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.
6, N
o
. 1
,
Mar
c
h
20
15
,
pp
. 92
~99
I
S
SN
: 208
8-8
6
9
4
92
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
Compari
s
on of E
s
timat
e
d Torqu
e
s Using L
o
w Pas
s
Filter an
d
Extended Kalman Filter fo
r Induction Motor Drives
Ibrahim
M
o
h
d
Als
o
f
y
ani*
,
Nik
Rumz
i Ni
k Idri
s
*
, Y
a
h
y
a A. Al
am
ri
*,
T
o
l
e
Su
ti
kn
o*
*,
Aree W
a
ngs
u
pphaphol*,
No
rjulia M. Nordin*
* UTM-PROTON Future Driv
e
Laborator
y
,
Power Electronics
an
d Drives Res
ear
ch Gr
oup Faculty
of Electrical
Engineering, Un
iversiti Teknolo
g
i Ma
lay
s
ia, 813
10 Skudai,
Johor
, Malay
s
ia
** Departement
of Electr
i
cal
En
g
i
neer
ing, Univer
sitas Ahmad Dahlan, Yog
y
akar
ta, Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 12, 2014
Rev
i
sed
Jan 28, 201
5
Accepte
d
Fe
b 8, 2015
Torque calcu
l
ation process is one of
the majo
r concerns for
controlling
induction m
o
tors in industr
y
,
whi
c
h requires ver
y
accur
a
t
e
state est
i
m
a
tion of
unmeasurable v
a
riab
les of nonlinear m
odels. This can be solved if the
variab
les
us
ed for torque ca
lcul
ation is
ac
cura
t
e
l
y
es
tim
at
ed.
This
paper
pres
ents
a torque cal
cula
tion based on a voltage model represented with a
low-pass filter
(LPF), and
an ext
e
nded
Kalm
an filt
er
(EKF). Th
e
experim
e
nt
al res
u
lts
s
howed that
the
estimated to
rque at low speed based on
EKF
is
m
o
re accura
te in
the
expens
e of m
o
re com
p
lic
at
ed
and larg
er
com
putation
a
l ti
m
e
.
Keyword:
Esti
m
a
ted
to
rqu
e
s
Ex
tend
ed
Kalman
filter
I
ndu
ctio
n m
o
to
r
Low p
a
ss filter
Real tim
e
control
Vol
t
a
ge/
H
z c
o
nt
r
o
l
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ib
rahim
M
.
Al
sofy
a
n
i,
UTM
-
PR
OT
O
N
F
u
tu
re
Dri
v
e
Lab
o
rat
o
ry
,
Power
Electronics a
n
d Drive
s
Researc
h
Gr
oup Fac
u
lty of
Electrical Engi
neeri
n
g,
Un
i
v
ersiti Tekn
o
l
o
g
i
Malaysia,
8
131
0 Sk
ud
ai,
Jo
hor
, Malaysia
Em
a
il: also
fyan
i20
02@yahoo
.co
m
1.
INTRODUCTION
In
t
h
e
hi
gh
-pe
r
fo
rm
ance dri
v
e
s
;
fi
el
d-
o
r
i
e
nt
e
d
or
di
rect
t
o
rq
ue c
o
nt
rol
,
acc
urat
e t
o
r
q
ue es
t
i
m
a
t
i
on i
s
essent
i
a
l
t
o
av
oi
d i
m
prope
r
dri
v
e o
p
erat
i
o
n an
d t
o
ac
hi
eve a hi
g
h
l
y
st
abl
e
sy
st
em
. M
o
st
of t
h
e
t
o
r
q
u
e
est
i
m
a
ti
on t
ech
ni
q
u
es
pr
o
p
o
s
e
d
s
o
far
are
bas
e
d
on
t
h
e
v
o
l
t
a
ge m
odel
(
V
M
)
,
or
t
h
e c
u
rre
n
t
m
odel
(C
M
)
.
The
v
o
l
t
a
ge m
odel
i
s
t
h
e c
o
m
m
on nam
e
for
a st
at
or fl
ux
estim
ato
r
u
s
ed
in sen
s
orless ind
u
c
tion
m
o
to
r d
r
iv
es sin
ce th
e ro
tor
sp
eed
in
form
at
io
n
is no
t requ
ired
fo
r t
h
e stato
r
flux
esti
matio
n
,
and
the o
n
l
y
essen
tial p
a
rameter o
f
the mo
d
e
l is t
h
e stato
r
resistan
ce
[1]. T
h
e VM is
norm
ally used
in a hi
gh spee
d range
,
since at low s
p
eed, s
o
m
e
proble
m
s arise. The
r
e are t
w
o we
l
l
-k
n
o
w
n
pr
obl
e
m
s
i
f
a pu
re i
n
t
e
grat
o
r
i
s
use
d
:
(
1
)
d
r
ift and
even
t
u
ally satu
ration
in
th
e esti
mated
flux
du
e to the presenc
e
of the DC
offset in
th
e
m
e
a
s
u
r
ed
cu
rren
t [1
]-[2
], an
d
(2
) ex
t
r
eme sen
s
itiv
ity
to
stato
r
re
sistan
ce mis
m
atch
d
u
e
to
tem
p
eratu
r
e in
crease, no
tab
l
y
at lo
w sp
eed
wh
en th
e stator
v
o
ltag
e
is low
[3
]. To
ov
ercome (1
), a low-p
a
ss
filter (LPF) is
n
o
rm
all
y
u
s
ed
in
place
of a
pure
integrator.
Howeve
r, this m
e
thod
redu
ces
the
perform
ance of t
h
e sy
stem drive
beca
use
of the
pha
se and m
a
gnitude e
r
rors due to the L
PF,
especially
whe
n
freque
ncies are close to
the
cuto
ff f
r
e
que
n
c
y
[4]
.
An
attem
p
t
to
so
lv
e th
is drawb
a
ck
,
Karan
a
yil e
t
. al.
[5]
have pr
o
p
o
sed a
sm
al
l
-
tim
e-const
a
nt
cascade
d
LPFs
to
r
e
d
u
c
e th
e
D
C
of
fset d
ecay ti
m
e
. Co
m
a
n
e
scu
an
d Lo
ngya [
6
] h
a
v
e
add
r
essed
f
l
ux
esti
m
a
tio
n
b
a
sed
o
n
a
pha
se l
o
c
k
e
d
l
o
o
p
(PLL
)
pr
o
g
ram
m
abl
e
LPF sh
o
w
i
n
g a
n
im
pro
v
em
ent
in t
h
e
m
a
gni
t
ude a
n
d
p
h
ase
of t
h
e
esti
m
a
ted
flu
x
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
mp
arison
o
f
Estima
t
ed
To
rq
u
e
s Using
Low Pa
ss F
ilter an
d Extend
ed
K
a
lma
n
…
(Ib
rah
i
m
Mohd
Alsofya
n
i
)
93
The cu
rre
nt
-m
odel
est
i
m
ati
on, o
n
t
h
e
ot
he
r
han
d
, i
s
n
o
r
m
a
l
l
y
appl
i
e
d at
low
fre
qu
ency
,
and
req
u
i
r
es
inform
ation on d a
n
d q
stator c
u
rre
n
t and rot
o
r spee
d
(or position)
[2],
[7]. In
prac
tice, accurate
spee
d
measurem
ent is im
portant for robust
an
d p
r
e
c
i
s
e cont
r
o
l
of
IM
s. H
o
we
ve
r,
the use of an i
n
crem
ental encode
r
to
g
e
t th
e sp
eed
or po
sition
of th
e ro
tor is un
attrac
tiv
e since it red
u
ces t
h
e ro
bu
st
n
e
ss
an
d
reliab
ility
o
f
the
dri
v
e, a
n
d inc
r
eases ha
rdwa
re
com
p
lexity and c
o
st [8].
T
hus, s
p
eed estim
a
tion tech
ni
q
u
es
base
d
on
t
e
rm
i
n
al
varia
b
les that can replace m
e
chanical spee
d sensors, ha
ve
receive
d incre
a
sing atten
tion in recent deca
des. It
is well-kn
own
th
at ev
en
t
h
oug
h
t
h
e u
s
e
o
f
CM h
a
s m
a
n
a
g
e
d
t
o
rem
o
v
e
th
e sen
s
itiv
ity to
th
e stato
r
resistor
v
a
riation
at lo
w sp
eed
,
o
n
t
h
e o
t
h
e
r h
a
nd
, it
in
trod
u
c
ed
p
a
ram
e
ter-sen
sitiv
ity
d
u
e
to
th
e ro
t
o
r p
a
rameter
vari
at
i
o
ns,
esp
eci
al
l
y
at
hi
gh
spee
d
re
gi
o
n
.
To
ad
d
r
ess t
h
i
s
pr
o
b
l
e
m
,
vari
o
u
s m
e
t
hods
have
be
en
p
r
o
pos
ed
.
For i
n
st
ance, S
a
lm
asi
and Naj
a
faba
di
[9]
ha
v
e
pr
op
ose
d
an adaptive observer
whic
h
is capable of conc
urre
nt
est
i
m
a
ti
on
of s
t
at
or cu
rre
nt
s a
n
d
r
o
t
o
r fl
uxes
wi
t
h
onl
i
n
e
ad
apt
a
t
i
on
o
f
r
o
t
o
r a
n
d st
at
o
r
re
si
st
ances. T
o
l
i
y
at
et
al
.
[
10]
h
a
v
e
d
e
v
e
lo
p
e
d
ar
tif
icial n
e
u
r
al
netw
or
k
s
(
ANNs)
in
clo
s
ed
lo
op
o
b
s
erv
e
r
f
o
r
esti
m
a
tin
g
r
o
tor
resistance a
n
d
m
u
tual inducta
nce. T
h
e
r
e is a
l
so a stoc
ha
stic
approach that
uses e
x
tende
d
Kalm
an filter (EKF
)
i
n
est
i
m
a
ti
ng t
h
e va
ri
abl
e
s o
f
an i
n
d
u
ct
i
on
m
o
t
o
r (IM
), s
u
ch as spee
d, t
o
rq
ue, a
nd fl
ux
[3]
.
Usi
ng E
K
F-b
a
sed
obs
er
ver
,
i
t
i
s
p
o
ssi
bl
e t
o
e
s
t
i
m
a
t
e
t
h
e un
kn
o
w
n
pa
ra
meters of
IM, t
a
k
i
ng
in
t
o
acco
u
n
t
th
e parameter
v
a
riation
s
and
measu
r
em
en
t no
ises, i
n
a
relativ
ely sho
r
t time in
terv
al [11
]-[16
].
Th
is p
a
p
e
r investig
ates th
e real ti
me ca
lcu
l
atio
n
of t
o
rq
ue
usi
n
g t
h
e est
i
m
at
ed st
at
e vari
abl
e
s base
d
o
n
th
e LPF filter an
d
EKF an
d
th
en
co
m
p
ares th
em
with
si
m
u
lated
to
rqu
e
s. In
th
is way, it wil
l
b
e
s
h
own
whi
c
h t
ech
ni
q
u
e i
s
cl
ose
r
t
o
si
m
u
l
a
t
i
on. The
pape
r i
s
or
ga
ni
zed i
n
f
i
ve sect
i
ons
.
The f
o
l
l
o
wi
n
g
sect
i
o
n
p
r
esen
ts th
e EKF-b
a
sed
torqu
e
calcu
lato
r. Sectio
n
3
d
eal
s with
th
e low p
a
ss
filter, wh
ich
rep
r
esen
ts th
e
vol
t
a
ge m
odel
.
Sim
u
l
a
t
i
on an
d ex
pe
ri
m
e
nt
al resul
t
s
are
p
r
e
s
ent
e
d i
n
Sect
i
ons
4.
Fi
nal
l
y
,
sect
i
on
5 co
ncl
ude
s
th
e work.
2
.
E
X
TENT
D
ED KALMAN FILTER ALGORIT
HM
In
this st
udy
,
EKF
is
used
t
o
c
o
ncu
rre
ntly
estim
a
te curr
ent,
rot
o
r
fl
ux
,
an
d
rot
o
r
s
p
e
e
d
fo
r s
p
ee
d
sen
s
o
r
less co
n
t
ro
l of IMs. Howev
e
r, th
e
precise esti
m
a
ti
on of t
h
es
e st
at
e vari
a
b
l
e
s i
s
ve
ry
m
u
ch rel
i
a
n
t
on
how
well the
fi
lter m
a
trices are selected
over a
wide
sp
ee
d
r
a
nge
[
1
7]
. T
h
e
ext
e
nde
d m
o
d
e
l
t
o
be
use
d
i
n
t
h
e
d
e
v
e
l
o
p
m
en
t of th
e EKF algo
rith
m
can
b
e
written
in
th
e
fo
llowing
g
e
neral form
(as referred
to
th
e
stato
r
stationary
fram
e
.
)
(
))
(
),
(
(
)
(
t
w
t
u
t
x
f
t
x
i
i
i
i
(1)
)
(
)
(
))
(
(
))
(
),
(
(
t
Bu
t
x
t
x
A
t
u
t
x
f
i
i
i
i
i
(2)
)
(
)
(
)
(
))
(
(
)
(
t
v
t
Bu
t
x
t
x
H
t
Y
i
i
i
i
(3)
There
i
= 1,
2, ext
e
nde
d st
at
e vect
or x
i
i
s
representing the estim
a
ted states,
f
i
is t
h
e no
n
lin
ear
function
of t
h
e
states and inputs,
A
i
is th
e syste
m
m
a
trix
,
u
i
s
th
e con
t
ro
l
-
inp
u
t
v
ector,
B
is th
e inpu
t m
a
tri
x
,
w
i
i
s
t
h
e proces
s noi
se
,
H
is th
e
m
easu
r
em
en
t
matrix
, an
d
v
i
i
s
t
h
e
m
easure
m
ent
noi
se. Th
e gene
ral
fo
rm
of IM
can be rep
r
ese
n
ted by
(4
)
a
n
d
(
5
).
)
(
.
0
0
0
0
0
0
/
1
0
0
/
1
.
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
t
w
v
v
L
L
i
i
L
R
L
L
R
L
R
L
R
L
L
R
L
L
L
L
L
L
R
L
L
R
L
L
L
L
L
R
L
L
L
R
L
L
R
i
i
u
sq
sd
B
X
r
rq
rd
sq
sd
A
r
r
r
m
r
r
r
r
r
r
r
r
r
m
r
m
r
r
r
m
s
r
m
r
r
r
m
r
r
m
s
X
r
rq
rd
sq
sd
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
9
2
– 99
94
)
(
.
0
0
0
1
0
0
0
0
0
1
t
v
i
i
i
i
X
r
rq
rd
sq
sd
H
sq
sd
(
5
)
Whe
r
e
i
sd
and
i
sq
are the d
and
q c
o
m
ponents of stator
current,
Ψ
rd
a
nd
Ψ
rq
are
d-q rotor fl
ux
com
pone
nt
s,
ω
r
is the
rotor el
ectric an
gul
a
r
spee
d i
n
ra
d/
s,
v
sd
and
v
sq
are
t
h
e st
at
or
v
o
l
t
a
ge c
o
m
pone
n
t
s,
L
s
,
L
r
and
L
m
are t
h
e st
at
or, r
o
t
o
r
and m
u
t
u
al
i
nduct
a
nces res
p
ect
i
v
el
y
,
R
s
is
the stator resis
t
ance, and
R
r
is th
e
rot
o
r resistance
.
In
th
is section
,
th
e EKF al
g
o
ri
th
m
u
s
ed
in
the IM m
o
d
e
l will b
e
d
e
rived
usin
g
th
e ex
ten
d
ed
m
o
d
e
l in
(4
) an
d (5
). F
o
r n
o
n
linear
pr
o
b
lem
s
,
such as the one in co
nsid
erati
o
n, th
e KF meth
od
is n
o
t
strictly
ap
p
licab
le, since lin
earity p
l
a
y
s an
i
m
p
o
r
tant ro
le in
its d
e
riv
a
tio
n
and
p
e
rform
a
n
ce as a
n
op
ti
m
a
l fi
lter. Th
e
EKF techn
i
que atte
m
p
ts
to
o
v
e
rco
m
e th
is d
i
fficu
lty
by using a linearized a
pprox
im
a
tio
n
,
wh
ere th
e
linearization is pe
rform
e
d about t
h
e c
u
rre
n
t state estim
a
t
e
. Thi
s
p
r
oce
ss
r
e
qui
res t
h
e
di
scret
i
zat
i
on
of
(
4
)
a
n
d
(5) as fo
llo
ws:
)
(
))
(
),
(
(
)
1
(
k
w
k
u
k
x
f
k
x
i
i
i
i
(
6
)
)
(
)
(
))
(
(
))
(
),
(
(
k
Bu
k
x
k
x
A
k
u
k
x
f
i
i
i
i
i
(
7
)
)
(
)
(
)
(
))
(
(
)
(
k
v
k
Bu
k
x
k
x
H
k
Y
i
i
i
i
(
8
)
Th
e lin
earizatio
n of
(7) is
p
e
rform
e
d
ar
ound the c
u
rrent
esti
m
a
ted state vector
i
x
ˆ
gi
ve
n as
f
o
l
l
o
w
s
.
)
(
ˆ
)
(
)
(
),
(
(
)
(
k
x
i
i
i
i
i
k
x
k
u
k
x
f
k
F
(
9
)
The res
u
lting EKF algorithm
can
b
e
presen
t
e
d
with
th
e fo
llo
wi
n
g
recu
rsive relatio
n
s
:
Q
k
F
k
P
k
F
k
P
1
)
(
)
(
)
(
)
(
(
1
0
)
1
)
)
1
(
)(
(
)
1
(
R
H
k
HP
k
P
H
k
K
T
T
(
1
1
)
))
(
ˆ
)
(
)(
(
))
(
),
(
(
ˆ
)
1
(
ˆ
k
x
H
k
Y
k
K
k
u
k
x
f
k
x
(
1
2
)
)
(
)
)
1
(
(
)
1
(
k
P
H
k
K
I
k
P
(
1
3
)
I
n
(1
0)
-(1
3)
Q
i
s
t
h
e c
o
vari
a
n
c
e
m
a
t
r
i
x
o
f
t
h
e
sy
st
em
noi
se,
nam
e
ly
, m
odel
err
o
r,
R
is the
cova
riance
matrix
o
f
th
e
ou
tpu
t
no
ise, n
a
mely,
measu
r
emen
t n
o
i
se, and
P
are the c
o
varia
n
ce m
a
tr
ix of state estimation
erro
r. Th
e algo
rith
m
in
vo
lv
es two m
a
in
st
ag
es: pred
ictio
n
an
d filtering.
In
th
e pred
ictio
n
stag
e, the n
e
x
t
p
r
ed
icted
states
)
(
ˆ
f
and predicte
d state-error cova
riance m
a
trices,
)
(
ˆ
P
are p
r
o
c
essed
,
wh
ile in
th
e filtering
stage, the
next
estim
a
ted states
)
1
(
ˆ
k
x
obt
ai
ned as
t
h
e sum
of t
h
e next
pr
e
d
icted states and the correction
term
[second t
e
rm
in (12)], a
r
e calculated. T
h
e stru
ct
u
r
e
of
t
h
e E
K
F al
go
ri
t
h
m
i
s
show
n i
n
Fi
gu
re
1.
The electrom
a
gnetic torque based on E
K
F i
s
expre
sse
d ba
sed on the sele
cted state varia
b
les which
are the
stator c
u
rrent a
n
d
rot
o
r fl
uxr:
qr
sd
dr
sq
r
m
e
i
i
L
L
p
T
2
2
3
(
1
4
)
The electrom
a
gnetic torque based on E
K
F i
s
expre
sse
d ba
sed on the sele
cted state varia
b
les which
are the
stator c
u
rrent a
n
d
rot
o
r fl
ux.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
mp
arison
o
f
Estima
t
ed
To
rq
u
e
s Using
Low Pa
ss F
ilter an
d Extend
ed
K
a
lma
n
…
(Ib
rah
i
m
Mohd
Alsofya
n
i
)
95
3
.
VOLT
AGE
-
MODEL-B
A
SED TORQUE ESTIMATOR
The st
at
o
r
fl
u
x
est
i
m
a
ti
on ba
sed o
n
t
h
e
v
o
l
t
a
ge m
odel
i
s
deri
ved
fr
om
the st
at
or
v
o
l
t
a
ge eq
uat
i
o
n
gi
ve
n by
:
.
dt
d
i
R
v
s
s
s
s
Th
e stator
flux
, th
eref
ore,
can b
e
written
as:
.
dt
R
i
v
s
s
s
s
(
1
5
)
Und
e
r sinu
so
idal stead
y-state
co
nd
itio
n, t
h
is
redu
ces t
o
:
.
s
R
s
i
s
v
s
e
j
.
e
s
s
s
s
j
R
i
v
(
1
6
)
Fig
u
re 1
.
Stru
ctu
r
e o
f
ex
ten
d
ed
Kalm
an
filter
To
avo
i
d
t
h
e i
n
tegratio
n drift p
r
ob
lem
d
u
e
to
the
d
c
o
f
fset o
r
m
easu
r
emen
t n
o
i
se, an LP
filter is
norm
ally used
in place
of the
pure i
n
tegr
at
or.
W
ith an LP fi
lter, (16)
bec
o
mes
.
c
e
s
s
s
s
j
R
i
v
(
1
7
)
whe
r
e
c
is th
e cu
to
ff frequ
en
cy
o
f
th
e LP filter in
rad
i
an
s
p
e
r
secon
d
an
d
s
is t
h
e esti
m
a
ted
st
ato
r
fl
u
x
whi
c
h i
s
o
bvi
ou
sl
y
n
o
t
e
qual
t
o
s
of
(
16)
.
Ch
oo
sing
a cu
t
o
ff freq
u
e
n
c
y
wh
ich
is cl
o
s
er to
th
e op
eratin
g frequ
e
n
c
y
will redu
ce t
h
e d
c
o
f
fset in
th
e estim
a
t
ed
stato
r
fl
u
x
,
wh
ich
o
n
th
e
o
t
h
e
r
h
a
nd
will in
trod
u
c
e ph
ase and m
a
g
n
itu
d
e
erro
rs.
The el
ect
r
o
m
a
gnet
i
c
t
o
r
que
equat
i
o
n
f
o
r
L
PF i
s
cal
cul
a
t
e
d
based
o
n
t
h
e
est
i
m
a
t
e
d st
ator
fl
u
x
a
n
d
measured stator c
u
rrent:
sd
sq
sq
sd
e
i
i
p
T
2
2
3
(
1
8
)
a
i
b
i
c
i
a
v
b
v
c
v
)
1
(
ˆ
k
x
)
1
(
k
P
)
1
(
k
K
B
)
(
k
z
/
1
z
/
1
z
/
1
mux
dq
i
dq
v
R
H
I
Q
z
/
1
)
(
ˆ
k
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
9
2
– 99
96
4
.
SIMU
LA
TION
AN
D
EX
PER
I
M
E
N
T
AL
R
E
SU
LTS
In
ord
e
r t
o
stud
y th
e
p
e
rfo
r
man
ce and
feasib
ility o
f
th
e
esti
m
a
to
rs, exp
e
rim
e
n
t
al resu
lts ob
tained
fr
om
bot
h t
h
e
EKF
-
an
d L
P
F
-
base
d est
i
m
ators a
r
e c
o
m
p
ar
ed
wit
h
th
e
resu
lts ob
tain
ed fro
m
si
m
u
la
tio
ns u
s
ing
M
a
t
l
a
b/
SIM
U
LIN
K
. I
n
b
o
t
h
sim
u
l
a
t
i
ons an
d ex
peri
m
e
nt
s, t
h
e i
nduct
i
on
m
o
t
o
r i
s
run us
i
ng co
nst
a
nt
V
o
l
t
s
per
Hert
z
(V/
H
z)
cont
rol
sc
hem
e
. I
n
t
h
e e
xpe
ri
m
e
nt
, t
h
e t
o
r
que
i
s
cal
cul
a
t
e
d
usi
n
g t
h
e
LPF a
n
d
E
K
F
-
base
d
esti
m
a
to
rs. The calcu
lated
torqu
e
fro
m
th
e ex
p
e
rim
e
n
t
is
th
en
co
m
p
ared
with
t
h
e id
eal o
r
‘act
u
a
l’ to
rqu
e
d
i
rectly ob
tained
fro
m
th
e i
n
du
ction
m
o
to
r SIMULINK
bl
oc
k i
n
t
h
e
sim
u
l
a
t
i
on. T
h
e param
e
t
e
rs of t
h
e
in
du
ctio
n m
o
to
r
u
s
ed in
t
h
e si
m
u
la
tio
n
an
d ex
p
e
rim
e
n
t
are
as shown in
Tab
l
e 1.
Th
e ex
p
e
rim
e
n
t
al set-up
con
s
ists of an
insu
late
d-
gat
e
bi
pol
a
r
t
r
a
n
si
st
o
r
i
n
vert
er
, a
d
SPAC
E
1
1
0
4
co
n
t
r
o
ller
card
, X
I
LIN
X
f
i
eld
p
r
og
r
a
mm
ab
le
g
a
te arr
a
y (
FPG
A)
an
d a
1
.
5
-
kW 4-
po
le squir
r
e
l-
cag
e
inductio
n
m
o
to
r. An
in
cre
m
en
tal en
co
der with
102
4
pp
r is u
s
ed
to
measure the rotor spee
d.
Fo
r s
a
fety
reaso
n
, the DC
vol
t
a
ge i
s
l
i
m
ited t
o
10
0 V
,
whi
c
h m
eans t
h
at
t
h
e bas
e
d s
p
eed i
s
red
u
ce
d t
o
28
rad/
s
.
The m
a
i
n
t
a
sks of t
h
e
dSP
A
C
E
are t
o
pr
o
duce t
h
e
P
W
M
co
nt
r
o
l
si
gnal
s
usi
ng t
h
e co
nst
a
nt
V/
Hz schem
e
and, m
o
re im
port
a
nt
l
y
, t
o
esti
m
a
te th
e to
rqu
e
u
s
i
n
g LPF and EKF al
go
rith
m
s
. Th
e FPGA
d
e
v
i
ce is u
s
ed
fo
r b
l
ank
i
ng
tim
e g
e
n
e
ratio
n.
Th
e sam
p
lin
g
p
e
ri
o
d
of th
e co
n
s
tan
t
V/Hz sch
e
m
e
, in
clu
d
i
n
g
th
e
state esti
m
a
to
rs, is
2
80
μ
s.
Th
e in
itial v
a
lu
es of th
e
P,
R
and
Q
in
th
e
EKF algorith
m
are fo
und
b
y
trial-an
d-e
r
r
o
r t
o
achi
e
ve
a
rap
i
d
in
itial co
nv
erg
e
n
ce as well as th
e
desired
tran
si
ent- and
stead
y
-
state p
e
rform
a
n
ce. Thu
s
, t
h
e in
itia
l
v
a
lu
es fo
r EKF schem
e
–
P
=
di
a
g
[
1
1 1 1 1
]
,
Q
=
di
ag[
10
-10
10
-10
10
-1
2
10
-12
10
-3
]
,
R
=
di
ag[
1
0
-2
10
-2
]
.
A
s
fo
r L
PF, t
h
e es
t
i
m
a
t
e
d st
at
or
f
l
ux i
s
base
d
o
n
t
h
e c
u
t
o
ff
fre
q
u
ency
set
t
o
5
r
a
d/
s.
Fi
gu
re
2.
Sc
he
m
a
t
i
c
represe
n
t
a
t
i
on
of
t
h
e e
x
peri
m
e
nt
al
set
u
p
Tabl
e 1. In
d
u
ct
i
on
M
o
t
o
r
Pa
ra
m
e
t
e
rs
R
s
[
Ω
]
R
r
[
Ω
]
L
s
[H
]
L
r
[H
]
L
m
[H
]
J
L
[Kg
.
m
2
]
F
3 4.
1
0.
3419
0.
3513
0.
324
0.
0095
2
4
The c
o
nst
a
nt
V/
Hz
d
r
i
v
e,
bo
t
h
i
n
si
m
u
l
a
t
i
o
n a
n
d e
xpe
ri
m
e
nt
, i
s
r
u
n
i
n
a
n
op
en
l
o
op
m
ode
w
h
e
r
e
a
st
ep c
h
an
ge i
n
t
h
e s
p
eed
re
fer
e
nce
fr
om
0 t
o
28
ra
d/
s i
s
a
p
pl
i
e
d at
t
=
2
.
8s
.
Fi
gu
re
3.
Si
m
u
l
a
t
i
on
res
u
l
t
s
:
d
-
q
st
at
or
cu
rr
ent
,
t
o
r
que
, a
n
d s
p
ee
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
mp
arison
o
f
Estima
t
ed
To
rq
u
e
s Using
Low Pa
ss F
ilter an
d Extend
ed
K
a
lma
n
…
(Ib
rah
i
m
Mohd
Alsofya
n
i
)
97
Fi
gu
re
4.
E
x
p
e
ri
m
e
nt
al
resul
t
s
:
d-
q st
at
o
r
v
o
l
t
a
ge,
d
-
q
st
at
or
cu
rre
nt
, a
n
d
m
easured
s
p
ee
d
Fig
u
re
3
shows th
e sim
u
latio
n
resu
lts,
u
n
d
e
r id
eal cond
itio
n, of th
e
d
-
q
stato
r
curren
t
s, si
m
u
lated
to
rq
u
e
an
d
ro
t
o
r sp
eed. Figure 4
shows the resu
lts ob
ta
ined
fr
om
experim
e
nt for
the
m
easured d-q stator
cur
r
ent
s
a
nd
v
o
l
t
a
ges, a
nd s
p
eed
, u
n
d
er t
h
e sam
e
condi
t
i
on. T
h
e
per
f
o
r
m
a
nce of t
h
e
EKF al
g
o
ri
t
h
m
i
s
evaluate
d expe
rim
e
ntally through the estim
a
t
ed spee
d an
d
t
h
e cal
cul
a
t
e
d
t
o
r
ques as s
h
o
w
n i
n
Fi
g
u
re
5. I
n
order to
further exam
ine the differe
n
ces
betwee
n
th
e si
m
u
lated
an
d
calcu
lated
torq
u
e
b
a
sed
on EKF
estim
a
tor, the
wave
form
s are
zoom
ed and s
h
own Fi
gure
8(a), whe
r
e t
h
e
diffe
re
nces
(
e
rr
or
) ar
e also p
l
o
tted.
Th
e EKF
n
o
t
o
n
l
y can
b
e
used
to
estim
at
e th
e to
rq
u
e
,
b
u
t
also
can
be u
tilized
to
esti
m
a
te
th
e speed
; th
e
est
i
m
a
t
e
d speed an
d m
easured spee
d o
b
t
a
i
n
ed fr
om
exper
i
m
e
nt
i
s
show
n i
n
Fi
g
u
re
6.
It
can be see
n
t
h
at
estim
a
ted and
measured s
p
ee
ds alm
o
st
coi
n
ci
ded e
x
ce
pt
at
st
art
-
up
, w
h
e
r
e si
gni
fi
cant
e
r
ro
r ca
n
be
obs
erve
d
due
to t
h
e lac
k
of flux
rotation at zero s
p
eed.
Fi
gu
re
5.
E
x
p
e
ri
m
e
nt
al
resul
t
s
:
d-
q
rot
o
r
fl
u
x
, e
s
t
i
m
a
t
e
d t
o
rq
ue,
an
d est
i
m
at
ed s
p
eed
f
o
r
EKF
The e
x
peri
m
e
nt
al
res
u
l
t
s
o
f
t
h
e
d-
q a
x
es
of
t
h
e
estim
ated stator
flux, an
d t
h
e
m
a
gni
t
ude
o
f
t
h
e
cal
cul
a
t
e
d t
o
rq
ue
wi
t
h
t
h
e
LP
F cut
o
f
f
fre
que
ncy
set
t
o
5
ra
d/
s i
s
s
h
ow
n i
n
Fi
g
u
re
7
.
T
h
e
di
ffe
re
nces
bet
w
ee
n
t
h
e cal
cul
a
t
e
d
t
o
r
que
base
d o
n
LPF
vol
t
a
ge
m
odel
and t
h
e sim
u
l
a
t
e
d t
o
rq
ue can
be cl
earl
y
seen i
n
Fi
gu
re
8(b), whe
r
e the wa
veform
s are zoom
ed. E
x
am
ining Figur
e 8(a) and
8(b), one ca
n cl
early see the t
o
rque
estim
a
tion usi
ng L
PF is poor
beca
use of the uncertain
ties o
f
p
a
rameters, non
lin
earty o
f
th
e i
n
verters,
measurem
ent noise
of c
u
rrent. For the
s
e rea
s
ons, t
h
e E
K
F
o
b
s
erv
e
r is u
s
ed
as it can
take in
to
accou
n
t
all
of
t
h
ese
unce
r
t
a
i
n
t
i
e
s and
n
o
i
s
es.
Thi
s
ca
n
be
p
r
ove
d
by
i
n
spec
t
e
d t
h
e
na
rr
ow
er er
r
o
r
ba
nd
o
f
t
h
e
EK
F t
o
r
q
ue.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
9
2
– 99
98
Fi
gu
re
6.
E
x
p
e
ri
m
e
nt
al
resul
t
s
:
M
easure
d
a
n
d estim
a
t
ed s
p
eed obtaine
d
from
EKF estimator
Fi
gu
re
7.
E
x
p
e
ri
m
e
nt
al
resul
t
s
:
d-
q st
at
o
r
fl
ux
an
d e
s
t
i
m
a
ted t
o
r
que
base
d
on
v
o
l
t
a
ge m
odel
(LP
F
)
(a)
(b
)
Fi
gu
re
8.
C
o
m
p
ari
s
on
bet
w
ee
n t
h
e
t
o
rq
ues
o
b
t
a
i
n
ed
f
r
om
t
h
e si
m
u
l
a
t
i
on a
n
d
ex
pe
ri
m
e
nt
fo
r
(a)
EK
F,
(b
) LP
F
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
mp
arison
o
f
Estima
t
ed
To
rq
u
e
s Using
Low Pa
ss F
ilter an
d Extend
ed
K
a
lma
n
…
(Ib
rah
i
m
Mohd
Alsofya
n
i
)
99
4. CO
N
C
L
U
S
I
ON
In
t
h
is
p
a
p
e
r, a co
m
p
arison
o
f
state esti
m
a
t
i
o
n
s
for torq
u
e
calcu
l
atio
n
b
a
sed
o
n
EKF an
d
LPF
filters
appl
i
e
d
f
o
r a
n
i
n
d
u
ct
i
o
n
m
o
t
o
r c
ont
r
o
l
has
b
een
per
f
o
rm
ed. The
pe
rf
o
r
m
a
nces
of
t
h
e
E
K
F an
d
LPF
sc
h
e
m
e
s
un
de
r t
h
e sam
e
con
d
i
t
i
ons a
r
e expe
ri
m
e
nt
all
y
eval
ua
ted
by co
m
p
aring
th
em
with
th
e resu
lts o
b
t
ai
n
e
d fro
m
the sim
u
lation.
W
h
e
n
c
o
m
p
aring
bot
h re
sult
s, the E
K
F-ba
s
e
d state estim
a
tion s
h
ows m
u
ch better
accuracy
than the
LPF-base
d state est
i
m
a
tion i
n
calc
u
lating the
t
o
rque
. T
h
e
EKF-base
d is
also
capable
of esti
mating
th
e sp
eed
un
der tran
sien
t and
stead
y
state co
nd
itio
ns. The d
r
awb
a
ck
of EKF-b
a
sed esti
m
a
tio
n
is th
e large
sam
p
lin
g
ti
m
e
d
u
e
to
t
h
e co
mp
lex
m
a
th
em
a
t
ical eq
u
a
tion
s
i
n
vo
lv
ed
.
REFERE
NC
ES
[1]
JW
Finch, D Gi
a
ouris, Contro
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ec
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E
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ith
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i
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,
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,
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Evaluation Warning : The document was created with Spire.PDF for Python.