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
)
Vol.
10, No.
1, Mar
ch 2019,
pp.
27~40
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v10
.
i
1.pp
2
7
-4
0
27
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Dou
b
le star induction mach
in
e usi
n
g nonli
n
ear i
n
tegral
bac
k
stepping c
ontrol
A
b
da
l
l
a
h
A
b
d
e
n
1
,
A. Bouch
et
ta
2
, O.
B
o
u
g
hazi
3
,
A.
Bagh
d
a
d
i
4
, I.
K
. Bousserhan
e
5
1
,
2,
3,
5
T
A
HRI
Mo
h
a
mmed Un
ive
r
si
t
y
,
Bec
h
ar, Alg
e
r
i
a
4
Djillali
Liabes
U
ni
vers
i
t
y,
S
i
d
i-
bel-Abbes,
A
lge
r
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
pr 11,
2
0
1
8
Re
vise
d S
e
p 24,
201
8
Ac
ce
p
t
ed
Oc
t
2
3
,
2
018
Th
is
p
a
p
er
p
r
e
se
nt
s
a
no
nl
in
ear
I
nt
egral
back
st
eppi
ng
c
o
n
tro
l
a
ppro
ach
b
ased
on
f
iel
d
-ori
ent
e
d
co
ntro
l
t
echniq
u
e,
a
p
p
li
ed
t
o
a
D
o
u
b
le
S
tar
I
nd
uct
i
on
M
achi
n
e
‘DS
I
M
’
f
eed
b
y
two
p
o
wer
vol
tag
e
s
o
u
rces.
W
e
p
resent
t
h
is
tech
ni
que
o
f
int
e
gral
b
ack
st
e
p
pi
ng
b
y
u
s
i
n
g
redu
c
e
d
an
d
co
m
p
let
e
m
a
th
ematical
m
odel
.
T
h
e
o
b
j
ecti
v
e
is
t
o
im
p
r
o
v
e
t
h
e
rob
u
stn
e
ss
o
f
m
achin
e
un
der
int
e
rnal
p
aram
et
er
v
ari
a
tio
n
w
i
th
n
o
n
l
i
n
ear
I
nt
egral
back
st
eppi
ng
con
t
ro
l.
T
he
r
o
b
us
tn
ess
t
e
st
r
esu
lts
o
b
t
a
i
ned
b
y
s
im
ulati
on
pro
ve
t
h
e
ef
f
ecti
v
enes
s of con
tro
l
w
it
h
u
s
i
n
g
com
p
le
te
m
o
d
el
o
f
DS
IM.
K
eyw
ord
s
:
D
u
al
s
ta
r in
d
u
c
t
i
on
F
i
eld
or
ien
t
e
d
c
on
t
r
o
l
(
F
O
C)
Inte
gra
l
bac
kst
e
ppi
ng
l
y
apu
nov
f
un
c
t
i
on
Mac
h
i
n
e
(DSIM)
Nonlinear
control
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
bda
lla
h
A
bde
n,
Con
t
ro
l a
n
a
l
ys
is
a
nd o
p
t
i
miz
a
t
i
o
n
o
f
Ele
c
t
ro-e
nerg
y sys
t
em
s lab
ora
t
ory,
Tahri
Mo
ha
mm
ed
U
niversi
t
y,
Bec
har,
A
lger
i
a
.
Em
ail:
abde
na
b
d
0
8
@
g
m
a
i
l
.c
om
1.
I
N
TR
OD
U
C
TI
O
N
F
o
r
ma
ny
ye
ars
D
S
IM
h
a
v
e
been
u
se
d
in
m
any
ap
p
lic
at
i
ons,
for
t
h
e
i
r
adva
n
t
age
s
,
am
ong
o
t
her
s
:
M
i
n
i
m
i
se
t
he e
lec
t
r
o
m
a
g
n
e
t
i
c
t
orque
an
d
t
he
rot
or losses,
u
ses
a p
o
w
e
r e
l
e
c
tro
n
ics
com
p
one
n
t
w
hic
h
a
l
l
ow
s a
hi
ghe
r
com
m
u
t
a
ti
on
fre
q
uen
c
y
a
n
d
t
h
e
im
pro
v
em
ent
of
r
e
l
ia
bil
ity
b
y
offeri
ng
the
p
o
ss
ib
i
l
i
t
y
o
f
o
p
era
tin
g
corr
ectl
y
i
n de
grade
d
re
g
ime
s
(one
o
r
m
o
re
o
p
e
n
ph
a
s
es
)
[
1
]-
[
3
]
. A
lot o
f
rese
a
rc
h
has appr
oa
che
d
the
c
o
n
tro
l
of
t
h
e
D
S
I
M
for
m
o
re
t
han
20
yea
r
s,
w
hil
e
s
eeki
n
g
to
h
ave
a
ve
r
y
g
o
o
d
rej
ecti
o
n
o
f
d
i
s
rupt
i
o
n
a
n
d
good
rob
u
st
n
e
ss i
n
t
he
f
ac
e of c
ha
n
g
i
ng
para
me
ters.
I
n
t
his
pa
per
w
e
p
rop
o
se
i
n
th
i
s
a
rt
i
c
l
e
a
B
ac
kste
p
p
i
n
g
con
t
ro
l
u
si
n
g
t
he
c
om
p
l
e
t
e
m
a
them
at
ica
l
mode
l
of
t
he
m
achine,
w
e
w
ill
the
n
m
a
k
e
a
com
p
aris
on
of
t
he
se
p
erfo
rma
n
ce
s
wit
h
t
h
e
B
ack
st
epp
i
ng
c
o
n
t
r
ol
us
i
n
g
re
duc
ed
m
ode
l
.
w
e
use
t
h
is
t
e
c
h
n
i
que
t
o
des
i
g
n
a
r
o
bus
t
c
o
n
tr
ol
b
a
s
e
d
o
n
the
pri
n
c
i
ple
of
f
ie
ld
o
r
i
ente
d
con
t
ro
l,
t
his
ne
w
versio
n
of
b
acks
t
ep
p
i
n
g
w
ith
i
nte
g
ral
a
c
t
ion
s
o
l
v
e
s
t
h
e
p
r
o
b
l
e
m
o
f
c
o
n
s
t
a
n
t
s
t
a
t
i
c
e
r
r
o
r
a
n
d
sens
iti
vi
ty
t
o
N
o
ise
ap
pea
r
e
d
i
n
the
c
l
ass
i
c
ve
rsion
o
f
b
acks
t
e
ppi
ng
.
Th
e
ef
f
ecti
v
en
ess
o
f
t
hi
s
p
r
op
o
s
e
d
con
t
ro
l
s
t
r
u
c
t
u
r
e
is
v
er
if
i
e
d
by
sim
u
la
tio
n
us
in
g
t
h
e
re
duc
e
d
a
n
d
c
om
plete
m
ode
l
of
D
S
I
M,
w
ith
t
h
i
s
pro
pose
d
c
o
n
tr
ol
,
the
l
o
a
d
d
is
tur
b
ance
re
j
ec
t
i
o
n
c
apa
b
i
l
ity i
s
hi
gh
l
y
im
p
ro
ved.
2.
DESCRIPTIO
N
O
F
TH
E
D
S
I
M
Th
is m
ac
h
i
n
e
i
s ba
se
d o
n
the
pri
nci
p
le of a
d
o
u
b
l
e
s
t
a
t
ors
di
sp
lace
d
b
y
γ
=
3
0°.
T
h
e
s
t
at
ors a
r
e si
m
ila
r
t
o
t
h
e
s
t
a
t
o
r
o
f
a
s
i
m
pl
e
i
nduc
t
i
o
n
ma
chi
n
e
a
n
d
fed
w
i
t
h
0
3
p
h
a
se
a
l
t
er
na
tin
g
c
u
rre
nt
a
n
d
p
ro
vi
de
a
r
o
t
a
tin
g
fl
u
x
,
eac
h star is com
p
osed b
y
th
r
ee
i
d
en
t
i
c
a
l win
d
i
n
gs wi
t
h ax
e
s
s
paced
by
α=
γ
=
30 ° [
1
]-[
3]
,
[
10]-[12
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
27
–
40
28
3.
M
O
DELL
IN
G OF TH
E
D
SIM IN (
D-Q)
R
E
F
ERENC
E
D
S
I
M
w
it
h
t
h
e
dis
t
r
i
bu
t
i
o
n
o
f
its
w
i
n
din
g
s
and i
t
s
ow
n
ge
o
m
e
t
r
y
i
s
ve
r
y
c
om
pl
e
x
t
o
le
n
d
itse
l
f
to
a
n
a
n
a
l
y
s
i
s
t
a
k
i
n
g
i
n
t
o
a
c
c
o
u
n
t
i
t
s
e
x
a
c
t
c
o
n
f
i
g
u
r
a
t
i
o
n
,
i
t
i
s
n
e
c
e
s
sa
r
y
t
o
ad
op
t
c
e
r
t
a
i
n
s
i
m
p
li
fy
i
ng
ass
u
mpt
i
o
n
s
.
In
a
d
d
it
ion
to
t
h
e
h
ypo
th
e
s
es
o
f
th
e
g
e
n
e
ral
i
z
ed
m
a
c
h
in
e
,
i
t
wi
ll
be
a
ss
u
m
e
d
t
ha
t
t
h
e
t
w
o
sta
t
or
t
hr
ee-
p
h
a
se
wi
nd
ing
s
a
re
b
a
l
a
n
ced
a
nd
i
den
t
i
cal
(
t
h
e
si
x
p
h
a
se
s
t
h
ere
f
ore
h
ave
the
sa
m
e
e
lec
t
rical
c
ha
rac
t
e
r
is
tic
s)
[
1]-[3]
,
[11
-
12
].
4.
DIRECT FIEL
D
O
R
I
ENTE
D
CONT
R
O
L FOR
DSIM
The
pri
n
c
i
p
l
e
of
f
i
e
l
d
O
rie
n
t
e
d
C
ontr
o
l
st
r
a
teg
y
i
s
to
e
l
i
m
ina
t
e
the
c
o
u
p
l
i
ng
pr
o
b
lem
betw
ee
n
t
h
e
tw
o
d
i
r
e
c
t
a
xe
s
(
d
)
a
n
d
q
u
a
d
r
a
tur
e
(
q)
,
w
h
ic
h
ma
kes
it
p
os
si
ble
t
o
a
s
sim
ila
t
e
t
he
a
sy
nc
hr
on
o
u
s
m
a
c
h
ine
t
o
a
n
in
de
pe
n
d
e
n
t
l
y
exci
te
d
D
C
m
a
c
hi
ne
a
s
i
t
s
ma
i
n
a
d
v
an
ta
g
e
t
o
be
e
a
sily
c
ont
ro
ll
abl
e
.
In
d
eed
,
t
h
e
ind
u
c
to
r
c
u
r
r
e
nt
i
s
a
f
l
ux
ge
ner
a
tor
w
h
ile
t
he
a
r
m
atur
e
c
u
r
r
e
nt
i
s
a
tor
qu
e
g
e
nera
t
o
r.
T
h
e
F
OC
c
on
si
s
t
s
in
m
a
k
i
n
g
φ
qr
=
0
w
h
i
l
e
t
h
e
r
otor
d
ir
e
c
t
f
l
ux
φ
dr
conver
g
e
s
t
o
t
h
e
r
e
f
e
r
e
nce
φ
r
*
[3
]-[
5
]
.
4.
1.
Co
mplete mo
d
el
o
f D
S
IM
The
Com
p
le
te
m
athem
a
t
i
cal
m
odel
o
f
t
he
D
ou
b
l
e
s
t
a
r
i
ndu
c
tio
n
mo
t
o
r
can
b
e
e
x
p
r
es
sed
i
n
t
h
e
(
d
-
q)
syn
c
hr
o
nou
s
r
o
ta
t
i
ng
fr
a
m
e
by
t
h
e
f
o
ll
ow
i
ng
no
n
line
a
r
equa
t
i
o
n
s
,
T
a
k
i
ng
in
to
acc
o
u
n
t
t
hat
the
r
o
t
o
r
of
t
he
DSIM is sh
o
r
t
-
circuited
[1
]-[3].
(1
)
4.
2.
Red
u
ced mo
d
el
By
a
p
p
l
y
i
ng
t
h
e
F
i
e
l
d
O
r
ie
nt
e
d
C
on
tr
ol
p
r
i
n
c
i
p
l
e
t
o
the
c
o
m
p
l
e
t
e
m
a
t
h
e
m
atica
l
m
ode
l
(
1
)
,
w
e
put
(φ
qr
=0
a
nd
φ
dr
=
φ
r
)
and
the
sy
st
e
m
o
f
equa
t
i
on
i
n
(
d,
q)
f
or
t
he
D
S
I
M
in
r
educe
d
m
ode
l
b
e
c
o
me
[
1]
-
[
3]
:
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
D
o
u
b
l
e
s
t
ar
i
n
duc
t
i
o
n
m
a
ch
i
n
e usin
g non
l
i
n
ea
r
in
te
gra
l
b
a
ck
s
t
e
p
p
i
n
g
co
nt
ro
l (
A
bd
a
l
l
a
h Abde
n)
29
(
2
)
with
:
)
(
r
s
gl
5.
BACKSTEPP
I
NG CONTROL
The
ba
sic
pr
in
c
i
p
l
e
of
b
a
c
k
s
t
e
pp
i
ng
c
o
nt
r
o
l
is
t
o
m
a
ke
c
l
o
sed
l
o
o
p
s
y
s
t
e
m
s
e
quiva
le
nt
t
o
fir
s
t-
or
de
r
su
bsy
s
t
e
ms
i
n
c
a
s
ca
d
e
t
h
a
t
a
r
e
Ly
ap
uno
v
st
a
b
i
l
ity
,
Th
i
s
g
i
v
es
e
ns
ur
e
s
r
obus
t
n
ess
a
nd
as
ympt
o
t
ic
g
l
oba
l
sta
b
i
l
i
t
y
[
2]
,
[1
0]
,
[
11]
.
O
u
r
ob
jec
tive
is
t
o
c
o
nt
r
o
l
t
h
e
fl
u
x
a
n
d
s
pe
ed
v
ar
i
a
b
l
es,
s
o
w
e
c
h
o
se
a
s
in
term
edia
te
v
ariab
l
es,
th
e
sta
t
or
c
ur
r
e
nt
s
(
i
ds1
,
i
qs1
,
i
ds2
,
i
qs
2
)
,
t
o
le
t
t
h
em
f
o
l
l
o
w
t
h
e
i
r
r
e
fe
r
e
nc
es
v
a
l
ue
s
def
i
ne
d
by
t
h
e
“
v
ir
tu
a
l
c
o
n
t
r
o
l
s
”
,
f
i
na
l
l
y,
w
e
c
o
mpute
t
h
e
sta
t
or
v
o
l
t
a
ges
co
ntr
o
ls
(
V
ds
1
,V
qs
1
,V
ds
2
,V
qs2
)
r
e
qu
ired
t
o
le
t
t
h
e
“
v
irtua
l
c
o
n
tr
ol
s
”
c
o
n
v
er
ge
t
o
t
h
e
desir
e
d
va
lu
e
s
w
ith
r
egar
d
s
t
o
the
s
t
ab
i
l
i
t
y
of
t
he
a
ssoc
ia
t
e
d
Lya
p
u
n
ov
f
unc
t
i
on
[
6
]
-
[8]
.
5.
1.
A
p
p
licat
ion
of
n
on
l
i
n
e
ar
i
n
t
e
g
ra
l
b
a
c
k
st
ep
p
i
n
g
c
ont
r
ol
t
o
DS
IM
I
n
our
w
or
k,
w
e
use
I
n
te
gr
al
b
a
c
k
s
t
ep
p
i
n
g
c
o
n
t
r
o
l
b
y
u
s
i
ng
bot
h
r
educ
ed
a
n
d
c
om
p
l
e
t
e
mode
l
o
f
or
i
e
nt
e
d
i
nd
uc
t
i
on
ma
chi
n
e
(
1
-
2
)
.
O
u
r
obj
e
c
t
i
v
e i
s
to
s
y
n
t
hesiz
e
t
he
e
xpr
e
s
s
i
on
of t
he
c
o
n
t
r
o
l va
riab
les V
sd
1
,V
sd2
a
nd V
sq1
,V
sq2
to
le
t t
h
e
sta
t
e
va
r
i
a
b
l
e
s
of
t
he
D
S
I
M
fol
l
o
w
t
h
e
de
si
r
e
d
r
e
f
e
r
e
nce
s
F
i
gur
es
1
,
2,
a
nd
3.
B
y
ma
king
a
va
r
i
a
b
les
chan
ge
,
the
new
o
n
es
a
r
e
t
he
e
r
r
or
s
betw
ee
n
the
se
t
po
i
n
ts
a
n
d
t
h
e
s
ta
t
e
va
r
i
a
b
l
e
s.
T
his
c
o
n
t
r
o
l
i
s
p
r
e
se
nt
e
d
i
n
si
x
ste
p
s
show
s
in
F
igur
e
2,
a
s
w
e
w
i
ll
sh
ow
i
n
t
h
is
s
e
c
ti
o
n
[
9]
.
5.
2.
Non
l
i
n
ear
int
e
gra
l
b
ac
kstep
p
ing
con
t
rol usi
n
g t
h
e re
du
c
e
d
m
o
del
I
n
t
h
i
s
pa
r
t
w
e
use
the
r
e
duce
d
m
athem
a
t
i
cal
m
ode
l
(
2
)
of
t
he
D
SIM[
9
]
.
5.
2.
1.
F
i
r
s
t
st
e
p
“
Sp
ee
d
Loo
p
”:
Th
is
f
i
r
st
s
te
p
con
s
is
t
s
i
n
i
d
e
n
ti
fy
i
ng
t
h
e
er
rors
e
1
w
hich
r
ep
resent
t
h
e
e
rro
r
b
e
t
w
een
real
s
p
eed
“
ω
”
a
nd
r
e
fer
e
nce
spee
d
‘
ω*
’,
f
or the e
le
ctrica
l s
p
ee
d “
ωr
”
,
we
d
efi
n
e
t
h
e r
acki
n
g e
rror
as:
*
1
e
(
3
)
A
nd
the
i
r
d
yna
mics
a
r
e
g
iv
en
b
y
:
*
1
e
(
4
)
)
(
2
1
*
s
q
s
q
qs
i
i
i
Then
t
he
e
r
r
or
d
y
n
a
m
ic
a
l
e
qu
a
tio
ns
a
r
e
:
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
27
–
40
30
*
17
1
2
8
9
()
dr
q
s
qs
r
eb
i
i
b
b
2
1
1
1
2
1
)
(
e
e
V
(
5
)
I
t
s
deriva
t
i
ve
i
s:
11
11
()
Ve
e
e
*
1
11
7
1
2
8
9
()
(
(
)
)
dr
qs
qs
r
Ve
e
b
i
i
b
b
(6)
*
*
98
1
1
7
r
qs
r
bb
C
e
i
b
(
7
)
W
ith
C
1
is a posit
i
ve
c
onstant.
Th
e
d
e
riv
a
t
i
v
e
o
f
th
e
Ly
ap
unov
f
un
c
t
ion
b
eco
me
s:
2
11
1
1
()
0
Ve
c
e
Si
n
c
e
t
h
e
c
u
rre
n
t
i
qs
i
s
n
o
t
a
c
ontr
o
l
i
n
p
u
t
a
n
d
i
s
o
n
l
y
one
v
ariab
l
e
of
t
he
s
ys
tem
w
i
t
h
i
t
s
o
w
n
d
y
n
a
m
i
c
s
.
W
e
w
ill
use
it
t
o
intr
od
uc
e
t
h
e
i
n
tegra
l
a
c
t
i
on,
s
o
w
e
c
ho
ose
t
h
e
desire
d
dy
n
a
mic
b
e
hav
i
or
o
f
t
h
e
vir
t
ua
l
c
ontr
o
l
’i
qs
*’ a
s
foll
ow
i
n
g
:
*
*
98
1
1
11
7
r
qs
r
bb
C
e
Ix
b
(8)
w
ith
λ
1
is
p
o
s
i
tive
c
ons
t
a
n
t
a
nd
0
1
1
)
(
d
e
x
i
s
t
h
e
i
nt
e
g
ra
l
ac
ti
o
n
b
r
ou
ght
i
n
acco
rd
an
c
e
w
it
h
t
h
e
fo
l
l
ow
i
n
g
er
ror
"e”
.
B
y
i
n
tr
od
uci
n
g
t
h
is
i
n
t
e
g
ra
l
i
n
t
he
v
ir
t
u
a
l
c
o
ntro
l,
w
e
ensure
t
he
c
on
verge
n
c
e
o
f
tra
c
k
in
g
err
o
r to
zer
o in stea
dy
st
a
t
e s
h
ow
s in
F
ig
ure
1.
F
i
gur
e 1.
Inte
g
ral a
c
ti
on bac
k
ste
p
p
i
ng d
i
a
g
r
a
m
5.2.
2.S
e
con
d
s
t
e
p
“iq
s
1
C
u
r
r
e
n
t
L
oop
”:
F
o
r
th
is
s
t
e
p
,
our
goa
l
is
t
he
r
e
p
la
ce
m
e
nt
o
f
t
h
e
v
i
rtua
l
c
u
rr
e
n
t
c
o
n
t
r
ol
by
c
o
mput
i
ng
c
o
nt
rol
vo
lt
ag
es.
We
def
ine
the
error
of
t
he (
q) a
xi
s
com
p
one
nt o
f
the
sta
t
or
c
ur
rent and
its r
ef
erence:
1
*
2
S
q
qs
i
I
e
(
9
)
The
deri
va
ti
ve
i
s
w
r
itt
e
n
as:
*
*
21
qS
qS
eI
i
(10)
*
21
1
3
/
qs
q
s
eI
V
b
With:
3
1
1
2
1
1
2
1
1
1
1
/
b
d
a
i
aa
i
b
a
i
b
r
ds
ds
qs
2
2
2
2
2
1
)
(
e
e
V
(11)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
o
u
b
le star
i
n
duc
t
i
o
n
m
a
c
h
i
n
e
us
ing n
o
n
l
i
n
ea
r i
n
te
gra
l
b
a
c
k
s
t
ep
p
i
ng co
nt
ro
l
(Abd
a
lla
h Ab
den)
31
I
t
s
deriva
t
i
ve
i
s:
22
22
()
Ve
e
e
*
2
22
1
1
3
()
(
/
)
qs
qs
Ve
e
I
V
b
(12)
F
o
r
a
negat
i
v
e
err
o
r de
rivat
i
v
e
e
2, w
e m
u
st cho
ose
as
t
he
first
c
o
n
tr
ol
v
o
lta
ge
:
*
*
11
2
2
3
()
qs
q
s
VI
C
e
b
.
2
22
2
2
()
0
Ve
C
e
Wit
h
C
2
is a pos
itive cons
tant.
5.2.
3.Th
ird
ste
p
“
i
q
s
2
Cu
rrent Loop”:
We
d
efin
e
t
h
e trac
k
i
n
g
e
r
ro
r a
s
:
*
32
qs
q
s
eI
i
(
13)
The
deri
va
ti
ve
i
s
w
r
itt
e
n
as:
*
32
qs
qs
eI
i
(14)
*
32
2
3
/
qs
q
s
eI
V
b
With
:
3
1
1
1
1
2
2
1
2
4
2
/
)
(
b
d
a
i
aa
i
b
a
i
b
r
ds
ds
qs
2
3
3
3
2
1
)
(
e
e
V
(15)
Its der
i
vati
ve is:
33
33
()
Ve
e
e
*
3
33
2
2
3
()
(
/
)
qs
q
s
Ve
e
I
V
b
(16)
F
o
r
a
negat
i
v
e
err
o
r de
rivat
i
v
e
e
2, w
e m
u
st cho
ose
as
t
he
s
ec
on
d co
ntr
o
l
vo
l
t
age.
**
22
3
3
3
()
qs
qs
VI
C
e
b
2
33
3
3
()
0
Ve
C
e
Wi
th
C
3
i
s
a
pos
it
ive
c
onsta
n
t
.
5.2.
4. S
te
p four
“φd
r
Fl
u
x
Loop
”:
We
def
ine
the
tr
acki
ng e
rror
a
s
:
*
4
rd
r
e
(
17)
A
nd i
t
s der
i
va
tive
w
i
th re
s
p
e
c
t
to
tim
e le
ads
to
:
*
4
rr
e
(18)
*
44
5
1
2
6
()
r
ds
ds
r
Ce
b
i
i
b
*
12
()
ds
ds
ds
ii
i
*
*
44
5
6
()
r
ds
r
Ce
b
i
b
*
*
64
4
5
r
r
ds
bC
e
i
b
(19)
w
ith
C
4
is a positive
c
onstant.
Th
e
d
e
riv
a
t
i
v
e
o
f
th
e
Ly
ap
unov
f
un
c
t
ion
b
eco
me
s:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
27
–
40
32
2
44
4
4
()
0
Ve
C
e
We
c
ho
ose
t
h
e
des
i
r
e
d
dy
nam
i
c
be
hav
i
our
o
f
the
vir
t
ua
l
con
t
r
o
l
i
ds
*
a
s
f
oll
o
wi
ng
:
*
*
64
4
22
5
r
r
ds
bC
e
Ix
b
(
20)
With
λ
2
i
s
p
o
s
iti
ve
c
onsta
n
t
a
nd
0
4
2
)
(
d
e
x
is
t
he
i
nte
g
r
a
l
a
c
t
i
o
n
br
oug
h
t
i
n
a
c
c
o
r
d
a
n
ce
w
it
h
t
h
e
follo
w
i
ng
e
rro
r
‘
’
e’
’
By
i
ntro
du
cing
t
h
i
s
in
t
e
g
r
al
i
n
th
e
v
i
r
t
u
a
l
c
o
n
t
r
o
l,
w
e
ensur
e
t
h
e
c
onve
r
g
e
n
c
e
of
t
h
e
tr
a
c
k
i
n
g
e
r
r
or
t
o
ze
r
o
i
n
stea
d
y
s
ta
te.
5.
2.
5.
S
t
ep
f
ive
“id
s1
C
u
r
ren
t
L
o
op
”:
*
51
ds
ds
eI
i
(
21)
I
t
s
de
r
i
va
t
i
ve
i
s
w
r
i
tten
as
:
*
51
ds
d
s
eI
i
(
22)
*
53
1
3
/
ds
d
s
eI
V
b
.
W
ith
:
2
55
5
1
()
2
Ve
e
(
23)
I
t
s
de
r
i
va
t
i
ve
i
s
**
5
55
3
1
3
()
(
/
)
ds
ds
Ve
e
I
V
b
(
24)
F
o
r
a
ne
gat
i
ve
e
r
r
o
r
der
i
va
tiv
e
e5,
w
e
m
ust
cho
o
se
a
s
the
Th
ir
d
c
ontr
o
l
v
o
lta
ge
*
*
13
5
5
3
()
ds
ds
VI
C
e
b
2
55
5
5
()
0
Ve
C
e
With
C
5
i
s
a
pos
iti
ve
c
ons
ta
n
t
.
5
.
2
.
6
.
S
t
ep Six
“
i
ds
2
C
u
r
ren
t
L
o
op
”:
*
62
ds
d
s
eI
i
(
25)
I
t
s
der
i
va
t
i
ve
i
s
w
r
itt
e
n
a
s
:
*
62
ds
ds
eI
i
(
26)
*
64
1
3
/
ds
ds
eI
V
b
Wit
h
:
]
)
(
(
[
2
2
1
1
1
6
2
1
5
1
2
4
4
qs
qs
r
ds
ds
ds
i
b
a
i
aa
b
i
i
b
d
i
b
2
6
6
6
2
1
)
(
e
e
V
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SSN: 2088-
8694
I
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J
P
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Elec
& Dr
i
S
y
st, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
27
–
40
34
F
o
r
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2
,
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s
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k
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(43)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
D
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p
five
“id
s1
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nt Loop”:
1
*
5
ds
ds
i
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e
(44)
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i
va
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ve
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s w
r
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:
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51
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(45)
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57
1
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s:
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55
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1
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2
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5
55
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1
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d
s
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V
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o
r
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r de
rivat
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v
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e
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se
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s
the t
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ird
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l v
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17
5
5
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d
s
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k
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2
55
5
5
()
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k
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th
k
5
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pos
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t
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v
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t
a
n
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6.S
t
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p
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i
x
“
i
d
s
2
C
u
r
r
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n
t
L
oop
”:
2
*
6
ds
ds
i
I
e
(48)
Its der
i
va
t
i
ve
i
s w
r
itten
as
:
*
2
6
ds
ds
eI
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(49)
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62
8
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V
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(
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ve
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s:
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6
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(51)
F
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err
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r de
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5
,
we
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st
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e
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ou
rt
h c
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n
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ro
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6
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6
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k
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h
k
6
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t
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.
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t
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p
sev
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n
“
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x
Loop
”:
qr
qr
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*
7
(52)
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ve
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s w
r
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as
:
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7
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d
*
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77
5
1
2
6
[(
)
]
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dr
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b
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b
(53)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
27
–
40
36
2
7
7
7
2
1
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e
e
V
(
54)
2
77
7
7
()
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k
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s
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se
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s
se
ve
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r
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s:
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51
2
6
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1
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7
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tive
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ns
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nt.
**
17
5
5
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ds
VI
k
e
**
28
6
6
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ds
ds
VI
k
e
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15
2
2
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qs
qs
VI
k
e
**
26
3
3
()
qs
q
s
VI
k
e
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Figure
2.
Back
ste
p
p
i
ng d
i
a
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a
m
of
dou
b
l
e
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ar Induc
t
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ac
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(
D
S
I
M
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using
Com
p
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e
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o
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6.
S
I
MULAT
I
ON R
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S
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(
ON LOAD)
T
h
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ral
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o
r
fl
ux
es
(
φ
dr
,
φ
qr
)
a
n
d
the
tw
o
sta
t
or
c
ur
r
e
nts
o
f
a
xi
s
(
d
-
q
)
stabi
liz
e
t
o
t
he
i
r
s
r
e
fer
ence
value
s.
7.
RESU
L
T
S
DISCU
SSION
The
ro
tor
s
p
e
e
d
f
o
llow
ve
ry
w
ell
its
r
efe
r
en
c
e
v
al
ue
w
it
h
a
go
o
d
r
e
je
c
tio
n
o
f
d
is
t
u
r
b
a
n
c
e
e
ve
n
w
i
t
h
the
a
p
plica
tio
n
of
t
he
l
oa
d
d
u
e
t
o
the
bac
k
s
t
epp
i
ng
r
egu
l
a
t
i
on,
a
nd
t
h
e
in
te
gr
al
a
c
t
i
o
n
a
l
l
o
w
e
d
us
t
o
ma
i
n
ta
in
the
s
t
a
t
i
c
e
r
r
or
a
t
a
valu
e
of
zer
o
F
i
gur
es
3
,
4,
a
nd
7.
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