Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
1
2
,
No.
1
,
M
a
r
202
1
, p
p.
59
~
66
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v
1
2
.i
1
.
pp
59
-
66
59
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
The ex
perim
ental id
en
ti
ficatio
n met
hod of the
dyna
mic
efficie
nc
y for f
requency r
egulatio
n algo
rithms
of A
EDs
Vlad
im
ir
L.
K
od
kin
, Ale
ksandr S
. Aniki
n
Depa
rteme
nt
of Theoretical
fund
am
en
ta
ls of
e
lect
ric
a
l
eng
ineeri
ng
,
South
Ur
al
S
t
ate
U
nive
rsi
ty
,
Ch
el
yab
insk,
Russ
i
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
ul
30, 2
020
Re
vised
Jan
12
, 2021
Accepte
d
Ja
n 2
9,
2021
The
art
i
cl
e
prop
oses
and
subs
ta
n
ti
ates
a
method
f
or
studying
th
e
d
ynam
i
cs
of
an
async
hronous
el
e
ct
r
ic
dr
ive
s
with
fre
qu
enc
y
c
ontrol
from
the
i
nput
side
of
the
sign
al
for
sett
ing
th
e
spee
d
of
rot
at
ion
of
the
el
e
ct
ri
c
motor.
In
this
me
thod
,
a
const
ant
spee
d
r
efe
re
nce
signal
is
ad
ded
to
a
har
mo
nic
var
i
able
fre
quenc
y
signal.
Th
e
set
of
a
m
pli
tude
ch
ange
s
and
phase
shif
ts
of
vel
o
ci
ty
oscil
lations
ar
e
the
initi
al
da
ta
f
or
ide
nt
ifyi
ng
t
he
dynamics
of
the
studi
ed
cont
rol
m
et
hod.
Th
e
logi
c
of
t
his
method
is
d
et
er
mi
ned
by
th
e
pr
evi
ousl
y
obta
i
n
ed
nonli
n
ea
r
tr
ansfe
r
fun
ct
ion
of
the
l
in
k
tha
t
for
ms
th
e
mecha
ni
cal
mom
ent
in
th
e
async
hronous
e
lectr
i
c
drive
with
fr
eque
n
cy
cont
rol
.
Expe
ri
me
nts
h
a
ve
show
n
the
d
ynam
i
c
ben
efi
ts
of
the
drive
with
posit
ive
stat
or curre
n
t
f
eedbac
k.
Ke
yw
or
d
s
:
Dynamic e
ff
ic
i
ency
Ex
per
ime
ntal i
den
ti
ficat
io
n
Scal
ar c
on
tr
ol
Var
ia
ble freq
ue
ncy drive
Vecto
r
c
on
tr
ol
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Aleksa
ndr S.
A
nik
in
Dep
a
rteme
nt of T
heoreti
cal
fundame
ntals
of ele
ct
rical
en
gi
neer
i
ng
South
Ural
Sta
te
U
ni
ver
sit
y
76, Le
nin p
ros
pek
t,
Chel
yab
i
ns
k, R
us
sia
. 4
5408
0
Emai
l:
an
ikina
s@susu
.ru
1.
INTROD
U
CTION
Async
hro
nous
el
ect
ric
dr
ive
s
with
f
reque
nc
y
co
ntr
ol
(
A
ED)
a
re
wi
del
y
us
e
d
in
va
riou
s
a
reas
of
industr
y
a
nd
e
nerg
y.
Un
ti
l
r
ecentl
y,
t
he
unit
s
with
w
hich
these
dri
ves
w
ork
had
sim
il
ar
operati
ng
modes.
These
m
odes
c
an
be
c
har
act
e
rized
as
sta
ti
c
or
qu
a
si
-
sta
ti
c
[1
]
-
[
4].
T
he
re
qu
i
red
ro
ta
ti
on
al
sp
ee
ds
of
el
ect
ric
mo
to
rs
in
t
hes
e
dr
iv
es
remai
n
unc
hange
d
f
or
a
s
uffici
ently
lo
ng
ti
me
or
change
very
s
lowly.
I
n
this
r
egard,
the
m
ai
n
cha
racteri
s
ti
cs
of
the
dr
ive
s
r
emai
ned
sta
ti
c
cha
racteri
sti
cs:
sli
p,
ef
fici
ency,
powe
r
factor,
Re
qu
ire
ments
for
dynamic
m
od
e
s
(time
of
the
tra
ns
ie
nt
process,
the
la
g
of
t
he
c
hange
in
the
ro
ta
ti
on
sp
ee
d
from
the
c
ha
nge
in
the
ref
e
re
nc
e
sign
al
s)
rem
ai
ned
sec
onda
r
y.
T
hi
s
sit
uatio
n
has
now
c
ha
ng
e
d.
Very
of
t
en
it
is
require
d
to
justi
fy
a
nd
sel
ect
su
ch
a
con
t
ro
l
met
hod
t
hat
will
pro
vid
e
fa
st
and
acc
urat
e
sp
ee
d
"repro
duct
ion
"
of
A
EDs
co
m
plex
a
nd
of
te
n
qu
it
e
dynamic
ref
e
ren
ce
sig
na
ls.
This
dy
nam
ism
of
reprod
uc
ti
on
determi
nes
t
he e
ff
ic
ie
nc
y of t
he
en
ti
re
mecha
nism
or co
mp
l
ex wit
h wh
ic
h t
he
el
ect
ric dri
ve wor
ks
.
Ther
e
are
seve
ral "ne
w" feat
ures
of co
mp
le
xe
s w
it
h asy
nc
hro
nous el
ect
ric drives:
1)
Un
it
s
an
d
mec
han
is
ms,
w
hic
h
a
re
eq
uippe
d
with
AE
D,
become
more
com
plica
te
d
a
nd
op
ti
mize
d
by
te
chnolo
gy,
in
connecti
on
w
it
h
wh
ic
h
sta
t
ic
modes
of
op
e
rati
on
re
qu
ire
cl
arifica
ti
on
an
d
bec
om
e
dynamic
or
"
quasi
-
dynamic",
i.e.
the
s
pee
d
of
r
otati
on
of
the
el
ect
ric
m
otor
i
n
them
"
adjusts"
to
the
op
e
rati
ng
co
nd
it
ion
s
[
5
]
,
[
6].
Su
c
h
mec
han
is
ms
inclu
de
,
for
exa
mp
le
,
pu
mp
dr
i
ves
in
powe
r
s
ys
te
ms,
wh
ic
h
see
k
t
o op
ti
mize
opera
ti
ng
m
odes
for reso
urce c
on
s
umpti
on.
2)
Eff
ic
ie
nc
y
a
nd
good
overl
oa
d
capaci
ty
of
as
yn
c
hro
nous
el
e
ct
ric
mo
to
rs
re
qu
i
re
their
im
pl
ementat
ion
i
n
areas
w
he
re
th
ey
we
re
no
t
previo
us
ly
us
e
d.
D
espite
the
fa
ct
that
the
ad
va
ntages
of
pe
r
mane
nt
ma
gn
e
t
sy
nc
hro
nous
m
otors
an
d
DC
mo
to
rs
as
c
on
t
ro
l
obje
ct
s
ove
r
asy
nc
hrono
us
mo
to
rs
re
main
,
in
some
cases
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
12
, N
o.
1
,
Ma
rch
202
1
:
59
–
66
60
the
us
e
of
t
he
la
tt
er
is
highly
de
sirable.
An
exa
mp
le
of
s
uch
a
n
a
ppli
cat
ion
ca
n
be
tra
ct
ion
dri
ves
f
or
unman
ne
d
ae
ri
al
ve
hicle
s.
T
he
re
qu
i
red
s
pe
ed
a
nd
to
r
qu
e
con
t
ro
l
ra
ng
es
,
usual
ly
not
e
xceed
i
ng
1:10,
can
be
im
plem
ented
on
as
ync
hro
nous
el
ect
ric
dr
ive
s,
an
d
t
he
ad
va
ntages
of
the
la
tt
er
in
weig
ht
a
nd
l
oa
d
capaci
ty
will
beco
me
a
dvanta
ges.
In
t
his
co
nn
ect
i
on,
it
is
necessa
ry
t
o
de
te
rmin
e
thei
r
dynamics
,
i.e.
to
determi
ne
the
"
li
mit
s" o
f
the
dyna
mic ch
aract
erist
ic
s o
f
the
AED that ca
n be im
pleme
nted [7
]
-
[
9].
3)
Cl
asses
of
dr
iv
es,
in
w
hich
it
is
abs
olu
te
ly
ne
cessar
y
to
so
l
ve
dynamic
pr
ob
le
m
s
pr
eci
se
ly
on
t
he
bas
is
of
AE
D,
hav
e
been
i
de
ntifie
d.
S
uc
h
area
s
include
,
f
or
e
xam
ple,
wi
nd
powe
r
pla
nts
op
e
rati
ng
on
a
commo
n
powe
r
sup
ply
s
ys
te
m
[
10].
In
su
c
h
instal
la
ti
on
s
,
the
co
nversi
on
of
mec
ha
nic
al
wind
ene
rgy
into
el
ect
rical
energ
y
is
car
ri
ed
out
us
in
g
a
double
-
fee
d
el
ect
ric
mac
hin
e
.
It
is
an
as
ync
hro
nous
el
ect
ric
mo
to
r
wit
h
a
wou
nd
ro
t
or,
into
the
ci
r
cuit
of
wh
ic
h
a
f
re
qu
e
nc
y
co
nver
te
r
is
connecte
d.
T
his
al
lows
yo
u
to
"a
dju
st"
to
non
-
sta
ti
on
a
ry
ai
r
flo
ws
a
nd
gen
e
rate
"
gree
n"
el
ect
rical
e
nerg
y
of
a
fixe
d
a
m
plit
ud
e
an
d
f
re
qu
e
nc
y.
The
ch
oice
of
the
m
os
t
dyna
m
ic
wa
y
to
c
on
tr
ol
a
n
as
yn
c
hro
nous
el
ect
ric
dri
ve
is
c
ompli
c
at
ed
by
t
he
fo
ll
owin
g
ci
r
cu
mstances:
1)
W
hen
us
ed
in
co
ntr
ol
s
ys
te
ms,
vecto
r
no
nlinear
e
qu
at
i
on
s
that
desc
r
ibe
AEDs
[11
]
-
[
13]
s
hould
be
gr
eat
ly
sim
plifie
d
an
d
li
neari
zed.
T
his
will
inevita
bl
y
le
ad
to
sig
nific
ant
ide
ntific
at
ion
er
rors
a
nd
po
s
sible
c
on
t
rol
error
s
.
T
her
e
f
or
e
,
the
us
e
of
known
meth
od
s
f
or
i
den
ti
f
ying
the
dy
namic
char
act
e
risti
cs
of
cl
os
e
d
aut
oma
ti
c
sy
ste
m
s
by
t
heir
math
emat
ic
al
desc
r
ip
ti
on
[
11
]
-
[
13]
is
unli
kely
t
o
be
ef
fecti
ve.
AEDs
with
f
re
qu
e
nc
y
c
on
t
ro
l
is
an
e
ssentia
ll
y
nonlinea
r
s
ys
te
m,
an
d
t
he
tradit
io
nal
co
ntr
ol
meth
ods
(v
ect
or
a
nd
sc
al
ar)
f
or
t
hem
are
f
ormed
un
der
a
num
ber
of
si
gn
i
ficant
assumpti
ons
[
2
]
,
[
3
]
,
[
6].
A
s
a
resu
lt
, t
h
eo
reti
cal
co
ncl
us
io
ns o
ften d
o no
t c
oin
ci
de
w
it
h pra
ct
ic
al
r
esults.
2)
The
e
xperime
nt
al
resu
lt
s
ob
ta
ined
unde
r
t
he
same
c
onditi
ons,
f
or
e
xam
ple,
at
sta
tor
volt
age
fr
e
qu
e
ncie
s
(and,
acc
ordin
gly
,
ro
ta
ti
on
s
peeds)
cl
os
e
to
the
nominal
ones,
are
not
c
onfir
med
at
sp
e
eds
tw
o
t
o
t
hr
e
e
ti
mes low
e
r.
T
his is a c
onse
quence
of t
he
sa
me drive
no
n
-
l
inearit
ie
s.
3)
Very
oft
en
,
th
e
con
t
ro
l
al
gor
it
hm
,
w
hich
is
op
ti
mal
in
te
r
ms
of
co
nsum
ed
res
ources
a
nd
dyna
mics
f
or
the
nominal
m
od
e
,
bec
om
es
emer
gen
c
y
f
or
oth
e
r
s
pee
ds
.
T
he
s
olu
ti
on
of
al
l
these
a
nd
oth
er
pr
ob
le
m
s
i
s
very
imp
or
ta
nt
f
or
m
oder
n
in
du
st
ry
a
nd
e
ne
rgy,
in
wh
ic
h
AEDs
a
re
m
ost
widel
y
us
e
d,
the
refor
e
,
t
he
assessme
nt
of
t
he
dy
namic
ca
pab
il
it
ie
s
of
one
or
a
no
t
her
A
ED
co
ntr
ol
al
gorith
m
from
t
he
po
i
nt
of
view
of
inc
r
easi
ng
t
he
e
ff
ic
ie
nc
y
of
it
s
op
e
rati
on
in
this
m
od
e
is
an
ext
remely
urge
nt
ta
sk
T
he
wa
y
t
o
s
olv
e
this p
roblem
c
an be
no
t
only
theo
reti
cal
, but also
e
xperime
ntal.
2.
PROBLE
M
DE
FINITIO
N
Trad
it
io
nally,
of
al
l
the
e
xisti
ng
AE
D
c
ontr
ol
m
et
hods,
ve
ct
or
co
ntr
ol
wi
t
h
feedbac
k
on
the
s
peed
of
ro
ta
ti
on
of
the
mo
to
r
s
haf
t
is
disti
nguish
e
d
[
1
4
]
-
[
1
7
].
Accord
i
ng
to
man
y
so
urces
[1
7
]
,
[
1
8
],
this
met
hod
of
con
t
ro
l
is
c
ons
idere
d
to
be
t
he
m
os
t
"
dyna
mic"
.
H
oweve
r,
a
se
ries
of
e
xp
e
rime
nts
[
1
9
]
,
[
20
]
s
howe
d
that
vecto
r
co
ntr
ol
d
oe
s
not
ha
ve
an
unc
onditi
onal
"dynamic"
adv
a
ntage
.
M
oreo
ver,
f
or
ce
d
scal
ar
co
ntr
ol
wit
h
dynamic
posit
ive
sta
tor
cu
rr
e
nt
fee
db
ac
k
(
DP
F
)
wit
hout
direct
meas
ur
e
ment
of
s
pee
d
has
al
m
os
t
th
e
same
transients
in
st
ep
s
pee
d
re
fer
e
nce
Fi
g
ure
1
as
tran
sie
nts in
vec
tor
c
ontrol
F
ig
ure
2.
(
a)
(
b)
Figure
1.
The
processes
of ac
cel
erati
on
of th
e drive
with
D
PF up t
o
s
pee
ds o
f 90 ra
d/s
(a
)
a
nd 17
0
ra
d/s
(b)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
Th
e ex
peri
ment
al iden
ti
fi
catio
n meth
od o
f t
he
d
y
namic eff
ic
ie
ncy fo
r
freq
ue
nc
y
…
(
Vla
di
mir L. Ko
dkin
)
61
(
a)
(
b)
Figure
2. Proce
sses of accel
e
r
at
ion
of a
dr
i
ve
w
it
h vecto
r
c
ontr
ol up
t
o
s
pe
ed
s
of 90
ra
d/s
(a)
a
nd
170 ra
d/
s
(b)
The
anal
ys
is
of
a
num
be
r
of
pa
rameter
s
of
the
AE
D
ope
rati
on,
acc
ordi
ng
to
s
pecial
ly
de
velo
pe
d
methods
[
19
]
,
[
20]
,
i
nclu
ding
the
s
pectra
of
currents
of
t
he
ro
t
or
s
of
as
ync
hro
nous
el
ect
ri
c
m
oto
r
s
[21
]
,
[
22]
,
sh
owe
d
that
t
he
er
rors
in
ve
ct
or
c
on
t
ro
l
are
ve
ry
sig
nificant.
T
hese
error
s
a
re
ca
use
d
by
as
sum
ptions
inevita
ble
in
the
synthesis
of
vecto
r
co
ntr
ol
e
quat
ion
s
.
I
n
man
y
stu
die
s
[
2
]
,
[
8
]
,
[
19]
it
is
no
te
d
t
hat
t
he
"discre
pan
ci
es
"
of
the
pa
ra
mete
rs
of
t
he
m
otor
model
use
d
in
t
he
vecto
r
c
ontr
ol
al
gorith
m
wi
th
th
e
par
a
mete
rs
of
a
real
m
otor
ar
e
very
sig
nific
ant
a
nd
ca
n
giv
e
sig
nificant
error
s
i
n
c
ontr
ol.
H
oweve
r,
i
t
is
no
le
ss
imp
ort
ant
that
the
r
otor
a
nd
sta
to
r
c
urre
nts
a
re
non
-
sin
us
oi
dal
a
nd
c
onta
in
ha
rm
on
ic
s
that
dif
fer
f
r
om
the
fun
dame
ntal
ha
rm
on
ic
t
hat
f
orms
th
e
to
rqu
e
in
t
he
AE
D.
A
nd
ve
ct
or
c
on
t
ro
l
“i
n
pr
i
nc
iple”
ne
glect
s
them
,
con
t
ro
ll
in
g
only
the
fun
dam
ental
ha
rm
on
i
cs
of
cu
rrent
and
volt
age.
On
e
wa
y
or
a
no
t
her,
acc
ord
ing
t
o
exp
e
rime
nts
w
it
h
acce
le
rati
on
t
o
va
rio
us
spe
eds,
the
"a
dv
a
ntage"
of
vect
or
c
on
tr
ol
is
i
nsi
gn
ific
a
nt.
Th
is
ma
y
ind
ic
at
e
bo
t
h
a
not
to
o
"
subtl
e"
meth
od
of
e
xp
e
rime
ntal
ev
al
uation
of
t
he
dyna
mic
pro
pe
rtie
s
of
a
dri
ve
,
a
nd
about
the
same
dyna
mic
ef
fici
ency
of
c
on
t
ro
l
meth
od
s
,
wh
i
ch
c
on
t
rad
ic
ts
the
ge
ne
rall
y
a
ccepte
d
c
once
pts
of
"dynamic"
ve
ct
or
co
ntr
ol.
To
obta
in
acc
ur
at
e
co
ncl
us
ion
s
,
a
m
or
e
"sub
tl
e"
ex
pe
r
imenta
l
te
ch
ni
qu
e
is
require
d.
3.
SOLUTI
ON
3.1.
Th
eore
tical sub
st
antiati
on
of the me
thod
To
assess
t
he
AED
by
dy
na
mic
char
act
e
risti
cs,
a
nonlin
ear
tran
sfe
r
f
unct
ion
of
the
li
nk
t
hat
forms
the el
ect
romag
netic
torq
ue
in
an
in
duct
io
n
m
otor
was pr
opose
d [19
]
,
[
23
].
It lo
ok
s
li
ke
t
his
(
)
=
2
(
2
′
+
1
)
1
[
(
1
+
2
′
)
2
2
+
2
]
(1)
wh
e
re,
2
′
=
2
–
the
tr
ansient ti
me c
onsta
nt
of the
r
ot
or
,
=
2
1
–
the
r
el
at
ive sli
p,
–
the
c
riti
cal
mo
me
nt,
–
t
he
c
riti
cal
sli
p
at
the
nomi
nal freq
ue
ncy
ω
1
The
blo
c
k
dia
gram
of
the
AE
D
with
s
uc
h
a
li
nk
is
sho
wn
i
n
Fi
gure
3.
As
can
be
seen
f
r
om
f
ormula
(1),
the
functi
on
c
ha
ng
es
w
hen
t
he
f
reque
ncy
of
t
he
sta
t
or
vo
lt
a
ge
ω
1
and
t
he
abs
olut
e
sli
p
β
change.
I
n
add
it
io
n,
it
shou
l
d
be
bor
ne
in
min
d
that
wh
e
n
ω
1
c
hanges,
the
c
riti
cal
mo
me
nt
M
k
al
so
cha
ng
e
s.
Wh
e
n
acce
le
rati
ng
f
r
om
one
f
reque
ncy
ω
1
(i
n
t
his
case
10
Hz
),
to
an
oth
e
r
f
re
qu
e
nc
y
ω
1
(50
Hz
),
the
f
re
quenc
y
ch
aracte
risti
cs change
from
W1 to
W
2
a
nd
W3 Fig
ure
4.
Soph
ist
ic
at
ed
methods
of
an
al
ys
is
of
nonlinear
sy
ste
m
s
a
nd
meth
ods
of
their
li
near
iz
at
i
on
[
24
]
,
[
25]
make
it
possib
le
to
asse
ss
t
he
sta
bili
ty
of
s
uch
s
ys
te
ms
in
en
gin
ee
rin
g
a
nalysis,
bu
t
it
is
rathe
r
dif
f
ic
ult
t
o
theo
reti
cal
ly
su
bs
ta
ntiat
e
the
ad
van
ta
ges
of
one
or
a
no
t
he
r
A
ED
c
ontr
ol
al
gorith
m
with
var
ia
ti
on
s
in
the
ref
e
ren
ce
sig
na
ls.
I
n
this
re
gard,
an
e
xp
e
r
imenta
l
te
ch
ni
qu
e
is
pro
pos
ed
t
hat
al
lo
ws
yo
u
t
o
e
valu
at
e
the
eff
ect
ive
ness
of
a
pa
rtic
ular
c
on
t
ro
l
met
hod.
It
is
with
thes
e
sign
al
s
that
var
ia
bles
are
be
st
interp
reted.
non
-
sta
ti
on
ar
y
ta
sk
sign
al
s
t
hat
ar
e
processe
d
by
auto
mati
c
cont
ro
l
syst
ems
in
op
ti
mize
d
co
mp
le
xe
s
in
robo
ti
c
s
and po
wer en
gi
neer
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
12
, N
o.
1
,
Ma
rch
202
1
:
59
–
66
62
Fig
ure
3
.
Th
e
work
i
ng secti
on
of the
mecha
nical
ch
a
racteri
sti
cs o
f
the i
nduction m
otor
Fig
ure
4
.
Fr
e
quenc
y res
pons
e
s of a
n
el
ect
ric
mo
to
r
at
a
stat
or volt
age
fr
e
quenc
y
of
10 H
z
(W1
),
30
Hz (
W2),
50
Hz
(W
3)
3.2.
Resul
ts of ex
peri
ments
The
e
xperime
nt
s
wer
e
car
ried
out
on
the
sta
nd
sho
wn
in
Fi
gure
5.
The
ph
ase
r
oto
r
of
th
e
M1
mo
t
or
al
lows
yo
u
to
con
t
ro
l
not
only
t
he
sta
t
or
cu
r
ren
ts,
bu
t
al
so
the
ro
t
or
cu
rr
e
nts.
A
s
pecial
gen
e
rato
r
SG1
al
lows
you
to
generat
e
a
ta
sk
sign
al
of
a
ny
c
ompl
exity.
Si
nce
th
e
AED
is
a
n
e
ssentia
ll
y
nonl
inear
s
ys
te
m,
i
t
is
no
t
enou
gh
to
obta
in
a
n
est
imat
e
of
the
dynamic
s
on
l
y
by
t
he
r
esp
on
se
to
a
st
ep
ta
s
k.
T
her
e
f
or
e
,
t
he
dri
ve
s
peed
ref
e
ren
ce
si
gnal
is
ge
ner
at
e
d
as
the
s
um
of
a
co
ns
ta
nt
value
sig
nal
a
nd
a
sin
usoidal
si
gn
al
gen
e
rated
in
the
SG1
sig
nal
ge
ner
at
or
.
Since
the
tra
ns
fe
r
f
un
ct
io
n
c
ha
nges
with
a
cha
ng
e
in
t
he
f
re
qu
e
nc
y
of
t
he
sta
tor
vo
lt
age
,
the
e
xperime
ntal
ide
ntific
at
ion
m
ust
be
carrie
d
ou
t
at
sever
al
of
the
most
char
a
ct
erist
ic
fr
eq
ue
ncies
of the stat
or
vo
lt
age and rotat
ion sp
eeds
of t
he
elec
tric
mo
t
or.
Fo
r
t
his,
durin
g
the
e
xp
e
rime
nts,
the
c
onsta
nt
com
pone
nts
of
the
ta
s
k
sig
nals,
c
orrespo
ndin
g
to
10,
20,
30
a
nd
50
Hz
(
30,
60,
90
an
d
15
0
rad
/s
),
wer
e
sel
ect
ed.
T
hese
sp
ee
ds
are
set
by
po
te
ntiometer
R
1.
The
su
m sig
nal
is
f
ed
to
the
i
nput o
f
t
he
fr
e
quenc
y
c
onve
rt
er A
I
1.
T
he
a
m
plit
ud
e o
f
t
he
per
i
odic
co
mpo
nen
t
of
th
e
ref
e
ren
ce
sig
na
l
from
t
he
S
G1
ge
ne
rator
s
hould
be
no
m
or
e
tha
n
10
%
of
the
le
vel
of
the
DC
c
omp
on
e
nt
in
order
t
o
sli
ghtl
y
cha
ng
e
t
he
trans
fer
funct
ion
of
t
he
li
nk
of
the
el
ect
romag
netic
tor
qu
e
dri
ver
W.
The
fr
e
qu
e
nc
y
of
th
e
per
i
od
ic
c
ompone
nt
of
the re
fer
e
nce
sig
nal
is
in
the
ra
nge
from
0
(
ste
p
r
efere
nce)
t
o
5 Hz,
of
wh
ic
h
0,
0.41,
1
a
nd
5
Hz
we
re
ch
os
e
n.
D
uri
ng
t
he
ex
pe
riments,
t
he
s
pe
ed
set
ti
ng
sig
na
l
and
t
he
real
value
of
the
mo
t
or
s
haft
r
otati
on
s
pee
d
we
re
rec
orde
d.
T
he
sig
nals
are
"c
ollec
te
d"
in
the
P
G
dig
i
ta
l
os
ci
ll
os
c
ope
a
nd
trans
ferred
to
the
la
pt
op.
Th
e
dy
namic
pro
per
t
y
i
den
ti
fier
s
will
be
the
r
ecorde
d
a
mp
li
tud
e
diff
e
re
nce
s
a
nd
ph
a
se
s
hift
bet
ween
these
sig
nals.
A
m
or
e
dyna
mic
a
uto
m
at
ic
sy
ste
m
“w
orks
out”
the
r
efere
nce
si
gnal
wit
h
le
ss amp
li
tu
de a
tt
enu
at
io
n
a
nd less phase
sh
i
f
t. [
20
]
,
[
23].
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
Th
e ex
peri
ment
al iden
ti
fi
catio
n meth
od o
f t
he
d
y
namic eff
ic
ie
ncy fo
r
freq
ue
nc
y
…
(
Vla
di
mir L. Ko
dkin
)
63
A
B
C
N
UZ
1
X
4
AO
1
U
/
T
1
V
/
T
2
W
/
T
3
R
/
L
1
S
/
L
2
T
/
L
3
X
6
CO
M
LI
2
+
24
B
LI
1
SB
1
M
1
G
N
D
SB
2
+
10
B
AI
2
X
1
AI
1
CO
M
AI
2
CO
M
X
1
X
2
+
5
B
A
-
A
+
CO
M
X
5
CO
M
X
2
X
3
U
S
B
BR
R
2
PG
QF
1
AI
1
O
U
T
CO
M
R
1
SG
1
Figure
5. Sc
he
mati
c d
ia
gram
of the
dr
i
ve wit
h
the
sli
p
-
rin
g
i
nductio
n
m
ot
or for
t
he
st
udy o
f
the
dy
namic
char
act
e
risti
cs o
f
the
dr
i
ve (S
G1
-
si
gn
al
ge
ne
rator
;
UZ
1
–
f
reque
ncy co
nv
erter; B
R
–
e
nc
od
e
r; P
G
–
os
ci
ll
os
co
pe;
M
1
–
sli
p
-
rin
g i
nduction m
otor)
The
pro
pose
d
meth
od
is
c
lose
t
o
t
he
i
den
ti
ficat
io
n
method
de
scri
bed
in
[11
],
[
13]
.
U
nlike
identific
at
ion
ob
je
ct
s
co
ns
i
de
red
in
[11
],
an
asy
nc
hro
nous
el
ect
ric
dr
i
ve
can
not
be
descr
i
bed
by
a
li
near
fr
act
io
nal
-
rati
onal
f
unct
ion
[
8],
in
this
case
,
the
tra
ns
f
er
f
un
ct
io
n
of
the
dr
i
ve
s
hould
be
"red
e
fine
d"
by
the
fr
e
qu
e
nc
y
of
t
he
sta
to
r
volt
age,
after
w
hich
the
i
nput
a
n
d
ou
t
pu
t
sig
nals
of
the
el
ect
ric
dr
i
ve.
With
th
e
same
ref
e
ren
ce
sig
na
l
Figure
6,
t
hr
ee
sens
orl
es
s
ones
-
scal
a
r
an
d
vecto
r
c
on
t
ro
l
Fi
gure
6
(
a
)
a
nd
f
our
con
t
ro
l
methods
we
re
analyze
d:
vect
or
with
sp
ee
d
feedbac
k
Fi
gur
e
6
(
b
)
,
scal
a
r
con
t
ro
l
with
D
PF
Fi
gure
6
(
c
)
.
The
sp
ee
d
dia
gr
a
m
s
in
a
dr
i
ve
with
op
e
n
l
oop
c
on
tr
ol
al
go
rithms
for
sca
la
r
an
d
vecto
r
co
ntro
l
ha
ve
minor
diff
e
re
nces,
th
eref
or
e
the
y
a
re
pr
e
sente
d
i
n
one
grap
h
F
igure
5
(
a
)
.
T
he
exact
re
su
lt
s
of
meas
ur
e
m
ents
of
diff
e
re
nces
in
amplit
udes
an
d
phase
sh
ifts
of
al
l
ex
pe
rim
ents
are
pr
e
se
nted
i
n
Table
1.
In
al
m
os
t
al
l
cases,
con
t
ro
l
with
D
PF
has
s
om
e
a
dv
a
ntage
,
w
hic
h
was
no
te
d
ea
rlie
r
i
n
t
he
ana
lysis
of
the
res
pons
e
to
a
ste
pwise
act
ion
.
For
the
amplit
udes
of
the
f
undame
nt
al
har
m
onic
s
of
the
s
pee
d
ch
ang
e
(
we
ar
e
l
arg
e
6.4
rad
/
s
ver
s
us
5.0
an
d
4.99
ra
d
/
s)
a
nd
f
or
th
e
ph
a
se
sh
i
fts
betwee
n
the
ta
sk
sig
nal
an
d
t
he
act
ual
s
pee
d
(t
he
le
ast
72
ver
s
us
84 el.
Deg) i
n al
l exp
e
riments
, th
e
best
res
ults we
re
ob
ta
ine
d
in
a circ
uit w
it
h
a DPF
on th
e stat
or
c
urre
nt
.
On
e
of the
rea
s
on
s
f
or
t
his shou
l
d
be rec
ogni
zed th
at
this c
on
t
ro
l met
hod "work
s" w
it
h
a
ll
h
arm
on
ic
s
of
t
he
m
otor
c
urren
ts
,
in
c
on
trast
to
se
nsorl
ess
vect
or
c
on
trol
a
nd
vect
or
co
ntro
l
with
sp
ee
d
fee
dbac
k.
As
sh
ow
n
in
[
20],
the
DP
F
li
nea
rizes
the
nonli
near
tran
sfe
r
f
un
ct
io
n
of
the
AED.
Howe
ve
r,
th
e
reas
ons
f
or
t
he
adv
a
ntage
s
of
scal
ar
c
on
t
ro
l
with
DPF
a
re
no
t
the
subje
ct
of
t
his
wor
k.
Subseque
ntly,
the
propose
d
metho
d
for
ide
ntif
ying
the
AED
dy
na
mics
was
ap
plied
to
a
m
ore
c
omplex
i
nput
s
ign
al
Fi
gure
7.
This
is
a
n
e
xa
m
ple
of
a
tria
ng
ular
ref
e
ren
ce
.
This
com
plex
sig
na
l,
with
a
pea
k
value
of
2
V,
was
ad
de
d
to
t
he
co
ns
ta
nt
refe
ren
ce
sign
al
to
r
otate
the
m
otor
at
90
ra
d/s,
i.e
.
co
r
respo
nd
i
ng
to
a
sta
tor
vo
lt
a
ge
f
reque
ncy
of
30
Hz
.
The
durati
on
of
t
he
"t
rian
gle"
cycle
is
1
s
.
The
ou
t
pu
t
sig
nal
meas
ur
e
d
the
ma
ximum
va
lue
in
V
olts
a
nd
t
he
phase
s
hift
i
n
seco
nd
s
.
Fig
ur
e
7
s
hows
t
he
ref
e
ren
ce
sig
nals
an
d
si
gn
a
ls
of
t
he
A
E
D
r
otati
on
sp
e
ed
f
or
three
c
on
t
ro
l
methods
.
E
nlar
ged
dia
gr
am
s
f
or
AE
D
wit
h
s
cal
ar
an
d
vector
c
ontr
ol
Fig
ur
e
8
(
a
)
a
nd
w
it
h
DP
F
Fig
ure
8
(
b
)
and
the
a
mp
li
tud
e
of
the
s
pee
d
diag
ram
(
0.8
9V
ver
s
us
0.
68V)
a
nd
the
ph
a
se
s
hift
(0.23s
ver
s
us
0.37
s
)
f
or
the
AED wit
h DP
F ar
e
noti
ceabl
y bett
er.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
.
12
, N
o.
1
,
Ma
rch
202
1
:
59
–
66
64
Fig
ure
6
.
Dia
grams
of
t
he
el
ec
tric
d
ri
ve wit
h a ha
rm
on
ic
si
gnal
of t
he
s
pee
d refe
ren
ce
w
it
h
a
fr
e
quenc
y of 1
Hz
(
a)
O
pen lo
op syst
em
(sca
la
r
an
d vecto
r c
on
t
ro
l)
,
(
b)
ve
ct
or
c
ontrol
wi
th s
peed fee
dback,
(
c)
scala
r
con
t
ro
l
with
D
PF,
(
d) s
pee
d r
efere
nce si
gn
al
Table
1
.
E
xper
imenta
l res
ults
with a
ha
rm
on
i
c sig
nal of th
e
sp
ee
d
r
e
fer
e
nc
e w
it
h
a
freq
ue
ncy of
1 Hz
Co
n
trol sy
stem
ty
p
e
Δ
ω
,
rad
/
s
Δ
φ, el.
Deg
O
p
en
loo
p
sy
stem
±5
,03
84
Sp
eed feedb
ack s
y
stem
±4
,99
84
Cu
rr
en
t f
eedb
ack s
y
stem
±6
,4
72
(
a)
(
b)
(
c)
Fig
ure
7
.
Dia
grams
of
t
he
el
ec
tric
d
ri
ve wit
h
the
ope
n
lo
op
c
on
t
ro
l
s
ys
te
m
a
nd
at
trian
gula
r
ref
e
re
nce
sig
na
ls
for fre
qu
e
ncies
1 Hz
(
a)
scala
r
contr
ol),
(
b)
ve
ct
or
c
ontrol
,
(
c) s
cal
ar
contr
ol w
it
h D
PF
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N:
20
88
-
8
694
Th
e ex
peri
ment
al iden
ti
fi
catio
n meth
od o
f t
he
d
y
namic eff
ic
ie
ncy fo
r
freq
ue
nc
y
…
(
Vla
di
mir L. Ko
dkin
)
65
(
a)
(
b)
Fig
ure
8.
Enla
r
ged d
ia
gr
a
ms
of the
elec
tric
dr
ive w
it
h
the
op
en
lo
op
c
on
t
ro
l
sy
ste
m
and
at
tria
ngular
ref
e
ren
ce
sig
na
ls for
fr
e
quenci
es
1 Hz
(
a)
vecto
r
c
ontrol,
(
b) scal
ar c
on
t
ro
l
with
DPF
4.
CONCL
US
I
O
N
Th
us
,
as
a
res
ult
of
t
he
rese
arch
car
ried
out,
t
he
fo
ll
ow
i
ng
pr
ov
isi
on
s
can
be
disti
ng
uish
e
d.
T
he
pro
po
se
d
e
xpe
rimental
te
ch
ni
qu
e
ha
s
s
how
n
it
s
eff
ic
ie
nc
y
and
se
ns
it
ivit
y
in
asse
ssin
g
t
he
dynamics
of
s
uch
essenti
al
ly
nonl
inear
str
uct
ur
e
s
as
a
sync
hronou
s
el
ect
ric
dr
i
ves
with
f
requ
ency
c
on
tr
ol.
It
can
be
us
e
d
in
thei
r
r
esearc
h
with
the
ai
m
of
op
t
imi
zi
ng
f
or
th
os
e
te
ch
nolo
gical
com
plexes
that
re
qu
ire
good
dyna
mics.
Th
e
te
chn
iq
ue
t
urn
ed ou
t t
o
be
m
or
e la
borio
us
t
han traditi
onal
exp
e
rime
ntal t
echn
i
qu
e
s that
est
imat
e the dy
namics
by
t
he
res
ponse
to
a jump
i
n
the drivin
g
sig
n
al
, b
ut for
a
no
nlinear syste
m
su
c
h
as A
E
Ds,
this la
borio
us
ne
ss is
inevita
ble.
The
te
c
hn
i
qu
e
is
base
d
on
t
he
pr
e
viousl
y
ob
t
ai
ned
f
or
m
ula
for
the
no
nline
ar
tra
ns
fe
r
fun
ct
ion
of
t
he
li
nk
formi
ng
the
el
ect
r
om
a
gnet
ic
tor
que,
ta
king
i
nto
a
cc
ount
t
he
c
hang
es
in
dy
namic
s
with
c
hanges
in
t
he
fr
e
qu
e
nc
y
of
the
sta
tor
vo
lt
a
ge
an
d
m
otor
l
oad.
This
me
a
ns
that
this
f
ormula
sho
uld
al
so
be
recog
nized
as
more
acc
ur
at
e
than
t
he
vect
or
e
quat
io
ns
of
as
yn
c
hro
nous
el
ect
ric
mo
t
or
s
us
e
d
i
n
th
e
der
i
vatio
n
of
vecto
r
con
t
ro
l
(at
le
as
t
with
c
ha
ng
es
in
the
f
re
qu
e
nc
y
of
the
sta
to
r
vo
lt
age
f
rom
10
to
50
Hz
a
nd
in
t
he
fr
e
qu
ency
range
of in
pu
t
sign
al
s
from
0
to 5 Hz
).
The
pro
pose
d
con
t
ro
l
meth
od
with
D
PF
f
or
th
e
sta
to
r
c
ur
ren
t,
li
near
iz
i
ng
t
he
nonlinea
riti
es
of
t
he
AE
D
an
d
forci
ng
the
ma
gne
ti
c
flu
xes
in
the
mo
to
r
is
th
e
m
os
t
ef
fecti
ve
m
et
hod
f
or
co
ntr
olli
ng
t
he
dyna
mic
char
act
e
risti
cs.
The
met
hod
of
c
on
t
ro
l
with
DP
F
f
or
the
st
at
or
c
urre
nt
propose
d
i
n
[20
]
,
[
22]
li
near
iz
e
s
the
nonlinea
riti
es
of
the
A
ED
and
f
orces
t
he
ma
gn
et
ic
fl
ux
e
s
i
n
t
he
mo
to
r.
Accordi
ng
to
the
res
ults
of
exp
e
rime
nts
usi
ng
t
his
te
ch
ni
qu
e
,
it
s
hould
be
recog
nized
as
the
mo
st
ef
f
ect
ive
meth
od
of
co
ntr
ol
acc
ordi
ng
to the dynamic
ch
aracte
risti
cs o
f
t
he
"re
pro
duct
ion
"
of sig
na
ls for sett
ing
t
he
r
otati
on
sp
e
ed
an
d reco
m
men
d
it
for
s
uc
h dr
ive
s
(
incl
ud
i
ng for
con
t
ro
ll
in
g dou
bly
-
fe
d
el
ect
ric
mach
i
ne of
w
i
nd tu
rb
i
nes).
REFERE
NCE
S
[1]
N.
A.
Sukhenko
,
G.
Ya.
Pyati
br
at
ov,
A.
A
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Dan
shina,
L.
L
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Alt
unyan,
“
Pros
pective
Elec
tro
mec
hani
c
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Con
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Sys
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ustria
l
Manipulator
Eff
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”
I
nte
rnational
Jo
urnal
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Powe
r
Elec
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cs
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d
Dr
iv
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PE
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Alekse
ev
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A.P.,
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ro
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l
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hik
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“
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c
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cur
ren
t
,
”
Technope
rs
pec
t
i
va
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pp
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200
6
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IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
Dr
i
S
ys
t
,
V
ol
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o.
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Ma
rch
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1
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59
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66
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Goun,
V.S.
,
An
iki
n,
A.S.
&
B
aki
n,
A.A.
,
“
Ex
per
imental
d
et
e
r
mi
nation
of
sub
opti
mal
p
arame
t
ers
for
ene
rgy
-
eff
icien
t
con
trol
of
an
induction
mot
or
,
”
In
te
rnat
ional
Journal
of
Powe
r
Elec
tron
ic
s
and
Dr
i
ve
S
y
stems
(IJ
PE
DS)
,
vol.
11
,
no
.
4
,
pp
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20
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ds
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na
A.G.
,
Us
o
lt
sev
A
.
A.
,
“
Opt
im
al
mo
ti
on
con
trol
dur
ing
posi
tioning
and
i
ts
mo
del
ing
in
the
Ma
thL
ab
Simul
ink
envi
ronm
ent
,
”
Iz
ve
sti
ya
VUZov
.
I
nstrum
ent
makin
g
,
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[7]
Ferre
ira,
F.J
.
T.E
.
,
De
Almeida
,
A
.
T.
,
“
Overv
i
ew
on
ene
rgy
savin
g
opportunitie
s
i
n
elec
t
ric
mot
o
r
drive
n
sys
tems
-
Part
1:
Sys
te
m
eff
icienc
y
im
pro
vem
en
t,
”
52nd
I
EE
E/IAS
Indust
rial
and
Comm
erc
ial
Powe
r
Sy
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Techni
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Confe
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OI:
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S.2016.
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olt
sev
A.
A.
,
“
Dete
r
mi
na
ti
on
of
the
par
amet
ers
of
the
async
hronous
mot
or
mode
l
ac
cor
d
in
g
to
the
r
efe
r
en
ce
dat
a
,”
News of u
niv
ersities. Ins
trument
making
, v
ol.
51
,
no
.
10
,
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–
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[9]
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li
n,
I
.
G.
Topo
l'Skaya
,
“
Ampli
tude
con
tr
ol
of
the
mo
ment
of
a
three
-
ph
ase
as
yn
chr
onou
s
drive
base
d
on
gene
r
a
li
z
ed ene
r
gy
-
flow
principl
es,
”
Russian
E
lectric
al
Eng
ineering
,.v
ol
.
85
,
n
o
.
4
,
pp
.
205
-
209
,
2
014
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[10]
Goudarz
i,
N.
,
Z
hu,
W
.
D.
,
“
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evi
ew
on
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e
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e
vel
opm
ent
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ind
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ine
gen
era
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ross
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he
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,”
Int.
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[11]
Li
,
K.
,
Luo,
H.
,
Yang,
C
.
and
Yin,
S.
,
“
Subs
pac
e
-
ai
d
ed
cl
osed
-
loop
sys
tem
id
ent
ifica
ti
on
with
app
li
c
at
ion
to
dc
mot
or
sys
tem,
”
I
EE
E
Tr
ansacti
o
ns on
Industrial Elect
ronics
,
vol
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67
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no.
3,
pp.
23
04
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2019
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[12]
Ahmad,
M.A.,
Mus
a,
Z
.
,
Suid,
M.H.
and
Tu
mari,
M
.
Z
.
M.,
“
Gr
ey
wolf
optimizer
for
id
ent
if
ic
a
t
ion
of
li
qu
id
slo
sh
beha
vior
using
co
nti
nuous
-
time
ham
m
erste
in
m
odel
,
”
Bu
ll
e
ti
n
of
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