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
. 55
4
~
56
6
I
S
SN
: 208
8-8
6
9
4
5
54
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 Review of th
e DTC Controll
er and Esti
mation of Stator
Resistan
ce in IM Drives
Na
veen
G
o
el,
R.
N. P
a
tel, S
a
ji Ch
ack
o
Electrical & Electronics Depar
tment, Sh
ri Shan
karach
ar
y
a
Group of Institutions
, Junwani, Bhilai
(CG), 490020, I
ndia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 19, 2015
Rev
i
sed
Ju
l 20
,
20
15
Accepte
d Aug 5, 2015
In rec
e
nt
ye
ars
an
advan
ced
c
ontrol
method
called
d
i
rect tor
que
con
t
rol
(DTC) has gain
ed importan
ce d
u
e to
its
capability
to produce
fast torq
u
e
control of indu
ction motor. Although in
these sy
stems such
variab
les as
torque, flux mod
u
lus and flux sector are r
e
quired
,
resulting DTC
structure is
particular
ly
simplistic. Conv
entional
DTC
does
not requ
ire an
y
mechanical
sensor or current regulator and coordina
te transf
ormation is not present, thus
reducing the complexity
.
Fast
and good d
ynamic perform
ances and
robustness has made DTC pop
ular
and is
now
used widely
in
all
industrial
appli
cat
ions
. De
s
p
ite th
es
e
adva
ntages
i
t
h
a
s
s
o
m
e
dis
a
dvant
ag
es
s
u
ch as
high torque ripp
le and slow tran
sient
response to step changes during start
up. Torque rippl
e in DTC is
becaus
e
of h
y
s
t
er
es
is
controll
er for s
t
ator flu
x
linkag
e
and
torq
ue. Th
e ripp
les can be r
e
duced
if
the errors of
the
torque an
d
the flux link
a
ge
and the angular r
e
gion of the flux
linkage ar
e subdivided into
s
e
veral s
m
all
e
r s
ubs
ections
. S
i
n
c
e the
errors
are d
i
vided in
to s
m
all
e
r s
ect
ions
differen
t
voltag
e
vector is selected for
small difference in error, thus a
more
accur
a
t
e
vol
tage
vec
t
or is
s
e
le
ct
ed and
hen
c
e
t
h
e torqu
e
and f
l
ux link
a
g
e
errors
are redu
ced. Th
e s
t
ato
r
res
i
s
t
ance
ch
anges
due to change i
n
temperatur
e during the operatio
n
of
m
achine
.
At high s
p
eeds
,
the s
t
ator
resistance drop is small and can be ne
glected. At low speeds, this drop
becomes dominant. An
y
change in st
ator r
e
sistance giv
e
s wrong estimatio
n
of stator f
l
ux
and consequen
t
ly of the torqu
e
and flux
. Th
erefore,
it
is
neces
s
a
r
y
to
es
t
i
m
a
te
the s
t
ator
res
i
s
t
an
ce
corr
ect
l
y
.
This
p
a
p
e
r a
i
m
s
to
review some of
the control tech
niques
of DTC
drives and stato
r
resistance
estim
ation
m
e
th
ods.
Keyword:
Artificial n
e
u
r
al n
e
two
r
k
Ada
p
t
i
v
e ne
ur
o fuzzy
Di
rect
t
o
rq
ue
c
ont
rol
In
fere
nce sy
ste
m
Space vector m
odulation
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
:
Navee
n
G
o
el,
Depa
rtem
ent of Electri
cal
& Electronics
,
Sh
ri
Shank
a
rach
arya
Grou
p of In
stitu
tio
n
s
, Jun
w
an
i,
Bh
ilai
(
C
G
)
, 49
002
0, I
n
d
i
a.
Em
ail: ngoel_18@redi
ffm
ail.com
1.
INTRODUCTION
D.C
.
m
o
t
o
rs h
a
ve bee
n
u
s
ed
wi
del
y
du
ri
n
g
t
h
e l
a
st century in applicati
ons where variable-spe
e
d
ope
rat
i
o
n was
neede
d
,
beca
us
e i
t
s
fl
ux a
nd t
o
r
q
ue can
be c
ont
rol
l
e
d easi
l
y
by
m
eans of
chan
gi
n
g
t
h
e
fi
el
d an
d
the arm
a
ture currents
res
p
ectiv
ely. DC m
o
t
o
rs
h
a
v
e
b
a
sically two
dra
w
backs, whic
h are
the
e
x
istence of
com
m
ut
at
ors and
br
us
hes. T
h
ese di
sa
d
v
ant
a
ges i
m
pl
y no
t
onl
y
peri
o
d
i
c
m
a
i
n
t
e
nance
but
al
so af
fe
ct
t
h
e
efficiency
of t
h
e m
achine. Induction
m
o
to
rs are
wid
e
ly
u
s
ed
in
m
a
n
y
in
dustrial appl
ications due t
o
their
m
echani
cal
r
o
bust
n
ess a
n
d l
o
w
cost
.
I
n
d
u
c
t
i
on m
o
t
o
rs a
r
e t
h
e m
o
st
w
i
del
y
used
m
o
t
o
rs am
on
g di
ffe
rent
electric
m
o
tors
because of hi
gh
le
vel
of
reliability, efficiency and safety.T
he ac drives
are broa
dly classified
[1
-2]
as
(i)
Sca
l
ar Co
ntr
o
lled
and
(ii) Vector cont
rolled.
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
:
55
4 – 566
55
5
Scal
ar C
o
nt
r
o
l
:
scal
ar co
nt
r
o
l
i
s
base
d o
n
st
eady
-
st
at
e rel
a
t
i
ons
hi
p
wi
t
h
m
a
gni
t
ude a
n
d
fre
que
ncy
only without space vect
or
orientation.
In
V/f scalar control schem
e
termin
al voltage
is proportional
to the
fre
que
ncy
,
w
h
i
c
h
resul
t
s
i
n
a
n
ap
pr
o
x
i
m
at
el
y co
nst
a
nt
st
at
or
fl
u
x
.
Vect
or C
o
nt
ro
l
: In vect
or c
o
ntrolled drives
voltage
, cu
rre
n
t and fl
ux s
p
ace vectors are cont
rolle
d
bot
h i
n
st
eady
st
at
e and
d
u
r
i
ng t
r
a
n
si
e
n
t
s
.
C
o
o
r
di
nat
e
t
r
ansf
o
r
m
a
ti
on (
3
phase
t
o
d-
q a
x
i
s
) t
o
ne
w fi
el
d
coo
r
di
nat
e
s i
s
a key
com
p
o
n
e
nt
o
f
st
an
dar
d
gi
vi
n
g
a l
i
n
ear
rel
a
t
i
ons
h
i
p bet
w
ee
n c
o
nt
r
o
l
vari
a
b
l
e
and
t
o
r
que
.
Vect
o
r
co
nt
r
o
l
t
echni
q
u
es c
a
n be cl
assi
fi
ed as i
ndi
rect
or fee
d
f
o
r
w
ard m
e
t
hod a
nd
di
rect
o
r
feed
bac
k
m
e
t
hod
de
pe
ndi
ng
on
t
h
e
m
e
t
hod
o
f
uni
t
vect
o
r
ge
nerat
i
o
n
f
o
r
vect
or
r
o
t
a
t
i
o
n
.
F
.
B
l
asc
h
k
e
[
3
]
i
nve
nt
ed t
h
e D
i
rect
Vect
o
r
co
nt
r
o
l
m
e
t
hod
. I
n
t
h
i
s
m
e
t
hod t
h
e u
n
i
t
vect
or
i
s
gene
rat
e
d
fr
om
t
h
e fl
ux
ve
ct
ors
wh
ich
are estimated
u
s
ing
m
ach
in
e term
in
a
l
v
o
ltag
e
an
d cu
rren
t
[4
].
2.
DIRE
CT TO
RQ
UE C
O
NT
ROL
A t
y
pe
of
pe
rf
orm
a
nce en
ha
n
ced scal
ar c
o
nt
rol
cal
l
e
d
DTC
co
nt
rol
was
p
r
o
p
o
sed
by
Ta
kaha
shi
[5]
and
M
.
Depe
n
b
r
o
c
k
[
6
]
i
n
1
9
8
0
s.
It
i
s
a
hi
gh
pe
rf
orm
a
nce t
echn
o
l
o
gy
whi
c
h i
s
devel
ope
d a
f
t
e
r t
h
e
Vect
o
r
Co
n
t
ro
l [7
]. To
rqu
e
and
f
l
ux o
f
a DTC-
b
a
sed
d
r
i
v
e ar
e
co
n
t
r
o
lled in
a clo
s
ed-
l
oop
man
n
e
r
w
ithout u
s
ing
cu
rren
t l
o
op
s i
n
co
m
p
ariso
n
with
th
e conv
en
tio
n
a
l
v
ect
or
co
n
t
r
o
lled
dr
ives.
Th
e D
T
C
based
d
r
i
v
es r
e
qu
ir
e
t
h
e
k
nowledg
e of
stato
r
resistan
ce o
n
l
y,
th
ereb
y
d
ecreasi
n
g
t
h
e asso
ciated
sensitiv
ity to
p
a
rameter v
a
riatio
ns [8
].
The co
nt
r
o
l
gi
ves fast
res
p
o
n
se. It
i
s
sim
p
l
e
t
o
im
pl
em
ent
due t
o
a
b
se
nce of cl
o
s
e l
o
o
p
cu
rre
nt
co
nt
r
o
l
,
trad
itio
n
a
l
PWM alg
o
rith
m
an
d
vect
or
t
r
an
s
f
o
r
m
a
ti
on.
The el
ect
r
o
m
a
gnet
i
c
t
o
r
que
a
n
d
st
at
or
fl
ux
l
i
nka
ge a
r
e est
i
m
a
t
e
d i
n
st
at
o
r
refe
re
nce
fram
e
s usi
n
g
t
h
e
measured stator
voltages
and
currents
. T
h
e
machine m
ode
l is de
pende
n
t
on stator resist
ance
onl
y
,
t
h
e st
at
or q
and
d a
x
i
s
fl
u
x
l
i
nka
ges
φ
qs
,
φ
ds
can be
obt
a
i
ned t
h
r
o
u
g
h
t
h
e i
n
t
e
grat
i
o
n
of t
h
e
di
ffe
re
n
ce bet
w
ee
n t
h
e
p
h
ase
vol
t
a
ge
an
d t
h
e
v
o
l
t
a
ge
dr
o
p
i
n
t
h
e
st
at
or
resi
st
ance as
bel
o
w [
9
-1
0]
∅
ʃ
and
∅
ʃ
Whe
r
e,
as t
h
e
f
l
ux l
i
n
ka
ge
p
h
a
sor
m
a
gni
t
ude
an
d a
ngl
e a
r
e:
∅
∅
∅
t
a
n
∅
/∅
In
t
e
rm
s of st
at
or
fl
u
x
,
el
ect
ro
m
a
gnet
i
c
t
o
r
q
u
e
i
s
gi
ven
by
:
3
2
2
∅
∅
Tw
o di
f
f
ere
n
t
hy
st
eresi
s
com
p
arat
ors f
o
r fl
ux a
nd t
o
r
que
are used t
o
g
e
nerat
e
co
nt
r
o
l
si
gnal
s
as
sh
own
in
f
i
gure 1
.
Flux
h
y
ster
esis co
m
p
arato
r
is two
lev
e
l
typ
e
wh
ile to
r
q
u
e
co
m
p
arator is th
ree lev
e
l typ
e
.
These c
o
m
p
arat
ors
use fl
u
x
and t
o
r
que i
n
s
t
ant
a
neo
u
s e
r
r
o
r
val
u
e as i
n
put
a
nd
gen
e
r
a
t
e
cont
r
o
l
si
g
n
al
s as
out
put
.
I
n
t
h
e
con
v
e
n
t
i
onal
DTC
dri
v
e as
sho
w
n i
n
fi
g
u
r
e
1
,
t
h
e
fl
ux
a
n
d
t
o
rq
ue
p
u
l
s
at
i
on ca
n
be
hi
gh
i
f
t
h
e
sw
itch
i
ng
f
r
e
qu
en
cy
of
th
e in
v
e
r
t
er
is no
t
ad
equ
a
te.
Th
ere is slug
g
i
sh
respo
n
s
e du
r
i
ng star
t up
o
r
dur
ing
a
ch
ang
e
o
f
flux o
r
torq
u
e
error and
also
t
h
e
flux
po
s
itio
n.
Th
ere is
no
meth
od
to
d
i
sting
u
i
sh
between v
e
ry
large a
n
d sm
all errors. T
h
us, the s
w
itchi
ng vect
ors
chos
e
n
fo
r lar
g
e
er
r
o
rs
are
th
e
sa
me as the s
w
it
ching
vect
o
r
s ch
ose
n
fo
r t
i
m
e
cont
rol
du
ri
n
g
n
o
r
m
a
l
operat
i
o
n.
A n
u
m
b
er o
f
im
pl
em
ent
a
t
i
on
o
f
t
h
e sc
he
m
e
has
been
m
a
de de
p
e
ndi
ng
o
n
h
o
w
t
h
e c
u
r
r
ent
s
an
d
vol
t
a
ge
s are
m
easured
& e
s
t
i
m
a
t
e
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
A Revi
ew
of
t
h
e DTC
C
o
nt
rol
l
er a
n
d
Est
i
m
a
t
i
on
of
St
at
or
R
e
si
st
ance i
n
IM
Dri
ves
(Navee
n Goel)
55
6
Fi
gu
re 1.
B
l
oc
k Di
ag
ram
of DTC
3.
DIFFE
RENT
CO
NTR
O
L T
E
CHN
I
Q
U
ES
OF
DTC
There
are
di
ffe
rent
c
o
nt
rol
t
e
c
hni
que
s f
o
r
DT
C
,
w
h
i
c
h
ha
ve
evol
ved
o
v
e
r
t
h
e y
ears
.
3.
1.
M
o
di
fi
ed DT
C
In co
n
v
e
n
t
i
ona
l
DTC
t
h
ere ar
e hi
gh t
o
r
que a
nd fl
ux
ri
p
p
l
e
s.
In m
o
st
of t
h
e wo
rk
s [1
1
-
1
7
]
t
h
e aut
h
ors
rectified
th
ese d
r
awb
ack
s with
th
e
usa
g
e o
f
SVM
t
ech
ni
q
u
e
. SVM
t
ech
ni
que ca
n be cl
a
ssi
fi
ed i
n
t
w
o way
s
,
(a) M
odi
fied
DTC sc
hem
e
-I:in this schem
e
flux torque
c
ont
rollers a
r
e
replaced
by PI
cont
rollers a
nd SVM
t
echni
q
u
e (
F
i
g
ure 2
)
an
d, (
b
)
M
odi
fi
ed
DT
C
schem
e
–II:
i
n
t
h
i
s
schem
e
t
h
e t
o
rq
ue err
o
r an
d fl
ux er
r
o
r ar
e
mad
e
as slid
in
g
m
o
d
e
co
n
t
rollers (Figu
r
e 3). Bo
th
th
e sch
e
m
e
s resu
lt i
n
less ripp
les with
less switch
i
ng
fre
que
ncy
b
u
t
m
odified DTC
schem
e
-II is s
upe
rio
r
in term
s of
r
o
b
u
stne
ss
to pa
ram
e
ter variations.
But,
it has
a drawbac
k
of
chattering in sl
ide m
ode control.
Fi
gu
re 2.
M
o
di
fi
ed DTC
Sche
m
e
-
1
B
l
oc
k D
i
agram
Fi
gu
re 3.
M
o
di
fi
ed DTC
Sche
m
e
-2
B
l
oc
k Di
agram
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
:
55
4 – 566
55
7
Fi
gu
re
4.
Sy
st
em
Di
agram
of t
h
e M
odi
fi
e
d
D
T
C
IM
Dri
v
e
Tang L. et al. [18]
propose
syst
e
m
where i
n
place of s
w
itching ta
bl
e and
hysteresis controllers, a
PI
cont
rol
l
e
r a
n
d
refe
rence
fl
u
x
vect
o
r
cal
cul
a
t
o
r a
r
e
use
d
t
o
fi
n
d
o
u
t
t
h
e re
f
e
rence
st
at
or
fl
ux
l
i
nka
ge
vec
t
or as
depi
ct
ed
by
Fi
gu
re 4.
A spac
e vect
or m
odul
at
or i
s
used t
o
gene
rat
e
t
h
e co
nt
r
o
l
si
gnal
s
f
o
r i
nve
rt
er. A s
p
eci
al
SVM p
a
ttern
is u
s
ed
t
o
redu
ce th
e switch
i
ng
frequ
e
nc
y. The c
u
rrent
harm
onics are greatly reduced in
m
odi
fi
ed DTC
.
The res
p
o
n
se
t
i
m
e
of t
h
e basi
c DTC
i
s
sho
r
t
e
r t
h
a
n
t
h
a
t
of
m
odi
fi
ed
DTC
.
M
o
di
fi
e
d
DTC
feat
ure
s
l
o
w t
o
rq
ue
ri
p
p
l
e
, l
o
w fl
u
x
ri
ppl
e a
n
d
al
m
o
st
fi
xe
d s
w
i
t
c
hi
n
g
fre
que
ncy
.
Kum
s
uwa
n
et
al
. [1
9-
2
0
]
pr
o
pos
e t
h
at
t
h
e p
e
rf
orm
a
nce of
DTC
can
be i
m
prove
d by
a
ppl
i
cat
i
o
n of
voltage
m
odul
ation
by
repla
c
ing the l
o
okup ta
ble of
vo
ltage
vector sel
ection. Th
is
voltage m
o
dulation is
base
d on
S
V
M
wi
t
h
co
nst
a
nt
swi
t
c
hi
n
g
fre
q
u
ency
.
I
n
t
h
i
s
pape
r DTC
i
s
base
d on
deco
upl
e
d
c
o
nt
rol
of
b
o
t
h
st
at
or fl
u
x
a
n
d
t
o
rq
ue
whi
c
h
i
s
di
ffere
nt
f
r
o
m
DTC
SVM
.
Thi
s
t
ech
n
o
l
o
gy
use
d
t
h
e
rel
a
t
i
ons
hi
p b
e
t
w
een
to
rq
u
e
slip
angu
lar
freq
u
e
n
c
y
and
ro
tor an
gu
lar
freq
u
e
n
c
y
for co
n
t
ro
lling
stator fl
u
x
an
g
l
e. Th
e drawb
ack of
t
h
e est
i
m
a
ti
on of t
h
e st
at
o
r
fl
ux
base
d o
n
v
o
l
t
a
ge
m
odel
u
s
in
g
op
en
lo
op
in
tegratio
n
is dc d
r
ift and
saturation
pr
o
b
l
e
m
.
In t
h
i
s
pa
per
i
m
prov
ed st
at
o
r
fl
u
x
est
i
m
a
ti
o
n
b
y
i
n
tegratin
g algorith
m
with
an
a
m
p
litu
d
e
limi
t
er in
pol
a
r
c
o
o
r
di
nat
e
s i
s
us
ed
t
o
o
v
e
rcom
e t
h
ese
p
r
o
b
l
e
m
s
.
3.
2.
DT
C w
i
t
h
T
w
o L
e
vel
o
r
Mul
t
i
l
e
vel
I
n
ver
t
er
Sri
n
i
v
asa R
a
o
S. an
d
Vi
nay
Kum
a
r T.
[2
1]
pr
o
pose
swi
t
c
h
i
ng st
at
e al
g
o
ri
t
h
m
for casca
d
e
d t
w
o l
e
vel
inve
rters (Figure 5).
In proposed
DTC m
e
thod applied
voltage s
p
ace
vect
or is a
function of rotor s
p
ee
d.
The p
r
o
p
o
se
d m
e
t
hod i
s
im
pl
em
ent
e
d fo
r l
o
w spee
d (
2
5
-
5
0
% o
f
rat
e
d s
p
eed)
,
very
l
o
w
speed (l
ess
t
h
an
2
5
%
of
r
a
t
e
d s
p
eed
),
hi
gh
spe
e
d
(a
bo
ve
50
% o
f
rat
e
d s
p
ee
d) a
n
d
fo
r
opt
i
m
u
m
fl
ux
an
d t
o
r
q
ue
ri
p
p
l
e
.
Th
e
d
r
awb
ack
o
f
th
is typ
e
of
co
nv
erter is t
h
e vo
ltag
e
im
b
a
lan
ce pro
d
u
c
ed in
th
e capacitors
o
f
t
h
e
DC lin
k.
Xavi
e
r
del
T
o
r
o
Ga
rci
a
et
al
.
[2
2]
an
d C
i
rri
n
c
i
one M
.
et
al
. [2
3]
desi
gne
d
t
h
ree l
e
vel
v
o
l
t
a
ge s
o
u
r
ce
i
nve
rt
er as sh
o
w
n i
n
Fi
g
u
re
6,
whi
c
h i
n
creas
es t
h
e n
u
m
b
er of
vol
t
a
ge
vect
ors s
o
t
h
at
t
h
e
t
o
r
que &
fl
u
x
r
i
ppl
es
are re
duced.
Thi
s
V
S
I
has a
dva
nt
age
s
l
i
k
e
l
o
we
r d
v
/
d
t
,
l
e
ss ha
rm
oni
c di
st
ort
i
o
n a
nd l
o
wer s
w
i
t
c
hi
ng
fre
que
ncy
.
Th
e
d
r
awb
ack
o
f
t
h
is typ
e
of co
nv
erter is t
h
e vo
ltag
e
im
b
a
lan
ce produ
ced
in
t
h
e cap
acito
rs
o
f
t
h
e
DC lin
k.
Three l
e
vel
i
nvert
er i
s
havi
n
g
a di
sad
v
a
n
t
a
ge o
f
m
o
re
co
m
p
lex
i
t
y
in
th
e circu
it an
d
is
m
o
re exp
e
n
s
i
v
e, bu
t it
cu
ts th
e co
st
of filters.
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 Revi
ew
of
t
h
e DTC
C
o
nt
rol
l
er a
n
d
Est
i
m
a
t
i
on
of
St
at
or
R
e
si
st
ance i
n
IM
Dri
ves
(Navee
n Goel)
55
8
Fi
gu
re
5.
Th
re
e l
e
vel
i
n
vert
e
r
co
nfi
g
u
r
at
i
o
n
usi
n
g casca
di
n
g
of
t
w
o l
e
vel
i
nve
rt
er
Fi
gu
re
6.
Th
re
e l
e
vel
n
e
ut
ral
poi
nt
cl
am
ped
vol
t
a
ge
s
o
u
r
ce
i
nve
rt
er
3.3
DTC with
Current Sour
ce Inverter
Sel
v
am
N. Pannee
r
et
al
. [2
4]
prese
n
t
C
S
I
fed
ind
u
c
tion
m
o
to
r driv
e
with
DTC. The to
rqu
e
and
st
at
or fl
ux l
i
n
k
a
ges are e
s
t
i
m
a
t
e
d usi
ng m
easure
d
st
at
o
r
v
o
l
t
a
ges a
nd c
u
rre
nt
s. T
h
i
s
est
i
m
a
ti
on i
s
de
p
e
nde
n
t
onl
y
o
n
st
at
or
resi
st
ance. C
S
I
fed d
r
i
v
es as s
h
o
w
n i
n
Fi
g
u
r
e
7, fi
n
d
ap
pl
i
cat
i
ons i
n
hi
gh
po
we
r dri
v
es s
u
ch as
fan
dri
v
es,
w
h
ere fast
dy
nam
i
c resp
on
se i
s
not
need
ed
, be
cause
of t
h
e a
dva
nt
age
s
o
f
i
nhe
re
nt
fo
u
r
q
u
ad
ra
nt
o
p
e
ration
and
reliab
ility. Th
e
stato
r
resistan
ce is co
m
p
en
sa
ted
as shown
in Fig
u
re 8
u
s
ing stato
r
curren
t
p
h
a
se
error. PI a
d
apti
ve c
o
m
p
ensator is
us
e
d
for
measure
d
stator current only.
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
:
55
4 – 566
55
9
Fi
gu
re
7.
B
a
si
c schem
e
of
DT
C
C
S
I-
fe
d IM
dri
v
e
Fi
gu
re
8.
B
l
oc
k
di
ag
ram
schem
a
t
i
c
of t
h
e a
d
aptive stator
re
sistance com
p
e
n
sator
3.4 F
u
z
z
y
Control
Scheme
Ab
dal
l
a
T.
Y e
t
al
. [2
5]
an
d
Zalm
an
M. and Ivica Kuric I. [26] us
ed
fuzzy co
n
t
ro
ller
is in
wh
ich
t
o
r
que er
r
o
r a
n
d st
at
or fl
ux a
ngl
e are t
a
ke
n
as i
n
p
u
t
vari
a
b
l
e
s and d
u
t
y
ra
t
i
o
cont
r
o
l
(s
) as out
put
va
ri
a
b
l
e
as
sho
w
n i
n
Fi
gu
re
9. B
y
t
h
e i
m
pl
em
ent
a
t
i
on o
f
fuzzy
c
o
nt
rol
l
e
r
t
o
r
q
ue a
n
d
cu
rr
ent
ri
p
p
l
e
s a
r
e r
e
d
u
c
e
d
i
n
transient a
n
d st
eady state res
p
ons
e.
Fi
gu
re
9.
B
l
oc
k
di
ag
ram
of f
u
zzy
d
u
t
y
rat
i
o
co
nt
r
o
l
So
lim
an
H.F.E. an
d Elbu
luk
M.E. [27
]
co
m
p
ar
e the
ba
sic DTC
with PI a
n
d
DTC
with
fuzzy
co
n
t
ro
ller as sh
own
in Figu
re 10
. Th
e
v
a
lue o
f
Kp
ch
an
ged
acco
r
d
i
ng
t
o
th
e op
eratin
g con
d
ition
s
,
h
e
n
ce t
h
e
authors
s
u
gges
t replacing t
h
e
PI c
o
ntro
ller with
th
e
fu
zzy l
o
g
i
c con
t
ro
ller.
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 Revi
ew
of
t
h
e DTC
C
o
nt
rol
l
er a
n
d
Est
i
m
a
t
i
on
of
St
at
or
R
e
si
st
ance i
n
IM
Dri
ves
(Navee
n Goel)
56
0
Fig
u
r
e
10
.
D
T
C syste
m
w
ith
PI
and
FLC
con
t
ro
ller
fo
r sp
eed
loop
The fuzzy input vectors a
r
e m
o
tor
speed variations
Δ
w a
nd t
h
e acceleration d/
dt(
Δ
w); wh
ile fu
zzy
out
put
i
s
t
h
e c
h
an
ge i
n
re
fere
nce t
o
rq
ue.
Th
e Si
m
u
l
i
nk res
u
l
t
s
sh
ow
bet
t
e
r dy
nam
i
c perf
orm
a
nce o
f
i
n
d
u
ct
i
o
n
m
o
t
o
r w
h
en
us
i
ng
DTC
wi
t
h
f
u
zzy
l
o
gi
c i
n
c
o
m
p
ari
s
on
wi
t
h
fi
xe
d P
I
c
ont
rol
l
e
r.
Abdalla T.Y et
al., [28] deliberate that the
PID
co
nt
r
o
l
l
e
r
m
a
y
not
p
r
o
v
i
d
e t
h
e
co
nt
r
o
l
per
f
o
r
m
a
nce
du
ri
n
g
t
h
e
vari
at
i
ons i
n
pl
ant
param
e
t
e
rs & ope
rat
i
ng
cond
itio
n
s
. Th
e
fuzzy b
a
sed
PI co
n
t
ro
ller is th
e self
ad
ap
tion
PI con
t
ro
ller as shown in
Figu
re
11
.
In th
is m
e
t
hod
scal
ed
val
u
es o
f
s
p
eed
er
r
o
r a
n
d c
h
a
nge
of
spee
d
er
ro
r ar
e
u
s
ed
b
y
th
e
fu
zzy con
t
ro
ller
to
update th
e valu
es
o
f
Kp
and
K
i
.
Fig
u
r
e
11
. Fu
zzy
PI
-
C
on
tr
o
l
l
e
r
b
a
sed
DTC
Say
eed M
i
r et
al
. [2
9]
fi
n
d
t
h
e rel
a
t
i
ons
hi
p
bet
w
ee
n
the c
h
ange i
n
stator resi
stance and s
t
ator curre
nt
(Figure
12). PI and fuzzy logic cont
ro
llers are u
s
ed
to
co
m
p
en
sate th
e
changes in st
ators resista
n
c
e
. The
fuzzy estim
ator
gives
better perform
a
nce.
At low s
p
eed al
s
o
fuzzy
resista
n
ce estim
ator is able t
o
ope
ra
te the
cont
roller.
Fi
gu
re 1
2
. Di
re
ct
t
o
r
que
co
nt
r
o
l with fuzzy resistance estimator
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
:
55
4 – 566
56
1
Zi
dani
F et
al
.
,
[
30]
d
e
scri
be
t
h
e st
at
or
resi
st
ance estim
a
t
ion
usi
ng
fuzz
y logic. T
h
is
approach is
b
a
sed
o
n
th
e
p
h
a
se an
d
m
a
g
n
itud
e
error b
e
tween
th
e
esti
m
a
ted
sta
t
o
r
flu
x
and
th
e filtered
on
e. Fo
r k
th
sam
p
lin
g
in
terv
al th
e errors are as no
ted b
e
low
wh
ic
h serv
e as inpu
t h
a
v
i
ng
t
h
r
e
e tr
iang
u
l
ar
me
m
b
er
fu
nct
i
o
ns eac
h.
e
1
(k
)=
│φ
s
(k
)
│
-
│φ
sf
(k)
│
e
2
(k
)=
phase
(
φ
sf
)
-
phase
(
φ
s
)
Th
e li
m
ita
tio
n
s
o
f
con
v
e
n
tional DTC an
d
AI u
s
ed
DTC like to
rqu
e
ripp
les, ripp
les in
flux
and
erro
r
in stator resista
n
ce estim
a
tion at low
speed
were overc
o
m
e
by estim
a
ting th
e cha
nge
s in stator resistanc
e
due
t
o
t
e
m
p
erat
ure
chan
ge.
B
y
o
b
s
ervi
ng
t
h
e
res
u
l
t
s
i
t
co
ul
d
be
co
ncl
u
ded
t
h
a
t
t
h
e est
i
m
at
or
per
f
o
r
m
s
wel
l
un
de
r
d
y
n
a
m
i
c o
p
e
ratin
g
co
nd
ition
also
.
4.
ESTIMATI
O
N
O
F
ST
ATO
R
RESIST
AN
CE
The stator
resis
t
ance cha
n
ges
due
to c
h
a
nge
in tem
p
erature
during the ope
r
a
t
i
on of
m
achi
n
e. At
hi
g
h
spee
ds, the sta
t
or resista
n
ce
drop IsRs is s
m
all and
can
be ne
glected. At low s
p
ee
ds
, this drop
be
com
e
s
dom
inant compare
d
to Vs. T
h
ere
f
ore,
any
chan
ge i
n
st
at
or resi
st
a
n
ce g
i
ves wr
o
ng est
i
m
a
ti
on o
f
st
at
or fl
ux
and c
onse
q
uen
t
l
y
of t
h
e t
o
rqu
e
and fl
u
x
. T
h
eref
ore i
t
i
s
necessary to estimate
the st
ator résistance. Differe
n
t
techniques
are
use
d
for the
es
t
i
m
a
ti
on
of
st
at
or
resi
st
ance
.
The adva
ntage of MARS is its
sim
p
le
im
ple
m
en
tatio
n
requ
irem
en
t. Th
e techni
que proposes
calcu
latio
n
of th
e p
a
ram
e
ter
v
a
lu
e to
b
e
id
en
tified
in
two
d
i
fferen
t
ways. Th
e first v
a
lue is calcu
lated
fro
m
refe
rence insi
d
e
the contr
o
l sy
stem
.
The second is calculated from
meas
ur
e
d
signal. One of the two
values
sho
u
l
d
be i
n
de
pen
d
e
n
t
o
f
t
h
e
param
e
t
e
r whi
c
h i
s
t
o
be est
i
m
a
t
e
d.
Fi
gu
re
1
3
. M
A
R
S
base
d
st
at
o
r
re
si
st
ance est
i
m
a
ti
on sc
hem
e
The
di
ffe
re
nce
bet
w
ee
n t
h
e t
w
o
val
u
es i
s
a
n
er
ro
r si
gnal
as sh
ow
n i
n
Fi
gu
re
13 a
n
d i
s
use
d
t
o
dri
v
e
an a
d
apti
ve m
e
chanism
either usi
n
g
a P
I
,
I c
ont
rol
l
e
r,
F
u
zz
y
l
ogi
c,
A
N
N
or
A
N
N
a
n
d
F
u
zzy
l
o
gi
c.
Oz
ko
p
E.
and
Ok
um
us H.I
.
[
31]
an
d
Yi
n
g
fei
W
et
al
. [3
2]
pr
op
ose
a
m
odel
refer
e
nce ada
p
t
i
v
e
sy
st
em
t
o
est
i
m
a
t
e
t
h
e
stato
r
resistan
ce fo
r
d
i
rect torq
u
e
con
t
ro
lled in
d
u
ctio
n
m
o
to
r. Th
e m
a
in
i
d
ea of MRAS
is th
at th
e eq
uatio
n
with
no
esti
m
a
ted
p
a
ram
e
ter i
s
tak
e
n
as referen
ce m
o
d
e
l, an
d
th
e eq
u
a
tion
with
esti
m
a
t
e
d
p
a
ram
e
ter i
s
tak
e
n
as t
h
e
re
gul
at
e
d
m
odel
.
T
h
e
t
w
o
m
odel
s
ha
ve t
h
e
di
ffe
re
n
t
out
put
s
wi
t
h
t
h
e sam
e
phy
si
cal
si
gni
fi
canc
e
. T
h
e
erro
rs
of th
e t
w
o
ou
tpu
t
s are u
s
ed
to
fram
e
th
e ad
ap
ter laws to
reg
u
l
ate
th
e p
a
ram
e
ter o
f
t
h
e regu
lated
m
o
d
e
l
and
o
u
t
p
ut
of
ob
ject
i
s
co
nt
r
o
l
l
e
d t
o
f
o
l
l
o
w t
h
e
out
put
o
f
refe
re
nce m
odel
.
T
h
e v
o
l
t
a
ge m
odel
i
s
t
a
ken a
s
referen
c
e m
o
d
e
l to
ob
tain
t
h
e ro
t
o
r flux
. The curren
t
m
o
d
e
l is tak
e
n as the reg
u
l
ated m
o
d
e
l to
ob
tain
the ro
t
o
r
flu
x
.
B
i
l
a
l A et
al
. [33]
use
d
a r
eact
i
v
e-p
o
w
er
base
d refe
renc
e
m
odel
deri
v
e
d i
n
bot
h m
o
t
o
ri
n
g
and
g
e
n
e
ration
m
o
d
e
s bu
t on
e of th
e d
i
sadv
an
tag
e
s of th
is algo
rith
m
is i
t
s se
n
s
itiv
ity to
d
e
tu
n
i
n
g
in
t
h
e stato
r
and
rot
o
r i
n
ductances.
Blaha
P. a
n
d Vacla
v
ek P. [34]
pre
s
ent
a stat
o
r
resistan
ce id
en
tificatio
n algo
rith
m
fo
r
AC
in
du
ctio
n
m
o
tor. Du
ri
n
g
th
e
op
eration
of th
e
m
o
to
r th
e Rs is d
e
term
in
ed
fro
m
th
e RMS v
a
lu
e o
f
th
e
v
o
l
t
a
g
e
,
current &actua
l active powe
r
.
The di
sad
v
a
n
t
a
ge i
s
t
h
e dep
e
nde
ncy
o
f
t
h
e
est
i
m
a
t
e
on t
h
e l
e
vel
of
m
a
gnet
i
c
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 Revi
ew
of
t
h
e DTC
C
o
nt
rol
l
er a
n
d
Est
i
m
a
t
i
on
of
St
at
or
R
e
si
st
ance i
n
IM
Dri
ves
(Navee
n Goel)
56
2
flux
ex
citation
.
Th
e
o
f
flin
e
measurem
ent of
stator induct
ance on
ex
citation
cu
rren
t is
p
r
o
p
o
s
ed
to
so
l
v
e th
is
pr
o
b
l
e
m
.
C
h
ange i
n
R
s
i
s
du
e t
o
cha
n
ge i
n
t
e
m
p
erat
ure
.
T
h
ere a
r
e t
h
ree
t
y
pes of
R
s
est
i
m
a
ti
on.
Fi
rst
one i
s
zero se
q
u
e
n
ce
m
odel
based
R
s
est
i
m
a
ti
on
by
sol
v
i
n
g l
east
squa
res m
i
nim
i
zati
on p
r
o
b
l
em
s. In t
h
i
s
m
e
t
hod
,
the access to neutral of the stator wi
ndi
ng is
neede
d
for c
u
rrent injection.
It has the
disa
dvanta
ge of heat
ing of
t
h
e wi
n
d
i
n
g. T
h
e seco
n
d
o
n
e
i
s
based
on
DC
m
odel
.
In
t
h
i
s
m
e
t
hod, t
h
e i
n
put
i
m
pedance
of t
h
e
m
o
t
o
r i
s
d
i
rectly equ
a
l
to
Rs for
DC
sig
n
a
l. Th
e th
i
r
d
m
e
th
od
requ
ires
kn
owledg
e
o
f
i
n
d
u
c
tion
m
o
to
r m
o
d
e
l. Th
is
p
a
p
e
r
p
r
esen
ts th
ird
m
e
th
o
d
. Th
is algorith
m
o
p
e
rates
o
n
lin
e and
req
u
i
res no
ex
tern
al ex
citatio
n
.
The
fol
l
o
wi
n
g
are
t
h
e di
f
f
ere
n
t
m
e
t
hods
fo
r
est
i
m
a
ti
on o
f
st
at
or resi
st
a
n
ce of i
n
d
u
ct
i
o
n m
o
t
o
rs f
o
r
vect
o
r
co
n
t
ro
lled drives:
Est
i
m
a
t
i
on of
St
at
or R
e
si
st
an
ce usi
n
g
PI
Est
i
m
a
t
i
on of
St
at
or
resi
st
anc
e
usi
n
g
F
u
zzy
Lo
gi
c
Ma
m
d
ani Type
fuzzy logic controller
Est
i
m
a
t
i
on of
St
at
or
resi
st
anc
e
usi
n
g
A
N
N
Esti
m
a
tio
n
o
f
Stato
r
r
e
sistan
ce u
s
in
g Fu
zzy
Log
i
c and
ANN
Change i
n
Stat
or resistance
due to tem
p
erature
va
riations
Est
i
m
a
t
i
on of
St
at
or
resi
st
anc
e
usi
n
g
EK
F
Est
i
m
a
t
i
on of
St
at
or
resi
st
anc
e
usi
n
g
Lu
n
b
er
ger
O
b
se
ver
T
echni
que
4.
1
E
s
ti
m
a
ti
o
n
o
f
S
t
at
or
Re
si
stanc
e
usi
n
g
PI
Lee Byeong-Seok a
n
d Krishnan R
.
[
3
5
]
presen
t a so
l
u
tion
to
track
th
e
stato
r
resistan
ce so
th
at th
e
p
e
rform
a
n
ce deg
r
ad
ation
and
a
p
o
ssib
l
e i
n
stab
ility p
r
o
b
le
m
can
b
e
av
o
i
d
e
d. Proportio
n
a
l-In
tegral (PI)
adaptive c
o
m
p
ensator using
only the m
eas
u
r
ed
stator curren
ts is ap
p
lied
.
An a
n
alytic expressi
on t
o
e
v
aluate
t
h
e st
at
or
cu
rr
e
n
t
com
m
and f
r
o
m
t
h
e t
o
r
que
and
st
at
or
fl
ux
l
i
nkage
com
m
a
nd
s i
s
deri
ved
an
d
prese
n
t
e
d
.
Thi
s
sch
e
m
e
req
u
i
res two filters
an
d on
e
PI con
t
ro
ller ap
ar
t fro
m
th
e ex
istin
g electro
m
a
g
n
e
tic to
rqu
e
an
d stator
fl
u
x
l
i
nka
ges c
a
l
c
ul
at
or i
n
t
h
e
dri
v
e c
ont
r
o
l
l
er. A si
g
n
al
p
r
op
o
r
t
i
onal
t
o
st
at
or resi
st
an
ce chan
ge i
s
de
ve
l
ope
d
using the error between the refere
nce
and actual stator current phas
or. T
h
is
error is processed through a PI
co
n
t
ro
ller fo
r
ap
p
lication
in
th
e co
n
t
ro
ller. Stato
r
re
sistan
ce p
a
ram
e
ter
ad
ap
tatio
n
resu
lts in
resto
r
i
n
g
the
preci
se a
n
d acc
urat
e est
i
m
at
i
o
n
of
st
at
or
fl
u
x
l
i
nka
ge m
a
gni
t
ude a
n
d i
t
s
po
si
t
i
on i
n
t
h
e c
o
nt
r
o
l
l
e
r.
4.
2
E
s
ti
m
a
ti
o
n
o
f
S
t
at
or
Re
si
stanc
e
usi
n
g
Fuz
z
y
L
ogi
c
In
DTC if t
h
e stato
r
resistance v
a
ries
du
e
to
h
eating
,
t
h
e p
e
rform
a
n
ce o
f
t
h
e system
will su
ffer
because the actual flux does not
m
a
tc
h with the calculated flux. Zhong L
et
al. [36] desc
ribe an
online
fuzzy
obs
erver for the stator
resistance es
tim
at
io
n
.
Th
e fu
zzy
m
o
d
e
l is u
s
ed with
t
h
ree inp
u
t
s curren
t
, sp
eed
&
ope
rat
i
o
n t
i
m
e. It
wa
s ve
ri
fi
ed wi
t
h
ex
pe
ri
m
e
nt
t
h
at
fuzz
y
obse
r
v
e
r est
i
m
a
t
e
s t
h
e var
i
at
i
on o
f
t
h
e
s
t
at
or
resistance
quit
e
well, wit
h
error le
ss t
h
a
n
6
.
3%
.The
di
f
f
er
ence
bet
w
ee
n
DTC
a
nd
DSC
i
s
t
h
e s
h
ape
o
f
t
h
e
p
a
th
along
which
th
e flux
vecto
r
is con
t
rolled
to
fo
llows. In
DTC th
e
p
a
th
is circle an
d
i
n
DSC it was a
hexa
g
o
n
.
C
h
au
ha
n S et
al
. [3
7]
descri
be
t
h
at
l
a
rge t
o
rq
ue ri
p
p
l
e
s are
pr
o
duce
d
i
n
D
T
C
due t
o
t
o
rq
ue err
o
rs. T
o
red
u
ce t
h
e t
o
r
que ri
ppl
e t
h
e
err
o
rs
have t
o
be di
vi
ded
in
t
o
sev
e
ral in
terv
als. In
co
nv
en
tio
n
a
l DTC it is n
o
t
pos
sible; he
nc
e fuzzy control is a
ssociated with SVM te
chni
que
. The
space vect
ors
are ge
nerate
d by two
fuzzy
l
o
gi
c co
nt
r
o
l
l
e
rs. Fi
rst
one i
s
f
o
r fl
ux a
nd sec
o
n
d
o
n
e i
s
fo
r t
o
r
q
ue co
nt
r
o
l
.
The usa
g
e o
f
fuzzy
cont
rollers
ins
t
ead o
f
P
I
c
o
ntr
o
llers p
e
rm
its a faster
re
spo
n
se
an
d m
o
re
r
o
b
u
stne
ss
. The
us
e o
f
SVM
t
echni
q
u
e
w
h
i
c
h
pr
o
v
i
d
es a
con
s
t
a
nt
i
n
ve
rt
er s
w
i
t
c
hi
n
g
fr
eque
ncy
resul
t
s i
n
sm
al
l
t
o
rq
ue
ri
p
p
l
e
an
d
cur
r
ent
d
i
sto
r
tion
.
Bu
t, b
ecau
s
e t
h
e
n
u
m
b
er o
f
ru
les is too
h
i
gh
,
t
h
e sp
eed
o
f
fu
zzy reason
ing
will
b
e
affected
.
Korkm
az F et
al. [38] propos
e
a fuzzy
b
a
sed
stato
r
flux
esti
m
a
to
r th
at o
p
ti
mizes itse
l
f t
o
regu
late th
e
st
at
or fl
ux
ref
e
rence
val
u
e
re
gar
d
i
n
g t
o
t
h
e
m
o
t
o
r l
o
ad.
A
d
apt
i
o
n
of
fl
u
x
t
o
l
o
a
d
va
ri
at
i
on ca
n
be
do
n
e
i
n
3
ways (i)
flux
co
n
t
ro
l as a
functio
n
of torq
u
e
(ii) fl
ux
co
n
t
ro
l b
a
sed
o
n
l
o
ss m
o
d
e
l an
d
(iii) flu
x
con
t
rol b
y
a
m
i
nim
u
m
l
o
ss searc
h
co
nt
r
o
l
l
er. A
u
t
h
o
r
s
pr
op
ose t
h
e fi
rst
way
i
.
e.
fl
u
x
cont
rol
l
e
d
as a
fu
nct
i
o
n
of t
o
rq
ue
wi
t
h
o
u
t
need
o
f
any
m
o
t
o
r
pa
ram
e
t
e
rs by
us
i
ng
fuzzy
al
go
rith
m
.
Fuzzy st
ator
flux
op
timizer u
s
es ju
st t
o
rqu
e
err
o
r a
n
d cha
n
ge o
n
t
o
r
que
err
o
r
wi
t
h
a
n
y
m
o
t
o
r
pa
ram
e
ter. Sim
u
latio
n
resu
lts shows th
at th
e prop
o
s
ed
syste
m
with
o
p
tim
ized
stat
o
r
flux
h
a
s
m
u
ch
sm
a
ller ripp
le in to
rq
u
e
with respect to
tim
e t
h
an the
co
nv
en
tio
n
a
l
DTC at all wo
rk
in
g cond
itio
n
s
.
Ebra
hi
m
i
A. and Fa
rs
had S.
[3
9]
devel
ope
d
M
a
m
d
ani
t
y
p
e
fuzzy
di
rect
t
o
r
que c
ont
r
o
l
l
e
r fi
rst
a
n
d
then rules are
m
odified using stator
cu
rrent
m
e
m
b
ersh
ip
fun
c
tion
.
Stator
curre
n
t is chose
n
as the control
param
e
t
e
r. Du
r
i
ng st
art
u
p o
r
du
ri
n
g
cha
n
ges
i
n
refere
nce fl
ux & t
o
rq
ue, a
fuzzy
l
o
gi
c bas
e
d swi
t
c
hi
ng v
ect
or
pr
ocess i
s
dev
e
l
ope
d.
In M
a
m
d
ani
t
y
pe fuz
z
y
t
h
ree i
n
put
s
are fl
u
x
e
r
r
o
r
,
t
o
r
que e
r
r
o
r
a
nd t
h
e p
o
si
t
i
o
n
of t
h
e
stator
flux s
p
ac
e vector i.e
.
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
:
55
4 – 566
56
3
Flux
er
ro
r
(e
Φ
)
∆
ds
=
ds
*
–
d
s
To
rqu
e
er
ro
r
(
e
T
)
∆
Ts
= Ts
* -
T
s
Stator
flux s
p
a
ce vector is
Φ
s.
In th
e im
p
r
ov
ed
system
o
n
e
m
o
re in
pu
t, stato
r
cu
rren
t is introd
u
c
ed
t
o
redu
ce th
e ov
er curren
t
pro
b
l
em
.
4.
3 E
s
ti
m
a
ti
o
n
o
f
S
t
at
or
Re
si
stanc
e
usi
n
g
AN
N
Cabre
r
a L.A et
al. [40] use
d
ANN
fo
r
on
lin
e
tun
i
ng
of
st
ato
r
r
e
sist
ance
. For the estim
a
tion
of stator
resistance ANN inputs are curre
nt error a
nd
change
i
n
cu
rr
ent
err
o
r
out
pu
t
of ne
ural
t
h
at
gi
ves
∆
Rs (k
)
whic
h
i
s
ad
ded
t
o
t
h
e
pre
v
i
o
us
val
u
e
of
R
s
(
k
-
1
) t
o
gi
ve a
n
e
s
t
i
m
a
te f
o
r t
h
e act
ual
val
u
e
o
f
R
s
.
∆
∗
∆
1
Whe
r
e
∗
the stat
or is comm
and curre
nt and
is th
e actual curren
t,
with
defi
n
e
d as:
I
k
i
k
i
k
Fig
u
r
e
14
.
On
-lin
e set up
f
o
r
t
r
ain
i
ng
t
h
e
n
e
ur
al n
e
t
w
or
k
The re
sults s
h
ow that the la
rge neural net
w
ork
gives m
o
re accurate result
s
(Figure
14). The only
dra
w
back of
usi
n
g m
o
re ne
ur
o
n
s i
n
t
h
e
hi
dde
n l
a
y
e
rs i
s
t
h
e i
n
cr
eased
i
n
num
ber
of
wei
g
ht
s s
o
t
h
e
cal
cul
a
t
i
on i
s
m
o
re
com
p
licated and lengthy.
4.
4
E
s
ti
m
a
ti
o
n
o
f
S
t
at
or
Re
si
stanc
e
usi
n
g
Fuz
z
y
L
ogi
c a
nd
AN
N
Jallu
r
i
S R. and
Ram
B .V
.S. [41
]
i
m
p
r
oved
co
nv
en
tio
nal D
T
C using
A
N
N
an
d fu
zzy lo
g
i
c (
a
s
sho
w
n i
n
Fi
g
u
r
e 1
5
)
.
A
N
N
i
s
use
d
f
o
r
spee
d est
i
m
at
i
on.
A fuzzy system is used to t
u
ne the
PI
of t
h
e spee
d
cont
rol
l
e
r a
n
d
an
AN
N est
i
m
at
es t
h
e st
at
o
r
resi
st
ance.
Thi
s
m
e
t
hod
of
A
C
dri
v
e sy
st
e
m
i
s
i
n
t
e
nde
d
fo
r a
n
efficien
t con
t
ro
l o
f
t
h
e to
rque & flux
withou
t ch
an
g
i
n
g
t
h
e
m
o
to
r p
a
rameters. Th
e sen
s
itiv
ity o
f
th
e DTC is
eli
m
in
ated
b
y
o
n
li
n
e
estim
a
t
io
n
o
f
stato
r
resistan
ce. Th
e
DTC is b
a
sed
o
n
t
h
e ev
alu
a
tio
n
of two
q
u
a
n
tities
that are stator flux a
nd torque
. Exact
evaluati
on of Vs
re
quires
accurate
measurem
ent and
good e
v
aluat
i
on
of
R
s
. The
val
u
e
of R
s
whi
c
h v
a
ri
es w
ith temperat
ure
needs
eith
er an acc
urate therm
a
l
model
or a
n
eval
uat
i
o
n
and
est
i
m
at
i
on
m
e
t
hod.
Evaluation Warning : The document was created with Spire.PDF for Python.