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n
’
s
la
w
a
n
d
L
ag
r
an
g
e
’
s
eq
u
a
tio
n
r
es
u
lte
d
in
th
e
s
a
m
e
s
o
l
u
tio
n
.
F
u
r
t
h
e
r
m
o
r
e,
in
[
1
4
]
,
th
e
au
th
o
r
p
r
esen
ted
Si
m
m
ec
h
an
ics
an
d
Si
m
u
li
n
k
m
o
d
el
s
f
o
r
ca
r
au
to
m
o
b
ile
s
u
s
p
e
n
s
io
n
an
d
i
m
p
le
m
en
ted
p
r
o
p
o
r
tio
n
al
-
i
n
teg
r
al
-
d
er
iv
at
i
v
e
(
P
I
D)
co
n
tr
o
l
s
tr
ateg
y
to
m
i
n
i
m
ize
b
o
d
y
ac
ce
ler
atio
n
.
I
n
[
1
5
]
,
[
1
6
]
,
th
e
au
th
o
r
s
e
s
tab
lis
h
ed
m
as
s
s
p
r
i
n
g
d
a
m
p
er
m
o
d
els
b
ased
o
n
Ne
w
to
n
’
s
la
w
o
f
m
o
tio
n
to
d
er
iv
e
a
s
ta
te
-
s
p
ac
e
m
o
d
el
f
o
r
n
u
m
er
ical
co
m
p
u
ta
tio
n
w
ith
t
h
e
aid
s
o
f
M
A
T
L
AB
an
d
Si
m
u
li
n
k
.
An
au
th
o
r
in
[
1
7
]
ex
a
m
in
ed
t
h
e
ef
f
ec
t o
f
t
h
e
p
o
s
itio
n
o
f
t
h
e
d
a
m
p
er
i
n
s
y
s
te
m
s
w
i
th
m
u
lti
-
d
e
g
r
ee
o
f
f
r
ee
d
o
m
.
T
h
eir
r
esear
ch
w
o
r
k
s
co
n
cl
u
d
ed
th
at
d
i
s
p
lace
m
e
n
t
o
f
a
n
o
s
c
illato
r
th
at
a
f
f
ec
ted
b
y
th
e
f
o
r
ce
s
h
o
w
m
o
r
e
e
n
er
g
y
ab
s
o
r
p
tio
n
f
o
r
lo
w
d
is
p
lace
m
e
n
t.
I
n
[
1
8
]
-
[
2
0
]
,
th
e
au
th
o
r
s
p
r
ese
n
ted
m
at
h
e
m
at
ical
m
o
d
elin
g
o
f
a
m
as
s
s
p
r
in
g
d
a
m
p
er
s
y
s
te
m
in
MA
T
L
A
B
an
d
Si
m
u
li
n
k
.
T
h
e
au
th
o
r
in
[
2
1
]
,
p
r
esen
ted
co
n
tr
o
l
o
f
co
u
p
led
m
as
s
s
p
r
in
g
d
a
m
p
er
s
y
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te
m
u
s
i
n
g
p
o
ly
n
o
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ia
l
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tr
u
ct
u
r
es
ap
p
r
o
a
ch
.
Ma
las
an
d
co
-
w
o
r
k
er
[
2
2
]
p
r
esen
ted
a
n
o
v
e
l
co
n
tr
o
l
s
t
r
ateg
y
f
o
r
in
d
u
cin
g
s
if
-
s
u
s
tai
n
ed
o
s
cillatio
n
o
f
a
s
in
g
le
d
eg
r
ee
-
of
-
f
r
ee
d
o
m
MD
S
m
ec
h
a
n
ical
s
y
s
te
m
s
.
T
h
e
r
esear
ch
er
s
co
n
clu
d
ed
in
th
eir
w
o
r
k
th
at
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
o
d
el
is
ca
p
ab
le
o
f
g
e
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er
atin
g
s
tab
le
s
el
f
-
ex
ci
te
d
o
s
cillatio
n
at
th
e
n
atu
r
al
f
r
eq
u
e
n
c
y
r
e
g
ar
d
less
o
f
th
e
v
al
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e
o
f
t
h
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co
n
tr
o
l g
ai
n
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T
h
e
o
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je
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t
i
v
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o
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th
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p
a
p
e
r
a
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o
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li
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a
m
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th
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a
t
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l
m
o
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th
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r
e
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en
t
t
h
e
d
y
n
am
i
c
b
e
h
av
i
o
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r
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c
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p
le
d
m
as
s
s
p
r
i
n
g
d
am
p
e
r
s
y
s
t
em
s
an
d
e
f
f
e
ct
iv
e
ly
c
o
n
t
r
o
l
th
e
m
a
s
s
p
o
s
i
t
i
o
n
u
s
in
g
b
o
th
S
im
u
l
in
k
an
d
Sim
e
l
e
ct
r
o
n
i
c
s
as
s
im
u
l
a
t
i
o
n
t
o
o
ls
2.
RE
S
E
ARCH
M
E
T
H
O
D
W
e
d
er
iv
ed
th
e
eq
u
atio
n
s
o
f
m
o
tio
n
(
E
OM
)
o
f
a
co
u
p
led
m
ass
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
s
u
s
i
n
g
s
ec
o
n
d
-
o
r
d
er
,
o
r
d
in
ar
y
d
i
f
f
er
e
n
tial
eq
u
atio
n
s
an
d
to
s
i
m
u
late
d
y
n
a
m
ic
ac
c
u
r
atel
y
[
2
3
]
th
e
L
a
g
r
an
g
e
’
s
eq
u
atio
n
w
a
s
ad
o
p
ted
.
T
h
e
m
o
tiv
a
tio
n
f
o
r
c
h
o
s
en
L
ag
r
a
n
g
e
’
s
eq
u
at
io
n
o
v
er
Ne
w
to
n
’
s
la
w
o
r
D
’
A
le
m
b
er
t
p
r
in
cip
le
is
t
h
at
it
allo
w
s
s
ig
n
i
f
ica
n
t
s
i
m
p
li
f
ic
atio
n
o
f
th
e
g
eo
m
etr
y
o
f
t
h
e
s
y
s
te
m
m
o
tio
n
f
o
r
s
o
lv
i
n
g
lar
g
e
co
m
p
le
x
s
y
s
te
m
s
an
d
also
eli
m
i
n
ate
s
ex
p
lic
it
r
e
w
r
iti
n
g
all
f
o
r
ce
s
ac
t
in
g
o
n
t
h
e
b
o
d
y
.
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
is
f
o
r
m
u
lated
b
ased
o
n
en
er
g
y
p
r
o
p
er
ty
o
f
L
a
g
r
an
g
e
ap
p
r
o
ac
h
an
d
th
e
co
n
tr
o
l
s
tr
ateg
y
a
n
d
Si
m
u
li
n
k
s
i
m
u
latio
n
ar
e
ex
p
an
d
ed
o
n
th
e
d
er
iv
ed
m
a
th
e
m
atica
l
m
o
d
el.
Ho
w
ev
er
,
th
e
lan
g
r
ag
e
’
s
eq
u
atio
n
d
o
es
n
o
t
i
m
p
r
o
v
is
e
f
o
r
d
is
s
ip
ativ
e
(
d
a
m
p
in
g
)
f
o
r
ce
in
t
h
e
m
ec
h
a
n
ical
s
y
s
te
m
,
h
e
n
ce
,
R
a
y
le
ig
h
’
s
d
is
s
ip
atio
n
f
u
n
ctio
n
is
in
tr
o
d
u
ce
d
in
to
L
a
g
r
an
g
e’
s
eq
u
atio
n
to
a
cc
o
u
n
t
f
o
r
d
is
s
ip
ati
v
e
f
o
r
ce
i
n
t
h
e
m
o
d
el
a
n
d
w
e
r
ef
er
to
th
is
as
au
g
m
e
n
ted
L
a
g
r
an
g
e’
s
eq
u
atio
n
.
I
n
o
r
d
er
to
d
escr
ib
e
th
e
p
h
y
s
ical
m
o
ti
o
n
o
f
a
co
u
p
led
m
a
s
s
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
s
,
w
e
n
ee
d
to
ch
o
o
s
e
a
s
et
o
f
v
ar
iab
les
o
r
co
o
r
d
in
ates
w
h
ic
h
ar
e
o
f
te
n
r
ef
er
r
ed
to
as
g
en
er
alize
d
co
o
r
d
in
ates.
T
h
u
s
,
th
e
d
is
p
lace
m
en
t o
f
th
e
m
as
s
e
s
is
ch
o
s
e
n
as t
h
e
g
en
er
alize
d
co
o
r
d
i
n
ates.
2
.
1
.
M
a
t
he
m
a
t
ica
l
m
o
delin
g
T
h
e
d
y
n
a
m
ic
o
f
t
h
e
m
a
s
s
s
p
r
in
g
d
a
m
p
er
s
y
s
te
m
s
w
it
h
t
w
o
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
DOF)
m
o
v
e
m
e
n
t
i
s
ex
p
licitl
y
d
er
iv
ed
b
ased
o
n
L
ag
r
an
g
e’
s
eq
u
atio
n
to
ex
p
o
u
n
d
th
e
p
r
o
b
le
m
s
in
v
o
lv
ed
in
d
y
n
a
m
ic
m
o
d
eli
n
g
.
Fig
u
r
e
1
d
ep
icts
a
co
u
p
led
m
a
s
s
s
p
r
in
g
d
a
m
p
er
s
y
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te
m
s
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w
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e
t
w
o
m
a
s
s
e
s
m
1
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m
2
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k
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f
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m
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T
h
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f
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,
F
(
t
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Fo
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p
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s
ar
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ass
u
m
ed
to
b
e
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eg
l
ig
ib
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
6
3
6
–
3
6
4
6
3638
Fig
u
r
e
1
.
A
co
u
p
led
m
a
s
s
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
s
ad
ap
ted
f
r
o
m
[
8
]
T
h
e
eq
u
atio
n
s
o
f
m
o
tio
n
(
E
OM
)
f
o
r
a
m
ec
h
a
n
ical
s
y
s
te
m
w
it
h
2
-
DOF
ca
n
b
e
d
er
iv
ed
b
y
a
n
au
g
m
e
n
ted
.
L
a
g
r
an
g
e’
s
eq
u
atio
n
in
t
h
e
f
o
r
m
i
i
i
i
Q
q
D
q
L
q
L
dt
d
.
.
(
1
)
2
1
,
x
x
q
i
(
2
)
W
h
er
e,
i
q
is
th
e
g
e
n
er
alize
d
co
o
r
d
in
ates to
d
escr
ib
e
th
e
d
is
p
la
ce
m
en
t o
f
t
h
e
m
a
s
s
es.
First
w
e
ca
lcu
late
t
h
e
k
in
etic
en
er
g
y
,
T
,
an
d
th
e
(
au
g
m
e
n
te
d
)
p
o
ten
tial
en
er
g
y
,
U,
o
f
th
e
s
y
s
te
m
,
t
h
e
k
in
e
tic
en
er
g
y
o
f
a
co
u
p
led
m
ass
s
p
r
in
g
d
a
m
p
er
s
y
s
te
m
s
a
s
f
u
n
ctio
n
m
a
s
s
v
elo
cit
y
is
ex
p
r
ess
ed
as:
.
2
2
2
.
2
1
1
2
1
2
1
x
m
x
m
T
(
3
)
T
h
e
au
g
m
en
ted
p
o
ten
tial e
n
er
g
y
i
s
ex
p
r
e
s
s
ed
as:
2
2
1
2
2
1
1
2
1
2
1
x
x
k
x
k
U
(
4
)
2
2
2
2
1
2
2
1
2
2
1
1
2
1
2
1
2
1
x
k
x
x
k
x
k
x
k
U
(
5
)
R
a
y
le
ig
h
d
is
s
ip
ativ
e
f
u
n
ctio
n
ac
co
u
n
t
f
o
r
d
am
p
i
n
g
f
o
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ce
in
t
h
e
m
ec
h
a
n
ical
s
y
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te
m
a
n
d
it is
ex
p
r
ess
ed
as:
2
2
.
.
1
2
.
2
1
1
2
1
2
1
x
x
b
x
b
D
(
6
)
.
2
1
2
2
.
1
.
2
.
2
1
2
.
2
1
1
2
1
2
1
2
1
x
b
x
x
b
x
b
x
b
D
(
7
)
Gen
er
al
ized
f
o
r
ce
s
:
0
,
2
1
Q
F
Q
(
8
)
T
h
e
L
ag
r
an
g
e
f
o
r
m
u
latio
n
d
ef
in
es
t
h
e
b
eh
av
io
u
r
o
f
a
d
y
n
a
m
ic
s
y
s
te
m
s
i
n
ter
m
s
o
f
w
o
r
k
an
d
en
er
g
y
s
to
r
ed
in
th
e
s
y
s
te
m
[
2
4
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
S
imu
lin
k
a
n
d
S
imelec
tr
o
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ics
b
a
s
ed
P
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itio
n
C
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l o
f a
C
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p
led
Ma
s
s
-
S
p
r
in
g
Da
mp
er
…
(
Oku
b
a
n
jo
A.A)
3639
T
h
e
au
g
m
en
ted
L
ag
r
a
n
g
e
f
u
n
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tio
n
L
i
s
d
en
o
ted
as:
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(
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e
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ate
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w
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n
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d
er
iv
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v
es b
ased
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n
eq
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n
E
q
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atio
n
(
7
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an
d
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u
atio
n
(
1
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)
:
1
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1
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1
x
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(
1
1
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2
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2
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x
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(
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2
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2
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x
k
x
k
x
k
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(
1
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1
2
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k
x
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(
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4
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2
.
2
.
1
2
1
.
1
.
1
x
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x
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x
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D
(
15
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2
.
2
1
.
2
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2
x
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x
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x
D
(
16
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Fo
r
g
en
er
alize
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co
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r
d
in
ate
1
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e
L
ag
r
a
n
g
e
’
s
eq
u
atio
n
i
s
:
1
.
1
1
.
1
Q
x
D
x
L
x
L
dt
d
(
1
7
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Af
ter
s
u
b
s
tit
u
tio
n
o
f
t
h
e
d
er
iv
ed
d
er
iv
ativ
es
in
E
q
u
atio
n
(
1
1
)
,
E
q
u
atio
n
(
1
3
)
,
an
d
E
q
u
atio
n
(
1
5
)
in
E
q
u
atio
n
(
1
7
)
,
w
e
o
b
tai
n
eq
u
a
tio
n
o
f
m
o
t
io
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f
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r
m
ass
1
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n
th
is
f
o
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m
:
F
x
k
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k
k
x
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x
b
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x
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2
2
1
2
1
2
.
2
1
.
2
1
..
1
1
(
1
8
)
Si
m
i
lar
l
y
,
f
o
r
th
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g
e
n
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alize
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co
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r
d
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ate
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L
a
g
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an
g
e’
s
eq
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atio
n
i
s
:
2
.
2
2
.
2
Q
x
D
x
L
x
L
dt
d
(
1
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
6
3
6
–
3
6
4
6
3640
I
n
th
e
s
a
m
e
v
ei
n
,
s
u
b
s
tit
u
tio
n
o
f
t
h
e
d
er
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d
er
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ati
v
es
in
E
q
u
atio
n
(
1
2
)
,
E
q
u
atio
n
(
1
4
)
,
an
d
E
q
u
atio
n
(
1
6
)
in
E
q
u
atio
n
(
1
9
)
,
w
e
o
b
tain
eq
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atio
n
o
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m
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tio
n
f
o
r
m
a
s
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2
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t
h
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m
0
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1
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m
(
2
0
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T
h
e
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OM
in
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u
atio
n
(
1
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a
n
d
E
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atio
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(
2
0
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ar
e
r
e
-
ar
r
an
g
e
to
f
ac
ilit
ate
t
h
e
i
m
p
le
m
e
n
t
atio
n
o
f
th
e
eq
u
atio
n
s
i
n
Si
m
u
li
n
k
as:
1
2
1
2
1
1
2
1
.
2
2
2
1
.
1
2
1
1
..
m
F
x
m
k
x
m
k
k
x
m
b
x
m
b
b
x
(
2
1
)
2
2
1
2
2
2
.
2
2
.
1
2
2
2
..
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k
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m
k
x
m
b
x
m
b
x
(
2
2
)
T
h
e
d
er
iv
ed
E
OM
is
f
u
r
t
h
er
w
r
itte
n
i
n
ter
m
s
o
f
m
as
s
,
d
a
m
p
in
g
,
s
ti
f
f
n
e
s
s
m
atr
ices
an
d
F
,
x,
x
,
x
ar
e
f
o
r
ce
,
d
is
p
lace
m
en
t,
v
elo
cit
y
a
n
d
ac
ce
ler
atio
n
v
ec
to
r
s
r
esp
ec
tiv
el
y
an
d
t
h
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y
ar
e
p
r
esen
ted
a
s
:
0
0
0
2
2
2
2
1
2
2
2
2
1
..
2
..
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F
k
k
k
k
k
b
b
b
b
b
x
x
m
m
2
1
(
2
3
)
I
n
t
h
e
l
ig
h
t
o
f
E
q
u
atio
n
(
2
3
)
,
th
e
E
OM
o
b
tai
n
ed
b
y
u
s
i
n
g
L
a
g
r
an
g
e’
s
eq
u
atio
n
f
o
r
lin
ea
r
s
y
s
te
m
s
r
ev
ea
led
th
at
i
n
er
tial,
s
tiff
n
es
s
m
atr
ices
a
s
w
el
l
as
d
a
m
p
i
n
g
m
atr
i
x
i
f
m
o
d
eled
b
y
R
a
y
l
eig
h
’
s
f
u
n
ctio
n
ar
e
s
y
m
m
etr
ic
2
.
2
.
Sta
t
e
s
pa
ce
re
presenta
t
io
n o
f
t
he
m
o
del
A
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
i
s
a
ti
m
e
d
o
m
a
in
ap
p
r
o
ac
h
o
f
m
o
d
eli
n
g
m
u
i
ltip
le
in
p
u
t
m
u
l
t
ip
le
o
u
tp
u
t
s
y
s
te
m
.
Ho
w
e
v
er
,
c
o
m
p
lex
s
y
s
te
m
w
i
th
m
a
n
y
d
e
g
r
ee
-
of
-
f
r
ee
d
o
m
,
d
escr
ip
tio
n
o
f
s
u
c
h
s
y
s
te
m
s
w
it
h
d
if
f
er
e
n
tial
eq
u
atio
n
s
ar
e
o
f
te
n
ti
m
e
i
n
ten
s
e
a
n
d
b
u
r
d
e
n
s
o
m
e.
So
,
s
tate
s
p
ac
e
r
ep
r
ese
n
t
atio
n
o
f
t
h
e
s
y
s
te
m
s
s
er
v
es
a
s
an
al
ter
n
ati
v
e
ap
p
r
o
ac
h
to
allev
ia
te
th
e
c
h
alle
n
g
es
.
A
l
s
o
,
th
e
s
ta
te
s
p
ac
e
r
ep
r
esen
tatio
n
o
f
a
s
y
s
te
m
r
ep
lace
s
th
e
h
i
g
h
er
-
o
r
d
er
d
if
f
e
r
en
tial
eq
u
atio
n
s
w
it
h
a
s
i
n
g
le
f
ir
s
t
-
o
r
d
er
m
atr
i
x
d
if
f
er
e
n
tial
eq
u
atio
n
t
h
at
g
i
v
es
an
ex
p
ed
ien
t
a
n
d
co
n
cise
w
a
y
to
m
o
d
el
an
d
an
al
y
ze
s
y
s
t
e
m
s
w
it
h
m
u
ltip
le
in
p
u
ts
a
n
d
o
u
tp
u
ts
.
T
h
e
s
tate
m
o
d
el
is
n
o
tab
l
y
ad
v
an
ta
g
eo
u
s
w
h
e
n
ap
p
lied
to
s
i
m
u
latio
n
.
Hen
ce
,
t
h
e
s
ta
te
an
d
o
u
tp
u
t e
q
u
atio
n
s
ar
e
g
iv
e
n
i
n
[
2
5
]
as:
t
u
D
t
x
C
t
y
t
u
B
t
x
A
t
x
.
.
.
..
.
(
2
4
)
W
h
er
e,
x
,
y
,
u
,
A
,
B
,
C
,
D
a
r
e
th
e
s
tate
v
ec
to
r
,
o
u
tp
u
t
v
e
cto
r
,
in
p
u
t
v
ec
to
r
,
s
y
s
te
m
m
a
tr
ix
,
in
p
u
t
m
atr
i
x
,
o
u
tp
u
t
m
atr
i
x
an
d
f
ee
d
b
ac
k
m
atr
i
x
r
esp
ec
tiv
el
y
.
L
et
d
ef
i
n
e,
dt
dv
dt
x
d
dt
dv
dt
x
d
2
2
2
2
1
2
1
2
,
2
2
1
1
,
v
dt
dv
v
dt
dx
So
th
at
2
1
2
1
,
,
,
v
v
x
x
ar
e
s
elec
ted
a
s
s
tate
v
ar
iab
les
a
n
d
eq
u
atio
n
E
q
u
ati
o
n
(
2
1
)
an
d
E
q
u
atio
n
(
2
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
S
imu
lin
k
a
n
d
S
imelec
tr
o
n
ics
b
a
s
ed
P
o
s
itio
n
C
o
n
tr
o
l o
f a
C
o
u
p
led
Ma
s
s
-
S
p
r
in
g
Da
mp
er
…
(
Oku
b
a
n
jo
A.A)
3641
ar
e
p
r
esen
ted
in
s
tate
s
p
ac
e
eq
u
atio
n
i
n
v
ec
to
r
m
atr
ix
f
o
r
m
a
s
:
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
2
1
2
2
1
1
2
2
2
2
1
2
1
2
1
1
2
2
2
1
.
2
.
2
.
1
,
1
t
F
m
v
v
x
x
m
b
m
b
m
k
m
k
m
b
m
b
b
m
k
m
k
k
v
x
v
x
(
2
5
)
An
d
th
e
o
u
tp
u
t a
r
e
th
e
d
is
p
lac
e
m
en
t x
1
a
n
d
x
2
o
f
m
as
s
es
m
1
an
d
m
2
r
esp
ec
tiv
e
l
y
.
He
n
ce
,
0
0
0
0
1
0
0
0
0
1
2
1
x
x
t
y
(
2
6
)
3.
M
O
DE
L
I
N
G
O
F
A
CO
UP
L
E
D
M
ASS
SPR
I
NG
DAM
P
E
R
SYS
T
E
M
S
USI
NG
SI
M
E
L
E
C
T
R
O
N
I
CS
AN
D
SI
M
UL
I
NK
A
co
u
p
led
m
a
s
s
s
p
r
in
g
d
a
m
p
er
s
y
s
te
m
is
m
o
d
eled
an
d
s
i
m
u
lated
u
s
i
n
g
Si
m
E
lectr
o
n
ic
s
to
o
lb
o
x
in
MA
T
L
A
B
s
o
f
t
w
ar
e
as
s
h
o
w
n
in
Fi
g
u
r
e
2
.
I
n
M
A
T
L
A
B
s
o
f
t
w
ar
e,
S
i
m
E
lectr
o
n
ics
is
a
c
o
m
p
o
n
en
t
s
l
ib
r
ar
ies
an
d
s
p
ec
ial
s
i
m
u
latio
n
f
ea
t
u
r
e
s
f
o
r
m
o
d
eli
n
g
a
n
d
s
ti
m
u
lati
n
g
p
h
y
s
ical
s
y
s
te
m
i
n
th
e
Si
m
u
li
n
k
e
n
v
ir
o
n
m
en
t.
T
h
e
d
is
tin
ct
f
ea
tu
r
e
o
f
Si
m
E
lectr
o
n
ics
is
t
h
e
u
s
e
o
f
p
h
y
s
ical
n
e
t
w
o
r
k
ap
p
r
o
ac
h
to
m
o
d
el
elec
tr
o
n
ic
a
n
d
m
ec
h
a
tr
o
n
ic
s
y
s
te
m
s
w
h
ic
h
m
i
m
ic
t
h
e
p
h
y
s
ical
s
y
s
te
m
.
T
h
er
ef
o
r
e,
th
e
u
s
e
o
f
p
h
y
s
ical
co
n
n
ec
ti
o
n
p
er
m
its
a
b
id
ir
ec
tio
n
al
f
lo
w
o
f
en
er
g
y
b
et
w
ee
n
co
m
p
o
n
e
n
ts
.
T
h
e
Si
m
E
lectr
o
n
ics
p
er
m
it
t
h
e
u
s
e
o
f
Si
m
u
li
n
k
lib
r
ar
y
i
n
m
o
d
eli
n
g
i
n
w
h
ic
h
Si
m
u
lin
k
-
PS
-
co
n
v
er
ter
b
lo
c
k
co
n
v
er
ts
t
h
e
S
i
m
u
li
n
k
s
ig
n
al
to
p
h
y
s
ica
l
s
y
s
te
m
s
i
g
n
al
an
d
PS
-
Si
m
u
lin
k
co
n
v
er
ter
b
lo
ck
d
o
es
th
e
r
ev
er
s
e
[
2
6
]
.
Ho
w
ev
er
,
Si
m
u
li
n
k
is
a
b
lo
ck
d
iag
r
a
m
e
n
v
ir
o
n
m
e
n
t
e
m
b
ed
d
ed
in
th
e
M
A
T
L
A
B
th
at
allo
w
s
m
o
d
eli
n
g
a
n
d
s
i
m
u
la
tio
n
o
f
m
u
l
ti
-
d
o
m
ain
d
y
n
a
m
ic
s
s
y
s
te
m
s
.
Fig
u
r
e
2
.
Si
m
elec
tr
o
n
ics
m
o
d
e
l f
o
r
a
co
u
p
led
m
a
s
s
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
Fu
r
t
h
er
m
o
r
e,
it
p
r
o
v
id
es
th
e
d
etailed
f
u
n
ctio
n
o
f
ea
ch
b
lo
ck
th
at
r
ep
r
esen
ts
th
e
m
ath
e
m
ati
ca
l
m
o
d
e
l
o
f
th
e
d
y
n
a
m
ic
s
y
s
te
m
a
n
d
s
u
ch
m
o
d
el
is
o
f
te
n
r
ed
u
ce
d
to
f
ir
s
t
o
r
d
er
d
if
f
er
en
tia
l
eq
u
atio
n
to
s
i
m
u
late
th
e
d
y
n
a
m
ic
ac
cu
r
atel
y
.
I
t
is
d
o
m
i
n
an
t
a
m
o
n
g
o
th
er
s
o
f
t
w
ar
e
in
th
e
e
n
g
i
n
ee
r
i
n
g
f
ield
b
ec
au
s
e
it
e
n
ab
les
r
ap
id
d
esig
n
,
s
i
m
u
lat
io
n
,
v
er
i
f
icatio
n
,
test
i
n
g
a
n
d
d
eb
u
g
g
i
n
g
o
f
v
ir
tu
a
l
p
r
o
to
ty
p
es
o
f
a
m
o
d
el
p
r
io
r
to
r
ea
l
-
ti
m
e
i
m
p
le
m
en
ta
tio
n
.
A
s
a
r
esu
lt
o
f
f
le
x
ib
ilit
y
a
n
d
ef
f
icie
n
t
in
u
s
e,
it
p
er
m
its
co
n
v
er
s
io
n
o
f
MA
T
L
A
B
co
d
e
to
o
th
er
s
o
u
r
ce
co
d
es
s
u
ch
as
C
,
C
++
f
o
r
r
ea
l
-
t
i
m
e
i
m
p
le
m
e
n
tat
io
n
esp
ec
iall
y
in
e
m
b
ed
d
ed
s
y
s
te
m
s
a
n
d
r
o
b
o
tic.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
8
:
3
6
3
6
–
3
6
4
6
3642
Si
m
u
li
n
k
m
o
d
el
o
f
a
co
u
p
led
m
as
s
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
i
s
p
r
ep
ar
ed
w
it
h
t
h
e
m
at
h
e
m
atic
al
m
o
d
el
p
r
esen
ted
th
r
o
u
g
h
E
q
u
atio
n
s
(
2
1
)
an
d
(
2
2
)
.
P
D
c
o
n
t
r
o
l
l
e
r
i
s
im
p
l
em
e
n
t
e
d
t
o
t
r
a
c
k
t
h
e
m
a
s
s
e
s
p
o
s
i
t
i
o
n
a
n
d
F
i
g
u
r
e
3
r
e
p
r
e
s
e
n
t
s
a
s
c
h
e
m
a
t
i
c
o
f
t
h
e
S
i
m
u
l
i
n
k
m
o
d
e
l
.
Fig
u
r
e
3
.
Si
m
u
li
n
k
m
o
d
el
f
o
r
a
co
u
p
led
m
a
s
s
s
p
r
i
n
g
d
a
m
p
er
s
y
s
te
m
4.
P
D
CO
NT
RO
L
L
E
R
I
M
P
L
E
M
E
NT
AT
I
O
N
T
h
e
co
n
tr
o
l g
o
al
is
to
s
tab
ilize
th
e
p
o
s
itio
n
o
f
t
h
e
m
ass
e
s
b
y
m
i
n
i
m
izi
n
g
t
h
e
er
r
o
r
an
d
to
ac
h
iev
e
t
h
i
s
s
tated
o
b
j
ec
tiv
e
a
p
r
o
p
o
r
tio
n
al
-
Der
i
v
ati
v
e
co
n
tr
o
ller
is
i
m
p
le
m
e
n
ted
i
n
s
u
ch
a
w
a
y
t
h
at
t
h
e
g
ai
n
o
f
t
h
e
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
,
k
,
i
s
h
ig
h
to
p
r
o
d
u
ce
a
f
ast
s
y
s
te
m
a
n
d
th
e
d
er
i
v
ati
v
e
g
ai
n
k
d
,
is
s
e
lect
in
a
m
a
n
n
e
r
to
d
ec
r
ea
s
e
th
e
o
s
cillatio
n
.
T
h
e
P
D
co
n
tr
o
ller
alg
o
r
ith
m
co
m
b
in
e
s
th
e
P
-
ac
tio
n
a
n
d
D
-
a
ctio
n
to
ad
j
u
s
t
th
e
s
y
s
te
m
.
I
t
i
s
a
t
w
o
-
ter
m
co
n
tr
o
ller
th
at
is
co
i
n
ed
f
r
o
m
t
h
e
P
I
D
co
n
tr
o
ller
b
y
s
etti
n
g
t
h
e
i
n
t
eg
r
al
ac
tio
n
to
ze
r
o
.
T
h
e
ter
m
d
o
m
ai
n
ex
p
r
es
s
io
n
f
o
r
P
D
c
o
n
tr
o
ller
is
g
iv
e
n
as:
dt
t
de
t
k
t
e
k
t
u
D
p
c
(
2
6
)
I
n
th
e
Si
m
u
lin
k
an
d
Si
m
elec
t
r
o
n
ics
m
o
d
els,
a
P
D
co
n
tr
o
lle
r
is
i
m
p
le
m
e
n
ted
f
r
o
m
t
h
e
P
D
b
lo
ck
in
th
e
Si
m
u
li
n
k
to
o
lb
o
x
lib
r
ar
y
an
d
co
n
v
er
ted
to
a
p
h
y
s
ic
al
s
y
s
te
m
w
it
h
Si
m
u
li
n
k
-
P
S
co
n
v
er
te
r
f
o
r
t
h
e
Si
m
elec
tr
o
n
ics.
T
h
e
tu
n
i
n
g
o
f
co
n
tr
o
l
p
ar
am
eter
s
is
d
o
n
e
u
s
in
g
P
I
D
tu
n
er
an
d
t
h
e
b
est
p
er
f
o
r
m
an
ce
o
f
t
h
e
co
n
tr
o
ller
p
ar
am
eter
v
a
lu
e
s
ar
e
s
elec
ted
.
5.
RE
SU
L
T
S
A
ND
AN
AL
Y
SI
S
T
h
is
p
ap
er
p
r
o
p
o
s
ed
a
n
o
v
el
ap
p
r
o
ac
h
o
f
s
i
m
u
lati
n
g
t
h
e
s
y
s
t
e
m
d
y
n
a
m
ics o
f
a
co
u
p
le
m
as
s
s
p
r
in
g
d
am
p
er
s
y
s
te
m
a
n
d
co
m
p
ar
ed
th
e
p
er
f
o
r
m
a
n
ce
w
it
h
th
e
Si
m
u
li
n
k
ap
p
r
o
ac
h
.
T
h
e
Si
m
u
lin
k
m
o
d
el
w
a
s
esta
b
lis
h
ed
b
ased
o
n
th
e
d
er
iv
ed
m
at
h
e
m
a
tical
m
o
d
el
a
n
d
th
e
f
o
r
ce
th
at
m
i
m
ic
a
n
o
b
s
tacle
co
m
m
o
n
l
y
ex
p
er
ien
ce
d
ar
e
b
u
i
ld
w
it
h
a
s
i
g
n
al
b
u
ild
er
b
lo
ck
.
P
ar
a
m
e
ter
s
u
s
ed
in
th
e
m
o
d
el
w
er
e
m
1
=
2
5
0
k
g
,
m
2
=
3
0
0
k
g
,
k
1
=
8
0
,
0
0
0
N/m
,
k
2
=
5
0
0
0
N/
m
,
b
1
=
200N
-
s
/
m
,
b
2
=
1
5
,
0
0
0
N
-
s
/
m
a
n
d
to
v
alid
ate
th
e
m
at
h
e
m
atica
l
m
o
d
el
a
Si
m
elec
tr
o
n
ic
s
an
d
S
i
m
u
li
n
k
m
o
d
els
w
er
e
co
m
p
ar
ed
an
d
th
e
s
i
m
u
latio
n
w
a
s
t
h
en
test
ed
w
it
h
a
n
d
w
it
h
o
u
t
a
co
n
tr
o
ller
.
T
h
e
r
esp
o
n
s
e
o
f
t
h
e
m
a
s
s
p
o
s
i
tio
n
s
ar
e
ill
u
s
tr
ated
in
Fig
u
r
e
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
S
imu
lin
k
a
n
d
S
imelec
tr
o
n
ics
b
a
s
ed
P
o
s
itio
n
C
o
n
tr
o
l o
f a
C
o
u
p
led
Ma
s
s
-
S
p
r
in
g
Da
mp
er
…
(
Oku
b
a
n
jo
A.A)
3643
an
d
Fi
g
u
r
e
5
.
T
h
e
cu
r
v
e
r
ev
ea
ls
t
h
at,
w
i
th
o
u
t
t
h
e
i
m
p
le
m
e
n
t
atio
n
o
f
t
h
e
co
n
tr
o
ller
t
h
e
p
o
s
i
tio
n
s
o
f
t
h
e
m
a
s
s
e
s
o
v
er
s
h
o
o
t s
h
ar
p
l
y
an
d
t
h
en
s
u
s
tain
ed
a
n
o
s
cillatio
n
f
o
r
ab
o
u
t 7
.
6
s
ec
s
b
ef
o
r
e
s
ettlin
g
to
ze
r
o
at
1
0
s
ec
.
Fig
u
r
e
6
s
h
o
w
s
t
h
e
p
er
f
o
r
m
an
ce
o
f
b
o
th
m
o
d
el
s
i
n
t
h
e
ab
s
e
n
ce
o
f
co
n
tr
o
l
s
tr
ate
g
y
,
h
e
n
ce
,
th
e
cu
r
v
e
s
h
o
w
s
t
h
at
th
e
s
y
s
te
m
h
a
s
co
m
p
lex
co
n
j
u
g
ate
p
o
les
n
ea
r
th
e
i
m
a
g
i
n
ar
y
a
x
is
an
d
th
i
s
d
o
m
i
n
ates
t
h
e
tr
a
n
s
i
e
n
t
r
esp
o
n
s
e
o
f
t
h
e
m
as
s
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s
p
r
in
g
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d
am
p
er
s
y
s
te
m
w
h
ich
e
v
e
n
t
u
all
y
r
es
u
lted
i
n
o
s
cil
latio
n
a
n
d
th
is
led
to
s
y
s
te
m
in
s
tab
il
it
y
.
Ho
w
e
v
er
,
it
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c
h
alle
n
g
in
g
to
s
tab
ilize
o
r
co
n
tr
o
l
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e
m
o
d
el
w
ith
th
e
p
r
o
p
o
r
tio
n
al
co
n
tr
o
ller
alo
n
e
ir
r
esp
ec
tiv
e
o
f
t
h
e
v
a
lu
e
o
f
g
a
in
K
c
h
o
s
en
,
h
en
ce
,
a
co
m
b
i
n
atio
n
o
f
p
r
o
p
o
r
tio
n
al
an
d
th
e
d
er
iv
ativ
e
co
n
tr
o
ller
is
i
m
p
le
m
e
n
ted
to
co
m
p
en
s
ate
f
o
r
f
ast
r
esp
o
n
s
e
a
n
d
s
t
ea
d
y
er
r
o
r
r
esp
ec
tiv
el
y
.
Fi
g
u
r
e
7
an
d
Fig
u
r
e
8
s
h
o
w
t
h
e
r
esp
o
n
s
es
o
f
t
h
e
d
is
p
lace
m
e
n
ts
o
f
th
e
m
as
s
es
w
it
h
th
e
i
m
p
le
m
en
ta
tio
n
o
f
P
D
co
n
tr
o
ller
.
A
cc
o
r
d
in
g
to
th
e
F
ig
u
r
e
7
,
Fig
u
r
e
8
,
th
e
P
D
-
ac
tio
n
d
a
m
p
ed
th
e
o
s
cillatio
n
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d
s
tab
ilized
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e
p
o
s
itio
n
s
b
y
co
m
p
e
n
s
at
in
g
f
o
r
th
e
s
tead
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er
r
o
r
.
I
n
Fig
u
r
e
9
,
b
o
th
m
o
d
els
w
er
e
co
m
p
ar
ed
u
n
d
er
th
e
in
f
l
u
e
n
ce
o
f
P
D
co
n
tr
o
lle
r
an
d
th
e
co
n
tr
o
ller
co
m
p
e
n
s
ate
s
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o
r
t
h
e
er
r
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r
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th
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p
o
s
itio
n
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n
d
s
tab
ilized
th
e
p
o
s
itio
n
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to
ze
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o
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it
h
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s
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ti
m
e
o
f
6
.
5
s
ec
an
d
s
i
g
n
i
f
ica
n
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y
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ce
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t
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er
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o
o
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y
9
9
.
5
%
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d
9
9
.
7
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in
Si
m
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l
in
k
a
n
d
Si
m
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tr
o
n
ics
r
esp
ec
ti
v
el
y
.
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t
ca
n
also
b
e
n
o
ted
f
r
o
m
t
h
e
g
r
ap
h
th
at,
th
e
r
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n
s
e
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o
f
b
o
t
h
m
o
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el
s
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o
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a
s
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m
ilar
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s
u
l
t
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r
t
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er
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o
r
e,
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e
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lt
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h
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o
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eli
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g
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th
e
m
ath
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m
atica
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eq
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ati
o
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m
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d
a
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li
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h
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h
y
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ical
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y
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te
m
i
n
Si
m
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tr
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n
ic
s
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v
e
a
s
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m
ilar
r
esu
lt.
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n
m
u
c
h
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elate
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r
esear
ch
w
o
r
k
[
2
7
]
,
th
e
d
y
n
a
m
ic
s
ar
e
tr
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s
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o
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ed
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s
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m
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s
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it
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m
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licated
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lex
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m
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h
e
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o
v
el
Si
m
e
lectr
o
n
ics
ap
p
r
o
ac
h
p
r
o
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u
ick
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d
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ast ap
p
r
o
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el,
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ate
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te
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co
n
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o
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u
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ai
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eli
m
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ati
n
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r
ig
o
r
o
u
s
m
at
h
e
m
atica
l
f
o
r
m
u
latio
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o
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h
e
s
y
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te
m
’
s
d
y
n
a
m
ic
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.
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a
ls
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itab
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o
r
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r
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g
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n
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p
er
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o
r
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lab
o
r
ato
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s
co
n
tr
o
l
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d
r
elate
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u
r
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es t
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r
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ir
e
m
o
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elli
n
g
an
d
s
i
m
u
lat
io
n
.
Fig
u
r
e
4
.
Dis
p
lece
m
e
n
ts
w
i
th
o
u
t c
o
n
tr
o
ller
in
s
i
m
e
lectr
o
n
ics
m
o
d
el
Fig
u
r
e
5
.
P
o
s
tio
n
s
w
i
th
o
u
t c
o
n
tr
o
ller
in
s
i
m
u
l
in
k
m
o
d
el
Fig
u
r
e
6
.
P
o
s
tio
n
s
in
b
o
th
s
i
m
elec
tr
o
n
ics an
d
s
i
m
u
li
n
k
m
o
d
e
ls
w
it
h
o
u
t c
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
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t J
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m
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,
Vo
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8
,
No
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5
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Octo
b
er
2
0
1
8
:
3
6
3
6
–
3
6
4
6
3644
Fig
u
r
e
7
.
P
o
s
itio
n
s
r
esp
o
n
s
e
with
P
D
co
n
tr
o
ller
in
Si
m
elec
tr
o
n
ics
m
o
d
el
Fig
u
r
e
8
.
P
o
s
itio
n
s
r
esp
o
n
s
e
with
P
D
co
n
tr
o
ller
in
Si
m
u
li
n
k
m
o
d
el
Fig
u
r
e
9
.
P
o
s
itio
n
r
esp
o
n
s
es o
f
b
o
th
Si
m
elec
tr
o
n
ic
s
an
d
Si
m
u
li
n
k
m
o
d
el
6.
CO
NCLU
SI
O
N
I
n
t
h
is
p
ap
er
,
Si
m
u
li
n
k
a
n
d
Si
m
elec
tr
o
n
ics
m
o
d
el
f
o
r
p
o
s
itio
n
co
n
tr
o
l
o
f
a
co
u
p
led
m
ass
-
s
p
r
in
g
-
d
am
p
er
s
y
s
te
m
w
er
e
d
e
v
elo
p
ed
an
d
p
r
esen
ted
.
T
h
e
m
at
h
e
m
atica
l
m
o
d
el
w
a
s
f
o
r
m
u
late
d
b
ased
o
n
e
n
er
g
y
p
r
o
p
er
ty
o
f
L
ag
r
a
n
g
e
ap
p
r
o
ac
h
a
n
d
R
a
y
lei
g
h
’
s
d
i
s
s
ip
atio
n
f
u
n
ctio
n
to
ac
co
u
n
t
f
o
r
d
is
s
i
p
ativ
e
f
o
r
ce
i
n
t
h
e
m
o
d
el,
h
e
n
ce
,
t
h
e
co
n
tr
o
l
s
tr
ateg
y
a
n
d
Si
m
u
li
n
k
s
i
m
u
lati
o
n
w
er
e
e
x
p
an
d
ed
o
n
th
e
d
er
iv
ed
m
a
th
e
m
atica
l
m
o
d
el
w
h
ile
t
h
e
p
h
y
s
ical
s
y
s
t
e
m
w
as
s
et
u
p
in
th
e
Si
m
elec
t
r
o
n
ics
to
s
ti
m
u
late
t
h
e
d
y
n
a
m
ic.
A
p
r
o
p
o
r
tio
n
al
-
Der
iv
ati
v
e
(
P
D)
co
n
tr
o
ller
w
as
i
m
p
le
m
e
n
ted
f
o
r
b
o
th
th
e
m
o
d
el
s
.
I
t
ca
n
b
e
co
n
clu
d
ed
f
r
o
m
t
h
e
s
t
u
d
y
t
h
at
b
o
th
m
o
d
els
p
r
o
d
u
ce
d
th
e
s
a
m
e
r
es
u
lts
,
b
u
t
th
e
r
e
s
p
o
n
s
e
ti
m
e
o
f
th
e
p
o
s
itio
n
s
w
a
s
s
lig
h
tl
y
s
h
o
r
ter
in
Si
m
u
li
n
k
t
h
an
t
h
at
o
f
th
e
Si
m
elec
tr
o
n
ic
s
.
I
t
ca
n
al
s
o
b
e
d
ed
u
ce
d
th
at
it
w
as
s
i
m
p
le,
ea
s
y
,
le
s
s
ti
m
e
-
i
n
te
n
s
e
an
d
r
eq
u
ir
es
n
o
m
a
th
e
m
atica
l
m
o
d
el
to
m
o
d
el
in
th
e
Si
m
elec
tr
o
n
ic
s
t
h
an
Si
m
u
li
n
k
,
alt
h
o
u
g
h
,
Si
m
u
li
n
k
p
r
o
v
id
ed
th
e
ad
v
an
tag
e
o
f
a
s
d
etailed
r
ep
r
esen
tatio
n
o
f
th
e
m
a
th
e
m
atica
l
m
o
d
el.
I
n
o
u
r
f
u
t
u
r
e
w
o
r
k
,
w
e
w
o
u
ld
lik
e
to
(
1
)
tak
e
i
n
to
ac
co
u
n
t
t
h
e
i
m
p
ac
t
o
f
n
o
n
li
n
ea
r
it
y
o
f
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h
e
s
p
r
in
g
a
n
d
d
a
m
p
er
i
n
o
u
r
m
o
d
el;
(
2
)
to
i
m
p
le
m
en
t
s
tate
f
ee
d
b
ac
k
co
n
tr
o
ller
an
d
L
QR
a
n
d
co
m
p
a
r
e
th
e
p
er
f
o
r
m
a
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ce
;
(
3
)
an
al
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f
ec
t
o
f
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p
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t p
ar
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m
eter
s
b
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ar
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n
g
t
h
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p
ar
a
m
e
ter
s
.
T
h
e
co
n
tr
ib
u
tio
n
o
f
t
h
is
w
o
r
k
is
s
ig
n
i
f
ica
n
tl
y
e
x
p
ed
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t
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ield
o
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h
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o
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o
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ical
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.
ACK
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r
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Un
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Scien
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p
o
r
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
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8
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8708
S
imu
lin
k
a
n
d
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a
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P
o
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C
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o
l o
f a
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p
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Ma
s
s
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p
r
in
g
Da
mp
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…
(
Oku
b
a
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jo
A.A)
36
45
RE
F
E
R
E
NC
E
S
[1
]
S.
-
M
.
S
.
A
n
a
ly
sis,
H.
A
h
m
a
d
,
M
.
T
a
ri
k
,
H.
A
.
Bh
u
tt
a
,
a
n
d
M
.
T
a
riq
,
“
A
n
In
tera
c
ti
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u
c
a
ti
o
n
a
l
To
o
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f
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Co
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tera
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e
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u
c
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o
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o
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Do
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le
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a
ss
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a
m
p
e
r
S
y
ste
m
A
n
a
l
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sis
&
Co
n
tr
o
l
”
,
i
n
Pro
c
e
e
d
in
g
s
o
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th
e
3
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ter
n
a
t
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o
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a
l
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n
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En
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&
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rg
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e
c
h
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o
lo
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ies
(
IC
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),
S
u
p
e
rio
r
Un
ive
rs
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y
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L
a
h
o
re
,
2
0
1
6
,
n
o
.
De
c
e
m
b
e
r.
[2
]
S
.
S
.
G
e
,
L
.
Hu
a
n
g
,
a
n
d
T
.
H.
L
e
e
,
“
P
o
siti
o
n
Co
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tro
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o
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Ch
a
in
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M
u
lt
ip
le
M
a
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p
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g
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Da
m
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b
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n
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o
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p
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a
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s
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,
In
t.
J
.
C
o
n
tr
o
l.
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u
to
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S
y
st.
V
o
l.
,
v
o
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2
,
n
o
.
2
,
p
p
.
1
4
4
-
1
5
5
,
2
0
0
4
.
[3
]
K.
V
.
A
ll
a
m
ra
ju
,
“
D
y
n
a
m
ic
A
n
a
ly
sis
o
f
a
n
A
u
to
m
o
b
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e
S
u
sp
e
n
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o
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S
y
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”
,
IPA
S
J
In
t.
J
.
M
e
c
h
.
En
g
.
,
v
o
l.
4
,
n
o
.
7
,
p
p
.
1
5
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1
,
2
0
1
6
.
[4
]
N.
Ka
tal
a
n
d
S
.
K.
S
in
g
h
,
“
Op
ti
m
iz
a
ti
o
n
o
f
P
ID
Co
n
tro
ll
e
r
f
o
r
Qu
a
rter
-
Ca
r
S
u
sp
e
n
sio
n
S
y
ste
m
u
sin
g
Ge
n
e
ti
c
A
l
g
o
rit
h
m
”
,
In
t.
J
.
A
d
v
.
Res
.
C
o
mp
u
t.
En
g
.
T
e
c
h
n
o
l.
,
v
o
l.
1
,
n
o
.
7
,
p
p
.
3
0
-
3
2
,
2
0
1
2
.
[5
]
A
.
El
-
Na
ss
e
r,
S
.
A
h
m
e
d
,
A
.
S
.
Ali,
N.
M
.
G
h
a
z
a
l
y
,
a
n
d
G
.
T
.
A
b
d
El
-
Ja
b
e
r,
“
P
id
Co
n
tro
ll
e
r
o
f
A
c
ti
v
e
S
u
sp
e
n
si
o
n
S
y
st
e
m
f
o
r
a
Qu
a
rter Car M
o
d
e
l
”
,
In
t.
J
.
Ad
v
.
En
g
.
T
e
c
h
n
o
l.
,
v
o
l
.
8
,
n
o
.
6
,
p
p
.
8
9
9
-
9
0
9
,
2
0
1
5
.
[6
]
M
.
Ak
p
a
k
p
a
v
i,
“
M
o
d
e
li
n
g
a
n
d
Co
n
tr
o
l
o
f
a
Ca
r
S
u
sp
e
n
sio
n
S
y
ste
m
Us
in
g
P
,
P
I
,
P
I
D
,
GA
-
P
ID
a
n
d
A
u
to
-
T
u
n
e
d
P
ID C
o
n
tro
ll
e
r
i
n
M
a
tl
a
b
/S
im
u
li
n
k
”
,
J
.
M
u
lt
id
isc
ip
.
En
g
.
S
c
i.
S
tu
d
.
,
v
o
l.
3
,
n
o
.
3
,
p
p
.
1
5
0
6
-
1
5
1
3
,
2
0
1
7
.
[7
]
G
.
S
rin
iv
a
sa
n
,
M
.
S
.
Ku
m
a
r,
a
n
d
A
.
M
.
J.
Ba
sh
a
,
“
M
a
th
e
m
a
ti
c
a
l
M
o
d
e
li
n
g
a
n
d
P
ID
Co
n
tr
o
ll
e
r
De
sig
n
Us
in
g
T
ra
n
s
f
e
r
F
u
n
c
ti
o
n
a
n
d
Ro
o
t
L
o
c
u
s
M
e
th
o
d
f
o
r
A
c
ti
v
e
S
u
sp
e
n
sio
n
S
y
st
e
m
”
,
M
id
d
le
-
Ea
st
J
.
S
c
i.
Res
.
,
v
o
l.
2
4
,
n
o
.
3
,
p
p
.
6
2
2
-
6
2
7
,
2
0
1
6
.
[8
]
N.
Ba
h
iah
,
M
.
No
o
r,
a
n
d
M
.
R.
A
h
m
a
d
,
“
M
o
d
e
li
n
g
th
e
V
i
b
ra
ti
o
n
a
l
D
y
n
a
m
ics
o
f
P
iez
o
e
lec
tri
c
A
c
t
u
a
to
r
b
y
S
y
ste
m
Id
e
n
ti
f
ica
ti
o
n
T
e
c
h
n
iq
u
e
”
,
v
o
l.
7
,
n
o
.
3
,
p
p
.
1
5
0
6
-
1
5
1
2
,
2
0
1
7
.
[9
]
S
.
Ku
n
d
u
a
n
d
H.
B.
Ne
m
a
d
e
,
“
M
o
d
e
li
n
g
a
n
d
S
im
u
latio
n
o
f
a
P
iez
o
e
lec
tri
c
V
ib
ra
ti
o
n
E
n
e
rg
y
Ha
r
v
e
ste
r
”
,
Pro
c
e
d
ia
En
g
.
,
v
o
l.
1
4
4
,
p
p
.
5
6
8
-
5
7
5
,
2
0
1
6
.
[1
0
]
R.
Ca
li
ò
e
t
a
l.
,
“
P
iez
o
e
lec
t
ric E
n
e
rg
y
Ha
r
v
e
stin
g
S
o
lu
ti
o
n
s
”
,
S
e
n
so
rs
,
v
o
l.
1
4
,
n
o
.
1
2
,
p
p
.
4
7
5
5
-
4
7
9
0
,
M
a
r.
2
0
1
4
.
[1
1
]
S
.
F
.
S
u
laim
a
n
e
t
a
l.
,
“
En
h
a
n
c
e
d
P
o
siti
o
n
C
o
n
t
ro
l
f
o
r
P
n
e
u
m
a
ti
c
S
y
ste
m
b
y
A
p
p
l
y
i
n
g
Co
n
st
ra
in
ts
in
M
P
C
A
l
g
o
rit
h
m
”
,
In
t.
J
.
El
e
c
tr.
C
o
mp
u
t.
En
g
.
,
v
o
l.
7
,
n
o
.
3
,
p
.
1
6
3
3
,
J
u
n
.
2
0
1
7
.
[1
2
]
R.
M
e
i
a
n
d
M
.
Ch
e
n
,
“
R
o
b
u
st
P
o
siti
o
n
C
o
n
tr
o
l
o
f
El
e
c
tro
-
m
e
c
h
a
n
ica
l
S
y
ste
m
s
”
,
T
EL
KOM
NIKA
(
T
e
lec
o
mm
u
n
ica
ti
o
n
,
Co
m
p
u
t
in
g
,
El
e
c
tro
n
ics
a
n
d
Co
n
tro
l)
,
v
o
l.
1
1
,
n
o
.
3
,
p
p
.
1
6
7
4
-
1
6
8
1
,
2
0
1
3
.
[1
3
]
P
.
S
iv
á
k
a
n
d
D.
Hro
n
c
o
v
á
,
“
S
tate
-
S
p
a
c
e
M
o
d
e
l
o
f
a
M
e
c
h
a
n
ica
l
S
y
st
e
m
in
M
ATLA
B/S
i
m
u
li
n
k
”
,
Pr
o
c
e
d
ia
E
n
g
.
,
v
o
l.
4
8
,
p
p
.
6
2
9
-
6
3
5
,
2
0
1
2
.
[1
4
]
A
.
T
a
n
d
e
l,
A
.
R.
De
sh
p
a
n
d
e
,
S
.
P
.
De
sh
m
u
k
h
,
a
n
d
K
.
R.
Ja
g
tap
,
“
M
o
d
e
li
n
g
,
A
n
a
l
y
sis
a
n
d
P
ID
C
o
n
tr
o
ll
e
r
Im
p
le
m
e
n
tatio
n
o
n
Do
u
b
le
W
ish
b
o
n
e
S
u
s
p
e
n
sio
n
Us
in
g
S
im
M
e
c
h
a
n
ics
a
n
d
S
im
u
li
n
k
”
,
Pro
c
e
d
ia
En
g
.
,
v
o
l.
9
7
,
p
p
.
1
2
7
4
-
1
2
8
1
,
2
0
1
4
.
[1
5
]
M
.
M
o
ra
v
ič,
O.
Os
terta
g
,
a
n
d
D.
Hro
n
c
o
v
á
,
“
S
im
u
latio
n
o
f
Th
re
e
-
m
a
ss
M
e
c
h
a
n
ica
l
S
y
ste
m
u
sin
g
M
ATLA
B
S
o
f
tw
a
r
e
”
,
J
.
Au
to
m.
C
o
n
tr
o
l
,
v
o
l
.
3
,
n
o
.
3
,
p
p
.
1
1
4
-
1
1
7
,
2
0
1
5
.
[1
6
]
E.
K.
Or
h
o
r
h
o
r
o
,
D.
S
.
P
o
ly
tec
h
n
ic,
M
.
E.
On
o
g
b
o
tse
re
,
D.
S
.
P
o
ly
tec
h
n
ic,
A
.
E.
Ik
p
e
,
a
n
d
U.
Ki
n
g
d
o
m
,
“
S
im
u
latio
n
o
f
a
m
a
ss
sp
rin
g
d
a
m
p
e
r
m
o
d
e
l
in
p
h
a
se
v
a
riab
le
”
,
E
L
K
Asia
Pa
c
if
ic
J
.
M
e
c
h
.
En
g
.
Res
.
,
v
o
l.
2
,
n
o
.
2
,
2
0
1
6
.
[1
7
]
J.
O.
Kira
n
a
n
d
D.
S
h
iv
a
li
n
g
a
p
p
a
,
“
S
tu
d
y
o
n
th
e
Ef
fe
c
t
o
f
P
o
siti
o
n
o
f
th
e
Da
m
p
e
rs
in
S
y
ste
m
s
w
it
h
3
De
g
re
e
s
o
f
F
re
e
d
o
m
”
,
In
t.
J
.
E
n
g
.
T
e
c
h
n
o
l.
A
d
v
.
En
g
.
,
v
o
l.
3
,
n
o
.
4
,
p
p
.
1
5
5
-
1
6
3
,
2
0
1
3
.
[1
8
]
R.
S
h
a
rm
a
,
D.
K.
P
a
th
a
k
,
a
n
d
V.
K.
Dw
iv
e
d
i,
“
M
o
d
e
li
n
g
&
S
im
u
latio
n
o
f
S
p
ri
n
g
M
a
ss
Da
m
p
e
r
S
y
ste
m
in
S
im
u
li
n
k
En
v
iro
n
m
e
n
t
”
,
in
X
VII
I
An
n
u
a
l
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
f
th
e
S
o
c
ie
ty
o
f
Op
e
ra
ti
o
n
s
M
a
n
a
g
e
me
n
t
T
h
e
me
:
Op
e
ra
ti
o
n
s M
a
n
a
g
e
me
n
t
in
Di
g
it
a
l
Eco
n
o
my
,
2
0
1
4
,
n
o
.
M
a
y
2
0
1
6
,
p
p
.
2
0
5
-
2
1
0
.
[1
9
]
P
.
F
ra
n
k
o
v
sk
ý
,
D.
Hro
n
c
o
v
á
,
I.
De
ly
o
v
á
,
a
n
d
I.
V
irg
a
la,
“
M
o
d
e
li
n
g
o
f
Dy
n
a
m
ic
S
y
ste
m
s
in
S
im
u
latio
n
En
v
iro
n
m
e
n
t
M
A
TL
A
B/S
i
m
u
li
n
k
–
S
im
M
e
c
h
a
n
ics
”
,
Am.
J
.
M
e
c
h
.
En
g
.
,
v
o
l.
1
,
n
o
.
7
,
p
p
.
2
8
2
-
2
8
8
,
2
0
1
3
.
[2
0
]
S
.
N.
J.Ra
h
m
a
n
,
M
.
M
u
s
h
taq
,
A
.
A
li
,
Y.N.
A
n
ja
m
,
“
Jo
u
rn
a
l
o
f
F
a
c
u
lt
y
o
f
En
g
in
e
e
rin
g
&
T
e
c
h
n
o
l
o
g
y
”
,
J
.
Fa
c
.
En
g
.
T
e
c
h
n
o
l
.
J
.
h
o
me
p
a
g
e
,
v
o
l
.
1
8
,
n
o
.
9
2
,
p
p
.
4
7
-
5
7
,
2
0
1
1
.
[2
1
]
S
.
Ra
n
n
e
n
,
C.
G
h
o
rb
e
l,
a
n
d
N.
B.
Bra
iek
,
“
No
n
li
n
e
a
r
I
d
e
n
ti
f
ica
ti
o
n
a
n
d
Co
n
tro
l
o
f
Co
u
p
led
M
a
ss
-
S
p
rin
g
-
Da
m
p
e
r
S
y
s
t
e
m
u
sin
g
P
o
ly
n
o
m
ial
S
tru
c
tu
re
s
”
,
In
t.
J
.
A
d
v
.
Co
m
p
u
t
.
S
c
i
.
A
p
p
l.
,
v
o
l.
8
,
n
o
.
5
,
2
0
1
7
.
[2
2
]
A
.
M
a
la
s
a
n
d
S
.
Ch
a
tt
e
rjee
,
“
Am
p
li
tu
d
e
Co
n
tr
o
ll
e
d
A
d
a
p
ti
v
e
F
e
e
d
b
a
c
k
Re
so
n
a
n
c
e
in
a
S
in
g
le
De
g
r
e
e
-
of
-
F
re
e
d
o
m
M
a
ss
-
S
p
rin
g
M
e
c
h
a
n
ica
l
S
y
ste
m
”
,
Pro
c
e
d
ia
En
g
.
,
v
o
l.
1
4
4
,
p
p
.
6
9
7
-
7
0
4
,
2
0
1
6
.
[2
3
]
A
.
A
.
Ok
u
b
a
n
jo
a
n
d
O.
K.
Oy
e
to
la,
Amit
y
J
.
En
g
.
T
e
c
h
n
o
l.
,
v
o
l.
2
,
n
o
.
1
,
p
p
.
1
-
1
8
,
2
0
1
7
.
[2
4
]
C.
U
rre
a
a
n
d
J.
P
a
sc
a
l,
“
P
a
ra
m
e
ter
Id
e
n
ti
f
ica
ti
o
n
M
e
th
o
d
s
f
o
r
Re
a
l
Re
d
u
n
d
a
n
t
M
a
n
i
p
u
lat
o
rs
”
,
J
.
Ap
p
l.
Res
.
T
e
c
h
n
o
l
.
,
v
o
l
.
1
5
,
p
p
.
3
2
0
-
3
3
1
,
2
0
1
7
.
[2
5
]
N.
No
rm
a
n
S
,
Co
n
tro
l
S
y
ste
m
s E
n
g
in
e
e
rin
g
,
S
ix
th
.
Riv
e
r
S
tree
t
H
o
b
o
k
e
n
:
S
o
n
s,
Jo
h
n
W
il
e
y
&
S
o
n
s,
2
0
1
1
.
[2
6
]
J.
M
.
Ka
n
e
,
“
A
u
se
r’
g
u
id
e
t
o
S
i
m
sc
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