In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
11, N
o.
1, Mar
ch 20
20,
p
p.
220~
2
2
7
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v11
.
i
1.pp
2
20-
22
7
220
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Structural correction of nonli
n
e
ar dynamics of frequency-
contr
o
lled induction motor drives
Vl
a
d
i
m
i
r
L
.
Ko
d
k
i
n
,
Al
ek
sandr
S
.
A
n
ik
i
n
,
Al
ek
sa
n
d
r
A. Bal
d
e
n
k
ov
D
e
partem
en
t of th
e
oret
ical f
und
am
ent
a
ls
o
f
e
l
ectrical
eng
in
eeri
n
g
,
Sou
t
h Ura
l
S
ta
te
Unive
rs
ity
, Ru
s
sia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Jul 7,
2019
Re
vise
d A
ug
1
2
,
201
9
Ac
ce
p
t
ed
No
v
1
8
,
2
019
F
r
equ
e
ncy
anal
y
s
is
o
f
p
r
oces
ses
i
n
t
h
e
f
req
u
ency
-con
trol
led
i
n
d
u
c
t
i
on
m
oto
r
dri
v
e
s,
a
s
in
a
uto
m
a
t
i
c
c
o
n
t
r
ol
s
ys
tems
w
it
h
dyn
a
m
i
c
n
o
n
-li
n
e
a
ri
ties
,
are
pres
ent
e
d
i
n
t
h
i
s
paper.
F
or
t
he
f
irst
t
im
e,
t
he
d
y
n
am
ic
t
ransf
er
f
un
cti
o
n
in
term
s
of
e
l
ectro
mag
n
et
ic
t
o
r
qu
e
(m
)
f
r
om
a
bs
olute
s
l
ip
d
eterm
i
n
ed
b
y
th
e
lo
ad
a
nd
f
r
equen
c
y
of
t
he
s
up
pl
y
vol
tag
e
a
re
p
rop
o
s
ed
.
T
o
s
tu
dy
t
h
e
d
y
n
a
m
i
c
chara
c
t
e
ri
stics
,
a
m
eth
od
for
con
s
t
r
ucti
ng
a
f
a
mily
o
f
f
r
eq
uenc
y
charact
e
ri
stics
for
fixed
val
u
es
o
f
abs
o
l
u
te
s
li
pss
and
frequen
cies
o
f
th
e
su
pp
ly
v
o
ltage
a
re
d
escri
b
ed
.
T
h
e
f
r
equ
e
ncy
char
act
eristics
co
r
resp
ond
in
g
to
th
ese
tran
s
f
er
f
u
n
ctio
ns
a
re
c
o
n
st
ruct
ed
i
n
the
Si
muli
nk
a
pplic
at
io
n
o
f
t
h
e
M
a
tL
ab
s
o
f
t
w
are.
B
a
s
ed
o
n
r
e
su
lts
o
f
t
h
e
analy
s
i
s
t
h
e
s
t
r
uct
u
ra
l
correcti
o
n
me
tho
d
s
t
ha
t
i
m
pro
v
e
t
h
e
d
yn
amic
s
o
f
s
u
c
h
no
nlin
e
a
r
s
ys
te
ms
a
re
p
r
o
p
o
s
e
d
.
T
h
i
s
p
a
p
e
r
i
s
a
n
e
x
a
m
p
l
e
o
f
h
o
w
t
h
e
i
n
i
t
i
a
l
c
o
m
p
l
i
c
a
t
e
d
(
b
u
t
m
o
re
accu
rate)
in
terp
re
t
a
ti
on
o
f
no
nl
in
earity
a
llo
w
ed
u
s
t
o
f
i
nd
a
new
bes
t
s
o
lut
i
on
t
o
the
probl
e
m
o
f
cont
r
olling
a
compl
e
x
dynamic ob
ject
.
K
eyw
ord
s
:
D
ynam
i
c p
o
s
i
t
i
ve
fe
e
d
b
ac
k
F
r
equenc
y
ana
l
ys
is
F
r
equenc
y
re
spons
e
Ind
u
ct
i
on m
o
to
r
drive
No
nl
i
n
ea
r d
yna
mi
c
Structur
al correction
Th
is
is a
n
o
p
en acces
s a
r
ti
cle u
n
d
e
r t
h
e
CC
B
Y
-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
Al
e
k
sand
r S
. A
n
i
ki
n
,
D
e
pa
rtem
ent o
f
T
heor
e
t
i
c
a
l
f
unda
me
n
t
a
l
s
of
e
lectric
a
l
e
ngi
nee
r
i
ng,
S
out
h U
r
al S
tate U
nive
rsity,
7
6
,
Le
n
i
n
p
rosp
e
k
t
,
Ch
e
ly
a
b
in
s
k
, Ru
ssi
a. 4
54
080
Em
ail:
ani
k
i
n
a
s
@
s
u
s
u.
ru
1.
I
N
TR
OD
U
C
TI
O
N
Th
e
wi
d
e
sp
re
ad
u
se
o
f
fre
qu
en
cy
c
on
v
e
rt
e
r
s
f
o
r
co
nt
roll
i
n
g
a
s
yn
chr
o
n
o
u
s
motors in
r
e
c
e
n
t
year
s has
cre
a
ted
t
h
e
im
pressi
o
n
t
ha
t
t
h
er
e
ar
e
no
pr
ob
lem
s
i
n
t
h
e
fie
l
d
of
i
n
d
u
ct
i
on
mo
t
o
r
drive
(
I
MD
).
H
ow
e
v
er
,
the
r
e
s
u
l
t
s
o
f
s
t
u
d
i
e
s
[
1
-
5
]
s
h
o
w
t
h
a
t
t
h
e
d
y
n
a
m
i
c
c
h
a
r
a
c
t
e
r
i
s
t
i
c
s
o
f
t
h
e
se
s
yste
ms
r
e
q
u
i
re
a
m
o
r
e
i
n
-d
e
p
th
s
t
udy
from
t
he
p
oi
n
t
o
f
v
i
ew
o
f
t
h
e
the
o
r
y
o
f
c
o
ntr
o
l
o
f
non
l
i
near
s
y
s
t
em
s.
F
re
quenc
y
co
n
t
rol
l
ed
I
MDs
a
r
e
a
hi
g
h
l
y
no
n-l
i
ne
ar
s
ys
te
m.
T
he
“
ma
i
n
”
pa
ram
e
ter
de
t
e
rm
ini
n
g
th
e
n
on-
li
n
ear
it
y
of
t
hese
s
yste
ms
i
s
the
v
a
riab
l
e
fre
que
nc
y
of
t
he
s
up
ply
v
o
l
t
a
ge.
U
n
l
i
k
e
t
h
e
sta
tio
nar
y
n
o
n
-l
ine
a
r
it
ies
o
f
t
he
r
eg
u
l
at
ory
sys
t
e
m
s
co
ns
i
d
ere
d
i
n
the 8
0
s
an
d 9
0
s
of the
2
0
th
c
e
n
t
u
ry,
the
var
i
a
b
le
f
re
q
u
e
n
cy
i
n
th
e
I
M
D
cha
n
g
e
s its
f
re
q
u
e
n
cy
r
esp
o
n
s
e.
V
a
riable
freq
u
e
ncy,
s
tric
tl
y
s
p
ea
ki
ng,
d
oes
no
t
a
llow
t
h
e
use
o
f
a
m
a
t
h
e
m
atica
l
a
ppa
ra
tu
s
des
i
gne
d
for
IMD
s
,
ba
s
e
d
on
v
e
c
t
o
r
ana
l
ys
is,
s
i
nce
t
h
e
vec
t
or
r
e
p
re
se
n
t
a
t
i
on
o
f
var
i
a
b
les
ov
e
r
t
i
m
e
im
p
l
ie
s
t
h
e
con
s
ta
nc
y
o
f
t
he
f
re
que
ncy
o
f
t
he
s
up
p
l
y
v
o
lta
ge,
or
t
he
f
r
e
que
nc
y
o
f
r
o
t
ati
o
n
o
f
t
hese
v
ec
tor
s
.
H
o
w
e
ve
r,
due
to
t
he
a
bse
n
c
e
of
a
no
the
r
,
vec
t
or
m
et
ho
ds
a
re
u
sed
in
m
o
s
t
rese
arc
h
o
r
educ
a
t
io
n
a
l
w
o
r
k
s
on
I
M
D
s
[
6-
8],
des
p
i
t
e
t
h
e
fac
t
that t
h
e
au
t
hor
s qu
ite o
ft
e
n
re
c
og
n
i
ze
th
e
il
l
e
g
al
i
t
y o
f
s
u
c
h a
n
appr
oa
ch.
2.
PROBL
E
M
ST
AT
EM
E
N
T
The
m
o
st
e
ffe
c
ti
v
e
e
n
g
i
nee
r
i
ng
me
t
hod
for
a
s
se
ssi
ng
t
h
e
dy
na
mic
s
of
e
l
e
c
t
ric
dri
v
e
s
i
s
the
me
t
h
o
d
of
fre
que
nc
y
anal
ys
is
[
9-1
1
].
D
irec
t
a
p
p
lic
atio
n
o
f
t
h
i
s
m
e
tho
d
t
o
IM
D
s
i
s
ha
mpe
r
ed
b
y
t
h
e
pr
ese
n
c
e
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
S
t
ru
ctu
r
a
l
c
o
rre
c
t
ion
o
f
nonl
in
e
a
r d
y
n
a
m
i
c
s
o
f
fre
q
u
e
n
c
y
…
(Vl
a
d
i
m
i
r L. Ko
d
k
in
)
22
1
significa
n
t
non-linear
ities
in
t
he
m
.
T
he
c
ons
t
r
u
ction
of
t
he
f
r
eque
nc
y
c
h
ara
c
ter
i
s
t
ics
o
f
s
uch sys
t
e
m
s
i
nvo
l
v
es
a
numbe
r
o
f
i
nev
i
tab
l
e
ass
u
m
p
ti
ons
[
1
2
-1
5].
A
f
t
e
r
cons
ide
r
i
ng
t
he
d
i
f
ferent
v
er
sions
of
t
hese
a
ssum
p
tions,
t
h
e
cal
cu
l
a
ti
on
o
f
t
h
e
dyn
a
m
ic
m
ec
h
a
n
i
c
a
l
ch
ara
c
t
e
ri
st
i
c
s
et
f
o
rth
in
t
h
e
U
sol
t
se
v’s
mono
gra
p
h
[12]
t
urne
d
o
u
t
t
o
b
e
t
h
e
m
o
s
t
a
c
c
e
p
t
a
b
l
e
.
T
h
e
c
a
l
c
u
l
a
t
i
o
n
i
s
r
e
p
e
l
l
e
d
b
y
e
qu
a
t
i
o
n
1.36
o
n
p
.23
[12]
.
It
e
sta
b
l
i
shes
a
con
n
ec
tio
n
be
t
w
een
t
he c
urre
nt
m
om
ent
(
m
)
and sl
ip (
β
)
at t
he
n
om
ina
l
fr
e
que
nc
y
ω
1n
o
m
:
(
1
)
Where,
–
t
he
t
ra
nsie
nt
t
ime
c
onsta
n
t
o
f
t
h
e
rot
o
r,
–
t
h
e
r
e
l
a
t
i
v
e
s
l
i
p
,
M
k
–
t
h
e
c
r
i
t
i
c
a
l
mom
e
nt,
S
k
–
t
he
c
ritic
al s
lip
a
t the
n
o
mi
na
l
fre
que
nc
y
ω
1н
о
м
.
A
t
t
he
b
e
g
i
n
ni
ng
of
t
he
w
ork
i
ng
c
h
ara
c
teris
tic
(for
М
≈
0
,
β
≥
0
)
,
t
h
e
t
r
a
n
s
f
e
r
f
u
n
c
t
i
o
n
i
s
s
i
m
p
l
i
f
i
e
d
and
red
u
ce
s to
a
dynam
i
c
li
n
k
of the
1
s
t
or
d
e
r
:
To
d
e
t
erm
i
ne
t
he
t
ra
nsfer
fu
nct
i
on
b
y
t
he
e
lec
t
r
o
ma
gne
t
i
c
t
orqu
e
(
)
from
a
bsol
ute
sl
ip
(
Δ
)
,
w
e
tr
ansform
it to t
he
form
:
2
H
o
w
e
ver,
t
he
r
e
s
ul
ts
o
f
ex
p
e
r
i
m
e
nts
g
i
ven
in
[
1,
16]
s
how
ed
t
ha
t
it
is
i
nc
orrec
t
t
o
e
x
t
e
n
d
t
his
form
ula
to
a
l
l
oper
a
tin
g
mod
e
s.
3.
SOLUT
I
ON
The
e
xpress
i
o
n
(
1)
a
l
l
ow
e
d
u
s
to
p
r
o
pos
e
a
n
o
t
he
r
vari
ant
o
f
l
i
n
ea
riz
a
t
i
o
n,
i
n
w
h
i
c
h
t
h
e
i
n
i
tial
equa
t
i
o
n
ta
k
e
s
the
f
orm
:
′
2
1
к
1
(
3
)
I
n
t
h
i
s
c
a
se,
expr
ess
i
on
(1),
t
he
b
in
d
i
n
g
t
or
que
(
),
r
elati
v
e
sli
p
(
),
a
nd
qu
ant
i
t
i
e
s
de
term
ine
d
b
y
the
par
a
m
e
ters
o
f
the
e
l
e
c
tric
m
otor
(
′
-
t
ra
nsiti
o
n
t
im
e
c
o
n
s
ta
nt
;
M
k
, s
k
-
c
ritic
al
m
om
en
t
and
c
r
i
t
i
c
a
l
s
l
i
p
,
depe
n
d
i
n
g on
the
freque
nc
y ω
1
) wi
ll be tra
nsform
ed to:
(
4
)
and
the
tra
n
s
f
e
r
f
unct
i
on (2)
w
i
l
l
b
e
repre
s
ente
d a
s
fo
l
l
o
w
s
:
(
5
)
wher
e
–
the
s
ta
t
o
r
su
pp
ly
v
o
lta
ge freq
u
e
n
c
y
.
Th
e
wo
rkin
g
se
ct
ion
(a
t
0
2
,
w
h
er
e
i
s
t
h
e
ra
t
e
d
t
o
rq
ue)
of
t
he
m
ec
han
i
ca
l
cha
r
ac
t
e
ris
tics
of t
he
I
MD
w
i
l
l be
desc
r
i
b
ed
by
the
struc
t
ura
l
dia
g
ra
m
sho
w
n
in F
ig
ure
1.
Eq
ua
ti
on
(
3
)
appe
ars
t
o
b
e
su
bs
tan
t
ial
l
y
no
n
line
a
r,
s
i
n
ce
i
t
w
i
ll
transfor
m
w
h
en
t
he
f
r
e
q
u
e
nc
y
o
f
t
h
e
sup
p
l
y
v
o
l
t
a
ge
a
nd
sli
p
o
f
t
h
e
motor
cha
n
g
e
.
F
o
rm
u
l
a
(
4
)
c
a
n
be
called
the
dyna
mic
K
l
oss
f
o
rmula
(
∙
кр
кр
). The form
u
las be
com
e
i
de
n
tica
l
w
he
n
subs
t
i
t
u
te
d i
n
t
o
the
f
orm
ula (4)
0
,
i.e. for
a
stat
i
c
state.
F
or
0
,
i.
e
.
w
ith
o
u
t lo
a
d
, form
u
l
a
(
4) c
oi
nc
ide
s
w
it
h
the form
ul
a gi
v
en i
n t
h
e U
s
oltse
v
mono
gra
p
h [1
2]
. These
cha
n
g
i
n
g
p
ro
p
e
rties
of
t
he
t
r
a
nsfe
r
fu
nct
i
o
n
d
eter
mi
ne
t
he
c
han
ge
i
n
t
h
e
dy
nam
i
c
s
o
f
I
M
D
w
ith
f
re
q
u
enc
y
c
o
n
t
r
o
l
,
n
o
t
e
d
e
a
r
l
i
e
r
i
n
e
x
p
e
r
i
m
e
n
t
s
.
T
h
u
s
,
t
h
e
"
f
r
e
e
z
i
n
g
"
o
f
t
h
e
tra
n
sfe
r
f
unc
t
i
o
n
s
is
e
ffe
c
tive
en
o
u
gh
to
int
e
rpret
t
h
e dynam
ic
c
har
acter
is
tics
o
f IMD.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
220
–
22
7
22
2
F
i
gure
1. Block diagr
am
of
I
M
D w
i
t
h
t
h
e
wo
r
ki
ng
sec
ti
on
o
f
th
e
m
echa
n
ic
al c
hara
cteris
t
i
cs
F
i
gures
2
a
a
n
d
2b
bel
o
w
sho
w
t
he
freq
u
e
n
c
y
c
hara
cter
ist
i
c
s
o
f
I
M
D
b
a
s
e
d
o
n
a
l
o
w
-
p
o
w
e
r
m
o
t
o
r
(0.37
k
W
)
w
i
t
h
a
s
qu
irre
l-ca
ge
r
otor
.
To
bui
l
d
freq
u
enc
y
c
hara
c
t
e
ri
st
i
c
s,
h
e
r
ei
n
a
ft
e
r
,
t
h
e
sof
t
ware
p
ack
a
g
e
Sim
u
l
i
nk
M
a
t
Lab
w
a
s
used.
Th
e
given
am
plitude
a
nd
phase-freque
n
cy
c
hara
cter
i
s
t
i
cs
o
f
t
h
e
m
o
t
o
r
for
t
h
e
fre
que
nc
ies
of
t
he
s
ta
tor
v
o
l
t
age
of
10
H
z
(
F
i
gure
2a
)
a
nd
5
0
H
z
(
F
igure
2b)
c
orre
spo
n
d
t
o
sl
ips
a
t
l
o
w
(
0.2
)
-
W1 a
nd ra
te
d loa
d
(
) - W2.
(a)
(b)
F
i
gure
2.
T
he
a
m
p
l
i
t
ude
a
nd p
h
ase
c
h
a
r
ac
teri
st
i
c
s of
t
he
IM
D
a
t
a frequenc
y of
t
he sta
tor
supp
l
y
vo
l
tage
o
f
10 (
a)
50
(b
) Hz
:
W1
-
sli
p at
a
loa
d t
o
rq
ue
o
f
0.2
,
W2 -
s
l
i
p a
t
a
l
oa
d t
o
rq
ue
of
The
g
i
ve
n
fre
q
u
e
nc
y
re
sp
o
n
s
e
s
w
e
ll
e
x
p
l
a
i
n
som
e
p
r
oble
m
s
of
A
C
dr
ive.
F
igure
2a
s
h
o
w
s
t
h
a
t
a
t
a
st
a
t
or
s
u
p
p
l
y
v
o
l
t
a
g
e fre
que
n
c
y of 1
0
H
z
a
nd
a
sma
ll
l
o
a
d
,
the
pha
se
s
h
i
ft
s
of
t
he
f
r
e
q
u
e
n
c
y
r
e
s
pon
se
(
W1) in
the
rang
e
fr
o
m
10
t
o
1
0
0
r
a
d
/
s
v
ar
y
fr
om
40
t
o
-
9
0
de
gree
s.
C
o
m
pariso
n
of
f
r
e
que
nc
y
re
s
p
on
s
e
s
a
t
fre
que
nc
ies
of sta
tor
vo
lta
ge
of 1
0
a
nd
5
0 H
z
sh
o
w
s
tha
t
in
t
h
e
r
a
n
g
e
f
ro
m
10
t
o 100
r
ad
/
s
t
h
e
ph
a
se
s
hif
t
s of
fre
que
nc
y
r
e
sp
onse
s
h
ave
si
g
n
if
i
c
an
t
l
y
d
i
ffe
r
e
n
t
v
a
lues
-
f
r
o
m
25
t
o
-
4
5
elec
tric
d
e
g
re
e.
T
hi
s
m
e
a
n
s
t
h
a
t
dur
in
g
a
c
c
e
l
era
t
i
o
n
an
d
dec
e
l
era
tio
n,
t
he
p
hase
s
hi
ft
s
cha
nge
i
n
s
u
c
h
a
w
a
y
t
h
a
t
a
s
y
s
t
e
m
w
i
t
h
a
s
t
a
b
i
l
i
t
y
ma
rgin
a
t
a
fre
que
nc
y
o
f
50
H
z
c
a
n
b
e
c
o
m
e
unsta
b
l
e.
T
he
f
re
qu
e
n
c
y
o
f
the
s
t
at
or
v
olta
g
e
w
ill
b
e
10
H
z
.
Thi
s
ma
y
be
t
he re
a
s
on for
the d
i
f
f
er
ent osci
l
l
a
tio
n o
f
the
dri
ve a
t
d
i
f
f
e
re
nt
f
requ
e
n
c
i
es
o
f
th
e
st
at
o
r
vol
t
a
g
e
,
wh
i
c
h
w
e
r
e
note
d
i
n
[1
7,
1
8]
.
Thus,
the
n
o
n
l
i
n
ear
itie
s
of
t
he
t
ra
n
s
fe
r
fu
nct
i
o
n
s
o
f
t
h
e
li
nk
of
t
he
t
orq
u
e
gen
e
r
a
tor
Fi
g
u
r
e
1
req
u
i
r
e
l
i
n
ea
ri
zati
o
n
t
o
in
c
rea
s
e
t
h
e ef
fi
c
i
en
c
y
o
f
t
h
e
e
l
ectr
i
c dri
v
e
and t
h
e sam
e
beha
v
ior a
t
d
iffere
nt
fre
que
nc
ies.
Mo
st
o
ften,
“
t
rans
vec
t
or
”
con
t
ro
l
is
u
se
d
t
o
l
i
n
ear
i
z
e
the
IMD.
W
it
h
t
h
is
c
on
trol,
d
yna
m
i
c
links
a
r
e
form
ed
i
n
the
con
t
ro
l
de
vi
ce
t
ha
t
a
r
e
i
n
ver
s
e,
m
ainl
y,
t
o
t
h
e
i
nertia
o
f
t
h
e
r
o
tor
c
i
rcu
its
,
w
i
t
h
t
he
r
o
t
or
s
pe
e
d
ada
p
t
i
n
g
t
o
t
h
e
freque
nc
y
o
f
t
he
s
ta
tor
v
o
lta
ge,
how
e
v
er
,
thi
s
do
es
n
ot
t
ak
e
int
o
a
c
c
ount
t
h
e
p
u
l
se
d
n
a
t
u
re
o
f
the
fr
eq
ue
nc
y
con
v
er
t
e
r
a
n
d
t
h
e
pre
s
e
n
ce
o
f
o
t
her
harm
o
n
ic
c
omp
o
n
en
t
s
i
n
the
r
o
tor
and
st
at
or
c
urre
nts
(exc
ep
t fu
nd
a
m
e
n
tal h
a
r
m
on
ic)
[19-
24
]
.
An
ot
h
e
r
fa
c
t
o
r
t
ha
t
sign
if
i
c
a
n
t
l
y
w
o
rse
n
s
t
h
e
o
p
e
rat
i
on
o
f
vec
t
or
c
on
tro
l
s
ho
u
l
d
be
r
ec
og
nize
d
t
h
at
a
numbe
r
o
f
p
ara
m
e
t
ers
(
f
or
e
xam
p
le,
st
a
t
or
a
nd
ro
tor
re
si
s
t
anc
e
s
)
c
a
n
c
h
ange
s
i
g
n
i
fica
ntl
y
d
ur
ing
o
p
e
rati
on,
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
S
t
ru
ctu
r
a
l
c
o
rre
c
t
ion
o
f
nonl
in
e
a
r d
y
n
a
m
i
c
s
o
f
fre
q
u
e
n
c
y
…
(Vl
a
d
i
m
i
r L. Ko
d
k
in
)
22
3
and
i
t
i
s
alm
o
st
i
mp
oss
i
b
l
e
t
o
t
ra
ck
t
he
se
c
han
g
es.
A
ll
t
h
i
s
c
o
ntri
bu
tes
to
t
he
n
o
n
l
inea
r
ity
o
f
the
ro
t
o
r
and
st
a
t
or c
urrents
dur
i
n
g
vec
t
or
c
on
tro
l
a
nd
lead
s
t
o
a
s
ig
ni
fica
n
t
decr
ease
i
n
i
ts effic
i
enc
y
[
1
,
4
,
16].
C
ons
ide
r
a
n
alterna
t
i
v
e
l
i
nea
r
i
zati
o
n
of
t
he
t
r
a
nsfer
fu
nct
i
on
w
it
h
re
spect
t
o
the
e
l
e
c
trom
agne
t
i
c
tor
que
(
5).
F
o
r
this,
i
n
t
he
s
truct
u
ral
di
a
g
ram
[25],
we
i
ntro
d
uc
e
lo
c
a
l
fe
e
dbac
k
(
F
i
gure
3
)
on
t
h
e
elec
tr
oma
gne
t
i
c
torq
ue
w
it
h
t
h
e tra
n
s
f
er
fun
c
t
i
o
n
(the
in
trod
uce
d
d
es
ig
na
tio
n
w
ill be
e
xpla
i
ne
d be
l
o
w
)
.
F
i
g
u
r
e
3
.
I
n
t
r
o
d
uc
tio
n
of feed
ba
ck
We
dete
r
mi
ne
t
he tra
nsfer
fu
n
c
ti
o
n
by
th
e e
l
e
c
trom
ag
net
i
c
tor
que
:
U
nder
the
f
o
llowi
ng
c
ond
i
tio
n
:
2
1
Th
at
i
s, i
f
t
h
e
c
o
rr
ect
iv
e
ele
me
nt
w
ill
h
a
ve
t
he
fol
l
o
w
i
ng tra
n
sfe
r
funct
i
o
n
:
(
6
)
The
n
t
he
tra
n
s
f
e
r
funct
i
on
by
t
h
e
ele
c
trom
ag
net
i
c
torq
ue
lo
oks
like
:
Whe
n
t
his
c
o
ndi
ti
o
n
i
s
fu
lfil
le
d,
t
he
t
r
a
ns
fer
func
tio
n
w
i
t
h
res
p
ec
t
to
t
h
e
e
l
ect
roma
g
n
e
tic
tor
que
w
ill c
o
mplete
l
y
c
o
i
nc
ide
w
ith
e
x
p
res
s
i
on (2)
gi
ven i
n
[
1
2].
Expr
ession
(6) f
o
r
t
h
e link
h
a
s
t
he
for
m
of a
n a
p
erio
d
i
c li
n
k
of
the firs
t
kind,
the
g
ai
n
of w
hic
h
in
t
he
f
ina
l
f
orm
de
pe
n
d
s
on
the
fre
que
nc
y
of
t
he
s
ta
t
o
r
su
pp
l
y
v
o
l
t
a
g
e
a
n
d
o
n
a
b
s
o
l
u
t
e
s
l
i
p
.
A
n
e
g
a
t
i
v
e
s
i
g
n
in
f
r
o
n
t
o
f
the
fra
c
ti
o
n
i
nd
ic
a
t
es
t
hat
the
prop
ose
d
c
orr
ect
ive
r
ela
t
ions
hi
p
sh
ou
ld
b
e
p
o
s
i
t
i
v
e.
B
ase
d
o
n
t
h
is,
the
des
i
gna
t
i
o
n
D
P
F
–
dy
nam
i
c
p
o
si
ti
ve
f
ee
dbac
k
w
a
s
i
n
t
rod
u
ce
d
abov
e
.
I
n
mo
d
e
rn
d
ri
ve
s,
i
t
is
qui
t
e
s
imp
l
e
t
o
rea
li
z
e
t
h
e nec
e
ssa
ry
d
e
p
e
n
d
e
n
c
e of
t
h
e
coe
f
f
i
c
i
e
nt
on
t
h
e f
re
quenc
y
o
f
t
he
v
o
lta
g
e
o
f t
h
e e
l
ec
tric
m
otor.
The
se
le
c
t
i
o
n
of
f
ee
dba
ck
c
oeffic
i
e
n
ts
a
c
c
o
rd
in
g
t
o
c
on
dit
i
o
n
(
6
)
m
a
k
e
s
i
t
po
s
s
i
b
l
e
t
o
obt
a
i
n
a
line
a
rize
d
t
r
an
sfer
f
unc
t
i
o
n
o
f
an
a
s
ync
hro
n
o
u
s
e
l
e
c
t
ric
m
o
tor
a
t
a
ny
f
re
q
u
e
n
c
y
of
t
he
s
up
ply
v
o
lt
ag
e
and
loa
d
.
S
u
ch
a
t
r
a
n
s
fer
fu
nc
tio
n
,
on
the
o
n
e
h
a
nd,
b
ecom
e
s
ide
n
t
i
ca
l
to
t
he
p
rev
i
o
u
s
l
y
k
n
o
w
n
f
orm
u
la
f
or
t
he
trans
f
e
r
func
t
i
o
n of an as
ync
hro
n
o
u
s
dr
ive
a
t
ze
r
o
sl
ip
(
i
.
e.
,
w
i
t
h
ou
t
l
o
a
d
)
,
and, on
the
ot
her han
d
, to
t
h
e
w
ell-
kn
ow
n K
l
oss for
m
ula
for
st
a
tic
m
odes of
o
p
e
ra
tion
o
f
a
n async
h
r
o
n
ous
m
ot
or.
The
ne
x
t
s
te
p
s
how
s
a
n
e
x
a
mple
o
f
de
t
e
rm
ini
n
g
the
c
o
eff
i
c
i
e
n
t
s
o
f
t
he
c
orr
ecti
v
e
lin
k
a
t
f
re
q
u
e
n
c
i
es
of
t
he
s
upp
ly
v
o
l
tage
o
f
10
a
nd
5
0
H
z
for
tw
o
ty
pes
o
f
l
oa
ds
0.2
a
nd
.
Th
e
ca
lcula
t
i
o
n
resu
lts
o
f
th
e
trans
f
e
r
f
unc
t
i
ons
o
f
t
h
e
t
o
r
q
ue
d
ri
ver
o
f
t
he
i
ni
t
i
a
l
I
M
D
a
nd
t
h
e
c
o
rr
ect
i
v
e
lin
k
ar
e
presen
te
d
i
n
T
a
b
l
e
1
.
T
h
e
resul
t
i
ng
a
m
p
l
itu
de
a
nd
p
has
e
c
ha
rac
t
eri
s
ti
c
s
a
re
c
omb
i
n
e
d
w
i
t
h
t
h
e
c
orres
p
o
ndi
ng
c
ha
ra
c
t
eri
s
ti
c
s
w
i
t
ho
ut
in
t
r
od
uc
in
g
the
c
o
rrec
t
i
v
e
l
i
n
k
(F
ig
ur
e
2
a
a
nd
2b)
a
nd a
r
e
pres
e
n
t
e
d i
n
F
igu
r
e 4
and F
i
gure
5, respec
tive
l
y
.
In
w
i
d
ely
u
s
ed
I
M
D
s,
i
t
i
s
v
ery
d
i
ffi
cul
t
t
o
re
a
l
i
z
e
t
h
e
lin
k
b
y
me
cha
n
i
c
al
t
orq
u
e
.
G
i
v
en
t
ha
t
the
tor
que
i
s
e
qua
l
to
∙
a
nd
in
a
lm
ost
all
ca
lc
ul
ati
ons
it
is
a
ssum
ed
t
ha
t
t
h
e
rot
o
r
fl
ux
l
in
ka
g
e
i
s
c
o
n
s
t
a
nt,
yo
u
c
a
n
r
e
p
lac
e
t
he
o
r
i
gi
na
l
s
i
g
n
a
l
i
n
t
h
is
l
o
c
a
l
c
on
ne
c
t
i
o
n
w
i
th
t
he
e
ffec
t
i
v
e
val
u
e
o
f
t
he
s
ta
t
o
r
cur
r
ent,
o
r
i
t
s
a
c
t
i
v
e
c
o
m
pone
n
t
, wh
i
c
h
i
s
ca
l
c
u
l
a
t
e
d
i
n
a
ll
f
re
q
u
e
n
c
y
c
o
nv
ert
e
rs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
220
–
22
7
22
4
F
i
gure
4.
T
he
a
m
p
l
i
t
ude
a
nd p
h
ase
c
h
a
r
ac
teri
st
i
c
s of
t
he
IM
D
a
t
a fr
e
quenc
y of
t
he sta
tor
supp
l
y
vo
l
tage
o
f
10 H
z
:
W1 and W
2
-
slip at
a
l
o
a
d
m
oment
of
0.2
and
w
ith
ou
t
corr
ecti
on,
W
3
a
nd W4
-
s
li
p a
t
a
l
o
a
d
mo
me
n
t
o
f
0.
2
a
nd
w
i
t
h
the
i
n
t
ro
duc
tio
n o
f
Tab
l
e
1
.
The
tra
nsfer
fu
nc
ti
o
n
s
o
f
t
h
e
t
o
rq
ue
d
ri
ver
of the
i
n
i
ti
al
IM
D
a
n
d
th
e co
rrec
t
i
v
e el
emen
t
*
10H
z
0
,
038
0
,226
0
,
00
02
0
,
0
2
2
9
1
,
3
8
0
,
707
0,003
8
0
,226
0
,
038
0
,226
0
,
00
02
0
,
0
22
9
4
,52
3,8
4
0,003
8
0
,226
50H
z
0
,
027
1
,548
0,
0
06
0
,
6
2
8
2
0
,
5
6
0
,
141
0
,
27
1,54
8
0
,
027
1
,548
0,
0
0
6
0
,
6
2
8
2
1
,
1
9
0,7
7
0
,
27
1,54
8
*
–
a
bsol
u
t
e
sli
p
at
0.
2
,
–
absol
u
t
e sli
p
at
For
stator c
urre
nt
f
ee
d
b
ack,
t
h
e
line
a
riza
tio
n
con
d
i
t
i
on wi
l
l
v
ar
y sl
i
g
h
t
ly
:
2
1
F
r
om
t
h
i
s
eq
u
a
li
t
y
i
t
fol
l
ow
s
th
a
t
t
he
h
ig
h
a
ccur
acy
o
f
t
h
e
IMD
c
an
b
e
ob
ta
ine
d
b
y
regu
la
ti
n
g
t
he
fl
ow
of t
h
e
rot
o
r
, w
hile
cor
rec
t
i
n
g the
line
a
riz
a
t
i
on
c
o
n
d
iti
on
s.
H
o
w
e
ver,
if
th
ere
is a
p
er
missible
des
i
gn er
ror
i
n
d
e
t
er
min
i
ng
the param
e
ters of
the
link,
i.
e
.
∙
0
Δ
the
am
pli
t
u
d
e
and
pha
se
c
har
acte
r
ist
i
cs
o
f
the
I
M
D
wi
l
l
b
e
simi
lar
t
o
t
he
c
hara
cteris
t
i
c
s
o
f
a
l
i
n
ear
l
i
n
k
o
f
t
h
e
fir
s
t
ki
n
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
S
t
ru
ctu
r
a
l
c
o
rre
c
t
ion
o
f
nonl
in
e
a
r d
y
n
a
m
i
c
s
o
f
fre
q
u
e
n
c
y
…
(Vl
a
d
i
m
i
r L. Ko
d
k
in
)
22
5
F
i
gure
5.
T
he
a
m
p
l
i
t
ude
a
nd p
h
ase
c
h
a
r
ac
teri
st
i
c
s of
t
he
IM
D
a
t
a fr
e
quenc
y of
t
he sta
tor
supp
l
y
vo
l
tage
o
f
50 H
z
:
W1 and W
2
-
slip at
a
l
o
a
d
m
oment
of
0.2
and
w
ith
ou
t
corr
ecti
on,
W
3
a
nd W4
-
s
li
p a
t
a
l
o
a
d
mo
me
n
t
o
f
0.
2
a
nd
w
i
t
h
the
i
n
t
ro
duc
tio
n o
f
I
n
t
he
l
a
s
t
par
t
o
f
t
h
e
a
r
tic
le,
the
in
flue
nc
e
o
f
t
h
e
a
ccura
cy
o
f
t
h
e
s
e
l
e
c
t
i
o
n
o
f
l
i
nk
para
me
ters
on
t
he
o
pera
ti
o
n
o
f
t
h
e
IMD
is in
v
e
s
t
i
g
a
t
ed.
F
o
r
th
is, a t
r
an
sm
issi
o
n
c
oe
ffi
c
ie
nt
err
or
o
f
±
5%
w
as i
n
t
ro
d
u
ce
d.
A
c
c
o
rdi
n
g
t
o
t
he
o
bta
i
ned
fre
que
ncy
c
h
ara
c
teris
t
i
c
s,
t
he
d
rive
re
ma
i
n
s
sta
b
le
b
ot
h
at
a
s
u
p
p
ly
v
ol
t
a
ge
fre
que
nc
y
of 1
0
H
z
(
F
i
gure
6)
a
nd
at 50
H
z
(
F
i
gure
7).
1
,
,
,
2
,
,
F
i
gure
6.
T
he
a
m
p
l
i
t
ude
a
nd p
h
ase
c
h
a
r
ac
teri
st
i
c
s of
t
he
IM
D
a
t
a frequenc
y of
t
he sta
tor
supp
l
y
vo
l
tage
o
f
10
H
z
: W
1
-
a
c
c
urate
, W2 -
when
t
he
tra
nsm
i
ssio
n
c
oe
ffic
i
e
n
t o
f
t
h
e
c
orre
ctio
n
lin
k
de
via
t
es by
5%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
220
–
22
7
22
6
3
,
,
,
4
,
,
,
F
i
gur
e 7.
The
am
p
li
tude
a
nd
p
h
ase
char
acte
r
i
s
t
i
cs
o
f t
h
e
IM
D a
t
a
f
r
e
quenc
y
of
t
he
s
ta
tor
sup
p
l
y
vo
l
t
age
of
50 Hz
:
W1 -
accur
a
te,
W2
-
when t
h
e
transm
i
s
s
i
o
n
c
oe
ffic
i
e
nt
o
f
t
he
c
or
r
e
c
t
i
o
n
l
i
n
k
d
e
v
i
a
te
s
by
5%
4.
CONCLUSIONS
I
n
t
h
e
p
r
e
s
e
n
t
e
d
a
r
t
i
c
l
e
,
t
h
e
t
r
a
n
s
f
e
r
f
u
n
c
t
i
o
n
o
f
t
h
e
t
o
r
q
u
e
f
or
m
e
r
in
f
r
e
qu
enc
y
-
c
on
tr
o
l
le
d
I
M
D
s
w
a
s
fi
r
s
t
p
r
op
o
s
ed
.
Th
is
t
ra
nsf
e
r
f
u
n
c
t
i
on
t
ak
es
i
nto
ac
c
oun
t
t
h
e
f
re
qu
e
n
c
y
o
f
st
at
o
r
vol
t
a
g
e
a
nd
s
l
i
p
.
Su
ch
a
fo
rmu
l
a,
o
n
t
h
e
on
e
h
a
nd
,
bec
o
me
s
id
en
ti
c
a
l
t
o
t
h
e
p
re
viou
sl
y
k
n
o
w
n
f
o
r
m
u
la
f
or
t
he
t
r
a
nsfe
r
f
u
nct
i
o
n
of
a
n
asy
n
c
h
r
ono
us
d
r
i
v
e
a
t
z
e
r
o
sli
p
(
i
.
e
.
,
wi
t
hout
l
o
a
d
)
,
a
n
d
,
o
n
t
he
o
t
h
er
h
a
n
d,
t
o
t
h
e
w
e
ll
-
k
n
o
w
n
K
loss
f
or
m
u
la
f
o
r
sta
tic
m
ode
s
of
o
pe
r
a
ti
o
n
o
f
an
a
sy
nc
hr
o
n
o
u
s
mot
o
r
.
Th
e
frequ
en
c
y
c
h
a
racteris
tics
o
f
th
e
I
M
D,
b
ui
lt
o
n
th
i
s
tran
s
f
e
r
f
u
nct
i
on,
g
a
v
e an a
de
qua
t
e
e
xp
la
na
t
i
o
n
of
t
he
c
ha
ng
i
n
g
dy
nam
i
cs
o
f
the
dr
ive,
n
o
t
e
d
i
n
e
x
per
i
m
e
n
t
s
c
o
n
d
u
c
t
e
d
e
arlier.
Th
e
p
r
opo
se
d
t
r
a
n
sf
e
r
f
un
c
t
ion
ma
d
e
it
p
o
s
s
i
bl
e
t
o
j
usti
fy
t
h
e
st
ru
ct
u
r
e
of
e
f
f
ect
i
v
e
co
rre
c
t
i
on
(
dyna
mic
pos
it
ive
fee
d
back
o
n
the
s
t
a
t
or
c
ur
r
e
nt)
for
sensor
les
s el
ect
ri
c
d
r
iv
e
s
.
REFERE
NC
E
S
[1]
V.L
.
K
o
d
k
i
n
,
A
.S.
An
i
k
i
n
,
A.
A
.
B
alde
nk
ov
,
“Th
e
d
y
n
amics
id
entif
icati
o
n
of
a
s
y
n
c
hron
ou
s
el
ectric
driv
es
v
ia
f
r
eq
uency
re
s
p
o
n
s
e”,
I
n
te
rn
a
t
io
na
l
J
o
u
r
na
l o
f
Po
we
r
Ele
c
t
ro
nic
s
an
d Driv
e
Sy
ste
m
s
(
IJP
E
DS
).
V
o
l
.
10
N
o.
1
,
p
p
.
6
6
-7
3,
2
01
9.
[2]
N.
A
.
Su
kh
enk
o
,
G
.
Ya
.
P
y
at
i
b
r
a
t
o
v,
A
.
A
.
D
a
n
sh
i
n
a,
L
.
L.
“
Altu
ny
an
P
ros
p
ecti
v
e
El
ectro
mechani
cal
C
on
tro
l
S
y
st
e
m
s
o
f
I
ndus
tri
a
l
M
a
n
i
pulat
or
E
ff
ort
s
”,
I
n
te
rn
at
io
na
l J
o
urna
l
o
f
Powe
r
Ele
c
t
ron
i
c
s
an
d Driv
e
Sy
ste
m
(
I
JPEDS)
,
Vo
l
.
7
,
No
. 2
, p
p
. 41
6
~
4
2
1
,
Ju
ne 2
01
6
.
[3]
K
o
zy
aru
k
А
.Е.,
Rud
a
ko
v
V.
V.,
"M
od
ern
an
d
p
e
rs
pect
iv
e
algo
rithm
i
c
m
a
i
n
t
e
nance
is
f
req
u
en
c
y
-
r
egu
l
ated
e
lect
ric
drive
s
,"
SPEC
. S
a
int
P
e
tersburg
,
20
0
4
.
[4]
V
.
L.
K
o
dkin
,
A
.S
.
Anik
in,
A
.
A.
B
ald
e
nk
ov
,
“
P
erf
o
rman
ce
i
d
en
tifi
c
a
t
io
n
o
f
t
he
a
sy
nc
h
r
on
o
u
s
e
l
e
c
tric
d
rive
s
b
y
t
h
e
s
p
ect
ru
m
o
f
r
otor
c
u
rrent
s,
”
Int
e
rn
at
ion
a
l
Jo
ur
na
l
of
P
o
wer
Electron
i
cs
a
n
d
D
r
ive
S
y
stem
s
(
I
J
PED
S)
,
Vo
l
.
1
0
N
o
.
1
.
–
P.
21
1-21
8,
2
0
1
9
.
[5]
V
.
L.
K
o
dkin,
A
.S
.
A
n
ik
in,
М.А.
M
al
cher, “P
ro
b
l
em
s
o
f
I
m
p
l
e
m
e
nta
tio
n of
F
req
u
ency
C
o
n
tro
l
in
M
i
ning
I
n
dustry”,
B
u
lleti
n
o
f
th
e S
o
ut
h Ural Sta
t
e
U
n
i
v
er
si
ty S
e
ri
es: E
n
er
gy
.
Vo
l
.
1
8
, No
.
3
7
, Pp
.
6
7-7
1
, 2
01
2.
[6]
P
o
zdeev,
A.
D
.,
"
E
l
ectro
m
a
gnet
i
c
an
d
el
ectro
me
ch
ani
cal
p
roc
e
ss
e
s
i
n
f
req
u
ency
-
c
on
trolled
asy
n
c
h
ro
no
us
e
lect
ric
drive
s
,"
Ch
e
b
o
k
sa
ry
:
Pu
b
lishing
ho
use
Chu
v
ash
Univ
e
rsity
,
p
p
.
172
,
1
998
.
[7]
Fi
g
aro
B.
I
.
Pav
l
y
achi
k
L
.
B.,
"
R
eg
ulat
in
g
elect
rical
d
riv
e
s
o
f
al
ternat
ing-current,”
M
i
sn
k: T
echno
per
s
p
ectiva
,
pp
.
3
6
3
,
20
06
.
[8]
S
o
ko
lov
s
k
y
G
.
G
.,
"El
ectrical
d
ri
ves
o
f
a
ltern
a
ti
ng-cu
rrent
w
it
h
frequency
c
ont
r
olling
,
“
M
:
A
c
adem
i
a
,
pp
.
2
6
7
,
20
06
.
[9]
L
o
u
i
s
J.
P
.,
"
Co
nt
ro
l
of
n
o
n
-co
nven
t
i
o
n
a
l
sy
nch
r
on
ous
m
o
t
ors
,
"
Great Brita
i
n
and the United Stat
es by ISTE L
t
d
an
d J
o
hn
W
i
le
y
&
S
o
n
s
,
In
c
,
pp.
4
28
,
2
0
1
2
.
[10]
Ch
iass
on
J
o
hn.
,
"M
od
eli
n
g
and
hi
gh
perf
orman
ce
con
t
rol
of
e
lect
ri
c
m
achines,
"
Jo
hn
W
i
ley
&
S
o
n
s
, In
c
,
pp
.
7
0
9
,
20
05
.
[11]
D
o
n
c
ker
R.
D
,
P
u
lle
D
.
W.
J
,
Veltm
an
A
.,
"
A
dv
anced
E
lect
ri
cal
D
r
i
v
e
s:
A
na
ly
sis
,
M
od
e
l
in
g,
C
o
n
tro
l
,”
Ad
van
ced
E
l
ectrica
l Dri
ves: A
nalysis,
M
o
d
e
l
i
ng
, Co
n
t
rol. Spr
in
ger
,
pp
.
4
7
4
,
2
011
.
[12]
U
s
o
l
ts
ev
A
.
A.
,
"
V
ector
c
ont
rol
of
a
syn
c
hro
n
o
u
s
m
o
to
rs,
"
T
u
torial
. - S
pb .
:
ITMO
, pp
.
1
2
0
, 20
0
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
S
t
ru
ctu
r
a
l
c
o
rre
c
t
ion
o
f
nonl
in
e
a
r d
y
n
a
m
i
c
s
o
f
fre
q
u
e
n
c
y
…
(Vl
a
d
i
m
i
r L. Ko
d
k
in
)
22
7
[13]
Us
oltsev
A
.
A,
V
oro
byo
v
N.
V
,
F
e
shi
n
B
.
N.
,
"M
eth
o
d
o
l
ogy
f
or
t
h
e
an
alys
is
o
f
elect
rom
a
gn
ets
o
f
p
ro
cesses
i
n
su
bs
ystem
s
of
a
n
aut
om
a
t
ed
elect
ric d
r
ive,
"
Au
to
ma
tio
n an
d
Infor
m
atics
,
Vol.
2
,
No
.
35.
p
p
.
50-53,
2
0
14.
[14]
Us
oltsev
A
.
A.,
"Det
erm
i
natio
n
of
t
he
p
aram
ete
r
s
o
f
t
he
a
sy
nc
hr
o
n
o
u
s
m
o
tor
m
o
d
e
l
accordi
n
g
t
o
t
h
e
r
ef
erence
dat
a
,
"
News of uni
versiti
es.
Instr
u
ment m
a
k
i
ng
,
Vo
l.
51,
N
o
10
, p
p.
35-4
1
,
2
0
0
8
.
[15]
Ily
i
n
a
A
.
G,
&
U
s
o
ltsev
A
.
A.
,
"Opt
im
al
m
otion
con
t
ro
l
duri
ng
p
os
iti
onin
g
a
nd
i
ts
m
od
eli
ng
in
t
he
M
ath
L
ab,
"
Si
mulin
k enviro
n
m
ent, Izves
ti
ya VUZ
o
v,
In
s
t
r
u
ment m
a
k
i
ng
,
Vo
l. 5
1, No
. 6
. pp
.
6
3
-
68
,
2
0
0
8
.
[16]
V.
L
.
K
od
k
i
n
,
A.S
.
A
n
i
k
i
n
,
A
.A
.
B
a
l
d
enk
o
v
,
“
Anal
y
s
i
s
o
f
st
abi
l
i
t
y of
el
ectric drives a
s
n
o
n
-
l
i
n
ear sy
s
t
e
ms
accord
in
g
to
P
op
ov
c
ri
terio
n
a
dj
ust
e
d
to
a
m
p
lit
u
d
e
a
nd
p
h
a
se
f
requ
ency
c
h
aracteri
s
t
i
cs
o
f
it
s
el
e
m
ents
”,
2nd Internation
a
l
Con
f
eren
ce on
Ap
pl
ied
M
a
th
ema
tics
,
S
i
mu
lati
on
,
a
nd
M
o
d
e
li
ng AM
S
M
201
7
–
P
r
o
ceedin
gs
. – 2
01
7.
[17]
V
.
L
.
K
o
d
k
i
n
,
A
.
S
.
A
n
i
k
i
n
,
A
.
A
.
B
a
l
d
e
n
k
o
v
.
“
T
h
e
a
n
a
l
y
s
i
s
o
f
t
h
e
q
u
ali
t
y
of
t
h
e
f
requen
c
y
con
t
rol
of
i
nd
uctio
n
m
o
t
o
r
carried
out
o
n
th
e
b
a
si
s
o
f
t
he
p
rocess
e
s
i
n
t
he
r
ot
or
c
i
rcu
i
t
”
X
I
I
n
te
r
n
a
t
i
o
na
l S
c
ie
n
t
i
f
ic
a
n
d
T
e
c
h
ni
c
a
l
Con
f
eren
ce Dyn
a
m
i
cs
o
f
Sys
t
ems,
M
echan
is
ms
and M
a
chin
e
s
–
Pr
oceed
in
gs
–
2
0
1
7.
О
m
sk,
1
4
-
16
.11
.
20
17
.
[18]
K
o
d
k
i
n
.
V
.
L
.
“
M
e
t
h
o
d
s
o
f
o
p
t
i
m
i
z
i
n
g
t
h
e
s
p
e
e
d
a
n
d
a
c
c
u
r
a
c
y
o
f
o
p
tical
c
o
m
pl
ex
g
u
i
d
a
nce
sy
st
ems
b
a
s
e
d
on
equ
i
v
a
lence
of
a
ut
om
ati
c
c
o
n
t
r
ol
s
yst
e
m
d
o
m
a
in
o
f
attract
ion
an
d
unconditional
stabil
ity
o
f
t
h
ei
r
equiva
lent
circuits,”
P
r
o
cee
d
i
n
g
s of SP
IE - T
h
e In
tern
a
t
io
nal S
o
cie
t
y f
o
r Op
tica
l
E
ngin
eerin
g
.
–
20
16
[19]
M
d
.
Rash
edu
l
I
s
l
am
,
M
d
.
M
a
rufu
l
Is
l
a
m,
M
d.
K
am
al
H
ossai
n
.,
"
P
i
n
tu
k
u
m
ar
s
ad
hu
p
erf
o
rm
ance
anal
ys
is
o
f
a
dtc
a
n
d
sv
m
ba
se
d
fie
l
d
-
orie
n
t
a
t
io
n
c
o
n
t
rol
ind
u
c
ti
on
m
otor
d
r
i
v
e
,"
In
te
rn
atio
na
l J
o
urna
l
o
f
Po
w
e
r
Ele
c
t
ro
n
i
c
s
a
n
d
Dr
ive S
y
s
t
e
m
(
I
JPEDS)
,
Vo
l.
5
, No
.
3
,
p
p
. 3
36
-3
4
3
, 20
1
5
.
[20]
Ho
ang
Le-H
uy
.
,
"
M
o
d
e
li
ng
a
nd
s
im
ul
a
t
i
o
n
of
e
lect
rical
d
ri
ves
us
ing
M
A
T
L
A
B
/
S
imu
link
and
Power
Syste
m
Blockset
,”
IE
CON'01
.
27th
An
nual
Confer
ence o
f
t
h
e IE
EE Ind
u
stri
a
l
El
ectr
o
n
i
cs So
c
i
ety,
20
01
.
[21]
M
a
r
c
P
e
r
r
o
n
,
&
H
o
a
n
g
L
e
-
H
u
y
,
"
F
u
l
l
l
o
a
d
r
a
n
g
e
n
e
u
r
a
l
n
e
t
w
o
r
k
e
f
ficien
cy opt
im
izati
on of
a
n
in
du
cti
on m
o
t
o
r
w
i
t
h
vect
or
c
o
n
tro
l
u
si
ng
d
i
s
co
ntin
uous
P
WM,
"
IEE
E
In
ter
natio
nal S
y
mp
osi
u
m
on Indus
trial
Elect
ron
i
cs
,
2
006
.
[22]
Ho
ang
L
e
-H
uy
;
G.
S
yb
ille
M
A
T
LAB,
“
Sim
u
link
a
n
d
P
S
P
i
ce
as
m
o
d
ell
in
g
tool
s
f
o
r
power
s
y
s
tems
a
n
d
p
o
w
er
elect
roni
cs”,
2000
P
o
wer
Engin
eering
S
o
ci
e
t
y
S
u
m
m
e
r M
eeti
ng.
[23]
Lo
uis-A.
D
essaint
,
&
R
og
e
r
C
ham
p
agne,
"Real-ti
m
e
sim
u
l
a
ti
on
o
f
elect
ric
driv
es,"
Mat
h
em
atics a
n
d Comput
ers
in
Si
mulation
,
V
ol.
6
3
,
No
.
3-5
,
p
p.
1
7
3
-18
1
,
20
03.
[24]
Louis-A.
D
essai
n
t,
&
K
ama
l
A
l
-
Ha
ddad,
"M
odelling
and
Si
mula
ti
on
o
f
Electri
c
M
achin
es,
Co
nv
erters
a
n
d
Sy
ste
m
s
,
"
M
a
t
h
em
atics
and Compu
t
er
s
i
n
S
i
m
u
l
a
ti
on
,
Vo
l. 6
3
,
N
o
.
3
-5
, p
p.
13
5
-
14
3, 20
0
3
.
[25]
Po
po
v V
. M
., "H
y
p
e
rst
a
b
i
l
ity o
f
dy
namic sy
st
e
m
s,
"
Sp
ring
e
r
-Ve
r
la
g
,
Berl
i
n
1973
.
Evaluation Warning : The document was created with Spire.PDF for Python.