Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
7, N
o
. 1
,
Mar
c
h
20
16
,
pp
. 17
~27
I
S
SN
: 208
8-8
6
9
4
17
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
High Performance Speed Contro
l of Single-Phase Induction
Mot
o
rs Using S
w
itching Forward and Backward EKF St
rat
e
gy
Mohammad Jann
ati
*
,
Tole Sutikn
o
**, Nik
Rumz
i Nik I
d
ris*,
Moh
d
Junaidi
Ab
dul
Az
iz
*
* UTM-PROTON Future Driv
e
Laborator
y
,
Faculty
of
Electr
ical Engin
eering
,
U
n
ivers
iti Teknologi Malay
s
ia, Jo
hor
Bahru, Malay
s
ia
** Departmen
t
o
f
Electr
i
cal
Engineering
,
Un
iv
ersitas Ahmad Dah
l
an, Yog
y
akarta,
Indonesia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 23, 2015
R
e
vi
sed Dec 5,
2
0
1
5
Accepte
d Ja
n
4, 2016
The aim of this
research
is to pr
ovide a high p
e
r
f
ormance vector
control of
single-phase
Ind
u
ction Motor
(I
M) drives. It is
shown that in
the rotating
referen
ce fr
am
e,
the s
i
ngle-phas
e
IM
e
quations can be separated in
to forward
and backward equations with the balan
ced structure. Based on this, a method
for vector con
t
r
o
l of the single-
phase
IM, using two modified Rotor Field-
Oriented Contro
l (RFOC) algorithm
s
is
presented. In order to accommodate
forward and b
a
c
k
ward rotor flux
es
in th
e pres
en
t
e
d contro
ll
er,
an
Extend
ed
Kalm
an Filter (
E
KF) with two differen
t
forwar
d and backward
currents th
at
are switched in
terch
a
nge
abl
y
(
s
witchi
ng forward and backwar
d
EKF), is
proposed. Simulation
results illustrate th
e eff
ectiveness of
the proposed
algorithm.
Keyword:
AC d
r
ive
s
Ro
to
r f
i
eld-
or
i
e
n
t
ed
con
t
ro
l
Ro
to
r fl
u
x
estimatio
n
Single
-
phase i
n
duction m
o
tors
Swi
t
c
hi
n
g
f
o
r
w
ar
d
a
n
d
backwa
rd E
K
F
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M
oham
m
ad Jannat
i
,
Facu
lty of Electri
cal Engineering,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
U
T
M Sku
d
a
i,
8
131
0 Joho
r,
Malaysia.
Em
a
il: m
_
j
a
n
n
atyy@yah
o
o
.co
m
1.
INTRODUCTION
Vari
a
b
l
e
Fre
q
uency
Dri
v
es
(VF
D
s
)
a
ppl
i
c
at
i
ons a
r
e a
ppl
i
e
d i
n
m
a
ny
i
n
d
u
st
ri
es t
o
c
o
nt
r
o
l
a wi
de
range
of spe
e
d
a
n
d torque
for electrical m
achines
. T
h
e a
i
m
of u
s
i
n
g
V
F
Ds i
n
t
h
e
s
e
appl
i
cat
i
o
ns c
a
n
be
sum
m
ari
zed as fol
l
o
ws:
ene
r
gy
savi
n
g
, t
o
r
que
s m
a
xim
i
zat
i
on, t
o
r
que
p
u
l
s
at
i
on m
i
ni
m
i
zat
i
on, po
w
e
r fact
o
r
i
m
p
r
ov
em
en
t, To
tal Harm
o
n
i
c Distortio
n (T
HD)
reduction
and etc [1].
In
part
i
c
ul
ar
, t
h
e use
of V
F
Ds f
o
r si
n
g
l
e
-
pha
se In
d
u
ct
i
o
n M
o
t
o
rs (IM
s
)
i
s
recom
m
en
ded i
n
s
o
m
e
ap
p
lication
s
such
as
b
l
owers, wash
ing
m
a
c
h
in
es, m
i
x
e
rs, air con
d
ition
e
r, pu
m
p
s, fan
s
an
d
etc
[2
]. B
e
sid
e
s
VFDs for single-phase IMs,
dri
v
ers c
ontrol
strategies suc
h
as scalar-bas
ed control and vector-ba
s
ed
cont
rol
h
a
v
e
b
e
en
also
propo
sed
to d
r
iv
e t
h
e sing
le-p
h
a
se
IMs sp
eed
[3
]-[2
1]. Recen
tly, Field
-
Orien
t
ed
Co
n
t
ro
l
(FOC
)
of
si
n
g
l
e
-p
hase
IM
s i
s
ext
e
nsi
v
el
y
ad
opt
e
d
t
o
o
b
t
a
i
n
hi
g
h
dy
nam
i
c per
f
o
r
m
a
nce i
n
d
r
i
v
e sy
st
em
s.
Som
e
of t
h
e
co
nt
r
o
l
st
rat
e
gi
es
suc
h
as
I
ndi
re
ct
R
o
t
o
r
Fi
el
d-
Ori
e
nt
ed C
ont
r
o
l
(
I
R
F
OC
) m
e
t
h
o
d
nee
d
s
speci
fi
c k
n
o
wl
edge
of t
h
e
rot
o
r fl
ux
. A m
o
st
com
m
on t
e
chni
que t
o
o
b
t
a
i
n
t
h
e i
n
f
o
rm
at
i
on o
f
r
o
t
o
r
fl
ux i
n
IRFOC strategy is u
s
in
g
a
pu
re i
n
teg
r
ati
o
n. Ho
wev
e
r, usin
g
a
pu
re i
n
teg
r
ation
to
ob
tain
th
e ro
tor fl
u
x
i
s
sen
s
itiv
e to
d
i
fferen
t typ
e
o
f
p
r
ob
lem
s
su
ch
as DC-o
ffse
t prob
lem
.
To
so
lv
e th
is prob
lem
,
man
y
effo
rt
s b
a
sed
o
n
Artificial Neu
r
al Net
w
ork
(ANN), Mod
e
l
Referen
ce
Adap
tiv
e System
(MRAS), Ex
ten
d
e
d
Kalm
an
Filter
(EK
F
),
Lue
n
b
e
rge
r
O
b
se
rve
r
(L
O)
, Sl
i
d
i
n
g M
o
de
Obse
r
v
er
(SM
O
) a
n
d et
c are m
a
de t
o
i
m
prove
on t
h
e
est
i
m
a
ti
on
of
r
o
t
o
r fl
ux i
n
t
h
e IM
d
r
i
v
es
[
2
2]
-[
3
3
]
.
M
o
st
of t
h
ese t
e
c
hni
que
s are
o
n
l
y
appl
i
cabl
e
t
o
v
ect
or
co
n
t
ro
lled 3-p
h
ase m
o
to
r drive syste
m
s.
The m
a
i
n
focu
s of t
h
e resea
r
c
h
pre
s
ent
e
d i
n
t
h
i
s
pape
r i
s
t
o
pro
p
o
se a n
o
v
e
l
m
e
t
hod t
o
es
t
i
m
a
t
e
rot
o
r
fl
u
x
f
o
r
t
h
e ca
se o
f
hi
gh
pe
r
f
o
r
m
a
nce IR
F
O
C
o
f
si
ngl
e-
pha
se IM
dri
v
es. I
n
or
der
t
o
est
i
m
a
t
e
forw
ard a
n
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
17
–
2
7
18
back
wa
rd r
o
t
o
r fl
u
x
es i
n
t
h
e
prese
n
t
e
d IR
F
O
C
st
rat
e
gy
, a
n
EK
F wi
t
h
t
w
o
di
ffe
re
nt
f
o
r
w
ar
d an
d
ba
ckwa
r
d
cu
rren
ts th
at are switch
e
d
interch
a
n
g
e
ab
ly (switch
i
n
g
forward
and
b
a
ckward
EKF) is
u
tilized
. In
sp
i
t
e o
f
com
put
at
i
onal
com
p
l
e
xi
t
y
of
t
h
e EK
F, t
h
i
s
m
e
t
hod
has
be
en rec
o
gni
ze
d
as an a
p
pr
op
ri
at
e
m
e
t
hod t
o
est
i
m
a
te
state variables
in ve
ctor
cont
rolled IM dri
v
e
syste
m
s
because of si
m
u
ltaneous
i
d
entifi
cation of pa
ra
meters
and t
a
ki
n
g
sy
st
em
/
p
rocess a
n
d m
easurem
ent noi
ses
.
M
a
t
h
e
m
at
i
cal anal
y
s
is and M
a
t
l
a
b si
m
u
l
a
t
i
ons ha
ve
been
per
f
o
r
m
e
d t
o
d
e
m
onst
r
at
e t
h
e
per
f
o
r
m
a
nce of
t
h
e
pr
o
pose
d
m
e
t
hod.
2.
SINGLE
-PHASE IM
MODEL
The
(d
-
q
)
m
odel
of
a si
ngl
e
-
p
h
ase
IM
wi
t
h
t
w
o
di
ffe
rent
w
i
ndi
n
g
s
can
be
descri
bed
by
t
h
e f
o
l
l
o
wi
n
g
equat
i
o
ns [
7
]
(i
n
t
h
i
s
pa
per su
persc
r
i
p
t
“
s
” an
d “
e
” indicate that the
varia
b
les are
in
t
h
e st
atio
n
a
ry and
rotatin
g
refe
rence
f
r
am
es res
p
ectively
)
:
St
at
or (d
-
q
) v
o
l
t
a
ge
eq
uat
i
o
ns
:
s
qr
s
dr
q
d
s
qs
s
ds
qs
qs
ds
ds
s
qs
s
ds
i
i
p
M
p
M
i
i
p
L
r
p
L
r
v
v
0
0
0
0
(1
)
R
o
t
o
r
(
d
-
q
)
vol
t
a
ge eq
uat
i
o
ns:
s
qr
s
dr
r
r
r
r
r
r
r
r
s
qs
s
ds
q
d
r
q
r
d
s
qr
s
dr
i
i
p
L
r
L
L
p
L
r
i
i
p
M
M
M
p
M
v
v
(
2
)
St
at
or (d
-
q
) fl
u
x
e
quat
i
o
ns:
s
qr
s
dr
q
d
s
qs
s
ds
qs
ds
s
qs
s
ds
i
i
M
M
i
i
L
L
0
0
0
0
(
3
)
Ro
to
r (d
-q)
f
l
ux
eq
u
a
tion
s
:
s
qr
s
dr
r
r
s
qs
s
ds
q
d
s
qr
s
dr
i
i
L
L
i
i
M
M
0
0
0
0
(
4
)
Mechanical a
n
d to
r
que
eq
uat
i
ons:
r
r
l
e
s
qr
s
ds
d
s
dr
s
qs
q
e
B
Jp
pole
T
T
i
i
M
i
i
M
pole
T
2
2
(
5
)
In (1
)-
(
5
),
v
s
ds
,
v
s
qs
are the stator
(d-q) a
x
es
voltages,
i
s
ds
,
i
s
qs
denote the stat
or
(d-q) a
x
es c
u
rrents
,
i
s
dr
,
i
s
qr
are the rot
o
r (
d
-
q
) a
x
es c
u
rre
nts,
λ
s
ds
,
λ
s
qs
are the stator (d-q) a
x
es
fluxe
s
and
λ
s
dr
and
λ
s
qr
indicate the
rot
o
r
(d
-q
) a
x
es
flu
x
e
s.
r
ds
,
r
qs
and
r
r
are the
stator a
n
d roto
r
(d-q) axes
re
sistances
. L
ds
,
L
qs
,
L
r
,
M
d
and
M
q
den
o
t
e
the stator a
n
d rotor (d-q) axes
self an
d
m
u
tu
al in
ductan
ces.
r
is
th
e
m
o
to
r sp
eed.
T
e
and
T
l
are
el
ect
rom
a
gnet
i
c
t
o
r
que a
n
d l
o
ad t
o
r
q
ue.
J
and
B
are the
m
o
ment of ine
r
tia and
viscous friction coe
f
ficient
respectively.
3.
ROTO
R F
I
ELD-O
RIE
N
TED C
O
NT
RO
L ST
RATEGY OF
A SINGLE-PHASE IM
It
can
be sh
o
w
n t
h
at
usi
n
g
con
v
e
n
t
i
onal
(bal
a
n
ced
) t
r
a
n
sf
orm
a
t
i
on m
a
t
r
i
x
, t
h
e si
ng
l
e
-p
hase I
M
(u
n
b
al
ance
d 2
-
pha
se IM
) eq
u
a
t
i
ons i
n
t
h
e r
o
t
a
t
i
ng re
fe
re
nce fram
e
can
be obtaine
d
as following equations
[3
4]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hi
g
h
Perf
or
ma
nce
Spee
d
C
o
n
t
rol
of
Si
n
g
l
e
-
P
h
a
se
In
d
u
ct
i
o
n M
o
t
o
rs
U
s
i
n
g
Sw
i
t
c
hi
n
g
…
(
M
. Ja
nn
at
i
)
19
(6
)
whe
r
e,
(
7
)
I
n
(7
),
“
θ
e
”
is t
h
e a
n
gle bet
w
e
e
n t
h
e stationa
ry re
fere
nce
fra
m
e and rotating re
fere
nce
fra
m
e
. As ca
n
be seen
fr
om
(6)
,
usi
ng c
o
nv
ent
i
onal
(bal
a
n
ced) t
r
a
n
s
f
o
r
m
a
t
i
on m
a
t
r
i
x
, t
h
e si
n
g
l
e
-
pha
s
e
IM
eq
uat
i
ons
can be
di
vi
de
d i
n
t
o
t
w
o
fo
r
w
ar
d (s
upe
rsc
r
i
p
t
“+
e
”)
and backwa
rd (supe
r
scri
pt
“-
e
”) e
q
uations.
It can
be a
l
so seen
that, the struct
ure of the fo
r
w
ard an
d bac
k
w
a
rd eq
uat
i
o
ns i
s
sim
i
l
a
r t
o
t
h
e R
F
OC
equat
i
ons
of a 3
-
p
h
a
s
e IM
.
As a
res
u
l
t
,
ve
ct
or c
o
nt
rol
o
f
t
h
e si
ngl
e-
p
h
a
s
e IM
usi
n
g t
w
o
i
n
depe
n
d
e
n
t
R
F
OC
al
g
o
r
i
t
h
m
s
(o
ne
of
t
h
em
t
o
com
p
ensat
e
fo
rwa
r
d e
quat
i
on
s and
one
of t
h
em
t
o
com
p
ensat
e
bac
k
wa
r
d
eq
uat
i
o
ns) i
s
possi
bl
e. The
bl
ock
di
ag
ram
of t
h
e
pr
o
pose
d
R
F
O
C
m
e
t
hod
f
o
r
a
si
n
g
l
e
-p
hase
I
M
is show
n in
Fig
u
r
e
1
.
In
t
h
is p
a
p
e
r, as sh
ow
n i
n
Fi
gu
re
1, t
h
e s
i
ngl
e-
p
h
ase I
M
i
s
fed f
r
om
a Si
ne P
u
l
s
e W
i
dt
h M
o
dul
a
t
i
on (
S
P
W
M
)
t
w
o
-
l
e
g
v
o
l
t
a
ge
sou
r
ce
in
v
e
r
t
er
.
In
Fi
gu
r
e
1, th
e conven
tio
n
a
l
(b
alanced
) tr
ansfo
r
m
a
tio
n
m
a
tr
ix
(
[
T
s
e
]) is as
fo
llows:
s
qs
s
ds
e
e
e
e
s
qs
s
ds
e
s
e
qs
e
ds
i
i
i
i
T
i
i
cos
sin
sin
cos
(
8
)
e
qr
e
dr
e
qs
e
ds
e
qr
e
dr
e
qs
e
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
q
d
q
d
r
e
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
v
v
v
v
e
qr
e
dr
e
qs
e
ds
r
r
r
r
e
q
d
q
d
r
e
r
r
e
r
r
q
d
r
e
q
d
q
d
q
d
e
qs
ds
qs
ds
qs
ds
e
q
d
e
q
d
qs
ds
e
qs
ds
qs
ds
e
qs
e
ds
i
i
i
i
dt
d
M
M
M
M
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
i
i
i
i
dt
d
L
r
L
dt
d
M
M
M
M
L
dt
d
L
r
M
M
dt
d
M
M
dt
d
M
M
M
M
dt
d
L
L
r
r
L
L
M
M
dt
d
M
M
L
L
dt
d
L
L
r
r
v
v
0
0
2
2
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
17
–
2
7
20
Fi
gu
re
1.
B
l
oc
k
di
ag
ram
of R
F
OC
m
e
t
hod
f
o
r
a si
n
g
l
e
-
p
ha
se IM
4.
SWITC
H
IN
G
FO
RW
AR
D
AN
D B
A
C
K
WA
RD
EKF
STRATEG
Y
OF
A SI
NGL
E
-PH
A
SE I
M
As m
e
nti
oned
befo
re, s
o
m
e
of t
h
e
cont
r
o
l
t
echni
ques s
u
ch as R
F
OC
st
rat
e
gy
requi
re part
i
c
ul
ar
kn
owl
e
dge
of
t
h
e r
o
t
o
r
fl
ux.
The m
o
st
popu
l
a
r
m
e
t
hod t
o
obt
ai
n t
h
e r
o
t
o
r fl
u
x
i
n
f
o
rm
ati
on i
n
i
n
di
rect
R
F
OC
m
e
thod is using integration.
Howe
ver,
using an integration to obtain the ro
tor
flux is se
nsitive to the different
t
y
pe of pr
obl
e
m
s such as DC
-of
f
set
pro
b
l
e
m
.
As sho
w
n i
n
F
i
gure 1, t
o
c
o
n
t
rol
a si
ngl
e-phase IM
, t
w
o
m
odi
fied R
F
OC
al
gori
t
h
m
s
(
f
or
ward a
n
d
backwar
d
F
O
C
s
) need t
o
be u
s
ed. In
or
der t
o
acco
m
m
odat
e
for
w
ard a
nd
ba
ckwar
d
rot
o
r fl
uxes (|
λ
rf
|
and |
λ
rb
|) in
Fi
gure
1, i
n
t
h
i
s
paper
an
EKF wi
t
h
t
w
o di
ffe
rent
f
o
rwar
d an
d ba
ckwar
d
cu
rren
t
s t
h
at
are swi
t
c
hed
i
n
t
e
rchangeabl
y
(swi
t
c
hi
ng fo
rwar
d and bac
k
war
d
EKF)
, i
s
pro
posed
. To
est
i
m
a
t
e
t
h
e forwa
r
d an
d ba
ckwar
d
rotor
fluxes, t
h
e stator current
s and
rotor
flu
x
es of
the
si
ng
l
e
-phase IM
ar
e chosen
as
the state variable
s. The
state space
m
o
del of a single-phase IM can
be shown as e
q
uations (9) a
nd
(10):
(9)
(10)
where,
(
1
1
)
(
1
2
)
(
1
3
)
In
(9)
an
d (
1
0
)
,
A
,
B
and
C
ar
e t
h
e sy
st
em
mat
r
i
x
, i
nput
m
a
tri
x
an
d
out
p
u
t
m
a
t
r
i
x
. M
o
reo
v
er,
x
,
u
and
y
are t
h
e sy
st
em
st
at
e
m
a
t
r
i
x
, sy
stem
i
nput
m
a
t
r
i
x
and sy
stem
out
put
m
a
t
r
i
x
. B
a
sed on equat
i
ons of t
h
e
si
ngl
e-
phase IM
in th
e rotating refer
e
nce fram
e
(equation (6
)), t
h
e
m
a
trices of
A
f
,
B
f
,
C
f
,
A
b
,
B
b
and
C
b
i
n
eq
uat
i
ons (
9
)
and (10) are
obtained as follows:
T
qr
dr
qs
ds
i
i
x
T
qs
ds
i
i
y
T
qs
ds
v
v
u
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hi
g
h
Perf
or
ma
nce
Spee
d
C
o
n
t
rol
of
Si
n
g
l
e
-
P
h
a
se
In
d
u
ct
i
o
n M
o
t
o
rs
U
s
i
n
g
Sw
i
t
c
hi
n
g
…
(
M
. Ja
nn
at
i
)
21
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
A
44
43
42
41
34
33
32
31
24
23
22
21
14
13
12
11
(14
)
T
f
f
f
f
f
f
f
f
f
b
b
b
b
b
b
b
b
B
24
23
22
21
14
13
12
11
(15
)
f
f
f
f
f
f
f
f
f
c
c
c
c
c
c
c
c
C
24
23
22
21
14
13
12
11
(16
)
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
A
44
43
42
41
34
33
32
31
24
23
22
21
14
13
12
11
(17
)
T
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
B
24
23
22
21
14
13
12
11
(18
)
b
b
b
b
b
b
b
b
b
c
c
c
c
c
c
c
c
C
24
23
22
21
14
13
12
11
(19
)
dt
L
r
a
dt
r
a
dt
L
M
M
r
a
a
dt
r
a
dt
L
r
a
a
dt
L
M
M
r
a
dt
L
k
M
M
r
a
dt
L
k
M
M
r
a
dt
L
M
M
r
r
r
k
a
a
dt
L
k
M
M
r
a
dt
L
k
M
M
r
a
a
dt
L
M
M
r
r
r
k
a
r
r
f
r
f
r
q
d
r
f
f
r
f
r
r
f
f
r
q
d
r
f
r
s
q
d
r
f
r
s
q
d
r
f
r
q
d
r
qs
ds
s
f
f
r
s
q
d
r
f
r
s
q
d
r
f
f
r
q
d
r
qs
ds
s
f
1
,
,
2
0
,
,
1
,
0
2
,
2
,
2
2
2
1
1
,
0
,
2
2
,
0
,
2
2
1
1
44
43
42
41
34
33
32
31
2
24
23
2
2
22
21
14
2
13
12
2
2
11
(20a
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
17
–
2
7
22
0
,
0
,
1
,
0
0
,
0
,
0
,
1
24
23
22
21
14
13
12
11
f
f
s
f
f
f
f
f
s
f
b
b
dt
k
b
b
b
b
b
dt
k
b
(20
b
)
0
,
0
,
1
,
0
0
,
0
,
0
,
1
24
23
22
21
14
13
12
11
f
f
f
f
f
f
f
f
c
c
c
c
c
c
c
c
(20c
)
whe
r
e,
(
2
0
d
)
m
o
reover,
a
a
a
dt
L
M
M
r
a
a
a
dt
M
M
a
a
a
a
a
dt
a
a
a
dt
a
a
b
b
b
r
q
d
r
b
b
b
q
d
r
b
b
b
b
b
r
b
b
b
r
b
b
1
,
0
,
0
,
2
0
,
1
,
2
,
0
0
,
0
,
1
,
0
,
0
,
,
1
44
43
42
41
34
33
32
31
24
23
22
21
14
13
12
11
(21a
)
0
,
0
,
0
,
0
0
,
0
,
0
,
0
24
23
22
21
14
13
12
11
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
(21
b
)
0
,
0
,
1
,
0
0
,
0
,
0
,
1
24
23
22
21
14
13
12
11
b
b
b
b
b
b
b
b
c
c
c
c
c
c
c
c
(21c
)
B
a
sed on (
14)
-
(
21c
), t
w
o E
K
F al
gori
t
h
m
s
w
ith
th
e f
o
rw
ar
d
and
b
a
ckw
a
r
d
cu
rr
en
ts can be use
d
t
o
estima
te forward a
n
d backwa
rd
roto
r flu
x
es
in the
FOC
(F
orwa
rd)
an
d F
O
C (Backwa
rd
)
of
Figure
1.
A
s
an
altern
ativ
e m
e
t
h
od
, to
sim
p
lify th
e p
r
opo
sed sch
e
m
e
, sin
g
l
e EKF algo
rithm with
o
n
l
y ch
ang
e
s in
th
e
m
o
to
r
param
e
t
e
rs can be used f
o
r est
i
m
a
t
i
on of r
o
t
o
r fl
uxes
.
In t
h
i
s
m
e
t
h
o
d
, t
h
e fo
rwa
r
d and
b
ackwa
r
d
cur
r
e
n
t
s
t
o
o
b
t
ain th
e
rot
o
r
fl
uxes
are switch
e
d in
terch
a
ng
eab
ly
for ev
ery sam
p
lin
g
ti
me.
It can
b
e
m
e
n
tio
n
e
d
t
h
at th
e stru
cture
o
f
p
r
op
o
s
ed
sch
e
m
e
d
u
ring
forward and
b
a
ckward con
d
ition
s
i
s
t
h
e sam
e
as
a con
v
ent
i
onal
EKF a
l
g
o
r
i
t
h
m
(
t
h
e
convent
i
onal
EK
F a
l
g
o
r
i
t
h
m
i
s
g
i
v
e
n
a
s
(
2
2
a
)
-
(
2
2
c
)
)
. Th
e
o
n
l
y d
i
fferen
c
e b
e
tween
p
r
op
o
s
ed
estim
ato
r
du
ri
n
g
fo
rward
and
b
a
ckward
con
d
ition
s
with
th
e con
v
e
n
tio
n
a
l
EKF al
g
o
ri
t
h
m
is in
t
h
e m
o
to
r p
a
ram
e
ters.
As ca
n
be
seen
fr
om
equat
i
o
n
(
6
),
t
h
e
si
n
g
l
e
-p
hase
IM
v
o
l
t
a
ge e
q
uat
i
ons
have
e
x
t
r
a t
e
r
m
s due t
o
t
h
e
backwa
rd
com
p
one
n
ts (s
uperscript “
-
e
”).
Si
nce t
h
e
bac
k
w
a
rd t
e
rm
s are pr
o
p
o
r
t
i
onal
t
o
t
h
e
di
ffe
re
nce
of
t
h
e
resistan
ces, m
u
tu
al and
self ind
u
c
tan
ces, it is p
o
ssib
l
e to
n
e
g
l
ect th
em
(In
th
is p
a
p
e
r it is
assu
m
e
d
th
at th
ere is
not t
h
e
backwa
rd term
s).
Th
is EKF alg
o
rith
m
is co
m
p
u
t
ed
in
to
th
ree
main
step
s as fo
llo
ws [2
2
]
:
1. Pre
d
i
c
t
i
on:
r
q
d
qs
ds
s
L
M
M
L
L
k
2
2
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hi
g
h
Perf
or
ma
nce
Spee
d
C
o
n
t
rol
of
Si
n
g
l
e
-
P
h
a
se
In
d
u
ct
i
o
n M
o
t
o
rs
U
s
i
n
g
Sw
i
t
c
hi
n
g
…
(
M
. Ja
nn
at
i
)
23
(2
2a)
2
.
C
o
m
p
u
t
atio
n
o
f
Kalm
an
Filter Gain
:
(
22b
)
3. U
pdat
e
:
(2
2c)
whe
r
e,
R
and
Q
a
r
e the
covariance m
a
trices of the
noises.
5.
SIMULATION RESULTS
To
veri
fy
t
h
e
per
f
o
r
m
a
nce o
f
t
h
e
pr
o
pose
d
dri
v
e sy
st
em
, di
ffe
re
nt
case
s
usi
n
g M
a
t
l
a
b/
Si
m
u
l
i
nk
soft
ware
f
o
r
a
si
ngl
e-
p
h
ase
I
M
wi
t
h
t
w
o
di
f
f
ere
n
t
wi
ndi
ng
s base
d
o
n
Fi
g
u
re
1
are
si
m
u
lat
e
d:
(1) Fi
gure
2:
v
ect
or cont
r
o
l
of
a si
ngl
e-phase
IM
usi
ng
pr
op
osed co
nt
rol
l
e
r
un
der l
o
ad
(2) Fi
gure
3:
v
ect
or cont
r
o
l
of
a si
ngl
e-phase
IM
usi
ng
pr
op
osed co
nt
rol
l
e
r
at
d
i
f
f
e
r
e
n
t
speed
In
t
h
e
si
m
u
l
a
tions
as
sh
o
w
n
i
n
t
h
i
s
Fi
g
u
r
e
1
t
h
e si
ngl
e
-
p
h
a
s
e IM
i
s
fe
d
fr
om
a 2-l
e
g
vol
t
a
ge s
o
u
r
c
e
i
nve
rt
er.
A
n
E
K
F
wi
t
h
t
h
e f
o
r
w
ar
d
a
nd ba
ckwa
r
d
cu
rre
n
t
s i
s
al
s
o
u
s
e
d
t
o
est
i
m
a
t
e
forwa
r
d
a
n
d
bac
k
wa
r
d
rot
o
r fl
uxe
s i
n
t
h
e FOC
(F
or
war
d
) a
nd
FO
C
(B
ackwa
r
d
)
of Fi
g
u
r
e 1.
The R
a
t
i
ngs a
nd
param
e
t
e
rs of t
h
e
si
m
u
lated
sing
le-ph
a
se
IM are as fo
llows:
V
o
ltag
e
: 110V
, f
=
6
0
H
z
,
No
. of
po
les=4, r
ds
=7.14
, r
qs
=2.02
, r
r
=4.12
, L
ds
=0
.188
5H
, L
qs
=0.184
4H
,
L
r
=0
.1
826
H, M
q
=0
.177
2H
, J=0
.
0
146
kg
.m
2
Fi
gure 2 sh
ows
t
h
e sim
u
l
a
ti
on resul
t
s
of t
h
e pro
pose
d
m
e
t
hod f
o
r vect
or c
ont
rol
o
f
a si
ng
l
e
-phase IM
un
der load. Fig
u
re 2 (a) sho
w
s
the reference speed, Fi
gure 2
(b) sh
ows t
h
e m
o
t
o
r speed, Fi
gure 2 (c) sho
w
s t
h
e
speed er
ro
r, Fi
gure
2
(d
) s
h
o
w
s the estim
a
ted r
o
tor
flux
(
f
or
ward
flu
x
)
and Fig
u
re
2
(
e
) sh
ows
the
m
o
tor
to
rq
u
e
. In
Figu
re 2
,
th
e referen
c
e ro
to
r flux
is set
to
1
.
1wb
.
Mo
reo
v
e
r, in
th
is fig
u
r
e, th
e v
a
lu
e o
f
l
o
ad
is
change
d fr
om
zero t
o
-0
.4 at
t
=
15s and re
m
oved at
t
=
17s. It
can be seen t
h
at
t
h
e pro
posed c
ont
r
o
l
l
e
r can
m
a
i
n
tai
n
t
h
e g
o
o
d
perf
orm
a
nce duri
ng zero
reference spee
d, ram
p
reference speed and
l
o
ad condi
t
i
on.
It
can
be seen that
the
m
o
tor speed
closely
follows the reference
speed befo
re and
after th
e lo
a
d
d
i
stu
r
b
a
n
ce.
In
th
is
test the
m
a
ximum
error betwe
e
n refere
nce an
d real m
o
tor sp
eed is abo
u
t 1.
5rpm
(see Figu
re 2
(c)).
It is e
v
ident
from
Figure 2 (d) that the estim
a
ted rotor flu
x
can fo
llow th
e reference rot
o
r flux
du
ri
ng di
fferent
con
d
i
t
i
ons.
As can be seen from
Fi
gure 2 (e), t
h
e torq
ue of si
ngl
e-phase IM
changes accor
d
i
ngl
y
t
o
appl
ied l
o
ad
di
st
urbance.
(a)
(b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
17
–
2
7
24
(c)
(d
)
(e)
Fig
u
re
2
.
Sim
u
latio
n
resu
lts
of th
e RFOC
of
a sing
le
-p
hase
IM
u
n
d
er
loa
d
; (a)
re
fere
nce s
p
eed
,
(b
) m
o
tor
sp
eed
,
(
c
) sp
eed
er
ro
r,
(d)
es
tim
ated flu
x
a
n
d
(e)
to
rq
ue
Fi
gu
re
3 sh
o
w
s sim
u
l
a
t
i
on re
sul
t
s
of t
h
e
pr
o
pos
ed m
e
t
hod
fo
r vect
or c
o
nt
rol
of a si
ngl
e-
pha
se IM
at
the differe
n
t values of re
fere
nce s
p
eed
. It
i
s
evi
d
e
n
t
fr
om
Fi
gu
re
3 t
h
at
u
s
i
ng
pr
o
pos
ed
t
echni
q
u
e t
h
e s
i
ngl
e-
pha
se IM
can
follo
w the re
f
e
rence s
p
ee
d without any overs
h
oot a
nd s
t
ead
y-state error (see Figure
3 (c)).
Fig
u
re
3
(d
) illu
strates th
e si
n
u
s
ud
al form
o
f
th
e curren
t
s of m
a
in
and
au
x
iliary
windin
g
s
du
ri
ng
d
i
fferen
t
val
u
es
of re
fer
e
nce spee
d.
As
sho
w
n
fr
om
Fi
gu
re 3 (e
),
t
h
e
si
ngl
e-
pha
se I
M
t
o
rq
ue has a
qui
ck
resp
o
n
s
e
wi
t
h
no
p
u
l
s
at
i
o
ns.
It
can
be
seen
fr
om
t
h
e prese
n
t
e
d si
m
u
l
a
tio
n
r
e
su
lts
(
F
igur
es
2
an
d 3)
that th
e p
e
r
f
or
man
ce
of
the prese
n
ted
c
ont
rol tec
hni
que and
propose
d
estim
a
tor for the si
ngle-phas
e IM
dri
v
e is a
cceptable.
(a)
(b
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Hi
g
h
Perf
or
ma
nce
Spee
d
C
o
n
t
rol
of
Si
n
g
l
e
-
P
h
a
se
In
d
u
ct
i
o
n M
o
t
o
rs
U
s
i
n
g
Sw
i
t
c
hi
n
g
…
(
M
. Ja
nn
at
i
)
25
(c)
(d
)
(e)
Fig
u
re
3
.
Sim
u
latio
n
resu
lts
of th
e RFOC
of
a sing
le-p
hase
IM
at di
ffe
rent
spee
d; (a
) re
fer
e
nce s
p
ee
d,
(b
)
m
o
tor spee
d,
(
c
) s
p
eed
er
ro
r,
(d
) m
o
tor c
u
r
r
e
n
ts a
n
d
(e
) to
rq
ue
6.
CO
NCL
USI
O
N
Thi
s
pape
r s
h
owe
d
t
h
at
t
h
e
eq
uat
i
o
n
s
of
a si
n
g
l
e
-ph
a
se IM
with
two d
i
fferen
t
wind
ing
s
i
n
the
ro
tating
referen
ce fram
e can
b
e
sep
a
rated
i
n
to
two
set of
e
quat
i
o
ns
wi
t
h
t
h
e bal
a
nced st
r
u
ct
u
r
e. B
a
sed
on t
h
i
s
,
a vect
or control m
e
thod
usi
n
g two
de
veloped RF
OC algorithm
s
was
pr
oposed. In order
to
accom
m
odate
forward
and
back
ward
ro
tor
flux
es in
t
h
e
presen
ted
RF
O
co
n
t
ro
ller, an
Ex
tend
ed
Kal
m
an
Filter (EKF) with
t
w
o
di
ffe
rent
f
o
r
w
ar
d a
nd
ba
ckwa
r
d
cu
rre
n
t
s t
h
at
are swi
t
ched i
n
t
e
rcha
ngea
b
l
y
was
p
r
o
p
o
sed
.
Si
m
u
l
a
t
i
o
n
resul
t
s
s
h
owe
d
t
h
at
t
h
e
pr
o
p
o
s
ed sc
hem
e
for
vect
o
r
c
ont
rol
of
si
n
g
l
e
-
phas
e
IM
s w
o
rks
w
e
l
l
over
m
o
st
spee
d
ran
g
es.
REFERE
NC
ES
[1]
C.
Mademlis,
I
.
Kioskeridis, and T.
Th
eodoulidis, "Optimization
o
f
single-
phase in
duction Motors-
p
art I: maximum
energ
y
effi
cien
c
y
contro
l",
I
E
EE Transactions on
Energy Conversion
, vol. 20
, no
.
1, pp
. 187–195
,
2005.
[2]
H.W. Beat
y
and
J.L. Kirtl
e
y
,
"El
e
ctri
c Motor
Han
dbook", McGraw-Hill, 1998
.
[3]
N.M. Abdel-R
a
him and A.A.
Shaltout, "Slip-f
r
e
quency
con
t
rol of singl
e-phase induction moto
r operated
as tw
o-
phase motor",
In
30th
Annual Co
nference of Indu
st
rial Electronics
Society (
I
ECON 2004)
, 2004, p
p
. 1417–1422
.
[4]
R. de F Campos, J. De Oliv
eira, L.C. Marqu
e
s,
A. Nied
,
a
nd S.I.
Se
le
me
Jr,
" SVPW
M-DT
C str
a
te
gy
for single
-
phase indu
ction
motor control"
,
I
n
El
ectr
i
c Ma
chi
n
es
&
Dr
ives
Confer
enc
e
(
I
EMDC'07)
, 2007, pp.
1220–1225.
[5]
N. Abdel-Rahim and A. Shal
tout, "A
n uns
y
mmetrical two-
phase induction
motor drive with slip-frequ
en
cy
control",
IEEE Transactions on
Energy Conversion
, vol. 24
, no
. 3
,
pp. 608–616
, 20
09.
[6]
M
.
J
e
m
li,
H. B
e
n Azza
, M
.
Bou
s
s
a
k, and
M
.
Go
s
s
a
, "S
ens
o
rles
s
indire
ct s
t
ator
fi
eld or
ient
ation
s
p
eed
control
for
single-phase ind
u
ction motor drive",
IEEE Transactions on Power Electronics
,
vol. 24
, no. 6,
pp. 1618–1627,
2009.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
:
17
–
2
7
26
[7]
M.B. de Rossiter Corrêa, C. B.
Jacobi
na, A.M.N. Lima, and E.R.
C. da Silv
a,
"Rotor-flux-oriented control of
a
single-phase ind
u
ction motor d
r
ive",
IEEE Transactions on In
dustrial Ele
c
t
ronic
s
, vol. 47
, no.
4, pp. 832–841,
2000.
[8]
M.
Ja
nna
ti,
N
.
R.N.
Idris,
M
.
J.
A.
Az
iz
, A.
Monadi,
and A.
A.
M. Faudzi, "A N
ovel
Scheme for Red
u
ction o
f
Torqu
e
and Speed R
i
p
p
le in
Rotor F
i
eld Oriented C
ontrol
of Sing
le Phase Indu
ction Motor Based on Rotational
Transformations
",
Research Jou
r
nal
of Applied Sc
ien
ces, Engin
eering and
Tech
nology
,
vol. 7
,
n
o
. 16, pp. 3405–
3409, 2014
.
[9]
M. Jannati, A.
Monadi, N.R
.
N. Idris,
and A.A.M. Faudzi, "An
a
ly
tical calc
u
l
ation of the RFOC method in single-
phase indu
ction
motor",
International Jour
nal of
Electronics
, pp.
1–19, 2015
.
[10]
M.B. de Rossiter Corrêa, C.B
.
Jacobin
a
,
E.
R.
C.
Da Silva,
and A.M.
N.
Lima,
"Vector contro
l strategies for single-
phase indu
ction
motor drive s
y
stems,"
IEEE Transactions on In
d
u
strial Electronics
,
vol. 51
, no
. 5
,
pp
. 1073–1080
,
2004.
[11]
S. Reic
y
and
S. Vaez-
Zadeh
,
"Vector Contr
o
l of
Single-Ph
ase Induct
i
on
Machine wi
th
Maxim
u
m
Torque
Operation"
,
Pro
ceed
ings of
the
I
EEE
Internat
ion
a
l Symposium o
n
Industrial
Ele
c
t
ronics
, 2005
, pp
. 923–928
.
[12]
M
.
J
e
m
li, H.B. Azza, and M
.
Gos
s
a
, "Real-tim
e
im
plem
en
tation
of IRFOC for Single-P
h
as
e Indu
ction M
o
tor driv
e
using dSpace DS 1104 control board",
Simulation Modelling Pr
actice and Theory
, vol. 17, no.
6, pp. 1071–1080,
2009.
[13]
H.
Be
n Az
za
,
N.
Za
idi,
M.
Jemli,
a
nd M.
Boussa
k,
"D
evelop
ment and experimental
ev
aluatio
n of a sensorles
s
speed control of
SPIM using adaptiv
e sliding
m
ode-MRAS strateg
y
"
,
IEEE
Jou
r
nal of Emer
gin
g
and Selected
Topics
in Power Electronics
, vol. 2, no. 2, pp. 319
–328, 2014
.
[14]
B. Zahed
i
and
S. Vaez-Zadeh
,
"E
fficiency
optimization con
t
rol of si
ngle-phase induction moto
r drives",
IEEE
Transactions on
Power Electronics
, vol. 24
, no
. 4
,
pp
. 1062–1070
, 2009.
[15]
F.
A.
Ne
ve
s, J.
M.
S.
Cruz,
R.
P. Landim, Z.D.
Lin
s
, and A.
G
.
H. A
ccio
l
y, "S
ingl
e-p
h
as
e indu
ction
m
o
tor drives
wit
h
direct torqu
e
con
t
rol",
In
28th
An
nual Conferen
ce of th
e Indus
trial Electronics Society (
I
ECON 02)
, 2002, pp
. 241–
246.
[16]
R. de F Campos, L.F.R
.
Pint
o,
J.
De Oliveira,
A.
Nied,
L.
C.
de Ma
rques,
an
d A.H. De Souza, "Single-Phas
e
Induction Motor
Control Ba
sed on DTC Strateg
i
es",
In
International Symposium on
Industrial Electronics (
I
SIE
2007)
, 2007, pp
. 1068–1073.
[17]
R.P. Vieir
a
and
H. Grundling, "Senso
rles
s
s
p
eed control with a
M
R
AS
s
p
eed es
tim
ator for s
i
ngl
e-phas
e
indu
ctio
n
m
o
tors drives",
I
n
13th
European
Conferen
ce
on
Powe
r E
l
ec
troni
cs and App
l
i
c
ati
ons (
EPE'09)
, 2009, pp
. 1–10
.
[18]
M. Jannati, T. Sutikno, N.R
.
N.
I
d
ris, and M.J.A. Aziz, "A
Novel Techn
i
que for
Fault-Toleran
t
C
ontrol of Single-
Phase Induction
Motor",
TELKOMNIKA (
T
elecommunication Computing Electro
n
ics and Control)
,
vol. 13, no
. 3,
pp. 783–793
, 20
15.
[19]
M. Jannati, T.
Sutikno, N.R.N.
Idris, and M.J.A. Aziz
, "A Novel Method for
Rotor Field-Oriented Contro
l of
S
i
ngle-P
h
as
e Ind
u
ction M
o
tor",
I
n
ternational
Jou
r
nal of Electrica
l
and Computer Engineering (
I
JECE)
, vol. 5, vol.
2, pp
. 205–212
,
2015.
[20]
M.
Ja
nna
ti, N.
R.N.
Idris, M.
J.
A.
Az
iz
, S.H. Asgari, A. Monadi
,
and A.A.M. Faud
zi, "A
new meth
od for RFOC o
f
single-phase ind
u
ction motor b
a
se
d on rotation
a
l
transformations",
In 2013 I
E
EE
Student Con
f
erence on
Research
and Developmen
t (
S
COReD)
, 2013, pp
. 215–220
.
[21]
S. Kascak, M.
Prazeni
c
a
,
and
B. Dobruck
y
, "Position
contro
l
of Two-Phase
Induction
m
o
tor using dSpac
e
environment",
I
n
38th Annua
l C
onference on I
E
EE Indus
trial Electronics Society (
I
ECON 2012)
, 2012, pp. 1958
–
1963.
[22]
M. Barut, R. Demir, E.
Ze
rd
ali
,
and R. In
an, "R
eal-
tim
e im
plem
enta
tion
of b
i
in
put-extended
Ka
lm
an filt
er-base
d
estimator for speed-sensorless
control of induction motors",
IEEE Transactions
on Industrial El
ectroni
cs
, vo
l.
5
9
,
no. 11
, pp
. 4197
–4206, 2012
.
[23]
M. Tursini, R
.
Petrella, and F. Paras
ilit
i, "Adapt
iv
e sliding-m
ode o
b
server
for speed-sensorless control of induction
mot
o
rs",
IEEE Transactions on
I
ndustry Applications
, vol. 36
, no
. 5, pp. 1380–138
7, 2000
.
[24]
B. Karana
yi
l
,
M
.
F
.
Rahm
an, and
C. Grantham
, "Online s
t
a
t
or and r
o
tor res
i
s
t
an
ce e
s
tim
a
tion scheme using artif
icial
neural n
e
tworks for vector
controlled
speed sen
s
orless inductio
n motor drive",
IEEE Transacti
ons on Industrial
Electronics
, vol. 54, no. 1, pp. 16
7–176, 2007
.
[25]
S. Bogosy
a
n, M
.
Barut,
and M. Goka
san, "Braid
ed extend
ed Kal
m
a
n filters
for sensorless estim
ation in induct
i
on
motors at high-
low/zero speed",
IET Control Theory Appl
., vol. 1
,
no. 4, pp. 987–9
98, 2007
.
[26]
E.S
.
De S
a
nt
ana
,
E. B
i
m
,
and
W
.
C.D. Am
aral,
"A pr
edictiv
e algorithm for co
ntrolling speed
and rotor flux o
f
induction
motor
"
,
IEEE Transactions on I
ndustrial Electronics
, v
o
l. 55
, no
. 12
, pp
. 4398–4407
, 20
08.
[27]
M. Hajian
,
J. So
ltani, G.A. Mark
adeh,
and S. Ho
sseinnia, "Adap
t
ive nonlinear
dir
ect torque contr
o
l
of
sensorless
IM
drives
with effici
enc
y
optim
i
zat
ion",
IEEE Transactions on
Industrial Electronics
,
vo
l. 57, no
. 3, pp. 975–985,
2010.
[28]
F
.
R. S
a
lm
as
i and T.A. Najaf
a
ba
di, "An adaptiv
e obs
erver with
online rotor an
d s
t
ator res
i
s
t
an
ce es
tim
at
ion for
induction motor
s
with one phase current sensor
",
IEEE T
r
ansactions on Energy Conversion
,
v
o
l. 26, no. 3, p
p
.
959–966, 2011
.
[29]
T. Orlowska-Kowalska and M. D
y
bkowski, "
S
tator-curr
e
nt-b
ased MRAS est
i
mator for a wide range speed
-
sensorless induction-motor drive",
IEEE Transactions on
Industrial Electronics
,
vol. 57, no
. 4
,
pp. 1296–1308,
2010.
Evaluation Warning : The document was created with Spire.PDF for Python.