ca
n
be
v
a
ri
e
d
ea
sil
y
b
y
si
m
p
le
me
a
n
s, w
h
i
c
h
is
no
t
th
e
c
a
s
e
w
ith
A
C
ma
ch
in
es.
How
e
v
e
r
,
th
e
DC m
a
c
h
in
e
s
suf
f
e
r
f
r
o
m
man
y
disa
d
v
an
t
a
ges li
ke
hi
g
h
e
r co
st
, wei
ght
and
i
m
p
o
r
t
a
n
tl
y,
pr
o
b
l
e
ms wi
t
h
c
o
mm
ut
at
or
and
i
t
s
mai
n
t
e
n
a
n
c
e
r
e
q
u
i
r
eme
n
t
s
.
The
s
e
di
sa
d
v
a
n
t
a
ge
s se
e
m
ed
t
o
ha
ve o
u
t
w
e
i
ghe
d
i
t
s
ad
va
nt
age
s
, c
a
usi
n
g a
sp
ur
t
in r
e
sear
ch
ac
ti
v
itie
s
ai
min
g
to
co
nv
er
t t
h
e
c
o
nsta
n
t
s
p
e
e
d
ind
u
c
tion
moto
r
in
t
o
a
v
a
r
i
ab
le
sp
e
e
d
A
C
d
r
i
v
e
.
In
ma
j
o
rit
y
o
f
in
du
st
ri
al en
v
i
ro
nme
n
ts,
an
ind
u
c
t
i
on mo
tor
is
pr
e
f
er
red
due to
its sim
p
le
me
c
h
a
n
i
c
a
l
con
s
t
r
u
c
ti
o
n
,
r
e
li
ab
i
lity
,
r
u
gge
d
n
ess
,
l
o
w c
o
st a
n
d
l
o
w
mai
n
te
na
nce
r
e
qui
reme
nt
s.
H
o
we
ve
r,
the
s
e
adva
nt
age
s
p
a
le
int
o
in
si
g
n
i
f
i
canc
e
whe
n
t
h
e m
o
t
o
r
i
s
jud
g
e
d
fr
o
m
c
o
ntr
o
l a
s
pe
ct
s.
As i
nduc
ti
on
mot
o
rs a
r
e no
n
-
l
i
n
ear
hi
g
h
er
or
der s
y
st
e
m
s o
f
c
o
mpl
e
xi
t
y
, an
a
dva
nce
d
co
nt
r
o
l t
e
c
h
niq
u
e
a
nd
fl
exi
b
l
e
co
n
t
rol
l
e
rs ar
e
re
qui
re
d in
or
de
r t
o
ext
e
nd t
h
e
u
s
e of
I
M
t
o
va
r
i
a
b
le
spee
d a
ppl
i
c
a
t
i
ons
. O
n
e
s
u
c
h
adva
nc
e
d
co
nt
r
o
l
t
echni
que i
s
Di
rec
t
T
o
r
q
ue
Cont
r
o
l
(
D
TC
),
o
r
Di
re
ct
Se
lf
C
o
ntr
o
l (
D
S
C
)
,
i
n
tr
o
d
uc
e
d
a
n
d
d
e
vel
o
ped
b
y
T
a
kaha
shi
&Na
guc
hi
i
n
1
9
84 [
1
]
a
n
d De
pe
n
b
r
oc
ki
n
1
988
[2]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
In
t
J Po
w
Ele
c
& Dri
Sy
st,
Vol.
1
1
,
No
.
3
,
Sep
t
e
m
b
e
r
20
20
:
116
5 – 117
4
1
166
In
[3
],
t
h
e
a
u
t
h
o
r
a
d
o
p
te
d a
spac
e ve
ct
or
mo
dul
at
i
o
n-
ba
sed
D
T
C
fo
r
IM
.
F
u
rt
he
r,
p
e
r
f
o
r
m
anc
e
e
v
al
uat
i
o
n
o
f
di
rec
t
t
o
r
q
u
e
-c
on
t
r
ol
l
e
d
dr
i
v
e
i
n
the
c
ont
i
nuo
us
P
W
M
squ
a
r
e
wa
ve
t
r
ansi
t
i
o
n
r
e
gi
o
n
wa
s
di
scuss
e
d
in
[4
].
In
mode
r
n
f
act
ori
e
s,
va
r
i
abl
e
f
r
eq
ue
nc
y dr
i
v
e
s
wi
th
high
pe
rf
o
r
ma
nc
e
co
nt
r
o
l
pe
rm
it
hig
h
vol
ume o
f
au
t
o
mat
e
d p
r
o
d
u
c
t
i
on
wit
h
s
u
pe
ri
or pr
o
d
u
c
t q
u
al
it
y.
One
suc
h
a
hi
g
h
-
p
er
fo
rma
n
ce
c
o
n
t
ro
l
te
ch
n
i
qu
e i
s
ide
n
ti
fi
ed
a
s
d
i
rec
t
to
rq
u
e
c
o
n
t
ro
l t
e
c
h
n
i
qu
e
in
in
du
c
tion
mo
t
o
r
dr
iv
e
[
5
,
6
]
. I
n
DTC,
th
e co
n
t
r
o
l
v
a
r
i
ab
le
s ar
e
t
h
e
mo
tor
to
rque a
n
d
ma
gn
et
i
z
in
g
fl
ux
and
th
ey
c
a
n
b
e
con
t
ro
l
l
e
d
d
i
re
c
tly
.
In
D
T
C,
t
h
e sp
eed
a
ccur
a
c
y
i
s
0
.
1%
wi
th
out
e
n
code
r
.
T
h
i
s
i
s
sa
ti
sfyi
n
g
t
h
e
acc
urac
y
re
qui
r
e
me
nt
f
o
r
95
%
o
f
i
n
d
u
str
i
al
d
r
i
v
es
ap
p
l
ic
ati
o
n
s
. A D
T
C
d
r
i
v
e
u
s
i
n
g an
e
n
cod
e
r ca
n
a
c
h
i
ev
e
a sp
e
e
d
ac
cur
a
c
y
o
f
0
.
01
%
[
7
]
.
Th
e
ad
va
n
t
ag
e
wi
th
D
T
C is
t
h
a
t
it
is c
h
a
r
a
c
t
e
r
iz
e
d
b
y
th
e
ab
sence
of
PI re
gu
lato
r
s
, co
ord
i
n
a
t
e
t
r
a
n
sfo
r
ma
ti
on
s, c
u
r
r
en
t r
e
gu
la
to
r
s
a
nd
p
u
lse
wi
dt
h
mod
u
l
a
t
e
d si
gnal
gene
rat
o
r
s
.
DTC
al
so al
l
o
ws a
g
o
o
d
to
rq
ue
co
nt
r
o
l
d
u
ri
ng st
ea
dy
st
at
e
as
w
e
ll
as tra
n
sien
t
o
p
e
r
a
ti
ng
c
o
n
d
ition
s
. On
e
maj
o
r
d
r
aw
b
ack
w
ith D
T
C
i
s
th
e prod
u
c
ti
on
o
f
t
o
rq
u
e
r
i
pp
le
s a
t
lo
w
sp
e
e
d op
er
at
io
n
s
.
Di
ffe
ren
t
ap
pr
o
ach
e
s
lik
e
b
a
nd co
nstr
ai
n
e
d
v
o
l
ta
ge v
e
cto
r
s
e
le
c
tio
n [8
], a con
s
ta
n
t
swi
t
c
hi
n
g
fr
e
q
uenc
y
t
o
r
que
c
ont
r
o
ll
e
r
[
9
,
10
],
u
n
i
f
i
e
d
fl
ux an
d to
r
que
co
nt
rol
l
e
r
[
1
1
]
,
f
u
z
z
y
l
o
gi
c
b
a
se
d
c
ont
r
o
l a
p
p
r
oa
ch ba
se
d o
n
A
I
base
d
c
o
ntr
o
ll
er
[
1
2
,
1
3
,
1
4
]
ar
e su
gge
ste
d
and el
a
b
ora
t
e
d
t
o
re
duce t
h
e t
o
r
q
ue
ripp
les.
An
ot
he
r i
m
po
r
t
a
n
t t
e
ch
ni
qu
e
ap
pl
ie
d f
o
r
re
d
u
ci
n
g
c
u
r
r
e
n
t r
i
p
p
l
e
s a
n
d
t
o
r
que
p
u
l
s
at
i
ons
d
u
ri
ng
st
ea
dy
sta
t
e
i
s
SV
M te
c
hni
qu
e. I
n
S
V
M ba
s
e
d D
T
C,
t
h
e
meri
t
s
of
D
T
C
a
r
e
p
r
ese
r
ve
d a
l
on
g w
i
t
h
i
m
pr
o
v
ed
ste
a
d
y
sta
t
e
ope
ra
ti
o
n
s
[
15]
.
In
[
1
6
]
,
t
h
e a
u
th
or
p
r
op
os
ed a s
lid
in
g mo
de c
o
n
t
ro
ll
er
-b
ased
in
du
c
tion mo
tor
dr
i
v
e
.
S
V
M-
D
T
C
ba
se
d I
M
dri
v
e i
n
or
der
t
o
re
duce
t
h
e
s
w
i
t
c
hi
n
g
har
m
oni
cs
.
S
V
M
b
a
sed
DTC
f
o
r
t
o
r
que
r
i
p
p
l
e
mi
ni
mi
z
a
t
ion i
s
a
l
so r
e
po
rt
ed i
n
t
h
e
li
t
e
ra
t
u
r
e
[
1
7
]
. I
n
[1
8
]
,
t
h
e
a
u
th
or
rep
o
r
te
d an
ot
he
r
te
ch
ni
q
u
e
na
me
d pr
e
d
i
c
t
i
v
e
co
nt
r
o
l
t
o
r
e
duc
e
fl
u
x
a
n
d
tor
q
ue
ri
p
p
le
s
i
n
I
M
dr
i
v
e
s
.
I
n
[
1
9],
modi
fi
e
d
D
T
C
in se
ns
orl
e
ss
dr
i
v
e
i
s
p
r
op
o
s
ed
by t
h
e
a
u
t
hor
. R
ece
nt da
ys,
DTC
wi
t
h
nine
sw
it
ch i
n
vert
e
r
s is p
r
op
ose
d
t
o
c
o
ntr
o
l t
w
o
i
n
d
u
ct
i
o
n
mot
o
rs
i
nde
pe
nde
nt
l
y
[
2
0
]
.
I
m
p
r
ove
d
pe
rf
or
ma
nce
o
n
DTC
base
d i
n
d
u
ct
io
n
mot
o
r
dri
v
e
is a
l
s
o
r
e
p
o
rt
e
d
[
2
1
]
.
I
n
ad
di
ti
on
t
o
in
d
u
ct
i
o
n mac
h
ine
s
,
D
T
C is em
plo
y
e
d
t
o
c
o
nt
r
o
l
P
e
r
m
a
n
e
n
t
M
a
gne
t
Syn
c
hro
nou
s M
o
t
o
r [22
]
.
In t
h
is
pa
per
,
i
t
i
s
pr
op
ose
d
t
h
at
t
h
e
r
e
d
u
ct
i
o
n
o
f
t
o
rq
ue
pul
sa
ti
on i
s
d
o
n
e
by r
e
d
u
ci
ng th
e
ba
n
d
w
idt
h
o
f
th
e
h
y
s
t
e
r
e
sis c
o
n
t
r
o
lle
r.
Th
e
sy
ste
m
is
c
o
mp
l
e
t
e
ly
simu
la
te
d
i
n
Ma
tla
b
a
n
d
th
e
r
e
su
lts
ar
e pr
esen
t
e
d.
Ch
a
p
te
r 2
e
x
p
l
a
i
n
e
d
a
bou
t SVM
b
a
sed
D
T
C,
ch
ap
t
e
r 3
prese
n
te
d
th
e
si
m
u
la
tio
n r
e
su
lts,
ch
a
p
t
e
r
4 d
i
sc
u
ssed
a
b
o
u
t
t
h
e dri
v
e
pe
r
f
o
r
m
anc
e
wi
th var
y
in
g st
at
or fl
u
x
c
o
nt
r
o
l
l
e
r
ban
d
w
i
d
t
h
.
Fi
nal
l
y
,
t
h
e
pape
r
is
co
nc
lu
de
d
i
n
ch
a
p
ter
4
2.
SVM
BASED D
T
C
The
b
a
sic
pri
n
ci
pl
e
of
D
T
C
i
s
t
o
r
e
g
u
la
te
el
e
c
t
r
oma
g
net
i
c
t
o
r
que
a
n
d
st
at
or
fl
u
x
mag
n
i
t
ude
b
y
t
h
e
di
re
ct
se
le
ct
io
n
o
f
a
s
p
a
ce
vec
t
or a
n
d c
o
r
r
e
s
p
o
n
d
i
n
g c
o
nt
r
o
l
signa
l
s
.
T
h
e
g
e
n
e
ri
c
DT
C sch
e
m
e
for a
Vo
lt
ag
e Sou
r
c
e
PWM inve
r
t
er
-f
ed
IM
d
r
iv
e
is
sho
w
n i
n
Figu
r
e
1
.
Thi
s
inc
l
u
d
e
s
t
w
o
c
o
nt
rol
l
e
rs
of
hyste
resi
s.
The
t
i
m
e
d
u
r
a
t
i
on
of
t
h
e
a
c
t
i
v
e
vol
t
a
ge
ve
ct
o
r
s i
s
i
m
pose
d
b
y
t
h
e
st
at
or
fl
u
x
,
w
h
i
c
h mo
ve
a
l
o
n
g
t
h
e
re
fe
r
e
nce
t
r
aj
ec
to
r
y
,
w
h
er
eas t
h
e t
i
m
e
du
rat
i
o
n of
th
e
zer
o
vol
t
a
ge
ve
ct
ors
d
e
t
e
r
m
in
ed
by
th
e
tor
q
u
e
con
t
r
o
lle
r
wh
ic
h
k
eep
th
e mo
to
r to
rqu
e
i
n
t
h
e
p
r
e
d
ef
i
n
e
d
hy
st
e
r
e
s
is
to
le
ran
c
e b
a
nd
.
The
i
n
ver
t
er
s
w
i
t
c
h
in
g
st
at
e
i
s
i
s
c
hose
n
b
y
the
v
o
l
t
a
ge
ve
ct
or
sel
e
c
t
i
o
n
bloc
k at
eac
h
s
a
mpl
i
n
g
t
i
m
e
(
S
a,
S
b
,
Sc
)
w
h
ich
re
duc
es th
e
in
sta
n
tan
e
ou
s
f
l
ux
a
n
d
th
e
tor
q
u
e
e
r
ror
s
[23
]
.
Fi
gu
re
1.
Ge
ne
ri
c sche
me
of
P
W
M i
nve
rt
er
fed
i
nduc
t
i
o
n
mot
o
r
wi
th
DT
C
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Perf
orma
nc
e
anal
y
s
i
s
o
n
dire
ct
t
o
rq
ue c
o
ntrol
l
e
d i
n
d
u
ct
i
o
n
m
o
t
o
r
dri
ve
wi
t
h
v
a
ry
in
g
…
(S.
Al
l
i
rani
)
1
167
2.1.
Basi
c sw
i
t
chi
n
g tab
l
e
a
n
d sel
ection
o
f
vol
ta
ge
vect
ors b
a
se
d o
n
sp
ace
ve
c
t
or
mo
du
l
a
ti
on
Th
e sw
it
ch
in
g
tab
l
e of
DTC
co
n
c
ep
t is show
n in F
i
gu
r
e
1
.
Th
e
co
mm
a
n
d
sta
t
or
f
l
ux
Ψ
sr
ef
, and T
ere
f
v
a
lu
e
s
a
r
e
comp
ar
ed
w
i
t
h
th
e
a
c
t
u
al
Ψ
s
an
d
T
e
va
lue
s
i
n
h
y
st
e
r
esi
s
fl
ux
an
d
t
o
rque
cont
rol
l
e
r
s
,
re
s
p
ec
ti
ve
ly
[2
3]. T
h
e
di
git
i
z
e
d
out
put
sig
n
a
l
s
o
f
t
h
e
fl
u
x
cont
rol
l
e
r
are
d
e
fi
ne
d a
s
i
n
e
q
u
a
t
i
on
s
(1
) a
n
d
(2)
1,
(1)
1,
(2)
An
d t
hos
e
of t
h
e
t
o
r
que
c
o
ntr
o
ll
er a
r
e
as i
n
(3), (4
),
(5
),
1,
(3)
0,
(4)
1,
(5)
Whe
r
e 2
H
Ψ
is th
e
f
l
ux
to
l
e
ra
nce
b
a
n
d
and
2H
m
i
s
t
h
e
t
o
rq
u
e
tol
e
ra
nce
ba
nd.
The
di
gi
ti
ze
d va
ri
a
b
l
e
s
Ψ
se
rr
, T
eerr
an
d the
s
t
at
or fl
ux
sec
t
i
o
n
(sect
or) N
obta
i
ne
d from
t
h
e an
g
u
la
r
posit
i
o
n
α
= arc
t
g (
Ψ
s
β
/
Ψ
s
α
)
(6)
Creat
e
a di
gi
ta
l
wo
rd whi
c
h i
s
use
d
t
o
sel
e
c
t
t
h
e
ap
p
r
o
p
ri
a
t
e
v
o
l
t
a
g
e
vect
or. T
h
e st
at
o
r
vol
t
a
ge
spa
ce
v
e
ct
o
r
V
s
is cal
cul
a
te
d
usi
n
g
t
h
e dc
l
i
nk v
o
l
t
a
g
e V
dc
and
the
ga
ti
n
g
si
gnal
s
S
a
, S
b
, S
c
as
give
n i
n
(7)
Π
Π
(7
)
The
SV
M
se
le
ct
s t
h
e i
nve
rt
e
r
v
o
l
t
a
g
e
ve
ct
o
r
fr
om t
h
e
Ta
bl
e 1
i
s
do
ne
b
y
de
pe
ndi
ng
on
tor
q
u
e
an
d
f
l
ux
hy
ste
r
esi
s
st
at
u
s
an
d
α
.T
h
e
o
u
t
p
uts
o
f
th
e
s
w
i
t
chi
ng t
a
b
l
e are
t
h
e
set
t
in
gs
for the
s
w
i
t
c
hi
n
g
de
vi
c
e
s of
t
h
e
i
nve
rt
er.
Tabl
e
1.S
w
i
t
c
h
ing ta
ble
o
f
Inv
e
rt
er
Vol
t
a
g
e Ve
ct
o
r
s
Ψ
s
err
T
ee
rr
α
(1
)
s
ec
t1
α
(2
)
s
ec
t2
α
(3
)
s
ec
t3
α
(4
)
s
ec
t4
α
(5
)
s
e
c
t
5
α
(6)
s
ect
6
1
1
V2
V3
V4
V5
V6
V
1
0
V7
V0
V7
V0
V7
V
0
-
1
V6
V1
V2
V3
V4
V
5
0
1
V3
V4
V5
V6
V1
V
2
0
V0
V7
V0
V7
V0
V
7
-
1
V5
V6
V1
V2
V3
V
4
2.2.
Sta
t
or f
l
u
x
c
o
ntr
o
l
By
se
lec
t
i
n
g
th
e su
it
ab
l
e
inve
r
t
er
ou
tpu
t
vol
ta
g
e
V
i
(
i
=1-6), the stator
f
l
ux
Ψ
s
r
o
ta
tes
a
t
th
e
d
e
sir
e
d
fre
que
nc
y
ω
s
i
n
si
de
a spe
c
i
f
i
e
d ba
n
d
. If
t
h
e
st
at
or oh
mi
c dr
o
p
s a
r
e
ne
gl
ec
te
d, t
h
e
sta
t
o
r
vol
ta
g
e
i
s
gi
ven
by
equations
(8)
and
(9).
(8)
(9)
Th
us t
h
e
va
ri
at
i
o
n
of t
h
e st
at
or fl
ux
s
p
ac
e
v
e
c
t
or
d
u
e t
o
t
h
e
ap
pl
i
cat
i
o
n
o
f
t
h
e
st
at
o
r
v
o
l
t
age
ve
ct
o
r
V
s
d
u
ri
ng a
ti
me
int
e
rval
of
Δ
t
c
a
n
be
a
p
p
r
oxi
ma
te
d
a
s
i
n
e
q
ua
ti
on
(
1
0
)
.
(10)
A
s
t
h
e
st
at
o
r
fl
ux
l
i
nka
ge
sp
a
ce vec
t
or
m
o
ve
i
n
th
e
di
rec
t
i
on of
t
h
e
sta
t
or
v
o
l
t
a
g
e
sp
a
ce vec
t
or
as
l
ong
as t
h
e
v
o
l
t
a
ge spa
ce
vec
t
or i
s
a
ppl
i
e
d
.
The a
i
m i
s
t
o
kee
p
t
h
e
m
o
dul
us o
f
the
sta
t
o
r
fl
u
x
l
i
nka
g
e
spac
e
vec
t
o
r
s
wi
thi
n
the
hy
st
eresi
s
ban
d
,
wh
ose
w
i
dt
h
i
s
2H
ψ
a
s
sh
own
i
n
F
i
gure 2. Th
e
si
x
s
e
c
t
o
r
s
a
r
e
sho
w
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
In
t
J Po
w
Ele
c
& Dri
Sy
st,
Vol.
1
1
,
No
.
3
,
Sep
t
e
m
b
e
r
20
20
:
116
5 – 117
4
1
168
i
n
Fi
gu
re
2.
Th
e traj
ec
tor
y
o
f
t
h
e sta
t
o
r
flu
x
vec
t
o
r
from
P
0
to
P
2
thr
oug
h
P
1
ca
n
be
e
x
pla
i
ned
in
t
h
e
f
o
l
l
owi
n
g
steps:
St
ep 1:
Flu
x
vecto
r
pa
t
h
from P
0
to
P
1
I
t
is as
su
med
th
at
in
iti
all
y
t
h
e sta
t
or
fl
ux
l
i
n
k
a
g
e
sp
a
c
e
ve
cto
r
is at
p
o
si
ti
o
n
P
0
,
i
n
sec
t
or
1.
I
f
it
i
s
ass
u
med
t
h
a
t
th
e
sta
t
or
f
l
u
x
v
e
ct
or
is ro
ta
tin
g
an
ti
clo
c
k
w
i
s
e
,
it f
o
llo
ws
t
h
a
t
at
po
sit
i
o
n
P
0,
th
e
sta
t
or
f
l
ux
ve
ct
o
r
i
s
at
t
h
e up
pe
r li
mi
t
sre
f
s
, an
d it
must
be
re
duce
d
.
Thi
s
c
a
n
be
a
c
h
i
e
ve
d by
a
p
plyi
n
g
s
u
i
t
a
bl
e
sw
itc
h
i
ng
v
e
c
t
o
r
.
Th
e
c
o
rr
espo
nd
ing
sw
itc
h
i
n
g
v
e
c
t
o
r
is
(0
, 1
,
0)
wh
i
c
h
will
p
r
o
v
i
d
e
V
3
.
Th
us
, t
h
e
st
a
t
o
r
f
l
ux
lin
k
a
g
e
sp
a
ce v
e
c
t
or
w
ill
mov
e
r
a
p
i
d
l
y f
r
om p
o
i
n
t
P
0
t
o
poi
nt
P
1
a
nd it
can
b
e
se
en th
a
t
P
1
is
in sec
t
o
r
2
[24
,
25
]
.
2.
3.
To
rq
ue cont
ro
l
The e
l
e
c
t
r
oma
gne
ti
c
to
r
que
g
i
v
e
n
by e
q
ua
ti
on
(1
1
)
is a
si
n
u
s
o
i
d
al
fu
nc
ti
on
of
γ
,
t
h
e
an
gl
e be
twee
n
Ψ
s
and
Ψ
r
.
Th
e
v
a
r
i
at
ion
o
f
sta
t
o
r
fl
ux
v
e
c
t
or w
ill pr
odu
c
e
a
v
a
ri
ati
o
n
i
n
t
h
e
d
e
v
e
l
o
pe
d to
rqu
e
b
e
c
a
u
se
o
f
th
e
va
ri
at
i
on of
t
h
e
an
gl
e
γ
bet
w
e
e
n
t
h
e
tw
o
vec
t
or
s as i
n
e
quat
i
on
(
1
2)
.
′
(
11)
′
(
12)
Wh
er
e L
s
’
= L
s
L
r
–
L
m
2
2.
4.
S
t
a
t
or fl
ux
es
t
i
mat
o
r
I
n
t
h
e
sta
tio
n
a
ry
re
f
e
r
e
n
ce fr
a
m
e,
t
h
e
d a
nd
q a
x
e
s
st
at
o
r
f
l
ux
e
s
ar
e
es
tima
t
e
d
b
a
sed
o
n
(13
)
,
(14
)
.
̄
(
13)
̄
(
14)
(
15)
2.
5.
E
l
e
c
tr
om
ag
ne
ti
c Tor
q
ue
E
s
t
i
mati
o
n
F
r
om
th
e e
s
tima
t
e
d
s
t
a
t
o
r
f
l
u
x
a
n
d cu
rr
e
n
t
com
pon
en
t
s
t
h
e el
ec
tro
m
agn
e
tic
t
o
rqu
e
of
th
e mo
to
r
i
s
c
a
l
c
ul
at
ed as i
n
(1
6)
3
̄
̄
(
16)
F
i
gu
re
2.
Traj
e
c
t
or
y of
sta
t
or
f
l
u
x
vect
or
an
d
i
nve
r
t
e
r
sw
it
c
h
i
n
g ve
ct
o
r
s
3.
SIM
U
LATI
O
N
:
RES
U
LT
S & DI
SCUS
SI
ONS
The
d
y
n
amic
mac
h
ine
mo
de
l
i
n
st
at
e
spac
e fo
rm i
s
p
r
efe
rre
d i
n
c
o
m
p
ut
er
sim
u
l
a
t
i
o
n
fo
r st
u
dyi
ng
tr
an
si
en
t
an
a
l
ysis
o
f
IM
. Fr
om
th
e
vo
l
t
ag
es
a
n
d
ma
ch
i
n
e
p
a
r
a
m
e
t
e
r
s
t
h
e st
at
e
sp
ac
e mo
d
e
l
is ob
t
a
i
n
e
d
as
i
n
Eq
ua
ti
on
(
1
7
)
,
whi
c
h i
s
i
n
the
fo
r
m
o
f
,
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
Perf
or
ma
nce
a
nal
ysi
s
o
n
di
re
ct
torq
ue c
o
nt
roll
e
d
i
n
d
u
ct
io
n
m
o
t
o
r
driv
e wi
t
h
va
ry
in
g
…
(
S
.
Al
l
i
rani
)
1
169
(
17)
Ini
t
i
a
l
l
y
the
m
o
t
o
r is sta
r
t
e
d
and
a
l
lowe
d
t
o
ope
rat
e
u
nde
r
no
-l
oa
d c
o
ndi
t
i
on
.
Af
t
e
r
so
me
ti
me,
a
t
0.
4s
in
sta
n
t a step
c
h
a
n
g
e
in
lo
ad
t
o
rqu
e
of
20
Nm is app
l
ied
a
s
i
n
pu
t a
n
d th
e
d
r
i
v
e
p
e
rf
orm
a
n
c
e
is
stu
d
i
ed
fro
m
t
h
e
r
e
sp
o
n
se
of t
h
r
e
e
pha
se sta
t
or
cur
r
e
nt
s (
i
ab
c
)
,
d an
d
q axe
s
s
t
at
or c
u
r
r
e
n
t
s
(
i
ds
a
nd i
qs
),
sta
t
or
f
l
uxe
s in
d
and
q
ax
e
s
ψ
ds
an
d
ψ
qs
, c
i
rcul
a
r
tr
aj
e
c
t
or
y
of
sta
t
or
fl
u
x
, i
n
ve
r
t
e
r
o
u
t
p
ut v
o
l
t
a
ge,
spee
d r
e
s
p
on
se
,
an
d est
i
m
a
t
e
d
a
nd
obs
er
ved
el
ect
r
o
ma
gne
t
i
c
t
o
r
que
.
T
he
d
a
n
d
q
axe
s
st
at
o
r
fl
u
x
r
e
sp
o
n
se
s
o
f
S
V
M-
DTC
ba
se
d
I
M
dri
v
e
a
r
e
sho
w
n in
Fi
gu
r
e
3.
It
i
s
f
o
und t
h
at
t
h
e t
w
o
fl
u
x
es
ar
e i
nde
pe
nde
nt
t
o
ea
ch
ot
he
r as t
h
ey
ar
e
o
r
t
h
o
g
o
n
al
.
The
q a
x
is f
l
ux
i
s
re
spo
n
si
bl
e
fo
r
to
r
que
co
nt
rol
w
h
e
r
ea
s
d
axi
s
fl
ux
is
r
e
s
p
o
n
si
bl
e f
o
r
sp
ee
d c
ont
rol
.
I
t
i
s
o
b
ser
v
e
d
f
r
o
mt
he
wa
ve
f
o
r
m
t
h
at
t
h
e
st
at
or
fl
ux
di
str
i
b
u
t
i
on i
s
a
l
most
si
n
u
s
o
ida
l
.
T
h
e
c
i
rc
ul
ar
t
r
a
j
e
c
t
o
r
y
of st
at
or
fl
u
x
ve
ct
o
r
sho
w
n i
n
Fi
gu
re
3(
b)
i
s
al
so
pr
o
v
in
g t
h
e
sm
oot
h si
nus
oida
l
di
st
ri
b
u
ti
o
n
of
st
at
or
fl
u
x
w
h
i
c
h l
e
a
d
s t
o
sm
o
o
t
h
c
ont
r
o
l of
t
o
rq
ue
.
(a)
(b)
Fi
gu
re
3.
d
a
n
d
q a
x
es
st
a
t
or
fl
uxe
s
of S
V
M –
DTC
base
d
I
M
dri
v
e
wi
t
h
st
ep
c
h
an
ge i
n
l
o
adt
o
rq
ue at
0.
4s
(
a
)
Act
u
al
d
& q
a
x
es
st
at
o
r
fl
ux
r
e
s
p
onse
;
(
b
) C
i
r
c
ul
ar t
r
aj
e
c
t
or
y of
sta
t
or
fl
u
x
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
3
,
S
e
p
t
e
m
b
e
r 20
20
:
116
5
– 11
7
4
1
170
F
i
gu
re
4. S
p
ee
d re
sp
onse
of S
V
M
–
D
T
C
b
a
se
d IM
d
r
i
v
e
w
i
t
h
st
ep c
h
a
nge
i
n
l
o
a
d
t
o
r
q
ue a
t
0.4s.
The
spe
e
d
res
p
ons
e
of S
V
M-DTC
base
d
IM
dri
v
e
wit
h
ste
p
c
h
a
nge
i
n
l
o
ad t
o
rq
ue,
a
p
pl
i
e
d at
0.4s
is
sh
own
in
Figur
e
4
.
A
s
and
w
h
en in
cr
ea
se in
lo
ad t
o
rq
u
e
is app
l
ied
,
t
h
e
sp
e
e
d o
f
th
e dr
iv
e p
r
op
ort
i
o
n
a
tel
y
re
duc
e
d
sinc
e
t
h
e
dri
v
e
i
s
o
p
e
rat
e
d i
n
t
o
rq
u
e
c
ont
rol
mod
e
. T
h
e
t
o
rq
ue
re
sp
onse
of
S
V
M
-
DTC
base
d
IM
d
r
i
v
e
w
h
en
app
l
y
i
ng
a
ste
p
ch
ang
e
i
n
l
o
a
d
t
o
rqu
e
is
sh
own
in
Fi
g
u
re
5
.
I
t
is
o
b
se
rv
e
d
th
at t
h
e
el
ec
tr
omag
n
e
tic
to
rq
u
e
t
r
a
c
k
s th
e r
e
f
e
re
n
c
e
tor
q
u
e
imme
d
i
a
t
e
l
y
a
f
te
ra
pp
ly
in
g l
o
a
d
torq
u
e
.
F
i
gure
5.
T
o
r
q
ue resp
o
n
se of
SV
M
– DTC
b
a
sed I
M
dri
v
e
wit
h
st
e
p
c
h
a
n
g
e
i
n
l
o
a
d
t
o
rq
ue at
0.4s.
4.
D
R
I
V
E
PERFO
R
MANC
E WITH VARYIN
G
STA
T
OR
FL
U
X
C
O
N
T
R
O
LLER BA
ND
WID
T
H
The
st
ead
y
st
a
t
e
perfo
rma
n
ce
of
th
e
d
r
i
v
e
is
st
udi
e
d
b
y
o
b
s
ervi
ng
t
h
e
ri
p
p
l
e
c
ont
e
n
t
in
st
at
or
fl
ux
,
st
ato
r
c
u
rr
en
t,
e
l
e
c
t
r
om
a
g
n
e
t
i
c to
rqu
e
r
e
spo
n
s
e
s
and
c
i
r
c
u
l
ar tr
aj
ec
tor
y
of sta
t
or
fl
ux vec
t
o
r
for d
i
ff
er
en
t
val
u
es
of hy
st
ere
s
is fl
ux co
nt
rol
l
e
r
ban
d
w
i
d
t
h
.
4
.
1
.
Ca
se i)
S
t
a
t
o
r
f
l
ux
contro
ller
ban
d
widt
h to
lera
n
ce:
0.
1
The
re
fe
re
nc
e
fl
u
x
i
s
se
t
a
t
0.9
we
be
r. The
u
ppe
r
l
i
mi
t
is se
t
at
0.
9+0
.
1
=
1
we
b
e
r,
a
n
d l
o
we
r
l
i
mi
t
is
set
a
t
-1 we
be
r. T
h
e
n
t
h
e re
spo
n
ses o
f
d
and q a
x
es st
at
or c
u
rrent
s, st
at
or fl
ux
, el
ect
ro
ma
gne
ti
c
t
o
rque
and
ci
rc
ul
ar
l
o
cus
o
f
sta
t
or
fl
ux
a
r
e
obse
r
ve
d
a
n
d a
r
e
s
h
o
w
n
i
n
F
i
g
u
r
e
6,
F
i
g
u
re
7,
F
i
gu
re
8,
Fi
gu
re
9
,
a
nd
Fi
gu
re
1
0
.
F
i
gu
re
6.
d
an
d
q
a
x
e
s
st
at
or
c
u
rre
n
ts
wit
h
Fl
ux
hyst
e
resi
sc
o
n
tr
oll
e
r
ba
ndw
i
d
t
h
0.1
0
0.
1
0.
2
0.
3
0.
4
0.5
0.6
0.
7
0.
8
0.
9
1
0
50
10
0
15
0
20
0
Ti
me
(
s
)
S
p
eed
(
r
p
s
)
Mot
o
r S
p
e
e
d
Loa
d
T
o
r
q
u
e
a
p
pl
i
e
d
a
t
0.
4s
Z
oom
por
tion
0.
3s
to 0.
5s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-100
0
100
200
T
o
rq
ue
(Nm
)
E
l
e
c
t
r
om
a
g
ne
t
i
c
T
o
rque
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
10
20
Time
(
s
)
T
o
r
que
(
N
m
)
sp
e
e
d
Z
o
o
m
p
o
r
t
i
o
n
(
0
.3
s
t
o
0
.
5
s
)
L
o
a
d
T
o
rque
a
ppl
i
e
d
a
t
0.4s
0.
3
0.
35
0.4
0.
4
5
0.5
-6
0
-4
0
-2
0
0
20
40
60
80
Ti
m
e
(
s
)
Id
q
C
u
rre
n
t
(
A
)
q
ax
i
s
s
t
ato
r
cu
r
r
e
n
t
d
ax
i
s
s
t
ato
r
c
u
r
r
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Perf
orma
nc
e
anal
y
s
i
s
o
n
dire
ct
t
o
rq
ue c
o
ntrol
l
e
d i
n
d
u
ct
i
o
n
m
o
t
o
r
dri
ve
wi
t
h
v
a
ry
in
g
…
(S.
Al
l
i
rani
)
1
171
F
i
gu
re
7.
d
an
d
q a
x
e
s
st
at
or fl
uxe
s wi
t
h
Fl
u
x
hyst
e
resi
sco
n
tr
oll
e
r
ba
n
d
w
i
dt
h
0.
1
Fi
gu
re
8. To
rq
ue resp
o
n
se w
i
t
h
F
l
u
x
h
y
s
t
e
res
i
sc
ontr
o
ll
er ba
n
d
w
i
dt
h
0.
1
Fig
u
re
9
.
Lo
c
u
s
of
st
at
or f
l
ux
w
i
th
f
l
u
x
hy
ste
r
esi
s
c
o
n
t
ro
ll
er
b
a
ndw
i
d
th
0.
1
F
r
o
m
t
h
ese
res
p
o
n
se
s
,
it
is ob
serve
d
t
h
at
th
e
ri
p
p
l
e
co
nt
ent
i
n
sta
t
or
c
u
rre
n
t
s
and flu
x
e
s
a
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nc
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n
t
o
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i
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re 1
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, a
n
d F
i
gu
re
13
. T
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e st
at
or
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x
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s
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l
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w
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x
a
go
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n
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t
e
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r
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ul
ar pat
h
.
4.2. C
a
se i
i
) S
t
ator
fl
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er ba
n
d
w
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d
th
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a
nce
:
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re
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x
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be
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we
be
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d
lo
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r
li
mit
is
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t
-
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.91
w
e
b
er.
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t
h
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sp
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cur
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om t
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t
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r
q
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e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
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-8
6
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I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
3
,
S
e
p
t
e
m
b
e
r 20
20
:
116
5
– 11
7
4
1
172
F
i
gu
re
10
. Ci
rc
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r
l
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cus
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f
st
at
or
fl
u
x
wi
t
h
F
l
ux
hy
st
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esi
s
c
ont
rol
l
e
r
4
.
3
.
Ca
se iii)
Stat
o
r
f
l
u
x
co
nt
ro
ller b
a
ndw
id
th
to
lera
nce:
0.
001
The
re
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rence
fl
u
x
i
s
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t
at
0
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9
webe
r.
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up
pe
r
li
mit
i
s
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t
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0
0
1
=
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1
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mit
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en th
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re
sponse
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of
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1
2
. T
h
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1
Tim
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s
f
l
ux
q a
x
i
s
fl
ux
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Perf
orma
nc
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anal
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s
i
s
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n
dire
ct
t
o
rq
ue c
o
ntrol
l
e
d i
n
d
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i
o
n
m
o
t
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r
dri
ve
wi
t
h
v
a
ry
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g
…
(S.
Al
l
i
rani
)
1
173
Fi
gu
re
1
3
.
El
ec
t
r
o
m
a
gne
ti
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t
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res
p
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se
wi
th Fl
ux
h
y
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s
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1
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gu
re
1
4
. Ci
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t
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ux
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s
is c
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b
a
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th
s H
ψ
=
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1; H
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=
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n
d H
ψ
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i
t
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b
se
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d
t
h
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t
h
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dy sta
t
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pe
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ma
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t
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ter
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is f
oun
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w
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h
H
ψ
=
0
.
001
.
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is ob
ser
v
ed
th
a
t
t
h
e
ri
ppl
e c
o
nt
ent
i
n
t
o
rq
ue
re
sponse
i
s
si
g
n
i
f
ic
ant
l
y
re
d
u
c
e
d
whe
n
t
h
e
fl
u
x
ba
nd i
s
adj
u
s
t
e
d
[
26].
5.
CON
C
L
U
S
I
ONS
In
t
h
is pa
per
,
SV
M ba
sed di
re
ct
t
o
rqu
e
co
nt
rol
o
f
IM d
r
i
v
e is re
-ex
a
mi
ned f
o
r
i
t
s merit
s
. T
h
e
conc
e
p
t
of s
w
i
t
c
h
ing
t
a
ble
a
n
d s
w
i
t
c
h
i
ng
vo
l
t
age
vect
or se
le
ct
ion
b
a
sed
o
n
S
V
M
te
c
hni
que
i
s
revi
e
w
e
d
a
n
d
p
r
es
e
n
t
e
d al
ong
w
i
th
t
echn
i
qu
e
s
fo
r sta
t
o
r
f
l
u
x
an
d
e
l
e
c
t
r
om
agn
e
ti
c tor
que e
s
tim
a
ti
o
n
s
.
Th
e
S
V
M-DTC
b
a
sed
IM
d
r
i
v
e i
s
mode
ll
e
d
a
n
d
simul
a
t
e
d i
n
MA
TL
AB/
S
IMU
L
IN
K e
n
viro
nme
n
t a
nd t
h
e
d
r
i
v
e
perfo
rma
n
ce
i
s
studi
e
d
usi
n
g
si
mul
a
t
i
o
n
res
u
l
t
s.
T
h
e
driv
e
pe
rfo
r
ma
nc
e i
s
fu
rt
he
r st
udi
ed
for
para
met
e
r
varia
t
i
o
ns.
In t
h
is
pape
r, t
h
e
h
y
s
t
ere
s
is c
ont
rol
l
e
r ba
n
d
wi
dt
h
i
s
va
ri
ed i
n
s
t
eps a
n
d
t
h
e c
o
r
r
es
po
n
d
i
n
g
dri
v
e
perfo
rma
n
ce
is
studi
e
d
i
n
M
A
TL
AB
/S
IMU
L
IN
K
e
n
vi
ron
m
e
n
t
.
It
i
s
o
b
se
rve
d
t
h
at
by
p
r
o
p
e
r
ly c
h
oosi
n
g t
h
e c
o
nt
rol
l
e
r
ban
d
w
i
d
t
h
,
t
h
e
t
o
rq
ue ri
pple
s
ca
n be mi
ni
mi
z
e
d.
RE
FERE
NC
E
S
[1]
Takah
a
sh
i, I
an
d
N
ogu
chi
,
T, "A
new
qui
ck r
e
s
p
on
se an
d
h
i
g
h
e
ffici
ency
co
n
t
rol
strategy
of
an
ind
u
ctio
n
mo
tor,
"
IE
E
E
Tran
sa
c
t
i
ons o
n
In
du
stry
Ap
pl
ic
a
t
i
o
ns
,
vo
l.
1A-2
2,
no
.
5,
pp
.
8
2
0
-
8
2
7
,
1
9
8
6
.
[2]
Depen
b
ro
ck
, M
,
"
D
irect S
e
lf
Co
ntrol (DS
C
) of
inv
e
rt
er f
e
d in
du
ction
mach
in
e,"
IEE
E
Tran
sac
t
io
ns on
P
o
we
r
Electro
nics
,
vol
.
3
,
n
o
.
4
,
p
p
.
42
0
-
42
9,
19
88
.
[3]
Habetler,
TG
.P
a
s
torelli
,
M,
an
d
To
lb
e
r
t,
L. M
,
"D
irect torq
ue
c
o
ntrol
o
f
ind
u
c
t
ion
mach
in
es u
s
ing
space v
e
c
t
or
modu
lat
i
o
n
,"
IEEE
Tra
n
sac
t
io
ns on
Ind
u
st
ry A
ppli
c
atio
n
s
, v
o
l
.
2
8
,
n
o
.
5
,
pp
.
10
45
-105
3,
19
92
.
[4]
Kazmierkows
k
i, M.
P and Kaspr
o
wicz, A.
B
,
"I
mp
roved
direc
t
t
o
rq
ue and
flux v
e
ctor
con
t
ro
l of
P
W
M
in
verter f
e
d
in
ductio
n
mo
to
r
drives,
"
I
E
EE
T
r
a
n
s
a
ct
ion
s
on
In
du
strial El
ec
tr
onics
, v
o
l
.
4
2
,
n
o
.
4,
pp.
34
4-3
50,
19
95
.
[5]
Al
li
ra
ni,
S a
n
d
J
a
g
a
n
n
at
ha
n,
V,
"Mod
e
l
in
g a
n
d
Sim
u
la
ti
on
of
H
i
g
h
Performance D
i
rect
T
o
rque C
o
nt
roll
ed
Induct
i
on
Mo
to
r Dri
v
e
,
"
Journal
of
El
ectrical
Systems
(JE
S
)
, v
o
l. 9,
n
o
. 3, pp.
35
5
-
36
6
,
Se
p
2
0
1
3
.
[6]
Al
li
ra
ni,
S a
nd
Ja
g
a
nn
ath
a
n, V,
"
D
ire
c
t To
rque Con
t
ro
l
T
e
c
h
n
i
q
u
e
i
n
Ind
u
c
t
i
on
M
o
to
r Dri
v
e
s
–
A
Re
v
i
e
w
,"
Jour
na
l
of T
h
eo
retical
a
n
d
App
lied
In
fo
rma
tion
T
echn
o
l
o
g
y
(J
AT
IT
)
,
v
o
l.
6
0
,
no.
3
,
pp.
4
52-4
7
2
,
Fe
b 20
14.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-20
0
20
40
60
80
100
120
140
Ti
me
(
s
)
Tor
que
(
N
m
)
E
l
e
c
t
r
om
a
g
ne
t
i
c
T
o
rque
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
, Vol.
11
,
No
.
3
,
S
e
p
t
e
m
b
e
r 20
20
:
116
5
– 11
7
4
1
174
[7]
Hels
in
ki,
"
D
irec
t to
rque
con
t
rol
— th
e wo
rld
’
s mo
st
ad
v
a
nc
ed
A
C
drive
te
ch¬n
olog
y,"
ABB
F
i
n
l
an
d, T
e
ch.G
uid
e
1
,
199
6.
[8]
Am
b
r
oz
i
c
,
V. Buj
a
,
G.
S,
a
n
d Me
ni
s,
R,
"
B
a
nd co
nstra
i
n
e
d
t
e
c
h
n
i
qu
e
fo
r di
re
c
t
to
rq
ue
c
o
ntro
l o
f
i
n
d
u
c
t
i
o
n
m
o
to
r,"
IE
E
E
Tran
sa
c
t
i
ons o
n
i
n
d
u
st
ri
al El
ec
tron
i
c
s
, vo
l. 51
, no
.
l
.
4
,
pp.
77
6-7
8
4
,
2
0
0
4
.
[9]
Id
ri
s,
N.
R.N.
Hal
i
m
,
A
a
nd Ya
ti
m
,
M, "
D
i
r
ec
t
to
rque
c
o
nt
rol
of i
n
du
cti
on
m
a
c
h
i
n
e
s
wit
h
c
o
n
s
t
a
nt swi
t
c
h
ing
fre
q
u
en
cy
and r
e
du
ced
torq
u
e
rip
p
le,"
IEEE Tr
ansact
ions
on Industrial
E
l
ect
r
oni
cs
,
vo
l.
51, n
o
.
4, p
p
.
75
8-7
67,
200
4.
[10]
Kang
,
J.K
and
S
u
l,
S
.
K,
"
N
ew
direct torq
ue
co
ntrol of
i
n
du
ct
ion
motor for m
i
ni
mum torqu
e
rippl
e and
cons
t
a
n
t
swit
c
hi
ng
fre
q
u
e
n
c
y,
"
I
E
EE T
r
an
sactio
ns
on
Ind
u
s
tr
y Ap
pl
icat
io
ns
,
vo
l.
3
5
,
no.
5,
p
p
. 1
0
7
6
-1
0
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[11]
Ryu,
J.
H.
Lee
,
K
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W
and
Le
e,
J
.
S
,
"A
un
ifi
e
d flux
and
to
rqu
e
con
t
r
o
l m
e
tho
d
fo
r D
T
C bas
e
d
ind
u
c
tion
mo
to
r
driv
es,
"
I
EEE
T
r
a
n
s
a
ct
io
n
s
on Po
w
e
r
E
l
e
c
tr
on
ics
,
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l.
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,
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,
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p
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4
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,
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S
udd
hir H, K
o
d
a
d
S
F
,
and
Su
rv
as
e, B, "Imp
rov
e
d fu
zzy
lo
gic
b
a
se
d
DT
C o
f
indu
c
t
i
o
n
m
a
c
h
ine fo
r wide
ra
ng
e
o
f
sp
e
e
d
c
o
n
t
rol usin
g AI ba
se
d
c
o
ntrol
l
e
r
,"
Jo
ur
na
l o
f
E
l
ec
trical Sys
t
ems
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l. 1
2
,
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2,
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0
1
-
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0
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6
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Veng
atas
hwara
Rao V
.
M
,
Chan
dra S
e
kh
ar G
a
n
d O
bulesh
Y.P
,
"
P
erformanc
e
C
o
mp
aris
on
o
f
P
I
an
d
F
u
zzy
Log
i
c
Co
n
t
ro
ll
e
r
s
of DT
C fo
r T
o
rq
ue
ri
pp
le
re
du
c
t
io
n,
"
I
n
te
rn
at
io
nal
J
o
urna
l
o
f
Eng
i
n
e
e
r
in
g
Re
searc
h
an
d Ad
v
a
n
c
e
d
T
e
ch
no
lo
gy
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v
o
l. 4, no
. 01
,
p
p
. 1-18
, Ja
n
2
0
1
8
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[14]
Al
li
ra
ni, S
a
nd Ja
g
a
nn
a
t
h
a
n V,
"
T
o
r
q
u
e
rip
p
l
e m
i
n
i
m
i
z
a
t
i
o
n
DTC
ba
se
d i
n
d
u
c
t
i
o
n
m
o
t
o
r
dri
v
e u
s
i
ng
fuzz
y
lo
g
i
c
techn
i
q
u
e,"
In
tern
atio
na
l
Jo
ur
nal
o
f
Co
mpu
t
er
Ap
plica
t
io
ns
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5
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1
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Ba
oh
ua
, L.
Jia
n
h
u
a
,
Y
a
n
d
We
i
guo
, L, "
R
e
s
ea
rc
h
on
sp
a
c
e
ve
ct
or
m
o
du
la
ti
on
m
e
thod
for im
pro
v
i
n
g
th
e
t
o
rqu
e
r
i
p
p
l
e
of di
rect t
o
rqu
e
cont
rol
,
"
In
te
rnati
o
n
a
l
Conf
e
r
e
n
ce
on
c
o
mpu
t
e
r
d
e
sig
n
a
n
d
Ap
p
l
ica
t
i
o
ns
(IC
CDA
20
10
)
,
p
p
.
V3-5
02
–V3
-
5
06,
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10
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S
un,
D
,
"S
lid
i
n
g
mo
de
dir
e
c
t
t
o
rq
ue
control
fo
r ind
u
c
t
ion
mo
to
r w
i
th
ro
bu
st s
t
ator
flux
o
b
s
e
r
v
er,"
In
ter
natio
na
l
Conferen
c
e
on
I
n
tell
igen
t
Co
mp
utation
T
e
chn
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lo
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.
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e
rk
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sk
i, M
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P
an
d
Blaab
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F
,
"
C
o
n
tr
o
ller d
e
sign
fo
r
d
i
r
ect to
rqu
e
co
ntro
lled
sp
ac
e
v
ect
or
modu
lat
e
d (D
TC
- S
V
M
)
in
du
c
t
io
n
moto
r
driv
es
,
"
IE
EE,
ISIE
,
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95
1-9
5
6
,
20
05
.
[18]
Be
ert
e
n, J.Verve
c
k
k
en
,
J
an
d Dris
en, J,
"
P
redictiv
e
d
i
r
e
ct
t
o
rque
cont
rol
for
fl
ux
an
d
t
o
rq
ue
ri
pple re
du
c
tio
n,
"
IE
E
E
T
r
an
sa
ctions
o
n
In
du
str
i
a
l
Elec
tro
n
ic
s
,
20
09.
[19]
Lascu
,
C.Bolde
a
,
I and
Bl
aab
jerg
, F,
"
A
mod
i
fied
d
i
re
ct
to
r
q
u
e
co
n
t
r
o
l f
o
r
in
duct
i
o
n
moto
r
s
e
ns
or
l
e
ss
d
r
iv
e,"
IE
E
E
T
r
an
sa
ctions
o
n
In
du
str
y
Appl
ica
t
ions
,
vol. 36
, no. 1,
p
p
. 1
2
2
-
13
0
,
2
0
0
0
.
[20]
Dra
o
ui
Ab
d
e
lg
h
a
n
i
a
nd All
a
ouaBo
um
o
d
i
e
ne
,
"
D
i
r
e
c
t
to
rqu
e
c
o
n
t
ro
l o
f
two in
du
ct
io
n
m
o
t
o
rs usi
n
g
th
e nin
e
swi
t
ch
i
n
verter,
"
Inte
rnat
io
na
l J
o
urna
l of
P
o
we
r E
l
e
c
tron
ic
s a
n
d
driv
e sy
st
e
m
(IJ
PE
DS)
,
v
o
l.
9,
no.
4,
pp.
1
5
5
2
-
15
64,
De
c
201
8.
[21]
Nou
r
M
ohamed
,
Tedjin
iH
am
z
a
an
d Gas
b
ao
u
i
Br
ah
im
, "
N
ov
e
l
DTC
in
duct
i
o
n
m
achin
e d
r
ive
im
p
r
ovemen
t
us
in
g
controlled rect
i
f
i
e
r
for D
C
voltage
tuning
,
"
I
n
ter
n
at
io
na
l
Jou
r
n
a
l
o
f
Po
w
e
r
E
l
ec
t
r
o
n
i
c
s an
d Dr
ive
Sys
t
ems
, vo
l
.
1
0
,
n
o
,
0
3
,
pp.
1
2
23-12
28
,
2
0
13.
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Am
i
r
Ya
si
m
,
Sai
d
W
a
hsh a
n
d
M. Ba
d
r
, "Cu
k
o
o
Se
a
r
c
h
ba
se
d
DTC of PMSM,
"
In
tern
atio
na
l Jour
na
l
of
Pow
e
r
Electro
nics a
n
d
Dr
ive S
y
stem
,
vol.
9
,
n
o
.
03,
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p
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6-1
1
1
5
,
Se
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[23]
Bi
mal. K
.
Bose,
M
o
d
e
rn Po
we
r
El
ec
tron
ic
s an
d
A
C
- Dri
v
e
s
, PHI L
e
a
m
in
g
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r
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ate
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ite
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02.
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Bo
l
d
ea,
I
& Nasar,
SA, ‘
Elec
t
ric Drives
’,
S
e
cond
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l
or &
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ran
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is
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06
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L
a
zi
m
,
M
.
T
.
Mut
h
a
n
na, J.
M.
Alk-Kh
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s
h
a
li
,
Isa,
A a
nd
Al
-Sha
wi, "Sp
a
c
e
v
e
ct
o
r
m
o
dul
a
t
i
on di
re
c
t
t
o
rq
ue spe
e
d
control
of
ind
u
ct
io
n mo
to
r,"
EL
SEVIE
R
,
Pro
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i
a
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mpu
t
er
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nce
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2
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Kris
hnan, R,
Ele
c
tr
ic
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tor
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Mod
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t
r
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l
, P
r
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tic
e
-H
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di
a
,
20
02
.
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