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266
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s
y
s
tem
.
T
h
e
r
ese
ar
ch
er
s
in
[
5
]
,
d
ev
elo
p
e
d
a
co
m
b
in
atio
n
o
f
PID
-
PI
co
n
tr
o
ller
f
o
r
th
e
cr
an
e
s
y
s
tem
to
m
in
im
ize
th
e
p
en
d
u
lu
m
-
lik
e
s
ettin
g
s
wh
ich
ca
u
s
ed
m
an
y
d
if
f
icu
lties
an
d
d
an
g
er
o
u
s
co
n
d
itio
n
s
with
n
e
w
p
er
f
o
r
m
an
ce
cr
iter
io
n
f
u
n
ct
io
n
th
at
u
s
ed
to
tu
n
e
th
e
PID
-
PD
co
n
tr
o
ller
u
s
in
g
PS
O
alg
o
r
ith
m
.
X.
Sh
ao
et
a
l.
[
6
]
,
p
r
o
p
o
s
ed
a
T
ak
ag
i
-
S
u
g
en
o
(
T
-
S)
f
u
zz
y
m
o
d
elin
g
an
d
r
o
b
u
s
t
L
in
ea
r
Qu
ad
r
atic
R
eg
u
lato
r
(
L
QR
)
b
a
s
ed
PS
O
alg
o
r
ith
m
f
o
r
p
o
s
itio
n
in
g
an
d
an
ti
-
s
win
g
c
o
n
tr
o
l
f
o
r
th
e
s
y
s
tem
.
Op
tim
izatio
n
tech
n
iq
u
e
is
th
e
r
o
u
tin
e
o
f
m
ak
in
g
s
o
m
eth
in
g
b
etter
th
r
o
u
g
h
f
i
n
d
in
g
t
h
e
s
em
i
-
o
p
tim
al
s
o
lu
tio
n
f
o
r
a
p
r
o
b
lem
to
p
er
f
o
r
m
ce
r
tain
o
b
jectiv
es
b
y
tr
y
in
g
v
ar
iatio
n
s
o
n
a
n
in
itial
s
o
l
u
tio
n
an
d
u
s
in
g
th
e
g
ain
ed
d
ata
to
g
et
th
e
g
lo
b
al
o
p
tim
u
m
[
7
]
.
T
h
e
s
to
ch
asti
c
s
war
m
-
b
ased
o
p
tim
izatio
n
alg
o
r
i
th
m
s
h
av
e
b
ec
o
m
e
as a
r
esear
ch
in
ter
est to
m
an
y
r
esear
ch
er
s
d
u
e
to
t
h
eir
ab
ilit
y
to
p
r
o
v
id
e
lo
w
co
s
t,
f
ast,
f
ea
s
i
b
le
an
d
r
ea
s
o
n
ab
ly
p
r
ec
is
e
s
o
lu
tio
n
s
f
o
r
th
e
co
m
p
lex
co
n
s
tr
ain
ed
p
r
o
b
lem
s
.
Sev
er
al
alg
o
r
ith
m
s
h
a
v
e
b
ee
n
d
ev
elo
p
ed
in
o
r
d
er
t
o
s
o
lv
e
a
v
ast
r
an
g
e
o
f
p
r
o
b
le
m
s
.
I
n
r
ec
en
t
y
ea
r
s
,
th
e
s
tan
d
ar
d
s
in
e
co
s
in
e
o
p
tim
izatio
n
(
SS
C
O)
alg
o
r
ith
m
i
s
f
o
u
n
d
to
b
e
o
n
e
o
f
t
h
e
s
u
cc
ess
f
u
l
alg
o
r
ith
m
s
an
d
h
as
d
em
o
n
s
tr
ated
g
r
ea
t
ef
f
ec
tiv
e
n
ess
in
b
o
th
cr
itical
f
ac
to
r
s
o
f
c
o
n
v
er
g
en
ce
r
ate
an
d
ca
p
a
b
ilit
y
in
a
v
o
id
in
g
lo
ca
l
o
p
tim
a
an
d
ac
h
iev
in
g
g
l
o
b
al
o
p
tim
a.
I
t
was
p
r
o
p
o
s
ed
b
y
S.
Mir
jalili
[
8
]
,
in
th
e
y
ea
r
2
0
1
6
,
in
s
p
ir
ed
b
y
th
e
c
y
clic
p
atter
n
o
f
th
e
s
in
e
an
d
co
s
in
e
tr
ig
o
n
o
m
etr
ic
f
u
n
ctio
n
to
allo
w
a
s
o
lu
tio
n
to
b
e
r
e
-
p
o
s
itio
n
ed
a
r
o
u
n
d
an
o
th
e
r
s
o
lu
tio
n
.
T
h
e
SS
C
O
alg
o
r
ith
m
was
ap
p
lied
o
n
th
e
s
ev
er
al
o
p
tim
izati
o
n
p
r
o
b
lem
s
ap
p
ea
r
ed
in
th
e
liter
atu
r
e
s
u
ch
as a
u
t
o
m
atic
g
en
er
atio
n
co
n
tr
o
ller
o
f
m
u
lti
-
ar
ea
t
h
er
m
al
s
y
s
tem
[
9
]
,
s
o
lv
in
g
o
f
g
lo
b
a
l
o
p
tim
izatio
n
an
d
s
tr
u
ctu
r
e
en
g
in
ee
r
in
g
d
esig
n
p
r
o
b
lem
s
[
1
0
]
,
s
o
lu
tio
n
o
f
ec
o
n
o
m
ic/ec
o
lo
g
ical
em
is
s
io
n
s
lo
ad
p
r
o
b
lem
s
[
1
1
]
,
d
e
s
ig
n
in
g
tr
u
s
s
s
tr
u
ctu
r
es
th
r
o
u
g
h
d
is
cr
ete
s
izin
g
an
d
o
p
tim
izatio
n
[
1
2
]
.
T
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
o
p
u
l
atio
n
-
b
ased
alg
o
r
ith
m
s
is
ex
am
in
ed
th
r
o
u
g
h
ch
ec
k
in
g
its
p
o
wer
to
f
in
d
a
p
r
o
p
er
tr
a
d
e
-
o
f
f
b
etwe
en
ex
p
lo
r
atio
n
a
n
d
e
x
p
lo
itatio
n
.
W
h
er
e
th
e
al
g
o
r
ith
m
h
as
a
wea
k
b
alan
ce
b
etwe
en
ex
p
lo
r
atio
n
a
n
d
ex
p
lo
itatio
n
b
e
m
o
r
e
p
r
o
b
ab
ly
to
tr
a
p
in
th
e
lo
ca
l
o
p
tim
a,
p
r
em
atu
r
e
co
n
v
er
g
e
n
ce
an
d
s
tag
n
atio
n
[
1
3
]
.
Dep
e
n
d
in
g
o
n
th
e
ab
o
v
e
r
eg
ar
d
s
,
i
n
th
is
p
ap
er
,
a
n
o
v
el
m
o
d
if
ied
s
in
e
c
o
s
in
e
o
p
tim
izatio
n
(
MSC
O)
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
to
en
h
an
ce
th
e
ex
p
l
o
r
atio
n
an
d
ex
p
lo
itatio
n
f
ea
tu
r
es
i
n
o
r
d
e
r
to
im
p
r
o
v
e
th
e
s
o
lu
tio
n
v
ec
to
r
s
.
Ad
d
itio
n
a
lly
,
th
e
d
ev
elo
p
e
d
alg
o
r
ith
m
is
u
s
ed
to
a
d
ap
t
t
h
e
co
n
v
er
g
en
ce
r
ate
an
d
th
e
q
u
ality
of
th
e
PID
co
n
tr
o
ller
with
a
s
er
ies
d
if
f
er
en
tial
co
m
p
e
n
s
ato
r
(
PID
C
)
tu
n
in
g
.
T
h
e
r
est
o
f
p
ap
er
is
o
r
g
an
ize
d
as
f
o
llo
ws.
Nex
t
s
ec
tio
n
d
escr
ib
e
s
th
e
g
an
tr
y
cr
a
n
e
n
o
n
lin
ea
r
m
o
d
el
in
d
etails.
Sectio
n
3
in
tr
o
d
u
ce
s
th
e
th
eo
r
etica
l
b
asics
o
f
PID
C
co
n
tr
o
l
lin
g
m
e
th
o
d
a
n
d
t
h
e
SS
C
O
alg
o
r
ith
m
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
if
ied
a
lg
o
r
ith
m
is
p
r
esen
ted
i
n
d
etails
in
s
ec
tio
n
4
.
Su
b
s
eq
u
e
n
tly
,
th
e
tu
n
i
n
g
o
f
th
e
PID
C
co
n
tr
o
ller
an
d
th
e
p
r
o
p
o
s
ed
o
b
j
ec
tiv
e
f
u
n
ctio
n
a
r
e
ex
p
lain
ed
i
n
s
ec
tio
n
5
.
T
h
e
t
esti
n
g
o
f
th
e
p
r
o
p
o
s
ed
al
g
o
r
it
h
m
'
s
p
er
f
o
r
m
an
ce
an
d
th
e
s
i
m
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
in
s
ec
tio
n
6
.
Fin
ally
,
g
en
er
al
co
n
clu
s
io
n
s
ar
e
d
r
aw
n
in
th
e
last
s
ec
tio
n
.
2.
G
ANTRY C
R
ANE
SYS
T
E
M
M
O
D
E
L
T
h
e
g
an
tr
y
cr
an
e
s
y
s
tem
,
s
h
o
wn
in
Fig
u
r
e
1
,
is
an
in
h
er
en
tly
n
o
n
lin
ea
r
an
d
u
n
s
tab
le
s
y
s
tem
wh
ich
ca
n
b
e
co
n
s
id
er
ed
as
an
im
p
o
r
tan
t
b
en
ch
m
ar
k
s
y
s
tem
f
o
r
test
in
g
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
llin
g
s
ch
e
m
e
an
d
o
p
tim
izatio
n
alg
o
r
ith
m
[
1
4
]
.
T
h
e
L
ag
r
an
g
e'
s
eq
u
atio
n
is
th
e
m
o
s
t
co
n
v
en
ien
t
to
o
l
th
at
u
s
ed
to
d
er
iv
e
th
e
g
an
tr
y
cr
an
e
m
o
d
el
.
T
h
e
g
an
tr
y
cr
a
n
e
s
y
s
tem
d
ep
en
d
s
m
a
in
ly
o
n
th
r
ee
v
a
r
iab
les n
am
ely
,
th
e
tr
o
lley
d
is
p
lace
m
en
t f
r
o
m
a
r
ef
er
e
n
ce
p
o
s
itio
n
(
)
,
th
e
p
a
y
lo
ad
s
win
g
a
n
g
le
(
)
,
an
d
th
e
s
teel
wir
e
el
o
n
g
atio
n
ℓ
(
)
.
T
h
e
d
y
n
am
ics
o
f
t
h
e
s
y
s
tem
is
g
iv
en
as f
o
llo
ws
[
5
,
1
5
-
1
7
]
:
T
h
e
tr
o
lley
a
n
d
p
a
y
lo
ad
p
o
s
itio
n
v
ec
to
r
s
ar
e
g
iv
e
n
b
y
,
⃗
=
{
,
0
}
⃗
ℓ
=
{
+
ℓ
s
in
,
-
ℓ
c
os
}
}
(
1
)
wh
er
e
=
,
=
0
,
ℓ
=
+
ℓ
s
in
,
an
d
ℓ
=
-
ℓ
c
os
.
T
h
e
k
i
n
etic
en
e
r
g
y
o
f
th
e
s
y
s
tem
is
,
=
1
2
(
1
2
+
2
ℓ
2
)
(
2
)
Hen
ce
,
2
=
(
̇
)
2
+
(
̇
)
2
=
̇
2
(
3
)
an
d
ℓ
2
=
(
̇
ℓ
)
2
+
(
̇
ℓ
)
2
=
̇
2
+
2
̇
ℓ
̇
c
os
+
ℓ
2
̇
2
+
2
̇
ℓ
̇
s
in
+
ℓ
̇
2
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
n
tr
o
ller
d
esig
n
fo
r
g
a
n
tr
y
cra
n
e
s
ystem
u
s
i
n
g
mo
d
ified
s
in
e
co
s
in
e
o
p
timiz
a
tio
n
.
.
.
(
N
iz
a
r
Ha
d
i A
b
b
a
s
)
267
Acc
o
r
d
in
g
ly
s
u
b
s
titu
te
as sh
o
wn
in
(
3
)
an
d
(
4
)
t
o
(
2
)
,
y
ield
s
,
=
1
2
(
1
̇
2
+
2
(
̇
2
+
2
̇
ℓ
̇
c
os
+
ℓ
2
̇
2
+
2
̇
ℓ
̇
s
in
+
ℓ
̇
2
)
)
(
5
)
an
d
th
e
p
o
ten
tial e
n
er
g
y
o
f
th
e
s
y
s
tem
is
,
=
−
2
ℓ
c
os
(
6
)
T
h
e
n
o
n
lin
ea
r
d
y
n
am
ics o
f
th
e
g
an
tr
y
c
r
an
e
s
y
s
tem
is
m
o
d
el
ed
b
ello
w
u
s
in
g
L
ag
r
an
g
ian
m
eth
o
d
,
=
−
=
1
2
(
1
̇
2
+
2
(
̇
2
+
2
̇
ℓ
̇
cos
+
ℓ
2
̇
2
+
2
̇
ℓ
̇
si
n
+
ℓ
̇
2
)
)
+
2
ℓ
cos
(
7
)
No
w,
u
s
in
g
L
ag
r
an
g
e'
s
eq
u
atio
n
s
,
Fo
r
d
is
p
lace
m
en
t,
x
,
(
̇
)
−
=
−
̇
(
8
)
⟹
̇
=
1
̇
+
2
̇
+
2
ℓ
̇
c
os
+
2
ℓ
̇
s
in
⇒
d
dt
(
∂
L
∂
x
̇
)
=
1
̈
+
2
̈
−
2
ℓ
̇
2
s
in
+
2
ℓ
̈
c
os
+
2
2
ℓ
̇
̇
c
os
+
2
ℓ
̈
s
in
⟹
=
0
T
h
er
ef
o
r
e,
d
is
p
lace
m
en
t e
q
u
at
io
n
ca
n
b
e
f
o
r
m
u
lated
as f
o
llo
ws,
(
1
+
2
)
̈
−
2
ℓ
̇
2
s
in
+
2
ℓ
̈
c
os
+
2
2
ℓ
̇
̇
c
os
+
2
ℓ
̈
s
in
=
−
̇
(
9
)
Fo
r
s
win
g
an
g
le,
,
(
̇
)
−
=
̈
+
̇
(
1
0
)
⇒
̇
=
2
̇
ℓ
c
os
+
2
ℓ
2
̇
⟹
(
̇
)
=
−
2
ℓ
̇
̇
s
in
+
2
̇
ℓ
̇
c
os
+
2
̈
ℓ
c
os
+
2
ℓ
2
̈
+
2
2
ℓ
ℓ
̇
̇
⟹
=
−
2
ℓ
̇
̇
s
in
+
2
̇
ℓ
̇
c
os
−
2
g
ℓ
s
in
T
h
er
ef
o
r
e,
s
win
g
an
g
le
eq
u
ati
o
n
ca
n
b
e
r
ep
r
esen
ted
as f
o
llo
ws,
2
̈
ℓ
c
os
+
2
ℓ
2
̈
+
2
2
ℓ
ℓ
̇
̇
+
2
g
ℓ
s
in
=
̈
+
̇
(1
1)
w
h
er
e
1
an
d
2
ar
e
th
e
m
ass
o
f
t
h
e
tr
o
lley
an
d
th
e
p
ay
lo
a
d
r
esp
ec
tiv
ely
;
an
d
ℓ
ar
e
th
e
s
p
ee
d
o
f
th
e
tr
o
lley
an
d
th
e
p
ay
lo
ad
r
esp
ec
tiv
ely
;
is
th
e
g
r
av
itatio
n
al
ac
ce
ler
atio
n
,
is
th
e
ac
tu
atin
g
f
o
r
ce
ac
ted
o
n
th
e
tr
o
lley
,
an
d
ar
e
v
is
co
u
s
f
r
ictio
n
co
ef
f
icien
t
with
th
e
r
ail
an
d
d
u
e
to
p
en
d
u
lu
m
ax
is
r
esp
ec
tiv
ely
;
is
th
e
m
o
m
e
n
t
o
f
in
er
tia
o
f
th
e
p
ay
lo
a
d
.
Fig
u
r
e
1
.
Ga
n
tr
y
cr
a
n
e
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
6
5
-
2
7
6
268
Ultim
ately
,
as
s
h
o
wn
in
(
9
)
an
d
(
1
1
)
r
ep
r
esen
t
th
e
n
o
n
lin
ea
r
m
o
d
el
o
f
th
e
s
y
s
te
m
d
u
e
to
th
e
ter
m
s
o
f
tr
ig
o
n
o
m
et
r
ic
f
u
n
ctio
n
s
a
n
d
th
e
q
u
ad
r
atic
ter
m
s
.
I
n
t
h
is
s
tu
d
y
,
it
is
ass
u
m
ed
th
at
th
e
ten
s
io
n
f
o
r
ce
o
f
t
h
e
h
o
is
tin
g
s
teel
wir
e
th
at
ca
u
s
es
th
e
ca
b
le
elo
n
g
atio
n
h
as
a
s
m
all
ef
f
ec
t,
wh
ich
ca
n
b
e
n
eg
lecte
d
,
th
u
s
th
e
len
g
t
h
o
f
th
e
ca
b
le
is
co
n
s
id
er
ed
t
o
b
e
c
o
n
s
tan
t a
n
d
h
en
ce
,
s
u
b
s
titu
te
ℓ
̇
=
ℓ
̈
=
0
as sh
o
wn
in
.
(
9
)
an
d
(
1
1
)
.
3.
T
H
E
O
R
E
T
I
CA
L
B
A
SI
CS
3
.
1
.
P
I
DC
s
chem
e
PID
co
n
tr
o
ller
was
class
if
ied
as
th
e
s
ec
o
n
d
co
n
tr
i
b
u
tio
n
o
f
2
0
th
ce
n
tu
r
y
in
t
h
e
f
ield
o
f
in
s
tr
u
m
en
ts
,
r
ig
h
t
b
e
h
in
d
m
icr
o
p
r
o
ce
s
s
o
r
,
d
ec
is
io
n
an
d
co
m
m
u
n
icatio
n
s
.
R
ec
en
tly
,
ad
d
itio
n
al
ad
ap
tatio
n
s
f
o
r
th
e
s
y
s
tem
s
h
av
e
co
n
tr
o
lled
lo
o
p
s
in
ter
m
s
o
f
p
er
f
o
r
m
an
ce
,
an
d
r
o
b
u
s
tn
e
s
s
ca
n
b
e
o
b
tain
ed
.
On
e
o
f
th
ese
m
o
d
if
icatio
n
s
is
m
er
g
in
g
t
h
e
PID
co
n
tr
o
ller
with
th
e
s
er
ies
d
if
f
er
en
tial
co
m
p
en
s
ato
r
to
f
o
r
m
th
e
PID
C
co
n
tr
o
ller
to
im
p
r
o
v
e
th
e
r
o
b
u
s
t
n
ess
in
co
m
p
a
r
is
o
n
with
th
e
co
n
v
en
tio
n
al
PID
C
co
m
p
en
s
ato
r
[
1
8
]
.
T
h
e
tu
n
in
g
p
ar
am
eter
s
o
f
a
PID
C
co
n
tr
o
ller
ar
e:
s
ec
o
n
d
o
r
d
er
d
er
iv
ativ
e
g
ain
p
r
o
p
o
r
tio
n
al
g
a
in
ℎ
,
d
er
iv
ativ
e
g
ain
,
p
r
o
p
o
r
tio
n
al
g
ain
,
in
teg
r
al
g
ain
an
d
f
ilter
tim
e
c
o
n
s
tan
t
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
PID
C
co
n
tr
o
ller
is
d
esc
r
ib
ed
as sh
o
wn
in
(
1
2
)
b
elo
w
a
n
d
t
h
e
g
a
n
tr
y
c
r
an
e
s
y
s
tem
with
tr
o
lley
a
n
d
a
n
ti
-
s
way
PID
C
co
n
tr
o
ller
s
is
d
ep
icted
in
Fig
u
r
e
2.
(
)
=
ℎ
3
+
2
+
+
0
.
5
2
3
+
2
+
(
1
2
)
Fig
u
r
e
2
.
Pro
p
o
s
ed
c
o
n
tr
o
llin
g
s
ch
em
e
f
o
r
g
an
tr
y
cr
an
e
s
y
s
te
m
3
.
2
.
SS
CO
a
lg
o
rit
hm
T
h
e
SS
C
OA
as
p
r
ev
io
u
s
ly
m
en
tio
n
ed
is
an
o
p
tim
izatio
n
tec
h
n
iq
u
e
in
v
en
ted
b
y
S.
Mir
jalil
i
[
8
]
.
T
h
e
f
u
n
d
am
e
n
tal
ch
ar
ac
ter
is
tic
o
f
th
e
SS
C
O
alg
o
r
ith
m
is
th
at
th
e
alg
o
r
ith
m
'
s
p
r
o
ce
d
u
r
e
is
s
lig
h
tly
s
im
p
le
m
ec
h
an
is
m
wh
er
e
th
e
d
esig
n
v
ar
iab
le
is
u
p
d
ated
u
s
in
g
o
n
ly
th
e
m
at
h
em
atica
l
m
o
d
elin
g
o
f
t
h
e
s
in
e
co
s
in
e
f
u
n
ctio
n
s
to
g
u
id
e
th
e
p
o
p
u
la
tio
n
to
s
ea
r
c
h
f
o
r
g
lo
b
al
o
p
ti
m
al
s
o
lu
tio
n
s
.
I
n
SS
C
O
alg
o
r
ith
m
,
th
e
p
o
s
itio
n
'
s
u
p
d
atin
g
r
u
le
o
f
a
n
ag
e
n
t'
s
p
o
p
u
latio
n
i
n
th
e
d
esig
n
s
p
ac
e
is
f
o
r
m
u
lated
in
ac
co
r
d
an
c
e
to
th
e
f
o
llo
win
g
eq
u
atio
n
[
1
9
-
2
1
]
:
,j
+
1
=
{
,j
+
1
×
s
in
(
2
)
×
|
3
−
,j
|
,
4
<
0
.5
,j
+
1
×
c
os
(
2
)
×
|
3
−
,j
|
,
4
≥
0
.5
(
1
3
)
wh
er
e
,
,j
: is th
e
p
o
s
itio
n
o
f
th
e
cu
r
r
e
n
t
s
o
lu
tio
n
in
ith
s
ea
r
ch
a
g
en
ts
at
tth
iter
atio
n
an
d
f
o
r
jth
d
im
e
n
s
io
n
.
: is th
e
n
u
m
b
e
r
o
f
t
h
e
s
ea
r
ch
a
g
en
ts
.
: is th
e
d
im
en
s
io
n
s
ize
o
f
t
h
e
co
n
s
id
er
ed
p
r
o
b
lem
.
1
: is a
r
an
d
o
m
n
u
m
b
er
in
[
,
0
]
.
2
: is a
r
an
d
o
m
n
u
m
b
er
in
[
0
,
2
].
3
: is a
r
an
d
o
m
n
u
m
b
er
in
[
0
,
2
].
: is th
e
p
o
s
itio
n
o
f
th
e
d
esti
n
atio
n
p
o
i
n
t
in
jth
d
im
e
n
s
io
n
at
tt
h
iter
atio
n
.
|
|
: in
d
icate
s
th
e
ab
s
o
lu
te
v
alu
e.
4
: is a
r
an
d
o
m
n
u
m
b
er
in
(
0
,
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
n
tr
o
ller
d
esig
n
fo
r
g
a
n
tr
y
cra
n
e
s
ystem
u
s
i
n
g
mo
d
ified
s
in
e
co
s
in
e
o
p
timiz
a
tio
n
.
.
.
(
N
iz
a
r
Ha
d
i A
b
b
a
s
)
269
1
=
−
(
1
4
)
wh
er
e,
: is th
e
cu
r
r
en
t iter
ati
o
n
.
: is th
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
iter
atio
n
s
.
: is a
co
n
s
tan
t a
n
d
e
q
u
al
to
2
.
T
h
e
s
tep
s
o
f
th
e
s
tan
d
a
r
d
s
in
e
co
s
in
e
alg
o
r
ith
m
a
r
e
s
u
m
m
ar
i
ze
d
in
Alg
o
r
ith
m
1
:
Alg
o
r
ith
m
1
.
T
h
e
s
tan
d
a
r
d
s
in
e
co
s
in
e
alg
o
r
ith
m
4.
M
SCO
A
L
G
O
RIT
H
M
T
h
e
SC
O
alg
o
r
ith
m
ca
n
d
is
cl
o
s
e
p
r
o
f
icien
t
ac
cu
r
ac
y
in
co
m
p
ar
is
o
n
with
o
th
er
w
ell
-
k
n
o
wn
n
atu
r
e
-
in
s
p
ir
e
d
o
p
tim
izatio
n
a
lg
o
r
ith
m
s
;
it
is
n
o
t
q
u
alif
ied
f
o
r
v
e
r
y
co
m
p
le
x
p
r
o
b
le
m
s
an
d
is
s
till
m
ay
f
ac
e
th
e
d
if
f
icu
lty
o
f
b
ec
o
m
in
g
tr
a
p
p
ed
in
lo
ca
l
o
p
tim
a
[
2
1
,
2
2
]
.
T
h
e
m
o
d
if
ied
alg
o
r
ith
m
i
s
p
r
o
p
o
s
ed
to
o
v
er
c
o
m
e
th
ese
s
h
o
r
tco
m
in
g
s
a
n
d
to
s
tep
-
u
p
its
s
ea
r
ch
ca
p
ab
ilit
y
f
o
r
s
o
lv
in
g
d
if
f
er
en
t
r
ea
l
-
life
p
r
o
b
lem
s
.
I
n
th
is
p
ap
e
r
,
th
e
im
p
r
o
v
em
e
n
ts
in
v
o
l
v
ed
i
n
th
e
MSC
O
alg
o
r
ith
m
y
ield
ed
b
y
th
e
f
o
ll
o
win
g
t
h
r
ee
d
ir
ec
tio
n
s
.
Firstl
y
,
th
e
in
s
er
tin
g
o
f
(
2
)
−
1
in
t
h
e
s
in
e
a
n
d
c
o
s
in
e
u
p
d
ate
eq
u
atio
n
s
,
a
n
d
b
y
th
e
lo
g
ar
ith
m
ic
d
ec
r
ea
s
in
g
o
f
th
e
co
n
tr
o
l
p
ar
am
eter
1
to
ac
ce
ler
ate
th
e
tr
an
s
itio
n
f
r
o
m
lo
ca
l
ex
p
l
o
itatio
n
to
g
lo
b
al
ex
p
lo
r
atio
n
a
b
ilit
y
.
T
h
is
id
ea
co
m
es
f
r
o
m
th
e
f
ac
t
th
at
th
e
lar
g
er
v
alu
e
1
ca
n
en
h
an
ce
th
e
g
lo
b
al
s
ea
r
ch
in
g
ca
p
ab
ilit
y
o
f
t
h
e
a
lg
o
r
ith
m
,
a
n
d
th
e
s
m
aller
v
alu
e
1
ca
n
s
tr
en
g
t
h
e
n
th
e
lo
ca
l
d
ev
elo
p
m
en
t
p
o
wer
o
f
th
e
alg
o
r
ith
m
[
2
3
]
.
S
ec
o
n
d
ly
,
d
y
n
am
ic
ch
an
g
in
g
2
,j
f
o
r
ea
ch
iter
atio
n
,
in
d
iv
id
u
als
an
d
d
im
e
n
s
io
n
will
g
u
id
e
th
e
alg
o
r
ith
m
to
j
u
m
p
o
u
t
f
r
o
m
t
h
e
lo
ca
l
o
p
tim
u
m
wh
ich
;
t
h
er
ef
o
r
e,
e
f
f
i
cien
tly
av
o
i
d
s
th
e
alg
o
r
ith
m
p
r
em
atu
r
e
c
o
n
v
er
g
en
ce
an
d
en
h
a
n
ce
s
th
e
s
ea
r
ch
i
n
g
p
r
ec
is
io
n
.
T
h
ir
d
im
p
r
o
v
em
en
t
d
ir
ec
tio
n
is
ac
co
m
p
lis
h
ed
b
y
ch
an
g
in
g
3
,j
s
in
u
s
o
i
d
ally
to
p
r
e
v
en
t
th
e
MSC
O
alg
o
r
ith
m
'
s
p
o
p
u
latio
n
in
d
iv
i
d
u
als
to
b
e
alter
n
ate
in
th
e
en
d
o
f
t
h
e
s
ea
r
ch
p
r
o
ce
s
s
wh
ich
lead
s
to
m
in
im
ize
th
e
n
u
m
b
er
o
f
iter
atio
n
s
r
e
q
u
ir
ed
.
T
h
e
m
o
d
if
icatio
n
s
m
ad
e
in
th
e
SS
C
O
alg
o
r
ith
m
ar
e
e
x
p
r
ess
ed
i
n
th
e
f
o
llo
win
g
e
q
u
atio
n
s
:
,j
+
1
=
{
,j
+
(
2
)
−
1
×
s
in
(
2
)
×
|
3
−
,j
|
,
4
<
0
.5
,j
+
(
2
)
−
1
×
c
os
(
2
)
×
|
3
−
,j
|
,
4
≥
0
.5
(
1
5
)
1
=
×
(
l
og
10
−
l
og
10
)
(
16)
2
,j
=
2
×
(
0
,
1
)
(
1
7
)
I
np
u
t:
Po
p
u
latio
n
s
ize
,
th
e
m
ax
im
u
m
n
o
.
o
f
g
e
n
er
atio
n
s
,
th
e
d
im
en
s
io
n
s
ize
,
th
e
u
p
p
er
an
d
lo
wer
b
o
u
n
d
o
f
ea
ch
d
im
en
s
io
n
,
t
h
e
co
n
s
ta
n
t
;
O
utput
:
T
h
e
g
lo
b
al
o
p
tim
a
∗
;
Sta
rt
:
1.
Gen
er
ate
th
e
in
itial p
o
p
u
latio
n
with
in
th
e
lo
wer
an
d
u
p
p
er
b
o
u
n
d
f
o
r
ea
c
h
d
im
en
s
io
n
s
p
ac
e;
2.
Dete
r
m
in
e
th
e
o
b
jectiv
e
f
u
n
cti
o
n
v
al
u
es a
n
d
s
p
ec
if
y
th
e
b
est
s
o
lu
tio
n
f
o
r
th
e
in
itial
p
o
p
u
latio
n
;
3.
f
o
r
=
1
to
4.
ca
lcu
late
1
u
s
in
g
E
q
.
(
1
4
)
;
5.
f
o
r
=
1
to
6.
f
o
r
=
1
to
7.
Gen
er
ate
th
e
v
alu
es o
f
alg
o
r
ith
m
'
s
co
n
tr
o
llin
g
p
a
r
am
eter
s
2
,
3
&
4
;
8.
Up
d
ate
th
e
ag
en
ts
'
p
o
s
itio
n
u
s
in
g
E
q
.
(
1
3
)
;
9.
e
n
d
f
o
r
10.
D
eter
m
in
e
th
e
n
ew
o
b
jectiv
e
f
u
n
ctio
n
b
ased
o
n
n
ewly
g
e
n
er
ate
d
ag
en
ts
'
p
o
s
itio
n
f
o
r
ea
ch
d
im
e
n
s
io
n
;
11.
if
(
,j
)
<
(
j
−
1
)
12.
T
h
e
n
,j
=
j
;
13.
e
n
d
if
14.
en
d
f
o
r
15.
en
d
f
o
r
16.
R
etu
r
n
th
e
g
lo
b
al
o
p
tim
a
(
∗
);
E
nd
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
6
5
-
2
7
6
270
3
,j
=
2
×
s
in
(
×
2
)
(
1
8
)
4
,j
=
(
0
,
1
)
(
1
9
)
5.
T
UNI
NG
O
F
CO
NT
RO
L
L
I
NG
SCH
E
M
E
S
5
.
1
.
P
I
DC
co
ntr
o
ller
t
un
ing
I
n
th
is
p
ap
er
p
r
esen
ts
an
ef
f
ec
tiv
e
d
esig
n
m
eth
o
d
o
f
PID
co
n
tr
o
ller
with
s
er
ies
d
if
f
er
en
tial
co
m
p
en
s
ato
r
.
T
h
e
b
o
u
n
d
a
r
y
v
alu
es
f
o
r
t
h
e
tu
n
in
g
p
ar
am
eter
s
o
f
a
PID
C
co
n
tr
o
ller
f
o
r
b
o
t
h
tr
o
lley
a
n
d
p
ay
lo
a
d
o
s
cillatio
n
;
ℎ
,
,
,
an
d
,
th
ey
ar
e
f
in
e
-
tu
n
e
d
with
in
th
e
r
an
g
e
g
iv
en
b
el
o
w,
Fo
r
tr
o
lley
co
n
tr
o
ller
,
=
[
100
,
1
,
1
,
0
,
1
]
;
=
[
800
,
70
,
70
,
10
,
10
]
.
Fo
r
p
ay
lo
a
d
o
s
cillatio
n
co
n
tr
o
ller
,
=
[
3
0
,
0
.
5
,
1
,
-
1
,
3
]
;
=
[
1300
,
50
,
55
,
10
,
20
]
.
5
.
2
.
P
r
o
po
s
ed
o
bj
ec
t
iv
e
f
un
c
t
io
n
T
h
e
p
er
f
o
r
m
a
n
ce
in
d
e
x
f
o
r
tr
o
lley
p
o
s
itio
n
an
d
p
ay
lo
a
d
o
s
cil
latio
n
s
o
u
tp
u
ts
is
as f
o
llo
ws,
=
(
.
O
+
)
+
(
−
)
+
+
(
2
0
)
wh
er
e
,
,
,
an
d
ar
e
weig
h
tin
g
f
ac
to
r
s
an
d
+
+
+
=
1
,
let
=
=
=
=
1
4
.
I
SE
s
tan
d
f
o
r
in
teg
r
al
o
f
t
h
e
s
q
u
ar
e
v
alu
e
o
f
th
e
er
r
o
r
&
MSE
s
tan
d
f
o
r
m
e
an
s
q
u
ar
e
er
r
o
r
.
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
NS
6
.
1
.
Sim
ula
t
i
o
n set
up
All th
e
ex
p
er
im
en
ts
in
th
is
p
ap
er
h
av
e
b
ee
n
co
n
d
u
cted
o
n
a
p
er
s
o
n
al
PC
with
an
I
n
tel
(
R
)
C
o
r
e
(
T
M)
i
7
-
6
5
0
0
U
C
PU@
2
.
5
0
GHz
p
r
o
ce
s
s
o
r
with
8
GB
R
AM
an
d
6
4
-
b
it
f
o
r
Mic
r
o
s
o
f
t
W
in
d
o
w
s
1
0
Pr
o
o
p
er
atin
g
s
y
s
tem
.
T
h
e
s
o
u
r
ce
c
o
d
e
h
as
b
ee
n
im
p
lem
e
n
ted
u
s
in
g
M
AT
L
AB
(
R
2
0
1
4
a)
.
T
h
e
g
an
t
r
y
cr
an
e
m
o
d
el
a
n
d
o
p
tim
izatio
n
alg
o
r
ith
m
p
ar
am
eter
s
u
s
ed
th
r
o
u
g
h
th
e
n
u
m
er
ical
s
im
u
latio
n
s
ar
e
o
b
tain
e
d
f
r
o
m
th
e
p
r
ac
tical
s
y
s
tem
'
s
d
ata
s
h
ee
t a
n
d
f
r
o
m
th
e
liter
atu
r
e,
r
esp
ec
tiv
ely
,
as lis
ted
in
T
ab
le
1
.
T
ab
le
1
.
Par
am
eter
s
'
s
ettin
g
f
o
r
th
e
s
y
s
tem
m
o
d
el
a
n
d
o
p
tim
izatio
n
-
alg
o
r
ith
m
s
P
a
r
a
me
t
e
r
V
a
l
u
e
1
5
K
g
2
1
K
g
ℓ
0
.
7
5
m
9
.
8
1
2
⁄
12
.
32
⁄
0
.5
⁄
0
.
0
3
K
g
2
T
5
0
0
f
o
r M
S
C
O
A
8
5
0
f
o
r
S
S
C
O
A
n
25
D
2
0
f
o
r
t
h
e
t
e
st
f
u
n
c
t
i
o
n
s
1
0
f
o
r
t
u
n
i
n
g
t
h
e
PI
D
C
c
o
n
t
r
o
l
l
e
r
a
2
6
.
2
.
Cha
ra
c
t
er
is
t
ics
o
f
t
he
t
e
s
t
f
un
ct
io
ns
I
n
th
is
r
esear
ch
wo
r
k
,
1
4
test
f
u
n
ctio
n
s
ar
e
tak
en
f
r
o
m
th
e
liter
atu
r
e
[
8
,
24
-
2
6
]
,
to
in
v
esti
g
ate
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
MSC
O
alg
o
r
ith
m
.
T
h
ese
p
r
o
b
lem
s
co
n
s
is
t
o
f
u
n
im
o
d
al,
h
ig
h
l
y
co
m
p
le
x
m
u
ltimo
d
al
a
n
d
ex
tr
em
ely
co
m
p
lex
c
o
m
p
o
s
ite
b
en
ch
m
a
r
k
f
u
n
ctio
n
s
.
T
h
e
d
etails
o
f
t
h
e
c
h
o
s
en
test
f
u
n
ctio
n
s
ar
e
d
em
o
n
s
tr
ated
in
T
ab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
n
tr
o
ller
d
esig
n
fo
r
g
a
n
tr
y
cra
n
e
s
ystem
u
s
i
n
g
mo
d
ified
s
in
e
co
s
in
e
o
p
timiz
a
tio
n
.
.
.
(
N
iz
a
r
Ha
d
i A
b
b
a
s
)
271
T
ab
le
2
.
T
est f
u
n
cti
o
n
s
'
d
etails
F
u
n
c
t
i
o
n
Ty
p
e
S
c
o
p
e
O
p
t
i
mu
m
01
(
)
=
∑
2
=
1
U
n
i
m
o
d
a
l
[
−
100
,
100
]
0
02
(
)
=
∑
|
|
=
1
+
∏
|
|
=
1
U
n
i
m
o
d
a
l
[
−
10
,
10
]
0
03
(
)
=
∑
(
∑
=
1
)
2
=
1
U
n
i
m
o
d
a
l
[
−
100
,
100
]
0
04
(
)
=
{
|
|
,
1
≤
≤
}
U
n
i
m
o
d
a
l
[
−
100
,
100
]
0
05
(
)
=
∑
[
4
+
(
0
,
1
)
]
=
1
U
n
i
m
o
d
a
l
[
−
1
.
2
8
,
1
.
2
8
]
0
06
(
)
=
∑
[
2
−
10
c
o
s
(
2
)
+
10
]
=
1
M
u
l
t
i
m
o
d
a
l
[
−
5
.
1
2
,
5
.
1
2
]
0
07
(
)
=
−
20
(
−
0
.
2
√
1
∑
2
=
1
)
−
(
1
∑
cos
(
2
)
=
1
)
+
20
+
M
u
l
t
i
m
o
d
a
l
[
−
32
,
32
]
0
08
(
x
)
=
1
4000
∑
2
=
1
−
∏
c
o
s
(
√
)
+
1
=
1
M
u
l
t
i
m
o
d
a
l
[
−
600
,
600
]
0
09
(
)
=
{
10
si
n
2
(
1
)
+
∑
(
−
1
)
2
[
1
+
10
si
n
2
(
+
1
)
]
+
(
−
1
)
2
−
1
=
1
}
+
∑
(
,
,
,
)
=
1
w
h
w
h
e
r
e
,
=
1
+
+
1
4
,
(
,
,
,
)
=
{
(
−
)
>
0
−
<
<
(
−
−
)
<
−
=
10
,
=
100
&
=
4
.
M
u
l
t
i
m
o
d
a
l
[
−
50
,
50
]
0
10
(
)
=
0
.1
{
s
i
n
2
(
3
1
)
+
∑
(
−
1
)
2
[
1
+
si
n
2
(
3
+
1
)
]
+
(
−
1
)
2
[
1
+
=
1
si
n
2
(
2
+
1
)
]
}
+
∑
(
,
,
,
)
=
1
w
h
w
h
e
r
e
,
(
,
,
,
)
=
{
(
−
)
>
0
−
<
<
(
−
−
)
<
−
=
5
,
=
100
&
=
4
.
M
u
l
t
i
m
o
d
a
l
[
−
50
,
50
]
0
11
(
1
)
:
1
,
2
,
3
,
…
…
.
.
10
=
ℎ
′
(
01
(
)
)
[
1
,
2
,
3
,
……
10
]
=
[
1
,
1
,
1
,
…1
]
[
1
,
2
,
3
,
…
…
10
]
=
[
5
/
1
0
0
,
5
/
1
0
0
,
5
/
1
0
0
,
…
5
/
1
0
0
]
C
o
m
p
o
si
t
e
[
−
5
,
5
]
0
12
(
2
)
:
1
,
2
,
3
,
…
…
.
.
10
=
′
(
08
(
)
)
[
1
,
2
,
3
,
……
10
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=
[
5
/
1
0
0
,
5
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5
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,
…5
/
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[
1
,
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,
3
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=
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,
1
,
1
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C
o
m
p
o
si
t
e
[
−
5
,
5
]
0
14
(
4
)
:
1
,
2
=
′
(
06
(
)
)
5
,
6
=
′
(
08
(
)
)
7
,
8
=
′
(
07
(
)
)
9
,
10
=
ℎ
′
(
01
(
)
)
[
1
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2
,
3
,
……
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]
=
[
1
,
1
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1
,
…1
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[
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=
[
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,
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0
.
5
,
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/
0
.
5
,
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1
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,
5
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C
o
m
p
o
si
t
e
[
−
5
,
5
]
0
6
.
3
.
P
r
o
po
s
ed
a
lg
o
rit
hm
a
s
s
ess
m
ent
T
h
e
s
to
ch
asti
c
n
atu
r
e
o
f
th
e
s
tan
d
ar
d
an
d
p
r
o
p
o
s
ed
SS
C
O
al
g
o
r
ith
m
is
with
s
em
i
-
r
an
d
o
m
s
tar
in
g
,
th
at
m
ea
n
th
e
in
itializatio
n
p
r
o
ce
s
s
is
d
if
f
er
en
t,
an
d
th
e
p
ath
s
f
o
ll
o
wed
ar
e
d
is
s
im
ilar
.
T
o
ad
d
r
e
s
s
th
ese
d
if
f
er
en
ce
s
an
d
to
test
if
y
th
e
f
ea
s
ib
ilit
y
,
co
n
v
er
g
en
c
e
an
d
ac
c
u
r
ac
y
o
f
t
h
e
alg
o
r
ith
m
s
clea
r
ly
,
ea
ch
al
g
o
r
ith
m
is
ev
alu
ated
b
y
ap
p
ly
in
g
t
h
e
o
p
tim
izatio
n
r
o
u
tin
e
th
ir
ty
tim
es
f
o
r
ea
c
h
o
f
th
e
f
o
u
r
teen
b
en
ch
m
a
r
k
f
u
n
ct
io
n
s
,
wh
er
e
f
i
v
e
o
f
wh
ich
ar
e
u
n
im
o
d
al,
f
iv
e
o
f
w
h
ich
ar
e
m
u
ltimo
d
al
an
d
f
o
u
r
o
f
wh
ich
ar
e
co
m
p
o
s
ite.
T
h
e
co
llected
n
u
m
er
ical
r
esu
lts
b
ase
d
o
n
s
tatis
tical
ca
l
cu
latio
n
s
wer
e
s
av
ed
in
Mic
r
o
s
o
f
t
ex
ce
l
f
ile.
T
h
is
o
p
er
atio
n
was
p
er
f
o
r
m
ed
t
o
d
eter
m
in
e
th
e
av
er
ag
e
b
est
-
so
-
f
ar
(
AB
)
s
o
lu
tio
n
an
d
s
tan
d
ar
d
d
ev
iatio
n
(
SD)
b
ased
o
n
th
e
s
av
ed
ex
ce
l
f
ile
an
d
r
ep
o
r
t
ed
in
T
a
b
le
3
.
I
t
is
clea
r
th
at
f
r
o
m
th
e
r
esu
lts
s
u
m
m
ar
ized
in
T
ab
le
3
,
th
e
p
r
o
p
o
s
ed
a
lg
o
r
ith
m
p
er
f
o
r
m
s
q
u
ite
well
in
ter
m
s
o
f
f
in
d
in
g
th
e
g
lo
b
al
o
p
tim
a
a
n
d
wit
h
a
f
ast
-
co
m
p
u
tatio
n
al
tim
e
f
o
r
th
e
s
elec
ted
test
f
u
n
ctio
n
s
.
E
ac
h
f
u
n
ctio
n
was
ex
ec
u
ted
in
s
tan
ta
n
eo
u
s
ly
o
n
a
m
o
d
er
n
lap
to
p
,
wh
ich
m
ea
n
t
h
e
co
m
p
u
tin
g
tim
e
f
o
r
5
0
0
iter
atio
n
s
tak
e
n
ap
p
r
o
x
im
ately
2
s
ec
o
n
d
s
.
T
h
e
r
esu
lts
in
d
icate
d
th
e
p
r
ed
o
m
in
an
ce
o
f
MSC
O
alg
o
r
ith
m
th
r
o
u
g
h
th
e
ca
p
a
b
ilit
y
to
ac
h
iev
e
th
e
b
est
o
p
tim
u
m
v
alu
e
i
n
2
9
o
u
t
o
f
3
0
r
u
n
s
with
a
r
ea
s
o
n
ab
le
co
n
v
er
g
en
ce
s
p
ee
d
.
T
h
ese
s
o
lu
tio
n
s
p
r
o
v
e
th
at
th
e
m
o
d
if
ie
d
ap
p
r
o
ac
h
h
as
e
x
ce
llen
ce
s
in
ter
m
s
o
f
ex
p
lo
r
atio
n
an
d
ex
p
lo
itatio
n
.
Fin
ally
,
f
r
o
m
th
e
a
b
o
v
e
o
b
s
er
v
atio
n
s
an
d
f
r
o
m
th
e
co
n
v
er
g
e
n
ce
cu
r
v
es
d
ep
icted
in
Fig
u
r
e
3
,
it
is
wo
r
th
m
en
tio
n
in
g
th
at
th
e
MSC
O
alg
o
r
ith
m
h
as
m
o
r
e
co
m
p
etitiv
e
ac
co
m
p
l
is
h
m
en
t
co
m
p
ar
e
d
with
SS
C
O
alg
o
r
ith
m
th
at
r
eq
u
ir
ed
8
5
0
g
e
n
er
atio
n
s
to
r
ea
ch
ar
o
u
n
d
6
0
% o
f
th
e
m
o
d
if
ied
alg
o
r
ith
m
’
s
b
est s
o
lu
ti
o
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
6
5
-
2
7
6
272
T
ab
le
3
.
Statis
tical
ass
e
s
s
m
en
t
f
o
r
th
e
s
ta
n
d
ar
d
a
n
d
p
r
o
p
o
s
ed
alg
o
r
ith
m
s
F
u
n
c
t
i
o
n
S
S
C
O
A
M
S
C
O
A
A
B
SD
A
B
SD
01
0
.
0
000
0
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0
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0
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1
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04
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5
8
2
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0
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0
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0
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0
0
0
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7
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0
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0
0
0
0
0
.
0
0
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0
07
0
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3
8
0
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0
0
0
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0
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0
0
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0
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0
1
3
0
Fig
u
r
e
3
.
C
o
n
v
er
g
e
n
ce
cu
r
v
es o
f
th
e
b
est s
o
lu
tio
n
s
o
b
tain
ed
f
o
r
th
e
s
elec
ted
b
en
ch
m
a
r
k
f
u
n
cti
o
n
s
b
ased
o
n
MSC
O
alg
o
r
ith
m
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
n
tr
o
ller
d
esig
n
fo
r
g
a
n
tr
y
cra
n
e
s
ystem
u
s
i
n
g
mo
d
ified
s
in
e
co
s
in
e
o
p
timiz
a
tio
n
.
.
.
(
N
iz
a
r
Ha
d
i A
b
b
a
s
)
273
6
.
4
.
Sim
ula
t
i
o
n r
esu
lt
s
a
nd
dis
cu
s
s
io
n
s
T
h
e
n
o
n
lin
ea
r
m
o
d
el
o
f
th
e
g
an
tr
y
cr
an
e
s
y
s
tem
is
im
p
lem
en
ted
in
Simu
lin
k
with
tr
o
l
ley
an
d
s
way
PID
C
co
n
tr
o
ller
s
.
T
h
e
PID
C
co
n
tr
o
ller
'
s
p
ar
am
eter
s
ar
e
tu
n
ed
b
y
SS
C
O
an
d
MSC
O
alg
o
r
ith
m
s
,
an
d
t
h
e
o
b
tain
ed
o
p
tim
u
m
v
al
u
es
ar
e
s
h
o
wn
i
n
T
ab
le
s
4
a
n
d
5
,
r
esp
ec
tiv
ely
.
Fo
r
MSC
O
alg
o
r
ith
m
,
th
e
o
b
jectiv
e
f
u
n
ctio
n
r
ea
c
h
es
th
e
o
p
tim
u
m
v
alu
e
af
ter
(
2
1
0
)
iter
atio
n
s
as
illu
s
tr
ated
in
Fig
u
r
e
4
,
th
e
co
n
v
er
g
en
ce
cu
r
v
e
f
o
r
th
e
s
y
s
tem
u
n
d
er
PID
C
co
n
tr
o
l
lin
g
m
eth
o
d
.
Fig
u
r
e
5
(
a)
s
h
o
w
s
th
e
p
o
s
itio
n
r
esp
o
n
s
e
o
f
th
e
g
an
tr
y
c
r
an
e
m
o
d
el,
wh
ich
is
tr
ac
k
in
g
th
e
r
ef
e
r
en
c
e
in
p
u
t
th
at
was
ap
p
lied
.
I
t
is
n
o
ticed
th
at
f
r
o
m
th
e
s
im
u
latio
n
r
esu
lts
,
a
s
m
all
o
v
er
s
h
o
o
t
a
n
d
r
is
e
tim
e
wer
e
o
b
tain
ed
;
h
e
n
ce
,
th
e
m
o
d
if
ie
d
alg
o
r
ith
m
p
r
o
v
id
es
a
g
u
ar
a
n
tee
to
co
n
tr
o
l
th
e
s
y
s
tem
with
b
est
p
er
f
o
r
m
a
n
ce
.
As
well
as,
Fig
u
r
e
5
(
b
)
s
h
o
ws
th
e
o
s
cillatio
n
r
esp
o
n
s
e
o
f
th
e
g
an
tr
y
c
r
an
e
m
o
d
el
in
r
ad
,
wh
ich
is
eq
u
al
to
ze
r
o
af
ter
5
s
ec
o
n
d
s
an
d
th
e
o
v
er
s
h
o
o
t
eq
u
al
to
0
.
0
5
r
ad
.
Fig
u
r
e
6
s
h
o
ws
th
e
co
n
tr
o
l
s
ig
n
al
o
f
t
h
e
g
a
n
tr
y
cr
an
e
s
y
s
tem
th
at
was
co
n
tr
o
lled
b
y
th
e
PID
C
-
MS
C
O
m
eth
o
d
.
T
h
e
r
es
u
lts
r
ev
ea
l
th
at,
th
e
co
n
tr
o
l
ac
tio
n
an
d
th
e
p
ay
lo
ad
s
win
g
d
ec
r
ea
s
ed
in
a
f
ast
b
eh
av
io
r
to
ac
h
iev
e
a
g
o
o
d
r
esp
o
n
s
e
u
s
in
g
th
e
p
r
o
p
o
s
ed
co
n
tr
o
llin
g
s
ch
e
m
e.
T
ab
le
4
.
Op
tim
ized
t
r
o
ll
ey
an
d
p
ay
lo
a
d
o
s
cillatio
n
PID
C
co
n
tr
o
ller
s
'
p
ar
am
eter
s
b
ased
o
n
SS
C
O
A
P
I
D
C
P
a
r
a
met
e
r
s
ℎ
O
p
t
i
mi
z
e
d
p
a
r
a
m
e
t
e
r
s fo
r
t
r
o
l
l
e
y
c
o
n
t
r
o
l
l
e
r
3
0
0
50
50
0
.
1
3
O
p
t
i
mi
z
e
d
p
a
r
a
m
e
t
e
r
s fo
r
p
a
y
l
o
a
d
o
s
c
i
l
l
a
t
i
o
n
c
o
n
t
r
o
l
l
e
r
1
0
0
1
.
0
3
1
.
7
2
1
7
T
ab
le
5
.
Op
tim
ized
t
r
o
lley
an
d
p
ay
lo
a
d
o
s
cillatio
n
PID
C
co
n
t
r
o
ller
s
'
p
ar
am
eter
s
b
ased
o
n
MSC
OA
P
I
D
C
P
a
r
a
met
e
r
s
ℎ
O
p
t
i
mi
z
e
d
p
a
r
a
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8
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4
.
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1
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2
0
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.
1
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p
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u
r
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4
.
C
o
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er
g
e
n
ce
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r
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e
o
f
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e
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jectiv
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f
u
n
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n
o
f
g
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n
tr
y
cr
a
n
e
s
y
s
tem
b
ased
o
n
PID
C
-
MS
C
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co
n
tr
o
llin
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s
ch
e
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e
Fo
r
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alg
o
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ith
m
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e
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j
ec
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n
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n
r
ea
ch
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t
o
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e
b
est
v
al
u
e
(
0
.
1
1
)
a
f
ter
(
8
5
0
)
iter
atio
n
s
.
Fig
u
r
e
7
(
a)
,
s
h
o
ws
th
e
p
o
s
itio
n
r
esp
o
n
s
e
o
f
th
e
g
a
n
tr
y
cr
a
n
e
s
y
s
tem
,
wh
ich
is
tr
ac
k
in
g
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e
u
n
it
s
tep
in
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u
t.
T
h
e
o
v
er
s
h
o
o
t
an
d
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e
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e
th
at
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er
e
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y
u
s
in
g
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m
eth
o
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lar
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er
s
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e
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ased
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e.
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o
r
e,
th
e
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r
ith
m
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u
itab
le
m
o
r
e
th
an
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ar
d
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o
r
it
h
m
f
o
r
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d
i
n
g
th
e
o
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tim
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m
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C
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ar
am
ete
r
s
'
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alu
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n
tr
o
l
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e
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y
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tem
an
d
with
o
p
tim
al
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er
f
o
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m
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ce
.
Fig
u
r
e
7
(
b
)
,
s
h
o
ws
th
e
o
s
cillatio
n
r
esp
o
n
s
es
o
f
th
e
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o
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ter
7
s
ec
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s
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d
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e
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er
s
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o
t
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al
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1
.
1
r
a
d
.
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e
d
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el
o
p
ed
MSC
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alg
o
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th
m
s
h
o
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d
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er
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ce
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ter
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ased
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lex
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o
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lem
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d
n
o
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lin
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tr
y
cr
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e
m
o
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el.
T
h
a
t
is
to
s
ay
,
th
e
o
b
tain
ed
r
esu
lts
f
o
r
th
e
p
r
o
p
o
s
ed
o
p
tim
izatio
n
alg
o
r
ith
m
ass
u
r
ed
its
p
e
r
f
o
r
m
an
ce
f
o
r
f
in
d
in
g
o
u
t
th
e
g
lo
b
al
o
p
tim
al
s
o
lu
tio
n
s
.
A
d
d
itio
n
ally
,
MSC
O
alg
o
r
ith
m
h
av
e
m
o
r
e
c
o
m
p
e
titi
v
e
ac
h
ie
v
em
en
ts
as
co
m
p
ar
e
d
with
th
e
s
tan
d
ar
d
alg
o
r
ith
m
in
ter
m
s
o
f
co
n
v
er
g
e
n
ce
r
ate,
s
o
lu
tio
n
ac
cu
r
ac
y
an
d
escap
e
f
r
o
m
lo
ca
l
o
p
tim
a
in
d
ices.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
2
6
5
-
2
7
6
274
(
a)
(
b
)
Fig
u
r
e
5
.
Sy
s
tem
r
esp
o
n
s
es o
f
th
e
g
an
tr
y
cr
an
e
s
y
s
tem
u
n
d
er
PID
C
-
MS
C
O
co
n
tr
o
llin
g
s
ch
e
m
e
(
a)
t
r
o
lley
p
o
s
itio
n
(
b
)
p
a
y
lo
ad
o
s
cillatio
n
Fig
u
r
e
6
.
T
h
e
co
n
tr
o
l sig
n
al
o
f
th
e
g
an
tr
y
cr
an
e
s
y
s
tem
b
ased
o
n
PID
C
-
MSC
O
co
n
tr
o
llin
g
s
ch
em
e
Evaluation Warning : The document was created with Spire.PDF for Python.