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
. 77
~85
I
S
SN
: 208
8-8
6
9
4
77
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
Effect of
Param
e
tric Vari
atio
ns and Voltage Unbalance on
Adaptive Speed Estimation Sc
hemes for Speed Sensorless
Induction Motor Drives
Mohan Kris
h
n
a.
S,
Febin
Daya.
J.L
School of
Electr
ical Eng
i
neering
,
VIT University, Chenn
a
i, Ind
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Sep 30, 2014
R
e
vi
sed Dec 8,
2
0
1
4
Accepte
d Ja
n
2, 2015
Speed Estimatio
n without speed
sens
ors is a complex phenomenon and is
overly
dep
e
nden
t
on the machin
e paramete
rs. It is all th
e more significan
t
during low s
p
eed or near zero s
p
eed oper
a
tion
.
There a
r
e s
e
ver
a
l approach
es
to s
p
eed
es
t
i
m
a
ti
on of an
indu
cti
on m
o
tor.
Event
u
all
y
,
th
e
y
can
b
e
c
l
as
s
i
fie
d
into two t
y
p
e
s,
nam
e
l
y
, estim
ati
on based on
the machine
model and
es
tim
ation bas
e
d on m
a
gnetic
s
a
lien
c
y
and air
gap s
p
ace har
m
onics
. This
paper an
al
ys
es
t
h
e effe
ct of in
c
o
rrect s
e
tting of
param
e
ters
l
i
ke
the s
t
ato
r
resistanc
e
, ro
tor
tim
e constan
t
,
load torqu
e
v
a
ria
tions and
al
so Voltage
unbalan
ce on various adaptiv
e control ba
sed speed estimati
on techniques fed
from the machin
e model. I
t
also
show
s how the convergence mechanisms of
the adap
tation schemes are aff
e
cted during th
es
e conditions. Th
e equivalent
m
odels are bu
ilt
and sim
u
lat
e
d offlin
e usi
ng MATLAB/SIMULINK
blocks
ets
and th
e
res
u
l
t
s
ar
e anal
ys
ed
.
Keyword:
Ad
ap
tiv
e con
t
ro
l
Ada
p
t
i
v
e spee
d obs
er
vers
Machine m
ode
l
M
odel refe
renc
e
Spee
d estim
ation
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
:
M
oha
n Kri
s
h
n
a
.S,
Sch
ool
o
f
El
ec
t
r
i
cal
En
gi
neer
i
ng
(SE
LEC
T)
,
VIT
U
n
i
v
e
r
si
t
y
, C
h
e
n
nai
C
a
m
pus
, C
h
en
nai
-
60
0
1
2
7
,
In
di
a.
Em
ail: s
m
k87.genx@gm
ail.com
1.
INTRODUCTION
The essence
of e
m
ployi
ng encoderless induction m
o
tor
drives is to elim
inate additional space and
cost
w
h
i
c
h
w
o
ul
d
ot
he
rwi
s
e
be at
t
r
i
b
ut
ed t
o
t
h
e s
p
eed
e
n
c
ode
r.
The
use
of s
p
ee
d e
n
coders also acts c
ont
rary
t
o
t
h
e
i
n
here
nt
rob
u
st
ness o
f
t
h
e i
nduct
i
o
n
m
o
t
o
rs. The
r
efo
r
e, est
i
m
a
t
i
on
of spee
d w
i
t
hout
spee
d s
e
ns
ors
em
erged
as a
n
im
port
a
nt
c
o
nc
ept
[
1
]
.
Great
am
ount
o
f
re
se
arch
has
bee
n
do
ne i
n
t
h
i
s
re
gar
d
a
n
d i
t
co
n
t
i
nues
to
in
sp
ire m
o
re,
with
th
e
o
n
s
et o
f
artifi
c
ial in
tellig
en
ce b
a
sed
sp
eed
estim
a
tio
n
an
d
o
t
h
e
r emerg
i
n
g
technologies.
The s
p
eed ca
n
be estim
a
t
ed
eith
er fro
m
th
e
mag
n
e
tic salien
c
ies or b
y
a
mach
in
e m
o
d
e
l fed
b
y
termin
al q
u
a
n
t
ities. Owin
g
t
o
th
e co
m
p
lex
ity o
f
sp
eed
esti
m
a
t
i
o
n
,
th
e m
o
st
d
i
scu
ssed
p
r
ob
lem
s
were th
e
esti
m
a
to
r’s sensitiv
ity to
m
o
t
o
r
p
a
ram
e
ter ch
ang
e
s, lo
w an
d
zero
sp
eed
o
p
e
ration
,
sp
eed
estim
a
tio
n
at field
weak
en
ing
reg
i
o
n
, stab
ility p
r
o
b
l
em
s in
th
e
reg
e
n
e
rativ
e m
o
d
e
etc.
Th
is p
a
p
e
r atte
m
p
ts to
p
r
esen
t a p
e
rform
a
n
ce an
al
y
s
i
s
o
f
vari
ou
s ada
p
t
i
v
e cont
r
o
l
schem
e
s when
th
ey are su
bj
ected
to
lo
ad
p
e
rt
u
r
b
a
tio
ns,
in
correct p
a
rameter sett
in
g
s
(Stato
r resist
an
ce and
Ro
t
o
r ti
me
con
s
t
a
nt
) a
nd
Vol
t
a
ge
u
nbal
a
nce. T
h
e ef
fe
ct
of t
h
e
sam
e
on the c
o
nve
rgence
of t
h
e a
d
aptive m
echanism
is
also prese
n
ted.
2.
MAT
H
EM
AT
ICAL
M
O
DE
L OF THE
IN
DU
CTIO
N
M
O
TOR
The
dynam
i
c state space m
odel
of the
induction m
o
to
r is prese
n
ted
below,
which, aids i
n
t
h
e
fo
rm
ul
at
i
on o
f
est
i
m
a
t
i
on an
d c
ont
rol
al
go
r
i
t
h
m
s
. It
al
so
hel
p
s i
n
det
e
r
m
i
n
i
ng t
h
e
i
n
t
e
rnal
be
havi
or
of
t
h
e
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
:
7
7
– 85
78
sy
st
em
al
ong
wi
t
h
t
h
e
desi
re
d i
n
put
a
n
d o
u
t
put
. T
h
e st
at
o
r
cu
rre
nt
a
nd t
h
e r
o
t
o
r fl
u
x
a
r
e t
h
e st
at
e
var
i
abl
e
s
[2]
:
p
i
ψ
A
A
A
A
i
ψ
B
0
V
(1)
x
A
x
B
v
(2)
i
C
x
(3)
Whe
r
e,
x
i
ψ
,i
i
i
,
ψ
ψ
ψ
(4)
The electrom
e
chanical t
o
rque
is gi
ven by,
T
i
ψ
i
ψ
,
(5)
3.
IND
U
C
TIO
N
MOTO
R
F
O
C AN
D SPEED
ESTIMATION
In t
h
e c
o
n
v
e
n
t
i
onal
sc
al
ar c
o
n
t
rol
o
f
In
d
u
ct
i
o
n
m
o
t
o
r, si
nc
e t
o
r
q
u
e
an
d
fl
ux
l
i
nka
ges a
r
e a f
unct
i
o
n
of
v
o
l
t
a
ge, c
u
r
r
ent
or
fre
q
u
en
cy
, t
h
ere i
s
a
n
i
nhe
rent
co
up
lin
g
presen
t
du
e to
wh
ich
t
h
e respo
n
s
e is
slugg
ish.
There
f
ore, t
h
er
e i
s
a need t
o
deco
u
p
l
e
t
h
e s
a
m
e
, by
m
a
ki
ng t
h
e t
o
rq
ue i
n
depe
n
d
ent
of
fl
ux
. Thi
s
i
s
kn
o
w
n
a
s
vect
o
r
co
nt
r
o
l
or
fi
el
d o
r
i
e
nt
e
d
co
nt
r
o
l
o
f
t
h
e In
d
u
ct
i
on
m
o
to
r. Th
is is similar to
th
e ortho
gon
al orien
t
atio
n
of
t
h
e fl
u
x
an
d t
o
rq
ue achi
e
ved i
n
a separ
a
t
e
l
y
exci
t
e
d dc m
o
to
r [3
]. Gen
e
rally, th
e stato
r
cu
rren
t is reso
lved
in
to
t
h
e t
o
r
q
ue p
r
o
duci
ng c
o
m
p
o
n
ent
a
nd
fl
u
x
pr
o
duci
ng c
o
m
p
o
n
e
n
t
.
T
h
e D
C
m
achi
n
e l
i
k
e per
f
o
r
m
a
nce i
s
onl
y
pos
si
bl
e i
f
t
h
e
fl
u
x
pr
o
duci
n
g c
o
m
pone
nt
of t
h
e c
u
r
r
e
n
t
i
s
ori
e
nt
ed i
n
t
h
e
di
rect
i
o
n
of
fl
u
x
a
n
d
t
h
e
Tor
q
ue
com
pone
nt
of
t
h
e cur
r
e
n
t
i
s
per
p
e
ndi
c
u
l
a
r
t
o
i
t
.
The o
r
i
e
nt
at
i
on i
s
p
o
ss
i
b
l
e
wi
t
h
ei
t
h
e
r
t
h
e r
o
t
o
r fl
u
x
(
ψ
r
),
airga
p
flu
x
(
ψ
m
) or st
at
or fl
ux
(
ψ
s
). H
o
we
ver
,
r
o
t
o
r
fl
u
x
ori
e
nt
e
d
co
nt
rol
gi
ves nat
u
r
a
l
deco
upl
i
n
g
effect
,
whe
r
eas ai
r
g
a
p
or st
at
or
fl
u
x
ori
e
nt
at
i
o
n
h
a
ve c
o
u
p
l
i
n
g i
n
t
h
e
fl
u
x
c
o
n
t
rol
l
o
op
. T
h
e
Fi
gu
re
1.
Sh
o
w
s t
h
e
di
ffe
re
nt
t
y
pes
of
Fi
el
d
Ori
e
nt
ed c
ont
rol
.
Fi
gu
re
1.
Fi
el
d O
r
i
e
nt
e
d
C
ont
rol
sc
h
e
m
e
s for
I
ndu
ctio
n Mo
t
o
r
Fi
gu
re
2.
C
l
assi
fi
cat
i
on
of
S
p
eed est
i
m
ati
on
m
e
t
hods
Fig
u
re 2
illu
strates th
e d
i
fferen
t
typ
e
s o
f
ad
ap
tiv
e con
t
ro
l sch
e
m
e
s fed
from th
e ter
m
in
al
q
u
a
n
tities
of the m
achine
.
These m
e
thods dis
p
la
y
g
o
o
d
pe
rf
orm
a
nce at
hi
gh a
n
d m
e
di
um
speeds.
B
u
t
t
h
ey
are n
o
t
st
abl
e
at very low operating s
p
ee
ds as they are
param
e
te
r dep
e
nde
nt
a
nd
pa
ram
e
t
e
r error
s
can
deg
r
ade
spee
d
perform
a
nce. The prom
inent
confi
g
urations
of a
d
aptive
speed estim
at
ion
schem
e
s are presented bel
o
w.
3.1.
Model Re
ference Ad
aptive Contr
o
l (MRAC)
As th
e
n
a
m
e
s
u
gg
ests, an
adap
tiv
e system
ad
ap
ts itself to th
e con
t
ro
lled syste
m
with
p
a
ram
e
ters
whi
c
h nee
d
t
o
be
est
i
m
a
t
e
d o
r
ar
e u
n
ce
rt
ai
n.
Unl
i
k
e
ro
b
u
st
co
nt
r
o
l
,
i
t
does
not
need a
n
y
fi
rst
ha
n
d
i
n
f
o
rm
at
i
on ab
out
t
h
e b
o
u
n
d
s
o
n
t
h
ese
est
i
m
a
t
e
d or
unc
ert
a
i
n
pa
ram
e
ters. T
h
e
pri
m
ary
aim
of a
d
apt
i
v
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Effect o
f
Pa
rametric Varia
tion
s
a
n
d
Vo
ltag
e
Un
ba
lan
ce
on
Ada
p
tive
S
p
e
ed
Estima
tion
…
(Mo
han
Krishn
a
)
79
co
n
t
ro
l is p
a
ra
m
e
ter esti
m
a
t
i
o
n
.
Th
e MR
AS form
s th
e crux
of a
d
aptive cont
rol.
T
h
e MRAS is
easy to
im
pl
em
ent
and has a hi
gh s
p
eed o
f
co
n
v
er
gence a
n
d ada
p
t
a
t
i
on a
nd i
t
al
so di
s
p
l
a
y
s
r
o
b
u
st
pe
rf
o
r
m
a
nce t
o
param
e
t
e
r vari
at
i
ons.
The
ge
neral
c
o
nfi
g
u
r
a
t
i
on
of
M
R
AS
i
s
sh
ow
n i
n
Fi
gu
re
3.
The
er
r
o
r
vect
or i
s
o
b
t
ai
ned
as the
differe
n
ce in t
h
e
out
puts
of t
h
e
refe
rence
and
adj
u
stab
le m
o
d
e
ls. Th
e two
m
o
dels are
fed from
th
e
machine term
inals. T
h
e a
d
a
p
t
i
ve m
echan
ism forces
the e
r
ror vector to ze
ro
in
order to c
onverge t
h
e estimated
out
put
t
o
t
h
e r
e
fere
nce o
u
t
p
u
t
[4]
.
D
u
ri
n
g
t
h
e de
si
g
n
of the adaptive cont
rol sc
hem
e
, special e
m
phasis has t
o
b
e
laid
o
n
th
e con
v
e
rg
en
ce
mech
an
ism
.
Sin
ce stab
ility o
f
th
e estim
a
t
o
r
is o
f
great co
n
c
ern
at all sp
eeds,
Lyap
uno
v
stabilit
y criterio
n
p
l
ays an
im
p
o
r
tan
t
ro
le in
deriv
i
ng
th
e con
t
ro
l laws and force conv
ergen
ce as
well as ensure
fast error
dyna
m
i
cs.
Adapti
ve m
echanisms can be in t
h
e
fo
rm
of fi
xe
d gai
n
PI R
e
g
u
l
a
t
o
rs
,
Fuzzy
Lo
gi
c (
F
L),
Sl
i
d
i
n
g
M
ode
(SM
)
ba
sed et
c. As
Se
nso
r
l
e
ss M
o
de
l
based s
p
ee
d est
i
m
a
ti
on m
e
tho
d
s a
r
e
sensitive t
o
m
achine
para
m
e
ters, seve
ra
l m
e
thods
a
n
d al
gorithm
s
have
been propose
d
for pa
ram
e
ter
ad
ap
tation
also [5
], in
o
r
d
e
r to
op
timise th
e p
e
rform
a
n
ce of the
drive etc. MRAS ba
se
d approach varie
s
wit
h
th
e qu
an
tity that is selected
as o
u
t
p
u
t
o
f
t
h
e referen
ce and ad
ju
stab
le m
o
d
e
l [6
]. Th
e m
o
re
po
pu
lar cho
i
ces
hap
p
e
n
t
o
be
r
o
t
o
r fl
ux
,
back
em
f, st
at
or
cu
rrents a
n
d Instantaneou
s reactive
powe
r [7].
Fi
gu
re
3.
Ge
ne
ral
C
o
nfi
g
u
r
at
i
o
n
o
f
M
R
A
S
The
f
o
l
l
o
wi
n
g
Eq
uat
i
on (
6
) – (1
0)
a
r
e use
d
t
o
cha
r
act
er
ize the
rotor
flux based
MR
AS speed estim
a
t
or a
l
ong
with
th
e ad
ap
ti
v
e
m
ech
an
ism
u
s
ed
[8
]:
a) Re
ference
Model:
ψ
qr
s
= L
r
/L
m
[
∫
(V
qs
s
-R
s
i
qs
s
-
σ
L
s
i
qs
s
)dt]
(6)
ψ
dr
s
= L
r
/L
m
[
∫
(V
ds
s
-R
s
i
ds
s
-
σ
L
s
i
ds
s
)dt]
(7)
Whe
r
e
σ
1
L
/L
L
b) Ad
jus
t
able Model:
d
ψ
qr
s
/d
t = -1
/T
r
ψ
qr
s
+
ω
r
ψ
dr
s
+ L
m
/T
r
i
qs
s
(8)
d
ψ
dr
s
/
d
t =
-1
/T
r
ψ
dr
s
-
ω
r
ψ
qr
s
+ L
m
/T
r
i
ds
s
(9)
c) Adapti
ve Mechanism
:
ω
K
φ
φ
φ
φ
(10)
3.2.
Adaptive Speed Obser
v
ers
H.
Ku
b
o
t
a
et
al
, [
9
]
pr
o
pose
d
a Ful
l
o
r
de
r s
p
eed A
d
a
p
t
i
v
e
Fl
ux
O
b
ser
v
e
r
(AF
F
O
)
base
d
on a
d
a
p
t
i
v
e
co
n
t
ro
l th
eo
ry. Th
e AFFO st
ab
ilises th
e p
e
rfo
r
m
a
n
ce o
f
t
h
e driv
e ev
en
at lo
w sp
eed
reg
i
on
b
y
allo
catin
g
p
o
l
es arb
itrarily. It m
a
k
e
s u
s
e o
f
eith
er t
h
e Lyap
un
ov’s
stabilit
y criterio
n
s
o
r
t
h
e Pop
o
v
’
s criterion
s to derive
th
e ad
ap
tiv
e sch
e
m
e
. Th
e
AFFO, ap
art fro
m esti
m
a
tin
g
th
e
Stator
cu
rre
nt
and
r
o
to
r
fl
ux,
also m
a
kes use
of a
g
a
in
m
a
trix
wh
ich
is u
s
ed
fo
r stab
ility p
u
rpo
s
e. Th
e
g
e
n
e
ral con
f
i
g
u
r
atio
n
of th
e ob
serv
er is sh
own
i
n
Fi
gu
re 4.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
7
7
– 85
80
Fi
gu
re
4.
A
d
a
p
t
i
v
e O
b
ser
v
e
r
s
c
hem
e
for
spee
d est
i
m
ati
on
Wh
ere,
‘A’ is th
e system
matr
ix
, th
e sym
b
o
l
‘^’ ind
i
cat
es es
tim
a
ted values
, ‘X’ com
p
rises
the state varia
b
les
whic
h are the
direct and qua
d
rat
u
re
a
x
es stator cu
rre
nts a
nd
rot
o
r fl
uxe
s, ‘G
’ is the o
b
ser
v
e
r
gain
m
a
trix,
cho
s
en i
n
s
u
c
h
a way
t
h
at
t
h
e Ei
ge
n val
u
es of t
h
e
ob
se
rve
r
are
pr
op
o
r
t
i
onal
t
o
t
h
e
Ei
gen
val
u
es
of t
h
e
m
achine to e
n
sure sta
b
ility unde
r
norm
al o
p
erating c
o
nd
ition. The
state equations de
picting the st
ruct
ure
of
t
h
e A
d
a
p
t
i
v
e P
s
eu
do
re
duce
d
or
der
s
p
eed
o
b
s
erve
r
(A
FF
O)
i
s
sh
o
w
n
[
10]
:
(a) Refere
nce Model
(Motor
model):
A
x
B
u
(11)
y
C
x
(
12
)
Whe
r
e,
x
i
,i
,
φ
,
φ
,
A
A
A
A
A
,
I
10
01
,
J
0
1
10
A
σ
σ
σ
I
a
I
,
A
σ
I
ω
J
a
I
a
J
,
A
I
a
I
,
A
1
T
I
ω
Ja
Ia
J
B
σ
I
0
,
C
I
,
0
,
u
V
V
(b)
A
d
ju
st
able
M
o
del
(Luen
b
erg
er Adapti
ve
Speed Obs
erver):
A
x
B
u
G
ı
̂
i
(13)
y
C
x
(
14
)
Whe
r
e,
ı
̂
e
stimat
edv
alueo
fs
t
at
o
r
c
urr
e
nt
a
nd
,
i
m
easur
e
d
v
a
lueof
st
a
t
o
r
curr
ent
A
A
A
A
A
A
σ
I
ω
J
a
Ia
J
,
A
I
ω
Ja
I
a
J
The term
G
ı
̂
i
is u
s
ed
as a correctio
n
term
fo
r th
e Ad
ap
tiv
e Sp
eed
Ob
serv
er. ‘G’ is the
red
u
ce
d or
de
r obs
er
ver gai
n
m
a
t
r
i
x
desi
gne
d so as t
o
m
a
k
e
(13
)
st
abl
e
. T
h
e pse
u
d
o
re
d
u
ced or
de
r gai
n
m
a
t
r
i
x
i
s
ch
osen
as fol
l
ows [
11]
, [
12]
:
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I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Effect o
f
Pa
rametric Varia
tion
s
a
n
d
Vo
ltag
e
Un
ba
lan
ce
on
Ada
p
tive
S
p
e
ed
Estima
tion
…
(Mo
han
Krishn
a
)
81
G
g
g
g
g
(15)
Th
e ob
serv
er gain
m
a
trix
is c
a
lcu
l
ated
b
a
sed o
n
th
e po
le p
l
ace
m
e
n
t
tech
n
i
q
u
e
, so
th
at th
e state o
f
th
e
o
b
s
erv
e
r will co
nv
erg
e
to
th
e referen
ce m
o
d
e
l (th
e
m
o
to
r)
. Th
erefore, th
e eig
e
n
v
a
lu
es are ch
osen
relat
i
v
e
ly
m
o
re negat
i
v
e
t
h
an t
h
e ei
gen
val
u
es
of t
h
e r
e
fere
nce m
odel
,
so as t
o
ens
u
re faster c
o
nvergence
.
It is chosen a
s
fo
llows:
g
k
1
a
,
g
k
,k
1
Whe
r
e,
g
de
pen
d
s o
n
t
h
e m
o
tor
param
e
t
e
rs,
g
and
k
are arb
i
trarily ch
o
s
en
an
d
k
is an
arb
itrary po
sitive
constant.
(c) Ad
ap
tive
Mech
anism
:
The Ly
a
p
u
n
o
v
fu
nct
i
o
n ca
ndi
dat
e
de
fi
ne
d
f
o
r t
h
e
ada
p
t
a
t
i
o
n sc
hem
e
i
s
[1
0]
:
Ve
e
ω
ω
λ
(16)
Whe
r
e
λ
is a
po
sitiv
e co
n
s
tant.
The tim
e derivative of ‘V’
be
com
e
s,
e
AG
C
AG
C
e
Δω
φ
φ
Δω
λ
ω
(17)
Whe
r
e,
e
i
ı
̂
and
e
i
ı
̂
By eq
u
a
lizing
t
h
e secon
d
term with
t
h
e th
i
r
d
term
,
th
e fo
llowing
ad
ap
tation
sch
e
m
e
is d
e
riv
e
d
,
i.e,
ω
λ
e
φ
e
φ
(18)
4. SIM
U
L
A
TI
ON A
NAL
YS
IS
A
N
D
RES
U
LTS
An
equ
i
v
a
len
t
si
m
u
latio
n
mo
d
e
l
o
f
th
e abo
v
e
esti
m
a
tio
n
sch
e
m
e
s is b
u
ilt in
Sim
u
li
n
k
and
the
per
f
o
r
m
a
nce i
s
obse
r
ve
d f
o
r di
ffe
re
nt
val
u
e
s
of l
o
a
d
pe
rt
u
r
bat
i
o
ns, i
n
co
r
r
ect
param
e
t
e
r set
t
i
ng an
d V
o
l
t
a
ge
Un
bal
a
nce
.
T
h
e In
d
u
ct
i
o
n
m
o
t
o
r i
s
fe
d
fr
om
a t
h
ree
p
h
ase a
c
vol
t
a
ge s
o
u
r
c
e
of
rat
i
n
g
41
5
V
,
50
Hz a
n
d i
s
ru
n
in
th
e m
o
to
ri
ng
m
o
d
e
.
Th
e mo
d
e
l is ru
n fo
r
two
sets of l
o
ad
torq
u
e
p
e
rturb
a
tio
ns resp
ect
iv
ely:
a)
Step
torq
u
e
– In
itially at n
o
load
, after a fi
x
e
d
tim
e in
terv
al, it is in
creased
to
rated
lo
ad
of 20
0 Nm
.
b)
For a Rated L
o
ad torque of 200
Nm
, the effect of ch
a
n
ge i
n
st
at
or
resi
st
ance an
d r
o
t
o
r t
i
m
e
const
a
nt
is ob
serv
ed
i
n
th
e p
e
rform
a
n
ce of th
e estim
a
t
o
r
s.
c)
For a Rated L
o
ad torque
of
200
Nm
, an unbala
nced t
h
re
e phase
voltage is supplie
d (each phase
vol
t
a
ge
ha
vi
ng
am
pl
it
ude of
2
0
0
V
,
18
0 V
a
n
d 22
0 V res
p
ec
t
i
v
el
y
)
.
The m
o
t
o
r
rat
i
ngs
an
d t
h
e pa
r
a
m
e
t
e
rs consi
d
ered
f
o
r si
m
u
l
a
t
i
on are
gi
ven
as fol
l
ows:
A
5
0
H
P
, t
h
ree
-
pha
se, 4
1
5
V
,
5
0
Hz, st
ar co
n
n
ect
ed,
fo
ur
-
p
ol
e i
n
d
u
ct
i
on
m
o
t
o
r wi
t
h
equi
val
e
nt
pa
ram
e
t
e
rs:
R
s
= 0.087
Ω
, R
r
= 0.228
Ω
, L
ls
=
L
lr
=
0.
8 m
H
, L
m
= 34.7 m
H
, I
n
ertia,
J =
1.
662
kgm
2
, fri
ct
i
on
fact
o
r
=
0.
1.
4
.
1
.
Ro
to
r F
l
ux
ba
s
e
d
M
RAS
Es
t
i
ma
to
r
a) Ste
p
T
o
rque
(Rated
Loa
d
is
applied at
5 se
conds
)
Fi
gu
re
5.
S
p
ee
d t
r
ac
ki
n
g
d
u
ri
ng
st
ep
t
o
r
q
ue
pert
ur
bat
i
o
n
Fig
u
r
e
6
.
Ro
tor Flux
er
ro
r du
r
i
n
g
step to
rqu
e
pert
ur
bat
i
o
n
Loa
d
A
pp
lie
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
IJPE
DS
V
o
l
.
6, N
o
. 1,
M
a
rc
h 20
1
5
:
7
7
– 85
82
b) Rated
Torqu
e
(with in
co
rrect settin
g
o
f
param
e
ters)
(a)
(b
)
(c)
Fi
gu
re
7.
S
p
ee
d t
r
ac
ki
n
g
fo
r
di
ffe
re
nt
val
u
e
s
o
f
St
at
o
r
R
e
si
st
ance (R
s
) a
n
d
Roto
r Tim
e
constant
(T
r
)
(a) R
s
, T
r
(b
) 0.
5R
s
, 0.
5T
r
(c)
1
.
5R
s
, 1.
5T
r
c) Rated
Torque (with
Vo
ltage Un
b
a
lan
ce)
Fi
gu
re
8.
S
p
ee
d t
r
ac
ki
n
g
d
u
ri
ng
V
o
l
t
a
ge
U
n
bal
a
nce
Fi
gu
re
9.
R
o
t
o
r
Fl
u
x
e
r
r
o
r
d
u
ri
ng
V
o
l
t
a
ge
U
n
bal
a
nce
4.
2. Ad
ap
ti
ve
Speed Obser
v
er
a) Ste
p
T
o
rque
(Rated
Loa
d
i
s
ap
pl
i
e
d at
3.
2
seco
nds
)
Fi
gu
re 1
0
. Spe
e
d
t
r
ac
ki
n
g
d
u
r
i
ng st
ep
t
o
r
que
pert
ur
bat
i
o
n
Fig
u
r
e
11
.
Ad
ap
tiv
e er
ro
r du
r
i
n
g
step to
rqu
e
pert
ur
bat
i
o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Effect o
f
Pa
rametric Varia
tion
s
a
n
d
Vo
ltag
e
Un
ba
lan
ce
on
Ada
p
tive
S
p
e
ed
Estima
tion
…
(Mo
han
Krishn
a
)
83
Fi
gu
re
1
2
.
St
at
or
C
u
rre
nt
er
ro
r
du
ri
n
g
st
e
p
t
o
rq
ue
pert
ur
bat
i
o
n
b)
R
a
t
e
d T
o
r
q
u
e
(I
nc
or
rect
set
t
i
ng
of
pa
ram
e
ters)
(a)
(b
)
(c)
Figu
re 1
3
. Spe
e
d
trac
kin
g
fo
r diffe
re
nt val
u
e
s
of Stator Resi
stance (R
s
) a
n
d
Roto
r Tim
e
constant
(T
r
)
(a) R
s
, T
r
(b
) 0.
5R
s
, 0.
5T
r
(c)
1
.
5R
s
, 1.
5T
r
c) Rated
Torque (with
Vo
ltage Un
b
a
lan
ce)
Fi
gu
re 1
4
. Spe
e
d
t
r
ac
ki
n
g
d
u
r
i
ng V
o
l
t
a
ge U
nbal
a
nce
Fi
gu
re 1
5
. A
d
a
p
t
i
v
e
s
p
ee
d
er
r
o
r
d
u
ri
ng
V
o
l
t
a
ge
Un
bal
a
nce
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
:
7
7
– 85
84
Fi
g
u
re
1
6
.
St
a
t
or C
u
r
r
ent
e
r
r
o
r
d
u
ri
ng
V
o
l
t
a
ge
Un
bal
a
nc
e
The dy
nam
i
c
per
f
o
r
m
a
nce of t
h
e ada
p
t
i
v
e cont
rol
schem
e
s can be di
sc
usse
d base
d o
n
t
h
e ab
ov
e
resul
t
s
.
In c
a
se
of t
h
e R
o
t
o
r F
l
ux
base
d M
R
AS S
p
ee
d est
i
m
at
i
on schem
e
, i
t
can be se
en
i
n
Fi
g
u
re
5 t
h
at
t
h
e
est
i
m
a
t
e
d speed t
r
ac
ks t
h
e
act
ual
spe
e
d
reas
ona
bl
y
wel
l
eve
n
un
der
st
ep t
o
r
q
ue
pert
ur
bat
i
o
ns.
The
conve
r
ge
nce of any ad
ap
tion sch
e
m
e
is an
i
m
p
o
r
tan
t
issu
e, in
Figu
re
6
th
e Ro
tor flu
x
erro
r is seen
t
o
co
nv
erg
e
to
zero,
wh
ich
is t
h
e reaso
n
th
e esti
m
a
ted
speed tracks
the
m
e
asure
d
spee
d i
n
a
ve
ry s
h
ort tim
e
in
terv
al. In
correct settin
g
o
f
p
a
ram
e
ters lead
s to h
i
g
h
oscillatio
n
s
in
t
h
e estim
ated
sp
eed wh
ich can
b
e
o
b
s
erv
e
d
i
n
Fig
u
re 7(b
)
an
d
(c). It is also
n
o
ticed
th
at th
e esti
m
a
ted
sp
eed tak
e
s m
o
re ti
me to
track
th
e actu
a
l
spee
d whe
n
there is a 50% increase in
th
e
set v
a
lu
e o
f
the Stato
r
resist
ance and Rotor tim
e
contant.
During
Vo
ltag
e
Un
balan
ce, ev
en
thou
gh
th
e Ro
tor
flu
x
erro
r co
n
v
e
rg
es t
o
zero
(Fi
g
ure
9
)
, th
e est
i
m
a
ted
sp
eed
settles
at a val
u
e
of
152.9 ra
d/s c
o
mpare
d
t
o
t
h
e
ac
t
u
al
spee
d
w
h
i
c
h i
s
a
b
out
1
3
0
.
2
rad/
s
(Fi
g
u
r
e
10
).
The
di
f
f
ere
n
ce
in
th
e v
a
lu
es
of th
e sp
eed
s
can
b
e
attribu
t
ed to
th
e ch
ang
e
in
th
e flux
level (b
o
t
h
in
th
e
referen
ce as
well a
s
th
e adju
stab
le
m
o
d
e
l) du
e to
u
n
b
a
lan
c
e in su
pp
ly vo
ltag
e
.
It can
be
distinctly seen that
t
h
e A
d
a
p
t
i
v
e S
p
eed
O
b
ser
v
e
r
exhi
bi
t
s
far
su
peri
or t
r
ac
ki
n
g
per
f
o
r
m
a
nce
t
h
an t
h
e R
o
t
o
r
fl
ux M
R
AS s
c
hem
e
. Thou
g
h
t
h
e t
r
acki
ng
per
f
o
r
m
a
nce in Fi
g
u
re
10 i
s
som
e
what
sim
i
l
a
r t
o
th
at o
f
th
e Ro
t
o
r Flux
MRAS, th
e d
i
fferen
c
e lies wh
en
th
e
sam
e
i
s
subject
ed t
o
pa
ram
e
t
r
ic vari
at
i
ons
. F
o
r al
l
the cases
of
Stator
resistance and R
o
tor Tim
e
cons
t
a
nt
va
ri
at
i
ons
,
a co
nsi
s
t
e
nt
,
near
sm
oot
h t
r
acki
n
g
per
f
o
r
m
a
nce i
s
obt
ai
ne
d w
h
i
c
h can be
not
i
c
e
d
i
n
Fi
g
u
re
13
(
b
) a
nd (c
). T
h
e
adapt
i
v
e er
r
o
r
fo
r spee
d de
ri
v
a
t
i
o
n
and the
Stator
current
error
fo
r th
e
ob
serv
er g
a
in co
nv
erg
e
ex
aclty to
zero
,
wh
ich is a
pr
im
ary reason
for the
su
perior
track
i
n
g
p
e
rform
a
n
ce. W
h
en
an
u
n
b
a
lan
c
ed
vo
ltag
e
is su
pp
lied
,
in
itially
th
ere are o
s
cillatio
n
s
in
th
e
esti
m
a
ted
sp
eed
,
b
u
t
it settles at a v
a
lu
e
(120
.5
rad
/
s)
somewh
at lo
wer
th
an
the actu
a
l
sp
eed
(1
30
.8
rad
/
s)
wh
ich
can
b
e
no
ticed
in
Fi
g
u
re 1
4
. Bu
t, the d
i
fferen
ces in
t
h
e sp
eed
s
is
relativ
ely lesser th
an
t
h
at of th
e
Ro
to
r
fl
u
x
M
R
A
S
sc
hem
e
. Thi
s
ca
n
be
pert
ai
ni
n
g
t
o
t
h
e
hi
g
h
st
at
or c
u
rre
nt
er
r
o
r
seen
i
n
Fi
g
u
re
1
6
.
w
h
i
c
h
affect
s
the correcti
o
n term
used
for th
e ada
p
tive
obs
e
rve
r
m
odel.
On c
o
m
p
aring the perform
a
nce
of the above s
p
ee
d estim
a
tion sche
mes, the Ada
p
tive Spe
e
d
Ob
serv
er is
p
r
esen
ted
as a
b
e
tter altern
ativ
e d
u
e
t
o
its robu
st track
i
n
g
p
e
rfo
r
m
a
n
ce and redu
ced
o
s
cillatio
n
s
.
It
t
r
acks t
h
e ac
t
u
al
speed i
n
a rel
a
t
i
v
el
y
l
e
ss
am
ount
of t
i
m
e. Thi
s
anal
y
s
i
s
con
f
i
n
es i
t
s
el
f
t
o
m
o
t
o
ri
ng m
ode at
spee
d ra
n
g
es
fr
om
m
e
di
u
m
t
o
base sy
nch
r
on
ous
s
p
eed
.
5.
CO
N
C
LUS
I
ON
Thi
s
pa
per
pre
s
ent
e
d a com
p
ari
s
o
n
o
f
per
f
o
rm
an
ce o
f
two
po
pu
lar
l
y u
s
ed
ada
p
tive control base
d
spee
d est
i
m
a
tion sc
hem
e
s, the R
o
t
o
r Fl
u
x
M
R
AS and
the Adaptive Speed
obse
r
ve
r, whe
n
subject
ed to
vari
at
i
o
ns i
n
l
o
ad t
o
rq
ue,
pa
ra
m
e
t
e
rs and
u
n
b
al
ance
d s
u
p
p
l
y
vol
t
a
ge
. It
al
so
prese
n
t
e
d t
h
e effect
of t
h
e
sam
e
o
n
t
h
e conv
ergen
ce m
ech
an
ism
s
o
f
th
e above ad
ap
tiv
e sche
m
e
s. Th
e Ad
ap
tiv
e Sp
eed
obser
v
e
r
is fo
und to
b
e
m
o
r
e
ef
f
i
cien
t an
d
ro
bu
st in
track
ing
th
e act
ual sp
eed. Thoug
h, it is also
suscep
tib
le to
speed
err
o
r
s
, t
h
e
scop
e
can
b
e
ex
tend
ed
for
jo
in
t state esti
m
a
tio
n
su
ch
th
at
, th
ere are no
m
i
s
m
a
t
ch
in
p
a
ram
e
ters d
u
ring
l
o
w and v
e
ry
lo
w sp
eed
s
.
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ati,
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han
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BIOGRAP
HI
ES
OF AUTH
ORS
M
o
han Kr
ishn
a.
S
receiv
e
d the
B.Tech and M
.
Tech degr
ees
fr
om
Am
rita Vishwa Vid
y
ap
eeth
a
m
,
Coimbatore, Ind
i
a,
in 2009 and
2012 respectiv
ely
.
Cu
rr
ently
,
he is pursuing Ph.D in Electrical
engineering fro
m VIT
University
, Chennai Campus,
in the do
main of control of induction motor
drives. His r
e
search
inter
e
sts in
clude s
e
nsorless
speed estimatio
n of Induction
motor drives, M
odel
Referen
ce Adap
t
i
ve S
y
s
t
em
s
,
Artifici
a
l In
tel
lig
en
ce bas
e
d
s
p
eed
e
s
tim
ation and o
t
her m
achin
e m
odel
ba
se
d spe
e
d
e
s
tima
t
i
on sc
he
me
s. He
i
s
a
me
mbe
r
of IAE
N
G
.
F
e
bin Day
a
J.
L.
rece
ived his
B.E. in El
ec
tric
al and
Electronics Engineer
ing from Manon
maniam
Sundarnar Univ
ersity
,
Tamiln
ad
u, India, in
2002
, M.
E. in Applied Electronics fro
m Anna University
,
Tamilnadu
,
India, in 2005 and
PhD in Infor
m
ation and Communication
from Anna Univ
ersity
,
Tamilnadu
,
India in 2013. From 2005 to 2011, he wa
s working in the Departm
e
nt of Electr
i
cal and
Electronics Engineer
ing at th
e Sri Krishna Colle
ge of Eng
i
neering and Techn
o
log
y
, Coimbatore,
India. Presen
tly he is an Assoc
i
ate Professor at
school of Electrical Engineerin
g, VIT University
,
Chennai, India.
He has published around 20 pap
e
rs in
Internatio
nal Journals
and
Conferen
ces. F
e
bin
Da
ya is
a Life
M
e
m
b
er of Indian S
o
ciet
y of T
echni
cal
Educa
t
ion. His
current
res
earch in
ter
e
s
t
s
includ
e e
l
e
c
tri
c
a
l
driv
es,
inte
llig
e
n
t s
y
st
em
s and r
e
newabl
e
energ
y
s
y
st
em
s.
Evaluation Warning : The document was created with Spire.PDF for Python.