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pl
a
c
e
o
pe
r
a
t
or
i
s
a
p
pr
oxi
m
a
te
d
b
y a
n
e
qui
va
l
e
nt
i
nt
e
ge
r
t
r
a
ns
f
e
r
f
unc
t
i
o
n,
whi
c
h c
o
nt
a
i
ns
t
he
i
nf
i
ni
t
e
pol
e
s
a
nd z
e
r
os
[
8
]
.
T
he
r
e
f
o
r
e
,
va
r
i
ou
s
a
dva
nc
e
d c
o
nt
r
ol
de
s
i
g
n m
e
tho
ds
be
ne
f
i
t
t
o t
hi
s
pr
ope
r
t
y
.
I
t
s
c
o
nt
r
ol
l
e
r
i
s
de
s
i
g
ne
d wi
t
h t
he
l
e
s
s
n
um
be
r
o
f
th
e
unk
now
n pa
r
a
m
e
te
r
s
[
8
],
[
9]
.
I
t
c
a
n
a
l
s
o
s
a
t
i
s
f
y
a
h
i
g
h
l
e
v
e
l
o
f
t
h
e
i
m
p
o
s
e
d
H
∞
s
p
eci
f
i
cat
i
o
n
s
w
h
er
e
t
h
e
m
ode
l
pa
r
a
m
e
te
r
s
c
ha
n
ge
i
n
wi
de
r
a
nge
.
I
t
i
s
f
u
r
t
h
e
r
n
o
t
i
c
e
d
t
h
a
t
t
h
e
FO
-
P
ID
c
o
nt
r
ol
l
e
r
s
ha
ve
be
e
n a
p
pl
i
e
d
by
r
e
s
e
a
r
c
he
r
s
i
n
di
f
f
e
r
e
nt
f
i
e
l
ds
o
f
e
ng
in
e
e
r
ing a
nd
indu
s
tr
ie
s
a
r
o
un
d t
he
w
or
l
d,
s
uc
h a
s
i
n m
ot
i
on c
ont
r
ol
o
f
D
C
m
ot
or
[
9
],
[
1
0]
,
a
ut
om
a
ti
c
vol
t
a
ge
r
e
g
ul
a
t
or
[
1
1
],
[
1
2]
,
a
e
r
o
s
pa
c
e
de
s
i
gni
ng c
o
nt
r
o
l
s
y
s
t
e
m
[
13]
,
w
e
a
po
n s
y
s
t
e
m
[
14]
,
wi
n
d e
ne
r
gy
s
y
s
t
e
m
[
15]
,
n
uc
l
e
a
r
r
e
a
c
t
o
r
[
16]
,
hy
d
r
o
p
ow
e
r
t
u
r
bi
ne
[
1
7]
,
a
n
d
m
os
t
of
t
h
e
a
b
ove
m
e
nt
i
one
d
r
e
s
e
a
r
c
h
r
e
s
ul
t
s
s
ho
w t
ha
t
t
he
FO
-
P
ID
c
o
nt
r
ol
l
e
r
ha
s
a
be
t
t
e
r
pe
r
f
or
m
a
nc
e
a
nd
r
ob
us
t
ne
s
s
t
ha
n a
c
o
nve
nt
i
ona
l
o
ne
.
Al
t
ho
ug
h
i
t
i
s
s
o
,
t
h
e
p
a
r
a
m
e
t
e
r
o
p
t
i
m
i
z
a
t
i
o
n
o
f
FO
-
PI
D
c
o
n
t
r
o
l
l
e
r
i
s
s
t
i
l
l
a
n
i
m
p
o
r
t
a
n
t
a
n
d
c
h
a
l
l
e
n
g
e
i
s
s
u
e
u
n
t
i
l
n
o
w
.
I
n
t
hi
s
pa
pe
r
,
t
he
r
o
bus
t
FO
-
PI
D
c
o
nt
r
ol
l
e
r
i
s
pr
op
os
e
d
u
s
i
ng
b
ot
h
s
t
r
uc
t
u
r
e
s
s
e
r
i
e
s
a
n
d
pa
r
a
l
l
e
l
.
T
h
e
ob
je
c
t
i
ve
i
s
t
o
opt
i
m
i
z
e
t
he
c
ont
r
ol
l
e
r
pa
r
a
m
e
t
e
r
s
f
r
om
s
ol
vi
n
g t
he
w
e
i
ght
e
d
-
m
i
xe
d p
r
o
bl
e
m
,
i
n w
hi
c
h t
h
e
a
dj
us
t
a
bl
e
pe
r
f
or
m
a
nc
e
w
e
i
g
ht
i
s
de
r
i
ve
d.
T
he
c
ont
r
ol
s
t
r
a
t
e
gy
i
s
a
ppl
i
e
d
on
D
C
m
o
t
o
r
t
o
v
a
l
i
d
a
t
e
t
h
e
ef
f
i
ci
en
cy
o
f
t
h
e
p
r
o
s
e
d
i
d
ea.
2.
O
N
T
H
E
F
R
AC
T
I
O
N
AL
C
AL
CU
L
US
F
r
a
c
t
i
o
n
a
l
c
a
l
c
u
l
u
s
i
s
a
g
e
n
e
r
a
l
i
z
a
t
i
o
n
o
f
i
n
t
e
g
r
a
t
i
o
n
a
n
d
d
i
f
f
e
r
e
n
t
i
a
t
i
o
n
o
f
t
h
e
n
o
n
-
i
nt
e
ge
r
or
de
r
ope
r
a
t
o
r
a
t
D
γ
,
w
h
er
e
a
a
nd
t
de
n
ot
e
t
he
l
im
i
t
s
of
t
he
ope
r
a
t
i
o
n [
18]
.
T
he
c
o
nt
i
nu
o
us
i
nt
e
g
r
o
-
d
i
f
f
e
r
e
n
t
i
a
l
o
p
e
ra
t
o
r
o
f
o
rd
e
r
γ
i
s
d
e
f
i
n
e
d
i
n
t
h
e
f
o
l
l
o
w
i
n
g
w
a
y
(1
):
(
)
:0
1 :
0
:
0
a
t
t
a
d
dt
D
d
γγ
γ
γ
γ
γ
τγ
−
>
=
=
<
∫
(
1)
S
o
t
h
a
t
t
h
e
Ri
e
m
a
n
n
–
L
i
o
u
v
i
l
l
e
d
e
f
i
n
i
t
i
o
n
i
s
g
i
v
e
n
a
s
s
h
o
w
n
i
n
(2
).
(
)
(
)
(
)
1
1
()
n
t
a
t
nn
a
f
d
D
ft
d
n
dt
t
γ
γ
τ
τ
γ
τ
−+
=
Γ−
−
∫
(
2)
A
c
c
o
r
d
i
n
g
t
o
(2
),
n
de
not
e
s
t
he
i
nt
e
ge
r
pa
r
t
of
γ
w
h
e
re
1
nn
γ
−
<
<
a
nd
(
)
.
Γ
i
s
t
h
e
E
u
l
e
r
'
s
ga
m
m
a
f
u
nc
t
i
o
n t
ha
t
gi
ve
n
b
y
(
)
n1
n
0
n
t
e
dt
Γ
+∞
−−
=
∫
,
w
h
e
re
(
)
1
!
nn
Γ
+=
.
T
h
e
L
ap
l
ace t
r
an
s
f
o
r
m
s
o
f
t
h
e
RL
f
r
a
c
t
i
o
n
a
l
d
e
r
i
v
a
t
i
v
e
/
i
n
t
e
g
r
a
l
(
2
)
u
n
d
e
r
z
e
r
o
i
n
i
t
i
a
l
c
o
n
d
i
t
i
o
n
s
f
o
r
o
r
d
e
r
γ
i
s
g
i
ve
n
by
(3
):
(
)
(
)
00
0
()
()
st
t
t
L
D
ft
e
D
ft
d
t
s
F
s
γ
γγ
+∞
±
−
±
±
=
=
∫
(
3)
N
o
t
i
c
i
n
g
t
h
a
t
,
t
h
e
i
m
pl
e
m
e
nta
t
i
on
FO
-
P
ID
c
o
n
t
r
o
l
l
e
r
n
e
e
d
s
t
o
a
p
p
r
o
x
i
m
a
t
e
i
t
s
f
r
a
c
t
i
o
n
a
l
p
a
r
t
o
f
p
o
w
e
rs
γ
by
the
us
ua
l
i
nt
e
ge
r
t
r
a
ns
f
e
r
f
unc
t
i
o
ns
w
i
t
h
a
s
im
il
a
r
be
ha
vi
or
.
T
he
m
e
t
hod i
s
ba
s
e
d o
n
a
pp
r
oxi
m
a
t
i
ng
s
γ
i
n
a s
p
eci
f
i
ed
f
r
e
q
u
en
cy
r
a
nge
[,
]
hb
ω
ωω
=
a
n
d o
f
i
nt
e
ge
r
or
de
r
N
b
y
a
r
a
t
i
o
n
a
l
t
r
a
n
s
f
e
r
f
u
nc
t
i
o
n
obt
a
i
n
e
d
i
n
t
he
f
ol
l
o
w
i
n
g
m
a
nne
r
(4
)
[
19]
:
kN
k
kN
k
s
sC
s
γ
ω
ω
=
=
−
′
+
=
+
∏
(
4)
F
r
o
m
(
4
)
t
h
e
z
er
o
s
,
p
o
l
es
an
d
g
ai
n
ar
e
r
es
p
e
ct
i
v
el
y
d
ef
i
n
e
d
as
s
h
o
w
n
i
n
(5
-
7)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
2
089
-
48
56
I
J
RA
,
V
o
l
.
7
,
N
o
.
2
,
J
un
e
201
8
:
1
08
–
1
18
1
10
1
(1
)
2
21
k
N
N
h
kb
b
γ
ω
ωω
ω
++
−
+
′
=
(
5)
1
(1
)
2
21
k
N
N
h
kb
b
γ
ω
ωω
ω
++
+
+
=
(
6)
2
N
hk
kN
bk
C
γ
ω
ω
ωω
−
=
−
=
′
∏
(
7)
I
n s
om
e
f
r
a
c
t
i
ona
l
c
ont
r
ol
l
e
r
-
s
t
r
uc
t
ur
e
,
d
ue
t
o t
he
c
om
m
ut
a
t
i
ve
pr
ope
r
t
y
of
t
he
f
r
a
c
t
i
o
na
l
o
pe
r
a
t
or
s
α
a
nd o
r
de
r
1
α
≥
,
i
t
c
a
n
be
a
p
pr
o
xi
m
a
t
e
d by
n
ss
αγ
+
=
w
h
e
re
n
αγ
=
−
i
s
t
h
e
i
n
t
e
g
e
r
p
a
r
t
o
f
α
a
nd
s
α
i
s
a
pp
r
oxi
m
a
t
e
d
a
c
c
or
di
n
g
t
o
e
qua
t
i
o
n
(
4)
.
3.
R
O
BU
S
T
P
A
R
A
LLEL/
S
ER
I
ES
F
O
-
P
I
D
D
ES
I
G
N
C
O
N
TR
O
LLE
R
S
o
m
e f
eed
b
ac
k
c
o
n
t
r
o
l
s
y
s
t
e
m
s
i
m
p
l
e
m
e
n
t
a
FO
-
P
ID
c
ont
r
ol
l
e
r
f
unc
t
i
on o
n
s
e
r
i
a
l
f
o
r
m
,
w
hi
l
e
ot
he
r
s
us
e
t
he
pa
r
a
l
l
e
l
f
or
m
.
T
he
a
i
m
of
t
hi
s
pa
pe
r
i
s
t
o
o
bs
e
r
ve
di
f
f
e
r
e
n
c
e
s
be
t
w
e
e
n t
h
e
m
f
or
t
he
D
C
m
o
t
o
r,
an
d
t
o
s
ee
t
h
e
p
er
f
o
r
m
an
ces
o
f
each
o
n
e
i
n
t
i
m
e
an
d
f
r
e
q
u
en
cy
d
o
m
ai
n
s
.
3.
1.
R
ob
u
s
t
P
ar
al
l
e
l
FO
-
P
I
D
Co
n
tr
o
l
l
e
r
T
h
e
Ro
b
u
s
t
p
a
r
a
l
l
e
l
FO
-
PI
D
c
o
n
t
r
o
l
l
e
r
c
a
l
l
e
d
a
l
s
o
P
FO
-
PI
D
i
s
t
h
e
g
en
e
r
al
cas
e o
f
t
h
e cl
as
s
i
cal
p
a
r
a
l
l
e
l
i
n
t
e
g
e
r
o
n
e
.
I
n
t
i
m
e
d
o
m
a
i
n
,
t
h
e
d
i
f
f
e
r
e
n
t
i
a
l
e
q
u
a
t
i
o
n
i
s
d
e
f
i
n
e
d
b
y
(8
)
[
20
]
-
[
21
]
:
00
()
*
()
*
()
*
()
p
i
t
d
t
u
t
K
et
K
D
et
K
D
et
λµ
−+
=
++
(
8)
Wh
e
re
()
et
an
d
()
ut
ar
e
r
es
p
ect
i
v
el
y
,
t
h
e s
et
-
e
r
r
or
a
n
d t
he
c
o
nt
r
ol
s
i
gna
l
.
T
he
tr
a
ns
f
e
r
f
un
c
tion
of
r
obu
s
t
P
FO
-
PI
D
c
ont
r
ol
l
e
r
i
s
t
he
r
e
f
o
r
e
gi
ve
n
t
hr
o
ug
h
t
he
f
o
l
l
owi
n
g
L
a
pl
a
c
e
t
r
a
ns
f
or
m
(
9
0
)
[
20]
.
(
)
,
pi
d
K
s
x
K
Ks
K
s
λµ
−
=
++
(
9)
A
c
c
o
r
di
n
g t
o (
9)
,
t
he
c
o
nt
r
ol
l
e
r
pa
r
a
m
e
t
e
r
s
a
r
e
gi
ve
n by
t
he
de
s
i
gn v
e
c
t
or
,
,
,,
pi
d
x
K
KK
λµ
=
w
h
e
r
e
i
t
s
d
e
r
i
v
a
t
i
v
e
p
a
r
t
i
s
u
s
u
a
l
l
y
r
e
p
l
a
c
e
d
b
y
t
h
e
t
e
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1
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s
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τ
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10
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o,
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a
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3.
2.
R
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11
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[2
2
],
[2
3
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0
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p
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et
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++
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(
11
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
IS
S
N
:
208
9
-
48
56
D
e
s
i
g
n
of
R
ob
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r
ac
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T
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k
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mi
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1
11
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r
om
(
1
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a
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f
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4.
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l
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of
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:
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.
1
.
R
S
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e
t
he
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4
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0
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(
1
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)
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15
)
()
∆
m
s
ω
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
2
089
-
48
56
I
J
RA
,
V
o
l
.
7
,
N
o
.
2
,
J
un
e
201
8
:
1
08
–
1
18
1
12
İ
n
t
he
ne
xt
s
e
c
t
i
on,
()
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Ws
w
i
l
l
be
a
s
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e
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s
t
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xe
d
t
r
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e
r
f
u
nc
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o
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(1
6
)
:
12
12
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)(
)
()
(
)(
)
T
T
k
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=
++
(
16
)
w
h
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r
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a
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4
.
2
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P
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t
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o
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s
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by
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l
e
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ing t
h
e
p
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f
o
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w
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h
t
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hi
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h
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he
s
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i
t
i
vi
t
y
f
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t
i
o
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a
s
f
ol
l
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(1
7
)
[
2
4]
,
[
20]
:
1
:
(
)
(
,)
1
(
,)
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S
S
N
P
W
j
Sj
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Sj
x
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≤
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mi
n
ma
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]
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17
)
w
h
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[
]
1
()
()
(
,
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S
s
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G
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u
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h de
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e
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m
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np
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s
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ds
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n
d
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n t
hi
s
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pe
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pe
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f
or
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n
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e
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i
ght
S
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w
i
l
l
b
e as
s
u
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j
u
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r
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e
r
f
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i
on t
ha
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de
f
i
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e
d i
n (
1
8)
.
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t
s
pa
r
a
m
e
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r
s
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joi
nt
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA
IS
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9
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56
D
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R
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Evaluation Warning : The document was created with Spire.PDF for Python.
IS
SN
:
2
089
-
48
56
I
J
RA
,
V
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C
ES
[1]
H
.
Z
ha
ng
,
X
.
Z
ha
ng,
J
.
W
a
ng,
“
Robus
t
Ga
i
n
-
S
c
he
dul
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n
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r
gy
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o
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k Cont
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ol
o
f
V
eh
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cl
e L
at
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D
y
n
am
i
cs
S
ta
b
ili
z
a
t
io
n
”,
V
eh
. S
ys
t
.
D
yn
,
V
ol
.
52
,
N
o
.
3
,
pp
.
309
–
340,
2014.
[2]
H
. Z
h
an
g
, Y
.
S
h
i
, J
. W
an
g
, “
O
n
E
ne
rg
y
-
t
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-
P
e
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k
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f
or N
onuni
form
l
y
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m
pl
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on
l
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r S
y
s
t
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m
s
:
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M
a
rkovi
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n
J
um
p S
y
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m
A
pproa
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h
”
,
IE
E
E
T
r
ans
.
F
uz
z
y
Sy
s
t
.
V
ol
.
22
,
N
o.
1,
pp.
2
12
–
222
,
2014
.
[3]
J
. K
an
g
, W
.J
.
M
en
g
, A
. A
b
r
a
h
am
, an
d
H
.B
.
L
i
u
, “
A
n
A
da
pt
i
ve
PI
D
N
e
ura
l
N
e
t
w
ork f
or C
om
pl
e
x N
onl
i
ne
a
r
Sy
s
t
e
m
”,
Ne
ur
o
c
om
put
i
ng
,
135,
pp.
79
–
85
,
201
4.
[4]
G
.Q
. Z
en
g
, K
.D
. L
u
, Y
.X
. D
ai
,
Z
.J
. Z
h
an
g
, M
.
R
. C
h
en
, C
.W
.
Z
h
en
g
, D
. W
u
,
an
d
W
.W
. P
en
g
, “
B
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n
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Code
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xt
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m
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m
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t
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on for
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s
i
gn o
f
PI
D
Cont
rol
l
e
rs
”,
N
e
ur
oc
om
put
i
ng
,
138
,
p
p.
180
–
188
,
20
14.
[5]
G.
Q.
Z
en
g
, J
. C
h
en
, M
.R
. C
h
en
, Y
.X
. D
ai
, L
.
M
. L
i
, K
.D
. L
u
, an
d
C
.W
. Z
h
e
n
g
, “
D
es
i
g
n
o
f M
ul
t
i
va
ri
a
bl
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P
I
D
Cont
rol
l
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s
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Code
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as
ed
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x
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r
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al
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p
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m
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zat
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o
n
”,
Ne
ur
oc
om
put
i
ng
,
15
1,
pp.
1343
–
1353,
2015.
[6]
K
. G
l
o
v
er
, J
. C
.
D
o
y
l
e
, “
S
t
at
e
-
S
pa
c
e
F
orm
ul
a
e
F
or A
l
l
S
t
a
bi
l
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ng Cont
rol
l
e
rs
t
h
a
t S
a
tis
f
y
a
n
H
∞
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orm
Bound
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n
d
Re
l
a
t
i
ons
t
o
Ri
s
k S
e
ns
i
t
i
vi
t
y
”.
S
ys
. C
o
n
t
. L
e
t
t
er
s
,
V
ol
.
11,
pp.
167
-
172,
1988
.
[7]
A
. A
. J
al
al
i
, H
.
G
o
l
m
o
h
am
m
ad
, “
L
i
n
e
-
of
-
S
ig
h
t
S
ta
b
iliz
a
t
io
n
b
y
Robus
t
L
1
Cont
rol
l
e
r Ba
s
e
d o
n
L
i
n
ear
M
at
r
i
x
Ine
qua
l
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t
y
(
L
MI
) A
pproa
c
h
”.
J
o
ur
nal
of
Cont
r
ol
E
ngi
ne
e
r
i
ng an
d A
ppl
i
e
d Inf
or
m
at
i
c
s
,
C
EA
I
,
V
ol
.
15,
N
o
.
1 pp.
63
-
70,
2013
.
[8]
I.
P
odl
ubn
y
,
“
F
r
a
c
t
i
ona
l
-
Or
d
e
r
S
y
st
e
m
s
a
nd
P
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D
λυ
Cont
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l
e
r
”.
I
E
E
E
T
r
ans
ac
t
i
on on aut
om
at
i
c
Cont
r
ol
,
V
ol
.
44,
pp.
208
–
214
,
19
99.
[9]
C
.I
. M
u
r
es
an
, S
.
F
o
l
ea, G
. M
o
i
s
,
an
d
E
.H
.
D
ul
f,
“
D
e
ve
l
opm
e
nt
a
nd
Im
pl
e
m
e
nt
a
t
i
on o
f
a
n
FPG
A
Ba
s
e
d F
ra
c
t
i
ona
l
O
rde
r Cont
rol
l
e
r
f
or
a
DC
M
ot
or
”.
M
e
c
ha
t
r
oni
c
s
,
V
ol
.
23,
pp.
798
–
804,
2013
.
[10]
J
. V
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