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
. 3
,
Sep
t
em
b
e
r
2015
, pp
. 53
8
~
55
3
I
S
SN
: 208
8-8
6
9
4
5
38
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
A Novel Rot
o
r Resist
ance Estimat
i
on Tech
nique for Vect
or
Controlled Induction Motor Drive Using TS Fuzzy
Saji
Ch
ack
o
*,
Ch
an
dras
hek
h
ar
N.
B
h
end
e
**
, S
h
ai
l
e
ndr
a
Jai
n
*
,
R
.
K.
Nem
a
*
* Departm
e
nt
of
Electri
cal
Eng
i
n
eering
,
Mau
l
ana
Azad Na
t
i
onal I
n
stitute of
Techn
o
log
y
(MANIT), Bhopal
(MP), I
ndia.
** School of
Electrical Sciences
,
Indian Institute
of Technolog
y
,
Bhubaneswar (O
rissa), India.
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 18, 2015
Rev
i
sed
Ju
l 17
,
20
15
Accepte
d Aug 1, 2015
Induction
motor with ind
i
rect f
i
eld or
ient
ed con
t
rol is w
e
ll suited for h
i
gh
perform
ance ap
plic
ations due to
its ex
cellent d
ynamic behavior
. However it
is sensitive to varia
tions in rotor tim
e
constant,
especi
all
y
var
i
at
ion in rotor
re
sista
n
ce
.
In this study
a
sc
he
me
based on the Rotor flux Mod
e
l Refer
e
nce
Adaptive Con
t
ro
ller
is used for
on line
ident
i
fi
c
a
tion of
the ro
to
r resistanc
e
and thus improving the stead
y
state perform
ance of the drive. The
overriding
featur
e of th
is
estim
ation
techn
i
que is
th
e a
c
c
u
rate
ident
i
fi
cat
i
on of rotor
res
i
s
t
anc
e
durin
g trans
i
ent
and s
t
ead
y
s
t
ate cond
itions for dr
ive
operation at
full load
and at
zero s
p
eed
cond
ition. M
o
roev
er,
the effe
ctiv
enes
s
of the TS
fuzz
y con
t
roll
er
utili
zing rotor f
l
ux for online es
tim
ation of rotor
resistanc
e
for four quadrant operation of motor driv
e is
inves
tigat
ed and co
m
p
ared with
the
conventional PI and
Mamdani fu
zz
y
controller
.
Simulation
results in
MATLAB/Simu
link environment have
been presented
to confirm
the
effectivin
ess of the proposed
tech
nique.
Keyword:
Ada
p
tive system
In
direct rot
o
r f
l
ux o
r
iented
I
ndu
ctio
n m
o
to
r
Ma
m
d
ani fuzz
y cont
roller
Taka
gi
S
uge
n
o
f
u
zzy
co
nt
r
o
l
l
e
r
Propo
rtion
a
l Integ
r
al
co
n
t
ro
ller
Rotor
fl
ux
M
o
del Refe
rence
Vector Control
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
:
Saj
i
C
h
acko
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
Mau
l
an
a Azad
Natio
n
a
l In
stitu
te
of
Techn
o
l
o
g
y
(MANIT)
Bhopal (M
P), India.
Co
n
t
act:
+91-
9
893
174
845
, Fax
.
: 07
55-
2670
562
E-m
a
i
l:ch
ack
osaj
i68
@
g
m
ail.
co
m
1.
INTRODUCTION
Till th
e b
e
g
i
n
n
in
g
of 19
80
’s all su
ch
ap
p
licatio
n
s
wh
ich
req
u
i
re h
i
gh
speed
ho
ld
ing
accu
racy, wi
d
e
ran
g
e
of s
p
ee
d
cont
rol
a
nd
fa
st
t
r
ansi
ent
re
s
p
o
n
se
us
ed
DC
m
o
to
r driv
es. Trad
itio
n
a
ll
y AC
m
ach
in
es were
use
d
i
n
ap
pl
i
cat
i
ons l
i
k
e fan
,
pum
p and c
o
m
p
ressor w
h
i
c
h re
qui
re
s ro
u
gh s
p
ee
d reg
u
l
a
t
i
on an
d w
h
e
r
e t
h
e
tran
sien
t respon
se is n
o
t
critical [1
].
The a
dva
nces i
n
t
h
e
fi
el
d of p
o
w
e
r
el
ect
roni
cs
h
a
s cont
ri
but
e
d
t
o
t
h
e
devel
opm
ent of cont
rol techniques whe
r
e the perform
a
n
ce of an AC m
a
c
h
ine becam
e c
o
m
p
arable with that
of a
DC m
a
c
h
ine
[2]. T
h
es
e techni
ques
are known as
vector c
ontrol techniques a
nd a
r
e classifi
ed a
s
Di
rect
/
f
ee
dbac
k
fi
el
d
o
r
i
e
nt
e
d
c
ont
r
o
l
m
e
t
hod
(
D
F
O
C
)
a
n
d i
n
di
rect
/
fee
d
f
o
rwa
r
d
m
e
tho
d
(IR
F
O
C
)
[
3
]
.
T
h
e
m
e
t
hod
de
pe
n
d
s o
n
t
h
e det
e
r
m
i
n
at
i
on of
i
n
st
ant
a
ne
ous
rot
o
r
fl
ux
phas
o
r posi
t
i
o
n
k
n
o
w
n as
fi
el
d a
n
gl
e
o
r
u
n
it v
ector.
On
e
o
f
th
e m
a
i
n
issu
es of v
e
cto
r
con
t
ro
l is it
s d
e
p
e
nd
en
ce
o
n
m
o
to
r m
o
d
e
l an
d
is th
erefo
r
e sen
s
itiv
e
to
th
e m
o
to
r
param
e
ter v
a
riatio
n
s
[4
].
Th
e
v
a
riation
s
are
main
ly d
u
e
to th
e saturation o
f
th
e m
a
g
n
e
tizin
g
in
du
ctan
ce and th
e stato
r
/ roto
r
resistan
ce
d
u
e
to
tem
p
er
atu
r
e an
d sk
i
n
effect. Th
ese
v
a
riatio
n
s
will lead
to
err
o
r
on t
h
e fl
ux am
pl
i
t
ude a
nd i
t
s
o
r
i
e
nt
at
i
on al
on
g t
h
e
d
-
axi
s
. T
h
e sy
st
em
t
hus bec
o
m
e
s unst
a
bl
e a
nd al
s
o
i
n
creases
t
h
e
l
o
sses
i
n
t
h
e s
y
st
em
. In
ge
n
e
ral
t
h
e
fi
el
d
ori
e
nt
ed c
o
nt
r
o
l
m
e
t
hod m
o
st
com
m
onl
y
use
d
i
n
industries is the indirect field orie
nted c
ont
rol whe
r
e the orientation
of
the flux space
vector is estimated
usi
n
g t
h
e sl
i
p
si
gnal
an
d t
h
e m
easured s
p
ee
d. H
o
weve
r t
h
e feed f
o
r
w
ar
d
adj
u
st
m
e
nt
of t
h
e sl
i
p
si
gnal
r
e
qui
res
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
53
8 – 553
53
9
kn
o
w
l
e
d
g
e
of
r
o
t
o
r resi
st
a
n
ce,
rot
o
r
i
n
duct
a
n
ce an
d m
a
gne
tizin
g
i
n
du
ctan
ce v
a
lu
es and
is esti
m
a
ted
from
th
e
equi
val
e
nt
ci
rc
ui
t
m
odel
[5]
.
It
has
bee
n
gi
v
e
n t
h
at
t
h
e
var
i
at
i
ons
of
rot
o
r
re
sistance a
nd there
f
ore the
ro
t
o
r tim
e co
nstan
t
is th
e
m
o
st critica
l
i
n
ind
i
rect fiel
d
orien
t
ed
v
e
cto
r
co
n
t
ro
lled
d
r
i
v
es [6
]. If
th
is ch
an
g
e
is n
o
t
estim
ated
, th
e
o
r
t
h
ogo
n
a
lity
b
e
tween
t
h
e syn
c
hrono
u
s
fra
m
e
v
a
riab
les is lo
st
lead
ing
t
o
cro
s
s coup
lin
g an
d
p
o
o
r
dy
nam
i
c perfo
rm
ance of t
h
e
dri
v
e sy
st
em
. There
f
ore m
a
jor e
f
f
o
rt
s
were
put
i
n
f
o
r o
n
l
i
n
e est
i
m
a
t
i
on of
rot
o
r
resistance. T
h
e online
para
meter es
t
i
m
a
tion
t
ech
ni
q
u
e can be br
oa
dl
y
classified a
s
spect
ral ana
l
ysis
t
echni
q
u
e,
ob
s
e
rve
r
base
d t
echni
que
, m
odel
refere
nce ad
apt
i
v
e sy
st
em
t
echni
q
u
e a
nd
art
i
f
i
c
i
a
l
i
n
t
e
l
ligenc
e
t
echni
q
u
es
[
7
-
12]
.
The m
odel
ref
e
rence a
d
apt
i
v
e sy
st
em
s schem
e
as show
n i
n
Fi
g
u
re
1 i
s
t
h
e m
o
st
pop
ul
arl
y
used f
o
r
rot
o
r re
si
st
anc
e
est
i
m
a
ti
on be
cause o
f
i
t
s
si
m
p
l
e
r im
pl
em
ent
a
t
i
on a
nd l
e
s
s
com
put
at
i
ona
l
effo
rt
s com
p
ared t
o
ot
he
r m
e
t
hods.
The t
e
c
hni
que
pr
o
pos
es cal
c
u
l
a
t
i
on
of
a pa
ram
e
t
e
r t
o
be i
d
ent
i
f
i
e
d i
n
t
w
o di
ffe
rent
wa
y
s
[1
3-
1
5
]
. Th
e fi
rst calcu
latio
n
is based
on
referen
ces in
si
d
e
th
e co
n
t
ro
l system k
n
o
wn
as the esti
m
a
ted
v
a
lu
e and
t
h
e seco
nd
kn
ow
n as t
h
e re
f
e
rence
val
u
e
d
e
pen
d
s
on m
e
asure
d
si
g
n
al
s.
One
of t
h
e t
w
o
val
u
es s
h
o
u
l
d
be
inde
pende
n
t of
the param
e
ter whic
h
is
t
o
be estim
a
ted.
The
accuracy
of t
h
is techni
que
is
base
d
heavily
on the
machine m
odel. The
differe
n
ce obtained
be
tween t
h
e re
fe
rence a
n
d the
esti
m
a
ted
v
a
lue is tak
e
n
as an
erro
r
sig
n
a
l an
d is used
to driv
e an ad
ap
tiv
e m
e
c
h
an
ism
.Bas
ed on the
form
ulation
of t
h
e e
r
ror
signal the
MRAC
are
fu
rt
he
r
su
bcat
eg
ori
z
e
d
a
s
el
ect
r
o
m
a
gnet
i
c
t
o
r
que
ba
sed,
r
o
t
o
r
fl
ux
ba
sed
,
vol
t
a
ge base
d
a
n
d
reactive
power base
d. T
h
e a
d
aptive m
echanism
norm
a
lly us
es a PI con
t
roller for th
e g
e
neratio
n
of th
e ch
ange
in
ro
tor resistan
ce
∆
[16
]
. Th
e
PI co
n
t
ro
ller
may n
o
t
g
i
v
e
satis
facto
r
y p
e
rform
a
n
ce for op
erating
co
nd
itio
n
whe
r
e f
r
eq
ue
nt
vari
at
i
on i
n
m
o
t
o
r spee
d an
d
l
o
ad t
o
r
q
ue
is requ
ired. Fu
zzy lo
g
i
c c
ontrol
l
ers as com
p
ared to
PI con
t
ro
ller do
no
t requ
ire precise
m
a
th
e
m
atical
m
o
d
e
l,can ha
ndle nonlinearity and ar
e
m
o
re ro
bust [
1
7
,
1
8
]
.
Based on the rule conseque
nt the fuzzy cont
rollers a
r
e
furt
her classifie
d
as Ma
m
d
ani and TS fuzzy controller.
In T
S
-F
uzzy
t
h
e l
i
n
g
u
i
s
t
i
c
r
u
l
e
co
nse
que
nt
i
s
m
a
de vari
a
b
l
e
by
m
eans of i
t
s
pa
ram
e
ters an
d
hence
,
i
t
can
pr
o
duce a
n
i
n
f
i
ni
t
e
num
ber o
f
gai
n
va
ri
at
i
o
n cha
r
act
eri
s
t
i
c
s [1
9]
.M
ore
v
er i
t
has a d
e
fi
ni
t
e
edge
o
v
er t
h
e
Ma
m
d
ani fuzz
y due to the le
ss num
b
er
o
f
fu
zzy sets
u
s
ed
for th
e inp
u
t
s, l
ead
ing
to lesser ru
le sets.
Fi
gu
re 1.
B
l
oc
k di
ag
ram
of M
R
AC
As
per
t
h
e
aut
h
o
r’s
kn
o
w
l
e
d
g
e,
n
o
w
o
r
k
ha
s bee
n
re
po
rt
ed
whe
r
e t
h
e T
S
f
u
zzy
c
ont
ro
l
l
e
r has
be
e
n
use
d
as a
n
ada
p
tive m
echanis
m for
i
d
ent
i
f
i
c
at
i
on
of
rot
o
r
r
e
si
st
ance base
d o
n
R
o
t
o
r Fl
u
x
M
o
del
R
e
fe
r
e
nce
Ad
ap
tiv
e C
o
n
t
ro
lller
(RF-M
R
AC) i
n
stead
o
f
th
e ex
isting
PI
and
Mam
d
an
i fu
zzy co
n
t
rollers as stated in
p
a
per
[1
6-
1
8
]
.
In t
h
i
s
pape
r t
h
e R
F
-M
R
A
C
usi
ng
TS fuzzy
co
nt
r
o
l
l
e
r as ada
p
t
i
v
e m
echani
s
m
i
s
devol
ope
d
and i
s
in
v
e
stig
ated
for an
IRFOC
in
du
ction
m
o
tor
d
r
i
v
e.Th
e
o
b
j
ect
i
v
e
o
f
t
h
e
pr
o
pose
d
w
o
r
k
i
s
1
)
t
o
obt
ai
n a
n
accurate
online rot
o
r resista
n
ce ide
n
tification sc
hem
e
for a
four
qua
d
ra
nt drive
operation a
n
d
also to
m
i
nim
i
ze t
h
e o
v
er
exci
t
a
t
i
on/
un
de
r e
x
ci
t
a
t
i
on
of t
h
e m
o
t
o
r
flu
x
d
u
e t
o
rot
o
r
resistance
v
a
riations,
2
)
ac
curat
e
id
en
tificatio
n of ro
tor
resistance un
d
e
r symmetrical sh
ort
circu
it con
d
ition
o
f
ro
to
r circu
it an
d 3) to ob
erve th
e
effectiv
en
ess
of th
e iden
tificatio
n
techn
i
qu
e
wh
en
the dr
iv
e is o
p
e
rating
at
zero
sp
eed
with
rated lo
ad
to
rqu
e
co
nd
itio
n. Th
i
s
p
a
p
e
r ev
al
u
a
tes th
e
p
e
rforman
ce in
dex
of
th
e ro
tor resistan
ce id
en
tifi
catio
n
as in
tegral ti
m
e
sq
uar
e
er
ror
(
I
TSE) fo
r th
e
pr
opo
sed sch
e
me and
is co
m
p
ared with th
e
o
t
h
e
r two
con
t
ro
llers i.e. t
h
e
PI and
the Mam
d
ani fuzzy.
The pa
per i
s
o
r
ga
ni
zed as f
o
l
l
ows:
Sect
i
o
n 2 pr
o
v
i
d
es a b
r
i
e
f ove
rvi
e
w o
f
t
h
e dy
nam
i
c
m
odel
i
ng of
t
h
e fi
el
d
ori
e
nt
ed ve
ct
or
co
nt
r
o
l
d
r
i
v
e.
Sect
i
on
3
desc
ri
bes
t
h
e f
unct
i
o
ns
o
f
t
h
e
vari
ous
b
l
ock i
n
v
o
l
v
e
d
i
n
t
h
e
m
odel
i
ng
of
t
h
e vect
or
co
nt
r
o
l
l
e
d
I.M
dri
v
e an
d al
s
o
t
h
e
r
o
t
o
r
re
si
st
an
ce i
d
e
n
t
i
f
i
cat
i
on sc
hem
e
usi
n
g R
F
-
.M
R
A
C
.
Sect
i
on
4 desc
ri
bes
t
h
e M
a
m
d
ani
fuzzy
cont
rol
s
c
hem
e
as
an adaptive m
ech
anism
of the rot
o
r fl
ux
m
odel
referenc
e adapt
i
v
e sy
st
em
. Sect
i
on 5 descri
bes i
n
de
t
a
i
l
t
h
e desi
g
n
and i
m
pl
em
entat
i
on o
f
t
h
e pr
op
o
s
e
d
TS fu
zzy con
t
ro
l sch
e
m
e
as t
h
e ad
ap
tiv
e m
e
ch
an
ism
o
f
RF-MRAS. Sectio
n
6
d
e
tails th
e si
m
u
latio
n
resu
lts of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
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:
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8-8
6
9
4
A N
o
vel
R
o
t
o
r
Resi
st
ance
Est
i
m
at
i
o
n
Tech
ni
que
f
o
r
Vect
or
C
ont
r
o
l
l
e
d
In
d
u
ct
i
o
n
M
o
t
o
r…
(S
a
ji Cha
cko
)
54
0
t
h
e PI
, M
a
m
d
ani
an
d
pr
op
o
s
ed TS
f
u
zzy
adapt
i
v
e
sche
m
e
un
der
di
f
f
e
rent
dri
v
e o
p
e
rat
i
ng c
o
ndi
t
i
ons
an
d
concl
u
si
o
n
i
s
g
i
ven i
n
Sect
i
o
n
7.
2.
DESIG
N
F
O
R VECTO
R
CO
NTR
O
L
D
R
IVE
S
The dy
nam
i
c
m
odel
of i
n
d
u
c
t
i
on m
o
t
o
r fo
r rot
o
r fl
ux
or
i
e
nt
ed vect
or
cont
rol
ap
pl
i
cat
i
on can b
e
written
as fo
llows
_
_
0
1
0
1
0
0
(1
)
Whe
r
e
de
not
e
s
t
h
e
deri
vat
i
v
e
o
p
erat
or
,
,
are t
h
e stator c
u
rre
n
ts and
,
th
e
ro
t
o
r
flu
x
es in
fra
m
e
. Sim
ilarly
,
,
and
are the
s
t
ator résista
n
ce
, stator sel
f
inducta
nce,
rot
o
r
resistance a
n
d
the rotor
self i
n
ductance
re
sp
ectiv
ely. Th
e ro
tor tim
e co
n
s
tan
t
is
g
i
v
e
n
as
and leaka
g
e
inductance
is
wh
er
e
1
.
Fo
r
r
o
to
r
f
l
ux
o
r
ien
t
ed con
t
rol th
e ro
tor f
l
ux
is
directe
d
al
ong the
d
-a
xi
s
and
i
s
e
qual
t
o
an
d
therefore
0
. Th
us
t
h
e e
quat
i
on
(
1
a)
m
odi
fi
es t
o
as s
h
o
w
n
bel
o
w
0
_
_
0
0
0
1
0
00
0
0
0
0
0
(2
)
From
equation
(2b) it can
be
s
een that t
h
e
axis vo
ltag
e
are co
up
led b
y
t
h
e
fo
llo
wi
n
g
term
s
:
(3
)
(4
)
To
ach
iev
e
lin
ear co
n
t
ro
l of stato
r
vo
ltag
e
it is
n
ecessary
to
re
m
o
v
e
the d
ecou
p
ling
term
s an
d
is
cancelled
by
using a
decoupled m
e
thod t
h
at
utilizes
nonlinear fee
d
bac
k
of
the
coupling
voltage
.
3.
MODELING
OF VOLT
AGE CONT
ROLLED IM
DRIVE WITH RO
T
O
R RESISTANCE
ESTIMAT
O
R
Th
e m
a
in
ai
m
o
f
th
e
v
ector co
n
t
ro
l of ind
u
ctio
n
m
o
to
r is to
con
t
ro
l it j
u
st lik
e a sep
a
rately ex
cited
DC m
o
to
r d
r
ive wh
ere on
e can
ob
tain
ind
e
p
e
nd
en
t con
t
rol of the two
variables arm
a
ture a
nd fiel
d current
whi
c
h a
r
e
ort
h
og
o
n
al
t
o
eac
h
ot
he
r t
hus
ha
v
i
ng i
nde
pe
nde
nt
co
nt
r
o
l
ove
r
t
o
r
q
ue a
n
d
fl
u
x
.
The
bl
ock
d
i
agram
of
an
i
n
di
rect
r
o
t
o
r fl
ux
ori
e
nt
ed s
p
ee
d c
ont
r
o
l
o
f
i
n
d
u
ct
i
o
n
m
o
t
o
r i
s
s
h
o
w
n i
n
Fi
gu
re
2.
The sc
hem
e
co
nsi
s
t
s
of t
h
e c
u
r
r
e
n
t
c
ont
rol
l
o
o
p
wi
t
h
i
n
t
h
e s
p
ee
d c
ont
rol
l
o
o
p
.
Th
e schem
e
uses
PI c
o
nt
rol
l
e
rs
f
o
r t
h
e
d-a
x
i
s
a
n
d
q
-
axi
s
c
u
r
r
ent
w
hos
e p
r
op
ort
i
o
n
al
an
d i
n
t
e
g
r
a
l
gai
n
s
are as
s
h
o
w
n i
n
A
p
pe
ndi
x-
II
I, t
h
e
ba
nd
wi
dt
h
of t
h
e
i
nne
r
cur
r
ent
l
o
op i
s
chose
n
hi
g
h
e
r
t
h
an t
h
e fl
u
x
and s
p
ee
d co
nt
rol
l
e
r. T
h
e v
o
l
t
a
ge dec
o
u
p
l
i
n
g
equat
i
o
ns (
3
)
& (4
)
are ad
ju
sted
with
th
e
ou
tpu
t
o
f
th
e con
t
ro
llers to ob
ta
in go
od
curren
t
con
t
ro
l actio
n. Th
e
d
-
ax
is and
q
-
ax
is
refe
rence
volta
ges
and
thu
s
ob
tain
ed are tran
sfo
r
m
e
d
t
o
t
h
e
stationa
ry
i.e
.
stato
r
refe
re
n
ce f
r
am
e
wi
t
h
t
h
e hel
p
of fi
el
d
an
gl
e
.The t
w
o p
h
ase
vol
t
a
ge
and
in the stator re
ference
fram
e
are the
n
t
r
ans
f
o
r
m
e
d t
o
t
h
ree
phas
e
s
t
at
or
refe
rence
v
o
l
t
a
ges
,
,
which
acts as mo
du
latin
g
v
o
l
t
a
g
e
for t
h
e
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I
S
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:
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088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
53
8 – 553
54
1
m
odul
at
or by
usi
n
g t
h
e si
ne
-
t
ri
angl
e p
u
l
s
e
wi
dt
h m
odul
at
i
on
(SP
W
M
)
sc
hem
e
. The
m
o
dul
at
o
r
o
u
t
p
ut
whi
c
h
is in
th
e fo
rm o
f
pu
lses is u
s
ed
to
d
r
i
v
e th
e IG
BT wit
h
an
ti-parallel d
i
o
d
e
acting
as switch
e
s for th
e
con
v
e
n
t
i
onal
t
w
o
l
e
vel
vol
t
a
ge s
o
urce i
nve
r
t
er (
V
S
I).
As s
h
ow
n i
n
F
i
gu
re
2 t
h
e st
at
or
cu
rre
nt
s a
r
e
m
easured a
n
d
t
r
ans
f
orm
e
d a
s
d-
q
ax
is
cu
rre
n
t
s
,
wh
ic
h
are the
n
used a
s
feedbac
k
signal
s for t
h
e curre
nt controller. The
d
- axis c
u
rrent
i
s
passe
d t
h
ro
u
gh a
l
o
w
p
a
ss
filter
with ti
m
e
co
n
s
tan
t
eq
u
a
l
to
ro
to
r t
i
m
e
co
n
s
tan
t
to
o
b
t
ai
n
th
e ro
t
o
r flux wh
ich acts as feedb
a
ck to
the fl
ux
c
ont
ro
ller. T
h
e
rot
o
r
spee
d
,
to
rqu
e
cu
rr
en
t
rot
o
r
fl
ux
an
d
rot
o
r
t
i
m
e const
a
nt
are us
e
d
to
d
e
term
in
e th
e slip
sp
eed
and
fro
m
it th
e roto
r
flux
p
o
sitio
n
fo
r
and
t
r
a
n
sf
orm
a
t
i
on.
Fi
gu
re
2.
B
l
oc
k
di
ag
ram
of a
vol
t
a
ge
co
nt
r
o
l
l
ed I
F
OC
d
r
i
v
e
.
a.
Rotor Resistance Identific
a
t
i
on usi
n
g
R
o
t
o
r Fl
u
x
The
bl
oc
k di
a
g
ram
of t
h
e
ro
t
o
r fl
ux
base
d
M
R
AC
fo
r i
d
e
n
t
i
f
i
cat
i
on
of
r
o
t
o
r resi
st
anc
e
i
s
sho
w
n i
n
Fi
gu
re 3,
whe
r
e
t
h
e
i
n
put
s
,
,
,
&
are th
e m
o
to
r termin
al v
o
ltages,
c
u
rrent
and s
p
eed feedbac
k
s.
The r
o
to
r flu
x
obt
ai
ne
d f
r
om
t
h
e vol
t
a
ge m
odel
whi
c
h act
s as t
h
e refe
re
n
ce out
put
o
f
t
h
e
m
odel
ada
p
t
i
v
e
refe
rence
sc
he
m
e
i
s
o
b
t
a
i
n
e
d
by
m
easuri
n
g t
h
e m
ach
in
e ter
m
in
al v
o
l
t
a
g
e
and
cu
rren
ts, wh
ich
are th
en
trans
f
orm
e
d to
the stationa
ry refere
nce
fram
e
as
,
,
&
.
Fi
gu
re
3.
Pr
o
p
o
se
d r
o
t
o
r
fl
u
x
base
d M
R
AC
f
o
r
r
o
t
o
r re
si
st
ance est
i
m
ati
o
n
The r
o
to
r fl
ux
whe
r
e
and
are the d-a
x
is a
n
d q-axis
rot
o
r
flux in t
h
e
stationary
refe
r
e
nce
fram
e
wh
ich are
de
rive
d
as:
(5
)
and
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
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SN
:
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8-8
6
9
4
A N
o
vel
R
o
t
o
r
Resi
st
ance
Est
i
m
at
i
o
n
Tech
ni
que
f
o
r
Vect
or
C
ont
r
o
l
l
e
d
In
d
u
ct
i
o
n
M
o
t
o
r…
(S
a
ji Cha
cko
)
54
2
gi
ve
n t
h
at
=
and
=
are t
h
e stat
or d-q fl
ux in
stationary
refe
rence
f
r
am
e,
is the
leaka
g
e inductance a
n
d
is the stator resistance
.
Sim
i
l
a
rl
y
t
h
e f
l
ux
out
put
is
o
b
t
a
i
n
e
d fro
m th
e cu
rr
e
n
t mo
d
e
l for
th
e ad
ju
s
t
ab
le
m
odel
i
s
obt
ai
ned
by
m
easuri
n
g
t
h
e c
u
rre
nt
and
m
o
t
o
r s
p
ee
d
, w
h
ere
1
(7
)
and
1
(8
)
The differe
n
ce
betwee
n
and
acts as
the e
r
ror signal fo
r the a
d
a
p
tive
mechanism
whos
e
out
put
indicates the
cha
n
ge i
n
rot
o
r re
sistance
∆
wh
ich
is then
add
e
d
u
p
with
th
e no
m
i
n
a
l resistan
ce valu
e
i.e.
to achie
ve
the actual
rotor
resistance
.The o
b
t
a
i
n
ed
new
val
u
e of
co
rr
esp
ond
ing to
ch
ang
e
i
n
ro
t
o
r
resistan
ce is th
en
u
s
ed
t
o
d
e
term
in
e the slip
sp
eed
an
d is ad
d
e
d
up
with
the ro
tor sp
eed
t
o
obt
ai
n
t
h
e sy
nc
hr
o
n
o
u
s
spee
d
.
4.
IMPLEME
N
TATION OF
FUZ
Z
Y
CONTROLLER
In t
h
i
s
st
udy
t
h
e co
nve
nt
i
o
nal
PI c
ont
r
o
l
l
er
as an ada
p
tive m
echanism has been
replace
d by
Ma
m
d
ani fuzz
y controller. T
h
e fuzzy controller as
sh
own
in
Fi
g
u
re
4 co
nsists o
f
two
i
n
pu
ts
e
k
and
e
k
and one output
∆u
. T
h
e
i
n
put
e
k
is
the differe
n
ce
between
the
reference
rot
o
r
fl
ux
“
ψr
” a
n
d act
ual
rot
o
r flu
x
"ψr
i.e.
k
ψr
ψ
r
, and th
e i
n
pu
t
e
k
w
h
i
c
h
i
n
di
cat
es t
h
e c
h
a
n
ge i
n
e
r
r
o
r
an
d
i
s
gi
ve
n
as
e
k
e
k
e
k1
.
T
h
ere
a
r
e t
w
o
norm
aliz
ing
factors
k1
&
k2
for
in
pu
ts
e1
and
e2
and
one
de-
no
rm
al
i
z
i
ng fa
ct
or f
o
r o
u
t
p
ut
∆u
.
In norm
alization proces
s
the input
val
u
es are scaled in the
range [-1,
1] and
t
h
e de
-n
orm
a
l
i
zat
i
on p
r
ocess
con
v
e
r
t
s
t
h
e cr
i
s
p o
u
t
p
ut
val
u
e of t
h
e f
u
zzy
cont
rol
l
e
r t
o
a
val
u
e
depe
n
d
i
n
g
o
n
the
out
put
cont
rol
elem
ent. In the
fu
zzifier t
h
e c
r
isp
values
of i
n
put
and
are converte
d i
n
to
fuzzy
value
s
[2
0]
. F
o
r t
h
i
s
pu
r
pose
seve
n
t
r
i
a
ng
ul
ar
fuzz
y
m
e
m
b
ershi
p
fu
nct
i
o
ns are
d
e
fi
ne
d f
o
r ea
ch
i
n
p
u
t
as wel
l
as t
h
e
out
put
.
Fi
gu
re
4.
B
l
oc
k
di
ag
ram
of a
Fuzzy
c
ont
rol
l
er
Fig
u
re
5
illu
strates th
e triang
le
m
e
m
b
ersh
ip
fun
c
tion
s
o
f
the first inp
u
t
i.e.
w
h
i
c
h a
r
e
de
fi
n
e
d
by
seve
n l
i
n
gu
i
s
t
i
c
vari
abl
e
s
as Ne
gat
i
v
e B
i
g (
N
B
)
Ne
gat
i
v
e M
e
di
um
(NM
)
, Ne
gat
i
v
e
Sm
al
l
(NS),
Z
e
ro
(Z
)
,
Po
sitiv
e Sm
all
(PS), Po
sitiv
e Med
i
u
m
(PM) an
d
Po
sitiv
e
B
i
g
(PB). Th
e
ov
erlap
rates of
th
e m
e
m
b
ersh
ip
are
t
a
ken a
s
50%
.
The fuzzy rule
base represe
n
t the knowledge of
hum
an o
p
erat
ors w
h
o m
a
ke necessar
y
changes i
n
t
h
e co
nt
r
o
l
l
e
r
out
put
t
o
obt
ai
n sy
st
em
wi
t
h
m
i
nim
u
m
erro
r an
d
fast
er
re
spo
n
se
. F
o
r
t
h
i
s
t
h
e
beha
vi
o
r
of t
h
e
er
ro
r sign
als
and
has t
o
be
o
b
ser
v
e
d
a
n
d a
ccor
d
i
n
gl
y
i
t
i
s
t
o
be
deci
de
d
whet
her
t
h
e
cont
rol
l
e
r
out
put
∆
is to be increase
d
or decreased. T
h
e cont
roller
for
t
h
e st
u
d
y
m
a
ke
use o
f
t
h
e sl
i
d
i
ng m
ode r
u
l
e
b
a
s
e
sh
own
in Fi
g
u
re 6
as it is easy
to
im
p
l
e
m
en
t fo
r real tim
e ap
p
licatio
n
The
de
vel
o
ped
f
u
zzy
l
o
gi
c u
s
es t
h
e m
i
n –
m
a
x com
posi
t
i
onal
r
u
l
e
of
i
n
fere
nce.
T
h
e
i
n
fe
renc
e
mech
an
ism
o
f
th
e fu
zzy
co
n
t
ro
ller is im
p
l
e
m
en
ted
with reg
a
rd to
t
h
e ru
le
b
a
se
g
i
v
e
n b
y
μ
minμ
1
,μ
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
I
J
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S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
53
8 – 553
54
3
The
de
fuzzi
fi
er
pr
ocess
m
a
kes u
s
e
of
t
h
e
ce
nt
re
o
f
gra
v
i
t
y
m
e
t
hod
an
d
i
s
gi
ve
n a
s
∆μ
∑
∑
wh
ere, n is th
e
n
u
m
b
e
r
o
f
fu
zzy sets in
th
e outp
u
t
.
Fi
gu
re
5.
I
n
p
u
t
va
ri
abl
e
e
1
(k
)
m
e
m
b
ershi
p
f
unct
i
o
n
NB
NM
NS
Z PB
PM
PB
NB
NB NB NB
NB
NM
NS
Z
NM
NB NB NB
NM
NZ
Z
PS
NB
NB
NB
NM
NS
Z
PS
PM
Z
NB
NM
NS
Z
PS
PM
PB
PS
NM
NS
Z
PS
PM
PB
PB
PM
NS
Z
PS
PM
PB
PB
PB
PB
Z
PB
PM
PB
PB
PB
PB
Fi
gu
re 6.
M
a
m
d
ani
Fuzzy
r
u
l
e
base
fo
r ro
tor r
e
sistan
ce estimatio
n
5.
DESIGN OF PROPOSE
D
TS
FUZ
Z
Y
CONTROLLER
The m
a
jor
difference
betwee
nthe Mam
d
ani and t
h
e TS
fuzzy controller
is that the former e
m
ploy
fuzzy
set
s
as t
h
e co
nse
que
nt
whe
r
e as t
h
e l
a
t
e
r em
pl
oy
l
i
n
ear fu
nct
i
o
n as
t
h
e conse
q
uen
t
[21]
. Th
e l
i
ngui
st
i
c
rul
e
co
nse
que
n
t
i
s
m
a
de vari
a
b
l
e
by
m
eans of i
t
s
param
e
t
e
rs an
d t
h
ere
f
o
r
e t
h
e TS fuzzy
cont
r
o
l
schem
e
can
pr
o
duce
a l
a
rg
e n
u
m
b
er
of
g
a
i
n
vari
at
i
o
ns.
F
o
r
t
h
e
st
u
d
y
t
h
e
i
n
put
va
ri
abl
e
s a
r
e
an
d
sam
e
as
d
e
fi
n
e
d abov
e.for Mam
d
an
i fu
zzy. Each v
a
riab
le was fu
zzified
b
y
two
i
n
pu
ts
fu
zzy sets n
a
m
e
d
as
po
sitiv
e
(P) and
n
e
g
a
tiv
e (N)
resp
ectiv
ely as sh
own
in
Fi
g
u
re 7. Th
e m
a
th
e
m
a
tical rep
r
esen
tatio
n
of po
sitiv
e and
negat
i
v
e
m
e
m
b
ershi
p
fu
nct
i
o
n
f
o
r t
h
e i
n
p
u
t
v
a
ri
abl
e
s a
r
e
gi
v
e
n
bel
o
w.
μ
0,
2
1,
,
(9
)
μ
1,
2
0,
,
(1
0)
The val
u
e of
μ
μ
i
s
ei
t
h
er
0 or
1 whe
n
is o
u
t
si
de th
e in
terv
al
[-L, L]. Th
e v
a
l
u
e
of
L
pl
ay
s a
n
i
m
port
a
nt
r
o
l
e
i
n
t
h
e c
ont
rol
l
e
r
pe
rf
orm
a
nce a
n
d
s
h
o
u
l
d
be
j
udi
ci
o
u
sl
y
c
h
o
s
en.
As
t
h
e
r
e a
r
e t
w
o
fu
zzy sets fo
r each
inp
u
t
, t
h
ere will b
e
(2
x
2) fu
zzy v
a
lu
es
to
cov
e
r all th
ese co
m
b
in
atio
ns. Th
e
fu
zzy con
t
ro
l
ru
les
fo
r t
h
e two
inpu
ts
u
s
e the fo
llo
wi
n
g
sim
p
l
i
fied
ru
les
as shown in
Tab
l
e 1.
-0
.
4
-0
.
3
-0
.
2
-0
.
1
0
0.
1
0.
2
0.
3
0.
4
0
0.
2
0.
4
0.
6
0.
8
1
Ef
l
u
x
De
gr
e
e
of
m
e
m
b
e
r
s
h
i
p
NL
NM
NS
Z
P
S
P
M
P
L
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
o
vel
R
o
t
o
r
Resi
st
ance
Est
i
m
at
i
o
n
Tech
ni
que
f
o
r
Vect
or
C
ont
r
o
l
l
e
d
In
d
u
ct
i
o
n
M
o
t
o
r…
(S
a
ji Cha
cko
)
54
4
Fi
gu
re
7. In
p
u
t
vari
a
b
l
e
s
m
e
m
b
ers
h
i
p
f
u
nct
i
o
n
Table
1. T
S
fuzzy rule set
Ru
le No
.
IF
1
AND
2
THEN
R1 Positive
Positive
1
1
1
∗
1
2
∗
2
R2 Positive
Negative
2
2
∗
1
R3 Negative
Positive
3
3
∗
1
R4 Negative
Negative
4
4
∗
1
The c
o
r
r
es
po
n
d
i
n
g i
n
c
r
em
ent
a
l
out
put
of t
h
e fuzzy control
l
er is
μ
1
∗
∑
μ
∑
μ
(1
1)
whe
r
e
1
1
∗
1
2∗
2
For
t
h
i
s
st
u
d
y
t
h
e al
g
o
ri
t
h
m
of t
h
e p
r
o
p
o
se
d TS
fuzzy
c
o
nt
r
o
l
l
e
r i
s
de
v
e
l
ope
d a
nd
pr
o
g
ram
m
ed i
n
M
A
TLAB
M
-
f
i
l
e
and i
s
t
h
en
use
d
as a
Si
m
u
l
i
nk
bl
oc
k i
n
t
h
e m
odel
wi
t
h
t
h
e hel
p
of
Em
bed
d
e
d
M
F
u
n
c
t
i
on
bl
oc
k a
v
ai
l
a
bl
e i
n
t
h
e M
A
TL
AB
/
S
i
m
ul
i
nk l
i
b
rary
.
The
val
u
es
of t
h
e si
x
c
onst
a
nt
s
1,
2,
3,
41
2
as gi
ve
n i
n
A
p
pen
d
i
x
-I
I a
r
e d
e
t
e
rm
i
n
ed by
t
r
i
a
l
and
er
ror with perform
a
nce
indice
as
t
h
e in
teg
r
al time squ
a
re
er
ro
r of
(k)
.
In
ge
ne
ral
t
h
e
nu
m
b
er of
un
k
n
o
w
n
c
onst
a
nt
s
f
o
r
2
r
u
l
e
s a
r
e
gi
ven
by
2
, w
h
ere
M
stan
d
s
fo
r th
e
nu
m
b
er
of
inpu
ts.
6.
R
E
SU
LTS AN
D ANA
LY
SIS
A si
m
u
l
a
t
i
on
m
odel
of
v
o
l
t
a
ge c
ont
rol
l
e
d
IR
F
O
C
as s
h
o
w
n i
n
Fi
g
u
r
e
2 i
s
devel
ope
d i
n
a
M
A
TLAB
/
Si
m
u
l
i
nk e
n
vi
r
o
n
m
ent
to ascert
a
in the effectiv
ene
ss of the
propose
d
a
d
aptive algorithm
.
T
h
e
param
e
t
e
rs an
d rat
i
n
gs
o
f
t
h
e t
e
st
m
o
t
o
r
are gi
ven
i
n
Ap
pe
ndi
x-
I. T
h
e SP
WM
bas
e
d i
n
di
rect
r
o
t
o
r
fl
u
x
o
r
ien
t
ed
co
n
t
ro
ller is tested
for step
increa
se in rotor
resistance by c
o
nnecting a t
h
ree
pha
se star c
onnecte
d
resisto
r
b
a
n
k
t
o
th
e ro
tor of th
e th
r
ee
ph
ase
slip
ring
in
du
ctio
n
m
o
to
r ex
t
e
rnally. Sim
i
la
rly a step decrease in
ro
t
o
r
resistan
ce is ob
tain
ed b
y
instru
m
e
n
tin
g
th
e wro
n
g
ro
t
o
r
resistan
ce
v
a
lu
e i
n
th
e con
t
ro
ller. The
si
m
u
latio
n
ti
me u
s
ed
are on
ly to
ex
p
l
ain
the co
n
c
ep
ts
, as
suc
h
sudde
n
practical change
s in rot
o
r resis
t
ance
due t
o
tem
p
erature variation
rarely occurs in practice du
e t
o
the large the
r
mal tim
e constant of t
h
e m
o
tor. T
h
e
IRFOC
driv
e is subj
ected to
d
i
fferen
t
op
eratin
g
con
d
ition
s
no
ted as Case-II to IV
b
e
low,
du
ri
n
g
wh
i
c
h
step
in
crease an
d
decrease in
ro
t
o
r resistan
ce is in
itiated
to
t
e
st th
e effectiv
en
ess of th
e
ad
ap
tiv
e m
ech
an
ism
.
Und
e
r th
ese
op
erating
co
nd
i
tio
n
s
th
e
pe
rform
a
nce analysis of t
h
e
pro
p
o
s
ed TS
f
u
zzy
cont
rol
l
e
r
base
d R
F
-
MRAC in
term
s
o
f
settlin
g
ti
m
e
an
d
stead
y state erro
r is
m
a
d
e
an
d
is co
m
p
ared
with
th
e o
t
h
e
r establish
e
d
co
n
t
ro
llers i.e.
th
e PI an
d Mam
d
an
i fu
zzy co
n
t
ro
ller.
6.
1. C
a
se-I
: S
p
eed and
Lo
a
d
Torq
ue Co
n
s
ta
nt
w
i
t
h
RF
-M
RA
S Disa
b
l
ed
Th
e
I
R
FO
C driv
e is
o
p
e
r
a
ted at con
s
tan
t
speed
set
of
1
000
r
p
m
an
d lo
ad
torq
u
e
of
4
N
m
. as shown
i
n
Fi
g
u
r
es
8 a
n
d
9.
A
st
ep c
h
ange
i
n
m
o
t
o
r
rot
o
r
resi
st
anc
e
ab
ove
by
5
0
%
an
d
bel
o
w
b
y
30
%
of i
t
s
n
o
m
i
nal
val
u
e
is
d
o
n
e
at t=12
sec
with
ro
t
o
r fl
u
x
m
o
d
e
l reference ad
ap
tiv
e mech
an
ism
k
e
p
t
in
activ
e. From
Fig
u
re 10
(a)
& (b) it is
o
b
s
erv
e
d
th
at th
e actu
a
l an
d
th
e referen
ce
v
a
lue o
f
th
e d
-
ax
is flux
rem
a
in
s s
a
m
e
i.e.
0.
93
6
ω
b
till th
e in
stru
m
e
n
t
ed
an
d actu
a
l
v
a
lue of
ro
t
o
r resist
an
ce are equ
a
l. At t=1
2
sec
wh
en th
e ch
ang
e
in
ro
t
o
r
resistan
ce is in
itiated
it is seen
t
h
at, the in
crease
in
roto
r
resistan
ce
has resu
lted
i
n
su
dd
en
ch
ang
e
s in
the
m
o
to
r actu
a
l flu
x
with
its valu
e in
creasi
n
g
fro
m
0
.
936
ωb
to
1
.
19
5
ωb
. Sim
i
larly the decrease in rotor
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
53
8 – 553
54
5
resi
st
ance
has
resul
t
e
d
i
n
t
h
e
act
ual
fl
u
x
dec
r
easi
n
g f
r
o
m
0.9
36
ωb
t
o
0.
6
re
spectively. T
h
e increase i
n
ro
t
o
r
flux
m
a
y
lead
to
o
v
er ex
citatio
n
o
f
t
h
e m
o
to
r resu
ltin
g
i
n
in
creased
core l
o
sses an
d
satu
ratio
n.
It also
seen f
r
o
m
Fi
gure
1
1 t
h
at
t
h
e
el
ect
rom
a
gnet
i
c
devel
ope
d
by
t
h
e m
o
t
o
r
has al
so
dec
r
e
a
sed
whe
n
t
h
e
rot
o
r
resistance is
de
creased.
Fi
gu
re 8.
Trac
ki
n
g
of
co
nst
a
nt
s
p
eed
re
fere
nce
of
1
0
0
0
r
p
m
Fi
gu
re
9.
Trac
ki
n
g
t
h
e
co
nst
a
nt
l
o
a
d
t
o
r
que
r
e
fere
nce
4Nm
(a)
0
5
10
15
20
25
0
100
200
300
400
500
600
700
800
900
1
000
1
100
tim
e
(s
e
c
)
R
o
t
o
r
sp
eed
(
r
p
m
)
R
e
f
e
r
e
n
c
e r
o
t
o
r
s
p
eed
A
c
tu
a
l
r
o
to
r
s
p
e
e
d
fo
r
PI b
a
s
e
d
M
R
A
S
A
c
t
u
al
r
o
t
o
r
sp
e
e
d
f
o
r
M
a
m
d
an
i
f
u
z
z
y
b
ase
d
M
R
A
S
A
c
t
u
al
r
o
t
o
r
sp
e
e
d
f
o
r
T
S
f
u
z
z
y
b
ase
M
R
A
S
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I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
o
vel
R
o
t
o
r
Resi
st
ance
Est
i
m
at
i
o
n
Tech
ni
que
f
o
r
Vect
or
C
ont
r
o
l
l
e
d
In
d
u
ct
i
o
n
M
o
t
o
r…
(S
a
ji Cha
cko
)
54
6
(b
)
Figu
re 1
0
.
R
o
tor
flu
x
f
o
r step
(a)
inc
r
ease (b
) decr
ease
in
roto
r resistan
ce with
id
en
tificatio
n
d
i
sab
l
ed
Fi
gu
re
1
1
. E
ffe
ct
on
T
o
r
que
d
e
vol
ped
f
o
r
st
e
p
i
n
c
r
ease i
n
ro
t
o
r
resi
st
ance
wi
t
h
i
d
e
n
t
i
f
i
cat
i
on
di
sa
bl
ed
6.
2. C
a
se-I
I: S
p
eed and
L
o
a
d
T
o
rq
ue Co
n
s
ta
nt
w
i
t
h
RF
-M
RA
S
E
n
abl
e
d
Th
e
IFOC drive is no
w
subj
ected
to
the sam
e
op
erating
co
nd
itio
n
as abov
e, with
step
ch
an
g
e
in
ro
t
o
r
resistance at t
= 12 sec
.
T
h
e i
n
tegral tim
e
square
erro
r
perform
ance index is use
d
for
finding the
c
o
efficients
k
and
k
of th
e PI
co
n
t
ro
ller acting
as t
h
e ad
ap
tiv
e m
ech
an
is
m
an
d ar
e
fo
und
t
o
b
e
5 and
80
resp
ectiv
ely.
I
t
i
s
obse
r
ved
fr
o
m
Fi
gure
1
2
(a
) an
d
(b
) t
h
at
d
u
ri
ng m
o
t
o
r st
a
r
t
i
ng c
o
ndi
t
i
o
n
wi
t
h
P
I
c
ont
r
o
l
l
e
r, pea
k
ove
r
s
ho
ot
o
f
ro
tor
f
l
ux
o
ccur
s
wh
ich
lasts f
o
r
about 1
.
5
s
ec b
e
fo
re tr
ack
ing
th
e r
e
f
e
r
e
n
ce f
l
ux
v
a
lu
e
w
h
er
eas f
o
r
M
a
m
d
ani
and
TS fuzzy
co
nt
rol
l
e
r n
o
s
u
ch
ove
rs
ho
ot
i
n
r
o
t
o
r fl
u
x
d
u
ri
n
g
st
art
i
ng t
r
a
n
si
ent
i
s
obser
v
e
d. At
t=12 sec t
h
e
c
h
ange
in resist
ance
has
res
u
lt
ed i
n
i
n
cr
e
a
s
e
o
f
th
e d-
ax
is
f
l
u
x
fro
m
its n
o
min
a
l v
a
lu
e of 0.936
ωb
for all th
e th
ree co
n
t
ro
llers
with
p
e
ak
o
v
e
rshoo
t ag
ain
m
o
re p
r
ono
unced
fo
r t
h
e PI co
n
t
ro
ller
b
e
fo
re
settlin
g
to
its stead
y state flux
v
a
lu
e. Fro
m
Fig
u
re
13
(a)
& (b
) it is also seen th
at th
e
p
e
rform
a
n
ce of th
e TS
fu
zzy co
n
t
ro
ller is ex
cellen
t
as it can
track t
h
e step cha
n
ge i
n
rotor re
sist
ance in 1.5 se
c c
o
m
p
ared to t
h
e
othe
r
two
con
t
ro
llers with
its steady state error tak
e
n as in
te
gral
tim
e
square
e
r
r
o
r
(I
TSE
)
ve
ry
low
as s
h
o
w
n
in
Tabl
e 2
.
The
s
a
m
e
perf
orm
a
nce i
nde
x i
s
o
b
t
a
i
n
ed
fr
om
the TS fuzzy controller
wh
en
the in
stru
m
e
n
t
ed v
a
lu
e
o
f
th
e
ro
t
o
r resistan
ce is m
a
d
e
less th
a
n
the
a
c
tual m
o
tor res
i
stance val
u
e.
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I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l.
6, No
. 3, Sep
t
em
b
e
r
2
015
:
53
8 – 553
54
7
(a)
(b
)
Figu
re
12
. Rot
o
r fl
ux
f
o
r
step
(
a
) inc
r
ease
(b) decrease
in rotor
resistance
, Case-II
(a)
Evaluation Warning : The document was created with Spire.PDF for Python.