TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4536 ~ 4
5
4
2
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.539
4
4536
Re
cei
v
ed
De
cem
ber 2
7
, 2013; Re
vi
sed
F
ebruary 24,
2014; Accept
ed March 1
0
, 2014
Resear
ch on Backlash Nonlinearity in
AC Servo-driven
Precision Transmissio
n
System
Wei Zhou, Ling Zhao, Xiaolun Li*, Lihong Lin
Coll
eg
e of Mechan
ical En
gi
ne
erin
g Cho
n
g
q
in
g Univ
ersit
y
, C
hon
gqi
ng, Ch
in
a, 4000
30
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:ling
x
i6
856
@1
63.com
A
b
st
r
a
ct
AC servo-
driv
en pr
ecisi
on t
r
ans
missi
on s
ystem
is
mai
n
ly co
mpose
d
of AC servo
motor
,
mec
h
a
n
ica
l
tra
n
smissio
n
p
a
rts and co
ntrol
parts. Be
caus
e of mutual c
oup
lin
g betw
e
en vari
ous p
a
r
t
s,
particularly transmission system
in
m
e
c
h
anical coupling v
i
brati
on i
n
non-
sm
ooth trans
ition, it w
ill be
of
great h
a
r
m
to safe op
eratio
n
of the system. This
pap
er made s
o
me ov
e
r
view
and
bui
lt the mod
e
l of
A
C
servo-driv
en
precision transm
i
ss
ion system mainly
fr
om the
pers
pective
of backlas
h nonlinear
character
i
stic
and
w
i
th si
mul
a
tion
too
l
of
Matlab/Si
muli
n
k
to a
n
a
l
y
z
e
t
he
influ
enc
e
o
f
backl
ash
on
the
precision
of servo system
, and then
corres
p
onding sim
u
lation curv
e and
conclusions were shown in this
pap
er. Do ho
p
e
the w
o
rk abo
ve w
ill have ce
rtain refere
nce
signific
anc
e to actual e
n
g
i
ne
e
r
ing a
ppl
icati
o
n
.
Ke
y
w
ords
:
AC
servo-driv
en p
r
ecisio
n trans
mission syste
m
,
backl
ash, no
nli
near
ity
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Curre
n
tly, electro
m
e
c
ha
ni
cal syste
m
is developi
ng
toward
s co
mplex, preci
s
ion an
d
miniaturi
z
atio
n. Resea
r
ch on these cou
p
ling p
r
o
c
e
s
s and e
s
tabli
s
hment of dyn
a
mic mo
del i
s
indispen
sabl
e
for
con
d
ition
dete
c
tion, d
e
sig
n
of
syst
em pa
ram
e
te
rs, o
p
timization a
nalysi
s
a
nd
fault diagno
sis of electro
m
ech
ani
cal system. At
th
e same time
, AC servo-d
r
iven pre
c
i
s
i
o
n
transmissio
n system i
s
wi
dely use
d
in
electrome
c
h
a
n
ical
system
s. It is nece
s
sary to study i
t
s
electrome
c
h
a
n
ical co
uplin
g
proce
s
s. In
pro
duc
tio
n
practi
ce, there are a
l
ways sin
gul
ar
con
d
ition
s
, e
v
en produ
ctio
n a
c
cura
cy i
s
se
riou
sly
aff
e
cted
[1]. For example, in
servo
sy
stem
o
f
pre
c
isi
on tra
n
smi
ssi
on
d
e
vice, me
ch
anical ha
rmo
n
ic vib
r
ation
and t
r
an
sm
issi
on
clea
ra
nce
nonlin
ear fa
ctors
will affect the stea
d
y
state
and dynamic ch
a
r
acte
ri
stics
o
f
servo syst
em
,
thereby
red
u
c
ing
the p
r
e
c
isi
on of
system [2]. In addition, the
ele
c
trom
ech
anical coupli
n
g
vibration
of AC
servo
sy
stem in
nonli
n
ear process has
a
g
r
e
a
t
i
n
fluen
ce o
n
safety of
syst
em.
Therefore,
an
alysis of the i
m
pact
of ele
c
trome
c
h
a
n
i
cal s
e
r
v
o
s
y
s
t
em fa
c
t
or
s o
n
th
e
pe
r
f
or
ma
nc
e
of system is o
f
great signifi
can
c
e.
In
the are
a
s of high runni
ng accu
ra
cy require
me
nts of system, su
ch as
servo p
r
eci
s
io
n
drive
system
s, ba
ckla
sh
n
online
a
rity ha
s b
een
on
e o
f
the mai
n
di
rection
s
of research. A
s
e
a
rly
as the
194
0
s
, there were so
me p
e
o
p
le who b
e
g
an to research the
probl
em of ba
ckl
a
sh
nonlin
ear
con
t
rol. Even now it also attracts mu
ch
at
tention. For e
x
ample, som
e
schola
r
s h
a
ve
studie
d
the effect of backla
s
h
on dyn
a
mi
cs of the enti
r
e sy
stem
on
the conditio
n
of friction an
d
time-varying
mesh
stiffness [3]. Some schol
ar
s al
so
have sim
u
lat
ed and
analy
z
ed th
e influe
nce
of backla
s
h
on the preci
s
ion of
rad
a
r
servo
syste
m
[4]. Besides,
some
schol
ars
have ma
de
some
pr
act
i
c
e
re
sea
r
ch i
n
wo
rk
sh
op.
S
o
me
of th
em stu
d
ied t
he o
c
curren
ce of ba
ckl
ash
phen
omen
a
at the me
ch
a
n
ical t
r
an
smi
ssi
on
system
and th
e effect
s of th
ese
ma
lfunction
s in
the
electri
c
al e
q
u
ipment in
ceme
nt indu
stry
[5], some studie
d
servo pn
e
u
matic a
c
tu
ators
con
s
id
erin
g the effect of servo valve ba
ckl
ash zo
ne [6]. This pap
e
r
mainly studi
es the influe
n
c
e
of backla
s
h o
n
the pre
c
isi
o
n of system, whi
c
h
reve
als the influence
mecha
n
ism of servo sy
st
em
pre
c
isi
on, it plays an impo
rt
ant role in
im
proving ove
r
a
ll perform
an
ce of system.
2. An Ov
er
v
i
e
w
of AC Se
r
v
o-driv
en Precision Tra
n
smission Sy
stem
AC se
rvo-d
r
iven pre
c
i
s
ion tran
smi
ssi
on system
which
is comp
osed
of AC servo motor,
pre
c
isi
on d
r
iv
e syste
m
, co
ntrol
system,
load
sy
stem
and oth
e
r
subsy
s
tems, i
s
on
e of typi
cal
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Backl
ash No
nlinea
rity in A
C
Servo-dri
v
e
n
Preci
s
io
n Tran
sm
issi
on
… (Wei Zhou
)
4537
compl
e
x ele
c
trome
c
ha
nica
l syste
m
s an
d sho
w
n i
n
F
i
gure
1. In
th
e compl
e
x el
ectro
m
e
c
ha
ni
cal
system
s, there are th
ree f
o
rm
s
of ele
c
t
r
ome
c
h
ani
cal
cou
p
ling a
s
follows: drive
sou
r
ce coupl
ed
to strong ele
c
trom
agn
etic fields and tran
smi
ssi
on control varia
b
les an
d me
cha
n
ical micro-
electrome
c
h
a
n
ical
cou
p
lin
g body mov
e
ment, and
external loa
d
coupli
ng wh
ich affect
s m
a
in
motion. In
order to b
e
tter
study m
u
tual
co
uplin
g p
h
enome
non
of
se
rvo
pre
c
i
s
i
on d
r
ive
syst
em
betwe
en vari
ous
sub
s
yste
ms, se
rvo mo
tor can b
e
si
mplified into one of output
torque, nam
ely T
PTO ba
sed
o
n
co
uplin
g di
agra
m
of the
analysi
s
. And
gea
r tran
smi
ssi
on i
s
the
most
comm
o
n
ly
use
d
in the
e
l
ectri
c
al
syste
m
drive, in
clu
d
ing
o
r
din
a
ry
gea
r, plan
etary ge
ar train
,
and ha
rmo
n
i
c
gear d
r
ive, worm
wh
eel a
nd
WO
RM-drive, and
so
o
n
. In gen
eral, these d
r
ive
device
s
can
be
simplified a
s
a spri
ng
-ma
s
s-d
a
mp
er sy
stem.
Figu
re 1.
Electrical System Couplin
g Diag
ram
There are 3
main aspe
cts of servo sy
stem
perfo
rma
n
ce, na
mely stability
,
spe
e
d
and
accuracy
, an
d its main ch
ara
c
teri
stic in
dexes ar
e preci
s
ion, stabil
i
ty and respo
n
se spee
d. The
basi
c
requirements of
AC servo
sy
stem
s are
shown
as follows: Fi
rs
t, it is good stability. Under
the condition
of a given
inp
u
t and i
n
terfe
r
en
ce, Se
rvo system ca
n
reach
a
ne
w e
quilibri
um
sta
t
e,
or return to t
he ori
g
inal
eq
uilibriu
m
stat
e after
sho
r
t tran
sition p
r
o
c
ess. Goo
d
st
ability and ful
l
of
stability marg
in is the p
r
e
r
equi
site for reliable o
pera
t
ion of se
rvo
system
. Second, it is hig
h
pre
c
isi
on.
A
c
cur
a
cy
of
se
r
v
o sy
st
e
m
re
f
e
rs
t
o
the
d
egre
e
of p
r
e
c
isi
on
of o
u
tput follo
ws in
put,
whi
c
h i
s
also the indi
cat
o
r of stati
c
cha
r
a
c
te
ri
stic and dyn
a
mi
c characte
ri
stic of syste
m
is
excelle
nt or n
o
t. Third, it is fast dynami
c
re
s
pon
se. T
hat is fa
st re
spo
n
se an
d small oversh
o
o
t.
Quick
re
spo
n
s
e i
s
an im
p
o
rtant
sign
o
f
servo
sy
ste
m
dynami
c
quality, whi
c
h re
qui
res th
a
t
transitio
n time is sh
ort while trackin
g
comm
and
si
gnal, and ov
ershoot is
small whe
n
speed
cha
nge
s, an
d
whe
n
loa
d
chang
es
su
dd
enly, the c
lim
bing
rate of transi
ent p
r
oce
ss
mu
st be bi
g,
recovery time
must be short, and it must be with no
n o
scill
ation.
2. Modeling of AC Serv
o-driv
en Precision Transm
ission Sy
ste
m
There are m
o
re an
d more research o
n
the modeli
ng of compl
e
x electrom
e
c
ha
nical
system
s,
a
n
d
also have m
ade so
me valuable rese
arch re
sult
s [7, 8]. For the
conve
n
ien
c
e
of
study, the el
ectro
m
e
c
ha
ni
cal
system m
odel can
b
e
simplified as mass-sp
r
ing
-
dampin
g
sy
stem
driven by AC
motor. The
si
mplified mod
e
l is sh
own in
Figure 2.
Figure 2. Electrom
echani
cal Cou
p
ling M
odel of
AC Servo-driven P
r
eci
s
io
n Tra
n
s
missio
n
Sys
t
em
The figu
re a
bove is
a si
mplified multi
-
deg
re
e of freedom
syste
m
of "Qualit
y-sp
ring
-
dampe
r" d
r
iven by
AC m
o
tor
.
Ultim
a
tely
, a se
rvo motor-preci
s
i
on
tran
smi
ssion-lo
ad syst
em
electrome
c
h
a
n
ical coupli
n
g
model is buil
t. In
the figure,
T
m
is output torque of servo moto
r
,
θ
m
is the angl
e of the drive shaft,
θ
L
is the angl
e of the load
shaft
,
B
m
an
d
B
L
is respectively
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4536 – 4
542
4538
visco
us d
a
m
p
ing co
ef
ficie
n
t of the driving whe
e
l and
the driven g
ear
,
J
m
an
d
J
L
is
r
e
s
p
ec
tive
l
y
equivalent in
ertia of drive
shaft and the
load shaft,
T
L
is the load torqu
e
,
K
is torsional stif
fness
coef
fici
ent of
drive shaft
，
is the twist angle of drive shaft
，
i
is the
transmi
ssi
on
ratio of
th
e
gear train.
Acco
rdi
ng to
Figure 2, bal
ance eq
uatio
ns of
the
syst
em input
shaf
t can b
e
ded
uce
d
by
dynamic p
r
in
ciple of me
ch
anical system
:
2
mm
m
2
()
TJ
B
K
m
m
dt
dt
dt
dt
(1)
mL
-i
(2)
The bala
n
ced
equation of the output sha
ft shows as fo
llows
：
2
LL
L
2
()
()
ik
J
B
T
LL
dt
d
t
dt
d
t
(3)
Lapla
c
e tra
n
sform of formu
l
a (1) a
nd (3
)
above can ob
tain:
2
mm
m
T(
)
J
s
(
)
B
s
(
)
k
mm
ss
s
(4)
2
LL
L
i k
J
s
(
)
B
S
(
)
T
(
)
LL
s
ss
(5)
The equival
e
nt inertia ca
n be define
d
as follows:
ei
2
1
JJ
J
L
i
(6)
Equivalent da
mping coeffici
ent is:
m
eL
2
1
BB
B
i
(7)
The tran
sfer
function of lo
ad port spee
d can
be d
e
duced from f
o
rmul
a (1
)~(7), and sho
w
s as
follows
:
2
L
22
1
()
1
(
)
(
)
s
1
mm
m
L
L
LL
m
m
L
m
L
iT
s
J
s
B
s
T
s
K
J
SB
J
S
B
S
i
J
J
S
i
B
B
K
（）
(8)
In addition, as syn
c
h
r
on
ous moto
r ro
tor pol
e axis and D-Axis coinci
de
s, the motor
current initial
phase angle i
s
90
o
,
na
me
ly
i
d
=0
,
thereb
y achievin
g
D and
Q axi
s
u
n
co
uple
d
in t
h
e
magneti
c
field orientatio
n of the vecto
r-control
method. The voltage
of motor and
electroma
gne
tic torque
can
be expre
s
se
d as:
qs
q
q
UR
i
L
q
f
di
dt
(9)
en
f
q
TP
i
(10)
Control blo
ck
diagram of el
ectro
m
e
c
ha
ni
cal
coupli
ng system driven
by AC motor
can b
e
dedu
ce
d from
(8)~(1
0), an
d
sho
w
s a
s
Fig
u
re 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Backl
ash No
nlinea
rity in A
C
Servo-dri
v
e
n
Preci
s
io
n Tran
sm
issi
on
… (Wei Zhou
)
4539
1
qs
L
sR
m
K
1
mm
J
sB
1
s
k
1
L
L
J
sB
1
s
()
m
Ts
()
m
s
()
m
s
()
ms
s
i
L
T
L
()
L
s
()
d
Us
Figure 2. Electrom
echani
cal Cou
p
ling Cont
rol Blo
ck
Diag
ram of Servo System
At the s
a
me time, s
i
mulink
dynamic
c
h
arts
of servo
system can
be i
n
ferred from
Figure
2 and sho
w
s
as Figu
re 3.
Figure 3. Simulink Simul
a
tion Model of
Servo Syste
m
3. Effec
t
s of
Bac
k
lash on
AC Serv
o-driv
en Precision Transmis
sion Sy
stem
Backl
ash no
n
linearity wi
del
y exists in th
e pr
e
c
i
s
ion g
ear d
r
ive sy
stem, and mo
stly the
clea
ran
c
e fa
ctor is i
nevitab
le be
cau
s
e
of the lim
it of p
r
ocessin
g
. Ta
king th
e preci
s
ion
gea
r d
r
ive
as the
examp
l
e, its meshin
g dra
w
in
g is
sho
w
n in
Fig
u
re 4. In the f
i
gure,
in
is the a
ngle of d
r
ive
s
haft,
ou
t
is the angle of moving shaft, and
is the an
gle of
Backl
ash. If there i
s
no
ba
ckl
ash in
the tran
smi
s
sion
chain, t
hen th
e relat
i
onship
b
e
tween in
put a
n
gle an
d o
u
tp
ut angle
will
be
linear, ju
st sh
own in Fig
u
re
5.
out
in
2
ou
t
in
0
Figure 4. Dia
g
ram of Me
sh
ing with Backl
a
sh
Figure 5. Rel
a
tionship bet
wee
n
Input a
nd
Output without Bac
k
l
as
h
Ou
t
1
1
T
r
ans
f
e
r
F
c
n
3
1
den
(s
)
Tr
a
n
s
f
e
r
F
c
n
2
1
Jm
.
s
+
B
m
T
r
ans
f
e
r
F
c
n
1
1
Lq
.
s
+
R
s
I
n
t
egr
at
or
2
1
s
I
n
t
egr
at
or
1
1
s
Gai
n
4
km
Ga
i
n
3
i
Ga
i
n
2
k1
Ga
i
n
1
K
Ga
i
n
Km
C
ons
t
ant
1
In
1
1
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4536 – 4
542
4540
Ho
wever, i
n
t
he mo
st
situ
ations,
ba
ckl
ash
al
ways
e
x
ists in
the transmi
ssion
chain. In
this o
c
ca
sion,
if the
rotated
angl
e of
driv
e shaft is
, the driven
shaft
will
not rotate. Only
when
the rotate
d a
ngle
of drive
shaft i
s
g
r
eat
er tha
n
,
the
driven s
haft will
rotate with drive s
haft
as
the relation
ship
sho
w
n
in
Figu
re
5.
When th
e
dr
ive
sh
aft rotat
e
s in
reve
rse, the d
r
iven
sh
aft
can
not follo
w immediately.
Only wh
en t
he ro
tate
d an
gle of d
r
ive shaft is g
r
eate
r
than
2
, the
driven
shaft will rotate wi
th drive
shaf
t in reve
rse. In the serv
o system, backlash i
s
of
ten
c
o
ns
idered to loc
a
te after the motor.
Output
ba
ckl
ash n
on-li
ne
ar sy
stem structure sh
own in
Figure 6.
Figure 6. System Block
Di
agra
m
of Backla
sh Nonline
a
rity on the O
u
tput Termin
al
Backl
ash n
o
n
linearity i
s
ca
use
d
by t
r
an
smissi
o
n
g
a
p
,
mainly o
c
cu
rre
d in
the
re
versin
g
and the sta
r
t time of servo
device, an
d the gap
will
affect accu
ra
cy and vibratio
n cha
r
a
c
teri
stic of
s
e
rvo s
y
s
t
em [9, 10]. Back
las
h
nonlinearity effe
cts
on outp
u
t m
a
inly in reversing tim
e
an
d it
woul
d ca
use output lag
s
. Simulation m
odel of Back
l
a
sh n
onlin
earity is sho
w
n i
n
Figure 7, a
nd
corre
s
p
ondin
g
simulatio
n
curve is
sho
w
n
in Figure 8.
Figure 7. Simulation Mod
e
l
of Cleara
n
ce
Nonli
nea
rity
Figure 8. Simulation Curve
of Cleara
n
ce
Nonli
nea
rity
Backl
ash ch
a
r
acte
ri
stics of simulation m
odel of
se
rvo pre
c
isi
on driv
e system is
shown in
Figure 9.
In
orde
r to
see
re
sp
on
se ti
me mo
re
int
u
itively, it is
rea
s
on
able
t
o
set
step
si
gnal
module
(i
e, t
he figu
re
ste
p
mo
dule
)
a
nd
step
time
of 0.5s. And other pa
ra
meters set a
s
follows
：
L
q
= 8.5mh, R
s
=0.1
Ω
, K
m
=0.5, J
m
=20kg·
m
2
, B
m
=B
L
=0.05, K=5N/
mm, i=1.8, J
L
=5
kg·m
2
, k
1
=1.
Figure 9. System Simulation Model of Cl
eara
n
ce No
nl
inearity
0
2
4
6
8
10
-1
.
5
-1
-0
.
5
0
0.
5
1
1.
5
t/
s
v1
/
v
2
v1
v2
T
r
ans
f
e
r
F
c
n
3
1
JL
.
s
+
B
L
Tr
a
n
s
f
e
r
F
c
n
2
1
Jm
.
s
+
B
m
Tr
a
n
s
f
e
r
F
c
n
1
1
Lq
.
s
+
R
s
Ste
p
Sc
o
p
e
I
n
t
e
gr
at
o
r
2
1
s
In
t
e
g
r
a
t
o
r
1
1
s
Gai
n
4
km
Gai
n
3
i
Ga
i
n
2
k1
Ga
i
n
1
K
Gai
n
Km
Co
n
s
t
a
n
t
1
Ba
c
k
l
a
s
h
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TELKOM
NIKA
ISSN:
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046
Re
sea
r
ch on
Backl
ash No
nlinea
rity in A
C
Servo-dri
v
e
n
Preci
s
io
n Tran
sm
issi
on
… (Wei Zhou
)
4541
Backl
ash n
o
n
linea
rity ha
s a
hug
e i
m
pact
on
system a
c
curacy a
nd vi
bration
cha
r
a
c
teri
stics. In this paper, the impact of
Backlash
nonlin
earity on the perform
ance of syste
m
will be shown by modifying the data
of Backlash. The
simulation re
sults of different Backl
ash are
sho
w
n in Fig
u
re 10
~ 12.
Figure 10. System Resp
on
se Curve a
s
the
Value of Backla
sh is 0.0
0
0
1
Figure 11. System Resp
on
se Curve a
s
the
Value of Backla
sh is 0.0
0
1
Figure 12. System Resp
on
se Curve a
s
the Value of Backla
sh is 0.0
1
4. Conclusio
n
This p
ape
r
has a
nalyze
d the mode
ling method
of AC servo-drive
n
preci
s
ion
transmissio
n system.
AC servo-driven p
r
eci
s
io
n
tra
n
smissi
on
syste
m
wa
s de
co
mposed into t
w
o
parts of ele
c
trical net
works and me
cha
n
i
c
al net
wo
rk. Variou
s pa
rts of kinetic mo
dels
were set
up
by electrom
a
gnetic an
d mech
ani
cal system dy
namics and dynam
ic model of AC se
rvo-d
r
i
v
en
pre
c
isi
on tra
n
s
missio
n sy
stem wa
s e
s
ta
blish
ed by
co
upling of the
para
m
eters.
Finally, several
simulatio
n
s
were mad
e
by Matlab/simulin
k
tool
and analy
z
ed the imp
a
ct of Backl
a
sh
nonlin
earity
on sy
stem p
e
rform
a
n
c
e,
with the
follo
wing
co
ncl
u
sions: the
uni
t step respo
n
se
increa
se
s a
s
the gap
ad
ds. When
the g
ap rea
c
he
s a
ce
rtain valu
e, Step Re
sp
onse ove
r
sho
o
t
increa
se
s. It mean
s that,
becau
se of t
he a
c
tion
of the cl
osed lo
o
p
co
rrectio
n
,
small
cle
a
ra
n
c
e
will only ca
use lag, and ha
ve little influence o
n
outpu
t preci
s
ion.
With the increa
sing of ga
p, the
system
will
have a
g
r
ea
ter
cha
nge
of accu
ra
cy, vibratio
n
wi
ll incre
a
se,
and th
e
syst
em
overshoot in
crea
se
s, thus
will a
ffect system stability and accu
ra
cy.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
t/s
X1
/
X
2
/
(
μ
m)
b
a
c
k
l
a
s
h
=
0
.
0001
x1
x2
0
0.1
0.
2
0.
3
0.4
0.
5
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
t/s
（）
X1
/
X
2
/
μ
m
b
a
ch
l
a
sh
=
0
.
0
0
1
x1
x2
0
0.
1
0.
2
0.
3
0.
4
0.
5
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
1.
6
t/s
x1
/x
2
/
(
μ
m)
ba
c
k
l
a
s
h
=
0
.
0
1
x1
x2
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ISSN: 23
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TELKOM
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Vol. 12, No. 6, June 20
14: 4536 – 4
542
4542
Ackn
o
w
l
e
dg
ements
The
autho
rs ackn
owl
edg
e the
supp
o
r
t prov
ided
by
the Natio
nal Natu
ral Scien
c
e
Found
ation
(
5
1005
254
) an
d Do
ctoral Progra
m
Foun
d
a
ti
on of Institutions of Hi
g
her Edu
c
atio
n of
Chin
a(2
010
0
1911
2000
7).
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ces
[1]
Dord
ea T
,
Munteanu
R, Camp
ean
u A.
Mode
li
ng a
nd Si
mulat
i
on of AC M
a
c
h
in
es Beh
a
vi
or in Dyn
a
mi
c
Operatio
n Criti
c
al Ana
l
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Advanc
ed El
e
c
tromecha
nica
l
Motion S
y
ste
m
s & Electric Drives Joi
n
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osi
u
m. 2009: 1-8.
[2]
Hua
b
in
g Yi
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ing
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hou.
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h
e
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d
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ototypin
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i
t
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in
ear Gea
r
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yu Ch
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n
y
u
an T
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