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ticle
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y:
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Two
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se
lf
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b
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c
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(T
WS
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ters
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2
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c
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i
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ter
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,
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term
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=
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0
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P
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r.
K
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:
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P
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rticle
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CC B
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C
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uth
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p
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Ar
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Do
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asiri
Dep
ar
tm
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Ph
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Facu
lty
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Ap
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Scien
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s
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Un
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ity
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g
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a
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Sri
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k
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m
ail:
d
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u
@
s
jp
.
ac
.
lk
1.
I
NT
RO
D
UCT
I
O
N
T
wo
-
wh
ee
led
s
elf
-
b
alan
cin
g
r
o
b
o
ts
(
T
W
SB
R
)
h
av
e
g
ar
n
er
ed
s
ig
n
if
ican
t
atten
tio
n
f
r
o
m
r
o
b
o
tics
ex
p
er
ts
[
1
]
–
[
4
]
.
“Seg
way
”
is
th
e
b
est ap
p
licatio
n
wh
er
e
T
W
SB
R
is
in
ac
tio
n
in
th
e
f
ield
o
f
tr
an
s
p
o
r
tatio
n
[
5
]
,
[
6
]
.
T
h
e
b
asic
p
h
y
s
ics
o
f
th
e
T
W
S
B
R
i
s
th
e
p
r
in
cip
le
o
f
an
i
n
v
er
ted
p
en
d
u
lu
m
[
7
]
.
T
h
e
in
v
er
ted
p
e
n
d
u
lu
m
is
a
wid
ely
u
s
ed
m
o
d
el
in
r
o
b
o
ti
cs
an
d
co
n
tr
o
l
th
eo
r
y
[
8
]
,
[
9
]
,
wh
er
e
it
co
n
s
is
ts
o
f
a
m
ass
h
eld
ab
o
v
e
a
p
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o
ted
p
o
in
t
a
n
d
th
e
s
y
s
tem
is
in
h
er
en
tly
u
n
s
tab
le.
B
u
t
it
ca
n
b
e
h
eld
with
o
u
t
f
allin
g
b
y
ap
p
ly
i
n
g
s
u
itab
le
to
r
q
u
es
with
th
e
aid
o
f
a
p
r
o
p
er
ly
t
u
n
e
d
co
n
tr
o
l s
y
s
tem
[
1
0
]
,
[
1
1
]
.
T
h
e
v
er
tical
o
r
ien
tatio
n
o
f
a
n
in
v
e
r
ted
p
en
d
u
lu
m
is
a
n
u
n
s
tab
le
eq
u
ilib
r
iu
m
s
tate.
An
y
s
lig
h
t
d
is
tu
r
b
an
ce
ca
n
t
o
p
p
le
th
e
p
en
d
u
lu
m
.
Ho
wev
e
r
,
p
r
o
v
id
in
g
co
u
n
te
r
b
alan
cin
g
to
r
q
u
es
at
ap
p
r
o
p
r
iate
tim
e
in
ter
v
als
th
r
o
u
g
h
m
o
to
r
s
co
n
n
ec
ted
to
its
wh
ee
ls
m
a
k
es
it
p
o
s
s
ib
le
to
k
ee
p
th
e
p
en
d
u
lu
m
v
er
tically
,
with
o
u
t
f
allin
g
.
I
n
o
r
d
e
r
t
o
g
en
er
ate
to
r
q
u
es
with
th
e
co
r
r
ec
t
m
a
g
n
itu
d
e
at
th
e
c
o
r
r
ec
t
tim
e,
t
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e
o
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o
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th
e
p
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l
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m
m
u
s
t
b
e
m
o
n
ito
r
ed
u
s
in
g
s
u
itab
le
s
en
s
o
r
s
.
Usi
n
g
th
is
f
ee
d
b
ac
k
f
r
o
m
s
en
s
o
r
s
,
a
s
u
itab
le
alg
o
r
ith
m
ca
n
b
e
u
s
ed
f
o
r
ca
lc
u
latin
g
th
e
co
u
n
ter
b
alan
cin
g
t
o
r
q
u
e.
I
n
s
o
m
e
p
r
ev
io
u
s
r
esear
c
h
wo
r
k
s
d
is
cu
s
s
th
e
ap
p
licatio
n
o
f
class
ical
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
-
d
er
iv
ativ
e
(
PID
)
co
n
t
r
o
ller
f
o
r
m
ain
tain
i
n
g
th
e
b
alan
ce
o
f
T
W
SB
R
[
1
2
]
–
[
1
5
]
.
T
h
e
d
esig
n
a
n
d
s
im
u
latio
n
o
f
a
T
W
SB
R
with
a
PID
co
n
tr
o
ller
to
m
ai
n
tain
b
alan
ce
b
y
ad
j
u
s
tin
g
th
e
an
g
u
lar
v
elo
city
o
f
d
ir
e
ct
cu
r
r
en
t
(
DC
)
m
o
to
r
s
th
r
o
u
g
h
p
u
ls
e
wid
th
m
o
d
u
lati
o
n
(
PW
M)
is
p
r
esen
ted
in
[
1
3
]
.
I
n
[
1
2
]
im
p
lem
en
tatio
n
o
f
a
two
-
wh
ee
l
s
elf
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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8
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I
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t J E
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&
C
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p
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,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
1
3
-
3620
3614
b
alan
cin
g
r
o
b
o
t
u
s
in
g
MA
T
L
AB
Simscap
e
m
u
ltib
o
d
y
t
o
s
im
u
late,
h
ar
d
war
e
d
esig
n
,
an
d
ca
lcu
late
th
e
to
r
q
u
e
an
d
s
p
ee
d
r
e
q
u
ir
em
en
ts
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o
m
ain
tain
th
e
s
tab
ilit
y
o
f
T
W
S
B
R
u
s
in
g
th
e
PID
alg
o
r
ith
m
was
d
is
cu
s
s
ed
.
Nev
er
th
eless
,
it
is
im
p
o
r
tan
t
to
n
o
te
th
at
n
o
n
e
o
f
th
e
s
tu
d
ies
p
r
esen
ted
in
[
1
2
]
–
[
1
5
]
s
p
ec
if
ically
ad
d
r
ess
p
ay
lo
ad
a
d
ap
tab
ilit
y
o
r
p
r
ac
tic
al
v
o
ltag
e
lim
itatio
n
s
.
T
h
e
ap
p
licatio
n
o
f
lin
ea
r
-
q
u
a
d
r
atic
r
eg
u
lato
r
(
L
QR
)
co
n
tr
o
l
f
o
r
T
W
SB
R
b
alan
cin
g
is
d
is
cu
s
s
ed
in
[
1
6
]
–
[
2
0
]
.
I
n
[
1
6
]
,
th
e
L
QR
co
n
tr
o
l
h
as
b
ee
n
d
ev
elo
p
ed
b
y
u
s
in
g
th
e
p
ar
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
alg
o
r
ith
m
,
lead
in
g
to
en
h
a
n
ce
d
co
n
tr
o
ller
p
er
f
o
r
m
a
n
ce
with
less
o
v
er
s
h
o
o
t
an
d
k
ee
p
in
g
th
e
s
tead
y
-
s
tate
er
r
o
r
ze
r
o
.
T
h
e
m
ath
em
atica
l
m
o
d
e
l
o
f
th
e
T
W
SB
R
s
y
s
tem
was
in
itially
an
aly
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d
u
s
in
g
New
t
o
n
ian
m
ec
h
an
ics
in
th
e
r
esear
ch
wo
r
k
p
r
esen
ted
b
y
[
1
7
]
.
Su
b
s
eq
u
e
n
tl
y
,
t
h
e
au
th
o
r
s
ef
f
ec
tiv
ely
im
p
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ted
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L
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n
tr
o
ller
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o
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th
is
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s
tem
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s
in
a
MA
T
L
A
B
/Si
m
u
lin
k
en
v
ir
o
n
m
en
t
to
ev
a
lu
ate
th
e
co
n
tr
o
ller
u
n
d
er
v
ar
io
u
s
co
n
d
itio
n
s
.
An
an
d
L
i
[
2
1
]
p
r
esen
ted
th
e
co
m
p
ar
is
o
n
o
f
th
e
p
er
f
o
r
m
a
n
ce
o
f
T
W
SB
R
with
th
e
PID
co
n
tr
o
l
alg
o
r
ith
m
an
d
lin
ea
r
-
q
u
a
d
r
atic
r
eg
u
la
to
r
(
L
QR
)
co
n
tr
o
l
alg
o
r
ith
m
,
th
e
r
esu
lt
s
h
o
ws
th
at
L
QR
h
as
a
b
etter
p
er
f
o
r
m
a
n
ce
th
an
PID
f
o
r
T
W
SB
R
co
n
tr
o
l.
So
m
e
r
esear
ch
er
s
em
p
lo
y
ed
n
o
n
lin
ea
r
co
n
t
r
o
ller
s
,
s
p
ec
if
ically
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
an
d
f
u
zz
y
PID
co
n
tr
o
ller
s
,
in
th
eir
s
tu
d
y
t
o
en
s
u
r
e
th
e
s
tab
ili
ty
o
f
T
W
SB
R
[
2
2
]
,
[
2
3
]
.
T
h
e
r
esu
lts
d
em
o
n
s
tr
ated
th
at
b
o
th
f
u
zz
y
lo
g
ic
co
n
t
r
o
l
an
d
f
u
zz
y
PID
co
n
tr
o
ller
ef
f
ec
tiv
ely
p
r
ev
en
ted
th
e
r
o
b
o
t
f
r
o
m
f
al
lin
g
,
ac
h
iev
in
g
th
e
d
esire
d
co
n
tr
o
l
o
b
jectiv
es
an
d
im
p
r
o
v
in
g
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
Hass
an
et
a
l.
[
2
4
]
p
r
esen
ts
a
d
etaile
d
o
v
er
v
iew
o
f
t
h
e
m
ath
em
atica
l m
o
d
el
d
ev
el
o
p
m
en
t
u
s
in
g
L
a
g
r
an
g
e
k
in
e
m
atics,
th
e
d
esig
n
o
f
a
s
tab
il
izin
g
PID
co
n
tr
o
ller
,
an
d
th
e
ev
alu
atio
n
o
f
r
ea
l
-
tim
e
o
p
tim
al
p
ar
am
et
er
esti
m
atio
n
tech
n
iq
u
es.
Had
d
o
u
t
[
6
]
d
is
cu
s
s
ed
th
e
u
tili
za
tio
n
o
f
n
o
n
h
o
lo
n
o
m
ic
m
ec
h
an
ics
f
o
r
th
e
p
u
r
p
o
s
e
o
f
m
o
d
elin
g
a
n
d
s
im
u
latin
g
t
h
e
T
W
SB
R
s
y
s
tem
.
T
h
e
p
ap
er
d
em
o
n
s
tr
ates
th
e
ap
p
licatio
n
o
f
r
ei
n
f
o
r
ce
m
en
t
lear
n
in
g
(
R
F)
to
ac
h
iev
e
eq
u
ilib
r
i
u
m
in
th
e
T
W
SB
R
s
y
s
tem
an
d
o
p
tim
ize
th
e
tr
ain
i
n
g
p
r
o
ce
s
s
b
y
in
co
r
p
o
r
atin
g
PI
D
co
n
tr
o
l.
Z
ad
et
al
.
[
2
5
]
p
r
o
p
o
s
ed
an
o
p
tim
al
co
n
tr
o
ller
d
esig
n
f
o
r
a
s
elf
-
b
alan
cin
g
two
-
wh
ee
led
r
o
b
o
t
s
y
s
tem
u
s
in
g
a
r
o
b
u
s
t
m
o
d
el
p
r
e
d
ictiv
e
co
n
tr
o
l
(
MPC
)
s
ch
em
e.
Ad
d
itio
n
ally
,
th
e
MPC
co
n
tr
o
ller
was
s
im
u
lated
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
an
d
co
m
p
ar
e
d
with
a
PID
co
n
tr
o
ller
.
T
h
e
s
im
u
latio
n
r
esu
lts
s
h
o
w
b
etter
s
tab
ilit
y
an
d
im
p
r
o
v
e
d
r
ef
e
r
en
ce
p
o
s
itio
n
tr
ac
k
i
n
g
f
o
r
th
e
MPC
co
n
tr
o
ller
,
with
g
o
o
d
r
o
b
u
s
tn
ess
ag
ain
s
t
p
er
tu
r
b
atio
n
s
in
th
e
s
y
s
tem
m
o
d
el.
Stu
d
y
[
1
]
p
r
esen
ted
a
n
ew
c
o
n
f
ig
u
r
atio
n
o
f
T
W
SB
R
d
esig
n
ed
to
e
n
h
an
ce
f
lex
i
b
ilit
y
an
d
in
cr
ea
s
e
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
u
s
in
g
a
m
o
v
a
b
le
lin
ea
r
ac
tu
ato
r
o
n
th
e
s
ec
o
n
d
p
e
n
d
u
l
u
m
lin
k
.
W
h
ile
v
ar
io
u
s
co
n
tr
o
l
tec
h
n
iq
u
es
h
av
e
b
ee
n
ex
p
l
o
r
ed
f
o
r
T
W
S
B
R
s
,
m
an
y
ex
is
tin
g
s
tu
d
i
es
ten
d
to
o
v
er
lo
o
k
k
ey
p
r
ac
tical
c
h
allen
g
es,
s
u
ch
as
th
e
lim
itatio
n
s
im
p
o
s
ed
b
y
m
o
to
r
v
o
lt
ag
e
an
d
th
e
r
o
b
o
t’
s
ab
ilit
y
to
h
an
d
le
s
u
d
d
e
n
ch
an
g
es
in
p
ay
lo
ad
with
o
u
t
ad
ju
s
tin
g
th
e
c
o
n
tr
o
ller
s
ettin
g
s
.
T
h
ese
f
ac
to
r
s
ar
e
h
ig
h
ly
r
ele
v
an
t
in
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
,
wh
e
r
e
a
T
W
SB
R
m
ay
ex
p
er
ien
ce
u
n
ex
p
ec
te
d
lo
ad
s
o
r
o
p
er
ate
with
in
s
tr
ict
p
o
wer
lim
its
.
T
h
is
s
tu
d
y
ad
d
r
ess
es
th
ese
g
ap
s
b
y
in
v
esti
g
atin
g
th
e
d
y
n
am
ic
p
e
r
f
o
r
m
an
ce
an
d
p
r
a
ctica
l
lim
itatio
n
s
o
f
a
T
W
SB
R
co
n
tr
o
lled
u
s
in
g
a
PID
alg
o
r
ith
m
.
Sp
ec
if
ically
,
w
e
ev
alu
ate
h
o
w
th
e
s
y
s
tem
b
eh
av
es u
n
d
er
v
ar
y
i
n
g
p
ay
lo
ad
co
n
d
itio
n
s
an
d
d
is
tu
r
b
an
ce
an
g
les,
wh
ile
ad
h
er
in
g
t
o
th
e
r
ea
l
-
wo
r
ld
co
n
s
tr
ain
t
o
f
a
1
2
V
m
o
to
r
in
p
u
t
lim
it.
Ou
r
s
im
u
latio
n
s
s
h
o
w
th
at
th
e
r
o
b
o
t
ca
n
r
ec
o
v
e
r
f
r
o
m
d
is
tu
r
b
an
ce
s
u
p
to
0
.
0
5
2
4
r
ad
ian
s
with
o
u
t
ex
ce
ed
in
g
t
h
is
v
o
ltag
e
th
r
esh
o
ld
.
Fu
r
th
er
m
o
r
e,
th
e
r
o
b
o
t
d
e
m
o
n
s
tr
ates
r
o
b
u
s
t
s
tab
ilit
y
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
p
ay
lo
ad
s
,
u
p
to
f
iv
e
tim
es
th
e
n
o
m
in
al
m
ass
,
with
o
u
t
r
eq
u
ir
in
g
an
y
r
etu
n
in
g
o
f
th
e
PID
co
n
tr
o
ller
.
T
h
ese
f
in
d
in
g
s
co
n
tr
ib
u
te
t
o
th
e
g
r
o
win
g
b
o
d
y
o
f
T
W
SB
R
r
esear
c
h
b
y
d
em
o
n
s
tr
atin
g
th
at
s
im
p
l
e
PID
co
n
tr
o
l,
w
h
en
p
r
o
p
er
l
y
d
esig
n
e
d
,
ca
n
m
ee
t p
r
ac
tic
al
p
er
f
o
r
m
an
ce
r
e
q
u
ir
em
en
ts
ev
en
u
n
d
er
v
ar
y
in
g
r
ea
l
-
wo
r
ld
co
n
s
tr
ain
ts
.
2.
M
E
T
H
O
D
T
h
e
f
ir
s
t
d
y
n
am
ic
m
o
d
el
f
o
r
th
e
T
W
SB
R
,
s
h
o
wn
in
(
1
)
,
w
as
estab
lis
h
ed
in
o
r
d
er
to
d
es
ig
n
a
PID
co
n
tr
o
ller
f
o
r
s
tab
ilizatio
n
.
B
a
s
ed
o
n
New
to
n
ian
m
ec
h
a
n
ics
an
d
th
e
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
1
,
th
e
f
o
llo
win
g
lin
ea
r
ized
s
tate
-
s
p
ac
e
r
ep
r
ese
n
tatio
n
o
f
th
e
T
W
SB
R
was
d
er
iv
ed
,
f
o
llo
win
g
m
eth
o
d
s
s
im
ilar
to
f
o
u
n
d
i
n
t
h
e
liter
atu
r
e
[
2
6
]
,
[
2
7
]
.
[
̇
̈
̇
̈
]
=
[
0
1
0
0
0
2
(
−
−
2
)
2
2
2
0
0
0
0
1
0
2
(
−
)
2
0
]
[
̇
̇
]
+
[
0
2
(
−
2
−
)
0
2
(
−
)
]
(
1
)
Her
e,
an
d
̇
r
ep
r
esen
t
th
e
h
o
r
iz
o
n
tal
d
is
p
lace
m
en
t
a
n
d
v
elo
ci
ty
,
r
esp
ec
tiv
ely
,
o
f
th
e
T
W
SB
R
an
d
is
th
e
in
clin
atio
n
an
g
le,
̇
=
is
th
e
an
g
u
lar
r
ate,
an
d
V
a
is
th
e
m
o
t
o
r
in
p
u
t
v
o
ltag
e.
T
h
e
m
o
d
el
p
a
r
am
eter
s
ar
e
d
ef
in
ed
as:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
E
va
lu
a
tio
n
o
f th
e
d
y
n
a
mic
p
er
fo
r
ma
n
ce
a
n
d
…
(
R
u
p
a
s
in
g
h
e
A
r
a
ch
ch
ig
e
Do
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Dh
a
n
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s
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ka
Dh
a
r
ma
s
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3615
=
(
2
+
2
2
+
)
=
[
+
2
2
(
+
2
)
]
=
m
ass
o
f
th
e
r
o
b
o
t’
s
ch
ass
is
,
=
m
o
m
e
n
t
o
f
in
er
tia
o
f
th
e
r
o
b
o
t’
s
ch
ass
is
,
=
d
is
tan
ce
b
etwe
en
th
e
ce
n
ter
o
f
t
h
e
wh
ee
l
an
d
th
e
r
o
b
o
t’
s
ce
n
ter
o
f
g
r
a
v
ity
,
=
m
a
s
s
o
f
th
e
r
o
b
o
t’
s
wh
ee
l,
=
m
o
to
r
’
s
to
r
q
u
e
co
n
s
tan
t
,
=
b
ac
k
elec
tr
o
m
o
tiv
e
f
o
r
ce
(
b
ac
k
E
MF)
c
o
n
s
tan
t
.
Fig
u
r
e
2
p
r
esen
ts
th
e
p
h
y
s
ical
p
r
o
t
o
ty
p
e
o
f
th
e
T
W
SB
R
u
s
e
d
in
t
h
is
s
tu
d
y
.
All
p
h
y
s
ical
p
ar
am
eter
s
wer
e
d
eter
m
in
ed
ex
p
e
r
im
en
t
ally
to
en
s
u
r
e
t
h
e
ac
cu
r
ac
y
o
f
th
e
s
im
u
latio
n
an
d
m
o
d
el
in
g
p
r
o
ce
s
s
es.
T
h
e
ch
ass
is
m
ass
an
d
wh
ee
l
m
ass
was
m
ea
s
u
r
ed
u
s
in
g
a
p
r
ec
is
io
n
d
ig
ital
s
ca
le,
wh
ile
t
h
e
wh
ee
l
r
ad
iu
s
was
d
e
ter
m
in
ed
u
s
in
g
a
d
ig
ital
ca
lip
er
.
T
h
e
ce
n
ter
o
f
m
ass
lo
ca
tio
n
was
id
en
tifie
d
th
r
o
u
g
h
a
s
tatic
b
alan
cin
g
m
eth
o
d
.
T
h
e
m
o
m
e
n
t
o
f
in
er
tia
o
f
th
e
ch
ass
is
was
ca
lcu
lated
m
ath
em
atica
l
m
eth
o
d
.
Mo
to
r
co
n
s
tan
ts
,
in
clu
d
in
g
th
e
t
o
r
q
u
e
co
n
s
tan
t
an
d
th
e
b
ac
k
elec
tr
o
m
o
tiv
e
f
o
r
ce
co
n
s
tan
t
,
wer
e
v
er
if
ie
d
u
s
in
g
b
o
t
h
d
atash
ee
ts
an
d
ex
p
er
im
en
tal
o
p
en
-
lo
o
p
test
s
.
Ad
d
itio
n
ally
,
th
e
m
o
t
o
r
r
esis
tan
ce
was
m
ea
s
u
r
ed
u
s
in
g
a
h
ig
h
-
ac
cu
r
ac
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m
u
ltime
ter
.
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h
e
p
h
y
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ical
p
ar
am
eter
s
d
eter
m
in
ed
ex
p
er
im
e
n
tally
ar
e
lis
ted
b
el
o
w.
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y
tak
in
g
th
e
tilt
an
g
le
θ
as
th
e
s
y
s
tem
o
u
tp
u
t
an
d
(
m
o
to
r
in
p
u
t
v
o
lt
ag
e)
as
th
e
in
p
u
t,
th
e
tr
an
s
f
er
f
u
n
ctio
n
G(
s
)
ca
n
b
e
d
er
iv
e
d
f
r
o
m
th
e
d
y
n
am
ic
m
o
d
el
o
f
T
W
SB
R
a
s
(
2
)
:
(
)
=
(
)
=
7.
697
3
+
28.
12
2
−
139.
7
−
2479
(
2
)
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
a
PID
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n
tr
o
ller
ca
n
b
e
e
x
p
r
ess
ed
as
(
3
)
:
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)
=
+
+
=
(
+
1
)
(
+
2
)
(
3
)
w
h
er
e
=
,
1
+
2
=
/
an
d
1
2
=
/
.
T
h
en
PID
co
n
tr
o
ller
ca
n
b
e
im
p
lem
e
n
ted
b
y
in
s
er
tin
g
th
e
PID
co
n
tr
o
ller
t
r
an
s
f
er
f
u
n
ctio
n
in
to
th
e
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W
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R
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y
s
tem
o
p
en
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lo
o
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tr
a
n
s
f
er
f
u
n
ctio
n
(
)
as
(
4
)
:
(
)
=
(
)
(
)
=
(
+
1
)
(
+
2
)
7.
697
(
3
+
28.
12
2
−
139.
7
−
2479
)
(
4
)
T
h
e
PID
co
n
tr
o
ller
d
esig
n
ca
n
b
e
p
er
f
o
r
m
ed
b
y
ad
d
in
g
two
ze
r
o
s
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d
a
p
o
le
at
th
e
o
r
ig
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t
o
th
e
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ain
(
)
=
(
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(
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,
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d
b
y
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eter
m
in
in
g
th
e
co
n
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g
ain
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ia
r
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o
t
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aly
s
is
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n
th
is
d
esig
n
,
th
e
f
o
llo
win
g
ze
r
o
s
ar
e
ch
o
s
en
to
m
ee
t th
e
tr
an
s
ien
t r
esp
o
n
s
e
s
p
ec
if
icatio
n
s
AS (
5
)
:
1
,
2
=
4
.
7
±
0
.
15
(
5
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T
h
en
,
u
s
in
g
th
e
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n
tr
o
l
g
ain
,
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e
,
an
d
v
alu
es
wer
e
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lcu
lated
,
an
d
th
e
en
tire
d
y
n
am
ic
m
o
d
el
an
d
PID
co
n
tr
o
ller
wer
e
im
p
lem
e
n
ted
in
MA
T
L
AB
/Si
m
u
lin
k
as
s
h
o
wn
in
Fig
u
r
e
3
.
Her
e,
t
h
e
d
y
n
am
ic
m
o
d
el
s
h
o
wn
in
(
1
)
was c
r
ea
ted
in
s
id
e
th
e
two
-
wh
ee
led
r
o
b
o
t b
lo
ck
,
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d
in
itially
,
th
e
s
et
an
g
le
wa
s
k
ep
t a
t
ze
r
o
.
Fig
u
r
e
1
.
Diag
r
a
m
o
f
f
o
r
ce
s
a
n
d
m
o
m
en
ts
ac
tin
g
o
n
th
e
T
W
S
B
R
Fig
u
r
e
2
.
Ph
y
s
ical
p
r
o
to
ty
p
e
o
f
th
e
T
W
SB
R
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
3
6
1
3
-
3620
3616
Fig
u
r
e
3
.
T
h
e
T
W
SB
R
s
y
s
tem
is
d
esig
n
ed
in
MA
T
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
e
n
t w
ith
a
PID
co
n
tr
o
ller
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
r
esu
ltin
g
r
o
o
t
lo
cu
s
o
f
th
e
tr
an
s
f
er
f
u
n
ctio
n
(
)
=
(
)
(
)
is
s
h
o
wn
in
Fig
u
r
e
4
.
I
t
ca
n
b
e
s
ee
n
th
at
th
e
clo
s
ed
-
lo
o
p
p
o
l
es
en
ter
th
e
o
p
en
lef
t
-
h
alf
-
p
l
an
e
f
o
r
a
lar
g
e
en
o
u
g
h
g
ain
.
At
a
d
am
p
in
g
r
atio
eq
u
al
to
1
,
we
o
b
tain
e
d
th
e
g
ain
K
=
2
0
.
T
h
e
v
alu
es o
f
,
an
d
wer
e
ca
lcu
lated
ac
co
r
d
in
g
ly
.
Fig
u
r
e
5
s
h
o
ws
th
e
r
esp
o
n
s
e
o
f
th
e
two
-
wh
ee
led
r
o
b
o
t
u
n
d
er
th
e
PID
co
n
tr
o
ller
d
esig
n
.
T
h
e
d
is
tu
r
b
an
ce
ap
p
lied
h
er
e
is
eq
u
iv
alen
t
to
r
elea
s
in
g
th
e
p
e
n
d
u
lu
m
af
ter
m
o
v
in
g
it
to
an
i
n
clin
atio
n
an
g
le
o
f
0
.
0
5
r
a
d
ian
(
2
.
8
6
d
e
g
r
ee
s
)
.
Fr
o
m
th
is
f
ig
u
r
e,
it
is
clea
r
th
at
th
e
s
y
s
tem
ca
n
co
m
e
to
a
v
er
tical
p
o
s
itio
n
with
in
ab
o
u
t 1
.
2
s
ec
o
n
d
s
.
Fig
u
r
e
4
.
R
o
o
t lo
cu
s
o
f
th
e
lo
o
p
g
ain
(
)
=
(
)
(
)
Fig
u
r
e
5
.
R
esp
o
n
s
e
o
f
th
e
two
-
wh
ee
led
r
o
b
o
t to
a
n
im
p
u
ls
e
d
is
tu
r
b
an
ce
u
n
d
e
r
PI
D
co
n
tr
o
ller
Fig
u
r
e
6
p
r
esen
ts
th
e
s
y
s
tem
’
s
r
esp
o
n
s
e
to
a
lar
g
e
d
is
tu
r
b
an
ce
an
g
le
o
f
θ
=
π/2
r
ad
.
As
s
h
o
wn
in
Fig
u
r
e
6
(
a)
,
wh
e
n
th
e
d
is
tu
r
b
an
ce
o
f
th
e
an
g
le
is
g
iv
en
as
θ
=
π/2
r
ad
,
th
e
s
y
s
tem
is
ca
p
ab
le
o
f
co
m
in
g
to
a
d
y
n
am
ic
b
alan
ce
with
in
ab
o
u
t
3
s
ec
o
n
d
s
.
Ho
wev
er
,
a
s
s
h
o
wn
in
Fig
u
r
e
6
(
b
)
,
th
e
m
o
to
r
i
n
p
u
t
v
o
ltag
e
with
in
th
e
f
ir
s
t
f
ew
s
ec
o
n
d
s
n
ee
d
s
to
b
e
u
n
r
ea
lis
tically
h
ig
h
.
B
ec
a
u
s
e
th
e
co
n
s
tr
u
cted
v
e
h
icle
is
o
p
er
ated
with
1
2
V
DC
m
o
to
r
s
,
s
u
ch
v
o
ltag
es
ca
n
n
o
t
b
e
u
s
ed
.
Als
o
,
as
s
h
o
wn
i
n
Fig
u
r
e
6
(
c)
,
wh
en
th
e
θ
=
π/2
r
a
d
d
is
tu
r
b
an
ce
an
g
le
is
g
iv
en
,
th
e
v
eh
icle
m
u
s
t
m
o
v
e
a
v
er
y
lar
g
e
lin
ea
r
d
is
tan
ce
(
ab
o
u
t
9
m
,
with
in
1
0
s
ec
o
n
d
s
)
b
ef
o
r
e
r
etu
r
n
in
g
to
s
tab
ilit
y
.
Fig
u
r
e
6
(
d
)
s
h
o
ws
th
at
th
e
in
itial
lin
ea
r
v
elo
city
n
ee
d
s
to
b
e
as
h
ig
h
as
ab
o
u
t
4
m
/s
.
T
h
ese
r
esu
lts
s
h
o
w
th
at
it
is
p
r
ac
tically
n
o
t
p
o
s
s
ib
le
f
o
r
th
e
v
eh
icle
to
r
etu
r
n
t
o
th
e
v
er
tical
p
o
s
itio
n
af
ter
s
u
ch
a
lar
g
e
d
is
tu
r
b
a
n
ce
.
A
f
t
e
r
c
o
n
d
u
c
t
i
n
g
a
s
e
r
i
e
s
o
f
s
i
m
u
l
a
t
i
o
n
s
w
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t
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v
a
r
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d
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n
g
l
es
,
i
t
w
as
f
o
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n
d
t
h
a
t
θ
=
0
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0
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2
4
r
a
d
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h
e
m
a
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m
d
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r
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e
m
w
h
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m
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t
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u
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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:
2088
-
8
7
0
8
E
va
lu
a
tio
n
o
f th
e
d
y
n
a
mic
p
er
fo
r
ma
n
ce
a
n
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(
R
u
p
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h
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ch
ch
ig
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a
n
u
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Dh
a
r
ma
s
ir
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)
3617
v
o
l
t
a
g
e
d
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s
n
o
t
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ce
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d
t
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1
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r
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h
i
s
r
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l
t
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o
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i
t
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a
v
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e
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m
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n
t
a
l
s
y
s
te
m
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
R
esp
o
n
s
e
o
f
th
e
r
o
b
o
t to
a
lar
g
e
d
is
tu
r
b
an
ce
a
n
g
le
o
f
θ
=
π/2
r
ad
:
(
a)
i
n
clin
atio
n
an
g
le
θ
v
s
.
t
im
e
(
b
)
m
o
t
o
r
in
p
u
t v
o
ltag
e
V
a
v
s
.
t
im
e
(
c)
p
o
s
itio
n
o
f
th
e
r
o
b
o
t v
s
.
t
im
e
an
d
(
d
)
s
p
ee
d
o
f
th
e
r
o
b
o
t v
s
.
t
im
e
Fig
u
r
e
7
p
r
esen
ts
th
e
s
y
s
tem
’
s
r
esp
o
n
s
e
to
a
d
is
tu
r
b
an
ce
a
n
g
le
o
f
θ
=
0
.
0
5
2
4
r
ad
(
a
p
p
r
o
x
im
ately
3
d
eg
r
ee
s
)
.
As
s
h
o
wn
in
Fig
u
r
e
7
(
a)
,
th
e
in
clin
atio
n
an
g
le
r
e
tu
r
n
s
to
th
e
v
er
tical
p
o
s
itio
n
(
θ
=
0
)
with
in
ab
o
u
t
3
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ec
o
n
d
s
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in
d
icatin
g
s
u
cc
ess
f
u
l
s
tab
ilizatio
n
an
d
o
p
tim
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d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
As
s
h
o
wn
in
Fig
u
r
e
7
(
b
)
,
wh
en
th
e
d
is
tu
r
b
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ce
o
f
th
e
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n
g
le
is
g
iv
e
n
as
θ
=
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.
0
5
2
4
,
th
e
in
itial
m
o
to
r
in
p
u
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v
o
ltag
e
is
ab
o
u
t
1
0
.
5
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ce
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to
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As
s
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Fig
u
r
e
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o
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ad
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r
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u
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7
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Fig
u
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s
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o
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e
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ay
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ile
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n
g
th
e
s
am
e
s
et
o
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n
tr
o
ller
p
ar
am
ete
r
s
.
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h
is
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aly
s
is
is
cr
u
cial
f
o
r
ev
alu
atin
g
th
e
r
o
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u
s
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ess
o
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th
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n
tr
o
l sy
s
tem
in
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ld
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n
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s
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er
e
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ay
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ad
s
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n
f
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ctu
ate
d
u
e
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ed
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m
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n
e
n
ts
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en
s
o
r
s
,
o
r
ca
r
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o
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I
n
Fig
u
r
e
8
(
a)
,
th
e
r
o
b
o
t
is
s
im
u
l
ated
with
a
n
o
m
in
al
p
ay
lo
a
d
m
ass
o
f
0
.
7
0
2
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g
.
T
h
e
i
n
clin
a
tio
n
an
g
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s
tab
ilizes
q
u
ick
ly
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n
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ir
m
in
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n
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itio
n
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.
I
n
Fig
u
r
e
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(
b
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,
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e
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ay
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o
ad
is
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c
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1
0
6
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ich
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h
r
ee
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es
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e
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o
m
i
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al
m
ass
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o
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g
h
th
e
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d
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iatio
n
f
r
o
m
th
e
v
e
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tical
p
o
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itio
n
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lar
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er
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d
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e
r
ec
o
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e
r
y
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e
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h
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o
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er
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m
p
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e,
th
e
s
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tem
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r
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r
iu
m
.
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h
is
d
em
o
n
s
tr
ates
th
at
th
e
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co
n
tr
o
ller
p
r
o
v
id
es
s
u
f
f
icien
t
co
r
r
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tiv
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to
r
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u
e
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en
with
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ig
n
if
ican
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in
cr
ea
s
ed
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ad
.
Fig
u
r
e
8
(
c)
s
h
o
ws
th
e
r
esp
o
n
s
e
with
a
p
ay
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ad
m
ass
o
f
3
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5
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0
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g
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iv
e
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es
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e
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o
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ass
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n
th
is
s
ce
n
ar
io
,
th
e
s
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ilizatio
n
p
r
o
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ess
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s
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wer
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d
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h
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lar
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er
o
s
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o
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t
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n
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eg
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n
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n
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o
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ar
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h
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s
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lt
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o
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ly
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u
p
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e
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im
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at
th
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tem
is
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o
b
u
s
t
t
o
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e
r
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e
o
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ay
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r
iatio
n
s
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h
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f
in
d
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g
s
ar
e
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ar
ticu
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s
e
m
an
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g
T
W
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R
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tu
d
ies
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s
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n
s
tan
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y
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ar
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d
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im
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ac
t
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a
y
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ar
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ilit
y
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h
e
ab
ilit
y
t
o
m
ain
tain
s
tab
ilit
y
u
n
d
er
s
u
c
h
co
n
d
itio
n
s
with
o
u
t
r
e
-
tu
n
in
g
th
e
co
n
tr
o
ller
e
n
h
a
n
ce
s
th
e
p
r
ac
ticality
an
d
v
er
s
a
tili
ty
o
f
th
e
s
y
s
tem
f
o
r
r
ea
l
-
wo
r
ld
d
e
p
lo
y
m
e
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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2
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I
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15
,
No
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4
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Au
g
u
s
t
20
25
:
3
6
1
3
-
3620
3618
(
a)
(
b
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(
c)
(
d
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e)
Fig
u
r
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.
R
esp
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e
o
f
th
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a
n
ce
an
g
le
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f
θ
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0
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0
5
2
4
r
a
d
:
(
a)
i
n
clin
atio
n
a
n
g
le
θ
v
s
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tim
e,
(
b
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m
o
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V
a
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tim
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o
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tim
e
(
a)
(
b
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c)
Fig
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r
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8
.
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n
clin
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a
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θ
v
s
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tim
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f
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(
a)
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0
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7
0
2
k
g
,
(
b
)
m
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2
.
1
0
6
k
g
,
an
d
(
c)
m
=
3
.
5
1
0
k
g
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:
2088
-
8
7
0
8
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va
lu
a
tio
n
o
f th
e
d
y
n
a
mic
p
er
fo
r
ma
n
ce
a
n
d
…
(
R
u
p
a
s
in
g
h
e
A
r
a
ch
ch
ig
e
Do
n
Dh
a
n
u
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r
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3619
4.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
ex
am
in
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th
e
ass
e
s
s
m
en
t
o
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th
e
d
y
n
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ic
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er
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o
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m
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ce
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d
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r
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tical
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n
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ts
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e
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R
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.
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h
e
d
y
n
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ic
m
o
d
el
f
o
r
th
e
T
W
SB
R
was
estab
lis
h
ed
in
o
r
d
er
to
d
esig
n
a
PID
co
n
tr
o
ller
to
m
ain
tain
s
tab
ilit
y
.
T
h
e
PID
c
o
n
tr
o
ller
was
d
esig
n
ed
a
n
d
i
m
p
lem
en
ted
a
n
d
t
h
e
s
y
s
tem
r
esp
o
n
s
e
ag
ain
s
t
th
e
im
p
lem
en
ted
co
n
tr
o
l
alg
o
r
ith
m
s
was
test
ed
an
d
s
im
u
lated
u
s
in
g
co
m
p
u
tatio
n
al
to
o
ls
.
Fro
m
th
e
PID
co
n
tr
o
ller
im
p
lem
en
ted
T
W
SB
R
s
y
s
tem
s
u
cc
ess
f
u
lly
s
tab
ilized
with
g
o
o
d
d
y
n
am
ic
p
er
f
o
r
m
an
ce
.
I
t
was
f
o
u
n
d
th
at
t
h
e
T
W
S
B
R
s
y
s
tem
wh
en
eq
u
ip
p
ed
with
a
PID
co
n
tr
o
ller
,
is
c
ap
ab
le
o
f
m
ain
tai
n
in
g
s
tab
ilit
y
u
p
to
a
m
a
x
im
u
m
d
is
tu
r
b
an
ce
an
g
le
o
f
θ
=
0
.
0
5
2
4
r
ad
ian
s
(
e
q
u
iv
alen
t
to
3
d
e
g
r
ee
s
)
an
d
it
ca
n
r
etu
r
n
to
th
e
v
er
tical
p
o
s
itio
n
in
ap
p
r
o
x
im
ately
3
s
ec
o
n
d
s
.
I
n
a
d
d
it
io
n
,
it
was
d
is
co
v
er
e
d
th
at
th
e
T
W
SB
R
s
y
s
tem
was
ca
p
a
b
le
o
f
m
ai
n
tain
in
g
s
tab
ilit
y
ev
en
wh
en
th
e
m
ass
o
f
th
e
s
y
s
tem
v
ar
ied
ac
r
o
s
s
a
wid
e
r
an
g
e
,
u
s
in
g
t
h
e
s
am
e
s
et
o
f
PID
s
ettin
g
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Fin
an
cial
ass
is
tan
ce
p
r
o
v
id
e
d
b
y
th
e
Un
iv
er
s
ity
o
f
C
o
lo
m
b
o
(
g
r
an
t N
o
:
-
AP/3
/2
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0
1
4
/R
G/1
0
)
.
AUTHO
R
CO
NT
RI
B
UT
I
O
NS ST
A
T
E
M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
tr
ib
u
to
r
R
o
les
T
ax
o
n
o
m
y
(
C
R
ed
iT)
to
r
ec
o
g
n
ize
in
d
iv
id
u
al
au
th
o
r
co
n
tr
ib
u
tio
n
s
,
r
ed
u
ce
au
th
o
r
s
h
ip
d
is
p
u
tes,
an
d
f
ac
ilit
ate
co
llab
o
r
atio
n
.
Na
m
e
o
f
Aut
ho
r
C
M
So
Va
Fo
I
R
D
O
E
Vi
Su
P
Fu
R
u
p
a
s
i
n
g
h
e
A
r
a
c
h
c
h
i
g
e
D
o
n
D
h
a
n
u
s
h
k
a
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h
a
r
m
a
s
i
r
i
✓
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M
a
l
a
g
a
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CO
NF
L
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C
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F
I
N
T
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R
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S
T
ST
A
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M
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T
h
e
au
th
o
r
s
s
tate
th
er
e
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n
o
c
o
n
f
lict o
f
i
n
ter
est.
DATA AV
AI
L
AB
I
L
I
T
Y
Data
av
ailab
ilit
y
d
o
es n
o
t a
p
p
l
y
to
th
is
p
ap
e
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as n
o
n
ew
d
ata
wer
e
cr
ea
ted
o
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an
aly
ze
d
in
th
is
s
tu
d
y
.
RE
F
E
R
E
NC
E
S
[
1
]
A
.
M
.
A
l
m
e
sh
a
l
,
K
.
M
.
G
o
h
e
r
,
a
n
d
M
.
O
.
T
o
k
h
i
,
“
D
y
n
a
m
i
c
mo
d
e
l
l
i
n
g
a
n
d
st
a
b
i
l
i
z
a
t
i
o
n
o
f
a
n
e
w
c
o
n
f
i
g
u
r
a
t
i
o
n
o
f
t
w
o
-
w
h
e
e
l
e
d
mac
h
i
n
e
s
,
”
Ro
b
o
t
i
c
s
a
n
d
A
u
t
o
n
o
m
o
u
s
S
y
s
t
e
m
s
,
v
o
l
.
6
1
,
n
o
.
5
,
p
p
.
4
4
3
–
4
7
2
,
M
a
y
2
0
1
3
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
r
o
b
o
t
.
2
0
1
3
.
0
1
.
0
0
6
.
[
2
]
M
.
R
.
H
a
g
h
i
g
h
a
t
a
n
d
S
.
S
a
d
e
g
h
n
e
j
a
d
,
“
S
i
mu
l
a
t
i
o
n
o
f
a
t
w
o
-
w
h
e
e
l
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1
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1
9
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2
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2
7
]
F
.
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r
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sser
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