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
)
Vol.
10, No.
1, Mar
ch 2019,
pp.
66~73
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v10
.
i
1.pp
6
6
-7
3
66
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
The dynamics identificati
o
n
of as
ynchronous electric drives via
frequ
e
ncy response
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
Dep
a
rt
m
e
nt of Theo
reti
cal F
un
da
m
e
n
t
als
of El
ectrical
En
g
i
n
eerin
g,
S
outh
Ural
S
tat
e
U
n
i
versit
y
(N
RU),
R
u
ssia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Au
g
2
3
,
2
018
Re
vise
d S
e
p 21,
201
8
A
c
c
e
pte
d
N
ov 4,
201
8
Th
e
art
i
cl
e
subst
a
ntiates
th
e
n
ecess
i
t
y
o
f
id
e
n
t
i
f
y
in
g
th
e
dy
n
a
mic
s
o
f
asy
n
ch
rono
us
e
l
ectri
c
d
r
iv
es
w
ith
f
r
eq
uen
c
y
con
t
rol.
I
t
i
s
p
ro
p
osed
t
o
u
s
e
no
nl
in
e
a
r
tran
sfer
f
u
n
cti
ons
a
n
d
t
h
e
f
orm
u
l
a
o
f
a
f
a
mil
y
o
f
f
r
e
q
u
ency
resp
on
ses
of
a
n
e
l
ectri
c
dri
v
e,
d
ep
end
i
n
g
o
n
th
e
f
r
equ
e
ncy
of
t
he
s
tator
vo
lt
age
and
s
l
ip
.
Ex
perim
e
n
t
s
an
d
simulatio
n
s
co
nfi
r
mi
ng
t
h
eo
re
tical
con
c
lu
sio
n
s
are
p
r
es
ent
e
d.
T
h
e
f
req
u
en
cy
r
esp
o
n
s
es
o
f
th
e
d
r
iv
e
o
f
t
h
e
stand
calcu
lated
by
t
h
e
p
ro
po
sed
m
e
t
h
o
d
a
ll
ow
ed
t
o
ex
plai
n
t
h
o
s
e
p
r
ob
lems
o
f
f
r
equ
e
ncy
con
t
rol
t
h
at
w
ere
not
e
x
p
l
a
ined
b
y
t
r
aditi
ona
l
m
e
t
hod
s
-
an
alyt
ical
,
vect
or
d
iagram
s
,
s
ubs
titu
ti
on
sch
e
m
e
s
,
e
tc.
Th
is
s
am
e
tech
ni
qu
e
a
l
l
o
w
e
d
u
s
to
f
ormu
l
a
te
a
s
truct
u
ral
correc
tio
n
o
f
t
h
e
a
s
ynchro
n
o
u
s
elect
r
ic
d
ri
ves.
I
n
con
t
ras
t
t
o
th
e
previ
o
u
s
l
y
publ
is
hed
re
s
earch
m
ateri
a
ls
o
f
a
s
y
n
ch
rono
us
elect
ric
dri
v
es,
a
det
a
il
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q
ualitativ
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analy
s
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o
f
th
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obtain
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d
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nl
ine
a
r
f
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equ
e
ncy
res
p
o
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a
nd
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h
e
in
terrelat
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o
n
o
f
t
h
es
e
ch
ara
c
teris
t
i
c
s
with
exp
e
rim
e
nt
al resul
ts
is sh
ow
n
f
o
r
the
first
time
i
n
the
a
rt
icl
e
.
K
eyw
ord
s
:
A
s
ync
hro
n
o
u
s e
l
e
c
tr
ic
d
ri
ve
Dynam
i
cs o
f t
h
e e
l
ec
tric
dri
v
e
F
r
equenc
y
con
t
ro
l
F
r
equenc
y
re
spons
e
Slid
ing
Torque
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Al
e
k
sand
r S
. A
n
i
ki
n
,
D
e
pa
rtme
nt
o
f
The
o
reti
ca
l F
u
nda
me
n
t
a
l
s
o
f
Ele
c
t
rica
l
Eng
i
ne
eri
n
g,
S
out
h U
r
al S
tate U
nive
rsity,
76,
L
en
in pro
s
p
ek
t,
Che
l
y
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
I
n
i
n
d
u
str
i
al
m
e
c
han
i
sm
s
t
h
e
e
l
e
c
tr
ic
d
ri
ve
s
of
t
he
a
c
t
ua
t
i
n
g
e
l
e
me
nt
s
pl
ay
a
v
e
r
y
i
m
po
rt
ant
ro
l
e
.
In
the
fina
l
a
n
a
l
y
s
is
t
h
e
ir
a
cc
ur
acy
d
epe
n
ds
on
the
q
u
a
l
i
t
y
o
f
t
he
e
xe
cu
t
i
o
n
o
f
tec
h
nol
og
ica
l
o
p
e
r
a
tio
ns,
o
n
t
h
eir
abi
l
i
t
y
t
o
"
p
ar
ry"
d
i
s
t
ur
banc
e
s
-c
han
g
es
i
n
a
i
r
tem
p
era
t
u
r
e,
"
fa
i
l
ur
es"
a
n
d
"thr
ow
s"
of
t
he
p
o
w
er
v
olta
ge
,
w
ear
of
m
echa
n
i
c
a
l
p
arts,
and,
w
hat
is
e
spe
c
i
a
l
l
y
i
mpor
t
a
n
t
,
the
q
u
a
l
i
t
y
o
f
t
echn
i
ca
l
c
o
mp
lexe
s
i
n
g
e
n
er
al,
and
their comp
etitivene
ss [1]-[3].
I
n
r
ece
nt
y
e
a
r
s,
i
n
the
h
i
g
h
-tec
h
e
x
e
c
u
t
i
v
e
me
cha
n
ism
s
m
ost
o
f
t
e
n
u
se
d
perm
an
e
n
t
m
a
g
n
et
syn
c
hro
n
o
u
s
m
otors.
T
heir
a
djus
t
i
n
g
c
a
p
a
b
i
lit
ies
a
r
e
co
m
m
e
n
sura
te
w
ith
D
C
dri
v
es,
an
d
t
h
e
a
b
se
nce
o
f
col
l
ec
t
o
rs
s
ig
ni
fic
a
n
tly
i
ncre
ases
t
h
e
ir
s
e
r
vic
e
l
ife.
H
oweve
r
,
t
hese
e
ng
i
n
e
s
can
p
ro
v
i
de
t
he
r
eq
uire
d
a
c
c
ur
ac
y
and
r
o
b
u
s
t
ne
ss
(roug
hne
ss)
t
o
exter
n
al
i
nf
lu
e
n
ces,
o
n
ly
w
i
t
h
s
u
ffic
ie
nt
l
y
c
om
pl
e
x
r
eg
u
l
at
ors,
w
i
t
h
n
u
m
e
rous
sens
ors - eng
i
n
e
s
peed,
a
cce
lera
t
i
on,
m
otor
c
urr
e
nts,
p
o
w
er
v
o
l
tage
,
etc.
[4
]
-
[
10].
S
i
gnif
i
cantly
b
etter
pr
operties
of
"
robus
t
ness"
ar
e
AC
d
rives
w
it
h
a
s
yn
c
h
ro
no
us
a
n
d
s
yn
chr
o
nou
s
mo
t
o
rs,
th
e
l
a
tt
e
r
,
as
a
r
ul
e,
d
i
f
f
e
r
fro
m
th
e
v
a
l
v
e
mot
o
rs
o
nl
y
i
n
t
h
e
c
on
t
r
o
l
m
et
hod
.
Bu
t
it
i
s
t
h
e
c
o
nt
r
o
l
pro
b
lem
s
tha
t
a
r
e
t
h
e
re
ason w
h
y
A
C
dri
ves
are sti
l
l r
a
re
l
y
u
se
d in
c
om
ple
x
tech
n
o
l
o
g
i
cal
m
e
c
hanisms.
2.
PROBL
E
M
DEFINI
T
I
ON
On
e
o
f
t
h
e
p
rob
l
e
m
s
th
at
g
re
at
ly
a
ff
ect
s
th
e
fo
rma
t
io
n
o
f
p
rov
i
sio
n
s
f
o
r
t
h
e
co
nt
rol
of
A
C
d
r
i
v
es
i
s
t
h
e
ab
se
n
c
e
(or
al
mo
st
a
b
s
enc
e
)
o
f
a
n
e
ngin
e
erin
g
app
a
rat
u
s
fo
r
e
s
t
i
m
at
in
g
t
h
e
d
ynam
i
c
s
o
f
A
C
d
r
i
v
e
s,
i
n
part
icu
l
ar
a
sy
n
c
hro
n
o
u
s
ele
c
t
ric
drive
s
.
A
ssumpt
i
ons,
w
h
i
c
h
ar
e
u
sua
l
ly
g
ive
n
i
n
the
w
o
rks,
i
n
par
tic
ula
r
,
in
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
h
e
dynam
ics
ide
n
tif
ic
a
tio
n
of
async
h
ro
n
o
u
s
e
l
e
c
t
r
i
c
dr
ive
s
via f
r
eq
ue
nc
y
re
sp
onse
(V
lad
i
m
i
r L.
Kodk
in)
67
the
mo
no
gra
p
h
o
f
A
.
A
.
U
s
oltse
v
[
11]
,
si
m
p
l
i
fy
t
he
s
truc
tur
e
s
o
mu
ch
t
h
a
t
th
e
y
d
o
not
r
ef
l
e
c
t
t
h
e
f
ea
tu
re
s
a
n
d
pro
b
lem
s
of
th
e
dynam
i
c
s
of t
h
ese
dri
v
es,
whic
h o
n
e
ha
s
t
o
f
a
c
e
i
n
pra
c
t
i
c
e
[
12],
[13].
The
n
o
n
l
i
n
ear
ity
o
f
a
dr
ive
w
ith
a
n
a
s
ync
hro
n
o
u
s
m
o
t
o
r
is
w
ell
k
n
ow
n;
i
t
is
s
tore
d
in
a
ll
k
now
n
con
t
ro
l
me
t
h
o
d
s
-
sc
a
l
ar,
v
ector,
DTC
(
D
irec
t
T
o
r
q
u
e
C
on
tro
l
).
Thi
s
n
o
n
li
nea
r
i
t
y
i
s
m
a
n
if
es
ted
in
t
h
e
expe
r
i
me
n
t
s
de
scr
i
b
e
d
in
[
14]
-[19].
The
ele
c
tric
d
r
i
ve
w
a
s
s
ub
s
eq
ue
nt
l
y
a
cc
eler
ate
d
t
o
spe
e
d
s
c
orr
e
sp
o
ndi
ng
to
t
he
freq
u
en
c
i
es
o
f
the
s
u
p
p
ly
vol
tage
o
f
10
-
2
0
-
30
-
40
–
5
0
H
z
,
at
e
ach
s
pe
e
d
o
f
rotat
i
on
a
loa
d
w
as
draw
n is sh
o
w
n
in F
i
g
u
r
e
s 1
and
2.
B
o
t
h
t
he
m
o
d
e
lin
g
o
f
t
he
p
roce
sse
s
i
s
sho
w
n
i
n
F
ig
ures
1
a
n
d
2
,
a
n
d
t
h
e
e
x
p
e
r
i
m
e
n
t
a
l
s
t
u
d
i
e
s
i
s
show
n
i
n
F
ig
ur
e 3. S
how
t
ha
t
the proce
s
se
s d
i
ffe
r
qua
lit
at
i
v
ely
a
t
dif
f
e
rent
d
r
i
ve
s
pee
d
s.
T
h
e
ref
o
re,
they
m
us
t
b
e
d
esc
r
ib
e
d
b
y
d
i
ff
e
r
ent
f
r
eq
u
e
n
c
y
re
sponse
s
.
Th
e
t
a
sk
t
o
b
e
s
ol
ved
first
of
a
ll
is
t
he
f
orm
a
tio
n
of
t
he
fre
que
nc
y
respons
es
o
f a
n
asy
nc
h
r
on
ous
d
ri
v
e
,
for
ea
ch pa
r
ti
c
u
l
ar
m
ode
.
F
i
gur
e 1.
Mo
d
e
ll
ing
pr
oce
s
se
s in a
n asy
n
chr
ono
us
e
lec
t
ric
dri
v
e
w
ith
s
cal
ar
c
on
tr
ol
w
ith
ou
t fee
dba
c
k
F
i
gure
2.
M
od
e
lli
ng pr
oc
esse
s in
a
n
asyn
c
h
ro
nou
s el
ect
ri
c
d
r
iv
e
w
it
h ve
ct
or c
on
t
r
ol
s
yst
e
m
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
66
–
73
68
Figure
3.
E
xpe
rim
e
nta
l
re
s
earches
o
f t
h
e
ele
c
t
ric dr
ive
wit
h
th
e
ope
ne
d
fre
q
u
e
nc
y c
o
n
t
ro
l
3.
PROPO
S
E
D
SOLUT
I
O
N
The
bas
i
s
for
c
hoos
i
ng
the
m
e
th
o
d
f
or
c
alcu
lat
i
ng
t
h
e
dy
na
m
i
c
m
echa
n
i
c
a
l
c
ha
rac
t
e
r
istic
,
propos
e
d
in t
he
s
a
m
e
m
o
no
grap
h
A
A
.
U
soltse
v
a
[1
1,
p.
1
3
5
]
.
,
(
1
)
wher
e:
∙
но
м
–
r
otary
ti
m
e
c
on
sta
n
t
,
ном
– absolute
sl
ip.
Th
is
f
orm
u
l
a
U
sol
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s
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igur
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2
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The
d
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as
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(
3),
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5
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z
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a
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o
f
3%,
8.6%
a
nd
17.2
%
a
re
show
n in F
ig
ures 4
a
nd
5.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
T
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nam
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c
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(Vl
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mir
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Kodk
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69
,
,
,
,
,
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(3
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F
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4
. Freq
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f
th
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c
h
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or
50
H
z
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
66
–
73
70
Th
e
main
c
h
a
ng
es
i
n
th
e
p
h
ase
ch
arac
t
e
ri
sti
c
s
f
a
ll
o
n
th
e
f
r
e
q
u
e
n
c
y
r
an
ge
f
rom
1
to
1
0
H
z
.
This
i
s
the
ra
nge
i
n
w
h
ic
h
t
h
e
c
u
t
-
off
fr
e
que
nc
i
e
s
of
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he
m
a
j
or
i
t
y
of
m
e
d
iu
m-p
o
we
r
i
n
d
u
s
t
r
i
a
l
d
r
i
v
es
(
f
r
o
m
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t
o
200
kW)
are
l
o
ca
te
d.
T
o
c
o
mpens
a
t
e
f
or
t
hi
s
ph
enom
en
o
n
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i
t
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s
ne
ce
s
sar
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t
o
reduc
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t
h
e
vari
abi
l
i
t
y
o
f
f
re
q
u
en
c
y
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n
ses.
T
h
i
s
is
d
o
n
e
by
v
ector
c
ontro
l.
B
ut
u
nsu
c
ce
ss
ful
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y.
Th
is
v
aria
bi
li
ty
a
l
s
o
d
o
es
n
o
t
c
han
g
e
w
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t
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ve
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ne
cti
ons
a
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h
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a
cce
l
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rat
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o
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o
f
in
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e
rna
l
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irc
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its.
I
t
ca
n
o
n
l
y
b
e
re
du
c
e
d
by
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nt
rodu
c
i
ng
t
erms
i
n
t
h
e
d
e
no
min
a
to
r
wi
t
h
n
eg
a
t
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v
e
co
e
f
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c
i
ent
s
,
i
.
e
.
i
n
t
rodu
c
i
ng
a
posi
tive
fe
ed
bac
k
.
The
mos
t
p
r
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v
ar
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o
f
suc
h
a
c
on
nec
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o
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m
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n
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t
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t
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E
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g
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wit
h
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con
s
ide
r
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i
n
ar
t
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cle
s
[
20].
The
fa
m
i
l
i
es
o
f
fre
que
nc
y
re
spo
n
se
s
prop
ose
d
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n
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s
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x
p
l
a
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l
l
it
s po
s
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t
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s
The
fa
mil
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s
o
f
freq
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t
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d
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d
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c
c
o
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d
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n
g
to
freq
u
enc
i
e
s
i
s
sh
ow
n
i
n
F
i
gure
4
a
nd
sli
p
i
s
s
h
ow
n
i
n
F
ig
ure
5.
T
he
c
ha
rac
t
e
r
i
s
tic
s,
g
r
ou
ped
acc
o
r
di
ng
to
t
he
s
li
p
va
lue
s
,
sh
ow
t
hat
dur
in
g
a
cce
lera
t
i
o
n
t
o
n
o
mi
n
a
l
spee
d,
t
he
n
e
g
at
ive
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h
a
s
e
sh
ift
in
t
he
o
p
e
ra
t
i
ng
fre
q
u
e
ncy
ran
g
e
(
1
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0
H
z
)
cha
nge
s
b
y
5
0
degr
ees.
Th
is
c
an
s
i
g
n
i
fica
n
t
l
y
a
ffec
t
t
h
e
s
t
ab
i
l
it
y
a
nd
dy
na
mic
s
o
f
o
v
e
r
c
l
oc
kin
g
p
r
o
c
e
s
se
s.
Th
is
i
n
f
l
u
e
n
c
e
is
o
b
s
erve
d
in
s
im
ul
a
tio
n
a
nd
e
x
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n
t
al
s
t
u
d
i
es,
ac
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at
io
n
s
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p
t
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1
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Hz
w
it
h
sca
l
ar
con
t
ro
l
ar
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ac
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p
an
ie
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b
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ur
rent
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nd
s
p
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e
d
osc
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lla
ti
ons,
w
h
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l
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oth
e
r
d
i
sp
ersa
l
s
a
re
p
ra
ct
i
c
a
l
l
y
m
o
not
oni
c.
The
ve
ct
or
c
o
n
tr
ol
p
ro
ble
m
s
a
r
ising
from
t
he
m
i
s
m
a
tc
h
o
f
t
he
c
o
n
t
ro
l
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t
m
o
del
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rs
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re
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lso
w
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ll
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l
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ne
d
b
y
t
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t
ra
ns
fer
fun
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ti
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n
s
a
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d
fre
q
uenc
y
r
e
s
p
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se
s,
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f
t
h
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i
r
p
a
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e
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h
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r
s
e
r
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a
l
con
n
ec
tio
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for
m
s a
com
p
lex
struc
t
ure
pro
n
e
to osc
il
la
ti
on.
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dy
na
mic
m
echa
n
i
cal
c
h
a
r
acte
r
ist
i
c
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t
h
a
s
li
p
of
3
%
has
the
f
orm
(5),
a
nd
a
t
8
.
6
%
has
the
form
(6),
a
nd
the
freque
nc
y
r
e
sp
o
n
ses
for
t
h
e
s
e
sl
ides
f
or
t
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s
up
pl
y
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ta
ge
f
re
que
nc
ies
1
0
,
3
0
a
n
d
5
0
H
z
a
r
e
gi
ve
n in F
ig
ure
s
6
a
nd 7.
,
,
.
(
5
)
F
i
gure
6.
F
r
e
quenc
y
re
spo
n
se
s
of the
l
ink
fo
r
t
h
e
for
m
a
t
i
o
n
o
f
torq
ue
w
he
n
slid
i
ng 3%
f
o
r
f
reque
nc
ies 1
0
,
30
a
nd 5
0
H
z
ω
ω
1
ω
2
ω
3
10
Гц
30
Гц
50
Гц
М
K
1,
80
5
4,38
4
5,15
8
S
K
0,
13
5
0,26
7
0,36
1
T
´
2
0
,
2
36 0
,
04
0
,
01
8
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
h
e
dynam
ics
ide
n
tif
ic
a
tio
n
of
async
h
ro
n
o
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s
e
l
e
c
t
r
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c
dr
ive
s
via f
r
eq
ue
nc
y
re
sp
onse
(V
lad
i
m
i
r L.
Kodk
in)
71
,
,
.
(
6
)
F
i
gur
e 7.
F
reque
nc
y r
e
spo
n
se
s of
t
he l
i
nk f
o
r
the
form
ati
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n
of
t
o
r
q
ue w
h
e
n sl
idi
ng
8.6%
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or freque
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ies
10,
30
an
d 5
0
H
z
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y
f
am
ily
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f
freque
nc
y
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n
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rou
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by
the
fre
que
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s
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s
how
n
i
n
F
i
gures 6
a
n
d
7
,
w
e
c
an
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va
lua
t
e
the na
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pr
oces
ses
i
n
t
he
c
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l
o
a
d
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s
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t
d
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rent
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pe
e
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t
5
0
H
z,
t
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s
l
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h
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ge
s
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l
l
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re
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here
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z
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han
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e
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re
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n
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c
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n
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r
e
for
e
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the
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c
esses
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t
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e
s
e
sp
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om
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s
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f
re
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lts
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ne
d
e
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lier
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t
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of
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s.
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hus,
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l
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t
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ram
e
ter
s
o
f
t
h
e
s
i
n
u
soi
d
a
l
r
efe
r
enc
e
si
gna
ls
(
am
p
litu
de
s
and
fr
eq
uenc
i
e
s)
d
escr
i
b
e
d
i
n
[1
6],
[21],
[22
]
can
b
e
e
x
p
l
a
i
ned
b
y
t
h
e
fa
ct
t
ha
t
t
h
e
sli
p
s
k
in
t
he
f
orm
u
la
(
2)
ca
n
c
h
a
n
ge
t
h
e
v
al
ue,
an
d
the
n
i
t
i
s
p
ra
ct
i
c
al
l
y
i
m
p
ossi
ble
t
o
a
v
o
i
d
t
h
e
u
n
s
t
a
b
le
c
har
acte
r
ist
i
c,
a
nd
t
o
ca
l
c
u
l
a
t
e t
h
ese
con
d
i
t
i
on
s
pret
ty har
d.
A
c
cordi
n
g
to
t
he
f
orm
u
las
i
s
s
how
n
i
n
F
i
g
ure
s
4
-7,
i
t
i
s
pos
sib
le
t
o
e
x
pl
a
i
n
t
h
e
e
ffic
i
ency
o
f
t
h
e
pos
it
ive
feed
b
a
c
k
o
n
the
c
u
r
r
ent
o
f
t
he
s
t
a
tor
of
t
he
e
lec
t
ric
mot
o
r,
d
escribe
d
i
n
t
h
e
arti
cles
[
14]
,
[20],
[2
3].
A
s
s
e
e
n
from
t
he
f
or
mu
la
(
7),
(
-
0,06p2
it
s
coef
fic
i
e
n
t
obt
a
i
ne
d
f
r
o
m
p
o
s
iti
ve
f
e
e
d
bac
k
)
,
posi
t
i
ve
f
e
e
dbac
k
reduc
es t
he
var
i
a
b
ili
t
y
of
the
fr
eque
nc
y re
spo
n
se
s
of
t
he
spe
e
d
of
rotati
on
a
nd s
l
ip.
,
,
,
,
,
,
.
(
7
)
Th
e
fo
rmu
l
a
s
(
7
)
f
o
r
t
h
e
fre
q
u
e
n
c
y
re
sponse
s
o
f
a
d
r
iv
e
wi
t
h
a
po
si
t
i
ve
s
ta
tor
c
u
r
r
ent
fee
dba
c
k
i
s
show
n
i
n
F
i
gur
e
8
ha
ve
a
s
i
g
n
i
fic
a
n
t
l
y
l
o
w
e
r
fr
eque
nc
y
re
spo
n
se
from
fr
eque
nc
y
f
a
nd
s
lip
S
,
w
h
i
c
h
e
x
pl
a
i
n
s
the
sta
b
i
l
ity
o
f
trans
i
en
ts
d
ur
ing
ac
ce
le
rat
i
o
n
a
n
d
l
o
a
d
s
p
i
ke
s
a
t
di
ffe
re
nt
r
ota
t
i
o
na
l
spee
d
s
.
T
h
is
a
ls
o
e
x
pl
a
i
n
s
t
h
e
co
n
s
id
e
r
ab
ly
s
mal
l
er
d
i
f
f
e
re
n
c
es
i
n
t
h
e
p
r
o
c
ess
e
s
at
d
if
fe
r
e
n
t
rota
t
i
o
n
al
s
pe
eds.
T
he
se
f
re
que
n
c
y
ω
ω
1
ω
2
ω
3
10
Гц
30
Гц
50
Гц
М
K
1,80
5
4,
38
4
5,15
8
S
K
0,13
5
0,
26
7
0,36
1
T´
2
0,23
6
0,
04
0,01
8
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
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
66
–
73
72
r
e
spo
n
se
s
ar
e
c
l
o
s
e
to
t
he
f
r
e
que
nc
y
r
e
sp
o
n
ses
of
D
C
dr
ive
s
,
w
h
i
c
h
o
p
e
n
s
u
p
p
r
o
s
p
e
c
t
s
f
o
r
t
h
e
i
r
u
s
e
i
n
c
o
mple
x
me
ch
ani
s
m
s
,
i
nc
l
u
d
i
ng
dr
ive
s
f
or
i
ndus
tr
ia
l
r
o
b
o
t
s.
F
i
gur
e
8.
F
r
e
quenc
y
r
e
spo
n
se
s
of
a
n
e
l
e
c
tr
ic
d
r
i
ve
w
i
t
h
a
po
si
t
i
v
e st
at
o
r
c
urren
t
f
ee
db
a
c
k
4.
CONCLUSIONS
The
pr
o
p
o
se
d
m
e
tho
d
o
f
ide
n
ti
fy
i
ng
A
C
d
r
i
ve
s
by
fa
mil
i
e
s
o
f
fr
e
q
u
e
n
cy
r
esponse
s
t
hat
de
pe
nd
o
n
the
fr
eq
ue
nc
y
of
s
u
p
p
l
y
v
ol
ta
ge
a
nd
s
li
p,
v
e
r
y
ef
fec
t
ive
l
y
e
x
p
l
a
i
n
t
h
e
n
o
n
linea
r
na
ture
o
f
t
h
e
proc
esses
i
n
t
h
e
AC
d
ri
v
e
.
Th
e
a
b
ov
e
id
e
n
ti
fi
ca
t
i
on
m
et
h
o
d
al
lo
ws
u
s
t
o
f
o
r
mu
l
a
t
e
t
h
e
pri
n
cip
l
es
o
f
corre
cti
o
n
of
A
C
e
l
e
c
tric
dr
ive
s
.
The
pr
o
p
ose
d
c
or
r
e
ct
io
n
-
dy
nam
i
c
pos
it
ive
fe
ed
ba
c
k
o
n
s
t
a
t
o
r
c
u
r
r
e
n
t
-
w
i
l
l
a
l
l
o
w
t
h
e
u
s
e
o
f
a
n
A
C
dr
ive
(
a
sy
nc
hr
on
o
u
s
dr
i
v
e)
i
n
tec
h
n
i
c
a
l
c
omple
x
e
s
.
REFERE
NC
E
S
[1]
Cu
bero
S
am
(
ed.)
I
n
d
u
s
t
r
ial
Rob
o
ti
cs.
T
h
e
ory,
Mod
elli
ng
a
nd
C
o
n
trol
/ Pro
L
iteratur Ver
l
ag
,
p
.
95
2, 20
0
7
.
[2]
L
o
w
K.
-H
.
(ed
.
) Ind
u
s
t
ri
al
R
o
botic
s
.
P
ro
gra
m
ming,
S
im
ul
a
t
i
on
an
d App
lic
a
tio
ns
/
I
nTe
c
h
,
p
.
7
00
,
2
0
0
7
.
[3]
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
.
[4]
A
n
i
k
in
A.
S
,
“D
y
n
ami
c
po
s
i
t
i
v
e c
o
up
li
ng in asy
nch
r
on
ous
el
e
c
t
ric
dri
v
e
s
wi
t
h
f
req
u
en
cy co
n
t
r
ol
/
А.
С
.
An
i
k
i
n
,
V
.L
.
Ko
dk
in,
A.A
.
B
a
l
de
nk
ov
,”
P
r
i
o
r
it
ie
s
o
f
w
or
ld
s
c
i
e
n
c
e
:
e
x
p
e
rime
n
t
a
n
d
s
c
ie
n
t
i
f
i
c
d
i
s
c
u
ss
io
n
,
M
a
te
r
i
a
l
s
of
t
h
e 8t
h
i
n
t
e
rnati
o
n
a
l scient
if
ic co
nf
erence
.
Scient
ific
a
nd
P
ublish
i
ng
Center
"
O
t
k
r
yt
ie".
N
orth
C
h
a
rl
est
o
n
,
S
C
,
US
A,
1
7
-
18
,
- P.
1
1
9
-1
24
, Jun
e
20
15
.
[5]
Ko
dk
in
V
.L.,
Ya.A.
Sh
ma
ri
n
,
A
.S
.
An
i
k
i
n
,
AA
B
al
d
e
n
k
o
v
,
N.A.
L
o
g
in
ov
a
,
C
o
rrectio
n
of
d
y
n
am
ic
m
omen
t
p
e
rtu
r
b
a
ti
on
s
in
e
lect
ric
driv
es
o
f
altern
ati
n
g
curren
t
,
S
c
ien
c
e
of
S
USU.
M
a
t
e
rials
o
f
th
e
68
th
s
c
ientific con
f
er
e
n
ce.
P
.
805
-81
4
,
20
1
6
.
[6]
L
i
Y
aoh
u
a,
M
a
Ji
an,
Yu
Q
i
a
ng
,
Liu
Ji
ang
y
u
,
“
N
o
vel
D
i
rect
T
o
r
que
C
on
tro
l
P
erm
a
nen
t
M
agnet
S
y
nchro
n
o
u
s
M
o
t
o
r
D
r
iv
e
u
s
ed
i
n
E
l
ectri
cal
V
eh
icl
e
,”
In
ter
n
a
t
i
ona
l Jo
urn
a
l
o
f
P
o
wer
Elect
ron
i
cs and Drive Sys
t
em
(
I
JP
EDS)
,
Vo
l.1
,
N
o
.2
, p
p
.
129
~1
3
8
, D
ecem
ber 201
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
T
h
e
dynam
ics
ide
n
tif
ic
a
tio
n
of
async
h
ro
n
o
u
s
e
l
e
c
t
r
i
c
dr
ive
s
via f
r
eq
ue
nc
y
re
sp
onse
(V
lad
i
m
i
r L.
Kodk
in)
73
[7]
Ka
me
l
Sa
le
h
,
“
Ma
rk
S
um
ne
r
S
e
n
s
or
less
C
ontrol
o
f
a
F
ault
T
o
le
ran
t
P
M
S
M
D
riv
e
s
i
n
C
ase
o
f
S
i
ngl
e-ph
ase
Op
e
n
Circui
t
Fault
,
”
In
ter
natio
nal Jou
r
n
a
l of
Po
wer Elect
ro
n
i
cs and Drive Syst
em
(
I
JPE
D
S)
,
V
o
l
.
7
,
N
o
.
4
,
p
p
.
10
61
~1
07
4,
D
ec
em
ber
2
0
1
6
.
[8]
S
h
ev
chenk
o
,
A
.
F
.
a
nd
A
b
d
el’
M
a
ks
ud
S
elim,
S
.
A
.,
“
V
ector
c
o
n
t
r
ol
o
f
st
a
t
or’s
c
urrent
i
n
s
y
n
c
hro
nou
s
m
o
tor
w
i
th
p
e
rma
n
e
n
t ma
gn
e
t
s
for
d
r
owne
d
pu
mp
d
r
i
ve
,”
Nauchn
.
V
e
st
n. No
vos
i
b.
Gos.
T
ekhn.
Univ
.,
2
0
1
1
,
no.
2
(43)
[9]
Lou
i
s
J-
P.
C
on
tr
ol
o
f
No
n-c
o
n
v
e
n
tion
a
l
S
y
n
c
h
ro
no
us
M
o
t
ors
/
Gre
a
t
B
r
i
t
a
i
n
a
n
d
t
h
e
U
n
i
t
e
d
S
t
a
t
e
s
b
y
I
S
T
E
L
t
d
a
n
d
Jo
hn
Wiley
&
Son
s
,
I
n
c
.,
4
28
p.
,
2
012
.
[10]
Rik
D
e
D
o
n
ck
er,
D
u
co
W
.J.
Pul
l
e,
A
n
d
re
V
eltm
an,
“Ad
v
an
ce
d
E
l
ect
rical
D
rives
:
A
nal
y
sis,
M
o
d
el
in
g
,
C
on
trol
.
Sp
ri
n
g
e
r,
” 4
7
4
p
., 20
1
1
.
[11]
Us
oltsev
,
A.
A.
Vect
or
c
o
n
tro
l
o
f
asy
n
ch
ron
ous m
o
t
ors
.
T
u
t
orial
.
- Spb
.:
IT
M
O,
1
2
0
p
.
,
20
0
2
.
h
t
tp
:
/
/
s
e
r
vo
mo
to
r
s
.ru/d
o
c
u
me
nta
t
io
n/
fre
q
ue
n
c
y_
c
o
n
t
rol_o
f
_a
sy
nc
h
ro
no
us_
m
o
t
ors/chas
tu
pr.
p
d
f
[12]
P
o
zd
eev,
A.D
.
,
“Elect
rom
a
gn
etic
a
nd
e
l
e
ctrom
ech
anical
p
rocess
e
s
i
n
f
r
equ
e
ncy-co
nt
rolled
asy
n
chro
no
us
e
lect
ric
dri
v
es,
”
-
Cheb
oks
a
r
y
:
Publish
i
ng h
o
u
s
e Ch
uvash
Uni
versit
y
,
172
p
.
,
1
9
9
8
.
[13]
So
ko
lov
s
k
y
,
G
.
G
. AC e
l
e
c
tr
ic
d
rive
s wi
th
f
re
qu
e
n
c
y
c
on
trol.
-
M
os
cow:
"
AC
ADE
M
I
A
",
2
67
p
.
,
2006
.
[14]
Ko
dk
in
V
.L.,
“
Exp
e
rim
e
nt
al
R
es
earch
o
f
A
s
y
n
chro
no
us
Electri
c
Dr
iv
e
wit
h
P
ositiv
e
D
y
n
a
m
i
c
F
e
ed
back
o
n
S
t
at
or
Current,”
III
Int
e
r
nat
ional Conf
er
e
n
ce on Indus
t
r
i
al
En
gineer
i
ng,
A
ppl
i
c
ations a
n
d Manufac
t
u
r
i
ng
,
ICIE
A
M
2
017
– P
r
o
ceedi
ngs
. – 20
17
[15]
V.L.
K
odk
i
n,
A
.
S
.
Anikin
,
Ya.
A
.
Shm
a
rin,
“
D
yna
m
i
c
Load
D
is
turba
nce
Correcti
o
n
f
o
r
Alterna
t
ive
Cur
r
ent
Elect
ric
Dri
v
es”
II
In
te
r
n
a
t
io
na
l
C
o
n
f
e
r
e
n
c
e
on
In
du
stri
al Eng
i
n
e
e
r
in
g,
App
lic
a
tion
s
an
d
Ma
nu
fa
c
t
u
r
in
g
,
ICIE
AM
2
016
–
P
r
oceedi
n
g
s
.
–
201
7
[16]
Ko
dk
in
V
.
L.
,
A
n
ik
in
A
.
S
.
,
“F
req
u
en
cy
c
on
tro
l
o
f
as
yn
chron
o
u
s
el
ec
t
r
ic
d
rive
s
in
t
ransport
,
”
20
1
5
In
ter
n
a
t
io
nal
Si
ber
i
an Con
f
erence o
n
Co
nt
rol
a
nd
Comm
unica
tio
n
s
(
S
IB
CON),
20
15
.
[17]
V.
L.
K
od
kin,
A
.
S
.
A
n
i
k
in
,
Y
a
.A.
,
“S
hm
arin
E
ffect
iv
e
F
r
equen
c
y
C
on
tro
l
f
o
r
I
nd
uc
tion
Ele
c
t
ric
Driv
e
s
u
nd
e
r
Overloading Rus
s
ian
El
ec
t
r
ical
E
ng
i
n
eering
,
” Vo
l
. 85
, No
. 1
0
, p
p
.
6
4
1–6
44
,
2
014
.
[18]
Park R., Robert
s
on
B. The reactances
of synchronous
m
achi
n
es.
/
/
Tr. AIEE
,
vo
l. 4
7
, 19
2
8
.
[19]
Chi
a
sso
n
Jo
hn.
M
o
d
eli
n
g
An
d
Hi
gh
P
erf
o
rm
an
ce
Con
t
rol
O
f
E
l
ectri
c
Mach
i
n
es
/
J
oh
n
Wiley
&
S
o
n
s
,
Inc.,
7
09
p
,
20
05
.
[20]
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 as n
o
n
-
l
i
n
ear sy
s
t
e
ms
accord
in
g
to
P
o
pov
c
r
iterion
a
d
j
usted
t
o
a
m
p
litu
de
a
nd
p
h
a
s
e
f
requ
ency
c
h
aract
eristics
of
its
e
l
e
ment
s”
2nd
In
ter
n
a
t
io
nal
Co
nfe
r
e
n
c
e
o
n
A
p
p
l
ie
d
Ma
the
m
a
tic
s,
Si
mula
t
i
o
n
,
an
d
Mo
de
lin
g
A
M
S
M
2
0
1
7
– P
r
oceedin
gs
. –
20
17.
[21]
V.
L.
K
od
ki
n
,
A
.
S
.
A
n
i
k
i
n
,
A.
A.
B
alden
k
o
v
,
“
S
pect
ral
Anal
ysis
o
f
R
ot
or
C
urren
t
s
in
F
req
u
en
cy-co
n
t
ro
lled
E
lect
ric
Dri
v
es”
2nd
Intern
at
ion
a
l
Confer
ence on
Au
to
matio
n,
M
echa
n
i
c
al a
n
d
El
ectrical
En
g
i
neeri
ng, AMEE
2
01
7
–
P
r
oceedi
n
g
s
.
–
201
7
[22]
V.L.
K
od
k
i
n,
A
.S
.
Ani
k
i
n
,
A.
A
.
B
ald
e
nko
v,
“
Th
e
an
aly
s
i
s
o
f
th
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
“
D
yn
am
ics o
f
Sys
t
e
m
s
,
M
echan
is
m
s
an
d
M
a
ch
ines
, P
r
o
ceedin
gs
, 2
0
1
7
.
Оms
k
, 14
-
16.11
.20
1
7
.
[23]
Ko
dk
in.
V.L
.
,
“M
etho
ds
o
f
op
tim
i
z
i
n
g
t
he
s
p
eed
a
nd
acc
u
r
acy
o
f
o
p
ti
cal
c
om
plex
gui
dan
ce
s
y
s
t
ems
b
a
sed
o
n
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
circu
its,” P
ro
cee
d
i
n
g
s of
S
P
IE
-
The
Internati
o
na
l Soc
i
e
t
y fo
r
Opt
i
cal
Eng
i
neeri
n
g
. – 2
01
6
.
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