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o
ller
w
h
er
e
th
e
o
r
d
er
o
f
s
lid
in
g
s
u
r
f
ac
e
is
a
f
r
ac
tio
n
a
l
v
al
u
e.
T
h
e
f
r
ac
tio
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
h
as
m
a
n
y
ad
v
a
n
tag
e
s
co
m
p
ar
ed
to
th
e
tr
ad
itio
n
al
s
lid
i
n
g
m
o
d
e
co
n
tr
o
ller
.
I
t
ca
n
ev
e
n
co
n
tr
o
l
t
h
e
o
b
j
ec
ts
w
it
h
u
n
ce
r
tai
n
d
y
n
a
m
ical
m
o
d
el
[
1
8
]
.
Hen
ce
,
r
ec
en
tl
y
,
th
e
f
r
ac
tio
n
a
l
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ll
er
h
as
b
ee
n
in
v
e
s
ti
g
ated
an
d
ap
p
lied
in
to
m
a
n
y
s
y
s
te
m
co
n
tr
o
ls
s
u
c
h
as:
s
i
n
g
le
-
li
n
k
f
le
x
ib
le
m
a
n
ip
u
lato
r
[
1
9
]
,
an
tilo
ck
b
r
ak
in
g
s
y
s
te
m
s
[
2
0
,
2
1
]
,
s
p
ee
d
c
o
n
tr
o
l
s
y
s
te
m
f
o
r
p
er
m
a
n
en
t
m
a
g
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
[
2
2
]
.
A
s
a
r
esu
lt,
t
h
e
s
y
s
te
m
s
w
i
th
t
h
e
f
r
ac
tio
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
ar
e
o
f
s
u
p
er
io
r
q
u
alit
y
to
tr
ad
itio
n
al
co
n
tr
o
ller
s
.
B
ec
au
s
e
o
f
th
e
ab
o
v
e
ad
v
an
tag
es,
in
t
h
is
p
ap
er
,
b
ased
o
n
th
e
d
y
n
a
m
ic
m
o
d
el
o
f
th
e
t
w
o
-
li
n
k
r
o
b
o
t
ar
m
,
th
e
a
u
th
o
r
w
ill b
u
ild
a
s
u
itab
le
f
r
ac
tio
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
an
d
p
r
o
v
e
th
e
s
tab
ilit
y
o
f
th
e
w
h
o
le
s
y
s
te
m
t
h
r
o
u
g
h
t
h
e
th
eo
r
y
o
f
L
y
ap
u
n
o
v
.
T
h
e
ac
h
iev
ed
f
i
n
d
in
g
s
w
ill
b
e
tr
an
s
p
ar
en
tl
y
d
is
p
lay
ed
th
r
o
u
g
h
Ma
tlab
Si
m
u
lin
k
.
T
h
e
r
esu
lts
w
i
ll
i
n
d
ic
ate
t
h
at
th
er
e
is
n
o
t
a
h
i
g
h
-
f
r
eq
u
e
n
c
y
ch
at
ter
in
g
i
n
th
e
co
n
tr
o
l
s
i
g
n
als
as
w
ell
a
s
a
s
tatic
er
r
o
r
,
th
e
q
u
alit
y
o
f
t
h
e
co
n
tr
o
l
s
y
s
te
m
is
ad
eq
u
ate,
an
d
th
e
r
esp
o
n
s
e
a
n
g
le
o
f
t
w
o
li
n
k
s
q
u
ic
k
l
y
ap
p
r
o
ac
h
es
t
h
e
d
esire
d
an
g
le.
T
h
e
r
em
ain
s
o
f
th
e
p
ap
er
a
r
e
as
f
o
l
lo
w
s
:
S
ec
tio
n
2
p
r
esen
ts
th
e
ca
lcu
lu
s
o
f
d
er
iv
ativ
e
s
an
d
in
teg
r
als
o
f
f
r
ac
tio
n
al
o
r
d
er
,
th
e
k
in
em
atic
eq
u
atio
n
o
f
t
w
o
-
li
n
k
r
o
b
o
t
a
r
m
,
an
d
th
e
f
r
ac
tio
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
.
S
ec
tio
n
3
p
r
esen
ts
t
h
e
r
esu
l
ts
a
n
d
an
al
y
s
i
s
.
Fin
a
ll
y
,
T
h
e
co
n
clu
s
io
n
s
ar
e
p
r
esen
t
ed
in
s
ec
tio
n
4
.
2.
DE
S
I
G
NIN
G
T
H
E
CO
NT
R
O
L
L
E
R
2
.
1
.
T
he
ca
lculu
s
o
f
deriv
a
t
i
v
es a
nd
inte
g
ra
ls
o
f
f
ra
ct
i
o
na
l o
rder
L
eib
n
iz
an
d
L
’
Ho
p
ital
p
r
o
p
o
s
e
f
r
ac
tio
n
al
ca
lc
u
l
u
s
o
n
t
h
e
b
asi
s
o
f
t
h
e
in
te
g
er
-
o
r
d
er
ca
lcu
lu
s
in
1
6
9
5
[
2
3
]
.
T
h
e
f
ir
s
t
-
o
r
d
er
d
er
iv
ati
v
e
is
d
eter
m
i
n
ed
b
y
th
e
(
1
)
:
′
(
)
=
ℎ
→
0
(
)
−
(
−
ℎ
)
ℎ
(
1
)
T
h
er
ef
o
r
e,
th
e
s
ec
o
n
d
-
o
r
d
er
an
d
n
-
o
r
d
er
d
er
iv
ativ
e
ar
e
d
eter
m
i
n
ed
as f
o
llo
w
s
:
″
(
)
=
ℎ
→
0
′
(
)
−
′
(
−
ℎ
)
ℎ
=
ℎ
→
0
(
)
−
2
(
−
ℎ
)
+
(
+
2
ℎ
)
ℎ
2
(
2
)
(
3
)
(
)
=
ℎ
→
0
″
(
)
−
″
(
−
ℎ
)
ℎ
=
ℎ
→
0
(
)
−
3
(
−
ℎ
)
+
3
(
−
2
ℎ
)
−
(
−
3
ℎ
)
ℎ
3
(
3
)
(
)
(
)
=
ℎ
→
0
∑
(
−
1
)
(
)
=
0
(
−
.
ℎ
)
ℎ
(
4)
w
h
er
e:
(
)
=
!
!
(
−
)
!
(
5
)
I
n
(
5
)
,
is
a
n
at
u
r
al
n
u
m
b
er
.
I
f
=
i
s
n
o
t a
n
at
u
r
al
n
u
m
b
er
,
(
5
)
is
r
e
w
r
itte
n
as f
o
llo
w
s
:
(
)
=
(
+
1
)
(
+
1
)
(
−
+
1
)
(
6
)
w
h
er
e
(
.
)
is
t
h
e
g
a
m
m
a
f
u
n
ctio
n
.
Fo
r
g
en
er
aliz
in
g
,
R
ie
m
an
n
-
L
i
o
u
v
ille
an
d
C
ap
u
to
h
a
v
e
d
e
f
in
ed
th
e
f
r
ac
tio
n
al
o
r
d
er
f
o
r
th
e
ca
lcu
l
u
s
o
f
d
er
iv
ativ
e
s
an
d
in
teg
r
al
s
as f
o
l
lo
w
s
[
2
4
]
:
(
)
=
1
(
−
)
∫
(
)
(
)
(
−
)
+
−
1
0
(
7
)
w
h
e
r
e:
(
)
=
∫
−
1
−
∞
0
,
−
1
<
<
(
n
i
s
an
in
t
eg
e
r
v
al
u
e
)
.
I
f
<
0
t
h
en
th
e
c
al
cu
lu
s
(
7
)
is
in
t
eg
r
a
t
i
o
n
,
e
l
s
e
if
>
0
th
en
th
e
c
a
lc
u
lu
s
(
7
)
i
s
d
i
f
f
e
r
en
ti
a
t
i
o
n
.
E
s
p
e
ci
a
l
ly
,
if
=
1
t
h
e
c
a
l
cu
lu
s
(
7
)
is
f
i
r
s
t
o
r
d
e
r
d
er
i
v
at
iv
e
f
u
n
c
t
i
o
n
.
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
F
r
a
ctio
n
a
l
-
o
r
d
er sl
id
in
g
mo
d
e
co
n
tr
o
ller
fo
r
th
e
tw
o
-
lin
k
r
o
b
o
t a
r
m
(
Tr
o
n
g
-
Th
a
n
g
N
g
u
ye
n
)
5581
2
.
2
.
T
he
m
o
del o
f
t
he
t
wo
-
lin
k
ro
bo
t
a
r
m
Fig
u
r
e
1
illu
s
tr
ate
s
th
e
t
w
o
-
li
n
k
r
o
b
o
t
ar
m
m
o
d
el,
in
w
h
ic
h
m
1
an
d
l
1
r
ep
r
esen
t
L
i
n
k
1
's
m
a
s
s
an
d
len
g
th
;
m
2
,
l
2
st
a
n
d
f
o
r
L
i
n
k
2
’
s
m
as
s
an
d
len
g
t
h
;
T
1
,
T
2
r
ep
r
esen
t
t
h
e
to
r
q
u
e
o
f
L
i
n
k
1
an
d
L
i
n
k
2
;
θ
1
an
d
θ
2
r
ep
r
esen
t
th
e
L
in
k
1
an
g
le
a
n
d
L
i
n
k
2
a
n
g
le.
Fig
u
r
e1
.
T
h
e
m
o
d
el
o
f
t
w
o
-
lin
k
r
o
b
o
t a
r
m
T
h
e
d
y
n
a
m
ic
eq
u
atio
n
o
f
t
h
e
t
w
o
-
li
n
k
r
o
b
o
t a
r
m
i
s
as t
h
e
f
o
l
lo
w
i
n
g
[
2
5
,
2
6
]:
[
1
2
]
=
[
11
12
21
22
]
[
1
2
]
+
[
1
2
]
[
1
2
]
+
[
1
2
]
(
8
)
w
h
er
e:
11
=
(
1
+
2
)
1
2
+
2
2
2
+
2
2
1
2
(
2
)
12
=
21
=
2
2
2
+
2
1
2
(
2
)
22
=
2
2
2
1
=
(
1
+
2
)
1
(
1
)
+
2
2
(
1
+
2
)
2
=
2
2
(
1
+
2
)
1
=
−
2
1
2
(
2
)
̇
2
−
2
1
2
(
2
)
(
̇
1
+
̇
2
)
2
=
2
1
2
(
2
)
̇
1
R
e
w
r
iti
n
g
(
8
)
,
w
e
g
et:
=
.
̈
+
.
̇
+
(
9
)
w
h
er
e:
=
[
2
2
]
;
=
[
11
12
21
22
]
;
̈
=
[
̈
1
̈
2
]
;
=
[
1
2
]
;
̇
=
[
̇
1
̇
2
]
;
1
2
G
G
G
2
.
3
.
T
he
co
ntr
o
l sy
s
t
em
o
f
t
w
o
-
lin
k
ro
bo
t
a
r
m
ba
s
ed
o
n
t
he
f
ra
ct
io
na
l
-
o
rder
s
lid
ing
m
o
de
co
ntr
o
ller
Settin
g
t
h
e
f
r
ac
tio
n
al
-
o
r
d
er
s
lid
in
g
s
u
r
f
ac
e
as f
o
llo
w
s
:
=
1
.
+
2
.
(
−
)
+
3
.
+
̇
(
1
0
)
w
h
er
e
e
is
th
e
er
r
o
r
:
=
−
=
[
1
_
2
_
]
is
th
e
v
ec
to
r
o
f
d
esire
d
an
g
le
v
alu
es;
=
[
1
2
]
is
th
e
v
ec
to
r
o
f
r
esp
o
n
s
e
an
g
l
e
v
alu
e
s
;
,
ar
e
f
r
ac
tio
n
al
o
d
er
s
,
th
o
s
e
v
al
u
es a
r
e
p
o
s
itiv
e
r
ea
l
v
alu
e
s
.
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
5
5
7
9
-
5
5
8
5
5582
1
,
2
,
3
ar
e
v
ec
to
r
s
o
f
p
o
s
itiv
e
g
ai
n
p
ar
a
m
eter
s
.
T
h
e
d
if
f
er
en
tia
l o
f
t
h
e
(
1
0
)
is
as:
̇
=
1
.
̇
+
2
.
(
1
−
)
+
3
.
(
1
+
)
+
̈
(
1
1
)
Settin
g
t
h
e
co
n
tr
o
l si
g
n
a
l
=
[
1
2
]
s
o
th
at
̇
=
−
.
(
)
(
>
0
)
.
T
h
e
to
r
q
u
e
f
o
r
ce
is
:
=
.
(
1
.
̇
+
2
.
(
1
−
)
+
3
.
(
1
+
)
+
.
(
)
)
+
.
̇
+
(
1
2
)
C
h
o
o
s
i
n
g
L
y
ap
u
n
o
v
f
u
n
ct
io
n
=
1
2
2
.
I
f
th
e
co
n
tr
o
l si
g
n
al
is
s
et
u
p
a
cc
o
r
d
in
g
to
th
e
eq
u
atio
n
(
1
2
)
,
̇
=
−
.
(
)
.
W
e
h
av
e:
̇
=
.
̇
=
−
.
|
|
<
0
∀
T
h
u
s
,
t
h
e
s
y
s
te
m
w
ill
at
tain
th
e
as
y
m
p
to
tical
s
tab
ilit
y
at
th
e
eq
u
ilib
r
iu
m
p
o
in
t
s
=
0
,
w
h
ic
h
in
d
icate
s
th
a
t
e
a
n
d
all
d
er
iv
ativ
e
o
f
e
w
ill eq
u
al
z
er
o
.
3.
T
H
E
R
E
SU
L
T
S AN
D
ANA
L
YS
I
S
A
cc
o
r
d
in
g
to
t
h
e
d
y
n
a
m
ic
(
8
)
an
d
th
e
m
o
d
el
i
n
tr
o
d
u
ce
d
in
F
ig
u
r
e
1
,
t
h
e
m
o
d
el
o
f
t
h
e
t
w
o
-
lin
k
r
o
b
o
t
ar
m
is
co
n
s
tr
u
cted
o
n
Ma
tla
b
-
Si
m
u
lin
k
a
n
d
p
r
esen
ted
in
Fig
u
r
e
2
.
Pa
r
a
m
eter
s
o
f
r
o
b
o
t
ar
e
s
et
u
p
a
s
th
e
f
o
llo
w
i
n
g
s
:
l
1
=
1
(
m
)
;
l
2
=
0
.
6
(
m
)
;
m
1
=
0
.
7
(
k
g
)
;
m
2
=
0
.
4
(
k
g
)
.
T
h
e
p
r
im
ar
y
a
n
g
le
s
o
f
t
w
o
li
n
k
s
:
=
[
1
2
]
=
[
−
/
6
−
/
12
]
(
)
Fig
u
r
e
3
p
r
esen
ts
t
h
e
d
iag
r
a
m
o
f
th
e
co
n
tr
o
ller
w
h
ich
i
s
co
n
s
tr
u
cted
f
o
llo
w
i
n
g
t
h
e
(
1
2
)
.
W
e
s
et
p
ar
am
e
ter
s
o
f
th
e
co
n
tr
o
ller
as b
elo
w
:
1
4
;
4
2
=
[
6
6
]
;
3
3
;
3
=
[
5
5
]
;
=
0
.
4
;
=
0
.
6
Fig
u
r
e
2
.
T
h
e
t
w
o
-
li
n
k
r
o
b
o
t a
r
m
m
o
d
el
R
u
n
n
in
g
th
i
s
s
y
s
te
m
,
t
h
e
ac
h
i
ev
ed
r
esu
lts
ar
e
p
r
esen
ted
i
n
Fig
u
r
es
4
-
7.
T
h
e
p
h
ase
-
s
tatu
s
tr
aj
ec
to
r
ies
o
f
t
w
o
j
o
in
ts
i
s
d
is
p
la
y
ed
i
n
Fig
u
r
e
4
.
T
h
e
r
esu
lts
o
f
s
i
m
u
l
atio
n
in
d
icate
t
h
at
a
ll
s
tatu
s
tr
aj
ec
to
r
ies
ap
p
r
o
ac
h
th
e
o
r
ig
i
n
O(
0
,
0
)
w
i
th
o
u
t o
s
cil
latio
n
s
.
T
h
u
s
,
th
e
r
esp
o
n
s
e
an
g
les
(
)
r
ea
ch
th
e
ex
p
ec
ted
an
g
le
s
(
)
.
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
8
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8708
F
r
a
ctio
n
a
l
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o
r
d
er sl
id
in
g
mo
d
e
co
n
tr
o
ller
fo
r
th
e
tw
o
-
lin
k
r
o
b
o
t a
r
m
(
Tr
o
n
g
-
Th
a
n
g
N
g
u
ye
n
)
5583
Fig
u
r
e
3
.
T
h
e
m
o
d
el
o
f
co
n
tr
o
ller
(
a)
(
b
)
Fig
u
r
e
4
.
T
h
e
p
h
ase
-
s
tat
u
s
tr
ajec
to
r
ies
,
(
a)
t
h
e
j
o
in
t1
,
(
b
)
t
h
e
j
o
in
t2
Fig
u
r
e
5
.
T
h
e
r
esp
o
n
s
e
an
g
le
a
n
d
co
n
tr
o
l e
r
r
o
r
o
f
th
e
j
o
in
t 1
Fig
u
r
e
6
.
T
h
e
r
esp
o
n
s
e
an
g
le
a
n
d
co
n
tr
o
l e
r
r
o
r
o
f
th
e
j
o
in
t 2
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.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
5
5
7
9
-
5
5
8
5
5584
Fig
u
r
e
s
5
an
d
6
s
h
o
w
th
e
ti
m
e
ch
ar
ac
ter
is
tics
o
f
L
i
n
k
1
an
d
L
in
k
2
r
esp
ec
tiv
el
y
.
E
ac
h
ch
a
r
ac
ter
is
tic
in
cl
u
d
es
t
h
e
d
esire
d
an
g
le
,
th
e
r
esp
o
n
s
e
an
g
le
(
)
,
an
d
th
e
er
r
o
r
(
−
)
.
T
h
e
o
u
tco
m
es
o
f
s
i
m
u
lat
i
o
n
d
em
o
n
s
tr
ate
t
h
at:
f
ir
s
tl
y
,
t
h
e
r
esp
o
n
s
e
an
g
le
s
ar
e
n
o
t
eq
u
al
to
th
e
ex
p
ec
ted
an
g
les,
t
h
en
t
h
e
r
esp
o
n
s
e
a
n
g
le
s
m
ee
t t
h
e
ex
p
ec
ted
v
al
u
e
s
af
ter
a
s
h
o
r
t ti
m
e
(
ap
p
r
o
x
i
m
atel
y
1
s
)
,
an
d
f
i
n
all
y
,
th
e
r
esp
o
n
s
e
an
g
les al
w
a
y
s
ad
h
er
e
th
e
d
esire
d
v
al
u
es,
t
h
e
er
r
o
r
s
(
1
,
2
)
ar
e
ze
r
o
.
A
cc
o
r
d
in
g
l
y
,
it
c
an
b
e
ass
er
ted
th
at
t
h
e
co
n
tr
o
l
s
y
s
te
m
h
a
s
a
h
ig
h
q
u
alit
y
.
T
h
e
co
n
tr
o
l
to
r
q
u
e
o
f
ea
ch
j
o
in
t
is
s
h
o
w
n
in
Fig
u
r
e
7
.
T
h
e
s
i
m
u
latio
n
r
es
u
l
ts
s
h
o
w
th
a
t
th
er
e
is
n
o
t
t
h
e
ch
a
tter
in
g
p
h
en
o
m
en
o
n
o
f
to
r
q
u
es,
w
h
ic
h
is
n
ec
e
s
s
ar
y
f
o
r
t
h
e
s
y
s
te
m
to
as
s
u
r
e
t
h
e
s
u
s
tain
ab
il
it
y
o
f
ac
tu
ato
r
s
an
d
d
ev
ice
s
.
(
a)
(
b
)
Fig
u
r
e
7
.
T
h
e
co
n
tr
o
l to
r
q
u
e
o
f
t
w
o
j
o
i
n
ts
,
(
a)
t
h
e
j
o
in
t1
,
(
b
)
t
h
e
j
o
in
t2
4.
CO
NCLU
SI
O
N
I
n
th
e
p
r
esen
t
r
esear
ch
,
th
e
au
th
o
r
g
ain
ed
s
u
cc
e
s
s
in
estab
li
s
h
in
g
th
e
co
n
tr
o
l
s
y
s
te
m
f
o
r
th
e
t
w
o
-
li
n
k
r
o
b
o
t
a
r
m
u
tili
zi
n
g
th
e
f
r
ac
t
i
o
n
al
-
o
r
d
er
s
lid
in
g
m
o
d
e
co
n
t
r
o
ller
.
T
h
e
s
i
m
u
la
tio
n
o
u
tco
m
es
d
is
p
la
y
ed
th
at
th
e
co
n
tr
o
l
s
y
s
te
m
h
as
r
e
m
ar
k
ab
l
y
h
i
g
h
q
u
alit
y
,
th
e
r
esp
o
n
s
e
an
g
le
o
f
t
w
o
li
n
k
s
al
w
a
y
s
r
ea
ch
es
t
h
e
d
esire
d
an
g
le
s
i
n
a
s
h
o
r
t
d
u
r
atio
n
a
n
d
th
e
s
tatic
er
r
o
r
eq
u
als
ze
r
o
.
N
o
tab
ly
,
t
h
e
c
h
atter
i
n
g
p
h
e
n
o
m
en
o
n
d
o
es
n
o
t
ex
is
t
in
t
h
e
to
r
q
u
es
a
n
d
th
er
ef
o
r
e
t
h
e
l
i
f
esp
an
o
f
t
h
e
co
n
tr
o
ller
a
n
d
ac
tu
ato
r
is
i
n
c
r
ea
s
ed
.
Si
n
c
e
th
e
al
g
o
r
ith
m
s
o
f
th
e
co
n
tr
o
ller
ar
e
an
al
y
ze
d
s
p
ec
if
icall
y
,
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
is
estab
lis
h
ed
q
u
ite
ea
s
il
y
i
n
p
r
ac
tice.
T
h
e
s
u
cc
ess
o
f
th
i
s
p
r
o
p
o
s
ed
a
lg
o
r
ith
m
is
t
h
e
b
asi
s
f
o
r
th
e
a
u
th
o
r
s
to
co
n
d
u
ct
ex
p
er
i
m
e
n
ts
i
n
f
u
r
t
h
er
s
tu
d
ie
s
.
RE
F
E
R
E
NC
E
S
[1
]
I.
Da
v
id
a
n
d
G
.
Ro
b
les
,
“
P
ID
c
o
n
t
ro
l
d
y
n
a
m
ics
o
f
a
Ro
b
o
ti
c
a
rm
m
a
n
ip
u
lato
r
w
it
h
tw
o
d
e
g
re
e
s
o
f
F
re
e
d
o
m
,”
Co
n
tr
o
l
d
e
Pro
c
e
ss
o
s y
Ro
b
o
ti
c
a
,
p
p
.
1
-
6
,
2
0
1
2
.
[2
]
P.
Ro
c
c
o
,
“
S
tab
il
it
y
o
f
P
ID
c
o
n
t
ro
l
f
o
r
i
n
d
u
strial
r
o
b
o
t
a
rm
s
,”
IEE
E
tra
n
sa
c
ti
o
n
s
o
n
ro
b
o
ti
c
s
a
n
d
a
u
to
ma
ti
o
n
,
v
o
l.
12
,
n
o
.
4,
p
p
.
6
0
6
-
6
1
4
,
1
9
9
6
.
[3
]
J.
Y.
Die
u
l
o
t
a
n
d
F
.
Co
las
,
“
Ro
b
u
st
P
ID
c
o
n
tr
o
l
o
f
a
li
n
e
a
r
m
e
c
h
a
n
ica
l
a
x
is:
A
c
a
se
stu
d
y
,”
M
e
c
h
a
tro
n
ics
,
v
o
l.
19
,
n
o
.
2
,
p
p
.
2
6
9
-
2
7
3
,
2
0
0
9
.
[4
]
F
.
J.
C
.
G
a
rc
ia,
e
t
a
l.
,
“
On
t
h
e
De
sig
n
o
f
a
4
De
g
re
e
s
-
of
-
F
re
e
d
o
m
P
ick
a
n
d
P
lac
e
Ca
b
le
S
u
s
p
e
n
d
e
d
P
a
ra
ll
e
l
M
a
n
ip
u
lato
r
,”
I
AE
S
I
n
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
R
o
b
o
ti
c
s a
n
d
Au
t
o
ma
t
io
n
(
IJ
RA
)
,
v
o
l.
6
,
n
o
.
4
,
p
p
.
2
8
6
-
3
0
2
,
2
0
1
7
.
[5
]
M
.
M
u
h
a
m
m
a
d
,
e
t
a
l.
,
“
V
e
lo
c
it
y
c
o
n
tr
o
l
o
f
a
tw
o
-
w
h
e
e
led
in
v
e
rt
e
d
p
e
n
d
u
l
u
m
m
o
b
il
e
ro
b
o
t:
a
f
u
z
z
y
m
o
d
e
l
-
b
a
se
d
a
p
p
ro
a
c
h
,”
Bu
ll
e
ti
n
o
f
El
e
c
trica
l
En
g
i
n
e
e
rin
g
a
n
d
I
n
fo
rm
a
ti
c
s
,
v
o
l.
8
,
n
o
.
3
,
p
p
.
8
0
8
-
8
1
7
,
2
0
1
9
.
[6
]
W
.
Ha
m
,
“
A
d
a
p
ti
v
e
c
o
n
tro
l
b
a
s
e
d
o
n
e
x
p
li
c
it
m
o
d
e
l
o
f
ro
b
o
t
m
a
n
ip
u
lat
o
r
,”
IE
EE
tra
n
s
a
c
ti
o
n
s
o
n
a
u
to
ma
ti
c
c
o
n
tro
l
,
v
o
l.
38
,
n
o
.
4,
p
p
.
6
5
4
-
6
5
8
,
1
9
9
3
.
[7
]
S.
Ku
m
a
r,
e
t
a
l.
,
“
Ro
b
o
ti
c
A
r
m
M
o
v
e
m
e
n
t
o
p
ti
m
iza
ti
o
n
u
si
n
g
S
o
f
t
Co
m
p
u
ti
n
g
,”
IAE
S
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Ro
b
o
ti
c
s
a
n
d
Au
t
o
ma
ti
o
n
(
IJ
RA
)
,
v
o
l.
6
,
n
o
.
1
,
p
p
.
1
-
14,
2
0
1
7
.
[8
]
M
.
R.
S
o
lt
a
n
p
o
u
r,
e
t
a
l.
,
“
Ro
b
u
st
n
o
n
li
n
e
a
r
c
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ter
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[9
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S.
Nu
rm
a
in
i
a
n
d
B.
T
u
t
u
k
o
,
“
In
telli
g
e
n
t
R
o
b
o
ti
c
s
Na
v
ig
a
ti
o
n
S
y
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e
m
:
P
r
o
b
lem
s,
M
e
th
o
d
s,
a
n
d
A
lg
o
rit
h
m
,”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
(
IJ
ECE
)
,
v
o
l.
7
,
n
o
.
6,
p
p
.
3
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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A
.
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.
Ha
n
d
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,
“
An
a
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o
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f
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z
y
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ic
,”
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d
o
n
e
sia
n
J
o
u
rn
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l
o
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El
e
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trica
l
En
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.
1
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p
.
48
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,
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0
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[1
2
]
G
.
C.
Hw
a
n
g
a
n
d
S
.
C.
L
in
,
“
A
sta
b
il
it
y
a
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ro
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sig
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,
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p
.
2
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[1
3
]
S
.
J.
Hu
a
n
g
a
n
d
J.
S
.
L
e
e
,
“
A
sta
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le se
lf
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o
rg
a
n
izin
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f
u
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z
y
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ll
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r
f
o
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ro
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o
ti
c
m
o
ti
o
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c
o
n
tr
o
l
,”
IEE
E
T
ra
n
s
a
c
ti
o
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s
o
n
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n
d
u
stria
l
El
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tro
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,
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o
l.
47
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o
.
2,
p
p
.
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8
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0
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.
[1
4
]
J.
L
.
M
e
z
a
,
e
t
a
l.
,
“
F
u
z
z
y
S
e
lf
-
T
u
n
in
g
P
ID
S
e
m
ig
lo
b
a
l
Re
g
u
lato
r
f
o
r
Ro
b
o
t
M
a
n
ip
u
lato
rs
,”
I
E
EE
T
ra
n
s
a
c
ti
o
n
In
d
u
stria
l
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e
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tro
n
ics
,
v
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l
.
59
,
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o
.
6,
p
p
.
2
7
0
9
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2
7
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,
2
0
1
2
.
[1
5
]
Y
.
Ih
e
d
ra
n
e
,
e
t
a
l.
,
“
Im
p
ro
v
e
d
w
in
d
sy
ste
m
u
sin
g
n
o
n
-
li
n
e
a
r
p
o
w
e
r
c
o
n
tro
l
,”
I
n
d
o
n
e
sia
n
J
o
u
rn
a
l
o
f
El
e
c
trica
l
E
n
g
i
n
e
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rin
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ter
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e
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l.
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o
.
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,
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.
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6
]
L
.
M
.
F
ri
d
m
a
n
,
“
A
n
a
v
e
ra
g
in
g
a
p
p
ro
a
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h
to
c
h
a
tt
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rin
g
,”
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EE
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ra
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sa
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ti
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ti
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l.
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p
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5
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1
.
[1
7
]
J.
J.
E.
S
lo
t
in
e
a
n
d
W
.
L
i.
, “
A
p
p
li
e
d
No
n
l
in
e
a
r
Co
n
tro
l
,”
P
re
n
t
ice
Ha
ll
In
c
.
,
L
o
n
d
o
n
,
UK
,
1
9
9
1
.
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8
]
S.
Da
d
ra
s
a
n
d
H.
R.
M
o
m
e
n
i,
“
F
ra
c
ti
o
n
a
l
term
in
a
l
slid
in
g
m
o
d
e
c
o
n
tro
l
d
e
sig
n
f
o
r
a
c
l
a
ss
o
f
d
y
n
a
m
i
c
a
l
s
y
ste
m
s
w
it
h
u
n
c
e
rtain
ty
,”
Co
mm
u
n
ica
t
io
n
s in
No
n
li
n
e
a
r
S
c
ien
c
e
a
n
d
Nu
me
ric
a
l
S
imu
l
a
ti
o
n
,
v
o
l.
17
,
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o
.
1,
p
p
.
367
-
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7
,
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0
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2
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9
]
A
.
M
u
ju
m
d
a
r,
e
t
a
l
.
,
“
F
ra
c
ti
o
n
a
l
o
r
d
e
r
sli
d
in
g
m
o
d
e
c
o
n
tr
o
l
f
o
r
sin
g
le
li
n
k
f
lex
ib
le
m
a
n
ip
u
lato
r
,”
i
n
2
0
1
3
IE
EE
In
ter
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a
t
io
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a
l
C
o
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fer
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C
o
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ro
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Ap
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ti
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s (
CCA)
,
p
p
.
2
8
8
-
293
,
2
0
1
3
.
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0
]
Y.
T
a
n
g
,
e
t
a
l.
,
“
F
ra
c
ti
o
n
a
l
o
rd
e
r
s
li
d
in
g
m
o
d
e
c
o
n
tr
o
ll
e
r
d
e
sig
n
f
o
r
a
n
ti
lo
c
k
b
ra
k
in
g
sy
st
e
m
s
,”
Ne
u
ro
c
o
mp
u
ti
n
g
,
v
o
l.
111
,
p
p
.
1
2
2
-
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,
2
0
1
3
.
[2
1
]
Y.
T
a
n
g
,
e
t
a
l.
,
“
A
d
a
p
ti
v
e
f
u
z
z
y
f
ra
c
ti
o
n
a
l
-
o
rd
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d
i
n
g
m
o
d
e
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o
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tro
ll
e
r
d
e
sig
n
f
o
r
a
n
ti
lo
c
k
b
ra
k
in
g
s
y
ste
m
s
,”
J
o
u
rn
a
l
o
f
Dy
n
a
mic
S
y
ste
ms
,
M
e
a
su
re
me
n
t,
a
n
d
Co
n
tro
l
,
v
o
l.
1
3
8
,
n
o
.
4
,
p
p
.
1
-
8
,
2
0
1
6
.
[2
2
]
B.
Zh
a
n
g
,
e
t
a
l
.
,
“
F
ra
c
ti
o
n
a
l
o
r
d
e
r
slid
in
g
-
m
o
d
e
c
o
n
tr
o
l
b
a
se
d
o
n
p
a
ra
m
e
ters
a
u
to
-
tu
n
i
n
g
f
o
r
v
e
lo
c
it
y
c
o
n
tro
l
o
f
p
e
rm
a
n
e
n
t
m
a
g
n
e
t
s
y
n
c
h
ro
n
o
u
s
m
o
to
r
,”
IS
A
tra
n
sa
c
ti
o
n
s
,
v
o
l.
51
,
n
o
.
5,
p
p
.
6
4
9
-
6
5
6
,
2
0
1
2
.
[2
3
]
Y.
Q.
C
h
e
n
,
e
t
a
l.
,
“
F
ra
c
ti
o
n
a
l
o
rd
e
r
c
o
n
tro
l
-
a
tu
t
o
rial
,
”
i
n
2
0
0
9
Am
e
ric
a
n
c
o
n
tr
o
l
c
o
n
fer
e
n
c
e
,
p
p
.
1
3
9
7
-
1
4
1
1
,
2
0
0
9
.
[2
4
]
N.
A
.
Ca
m
a
c
h
o
,
e
t
a
l.
,
“
Ly
a
p
u
n
o
v
f
u
n
c
ti
o
n
s
f
o
r
f
ra
c
ti
o
n
a
l
o
rd
e
r
sy
st
e
m
s
,”
Co
mm
u
n
ica
ti
o
n
s
in
N
o
n
li
n
e
a
r
S
c
ien
c
e
a
n
d
Nu
me
ric
a
l
S
im
u
la
t
io
n
,
v
o
l.
19
,
n
o
.
9,
p
p
.
2
9
5
1
-
29
57
,
2
0
1
4
.
[2
5
]
T
.
N
.
T
ro
n
g
a
n
d
M.
N
.
Du
c
,
“
S
li
d
in
g
S
u
rf
a
c
e
in
Co
n
se
n
su
s
P
ro
b
le
m
o
f
M
u
lt
i
-
A
g
e
n
t
Rig
id
M
a
n
ip
u
la
to
rs
w
it
h
Ne
u
ra
l
Ne
tw
o
rk
Co
n
tro
ll
e
r
,”
En
e
rg
ies
,
v
o
l.
10
,
n
o
.
12,
p
p
.
2
1
2
7
-
2
1
4
0
,
2
0
1
7
.
[2
6
]
R.
M
.
M
u
rra
y
,
e
t
a
l.
,
“
A
m
a
th
e
m
a
ti
c
a
l
in
tro
d
u
c
t
io
n
to
ro
b
o
ti
c
m
a
n
i
p
u
lati
o
n
,”
CRC
p
re
ss
,
1
9
9
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.