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.
5, N
o
. 3
,
Febr
u
a
r
y
201
5,
pp
. 43
3
~
44
0
I
S
SN
: 208
8-8
6
9
4
4
33
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
Experim
e
ntal Evaluati
on of T
o
rque Performance of Voltage
and Current Models using Meas
ured Torque for Induction
Mot
o
r Drives
Ibrahim
M.
Alsofyani
1
, Tole
Sutik
no
2
, Ya
hy
a A. Alam
ri
3
, Nik
Ru
mz
i Nik Idris
4
,
N
o
rj
u
lia Mo
ha
ma
d
N
o
rd
in
5
, Aree
. W
a
n
g
s
upph
ap
hol
6
1,3,4,5,6
UTM-PROTON Future Drive
Labor
ator
y,
Universiti
Tekno
logi Ma
la
ysia
4
P
o
wer Ele
c
tron
i
c
s
and Dr
ives
Re
s
earch Group
, F
acul
t
y
of
El
ectr
i
cal
Engin
eer
ing,
Univers
iti
Tekno
logi M
a
la
ys
ia
,
81310 Skudai, Johor, Malay
s
ia
2
Departement of
Electr
i
cal
Engin
eering
,
Univ
ersi
tas Ahmad Dahlan, Yog
y
ak
arta 5
5164, Indon
esia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Nov 9, 2014
Rev
i
sed
Jan 12, 201
5
Accepte
d
Ja
n 26, 2015
In this paper, two kinds of
ob
servers are proposed to investigate torqu
e
estim
ation
.
The
first one is based
on a
voltage m
o
del repr
esented
with a low-
pass filter (LP
F
); which is norm
a
ll
y
used
a
s
a replac
em
en
t for a pure
integr
ator
to avo
i
d integration drift pr
oblem due to dc offs
et
or m
eas
urem
en
t
error.
The
s
eco
nd es
tim
ator
us
ed is
an ex
tend
ed Kalm
an f
ilt
e
r
(EKF
) as
a
current model,
which puts into
accoun
t
all noise problems. Both estimation
algorithm
s
are
i
nves
tigat
ed duri
ng the s
t
e
a
d
y
a
nd trans
i
en
t s
t
a
t
es
, t
e
s
t
ed
under light lo
ad, and then compared with the measured mechanical torque. In
all
condit
i
ons, i
t
will be shown that th
e torqu
e
es
tim
ation
error fo
r EKF has
remained within
narrower
error
band
and
y
i
eld
e
d minimum torque ripples
when com
p
ared to LP
F
es
tim
ati
on. This
m
o
tivat
es
the us
e of E
K
F
obs
erver
in high performance control
drives
of induction machines for achiev
i
n
g
improved torque response.
Keyword:
C
u
r
r
ent
m
odel
Esti
m
a
ted
to
rqu
e
Ex
tend
ed
Kalman
filter
I
ndu
ctio
n m
o
to
r
Low p
a
ss filter
Mechanical torque
Vol
t
a
ge
m
odel
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,
U
n
i
v
ersiti Tekn
o
l
o
g
i
Malaysia, 813
10
Skudai, Joho
r, Malaysia.
Em
a
il: also
fyan
i20
02@yahoo
.co
m
1.
INTRODUCTION
Most real
world a
pplications
need accurate
spee
d
and t
o
rque estim
ations
in orde
r to avoid im
prope
r
o
p
e
ration
and
to
ach
iev
e
h
i
gh stab
lity. W
h
en
d
e
si
g
n
i
n
g
an o
b
s
erv
e
r fo
r an
electrical d
r
iv
e syste
m
, two k
i
n
d
s
of est
i
m
at
i
on m
e
t
hods
ha
ve
been
i
n
vest
i
g
a
t
ed t
o
dat
e
w
h
i
c
h are
base
d
on t
h
e
vol
t
a
ge
m
odel
(
V
M
)
,
or t
h
e
current m
odel
(CM). T
h
e
VM is known
for a stator fl
u
x
esti
m
a
to
r u
s
ed in
sensorless i
n
du
ction
m
o
to
r (IM)
dri
v
es si
nce t
h
e rot
o
r spee
d i
n
f
o
rm
at
i
on i
s
not
re
q
u
i
r
ed
fo
r t
h
e st
at
or fl
u
x
est
i
m
a
t
i
on, and t
h
e
onl
y
im
po
rat
n
t
vari
a
b
l
e
of t
h
e
obse
r
ve
r i
s
t
h
e st
at
or resi
st
ance [1]
.
VM
i
s
norm
a
l
l
y
used
i
n
hi
gh s
p
eed
appl
i
cat
i
o
ns, si
nce at
l
o
w
spee
d,
s
o
m
e
pr
obl
em
s are e
n
co
u
n
t
e
re
d
.
T
hus
, t
w
o
rec
o
gnized
proble
m
s are asso
ciatied wit
h
VM s
i
nce a
p
u
re in
tegrator is u
s
ed
: Th
e first o
n
e
is a d
r
i
f
t an
d
saturation
in
th
e esti
m
a
ted
flu
x
d
u
e
to th
e p
r
esen
ce of th
e
DC o
f
fset in
the
m
easu
r
ed
curren
t [1
-2
], and
th
e secon
d
p
r
ob
lem is th
e ex
t
r
em
e sen
s
itiv
it
y to
stato
r
resistan
ce
mis
m
a
t
ch due
to te
m
p
erature
increase,
parti
c
ularly at low
spee
d when t
h
e
stato
r
vo
ltage is lo
w [2
]. Sev
e
ral
sol
u
t
i
o
ns t
o
t
h
ese pr
o
b
l
e
m
s
have
bee
n
pr
o
pos
ed
. F
o
r t
h
e
dri
f
t
pr
o
b
l
e
m
,
a l
o
w
-
pa
ss fi
l
t
er (LP
F
) i
s
n
o
rm
al
ly
use
d
in place
of a pure i
n
tegra
t
or.
Howe
ver, this m
e
thod re
duces the
perform
ance of t
h
e s
y
stem
drive be
cause
of t
h
e
p
h
ase
and m
a
gni
t
u
de
err
o
rs
d
u
e to the LPF, es
pecially when fr
eque
ncies are
close to the
cutoff
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
4
33 –
44
0
43
4
freq
u
e
n
c
y
[3
].
In an atte
m
p
t to
so
lv
e th
is
p
r
o
b
l
em
, Ka
ran
a
yil et. al. [4
]
hav
e
ad
dressed
sm
a
ll-ti
me-co
n
stan
t
cascade
d
LPFs to
decrease
the DC
offset
decay tim
e.
Com
a
nescu and L
o
ngya [5]
have
prese
n
ted fl
ux
est
i
m
a
ti
on b
a
sed
on a
p
h
ase
l
o
cke
d
l
o
o
p
(
P
LL)
pr
o
g
ram
m
abl
e
LPF de
pi
ct
i
ng a
n
e
n
h
a
ncm
e
nt
i
n
t
h
e pha
se
an
d
m
a
g
n
itud
e
o
f
the esti
m
a
t
e
d
fl
u
x
. On
line ad
ap
tation
of th
e stator resistan
ce is ad
d
i
tio
n
a
lly i
m
p
o
r
tan
t
to
enha
nce t
h
e p
e
rf
orm
a
nce o
f
t
h
e VM
at
l
o
w f
r
eq
ue
ncy
r
a
nge
. T
o
s
o
l
v
e
t
h
i
s
d
r
aw
bac
k
, [
6
]
has
pr
o
p
o
se
d a
si
m
u
ltan
e
o
u
s
esti
m
a
t
i
o
n
o
f
roto
r and
stator resistan
ces
u
s
ing
ex
tend
ed Kal
m
an
filter (EKF).
Altern
ativ
ely,
CM esti
matio
n
,
on
th
e o
t
h
e
r
han
d
, is su
itab
l
e to
b
e
app
lied
at v
e
ry lo
w
freq
u
e
n
c
y, an
d
req
u
i
r
es i
n
fo
r
m
at
i
on on
d and
q st
at
or c
u
r
r
ent
an
d sp
eed
[
2
],
[7
].
I
n
real ti
me
applications, acc
urate
speed
m
easurem
ent
is im
port
a
nt
fo
r
ro
b
u
st
an
d p
r
e
c
i
s
e cont
r
o
l
of
IM
s. H
o
weve
r,
t
h
e use
of
a sp
eed se
nso
r
t
o
g
e
t
t
h
e
sp
eed
o
r
po
sitio
n of t
h
e ro
tor
is no
t fav
o
red
as it d
ecr
eases
th
e reliab
ility an
d rob
u
s
t
n
ess
o
f
th
e m
o
to
r co
n
t
ro
l
,
and i
n
creases
har
d
ware c
o
m
p
l
e
xi
t
y
and c
o
st
[
8
]
.
Th
us,
speed est
i
m
at
i
on t
ech
ni
q
u
e
s
base
d o
n
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 l
o
w sp
eed, it
h
a
s i
n
tro
d
u
c
ed
p
a
ram
e
ter-sen
sitiv
ity d
u
e
to
t
h
e
ro
t
o
r p
a
ram
e
ter v
a
riatio
n
s
,
especi
al
l
y
at
hi
gh
s
p
eed
re
gi
o
n
.
To
ad
d
r
ess t
h
i
s
pr
obl
em
, v
a
ri
o
u
s m
e
t
hods
ha
ve
bee
n
pr
o
pos
ed
. F
o
r
i
n
st
ance,
Salm
asi
and N
a
jafa
ba
di
[9]
h
a
ve ad
dres
sed
an ada
p
t
i
v
e
o
b
s
erve
r w
h
i
c
h i
s
capabl
e
o
f
co
n
c
ur
rent
est
i
m
ati
on o
f
stato
r
cu
rren
ts
an
d ro
tor fl
u
x
e
s with
on
lin
e ad
ap
tation
o
f
rotor a
n
d stator resistances. T
o
l
i
yat et al.[10]
have
devel
ope
d a
r
t
i
f
i
c
i
a
l
neu
r
al
n
e
t
w
o
r
ks
(
A
N
N
s
) i
n
cl
osed
loo
p
ob
ser
v
er
fo
r estim
ating rot
o
r
resistan
ce a
n
d
m
u
t
u
al
i
nduct
a
nce. T
h
ere i
s
a
l
so a st
oc
hast
i
c
app
r
oach t
h
at
uses E
K
F i
n
es
t
i
m
a
t
i
ng t
h
e
va
ri
abl
e
s o
f
IM
,
suc
h
as speed
, t
o
r
q
ue, an
d fl
ux
[1
1]
-[
1
4
]
.
Usi
ng E
K
F
-
base
d
obse
r
ve
r, i
t
is possi
bl
e t
o
est
i
m
a
t
e
t
h
e unkn
o
w
n
param
e
ters of
IM, taking int
o
account the
pa
ram
e
ter va
riations
and m
easurem
ent noises,
in a relatively short
ti
m
e
in
terv
al [1
5
]-[1
6
]
.
The m
a
i
n
cont
ri
b
u
t
i
on
of t
h
i
s
pape
r i
s
t
o
eval
uat
e
t
h
e t
o
r
que
per
f
o
r
m
a
nce for
bot
h LP
F and E
K
F
obs
ervers
under the
sam
e
conditions. Unlike previ
ous
st
udies,
where t
h
e em
phasis is
only
on spe
e
d, rot
o
r
fl
u
x
, st
at
o
r
fl
u
x
,
or
m
o
t
o
r
pa
ram
e
t
e
rs, t
h
i
s
pape
r
foc
u
ses
on
i
n
vest
i
g
at
i
o
n
of t
h
e t
o
r
q
u
e
be
havi
or
bas
e
d
o
n
b
o
t
h
ob
serv
ers du
r
i
n
g
th
e st
ead
y an
d
tra
n
sient states, a
n
d the
n
c
o
m
p
ared
with the
measured m
e
c
h
anical
t
o
r
que
. T
h
e
p
a
per i
s
o
r
ga
ni
zed i
n
fi
v
e
se
ct
i
ons.
Th
e follo
wing
section
p
r
esen
ts th
e EKF-b
a
sed to
rqu
e
calcu
latio
n
.
Sectio
n
three d
e
als with
th
e low p
a
ss filter,
wh
ich
rep
r
esen
ts th
e
v
o
ltag
e
m
o
d
e
l. Ex
p
e
ri
men
t
al
resul
t
s
a
n
d
di
scussi
o
n
a
r
e
pre
s
ent
e
d
i
n
Sect
i
o
n
f
o
ur.
Fi
nal
l
y
,
sect
i
o
n
fi
v
e
concl
ude
s t
h
e
wo
rk
.
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
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Experi
me
nt
al
Eval
u
a
t
i
o
n
of
Tor
que
Perf
or
ma
nce
of
V
o
l
t
a
ge
an
d C
u
rre
nt
Mo
del
s
…
(
I
b
r
ahi
m M
.
Al
s
o
f
y
ani
)
43
5
)
(
.
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 t
h
e d an
d
q com
pone
nt
s
of st
at
o
r
cu
rre
n
t
,
Ψ
rd
and
Ψ
rq
ar
e d-
q
ro
t
o
r
f
l
ux
co
m
p
on
en
ts,
ω
r
is
t
h
e r
o
t
o
r el
ect
r
i
c ang
u
l
a
r s
p
ee
d i
n
ra
d/
s,
vsd
and
vs
q a
r
e t
h
e st
at
or
vol
t
a
g
e
com
pone
nt
s,
L
s
, L
r
and
L
m
ar
e
th
e
stator,
rotor and m
u
tual induc
tances re
specti
v
ely,
R
s
is t
h
e s
t
ator re
sistance
, and
R
r
is th
e ro
tor resistan
ce.
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
(
10)
-(
13
)
Q
i
s
t
h
e co
vari
a
n
ce
m
a
t
r
i
x
of t
h
e sy
st
em
noi
se,
nam
e
l
y
,
m
odel
erro
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-e
r
ror
c
ova
riance
m
a
tr
ices,
)
(
ˆ
P
are pro
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
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
4
33 –
44
0
43
6
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.
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
From
t
h
i
s
eq
u
a
t
i
on, t
h
ree
c
o
m
pone
nt
s are
k
n
o
w
n, i
.
e
.,
t
h
e vect
or
v
o
l
t
age, st
at
o
r
re
si
st
or, a
n
d
measu
r
ed curren
t
. Th
e
on
ly missin
g
v
a
riab
le
is th
e stator
fl
ux
.
Th
erefo
r
e, t
h
e stator
flux
can
b
e
written
as:
.
dt
R
i
v
s
s
s
s
(
1
5
)
In
practice, th
e pu
re i
n
tegrator used
i
n
estimatin
g
th
e stato
r
flux
is
o
f
ten
su
b
s
titu
ted
wit
h
a lo
w p
a
ss
filter to
av
o
i
d
th
e in
tegratio
n
d
r
ift pro
b
l
em
d
u
e
to
th
e
d
c
o
ffset o
r
m
easu
r
emen
t n
o
i
se. Howev
e
r, th
ere sho
u
l
d
be a
pr
ope
r sel
ect
i
on f
o
r t
h
e c
u
t
o
ff
fre
que
nc
y
used i
n
LP
F.
W
h
ile it is goo
d
t
o
set th
e cuto
ff
frequ
ency as lo
w
as po
ssib
l
e so
th
at th
e ph
ase
an
d
m
a
g
n
itud
e
erro
rs are
m
i
n
i
m
i
zed
, it
m
u
st
b
e
n
o
t
ed
th
at
th
is will redu
ce th
e
effectiv
en
ess of th
e LP-filter-
b
a
sed
estim
ato
r
to filter
o
u
t
t
h
e
DC
o
f
fset
wh
ich
is lik
ely
presen
t i
n
t
h
e
sen
s
ed
cu
rren
ts or vo
ltag
e
s. Selecting
a cu
to
ff frequ
en
cy wh
ich
is clo
s
er to
th
e o
p
e
rating
frequ
en
cy will redu
ce th
e
d
c
o
f
fset in
th
e esti
mated
stat
o
r
fl
u
x
, wh
ich
o
n
th
e o
t
h
e
r
h
a
n
d
will in
tro
duce p
h
a
se and
mag
n
itu
d
e
errors. In
order t
o
use the low pa
ss filter, (16)
s
h
ould be unde
r sinusoidal steady-
s
t
ate
condition, whic
h
can be written
in
th
e fo
llo
wi
ng
form
:
.
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
W
i
t
h
a
ddi
n
g
t
h
e cut
o
ff
f
r
eq
ue
ncy
t
o
(
1
7
)
, t
h
e
LPF
bec
o
m
e
s:
.
c
e
s
s
s
s
j
R
i
v
(
1
7
)
Whe
r
e
ω
c
is t
h
e cu
toff frequ
e
n
c
y of th
e LP filter in
rad
i
an
s p
e
r secon
d
,
ω
e
is th
e
syn
c
hr
ono
us an
gu
lar
fre
que
ncy
a
n
d
i
s
t
h
e
est
i
m
ated st
at
o
r
fl
u
x
.
Eq
uat
i
o
n
(
1
6)
and
(
1
7)
cl
earl
y
i
ndi
cat
ed
t
h
a
t
u
nde
r st
ea
dy
-
s
t
a
t
e
co
nd
itio
n (an
d
o
b
v
i
o
u
s
ly transien
t states), there will b
e
d
i
fferen
ces in
th
e
mag
n
itu
d
e
and p
h
a
se b
e
t
w
een
th
e
pu
re i
n
t
e
grat
or
an
d L
PF
base
d est
i
m
ati
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Experi
me
nt
al
Eval
u
a
t
i
o
n
of
Tor
que
Perf
or
ma
nce
of
V
o
l
t
a
ge
an
d C
u
rre
nt
Mo
del
s
…
(
I
b
r
ahi
m M
.
Al
s
o
f
y
ani
)
43
7
Hence
,
t
h
e el
e
c
t
r
om
agnet
i
c
t
o
r
q
ue e
quat
i
o
n
f
o
r
LPF
i
s
cal
cul
a
t
e
d
base
d
on
t
h
e
est
i
m
ated st
at
o
r
fl
u
x
an
d
m
easu
r
ed stato
r
cu
rren
t
as g
i
v
e
n
b
y
(18
)
. Th
e
error in
th
e stato
r
flu
x
esti
m
a
ti
o
n
will o
b
v
i
ou
sly b
e
reflected in t
h
e
torque estim
ation.
sd
sq
sq
sd
e
i
i
p
T
2
2
3
(
1
8
)
4.
E
X
PE
RIM
E
NTAL RES
U
LTS AN
D D
I
SC
USS
I
O
N
In
ord
e
r to 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 acqu
i
red
fr
om
bot
h t
h
e EKF an
d LP
F-b
a
sed est
i
m
at
ors are c
o
m
p
are
d
with the
m
easured re
sults obtaine
d using
electrical torque transducer
(TM308
) f
r
o
m
M
a
gt
rol
an
d
rat
e
d at
2
0
N
.
m
.
The experi
m
e
nt
al
set
-
up
al
so
con
s
i
s
t
s
of an i
n
sul
a
t
e
d-
gat
e
b
i
pol
ar t
r
a
n
si
st
o
r
i
nve
rt
er, a dS
PAC
E
1
1
04 co
nt
r
o
l
l
e
r card
,
and a 1.
5
-
k
W
4
-
pol
e
squi
rrel
-
ca
ge i
n
d
u
ct
i
o
n m
o
t
o
r. T
h
e l
o
a
d
i
s
gene
rat
e
d t
h
r
o
ug
h a
hy
st
eres
i
s
bra
k
e
by
M
a
gt
r
o
l
an
d co
n
t
rol
l
e
d
th
ro
ugh
a propo
rtion
a
l am
p
lifier. Th
e
pa
rameters
of the i
n
duction m
o
tor
used i
n
t
h
e e
xpe
rim
e
nt are as s
hown
in
Tab
l
e 1
.
An
in
cr
em
en
tal en
co
d
e
r
w
ith
1024
pp
r
is u
s
ed
to
m
easu
r
e th
e
r
o
t
o
r
sp
eed
,
wh
ich
is sam
p
le
d
ev
er
y
2
m
s
. For safety reason
, th
e
DC vo
ltag
e
is
li
mited
to
2
00V,
wh
ich
m
ean
s t
h
at th
e
b
a
sed
sp
eed
is
redu
ced t
o
55
ra
d/
s.
The
m
a
i
n
t
a
sk
of
t
h
e
dSP
A
C
E
i
s
t
o
ge
nerat
e
t
h
e P
W
M
co
nt
r
o
l
si
g
n
al
s
usi
n
g t
h
e
c
onst
a
nt
V/
H
z
schem
e
. The t
a
sk
of
FP
GA
i
s
t
o
ge
nerat
e
t
h
e bl
a
nki
ng t
i
m
e
. The sam
p
l
i
ng
peri
o
d
of
t
h
e co
nst
a
nt
V/
H
z
sch
e
m
e
, in
clu
d
in
g
th
e state esti
m
a
to
rs, is 1
0
0
μ
s
.
The f
u
l
l
schem
a
t
i
c
of t
h
e experi
m
e
nt
al
set
up can be s
een i
n
Fi
gu
re 2.
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
W
i
t
h
assu
m
p
ti
o
n
o
f
wh
ite no
ise, th
e state esti
m
a
t
i
o
n
erro
r m
a
trix
P
is in
itiated
with
th
e d
i
ago
n
a
l
matrix
o
n
e
, whereas th
e in
itial v
a
lu
es
of filters in
th
e EKF
alg
o
rith
m
are
fo
und
b
y
using
th
e GA algo
rith
m
in
[18
]
bu
t
with
o
p
tim
izin
g
on
ly two
cov
a
riance filters;
R
and
Q
. Th
is is to ach
iev
e
a
rap
i
d
in
itial conv
erg
e
n
ce
as well as t
h
e
d
e
sired
tran
sien
t- and
stead
y
-
state p
e
rfor
m
a
n
ce. Thu
s
,
th
e in
itial
v
a
lu
es fo
r EKF
sch
e
me
can
b
e
d
e
f
i
n
e
d und
erneath
:
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
P
10^-5
*
1.62
0
0
0
0
0
10^-16
*
1.0
0
0
0
0
0
10^-13
*
3.60
0
0
0
0
0
10^-6
*
2.38
0
0
0
0
0
10^-14
*
8.47
Q
10^-5
*
1.62
0
0
0.0053
R
Evaluation Warning : The document was created with Spire.PDF for Python.
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uar
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44
0
43
8
As
for LPF, the esti
m
a
ted
stato
r
flux
is
b
a
sed
o
n
th
e cu
t
o
ff
frequ
en
cy
set to
5
r
ad
/s. Th
e co
nstan
t
V/
Hz
d
r
i
v
e i
s
ru
n i
n
a
n
ope
n
l
o
o
p
m
ode
w
h
ere
a st
ep
ch
ange
i
n
t
h
e s
p
eed
refe
rence
fr
om
0 t
o
55
ra
d/
s i
s
ap
p
lied. Th
e
co
n
t
ro
ller algo
rith
m
is au
to-gen
erated
thro
ug
h SI
MU
LI
NK
, and
is
applied
in
real-time v
i
a
dSPC
E
c
o
nt
r
o
l
d
esk o
n
a
wi
nd
o
w
s based PC
.
The
t
w
o pha
ses
o
f
c
u
r
r
e
nt
are
m
easured usi
n
g Hal
l
Effect
current se
ns
ors
and se
nt to a
n
alog
di
gital conve
r
sion (ADC) cha
nnels
of dSPCE inte
rface, whereas t
h
e d-q
vol
t
a
ge
vect
o
r
s, sh
ow
n i
n
Fi
gu
re 3
,
are
di
r
ect
l
y
cal
cul
a
t
e
d base
d
on t
h
e
cont
r
o
l
si
g
n
al
s obt
ai
ne
d f
r
o
m
t
h
e
co
n
t
ro
ller as
follo
ws.
)
2
(
3
1
c
S
b
S
a
S
DC
V
sd
v
(
1
9
)
)
(
3
1
c
S
b
S
DC
V
sq
v
(
2
0
)
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
Fi
gu
re
3.
The
d-
q i
n
p
u
t
vol
t
a
ge
fo
r c
o
n
s
t
a
nt
V/
Hz
co
nt
r
o
l
l
e
r
Fi
gu
re
4 sh
o
w
s t
h
e res
u
l
t
s
o
b
t
a
i
n
ed
fr
om
expe
ri
m
e
nt
al
const
a
nt
V/
Hz
cont
rol
l
e
r;
i
.
e.
d-
q st
at
o
r
cu
rr
en
ts, sp
eed, and
t
o
rqu
e
. Th
e
p
e
rf
or
m
a
n
ce o
f
th
e
EKF alg
o
r
ith
m
is ev
alu
a
ted
ex
p
e
r
i
men
t
ally th
r
ough
the
estim
a
ted speed and t
h
e calculated torq
ues
as sh
ow
n i
n
Fi
gu
re
5. I
n
or
de
r t
o
f
u
rt
he
r exa
m
i
n
e t
h
e di
f
f
er
ence
s
b
e
tween
th
e measu
r
ed
an
d
calcu
l
ated
to
rqu
e
b
a
sed
on
EKF esti
m
a
to
r, th
e
zo
o
m
ed
wav
e
fo
rm
s will b
e
sh
own
latetr in
th
e d
i
scu
ssion
. Th
e
EKF
no
t on
ly can
b
e
u
s
ed
t
o
esti
m
a
te th
e t
o
rqu
e
,
b
u
t
also
can b
e
u
tilized
to
esti
m
a
te th
e sp
eed
; th
e esti
m
a
ted
sp
eed b
a
sed
o
n
EKF
a
n
d
m
easured
s
p
ee
d
obt
ai
ne
d
fr
o
m
V/
Hz cont
ro
l
l
e
r i
s
sh
own
in Fi
g
u
re 5(
b)
.
(a)
(b
)
Fi
gu
re
4.
M
eas
ure
d
res
u
l
t
s
f
o
r
co
nst
a
nt
V/
Hz
co
nt
r
o
l
l
e
r:
(a
)
d-
q st
at
o
r
c
u
r
r
e
n
t
,
(b
) m
easure
d
s
p
ee
d a
n
d
t
o
r
que
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-20
0
-10
0
0
10
0
20
0
v
sd
[V
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-20
0
-10
0
0
10
0
20
0
v
sq
[V
]
t[
s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-4
-2
0
2
4
i
sd
[A
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-4
-2
0
2
4
i
sq
[A
]
t[s]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-2
0
0
20
40
60
s
p
eed [
r
ad/
s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-2
-1
0
1
2
t
o
r
que [
N
.
m
]
t[s
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8-8
6
9
4
Experi
me
nt
al
Eval
u
a
t
i
o
n
of
Tor
que
Perf
or
ma
nce
of
V
o
l
t
a
ge
an
d C
u
rre
nt
Mo
del
s
…
(
I
b
r
ahi
m M
.
Al
s
o
f
y
ani
)
43
9
The experim
e
ntal results of the d-q a
x
es of t
h
e es
ti
m
a
ted
st
ato
r
flux
, and
th
e calcu
lated
to
rqu
e
b
a
sed
on
t
h
e L
PF
v
o
l
t
a
ge m
odel
i
s
sh
ow
n i
n
Fi
gu
re
6. E
x
am
ini
n
g Fi
gu
re
7(
a) an
d
(b
),
o
n
e
can cl
earl
y
see t
h
e
sup
e
ri
o
r
pe
rf
or
m
a
nce o
f
t
h
e
EKF
-
bas
e
d
t
o
r
que
cal
cul
a
t
i
o
n
ov
er t
h
e
v
o
l
t
a
ge m
odel
bas
e
d est
i
m
at
or t
h
r
o
ug
h
t
h
e er
ro
r
ba
nds
(t
he
di
f
f
ere
n
ce
bet
w
ee
n t
h
e m
easure
d
a
n
d est
i
m
a
t
e
d val
u
es
).
(a)
(b
)
Fi
gu
re
5.
Ex
pe
ri
m
e
nt
al
resul
t
s
f
o
r
EK
F
obse
r
ve
r
wi
t
h
no
l
o
ad:
(a
)
d-
q
rot
o
r fl
ux
,
(b
) est
i
m
a
t
e
d spee
d, a
n
d
esti
m
a
ted
to
rqu
e
Fi
gu
re
6.
Ex
pe
ri
m
e
nt
al
resul
t
s
o
f
d-
q st
at
o
r
f
l
ux a
n
d est
i
m
ated t
o
r
que
f
o
r
L
PF est
i
m
at
or w
i
t
h
n
o
l
o
a
d
(a)
(b
)
Fi
gu
re
7.
C
o
m
p
ari
s
on
bet
w
ee
n t
h
e
m
easured
t
o
r
q
ue a
n
d
est
i
m
at
ed t
o
r
que
o
b
t
a
i
n
ed
f
r
om
(
a
) E
K
F a
n
d
(b
)
LPF
d
u
r
i
ng
tr
an
s
i
ent s
t
a
t
e
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
th
e m
easu
r
ed
v
a
lu
es.
It is
rev
ealed th
at t
h
e m
easu
r
ed
and esti
m
a
ted
to
rq
u
e
s
h
a
v
e
similarities in
term
s o
f
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-1
-0
.
5
0
0.
5
1
fl
u
x
rd
[
V
.s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-1
-0
.
5
0
0.
5
1
fl
u
x
rq
[V
.s
]
t[
s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-20
0
20
40
60
s
p
ee
d [
r
ad
/
s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-1
0
1
2
to
r
q
u
e
[N
.
m
]
t[
s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-1
0
1
flu
x
sd
[V
.s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-1
0
1
flu
x
sq
[V
.s
]
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
4.
5
-2
0
2
to
r
q
u
e
[N
.
m
]
t[
s]
0.
0
5
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
0.
5
0.
5
5
-2
-1
0
1
2
T
o
r
que [
N
.
m
]
0.
0
5
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
0.
5
0.
5
5
-2
-1
0
1
2
T
o
r
que er
r
o
r
[
N
.
m
]
t[s]
m
e
a
s
ur
ed -
e
s
t
i
m
a
t
ed (
E
K
F
)
es
t
i
m
a
t
e
d (
E
K
F
)
m
e
as
ur
e
d
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
45
0.
5
0.
55
-2
0
2
T
o
r
q
u
e
[N
.m
]
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
45
0.
5
0.
55
-2
0
2
T
o
r
que e
r
r
o
r
[
N
.
m
]
t[
s]
es
t
i
m
a
t
ed (LP
F
)
m
eas
ured
m
e
as
ur
ed -
es
t
i
m
a
t
e
d
(
LP
F
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
PED
S
Vo
l.
5
,
No
.
3
,
Feb
r
uar
y
201
5 :
4
33 –
44
0
44
0
switch
i
ng
p
a
ttern
s. Wh
en
co
m
p
arin
g
bo
th
resu
lts,
t
h
e
EKF
-
ba
sed
s
t
at
e est
i
m
a
t
i
on s
h
o
w
s m
u
ch bet
t
e
r
accuracy tha
n
the LPF-base
d state es
tim
a
t
ion in calculati
ng the torque
. Th
e EKF-ba
s
e
d is also capable of
estim
a
ting the
spee
d unde
r transient
and
stead
y
state co
nditio
n
s
with
in
a s
m
aller erro
r
b
a
nd
wit
h
min
i
m
u
m
to
rq
u
e
ripp
les.
Th
is m
o
tiv
ates th
e
u
s
e
o
f
th
e
EKF esti
m
a
t
i
on al
g
o
r
i
t
h
m
i
n
hi
g
h
per
f
o
r
m
a
nce c
ont
rol
d
r
i
v
es
of
IM
s.
REFERE
NC
ES
[1]
J. W. Finch and D. Giaouris, "C
ontrolled AC El
ectr
i
ca
l Drives,"
IEEE T
r
ans. Ind. Ele
c
tron.
,
vol. 55, pp. 481-491,
2008.
[2]
I.
M.
Alsofy
ani and N.
R.
N.
Idris,
"A review on sensorless techn
i
ques fo
r
s
u
s
t
ainabl
e rel
i
a
b
lit
y and
effi
cie
n
t
variab
le frequ
en
cy
driv
es of induction motors,"
J. Renewable and Sustai
nable Energy Reviews,
vol. 24, pp. 111-121,
2013.
[3]
N.
R.
N.
Idris and A.
H.
M.
Yatim,
"A
n improv
ed stator flux es
timation in st
e
a
d
y
-sta
te oper
a
tion
for direct torqu
e
control of
induction machin
es,"
I
EEE Trans. Ind.
Appl.,
vo
l. 38, p
p
. 110-116
, 200
2.
[4]
B. Karana
yi
l, M.
F. Rahm
an, and
C. Grantham
, "An im
plem
entati
on of a program
m
a
ble casc
a
ded
low-pass filter f
o
r
a rotor
flux
s
y
n
t
hesizer
for
an
in
duction
m
o
tor dr
ive,"
IEEE Trans. Power
Electro
n.,
vol. 19, pp. 2
57-263, 2004
.
[5]
M. Comanescu and X. Long
y
a
, "
A
n im
proved flux observer based
on PLL frequen
c
y
estimator
for sensorless
vector
control of
induction motors,"
IEEE Trans. Ind. Electron.,
vo
l. 53,
pp. 50-56
, 2006
.
[6]
M. Barut
,
R. D
e
m
i
r, E.
Zerd
ali
,
and R. In
an, "R
e
a
l-T
i
m
e
Im
plem
enta
tion of B
i
In
put-Ext
ended Ka
lm
an Filter-B
ase
d
Estimator for Speed-Sensorless Control of Induction Motors,"
IEEE T
r
ans. Ind. Electron
.,
vol. 59, pp. 4197-4206,
2012.
[7]
J. Holtz, "Sensor
l
ess Control of I
nduction
M
achin
es;With or With
out Signal Injection
?
,"
IEEE Trans. Ind. Electron.,
vol. 53
, pp
. 7-30
, 2006
.
[8]
M. Barut, S. Bogos
y
a
n
,
and M. Goka
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