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l J
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E
lect
rica
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(
I
J
E
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)
Vo
l.
7
,
No
.
3
,
J
u
n
e
201
7
,
p
p
.
1506
~
1
5
1
2
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
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1512
1506
J
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h
ttp
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m
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g
ti
m
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.
K
ey
w
o
r
d
:
A
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u
ato
r
P
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elec
tr
ic
S
y
s
te
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id
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ti
f
icatio
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2
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1
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In
stit
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te o
f
A
d
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E
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g
a
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S
c
ien
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e
.
Al
l
rig
h
ts
re
se
rv
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d
.
C
o
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s
p
o
nd
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A
uth
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r
:
Nu
r
u
l B
a
h
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Mo
h
d
No
o
r
,
Dep
ar
t
m
en
t o
f
C
o
n
tr
o
l a
n
d
Me
ch
atr
o
n
ics E
n
g
in
ee
r
i
n
g
,
Facu
lt
y
o
f
E
lectr
ical
E
n
g
in
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r
in
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,
Un
i
v
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s
iti T
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E
m
ail:
n
u
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lb
ah
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m
n
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@
g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
P
iezo
elec
tr
icity
f
r
o
m
th
e
Gr
ee
k
w
o
r
d
,
p
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o
r
p
iezin
m
ea
n
s
p
r
ess
u
r
e
elec
tr
icit
y
w
a
s
fi
r
s
t
d
is
co
v
er
ed
b
y
J
.
an
d
P
.
C
u
r
ie
in
1
8
8
0
in
q
u
ar
tz
cr
y
s
tal.
P
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elec
tr
icit
y
i
s
a
f
u
n
d
a
m
e
n
tal
p
r
o
ce
s
s
in
elec
tr
o
m
ec
h
an
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y
co
n
v
er
s
io
n
i
n
ce
r
tain
cr
y
s
talli
n
e
m
ater
ials
[
1
]
.
T
h
ese
cr
y
s
talli
n
e
m
ater
ial
s
tu
r
n
o
u
t
to
b
e
elec
tr
ically
p
o
lar
ized
w
h
e
n
s
u
b
j
ec
ted
to
m
ec
h
a
n
ical
s
tr
es
s
a
n
d
co
n
v
er
s
el
y
c
h
an
g
e
s
h
ap
e
i
n
t
h
e
p
r
ese
n
ce
o
f
elec
tr
ic
fi
eld
.
So
o
n
a
f
ter
,
it
w
as
d
is
co
v
er
ed
th
at
m
ater
ial
s
s
h
o
w
ed
d
e
f
o
r
m
atio
n
a
s
elec
tr
ical
s
i
g
n
al
i
s
ap
p
lied
p
r
esen
ted
f
o
r
ac
tu
ato
r
s
m
ater
ia
l.
P
iezo
elec
tr
ic
ac
tu
ato
r
s
ar
e
s
m
ar
t
m
a
ter
ial
d
ev
ices
b
ec
o
m
e
co
m
p
etiti
v
e
ch
o
i
ce
s
f
o
r
m
icr
o
ap
p
licatio
n
s
[
2
]
.
P
iezo
elec
tr
i
c
ac
tu
ato
r
s
h
av
e
b
ee
n
i
n
cr
ea
s
in
g
l
y
u
s
ed
b
ec
au
s
e
o
f
h
i
g
h
s
tiff
n
es
s
,
h
i
g
h
r
eso
lu
tio
n
,
f
a
s
t
r
esp
o
n
s
e,
n
o
m
ag
n
etic
fi
eld
a
n
d
h
i
g
h
p
r
ec
is
io
n
[
3
]
-
[
4
]
.
A
s
an
e
x
a
m
p
le,
p
i
ez
o
elec
tr
ic
ac
tu
ato
r
is
u
s
ed
in
ato
m
ic
f
o
r
ce
m
icr
o
s
co
p
y
(
A
FM)
a
n
d
s
ca
n
n
i
n
g
p
r
o
b
e
m
icr
o
s
co
p
y
(
SP
M)
f
o
r
m
i
cr
o
an
d
n
an
o
s
ca
le
s
ap
p
licatio
n
s
[
3
]
.
T
h
ey
ar
e
al
s
o
w
id
el
y
u
s
ed
i
n
m
ec
h
atr
o
n
i
c
ap
p
licatio
n
s
s
u
c
h
as
ca
r
f
u
el
in
j
ec
to
r
,
m
ed
ical
s
u
r
g
er
y
eq
u
ip
m
e
n
t
a
n
d
ac
tiv
e
v
ib
r
atio
n
co
n
tr
o
l
[
5
]
.
Nev
er
th
eles
s
,
p
iezo
elec
tr
ic
ac
tu
ato
r
s
r
ev
ea
l
u
n
d
es
ir
ab
l
e
d
is
p
lace
m
e
n
t b
eh
a
v
io
r
th
at
li
m
it
s
th
e
ac
c
u
r
ac
y
a
n
d
s
tab
ilit
y
o
f
th
e
ac
t
u
ato
r
s
.
T
h
e
m
aj
o
r
is
s
u
e
s
ar
e:
i.
H
y
s
ter
e
s
is
:
T
h
e
s
y
s
te
m
h
as
d
i
f
f
er
en
t
o
u
tp
u
t
w
it
h
t
h
e
s
a
m
e
i
n
p
u
t
ap
p
lied
to
p
iezo
elec
tr
ic
ac
tu
ato
r
.
T
h
e
er
r
o
r
g
en
er
ates
1
0
-
15
%
er
r
o
r
u
n
d
er
o
p
en
-
lo
o
p
v
o
lta
g
e
co
n
tr
o
l.
T
h
o
u
g
h
,
th
e
er
r
o
r
r
ea
ch
es
3
5
%
w
h
e
n
th
e
f
r
eq
u
e
n
c
y
o
f
t
h
e
in
p
u
t si
g
n
al
is
in
cr
ea
s
ed
[
6
]
.
ii.
C
r
ee
p
: T
h
e
am
p
lit
u
d
e
o
f
d
is
p
l
ac
e
m
en
t o
u
tp
u
t i
s
ch
a
n
g
e
o
v
er
ti
m
e
at
co
n
s
tan
t in
p
u
t v
o
lta
g
e
s
ig
n
al
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
Mo
d
elin
g
th
e
V
ib
r
a
tio
n
a
l D
yn
a
mics o
f P
iezo
elec
tr
ic
A
ctu
a
to
r
b
y
S
ystem
....
(
N
u
r
u
l B
a
h
ia
h
Mo
h
d
N
o
o
r
)
1507
iii.
R
esid
u
al
v
ib
r
atio
n
:
T
h
e
ac
tu
ato
r
v
ib
r
ates
b
ef
o
r
e
r
ea
ch
s
tead
y
s
tate
o
r
fin
al
p
o
s
itio
n
.
T
h
is
is
d
u
e
to
m
ec
h
a
n
ical
p
r
o
p
er
ties
s
u
c
h
as
m
as
s
,
s
ti
f
f
n
e
s
s
a
n
d
d
a
m
p
in
g
[
8
]
.
T
h
e
h
y
s
ter
esis
b
e
h
av
io
r
i
n
p
iezo
elec
tr
ic
ac
tu
ato
r
ca
u
s
e
s
i
n
ac
cu
r
ac
y
an
d
i
n
s
tab
ilit
y
to
its
ap
p
lied
s
y
s
te
m
.
H
y
s
ter
e
s
is
is
c
h
ar
ac
t
er
ized
as
n
o
n
lin
ea
r
b
ec
au
s
e
t
h
e
v
o
lta
g
e
-
d
is
p
lace
m
e
n
t
c
u
r
v
e
is
n
o
t
o
n
e
-
o
n
e
m
ap
p
in
g
[
3
]
,
[
9
]
.
T
h
e
s
a
m
e
in
p
u
t
v
o
ltag
e
p
r
o
d
u
ce
s
d
i
f
f
er
en
t
o
u
tp
u
t
d
is
p
lace
m
e
n
t
f
o
r
in
cr
ea
s
in
g
a
n
d
d
ec
r
ea
s
in
g
i
n
p
u
t
v
o
ltag
e.
I
n
a
d
d
itio
n
,
h
y
s
ter
esis
b
eh
a
v
io
r
al
s
o
ch
ar
ac
ter
ized
as
r
ate
-
d
ep
en
d
en
c
y
b
ec
au
s
e
t
h
e
h
y
s
ter
esi
s
cu
r
v
e
o
r
ien
tatio
n
a
n
d
s
h
ap
e
is
ch
a
n
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ed
as th
e
f
r
eq
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en
c
y
o
f
i
n
p
u
t
v
o
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g
e
is
ch
a
n
g
ed
.
Fig
u
r
e
1
s
h
o
w
ed
t
h
e
h
y
s
ter
es
is
n
o
n
l
in
ea
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o
m
e
n
o
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in
t
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p
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o
r
o
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.
T
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y
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ter
es
is
e
f
f
ec
t
f
o
r
t
h
e
ac
t
u
at
o
r
is
m
in
i
m
ized
b
y
u
s
i
n
g
co
n
tr
o
ller
.
Fi
g
u
r
e
2
s
h
o
w
ed
e
f
f
ec
t
o
f
cr
ee
p
p
h
e
n
o
m
en
a
in
p
iezo
elec
tr
ic
ac
t
u
ato
r
.
T
h
is
p
h
e
n
o
m
e
n
o
n
w
il
l
g
iv
e
s
ig
n
i
fican
t
er
r
o
r
w
h
en
t
h
e
P
E
A
ex
te
n
d
ed
p
er
io
d
s
o
f
ti
m
e.
I
t
ca
n
b
e
o
b
s
er
v
ed
th
at,
at
th
e
s
a
m
e
i
n
p
u
t
v
o
ltag
e
s
i
g
n
al,
th
e
d
is
p
lace
m
en
t
o
u
tp
u
t
i
s
ch
a
n
g
ed
o
v
er
ti
m
e.
A
cc
o
r
d
in
g
to
[
1
0
]
,
th
e
h
y
s
ter
es
is
an
d
cr
ee
p
s
tr
o
n
g
l
y
af
f
ec
t
t
h
e
ac
t
u
ato
r
at
f
r
eq
u
e
n
c
y
lo
w
er
t
h
a
n
1
0
Hz
.
Mo
r
eo
v
er
,
v
ib
r
atio
n
is
r
ep
etitiv
e
m
o
tio
n
s
th
a
t
o
cc
u
r
in
ti
m
e
i
n
ter
v
al
w
it
h
r
es
p
ec
t
to
a
p
o
in
t
o
f
r
ef
er
en
ce
.
T
h
e
v
ib
r
atio
n
is
ca
u
s
e
d
b
y
p
o
te
n
tial
e
n
er
g
y
s
to
r
ag
e
in
s
p
r
in
g
,
k
in
et
ic
en
er
g
y
s
t
o
r
ag
e
f
o
r
m
a
s
s
a
n
d
g
r
ad
u
al
e
n
er
g
y
d
a
m
p
i
n
g
f
o
r
d
a
m
p
er
.
T
h
ese
ef
f
ec
ts
r
ed
u
ce
d
th
e
p
er
f
o
r
m
a
n
ce
ac
cu
r
ac
y
an
d
i
n
cr
ea
s
e
d
th
e
u
n
ce
r
tai
n
t
y
o
f
m
ea
s
u
r
e
m
e
n
ts
[
1
1
]
.
Mo
r
eo
v
er
,
v
ib
r
atio
n
is
a
r
ep
etitiv
e
m
o
tio
n
t
h
at
o
cc
u
r
i
n
ti
m
e
i
n
ter
v
a
l
w
ith
r
esp
ec
t
to
a
p
o
in
t
o
f
r
ef
er
en
ce
.
T
h
e
v
ib
r
atio
n
o
cc
u
r
r
ed
b
ec
au
s
e
o
f
p
o
ten
tial
en
er
g
y
s
t
o
r
ag
e
in
s
p
r
in
g
,
k
in
e
tic
en
er
g
y
s
to
r
ag
e
f
o
r
m
a
s
s
an
d
g
r
ad
u
al
en
er
g
y
d
a
m
p
i
n
g
f
o
r
d
a
m
p
er
.
T
h
is
ef
f
ec
t
r
ed
u
c
ed
th
e
p
er
f
o
r
m
a
n
ce
ac
cu
r
ac
y
an
d
in
cr
ea
s
e
d
t
h
e
u
n
ce
r
tai
n
t
y
o
f
m
ea
s
u
r
e
m
en
t
s
[
1
0
]
.
Fu
r
th
er
m
o
r
e,
th
e
v
ib
r
at
io
n
f
r
eq
u
e
n
c
y
r
estra
i
n
ed
th
e
d
ev
elo
p
m
en
t
o
f
h
i
g
h
s
p
ee
d
-
SPM
to
be
u
s
ed
in
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e
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ico
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i
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d
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s
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ie
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,
to
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d
y
t
h
e
m
ec
h
a
n
is
m
o
f
f
a
s
t
s
u
r
f
ac
e
p
r
o
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s
s
es,
a
n
d
to
d
ev
elo
p
ed
SP
M
-
b
ased
n
an
o
f
ab
r
icatio
n
eq
u
ip
m
en
ts
Fig
u
r
e
1
.
H
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s
ter
es
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n
o
n
li
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p
en
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o
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an
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o
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m
Fig
u
r
e
2
.
C
r
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p
p
r
o
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Evaluation Warning : The document was created with Spire.PDF for Python.
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2
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3
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1
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5
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2
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T
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
P
E
A
ca
n
b
e
d
ev
elo
p
ed
b
y
u
s
i
n
g
p
h
y
s
ic
s
la
w
an
d
p
ar
a
m
eter
esti
m
atio
n
ap
p
r
o
ac
h
.
T
h
e
p
h
y
s
ics
la
w
n
ee
d
f
u
l
l
u
n
d
er
s
ta
n
d
in
g
o
f
th
e
s
y
s
te
m
an
d
p
h
y
s
ical
i
n
ter
ac
tio
n
s
r
elate
d
to
it
.
Me
an
w
h
ile,
p
ar
a
m
eter
esti
m
atio
n
ap
p
r
o
ac
h
o
n
l
y
r
eq
u
ir
ed
in
p
ut
-
o
u
tp
u
t
d
ata
[
1
2
]
.
T
h
e
p
ar
a
m
eter
s
o
f
m
at
h
e
m
a
tical
m
o
d
el
th
at
o
b
tain
ed
b
ased
o
n
p
h
y
s
ics
la
w
t
h
en
n
ee
d
to
b
e
o
p
tim
ized
.
A
cc
o
r
d
in
g
to
[
1
3
]
,
th
e
p
ar
am
eter
s
o
f
m
o
d
el
w
a
s
o
b
tain
ed
b
y
u
s
i
n
g
ar
tif
ic
ial
n
e
u
r
al
n
et
w
o
r
k
(
ANN)
.
T
h
e
n
eu
r
al
n
et
w
o
r
k
s
h
ad
to
b
e
tr
ain
ed
u
n
til
t
h
e
s
i
m
p
le
m
o
d
el
w
a
s
ac
h
iev
ed
.
B
esid
es,
t
h
e
f
aster
tr
ai
n
i
n
g
o
f
s
i
m
p
le
m
o
d
el
r
esu
lti
n
g
le
s
s
co
m
p
u
tatio
n
in
ac
tu
al
co
n
tr
o
l
.
T
h
o
u
g
h
,
t
h
e
n
e
u
r
al
n
et
w
o
r
k
n
ee
d
to
b
e
cr
ea
ted
,
tr
ain
ed
,
an
d
ev
al
u
ated
f
o
r
v
ar
io
u
s
f
ee
d
f
o
r
w
ar
d
b
ac
k
p
r
o
p
ag
atio
n
n
et
w
o
r
k
s
u
n
til
t
h
e
n
et
w
o
r
k
g
av
e
ac
c
u
r
ate
m
o
d
e
l.
Fu
r
t
h
er
m
o
r
e,
th
e
p
ar
am
etr
ic
id
en
tific
atio
n
s
u
c
h
as
r
ec
u
r
s
i
v
e
least
s
q
u
ar
e
m
et
h
o
d
,
g
en
etic
al
g
o
r
ith
m
a
n
d
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
also
ca
n
b
e
u
s
ed
f
o
r
p
ar
am
eter
s
o
p
ti
m
izatio
n
.
T
h
e
g
en
etic
alg
o
r
it
h
m
(
G
A
)
is
a
h
eu
r
is
tic
m
et
h
o
d
to
esti
m
ate
t
h
e
p
ar
a
m
eter
s
b
as
ed
o
n
ev
o
lu
tio
n
ar
y
id
ea
s
o
f
n
a
tu
r
al
s
elec
tio
n
an
d
g
e
n
etic
s
[
1
4
]
.
T
h
e
p
ar
am
eter
s
th
at
n
ee
d
to
b
e
r
ec
o
g
n
ized
k
n
o
w
n
as
c
h
r
o
m
o
s
o
m
e
s
t
h
at
f
o
r
m
a
s
tr
i
n
g
ca
lled
g
e
n
e.
T
h
e
p
r
o
ce
s
s
of
GA
wa
s
s
tar
ted
w
it
h
i
n
itialized
th
e
v
al
u
es
o
f
c
h
r
o
m
o
s
o
m
es.
T
h
e
v
al
u
es
we
r
e
r
an
d
o
m
l
y
c
h
o
s
e
n
to
f
o
r
m
a
p
o
p
u
latio
n
.
T
h
en
,
th
e
e
v
al
u
atio
n
fi
t
n
es
s
a
n
d
alg
o
r
it
h
m
w
er
e
ca
lc
u
lated
u
n
t
il
t
h
e
b
est
e
s
ti
m
atio
n
v
a
lu
e
wa
s
ac
co
m
p
li
s
h
ed
.
T
h
e
ad
v
an
ta
g
e
f
o
r
th
i
s
id
e
n
ti
fi
ca
t
io
n
o
p
ti
m
izatio
n
tec
h
n
iq
u
e
is
,
t
h
e
w
r
o
n
g
i
n
it
ializat
io
n
v
alu
e
f
o
r
esti
m
atio
n
p
ar
am
eter
s
ca
n
b
e
id
en
ti
fied
s
in
ce
t
h
e
o
p
ti
m
a
l
p
ar
a
m
eter
s
lies
o
u
t
s
id
e
in
ter
v
al.
Hen
ce
,
r
esu
lt
s
ten
d
to
b
e
clu
s
ter
ed
n
ea
r
t
h
e
s
id
e
o
f
t
h
e
in
ter
v
al
t
h
at
s
h
o
u
ld
b
e
tu
n
ed
.
Nev
er
th
eles
s
,
G
A
m
e
th
o
d
ca
n
n
o
t
k
ee
p
th
e
m
e
m
o
r
y
w
h
e
n
t
h
e
p
o
p
u
lat
io
n
w
a
s
ch
a
n
g
ed
[
15
].
T
h
er
ef
o
r
e,
r
esear
ch
er
[
1
6
]
w
as
i
m
p
le
m
en
tin
g
p
ar
ticle
s
w
ar
m
o
p
tim
izatio
n
(
P
SO)
tech
n
iq
u
e
.
P
SO
is
k
n
o
w
n
a
s
a
n
e
w
h
e
u
r
is
tic
m
et
h
o
d
w
h
ic
h
is
ea
s
y
to
u
n
d
er
s
ta
n
d
an
d
i
m
p
le
m
en
t
to
o
p
ti
m
ize
t
h
e
p
ar
am
eter
s
.
I
n
ad
d
itio
n
,
P
SO
p
r
o
v
id
ed
ad
v
an
tag
e
s
w
it
h
h
ig
h
o
p
ti
m
izat
io
n
p
er
f
o
r
m
a
n
ce
a
n
d
g
o
o
d
m
e
m
o
r
y
w
h
er
e
ea
c
h
p
ar
ticle
in
P
SO
wa
s
p
r
ep
ar
ed
w
it
h
a
s
m
all
m
e
m
o
r
y
co
m
p
r
is
i
n
g
its
p
r
ev
io
u
s
b
es
t
p
o
s
itio
n
.
T
h
is
t
ec
h
n
iq
u
e
wa
s
b
ased
o
n
th
e
i
d
ea
o
f
co
llab
o
r
ativ
e
b
eh
a
v
io
u
r
an
d
s
w
ar
m
i
n
g
i
n
b
io
lo
g
ical
p
o
p
u
latio
n
[
17
]
.
T
h
e
p
ar
ticles
h
o
ld
a
p
o
s
itio
n
(
x
j
)
an
d
v
elo
cit
y
(
v
j
)
w
it
h
tr
i
al
s
o
lu
tio
n
o
f
t
h
e
o
p
tim
u
m
p
r
o
b
lem
.
Ho
w
e
v
er
,
th
e
m
ai
n
d
r
a
w
b
ac
k
f
o
r
t
h
is
tec
h
n
iq
u
e
wa
s
t
h
e
fi
t
n
ess
f
u
n
ct
io
n
m
u
s
t
b
e
s
elec
ted
b
ased
o
n
s
u
itab
ilit
y
o
f
m
o
d
els
an
d
PS
O
h
as
s
lo
w
co
n
v
er
g
en
ce
s
p
ee
d
[
1
8
]
.
Nex
t,
p
ar
a
m
eter
esti
m
atio
n
ap
p
r
o
ac
h
s
u
ch
a
s
s
y
s
te
m
id
en
ti
f
icatio
n
(
SI)
is
a
tec
h
n
iq
u
e
to
o
b
tain
ed
th
e
m
at
h
e
m
a
tic
al
d
escr
ip
tio
n
f
r
o
m
m
ea
s
u
r
e
m
e
n
t
s
o
f
th
e
in
p
u
t
a
n
d
o
u
tp
u
t.
T
h
is
tec
h
n
iq
u
e
o
n
l
y
r
eq
u
ir
ed
d
ata
co
llectio
n
o
f
i
n
p
ut
-
o
u
tp
u
t
d
ata
to
f
i
n
d
th
e
ex
ac
t
o
r
ap
p
r
o
x
i
m
ate
m
o
d
els
o
f
d
y
n
a
m
ic
s
y
s
te
m
[
1
9
]
.
T
h
e
o
b
j
ec
tiv
e
o
f
SI
is
t
o
f
in
d
th
e
e
x
ac
t
o
r
ap
p
r
o
x
im
a
te
m
o
d
els o
f
d
y
n
a
m
ic
s
y
s
te
m
b
ased
o
n
k
n
o
w
led
g
e
o
f
th
e
o
b
s
er
v
ed
in
p
u
t a
n
d
o
u
t
p
u
t d
ata.
2.
M
E
T
H
O
D
O
L
O
G
Y
T
h
e
m
ain
co
m
p
o
n
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n
t.
RE
F
E
R
E
NC
E
S
[1
]
B.
Ja
ff
e
,
“
P
iez
o
e
lec
tri
c
c
e
ra
m
ic
s
,”
El
se
v
ier,
v
o
l.
3
,
2
0
1
2
.
[2
]
Q.
Xu
,
“
Id
e
n
ti
f
ica
ti
o
n
a
n
d
c
o
m
p
e
n
sa
ti
o
n
o
f
p
iez
o
e
lec
tri
c
h
y
ste
r
e
sis
w
it
h
o
u
t
m
o
d
e
li
n
g
h
y
ste
re
sis
in
v
e
rse
,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
In
d
u
stri
a
l
El
e
c
tr
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n
ics
,
v
o
l
.
6
0
,
p
p
.
3
9
2
7
-
3
9
3
7
,
2
0
1
3
.
[3
]
B.
M
.
Ba
d
r
a
n
d
W
.
G
.
A
li
,
“
Na
n
o
p
o
siti
o
n
in
g
f
u
z
z
y
c
o
n
tr
o
l
f
o
r
p
iez
o
e
lec
tri
c
a
c
tu
a
to
rs,
”
In
t.
J
.
E
n
g
.
T
e
c
h
.
(
IJ
ET
-
IJ
ENS
),
v
o
l.
1
0
,
p
p
.
7
0
-
7
4
,
2
0
1
0
.
[4
]
M
.
A
b
d
e
laz
iz,
e
t
a
l.
,
“
A
H
y
b
rid
F
u
z
z
y
Ro
b
u
st
c
o
n
tr
o
l
f
o
r
P
iez
o
e
lec
tri
c
a
c
tu
a
to
rs,
”
J
o
u
rn
a
l
o
f
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ric
a
n
S
c
ien
c
e
,
v
o
l.
8
,
p
p
.
4
8
3
-
4
8
9
,
2
0
1
2
.
[5
]
S
.
X
ia
o
a
n
d
Y.
L
i,
“
M
o
d
e
li
n
g
a
n
d
h
ig
h
d
y
n
a
m
ic
c
o
m
p
e
n
sa
ti
n
g
th
e
ra
te
-
d
e
p
e
n
d
e
n
t
h
y
ste
re
sis
o
f
p
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e
lec
tri
c
a
c
tu
a
to
rs
v
ia
a
n
o
v
e
l
m
o
d
if
ied
in
v
e
rse
P
re
isa
c
h
m
o
d
e
l,
”
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
Co
n
tro
l
S
y
ste
ms
T
e
c
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o
g
y
,
v
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l.
2
1
,
p
p
.
1
5
4
9
-
1
5
5
7
,
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0
1
3
.
[6
]
Z.
Ch
i
a
n
d
Q.
Xu
,
“
Re
c
e
n
t
a
d
v
a
n
c
e
s
in
th
e
c
o
n
t
r
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l
o
f
p
iez
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e
lec
tri
c
a
c
tu
a
to
rs,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ad
v
a
n
c
e
d
Ro
b
o
ti
c
sy
ste
ms
,
v
o
l.
1
1
,
p
p
.
1
-
1
1
,
2
0
1
4
.
[7
]
Y.
L
iu
,
e
t
a
l
.
,
“
Hy
ste
re
sis a
n
d
c
re
e
p
m
o
d
e
li
n
g
a
n
d
c
o
m
p
e
n
sa
ti
o
n
f
o
r
a
p
iez
o
e
lec
tri
c
a
c
tu
a
to
r
u
sin
g
a
f
ra
c
ti
o
n
a
l
-
o
r
d
e
r
M
a
x
w
e
l
l
re
sistiv
e
c
a
p
a
c
it
o
r
a
p
p
r
o
a
c
h
,
”
S
ma
rt M
a
ter
i
a
ls
a
n
d
S
tru
c
t
u
re
s
,
v
o
l.
2
2
,
p
p
.
1
1
5
0
2
0
,
2
0
1
3
.
[8
]
H.
S
h
e
n
,
e
t
a
l.
,
“
A
lo
w
-
p
o
w
e
r
c
ircu
it
f
o
r
p
iez
o
e
lec
tri
c
v
ib
ra
ti
o
n
c
o
n
tro
l
b
y
sy
n
c
h
ro
n
ize
d
sw
it
c
h
in
g
o
n
v
o
lt
a
g
e
so
u
rc
e
s,
”
S
e
n
so
rs
a
n
d
a
c
t
u
a
t
o
rs
A:
Ph
y
sic
a
l
,
v
o
l.
1
6
1
,
p
p
.
2
4
5
-
2
5
5
,
2
0
1
0
.
[9
]
P
.
L
i,
e
t
a
l.
,
“
A
sim
p
le
f
u
z
z
y
s
y
ste
m
f
o
r
m
o
d
e
ll
in
g
o
f
b
o
t
h
ra
t
e
-
in
d
e
p
e
n
d
e
n
t
a
n
d
ra
te
-
d
e
p
e
n
d
e
n
t
h
y
ste
re
sis
in
p
iez
o
e
lec
tri
c
a
c
tu
a
to
rs,
”
M
e
c
h
a
n
i
c
a
l
S
y
ste
ms
a
n
d
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
3
6
,
p
p
.
1
8
2
-
1
9
2
,
2
0
1
3
.
[1
0
]
L
.
L
iu
,
e
t
a
l
.,
“
De
v
e
lo
p
m
e
n
t
o
f
a
n
a
p
p
ro
a
c
h
to
w
a
rd
c
o
m
p
re
h
e
n
siv
e
id
e
n
ti
f
ica
ti
o
n
o
f
h
y
ste
re
t
ic
d
y
n
a
m
ics
in
p
iez
o
e
lec
tri
c
a
c
tu
a
to
rs,
”
IEE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
Co
n
tro
l
S
y
ste
ms
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
2
1
,
p
p
.
1
8
3
4
-
1
8
4
5
,
2
0
1
3
.
[1
1
]
J.
R
.
F
o
rtu
n
,
e
t
a
l.
,
“
F
latn
e
ss
-
b
a
se
d
a
c
ti
v
e
v
ib
ra
ti
o
n
c
o
n
t
ro
l
f
o
r
p
i
e
z
o
e
lec
tri
c
a
c
tu
a
to
rs,
”
IEE
E/
AS
M
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
e
c
h
a
tr
o
n
ics
,
v
o
l
.
1
8
,
p
p
.
2
2
1
-
2
2
9
,
2
0
1
3
.
[1
2
]
M.
Jo
u
a
n
e
h
,
“
F
u
n
d
a
m
e
n
tals o
f
m
e
c
h
a
tro
n
ics
,”
Ce
n
g
a
g
e
Lea
rn
in
g
,
2
0
1
2
.
[1
3
]
P
.
Ro
n
k
a
n
e
n
,
e
t
a
l.
,
“
Disp
lac
e
m
e
n
t
c
o
n
tro
l
o
f
p
iez
o
e
lec
tri
c
a
c
tu
a
to
rs
u
si
n
g
c
u
rre
n
t
a
n
d
v
o
lt
a
g
e
,
”
IEE
E/
AS
M
E
T
ra
n
sa
c
ti
o
n
s
o
n
M
e
c
h
a
tro
n
ics
,
v
o
l.
1
6
,
p
p
.
1
6
0
-
1
6
6
,
2
0
1
1
.
[1
4
]
P
.
S
e
n
g
u
p
ta
a
n
d
B.
L
i,
“
M
o
d
if
i
e
d
Bo
u
c
–
W
e
n
m
o
d
e
l
f
o
r
h
y
ste
r
e
sis
b
e
h
a
v
io
r
o
f
RC
b
e
a
m
–
c
o
lu
m
n
jo
in
ts
w
it
h
li
m
it
e
d
tran
sv
e
rse
re
in
f
o
rc
e
m
e
n
t,
”
En
g
i
n
e
e
rin
g
S
tru
c
t
u
re
s
,
v
o
l.
4
6
,
p
p
.
3
9
2
-
4
0
6
,
2
0
1
3
.
[1
5
]
V
.
Ha
ss
a
n
i,
e
t
a
l.
,
“
A
s
u
rv
e
y
o
n
h
y
st
e
re
sis
m
o
d
e
li
n
g
,
id
e
n
ti
f
ica
ti
o
n
a
n
d
c
o
n
tr
o
l
,”
M
e
c
h
a
n
ica
l
sy
st
e
ms
a
n
d
sig
n
a
l
p
ro
c
e
ss
in
g
,
v
o
l.
4
9
,
p
p
.
2
0
9
-
2
3
3
,
2
0
1
4
.
[1
6
]
J.
W
.
L
ian
g
,
e
t
a
l.
,
“
M
o
d
e
l
-
Ba
se
d
Co
n
tr
o
l
f
o
r
P
iez
o
e
lec
tri
c
-
A
c
t
u
a
ted
S
y
ste
m
s
Us
in
g
In
v
e
rse
P
ra
n
d
tl
-
Ish
li
n
sk
ii
M
o
d
e
l
a
n
d
P
a
rti
c
l
e
S
w
a
r
m
Op
ti
m
iza
ti
o
n
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
M
e
c
h
a
n
ic
a
l,
Aer
o
sp
a
c
e
,
In
d
u
stria
l
a
n
d
M
e
c
h
a
tro
n
ics
E
n
g
i
n
e
e
rin
g
,
v
o
l.
8
,
p
p
.
6
0
9
,
2
0
1
4
.
[1
7
]
H.
Ho
ss
e
in
i,
e
t
a
l.
,
“
T
h
e
d
e
sig
n
o
f
ro
b
u
st
s
o
f
t
se
n
so
r
u
sin
g
A
NFIS
n
e
t
w
o
rk
,
”
J
o
u
rn
a
l
o
f
I
n
stru
me
n
ta
ti
o
n
T
e
c
h
n
o
l
o
g
y
,
v
o
l.
2
,
p
p
.
9
-
1
6
,
2
0
1
4
[1
8
]
G
.
W
a
n
g
,
e
t
a
l.
,
“
M
o
d
e
li
n
g
a
n
d
i
d
e
n
ti
f
ica
ti
o
n
o
f
a
s
y
m
m
e
tri
c
Bo
u
c
–
W
e
n
h
y
ste
re
sis
f
o
r
p
iez
o
e
lec
tri
c
a
c
tu
a
to
r
v
ia
a
n
o
v
e
l
d
if
f
e
re
n
ti
a
l
e
v
o
lu
ti
o
n
a
lg
o
ri
th
m
,
”
S
e
n
so
rs
a
n
d
Act
u
a
t
o
rs
A:
P
h
y
sic
a
l
,
v
o
l.
2
3
5
,
p
p
.
1
0
5
-
1
1
8
,
2
0
1
5
.
[1
9
]
M
.
N.
M
a
sla
n
,
e
t
a
l.
,
“
De
v
e
lo
p
m
e
n
t
o
f
S
y
ste
m
Id
e
n
ti
f
ica
ti
o
n
f
o
r
P
iez
o
e
lec
tri
c
P
a
tch
A
c
tu
a
t
o
r,
”
in
Ap
p
li
e
d
M
e
c
h
a
n
ics
a
n
d
M
a
ter
ia
ls
,
p
p
.
2
4
5
-
2
4
9
,
2
0
1
5
.
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