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.
10, N
o.
2, June
2
01
9, pp.
720~
7
3
0
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
7
20-
73
0
7
20
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
Backstepping control of two-mass
system usi
n
g inducti
on motor
drive fed by v
ol
tage source in
verter with
idea
l
control
perfo
r
ma
nce of stator cu
rrent
V
o
Th
a
n
h
H
a
,
Le
Tr
on
g
Ta
n
, N
g
u
yen
Du
c
N
a
m, N
gu
ye
n
Phu
n
g Qu
an
g
In
stit
u
t
e f
o
r Co
n
t
rol
Engin
eerin
g an
d
A
u
t
o
m
a
ti
on
-
ICEA,
Han
o
i
U
n
i
v
e
rsity
o
f S
c
i
e
nce an
d T
e
ch
no
lo
gy
, V
i
e
tn
am
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Oct
1
0
,
2
018
Re
vise
d N
ov
1
9
,
201
8
Ac
ce
p
t
ed
M
ar 3
, 2
0
19
Th
is
p
aper
d
es
cr
ibes
t
he
d
e
s
ig
n
and
the
s
i
m
u
l
a
ti
o
n
o
f
a
n
on-lin
e
a
r
c
on
tr
o
l
le
r
f
o
r
tw
o-m
a
s
s
s
y
s
t
e
m
usi
ng
i
n
d
u
ct
ion
m
o
to
r
bas
i
ng
o
n
t
h
e
back
st
e
pp
ing
m
e
th
od.
T
he
a
im
i
s
t
o
c
ont
ro
l
the
sp
eed
actual
v
a
lu
e
o
f
l
o
a
d
mo
t
o
r
m
a
tch
i
ng
with
t
h
e
s
peed
r
ef
erence
lo
ad
m
o
t
or,
m
o
reov
er,
elect
rical
d
rive
’s
r
es
pon
e
ens
u
ri
ng
th
e
“f
a
s
t,
accurate
a
nd
s
m
a
ll
ov
ers
h
o
o
t”
a
n
d
r
ed
u
c
i
n
g
the
re
so
na
nce
oscillations
f
or
t
wo-m
ass
sys
t
em
u
sing
i
nducti
o
n
mot
o
r
f
e
d
by
v
oltage
s
ource
in
vet
e
r
w
i
t
h
i
deall
y
c
on
tro
l
p
erf
o
rman
ce
of
s
t
a
to
r
cu
rrent.
Bac
kste
p
p
in
g
con
t
ro
ller
u
ses
the
no
n-l
i
near
e
q
u
a
ti
on
s
o
f
a
n
i
n
d
u
cti
o
n
m
o
to
r
an
d
th
e
lin
ear
dy
nam
i
cal
e
qu
ati
o
n
s
o
f
tw
o-m
a
ss
s
y
s
t
e
m
,
t
h
e
L
y
a
pu
no
v
an
alys
is
a
nd
t
h
e
errors
b
etween
t
he
r
eal
a
nd
t
he
d
esi
r
ed
v
al
ues.
T
he
c
ont
roller
has
b
een
im
plem
en
t
e
d
i
n
b
ot
h
s
i
m
u
l
a
ti
o
n
a
nd
h
ard
w
a
r
e
-
in-t
he-l
oo
p
(HIL
)
r
eal-t
im
e
exp
e
rim
e
nt
s
u
s
in
g
T
yph
oo
n
HIL
40
2
system
,
wh
en
t
he
d
riv
e
s
y
s
t
e
m
o
p
e
r
a
t
e
s
at
a
s
t
a
ble
speed
(rot
o
r
fl
ux
i
s
con
s
t
a
nt
)
and
great
er
t
h
a
n
rat
ed
s
peed
(fi
e
l
d
weak
enin
g
ar
ea).
Th
e
s
i
m
u
la
ti
on
an
d
H
I
L
resul
t
s
p
r
esent
e
d
th
e
c
orrect
ness
and
ef
fect
iv
eness
of
t
h
e
c
on
troller
i
s
p
ro
po
sed
;
f
urt
h
erm
o
re,
c
o
m
pared
t
o
P
I
m
e
th
od to see t
h
e res
p
o
n
s
e
of t
h
e s
y
stem cl
early.
K
eyw
ord
s
:
B
ack
st
epp
i
ng
c
o
n
t
r
oll
e
r
D
r
ive
ind
u
c
t
i
o
n m
o
tor
P
e
rform
a
nc
e
of stat
o
r
curr
ent
R
e
d
u
c
ed
-o
rd
e
r
mat
h
e
ma
t
i
c
al
mode
Two-m
a
ss system
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:
Ng
uy
e
n
Ph
ung Qu
an
g
,
In
sti
t
ut
e
f
o
r Con
t
ro
l
Engi
ne
eri
n
g
a
n
d
Au
t
o
ma
t
i
on
- IC
EA,
Ha
n
o
i
U
n
iv
ersi
t
y
o
f S
c
i
e
n
c
e
an
d
Te
c
h
nol
ogy,
N
o
.1,
D
a
i
Co
V
iet R
o
a
d
,
H
a
i
Ba
Trung,
H
a
n
o
i
,
V
i
etna
m.
Em
ail:
qua
n
g
.n
gu
ye
np
h
u
n
g
@
hus
t
.
ed
u.v
n
1.
I
N
TR
OD
U
C
TI
O
N
The
tw
o-m
a
ss
sys
t
em
w
i
t
h
fle
x
ib
l
e
s
haf
t
c
a
n
b
e
fou
n
d
i
n
m
a
ny
i
n
du
st
ri
al
a
p
p
l
i
c
a
t
i
on
s
su
ch
a
s
ma
chine
t
o
o
l
s,
r
oll
i
n
g
-m
ills,
rob
o
t
a
rm
s,
c
on
ve
ye
r
be
l
t
s
,
e
tc.
D
u
e
to
t
he
f
i
n
it
e
s
tiffness
a
nd
da
m
p
i
n
g
c
o
eff
i
ci
ent
s
o
f
th
e
sh
a
f
t
,
t
h
e
s
p
e
e
d
o
sc
ill
a
ti
o
n
o
f
t
h
e
d
r
i
v
e
s
ys
tem
i
s
i
n
e
vita
ble
a
n
d
m
a
y
ca
u
s
e
de
t
r
im
enta
l
in
flue
nce
s
on
no
t
onl
y
t
h
e
q
u
al
ity
o
f
t
h
e
p
r
od
uc
t
s
b
ut
a
l
s
o
t
h
e
m
e
c
ha
ni
ca
l
an
d
e
l
ectr
i
ca
l
com
p
o
n
en
t
s
o
f
th
e
dri
v
e
sy
stem
.
He
nce,
s
pee
d
c
on
tro
l
d
es
ign
for
t
h
ese
drive
sys
t
e
m
s
p
l
a
y
s
a
k
e
y
r
o
l
e
i
n
i
m
p
r
o
v
i
n
g
t
h
e
s
y
s
t
e
m
cha
r
ac
t
e
ris
tic
a
nd
p
ro
d
u
ct
s
q
u
al
i
t
y
.
S
u
ppres
si
ng
t
h
e
sha
f
t
tors
io
na
l
vi
bra
t
i
o
n,
r
eje
c
t
i
ng
t
he
l
oa
d
di
s
t
urbanc
e
tor
que
a
n
d
t
r
a
c
k
i
n
g
t
h
e
r
e
fe
re
nc
e
s
p
ee
d
are
m
a
in
g
oals
o
f
the
c
on
t
r
o
ller
[1-4]
.
H
ow
e
v
er,
these
ta
sk
s
a
r
e
no
t
ea
sy
t
o
be
a
c
h
ieve
d
d
u
e
t
o
t
he
f
ac
t
tha
t
n
o
t
a
ll
sys
t
e
m
s
ta
te
v
a
r
ia
bles
a
re
a
va
ila
ble.
F
urt
h
erm
o
re
,
unkn
ow
n
no
n
l
i
n
ea
ri
t
i
e
s
such
as fric
tio
n
and ba
c
k
las
h
m
ay
a
lso c
a
use
und
e
s
i
r
a
b
l
e
ina
cc
u
r
ac
y
f
o
r t
h
e c
o
n
t
ro
l
syst
em.
Vari
o
u
s
c
o
n
t
r
ol
s
c
h
emes
h
ave
b
e
en
d
e
v
e
l
op
ed
i
n
t
h
e
l
i
t
e
rat
u
re
t
o
su
p
p
re
ss
t
he
t
orsi
ona
l
v
i
bra
t
i
o
n
of
t
h
e
afo
r
emen
t
i
o
n
e
d
t
w
o
-
mass
s
y
s
t
e
m.
O
b
v
io
u
s
ly
,
th
e
cl
a
s
si
cal
c
a
sca
d
e
s
t
ruc
t
ure
us
in
g
pro
port
i
ona
l-i
n
t
e
gra
l
(PI)
speed
controller
i
s
t
he
m
os
t
po
p
u
l
a
r
c
ontr
o
l
sc
h
e
me
.
H
o
w
e
v
er
,
th
is
m
e
t
ho
d
c
a
n
n
o
t
effec
tiv
el
y
s
u
ppre
s
s
the
v
i
brat
io
n
s
i
nce
the
P
I
c
o
n
tr
ol
ler
d
o
e
s
n
ot
h
a
v
e
e
n
ou
g
h
d
egr
e
e
-o
f-fre
edom
t
o
ha
n
d
le
s
uch
h
i
gh
o
r
d
er
dy
nam
i
c
sys
t
e
m
l
ike
t
h
i
s
[
5]
.
Th
us,
adva
nc
e
d
c
o
n
t
ro
l
te
c
h
n
i
q
u
e
s
s
uc
h
as
s
lid
in
g
mo
de
c
ontr
o
l,
f
l
a
tne
s
s-
base
d
con
t
ro
l,
a
dap
t
i
v
e
con
t
ro
l, a
nd
fuz
zy
a
da
p
t
i
v
e
c
ont
r
o
l
are
a
l
so
em
pl
o
y
e
d
t
o ge
t
a
b
e
t
t
e
r
pe
r
for
m
a
n
ce
[6-1
1].
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
Back
step
p
i
n
g
c
o
n
t
r
o
l
of tw
o-
m
a
ss
system
us
ing i
n
d
u
c
tio
n m
o
tor driv
e
fe
d…
(
N
guy
en P
h
u
ng Q
u
a
ng)
72
1
I
n
t
his
r
e
sear
ch,
t
h
e
f
i
e
l
d-
or
i
e
nte
d
c
o
n
tr
ol
(
F
O
C
)
w
hic
h
h
a
s
b
e
en
w
id
el
y
u
s
ed
i
n
in
du
st
ri
a
l
i
nv
ert
e
rs
is
u
se
d
t
o
c
o
n
t
r
ol
t
he
i
nd
uc
t
i
on
m
o
t
o
r
of
t
he
d
r
i
ve
s
y
s
tem
[
12]
.
Base
d
o
n
a
n
o
bse
r
va
t
i
on
t
h
a
t
i
f
t
h
e
r
e
sp
onse
of
t
he st
a
tor
c
u
r
r
e
nt
c
o
n
tr
ol
ler
is
f
a
s
t
e
n
o
u
gh,
t
he or
d
er
o
f
t
h
e
t
w
o
-ma
ss
dy
nam
i
c
s
y
ste
m
ca
n
b
e
re
d
u
ce
d
from
7t
h
to
3
r
d
i
n
n
o
mina
l
s
p
e
e
d
r
a
nge
a
n
d
f
r
o
m
7t
h
t
o
4
t
h
i
n
f
i
e
l
d
we
ak
eni
n
g
ran
g
e.
C
on
se
q
u
e
n
t
ly
,
t
h
e
co
nt
rol
de
sig
n
f
or
t
he
r
educ
e
d
o
rder
s
ys
tem
can
b
e
simp
li
fie
d
.
S
i
n
ce
th
e
dea
d
-be
a
t
co
ntr
o
l
l
er,
whi
c
h
f
o
rce
s
t
h
e
s
tat
o
r
c
u
r
r
e
nt
t
o
i
t
s
d
e
sir
e
d
val
u
e
in
f
i
n
it
e
s
t
e
p
,
ha
s
a
l
r
e
a
dy
s
u
c
c
e
s
sfu
l
l
y
b
ee
n
d
e
vel
o
ped
f
o
r
t
h
e
stat
or
c
ur
r
e
nt
l
oo
p
in
o
ur
p
r
e
vi
o
u
s
s
tu
dy
[
13]
,
the
r
e
ma
i
n
i
n
g
ob
jec
t
i
v
e
o
f
t
h
i
s
r
e
s
e
a
r
c
h
is
t
o
ach
ie
ve
a
h
ig
h
d
yna
mic
spe
e
d
c
o
n
t
r
o
l
with
t
o
r
sio
n
a
l
o
sci
lla
ti
on r
e
d
u
ct
i
on fo
r
the
drive sys
t
em
.
In
t
hi
s
p
a
p
e
r,
a
b
a
c
k
s
t
e
pp
i
ng
c
o
nt
rol
al
go
rit
h
m
i
s
p
ropo
sed
to
co
n
t
ro
l
t
h
e
loa
d
s
pe
ed
o
f
two-m
a
ss
sys
t
em
s.
F
or
a
c
h
ie
v
i
n
g
t
h
i
s
g
o
al,
a
tw
o-
bl
oc
k
c
o
n
t
r
o
l
st
r
a
te
gy
i
s
p
rop
o
se
d.
I
t
is
b
ac
kste
p
p
i
n
g
con
t
ro
l
a
l
g
o
r
i
t
h
m
f
o
r
l
o
a
d
s
p
e
e
d
a
n
d
m
o
t
o
r
s
p
e
e
d
.
O
n
t
h
e
o
t
h
e
r
h
a
n
d
,
r
o
t
o
r
fl
ux
c
o
ntr
o
l
is
d
es
ig
ne
d
ac
or
din
g
t
o
b
a
c
k
st
epp
i
n
g
co
nt
rol
alg
o
r
ithm.
G
en
erat
i
n
g
t
h
e
d
e
si
re
d
mot
o
r
to
r
que
b
y
dea
d
-
b
ea
t
cur
r
ent
co
n
t
r
o
l,
n
ot
o
n
l
y
g
u
a
ran
t
e
e
s a
ccu
rat
e
lo
a
d
sp
eed
b
ut
a
l
s
o
p
r
oves
t
h
e
st
ab
ilit
y
o
f
t
he
s
ys
t
e
m
[14,
15]
.
2.
MO
DELI
N
G
O
F
DRIVE
S
YSTE
M
2.
1.
M
a
thematical model
o
f th
ree
ph
as
e induction
m
otor
I
n
f
ie
ld
s
yn
c
h
r
o
n
o
u
s
c
oor
d
i
n
a
te,
t
h
e
t
h
r
e
e-
p
h
ase
in
duc
t
i
on
m
ot
o
r
c
a
nb
e
d
e
s
c
rib
e
d
by
t
h
e
f
ol
l
o
wing
dy
na
mic
eq
ua
ti
ons
[
1
2
]
.
(
1
)
In
w
hi
ch
,
;
sd
sq
ii
a
r
e
dq
c
om
p
one
n
t
s
o
f
t
he
s
tat
o
r
c
u
r
r
e
nt;
,
s
ww
a
r
e
m
ec
h
a
ni
c
a
l
roto
r
ve
l
o
city
a
nd
synchr
onous
s
p
eed,
respec
ti
vel
y
;
,,
,
rd
r
q
yy
a
r
e
dq
c
o
m
pone
n
t
s
of
t
h
e
r
ot
or
f
l
u
x
;
s
i
s
tota
l
lea
k
a
g
e
fa
ctor
;
r
T
is
r
o
tor
ti
m
e
c
ons
tat
:
sd
u
,
sq
u
are
dq
c
om
po
nen
t
s
o
f
t
he
s
ta
tor
v
o
l
t
a
g
e;
s
L
is stat
o
r in
d
u
cta
n
c
e
.
It
c
a
n
b
e
se
en
t
ha
t
the
ori
g
i
n
al
s
ta
te
(
1)
i
s
bil
i
n
ea
r
and
is
o
f
4
th
o
rd
er.
Assu
me
t
h
a
t
th
e
c
u
rrent
c
o
n
t
r
o
ller
is
p
e
r
fec
t
w
it
h
id
ea
l
r
e
sponse,
t
he
i
n
d
uc
t
i
o
n
m
ot
or
mode
l
can
b
e
reduc
e
d
a
s:
(
2
)
W
h
ere:
22
3
;
2
pm
rd
m
mr
zL
ik
LL
J
y
==
In
w
h
i
ch
,
,
mr
LL
is
m
ut
ua
l,
r
ot
or
i
nd
ucta
nc
e
;
m
i
is
v
e
c
t
o
r
of
m
a
g
ne
tiz
ing
c
u
rre
nt;
L
m
is
t
or
que
l
oad
;
p
z
is
n
umbe
r
o
f
p
ole
pa
ir
s;
J
is
t
or
que
o
f
i
n
er
t
i
a;
The
s
t
a
t
e
(2)
i
s
o
f
2
nd
or
der
,
s
ta
tor
c
u
r
r
ent
i
sd
is
u
se
d
t
o
c
o
n
t
r
ol
t
he
m
o
t
o
r
f
lu
x
a
n
d
i
sq
i
s
de
dica
te
d
t
o
spee
d
c
ontr
o
l.
2.
2.
M
o
del
of the
t
wo-
m
ass system
Ty
pica
l
c
o
nf
i
g
ur
at
io
n
of
a
t
w
o
-
m
a
s
s
syst
e
m
s
how
a
s
F
i
gur
e
1:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
7
20
–
7
3
0
72
2
1
J
2
J
c
d
Mo
t
o
r
Lo
a
d
L
m
1
11
1
n
2
22
2
n
M
m
M
m
Sh
a
f
t
IM
F
i
gur
e
1.
T
yp
i
c
a
l
c
on
f
i
g
u
r
a
t
i
on
o
f
a
t
w
o
-
m
a
ss
system
T
h
e
t
y
p
i
c
a
l
c
o
n
f
i
g
u
r
a
t
i
o
n
o
f
a
t
w
o
-
m
a
s
s
s
y
s
t
e
m
i
s
i
l
l
u
s
t
r
a
t
e
d
i
n
F
i
g
u
r
e
1
.
T
h
e
s
y
s
t
e
m
c
a
n
b
e
de
sc
r
i
bed
b
y
t
h
e
f
oll
o
w
i
ng
l
i
n
ear
dynam
i
ca
l
equa
t
i
o
n
s
[
2
]
.
(
3
)
Where
:
12
,
A
r
e
motor
spe
e
d,
l
oa
d
s
p
eed
;
12
,
are
m
o
t
o
r
and
loa
d
a
n
g
l
e
ac
cele
r
at
io
n
;
is
a
ng
le
;
d
is
shaf
t dam
p
in
g coe
f
fic
i
e
n
t;
c
i
s
s
h
a
ft stiff
n
e
s
s
.
Whe
n
t
he
d
r
i
ve
s
ys
tem
o
p
e
r
a
t
e
s
a
t
f
i
e
l
d
w
e
aken
in
g
r
a
nge,
t
h
e
ma
the
m
a
tic
al
m
o
d
el
o
f
t
h
e
sys
t
em
is [2].
(
4
)
For
contro
l de
s
i
g
n
p
urp
o
se,
term (
4) is r
e
written
in
t
he
fol
lo
w
in
g sta
t
e-
spa
ce
form
:
(
5
)
W
ith
:
(
6
)
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
Back
step
p
i
n
g
c
o
n
t
r
o
l
of tw
o-
m
a
ss
system
us
ing i
n
d
u
c
tio
n m
o
tor driv
e
fe
d…
(
N
guy
en P
h
u
ng Q
u
a
ng)
72
3
3.
BACKSTEPPI
NG
C
O
N
T
R
OL DESIGN FOR
T
H
E
FLUX
AN
D
S
PE
ED C
O
N
TROL
B
a
se
d
o
n
[
13]
a
n
d
t
he
c
o
n
ce
pt
o
f
the
bac
k
ste
p
p
i
ng
des
i
g
n
f
or
i
n
d
u
c
ti
on
m
ot
o
r
[
10
],
t
h
e
p
ropo
sed
c
o
n
t
r
o
l
sc
he
me
f
or
t
he
t
w
o
-
m
a
s
s
system
u
s
i
n
g
i
n
d
u
c
t
i
o
n
mot
o
r
fe
d
b
y
V
S
I
w
it
h
p
e
r
f
ec
t
s
t
at
or
c
ur
r
e
nt
c
o
n
t
r
o
ller
is
s
how
n
i
n
F
igur
e
2.
F
i
gur
e
2.
B
l
o
c
k
d
ia
gr
am
c
ontr
o
l
of
t
w
o
-
m
ass
system
I
n
this
se
ct
i
o
n,
a
b
a
c
k
ste
p
pi
ng
con
tr
o
l
s
ta
ge
g
y
i
s
pr
op
ose
d
t
o
c
o
ntr
o
l the
r
o
tor
f
l
u
x
a
n
d
s
pee
d
l
oa
d o
f
tw
o-
m
a
ss
sys
t
e
m
w
i
t
h
f
l
e
x
i
b
l
e
c
o
upl
in
gs.
T
h
i
s
p
aper
p
r
e
sente
d
t
he
i
n
d
u
c
t
io
n
mo
t
o
r
s
o
pe
r
a
te
a
t
r
a
te
d
r
e
qu
i
r
e
sp
ee
d
is
g
reat
e
r
t
h
a
n
th
e
rated
s
p
eed;
t
h
e
refo
re,
th
e
flux
m
u
s
t
b
e
r
e
d
u
ce
d
to
e
nsur
e
t
h
a
t
t
he
p
ow
e
r
s
up
ply
is
n
o
t
ov
erlo
a
d
ed.
3.
1.
Flu
x
c
on
t
r
ol
le
r
d
e
si
gn
S
i
nce
r
o
t
o
r
flu
x
m
agni
t
u
d
e
a
re
our
c
on
tr
ol
v
ar
i
a
b
l
e
s
,
t
h
e
tr
a
c
k
ing
er
ro
rs ar
e
d
efin
e
d
b
y:
*
1
mm
zi
i
=-
(
*
m
i
i
s
t
h
e d
e
sired v
a
lu
e of
f
lux
)
(7
)
tak
i
ng
t
h
e
der
i
va
ti
ve
o
f
b
o
th
s
i
d
e
s
o
f
(
7
)
G
i
ve
s:
(
8
)
w
e
c
an
s
e
e
t
ha
t
(
8
)
i
s
t
h
e
n
on-
li
nea
r
e
qua
t
i
on
(,
,
)
d
ft
dt
=
x
xu
wh
ere:
1
z
is the
sta
t
e
variab
le
;
sd
i
i
s
t
h
e
i
n
pu
t
si
gna
l
(
o
r
con
t
r
o
l
si
gna
l)
.
to
s
tab
i
lize
t
h
e
f
l
u
x
s
i
g
na
l
giv
e
n
by
(
8
)
,
t
he
c
and
i
date
L
yap
u
n
o
v
f
uc
t
i
o
n
can
b
e
def
i
ned
a
s
f
oll
o
w
i
ng
:
(
9
)
w
h
ic
h
the
de
r
i
vat
i
v
e
of
(
9)
i
s:
(
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
7
20
–
7
3
0
72
4
Th
e
Ly
apun
ov
s
t
a
bi
l
ity
c
ondi
t
i
o
n
can
b
e
ve
ri
f
i
ed
i
f
t
h
e
st
a
b
il
i
z
a
t
i
on
fu
nct
i
on
i
s
c
hose
n
a
s
fo
llows
:
(
11)
wh
ere
1
c
is the
p
o
s
i
t
i
v
e
c
onsta
nt
d
es
ig
n
t
h
at i
s de
t
e
rm
ine
the
clo
s
ed-l
oo
p
dyn
a
m
i
c
s
S
ubst
i
t
ute
(
11)
i
nt
o
(
10)
Res
u
lt
i
n
:
*
11
m
sd
r
m
r
di
ic
T
z
i
T
dt
=-
+
+
(
12)
w
i
t
h
:
(
13)
The
(
12)
a
s
show
n
:
*
*
11
m
sd
r
m
r
di
ic
T
z
i
T
dt
=-
+
+
(
14)
so,
the
*
sd
i
i
s
the
ac
t
u
a
l
c
o
n
t
r
o
l
s
i
gna
l,
t
he
c
o
n
t
r
o
l
r
u
le
f
or
t
he
f
lu
x
co
ntr
o
lle
r.
3.
2.
S
p
e
e
d
c
on
t
r
oll
e
r
d
e
sign
For
de
si
g
n
i
n
g
t
his
no
n
line
a
r
c
ontro
l
law,
i
t
is
a
ssume
d
tha
t
a
l
l
fe
e
dbac
k
s
i
gna
ls
f
r
o
m
t
h
e
m
o
t
o
r
,
t
he
shaf
t
a
nd
t
h
e
l
o
ad
s
i
d
e
s
a
r
e
a
vai
l
a
b
l
e
i
n
th
is
s
ect
io
n.
A
s
F
i
gu
re
3
s
ho
ws,
t
h
e
p
r
opo
sed
ba
ck
st
e
ppi
ng
c
on
t
r
o
l
a
l
g
o
r
i
t
h
m
i
s
de
s
i
g
n
e
d
i
n
tw
o
s
t
e
p
s
.
I
n
e
a
c
h
s
t
e
p
a
s
u
b
s
y
s
t
e
m
w
i
ll be
s
t
u
di
e
d
.
Eac
h
s
te
p
i
n
clu
d
es
t
he
d
y
n
a
m
i
cs
o
f
t
h
e
p
re
vio
u
s
s
u
bsy
s
t
e
ms
f
or
b
a
c
k
s
t
e
ppi
ng
t
e
chni
qu
e.
S
e
l
e
c
t
in
g
a
pr
ope
r
Lya
p
u
n
ov
fu
n
c
t
i
o
n
f
or
eac
h
ste
p
,
gua
r
a
ntee
s
t
h
e
asym
p
t
o
tic
s
ta
bi
l
i
t
y
o
f
the
r
e
l
a
te
d
su
bs
ys
t
e
m.
C
om
p
l
et
ing
a
ll
t
w
o
ste
p
s,
r
e
s
u
l
ts
i
n
no
t
on
ly
t
he
a
s
y
m
p
t
o
tic
s
ta
bil
i
t
y
o
f
the
w
h
o
l
e
sy
ste
m
,
but
a
l
s
o
the
de
sir
e
d
in
pu
t
(
m
ot
or
t
or
que)
la
w
for
a
ccur
a
te
l
oa
d
spee
d
c
ontr
o
l.
Fi
r
s
t
s
t
e
p
S
e
c
ond
s
t
e
p
1
2
21
x
12
x
*
s
q
ui
F
i
gur
e
3.
B
l
o
c
k
d
i
a
gr
am
o
f
t
w
o-
step
b
ac
ks
t
e
pp
i
ng
c
o
n
t
r
o
l
alg
o
r
i
th
m o
f
a two
-mass sy
stem
The
sp
e
e
d
c
on
t
r
ol
e
q
u
a
t
i
on
is
g
ive
n
:
(
15)
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
Back
step
p
i
n
g
c
o
n
t
r
o
l
of tw
o-
m
a
ss
system
us
ing i
n
d
u
c
tio
n m
o
tor driv
e
fe
d…
(
N
guy
en P
h
u
ng Q
u
a
ng)
72
5
The
(15)
h
as trian
g
u
lar
for
m
a
s foll
ows:
(
16)
the
s
e
two ste
p
f
or
d
es
ig
nin
g
t
he
bac
k
s
t
e
p
p
in
g
con
t
ro
l law
are
m
enti
o
n
ed
i
n
t
h
e
f
o
ll
ow
i
n
g:
Ste
p
1:
ap
p
l
y t
h
e
bac
k
s
te
p
p
i
ng fo
r
lo
ad spee
d
:
S
i
nce
loa
d
s
pe
ed
m
a
gnit
u
de
a
r
e
our
c
ontr
o
l
va
r
i
a
b
les,
t
h
e
t
r
a
ck
in
g
erro
rs are d
ef
in
ed
by:
(
I
s
th
e
referen
c
e lo
ad
s
p
e
ed
)
(1
7
)
tak
i
ng
t
h
e
der
i
va
ti
ve
o
f
b
o
th
s
i
d
e
s
o
f
(
17)
G
i
v
e
s
:
(
18)
to
s
tab
i
lize
t
h
e
f
l
u
x
s
i
g
na
l
giv
e
n
by
(
1
8)
,
the c
a
nd
i
d
at
e
Lyap
u
n
o
v
f
uc
t
i
o
n
can
b
e
def
i
ned
a
s
f
oll
o
w
i
ng
:
(
19)
w
h
ic
h
the
de
r
i
vat
i
v
e
of
(
19)
I
s:
(
20)
the
n
:
(
21)
the
(2
1)
I
s r
e
sult
i
n
:
(
22)
Th
e
Ly
apu
nov
st
a
b
il
ity
c
on
di
t
i
o
n
c
a
n
b
e
v
eri
f
i
e
d
i
f
t
h
e
s
t
a
bil
i
za
t
i
on
f
u
nc
ti
on
2
()
Vz
i
s
c
h
o
s
e
n
a
s
fo
llows
:
(
23)
wh
ere
d
is the
p
o
s
i
t
i
v
e
c
onsta
nt
d
es
ig
n
t
h
at i
s de
t
e
rm
ine
the
clo
s
ed-l
oo
p
dyn
a
m
i
c
s.
F
r
om
(
18)
a
nd
(
1
5
)
W
e
ob
tai
n
:
(
24)
the
n
(
25)
so
l
oa
d
spee
d
s
how
n
a
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
7
20
–
7
3
0
72
6
(
26)
Ste
p
2:
ap
p
l
y t
h
e
bac
k
s
te
p
p
i
ng fo
r
mo
to
r
sp
eed
(
)
:
S
i
nce
loa
d
s
pe
ed
m
a
gnit
u
de
a
r
e
our
c
ontr
o
l
va
r
i
a
b
les,
t
h
e
t
r
a
ck
in
g
erro
rs are d
ef
in
ed
by:
(
I
s
th
e
referen
c
e mo
t
o
r
sp
eed)
(
2
7
)
tak
i
ng
t
h
e
der
i
va
ti
ve
o
f
b
o
th
s
i
d
e
s
o
f
(
27)
G
i
v
e
s
:
(
28)
To
s
t
a
bil
i
ze
t
he
f
lu
x
s
i
gna
l
g
i
ve
n
by
(
2
8)
,
the
c
a
n
d
i
da
te
L
ya
pu
no
v
fu
c
tio
n
c
a
n
b
e
d
e
f
in
ed
a
s
fo
llow
i
n
g
:
22
12
1
11
22
Vz
z
=+
(
29)
w
h
ic
h
the
de
r
i
vat
i
v
e
of
(
29)
i
s:
(
30)
the
n
s
u
b
sti
t
u
te
(
15)
a
nd
(
28)
i
nt
o
(
30)
,
w
e
g
et
(
31)
the
(3
1)
i
s
result i
n
:
(
32)
so,
the
*
sq
i
i
s
the
ac
t
u
a
l
c
o
n
t
r
o
l
s
i
gna
l,
t
he
c
o
n
t
r
o
l
r
u
le
f
or
t
he
s
pee
d
c
on
tro
ller
.
3.
3.
De
si
gn
t
he
r
e
f
er
en
ce traj
ectorie
s
Whe
n
d
es
ig
n
i
ng
t
h
e
co
n
t
r
o
ller
,
w
e
usua
lly
s
et
t
he
d
e
s
ir
e
d
v
a
l
ue
t
o
a
c
o
nst
a
nt
(
st
e
p
-b
y
-
st
ep
tr
a
j
e
c
t
or
y)
.
A
t
the
f
i
r
st i
nte
r
va
l of
t
ime
,
the
la
r
ge de
v
iat
i
on
will cause
a
large
input
r
equir
e
m
e
nt
. However, the
re
sp
on
s
e
o
f
the
ac
tu
a
t
o
r
i
s
fi
ni
t
e
,
it
i
s
un
li
k
e
ly
t
h
a
t
th
e
c
o
n
tro
l
l
e
r
will
m
ee
t
t
h
e
re
q
u
irem
en
ts.
Th
us
t
h
e
ba
ck
ste
p
pi
ng
con
t
r
o
l m
e
th
o
d
w
i
l
l "so
f
t
e
n" t
h
e
d
esir
ed
s
i
g
na
l
b
y
c
ha
ng
ing
t
h
e de
s
i
r
e
d
si
g
n
a
l
sl
ow
l
y
so
th
a
t
t
he
r
e
spo
n
se
o
f
the
sys
t
em
i
s
s
o
ft
a
nd
be
tter
.
F
or
t
h
i
s
r
e
a
s
on,
t
he
s
ec
o
n
d
or
der
is
c
ho
se
n
f
o
r
de
sig
n
i
n
g
t
he
r
e
fe
renc
e
tra
j
e
c
tor
i
es.
Beca
u
s
e
the
c
o
n
t
r
o
l
rules
a
r
e
r
e
pre
s
ent
e
d
i
n
(
14)
A
nd
(
3
2
)
U
se
t
he
f
ir
st
o
r
d
e
r
d
e
riv
a
tiv
e
,
t
h
e fo
rm
o
f
t
r
ajecto
ries
*
m
i
an
d
*
w
will
have
to be
f
irs
t
orde
r
d
i
f
fere
n
t
i
a
b
l
e
.
Fl
ux refere
nc
e t
r
ajec
tory
des
i
gn
ing
*
m
i
()
*
22
2
11
1
()
11
()
1
2
1
m
d
m
is
is
T
s
T
s
Ts
==
++
+
(
33)
wh
ere:
1
T
i
s time
cons
ta
nt
;
*
m
i
i
s
out
put
o
f
f
l
ux
ref
e
r
e
n
c
e
t
raj
e
c
t
o
r
y;
d
m
i
is
i
n
p
u
t
o
f
fl
ux
r
e
fe
r
e
nc
e
tr
a
j
ect
or
y.
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
Back
step
p
i
n
g
c
o
n
t
r
o
l
of tw
o-
m
a
ss
system
us
ing i
n
d
u
c
tio
n m
o
tor driv
e
fe
d…
(
N
guy
en P
h
u
ng Q
u
a
ng)
72
7
The
r
ef
or
e,
on
the
time
dom
a
i
n:
2*
*
2*
11
2
2
d
mm
mm
di
d
i
TT
i
i
dt
dt
++
=
(
34)
tr
a
j
e
c
t
or
ies
of
f
l
u
x
r
e
f
e
r
e
nce:
(
35)
Spe
e
d
re
f
e
re
nc
e
tra
j
e
c
t
o
ry de
sign
i
ng
*
w
()
*
22
2
22
2
()
1
1
()
1
2
1
d
s
sT
s
T
s
Ts
w
w
==
++
+
(
36)
wh
ere:
2
T
i
s
time
c
o
n
s
t
a
nt;
*
w
i
s
o
u
t
p
u
t
o
f
s
p
e
e
d
r
e
f
e
r
e
n
c
e
t
r
a
j
e
c
t
o
r
y
;
d
w
i
s
i
npu
t
o
f
s
p
eed
r
e
f
ere
n
ce
tr
a
j
e
c
t
or
y.
T
her
e
for
e
,
on
the
tim
e
doma
i
n:
2*
*
2*
22
2
2
d
dd
TT
dt
dt
ww
ww
++
=
(
37)
tr
a
j
e
c
t
or
ies
of
f
l
u
x
r
e
f
e
r
e
nce:
(
38)
4.
RESU
L
T
AND
A
NALYS
I
S
I
n
t
hi
s
sec
t
i
o
n,
t
he
p
r
o
p
o
se
d
co
ntrol
s
t
rategy
i
s
verified
b
y
s
i
m
u
l
a
t
i
o
n
usin
g
Ha
r
d
wa
re-i
n
-
th
e
-
Loop
(
H
IL
).
T
h
e
p
ro
po
sed
con
t
r
o
l
is
a
lso
v
e
rified
i
n
Hard
ware
-
i
n
-
th
e
-Loo
p
(
H
I
L
)
en
v
i
r
o
nmen
t
u
s
i
n
g
a
Typ
hoon
de
v
i
c
e
i
n
F
i
g
u
r
e
4.
T
his
de
vi
c
e
c
onsis
ts
o
f
a
n
H
I
L
4
0
2
car
d
t
h
at
s
imu
l
a
t
e
s
g
r
i
d
s
our
ce
,
l
o
a
d
,
a
nd
thr
e
e
ful
l
-
br
idge
w
i
t
h
a
c
om
mon
D
C
-
l
in
k
ca
pac
i
tor
using
I
G
BT
s.
T
he
s
ys
tem
ha
rdwar
e
i
s
simu
la
te
d
i
n
r
ea
l
time
on
t
h
e
H
I
L
pla
t
f
o
r
m
w
it
h
a
t
i
m
e
s
t
e
p
of
1
μ
s
t
h
at
m
eans
ver
y
n
e
a
r
l
y
ph
ysic
al
m
o
d
el,
w
h
i
l
e
the
p
u
l
se
w
i
d
t
h
m
odu
la
tio
n
(
P
WM)
car
r
i
er
f
r
e
que
nc
y
is
5
k
H
z
.
V
o
lta
ge
a
nd
c
u
r
r
en
t
c
o
n
t
ro
lle
rs
a
s
we
ll
as
P
LL
ar
e
im
pl
e
m
e
n
te
d
i
n
D
SP
T
MS
320F
28
08
ca
r
d
.
The
simu
la
ti
o
n
p
ara
m
e
t
e
r
s
for
r
a
ted
p
o
w
e
r:
0
.
5kW
;
r
a
ted
pha
se
v
o
l
tage
:
2
2
0
V
RMS
;
r
ated
f
r
e
que
n
c
y:
5
0
H
z;
d
=0.
3
13N
m
/
r
a
d/s
;
c
=3
00
00
0N
m
/
r
a
d.
S
i
mulat
i
o
n
pr
o
c
edur
e
is
a
s
fo
l
l
ow
s:
A
t
t
=
0s,
t
he
m
agne
tic
c
ur
r
e
nt
i
s
cr
e
a
te
d.
T
he
n
a
t
t
i
m
e ins
t
a
n
c
e
t
=
0
.
4
s
,
t
h
e
m
o
t
o
r
s
t
a
r
t
s
t
o
s
p
e
e
d
u
p
to
250
0r
pm.
At t=
1
s,
the
f
u
l
l
l
o
a
d
i
s in
ser
t
e
d
.
A
t
t
=
1,
4
s,
th
e
m
o
tor
i
s
co
n
t
inue
d
t
o
spe
e
d
up to 35
0
0
r
p
m
w
i
th
f
u
ll
loa
d
.
F
i
na
l
l
y,
t
he
m
o
t
or
s
tar
t
s
t
o
c
ha
n
g
e
the
r
o
ta
t
i
ng
d
i
r
ect
io
n
wi
t
h
a
r
e
f
er
ence
s
pe
ed,
i.e,
2
5
00rp
m
,
at
time instan
ce t = 2
.
0
s.
The
s
i
m
u
la
t
i
on
r
e
sults
o
f
the pr
o
pose
d
m
e
t
h
o
d
ar
e pr
ese
n
te
d
an
d
c
om
par
e
d
to those
ge
t
t
i
ng
f
r
o
m
t
h
e
c
o
n
v
e
n
t
i
ona
l
P
I
c
ontr
o
ller
t
o
e
va
lua
t
e
t
h
e
ad
van
t
a
g
e
of
t
he
b
ac
kst
e
pp
ing
me
t
h
od
.
The r
e
sp
o
n
ses
of ma
gne
tiz
in
g
cur
r
ent
a
r
e s
h
ow
n in
F
ig
ur
e
5.
Bot
h
c
o
nve
n
tio
na
l P
I
a
n
d
b
ac
kste
pp
in
g
me
t
h
od
s
sho
w
s
t
a
b
l
e
op
era
tio
n
not
onl
y
i
n
n
o
m
i
n
al
b
u
t
a
l
s
o
fi
e
l
d
we
ak
eni
n
g
ra
n
g
e
.
Ho
wev
e
r,
i
t
can
b
e
obs
er
ved
tha
t
t
he
b
ac
k
s
tep
p
i
n
g
g
ive
s
b
e
t
ter
t
r
a
n
sie
n
t
r
e
spo
n
s
e,
i
.
e
.
,
w
itho
u
t
o
ver
s
h
o
o
t
a
s
s
ee
n
i
n
F
i
gur
e
5
an
d
shor
ter
sett
l
i
n
g
t
i
m
e
(
0.
2s
i
n
com
p
ar
is
on
w
i
t
h
0
.
35s
f
or
P
I
c
o
n
tro
l
).
The
res
p
o
n
se
o
f
t
h
e
t
o
rque
,
spee
d
as
w
e
l
l
as
t
orq
u
e
ri
p
p
le
o
f
t
he
m
otor
a
r
e
s
h
o
w
n
i
n
F
i
gur
e
6.
A
s
c
a
n
be
obse
r
v
e
d,
t
he
t
or
q
u
e
a
nd
s
p
e
e
d
q
ui
ckl
y
m
a
t
c
h
t
he
ir
c
om
m
a
nds
f
o
r
b
o
t
h
m
e
th
o
d
s.
N
eve
r
the
l
e
s
s,
t
he
ba
ck
ste
p
pi
ng
a
l
w
a
ys
s
h
o
w
s
b
etter
per
f
or
ma
nce,
i
.
e
,
lo
w
e
r
tor
que
r
ip
ple
a
nd
s
h
orte
r
acc
eler
at
ing
tim
e,
a
s
c
a
n
be
s
ee
n
i
n
F
i
g
u
r
e
7.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
7
20
–
7
3
0
72
8
F
i
gur
e
4
.
P
i
ctu
r
e
of ha
r
dwar
e HIL pla
t
f
o
rm
.
F
i
gur
e
5
.
Ma
g
n
et
i
z
ing
cur
r
en
t r
e
spo
n
se
F
i
gur
e
6.
S
p
ee
d
and
t
o
r
q
ue
r
espo
nses
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
Bac
k
s
t
ep
p
i
n
g
c
o
n
t
r
o
l
of t
w
o-m
a
ss
system
us
in
g i
n
d
u
c
t
i
o
n m
o
t
o
r dr
ive
f
e
d… (N
gu
yen
P
h
u
n
g
Q
u
a
ng)
72
9
(a)
(b)
F
i
gure
7
.
C
hart
of torq
ue
a
n
d
spe
e
d
r
espo
nse
s
, (a) torque
r
espo
nses,
(b)
s
peed
r
espo
nses
5.
CONCL
U
S
ION
I
n
t
h
i
s
paper
,
t
he
t
w
o
-m
ass
s
y
s
t
e
m
w
it
h
fle
x
i
b
l
e
c
ou
pl
i
n
g
s
c
om
p
rises
of
a
n
ind
u
c
t
i
o
n
m
o
tor
a
nd
a
loa
d
i
s
co
nsi
d
ere
d
.
A
t
t
he
m
ot
or
s
ide
,
t
he
c
urr
e
nt
r
esp
o
n
s
e
is
a
s
sum
e
d
to
b
e
ide
a
l
l
e
a
d
i
n
g
t
o
a
s
imp
l
i
f
ied
mode
l.
B
a
c
k
s
t
e
pp
i
ng
c
o
ntrol
is
e
mp
lo
ye
d
to
s
o
l
ve
f
lu
x
a
n
d
spe
e
d
c
o
n
t
ro
l
pro
b
l
e
m
o
f
t
he
s
ys
t
e
m.
T
he
s
ystem
ca
n
ope
ra
te
a
t
fie
l
d
w
e
a
k
e
n
in
g
r
e
g
i
on.
T
he
s
i
m
ula
t
i
on
re
su
lts
s
how
t
ha
t
high
d
y
n
am
ic
a
n
d
s
up
press
i
on
of
t
h
e
me
cha
n
ic
al osc
il
la
t
i
o
n
o
f t
h
e
d
r
ive
system
can
b
e a
c
hie
v
e
d
.
ACKNOW
LEDG
E
MEN
T
S
The
a
u
th
ors
w
o
u
l
d
like
t
o
t
han
k
s
I
n
sti
t
ut
e
for
C
o
nt
r
o
l
En
gine
er
i
n
g
a
n
d
A
u
tom
a
tio
n
of
H
a
N
o
i
Uni
v
ersi
ty o
f
Scie
nce
a
nd T
ech
nol
ogy
f
o
r
t
he
i
r
assi
st
an
ce
.
REFE
RENCES
[1]
J. Arellano-Padi
l
la,
G.
M
.
A
s
her
, and
M.
S
u
m
ner,
"
Control
o
f
a
dynam
o
m
e
t
e
r f
o
r
dyn
am
ic
e
m
u
l
a
ti
o
n
o
f
mech
ani
cal
loads w
ith
s
ti
ff
a
nd fl
e
xi
b
l
e
sha
f
ts,
"
IEEE
T
r
an
s. In
d. Ele
c
t
ro
n
, vo
l
.
5
3
(4
), p
p.
1
25
0–
12
60
, 20
0
6
.
[2]
Gh
azanf
e
r
Sh
ah
g
h
o
lian
,
J
aw
ad
F
aiz,
P
egah
S
h
a
f
a
g
h
i,
"
M
o
del
i
n
g
a
n
d
S
i
mulation
of
a
T
wo
-M
ass
Res
onan
t
S
ystem
with
S
peed
C
ont
r
oller,"
In
te
rna
tio
na
l J
o
ur
na
l o
f
In
fo
rma
tion
an
d
Ele
c
t
ron
i
c
s
En
g
i
n
e
e
r
ing
,
vo
l
.
3
(
5
),
S
e
pt
emb
e
r
20
13
.
[3]
Mattias
Nordin,
"
P
er-Ol
o
f
Gutman
C
ont
roll
i
n
g
mechanical
s
ys
t
e
ms
w
it
h
b
ackl
a
sh—a
s
u
r
vey,
"
A
u
to
ma
ti
c
a
,
v
o
l
.
3
8,
pp
.
1
633
–1
64
9,
200
2.
[4]
Y.
S
.
K
i
m,
S
.
B.
K
im,
J.
S
.
K
i
m,
C
.
H.
Y
oo
,
H.
J
.
Kim,"
Two
d
e
g
ree
o
f
f
reedo
m
s
peed
c
on
tro
l
o
f
in
du
c
tio
n
m
o
t
o
r
h
a
ving
two
ma
s
s
re
so
na
n
t
s
ys
te
m
,
"
IEEE
/IE
C
ON
,
vo
l. 2
, p
p
. 12
1
0
-
12
1
5
, Au
g
. 1
99
6.
[5]
K.
S
zab
at
a
nd
T
.
Orl
o
ws
ka-K
o
w
alsk
a,
"
V
i
b
r
ation
s
u
p
p
ressio
n
i
n
t
wo-
m
ass
drive
system
u
s
i
ng
P
I
spee
d
controller
and additional fe
edback
s— Comparati
ve study,
"
I
E
E
E
Tran
s.In
d.
Ele
c
t
ro
n
.,
v
o
l
.
54(2),
pp
.
11
93
–120
6,
2
00
7.
[6]
Karro
l
W
r
obel,
"F
u
zzy
adap
t
i
v
e co
ntro
l
of n
on
lin
e
ar t
wo-m
ass s
y
st
e
m
,"
Internation
a
l Journa
l
of
P
o
wer
E
l
ec
t
r
oni
c
s
an
d D
r
i
ve Sys
t
e
m
s
(
I
JPE
D
S)
,
vol.
1
(2),
R
etri
eved
from
DO
I:1
0
.
5
2
7
7/
PED1
60
208,
S
ep
tem
b
er
201
6.
[7]
K
.
E
r
e
n
t
ur
k
,
"
N
o
n
l
i
n
e
a
r
tw
o
-
ma
ss
s
ys
te
m
c
o
n
t
r
o
l
w
i
th
s
l
i
d
i
n
g
m
o
d
e
and
o
p
t
i
mis
e
d
pro
p
o
r
ti
onal
-
in
teg
r
al
d
eri
v
ati
v
e
c
o
ntrol
l
e
r
c
omb
i
n
e
d with
a
g
re
y
e
s
ti
ma
tor
,
"
Cont
rol Theory
&
Ap
plicati
ons,
IE
T
, v
ol
.
2
(
7),
p
p
.
635–6
42
,
J
u
l
y
2
008.
[8]
S
.
T
hom
sen,
F
.
W.
F
u
c
hs,
"Des
ig
n
and
anal
ys
is
o
f
a
f
l
at
ness-b
a
s
ed
c
on
trol
a
p
p
ro
a
c
h
f
o
r
sp
eed
c
ont
rol
o
f
d
ri
ve
sy
st
e
m
s
wit
h
e
lastic
c
ou
pl
ings
a
nd
u
ncertai
n
l
oad
s
,
"
Pro
ceedi
n
g
s
of
th
e 2
011
1
4
t
h
Eu
rop
e
an
Co
nfer
ence
on
Po
we
r
El
ectron
i
cs
and
Applicat
ions
. 20
0
1
.
[9]
Em
re
S
ari
y
ildi
z
,
Haoy
on
g
Y
u
,
Tak
a
hiro
N
ozaki
,
T
os
h
i
yuk
i
M
u
rakam
i,
"
Ro
bu
st
V
ibra
t
i
o
n
Co
nt
rol
of
T
wo
-
M
a
s
s
Reso
nant
S
y
s
te
m
s
in Stat
e S
p
ace,"
IE
EE Ad
v
a
nced
M
o
ti
on Contro
l
April
22-2
4
,
A
u
c
klan
d
N
e
w Z
ealan
d,
2
01
6.
[10]
Jacek
K
abziń
s
k
i
,
P
r
zem
ysław
Mo
siolek
,
"
A
dapt
iv
e
Co
nt
rol
of
T
wo
-
M
a
s
s
D
ri
ve
S
ys
te
m
wit
h
N
onl
in
ear
S
t
i
ff
ness,
"
Pr
zeglad
El
ektr
o
t
echni
czn
y
,
ISSN
003
3-2
0
9
7
,
R.
9
4
NR
3
/2
01
8,
doi
:1
0
.
1
5
1
9
9
/
4
8
.
2
01
8.
0
3
.
0
9
,
S
e
p
t
em
b
e
r
20
16.
[11]
R.
G
un
abal
a
n
,
V.
S
ub
b
i
ah
,
"
S
p
eed
S
en
so
rless
V
ecto
r
C
on
trol
o
f
I
ndu
cti
o
n
M
o
t
o
r
Dri
v
e
wit
h
P
I
an
d
F
u
zzy
Controller,"
Interna
t
i
o
n
a
l Jou
r
nal
of
Po
wer
Electr
onics
a
nd
Drive
Sys
t
em (
I
J
P
ED
S),
vol.
5(3
)
,
p
p
.
3
15-3
2
5
,
I
S
S
N
:
20
88
-869
4,
F
ebruary
20
15
.
[12]
N.
P
.
Quan
g
and
J
.
-A.
D
itt
rich
,
"Vect
or
c
ont
rol
o
f
t
hree-ph
ase
AC
m
ach
in
es
-
S
ys
tem
devel
o
p
m
e
n
t
in
t
he
p
ract
ice,
2nd edition
, "Sp
ri
nger, 2015.
[13]
Ng
uy
en
P
hu
ng
Q
u
a
ng
,
Vo
T
h
a
nh
H
a,
T
ran
V
u
T
run
g
,
"A
n
ew
c
o
n
t
r
ol
design
w
ith
d
ead
-beat
b
eh
avio
r
f
o
r
stator
curren
t
v
ecto
r
i
n
three
ph
ase
AC
d
riv
e
,"
SS
RG In
tern
atio
na
l
J
o
ur
na
l
o
f
El
ectrica
l a
n
d
Elect
ro
n
i
cs
E
ngineer
ing
(
SSRG-IJEEE),
vo
l.
5
(4
),
I
S
S
N:23
49-9
1
7
6
,
Apr
20
18.
[14]
M
i
rh
a
m
ed
M
ola,
A
lireza
Kh
a
y
a
t
i
a
n,
M
aryam
D
e
hg
han
i
,
"Ba
c
k
s
t
e
pp
in
g
P
o
siti
on
Co
ntro
l
o
f
T
wo-M
ass
Sy
st
ems
with
U
n
known
,
"
IE
E
E
9
78
-1-4673
-57
6
9
-
2
/
1
3
/
$31.
0
0
©
20
13
.
[15]
M
a
rou
a
n
e
E
l
Azzaou
i
,
Has
s
an
e
M
a
hm
o
udi,
d
K
a
rim
a
B
oud
araia,
"
Bac
k
s
t
e
ppi
ng
C
o
n
tro
l
o
f
Wind
a
nd
P
h
o
to
vo
lt
aic
Hy
brid
R
en
ewab
le
E
nerg
y
S
y
stem
,"
In
tern
atio
n
a
l Jour
nal o
f
P
o
wer El
ectr
oni
cs
an
d Drive Syst
ems
(
I
JPEDS)
,
vol
.
7(3
)
,
p
p
.
6
77
-686,
S
eptem
b
er
2
0
1
6.
10.
52
6.
5
0
5
10
15
Ripp
le
t
or
qu
e
(
%
)
PI
c
ontrol
Ba
ck
st
e
p
pi
ng
co
n
t
r
o
l
0.
5
0.
7
0.
2
0.
25
0
0.
2
0.
4
0.
6
0.
8
A
ccele
r
a
tin
g
time (s)
Re
v
e
r
s
e
t
i
m
e (
s
)
PI
C
on
tro
l
B
a
c
k
s
t
ep
pi
ng
c
o
n
t
ro
l
Evaluation Warning : The document was created with Spire.PDF for Python.