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Ada
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beam
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SNA
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PID
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mbined wi
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ID)
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K
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all
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s
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I
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o
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tr
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MA
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im
u
lin
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No
n
lin
ea
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s
y
s
tem
Pro
p
o
r
tio
n
al
in
teg
r
al
d
e
r
iv
ativ
e
SNA
-
PID
-
R
F
NNI
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Min
h
-
T
h
an
h
L
e
Dep
ar
tm
en
t o
f
C
o
n
tr
o
l a
n
d
Au
to
m
atio
n
E
n
g
in
ee
r
in
g
,
Facu
lty
o
f
E
lectr
ical
an
d
E
lectr
o
n
ics
Vin
h
L
o
n
g
Un
iv
er
s
ity
o
f
T
ec
h
n
o
lo
g
y
E
d
u
ca
tio
n
Vin
h
L
o
n
g
,
Vietn
am
E
m
ail:
th
an
h
lm
@
v
lu
te.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
b
all
a
n
d
b
ea
m
s
y
s
tem
is
a
well
-
k
n
o
wn
class
ical
b
en
c
h
m
ar
k
m
o
d
el
in
th
e
f
ield
s
o
f
au
to
m
atic
co
n
tr
o
l
r
esear
ch
a
n
d
ed
u
ca
tio
n
,
d
u
e
to
its
u
n
s
tab
le
an
d
n
o
n
lin
ea
r
ch
ar
ac
ter
is
tics
[
1
]
.
I
n
ter
m
s
o
f
p
h
y
s
ical
s
tr
u
ctu
r
e,
th
e
s
y
s
tem
co
n
s
is
ts
o
f
a
b
all
ca
p
ab
le
o
f
r
o
llin
g
al
o
n
g
a
lo
n
g
r
o
d
.
T
h
is
r
o
d
h
as
o
n
e
f
ix
ed
en
d
;
th
e
o
th
er
en
d
ca
n
b
e
tilt
ed
b
y
co
n
t
r
o
llin
g
a
m
o
to
r
with
a
co
n
n
ec
t
in
g
r
o
d
attac
h
ed
to
it;
th
e
co
n
t
r
o
l
g
o
al
is
to
k
ee
p
th
e
b
all
s
tab
le
at
a
p
r
e
-
d
ef
in
ed
lo
ca
tio
n
o
n
th
e
r
o
d
[
2
]
.
Du
e
t
o
th
e
in
f
lu
en
ce
o
f
g
r
a
v
ity
,
th
e
m
ater
ial
o
f
th
e
b
all
an
d
th
e
s
lid
er
,
wh
en
ad
ju
s
tin
g
th
e
tilt
an
g
le
o
f
th
e
r
o
d
(
ev
en
v
er
y
s
m
all)
,
th
e
b
all
will
r
o
ll
q
u
ick
ly
to
o
n
e
s
id
e,
ca
u
s
in
g
th
e
s
y
s
tem
to
f
all
in
to
an
u
n
b
alan
ce
d
s
tate
ea
s
ily
[
3
]
.
T
h
e
u
n
s
tab
le
an
d
n
o
n
lin
ea
r
c
h
ar
ac
ter
is
tics
m
ak
e
th
e
b
all
-
an
d
-
r
o
d
b
alan
cin
g
s
y
s
tem
id
ea
l
f
o
r
test
in
g
m
o
d
er
n
co
n
tr
o
l
alg
o
r
ith
m
s
,
f
r
o
m
class
ical
p
r
o
p
o
r
tio
n
al
in
teg
r
al
d
e
r
iv
ativ
e
(
PID
)
co
n
t
r
o
l
to
in
tellig
en
t
m
et
h
o
d
s
s
u
c
h
as
f
u
zz
y
c
o
n
tr
o
l,
n
e
u
r
al
n
et
wo
r
k
s
,
an
d
h
y
b
r
i
d
m
eth
o
d
s
[
4
]
,
[
5
]
.
PID
c
o
n
tr
o
l
is
s
till
th
e
m
o
s
t
p
o
p
u
lar
s
o
lu
tio
n
d
u
e
to
its
ea
s
e
o
f
tu
n
i
n
g
an
d
s
ig
n
if
ican
t
ef
f
icien
cy
in
p
r
ac
tice.
Ho
we
v
e
r
,
class
ical
PID
co
n
tr
o
ller
s
ar
e
o
f
ten
d
esig
n
ed
with
f
ix
e
d
p
ar
am
eter
s
,
lead
in
g
to
p
o
o
r
p
er
f
o
r
m
an
ce
wh
en
th
e
co
n
tr
o
l o
b
ject
c
h
an
g
es o
r
wh
en
t
h
er
e
is
s
ig
n
if
ican
t n
o
is
e
an
d
s
ig
n
al
d
elay
s
[
6
]
.
T
o
im
p
r
o
v
e
th
e
ad
ap
ta
b
ilit
y
a
n
d
ac
cu
r
ac
y
o
f
th
e
s
y
s
tem
,
a
p
r
o
m
in
e
n
t
ap
p
r
o
ac
h
is
to
u
s
e
an
ad
ap
tiv
e
s
in
g
le
n
eu
r
o
n
n
etwo
r
k
to
o
p
tim
ize
th
e
PID
co
n
tr
o
ller
,
wh
e
r
e
th
e
co
ef
f
icien
ts
Kp
,
Ki,
an
d
Kd
ar
e
ad
ju
s
ted
o
n
lin
e
th
r
o
u
g
h
th
e
n
e
u
r
al
n
etwo
r
k
[
7
]
.
I
n
ad
d
itio
n
,
ac
co
m
m
o
d
atin
g
th
e
n
o
n
li
n
ea
r
a
n
d
tim
e
-
d
ep
e
n
d
en
t
ch
ar
ac
ter
is
tics
o
f
r
o
d
an
d
b
all
s
y
s
tem
,
th
e
s
y
s
tem
id
en
tifie
r
p
lay
s
an
ess
en
tial
r
o
le
in
p
r
o
v
id
in
g
i
n
f
o
r
m
atio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
d
a
p
tive
co
n
tr
o
l o
f b
a
ll
a
n
d
b
ea
m
s
ystem
u
s
in
g
S
N
A
-
P
I
D
co
mb
in
ed
w
ith
r
ec
u
r
r
en
t
…
(
Min
h
-
Th
a
n
h
Le
)
1203
f
o
r
ad
ap
tiv
e
c
o
n
tr
o
l.
R
ec
u
r
r
en
t
f
u
zz
y
n
eu
r
al
n
etwo
r
k
id
e
n
tif
ier
(
R
FNNI
)
is
a
s
u
itab
le
to
o
l
f
o
r
m
o
d
elin
g
an
d
id
en
tify
in
g
n
o
n
lin
ea
r
s
y
s
tem
s
th
at
ca
n
h
an
d
le
tim
e
an
d
f
u
zz
y
in
f
er
en
ce
[
8
]
.
T
h
is
p
ap
er
p
r
o
p
o
s
es
a
n
ew
co
n
tr
o
l
m
eth
o
d
co
m
b
in
in
g
a
s
in
g
le
-
n
eu
r
o
n
ad
ap
tiv
e
PID
co
n
tr
o
ller
an
d
R
FNNI
,
ap
p
lied
to
a
b
all
an
d
b
ea
m
s
y
s
tem
.
T
h
is
m
eth
o
d
is
v
er
if
i
ed
th
r
o
u
g
h
s
im
u
latio
n
o
n
th
e
MA
T
L
AB
/S
im
u
lin
k
p
latf
o
r
m
,
s
h
o
win
g
th
at
th
e
alg
o
r
ith
m
s
h
elp
im
p
r
o
v
e
ac
cu
r
ac
y
,
r
ed
u
ce
th
e
tr
a
n
s
ien
t tim
e,
an
d
im
p
r
o
v
e
th
e
s
y
s
tem
'
s
s
tab
i
lity
[
9
]
,
[
1
0
]
.
2.
M
AT
H
E
M
AT
I
CA
L
M
O
D
E
L
L
I
NG
T
h
e
b
ea
m
an
d
b
all
s
y
s
tem
co
n
s
is
t
s
o
f
a
cir
cu
lar
b
all
th
at
ca
n
r
o
ll
alo
n
g
a
lo
n
g
b
ea
m
.
A
m
o
to
r
p
lace
d
at
o
n
e
en
d
o
f
th
e
b
ea
m
ad
ju
s
ts
th
e
an
g
le
o
f
in
clin
atio
n
o
f
th
e
b
ea
m
,
an
d
a
co
n
n
ec
tin
g
r
o
d
co
n
n
ec
ts
th
e
r
o
tatin
g
d
is
k
to
t
h
e
b
ea
m
[
9
]
.
T
h
e
s
y
s
tem
is
d
ep
icted
in
Fig
u
r
e
1
,
wh
e
r
e
Fig
u
r
e
1
(
a)
s
h
o
ws
th
e
s
y
s
tem
m
o
d
elin
g
a
n
d
Fig
u
r
e
1
(
b
)
s
h
o
ws th
e
ex
p
er
im
en
tal
p
r
o
to
ty
p
e
.
T
h
e
s
y
s
tem
p
ar
am
eter
s
ar
e
p
r
esen
ted
in
T
ab
le
1
.
(
a)
(
b
)
Fig
u
r
e
1
.
Mo
d
elin
g
a
n
d
ex
p
er
i
m
en
tal
s
etu
p
o
f
t
h
e
b
all
an
d
b
e
am
s
y
s
tem
: (
a)
s
y
s
tem
m
o
d
eli
n
g
an
d
(
b
)
ex
p
er
im
en
tal
p
r
o
to
ty
p
e
T
ab
le
1
.
Actu
al
p
a
r
am
eter
s
o
n
th
e
m
o
d
el
t
h
at
th
e
team
h
as
b
u
ilt
P
a
r
a
me
t
e
r
U
n
i
t
V
a
l
u
e
M
e
a
n
i
n
g
L
(m)
0
.
4
Le
n
g
t
h
o
f
t
h
e
b
e
a
m
m
(
k
g
)
0
.
1
1
M
a
ss
o
f
t
h
e
b
a
l
l
M
(
k
g
)
0
.
4
M
a
ss
o
f
t
h
e
b
e
a
m
g
(
m
/
s2
)
9
.
8
G
r
a
v
i
t
a
t
i
o
n
a
l
a
c
c
e
l
e
r
a
t
i
o
n
r
(m)
0
.
2
B
a
l
l
p
o
si
t
i
o
n
R
(m)
0
.
0
1
5
R
a
d
i
u
s
o
f
t
h
e
b
a
l
l
α
(
ra
d
)
0
B
e
a
m
a
n
g
l
e
c
o
o
r
d
i
n
a
t
e
θ
(
ra
d
)
0
S
e
r
v
o
g
e
a
r
a
n
g
l
e
d
(m)
0
.
0
2
Le
v
e
r
a
r
m
o
f
f
se
t
T
h
e
b
all
d
y
n
am
ics
ar
e
p
r
im
a
r
ily
in
f
lu
en
ce
d
b
y
g
r
av
ity
a
n
d
its
m
o
m
en
t
o
f
in
e
r
tia
.
T
h
is
r
esu
lts
in
a
s
y
s
tem
th
at
is
u
n
s
tab
le
an
d
n
o
n
lin
ea
r
.
T
h
e
d
ev
el
o
p
m
en
t
o
f
an
ef
f
ec
tiv
e
co
n
tr
o
ller
r
e
q
u
ir
es
an
ac
cu
r
ate
m
ath
em
atica
l r
ep
r
esen
tatio
n
o
f
th
e
s
y
s
tem
[
1
]
.
Acc
o
r
d
in
g
t
o
th
e
liter
atu
r
e
[
1
0
]
–
[
1
3
]
,
th
e
m
ath
em
atica
l e
q
u
at
io
n
o
f
p
lan
t is d
escr
ib
ed
as (
1
)
an
d
(
2
)
.
(
2
+
)
̈
+
2
̇
̇
+
2
+
=
(
1
)
(
+
2
)
̈
−
̇
2
+
=
0
(
2
)
W
ith
,
ar
e
th
e
m
o
m
e
n
ts
o
f
in
er
tia
o
f
th
e
b
ea
m
an
d
b
all,
is
th
e
to
r
q
u
e
g
en
er
ate
d
b
y
th
e
m
o
to
r
.
L
et
1
=
,
2
=
̇
,
3
=
,
4
=
̇
[
9
]
,
we
g
et
(
3
)
an
d
(
4
)
.
̇
1
=
2
;
̇
2
=
1
4
2
−
3
+
2
(
3
)
̇
3
=
4
;
̇
4
=
−
2
1
2
4
−
2
3
−
1
3
1
2
+
(
4
)
T
h
is
m
o
d
el
d
escr
ib
es
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
b
ea
m
an
g
l
e
an
d
th
e
b
all
p
o
s
itio
n
.
B
ased
o
n
(
3
)
an
d
(
4
)
,
th
e
s
y
s
tem
is
im
p
lem
en
ted
i
n
M
AT
L
AB
/Si
m
u
lin
k
en
v
ir
o
n
m
e
n
t,
as
illu
s
tr
ated
in
Fig
u
r
e
2
,
f
o
r
m
in
g
th
e
b
asis
f
o
r
th
e
s
u
b
s
eq
u
en
t c
o
n
tr
o
ller
d
esig
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
26
:
1
2
0
2
-
1
2
1
0
1204
Fig
u
r
e
2
.
Mo
d
elin
g
o
f
b
all
a
n
d
b
ea
m
s
y
s
tem
in
MA
T
L
AB
/Si
m
u
lin
k
3.
DE
S
I
G
N
O
F
T
H
E
CO
N
T
R
O
L
L
E
R
I
n
th
is
s
tu
d
y
,
th
e
co
n
tr
o
ller
is
p
r
o
p
o
s
ed
b
ased
o
n
th
e
s
in
g
le
n
eu
r
o
n
ad
ap
tiv
e
(
SNA)
-
PID
al
g
o
r
ith
m
.
I
t
is
co
m
b
in
ed
with
th
e
R
FNNI
t
o
co
n
tr
o
l th
e
b
all
an
d
b
ea
m
s
y
s
tem
.
T
h
e
g
o
al
is
to
ad
ap
t a
n
d
r
esp
o
n
d
q
u
ick
ly
to
ch
an
g
es
in
th
e
s
y
s
tem
s
tate
w
h
ile
h
an
d
lin
g
th
e
n
o
n
lin
ea
r
a
n
d
n
o
is
y
ch
ar
ac
te
r
is
tics
o
f
th
e
en
tire
clo
s
ed
-
lo
o
p
s
y
s
tem
well.
3
.
1
.
T
he
s
ing
le
neuro
n a
da
p
t
iv
e
-
pro
po
rt
io
na
l int
eg
ra
l
deriv
a
t
iv
e
co
ntr
o
ller
Fig
u
r
e
3
d
e
p
icts
th
e
s
tr
u
ctu
r
e
o
f
PID
co
n
tr
o
ller
.
T
h
e
co
n
t
r
o
l
ler
is
co
n
s
tr
u
cted
u
s
in
g
a
lin
e
ar
n
eu
r
o
n
.
T
h
is
d
esig
n
in
teg
r
ates p
r
o
p
o
r
tio
n
al,
in
teg
r
al,
an
d
d
er
iv
ativ
e
c
o
m
p
o
n
en
ts
with
in
a
n
eu
r
al
-
b
a
s
ed
f
r
am
ewo
r
k
.
Fig
u
r
e
3
.
Stru
ctu
r
e
o
f
SNA
-
PID
co
n
tr
o
ller
As g
iv
en
in
(
5
)
,
th
e
p
r
o
p
o
r
tio
n
al,
in
teg
r
al,
an
d
d
er
iv
ativ
e
ter
m
s
ar
e
co
m
p
u
ted
f
r
o
m
th
e
er
r
o
r
b
etwe
en
th
e
r
ef
er
en
ce
in
p
u
t a
n
d
th
e
s
y
s
tem
o
u
tp
u
t.
1
=
(
)
;
2
=
∫
(
)
;
3
=
(
)
∞
0
(
5
)
T
h
e
eq
u
atio
n
d
escr
ib
in
g
th
e
PI
D
co
n
tr
o
ller
is
d
ef
i
n
ed
as (
6
)
[
1
4
]
,
[
1
5
]
.
(
)
=
1
+
2
+
3
+
(
−
1
)
(
6
)
Her
e,
z
(
k)
(
with
k
=1
,
2
,
3
)
d
en
o
tes
th
e
er
r
o
r
b
etwe
en
th
e
r
ef
er
en
ce
s
ig
n
al
an
d
th
e
s
y
s
tem
r
esp
o
n
s
e.
I
n
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
,
th
e
n
eu
r
o
n
o
u
tp
u
t
is
eq
u
iv
ale
n
tly
r
e
g
ar
d
ed
as
t
h
e
PID
c
o
n
tr
o
ller
o
u
tp
u
t,
wh
ich
is
s
h
o
wn
in
(
7
)
[
1
6
]
.
=
(
11
1
+
12
2
+
13
3
)
(
)
=
(
)
=
(
)
=
(
)
+
(
−
1
)
(
7
)
W
h
er
e,
1
|
=
1
,
2
,
3
ar
e
th
e
weig
h
ts
o
f
th
e
n
eu
r
o
n
s
,
co
r
r
esp
o
n
d
in
g
t
o
th
e
PID
g
ain
s
et
(
K
p
,
K
i
,
K
d
)
,
an
d
th
ey
ar
e
ad
ap
tiv
ely
u
p
d
ated
i
n
r
ea
l tim
e.
T
h
e
tr
ain
i
n
g
p
r
o
ce
s
s
f
o
r
th
e
S
NA
-
PID
co
n
tr
o
ller
aim
s
to
m
i
n
im
ize
th
e
co
s
t
f
u
n
ctio
n
s
h
o
w
n
in
(
8
)
b
y
u
p
d
atin
g
th
e
n
etwo
r
k
weig
h
ts
1
|
=
1
,
2
,
3
.
(
)
=
1
2
2
(
)
ℎ
(
)
=
(
)
−
(
)
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
A
d
a
p
tive
co
n
tr
o
l o
f b
a
ll
a
n
d
b
ea
m
s
ystem
u
s
in
g
S
N
A
-
P
I
D
co
mb
in
ed
w
ith
r
ec
u
r
r
en
t
…
(
Min
h
-
Th
a
n
h
Le
)
1205
Her
e,
(
)
an
d
y(
k)
d
en
o
te
r
ef
er
en
ce
s
ig
n
al
an
d
s
y
s
tem
r
esp
o
n
s
e,
r
esp
ec
tiv
ely
.
T
h
e
g
r
ad
i
en
t
d
escen
t
m
eth
o
d
was e
m
p
lo
y
ed
to
ad
ap
t th
e
n
etwo
r
k
weig
h
t set
1
|
=
1
,
2
,
3
,
as d
escr
ib
ed
in
[
1
7
]
,
[
1
8
]
.
3
.
2
.
T
he
re
curr
ent
f
uzzy
neura
l net
wo
rk
identif
ier
T
h
e
R
FNN
I
as
s
h
o
wn
in
Fig
u
r
e
4
,
is
a
m
u
lti
-
lay
er
r
ec
u
r
r
en
t
n
eu
r
al
n
etwo
r
k
f
o
r
f
u
zz
y
in
f
e
r
en
ce
th
at
ca
n
b
e
f
o
r
m
u
lated
u
s
in
g
a
s
et
o
f
f
u
zz
y
in
f
e
r
en
ce
r
u
les
[
1
7
]
.
i)
L
ay
er
1
-
i
n
p
u
t
lay
er
:
th
e
R
FNNI
u
s
es
th
e
cu
r
r
en
t
c
o
n
tr
o
l
in
p
u
t
a
n
d
th
e
p
r
e
v
io
u
s
s
y
s
tem
o
u
tp
u
t
as
i
n
p
u
t
v
ar
iab
les,
wh
o
s
e
co
n
n
ec
tio
n
weig
h
ts
ar
e
u
p
d
ated
at
t
h
e
c
u
r
r
en
t
tim
e
in
s
tan
t
k
as
ex
p
r
ess
ed
in
(
9
)
.
Sp
ec
if
ically
,
th
e
in
p
u
t
s
ig
n
als ar
e
d
ef
in
e
d
as (
1
0
)
.
1
(
)
=
1
(
)
+
1
(
−
1
)
ℎ
=
1
,
2
(
9
)
1
1
(
)
=
(
)
2
1
(
)
=
(
−
1
)
(
1
0
)
ii)
L
ay
er
2
-
f
u
zz
y
lay
er
:
th
is
lay
er
is
co
m
p
o
s
ed
o
f
(
2
×
5
)
n
o
d
e
s
,
ea
ch
n
o
d
e
r
ep
r
esen
ts
a
Gau
s
s
ian
f
u
n
ctio
n
with
m
ea
n
,
s
tan
d
ar
d
d
e
v
iatio
n
,
as d
ef
in
e
d
b
y
(
1
1
)
.
2
(
)
=
[
−
(
1
(
)
−
)
2
]
,
ℎ
=
1
,
2
=
1
,
2
,
3
,
4
,
5
(
1
1
)
T
h
e
R
FNNI
’
s
o
n
lin
e
lear
n
in
g
m
ec
h
an
is
m
in
v
o
lv
es
th
e
a
d
a
p
tiv
e
ad
ju
s
tm
en
t
o
f
two
s
p
ec
i
f
ic
p
ar
am
eter
s
an
d
f
o
r
ea
c
h
n
o
d
e
with
in
th
e
f
u
zz
y
lay
e
r
.
iii)
L
ay
er
3
-
r
u
le
la
y
er
:
t
h
is
lay
er
co
n
tain
s
(
5
×
5
)
n
o
d
es,
an
d
t
h
e
o
u
tp
u
t
o
f
th
e
n
o
d
e
is
g
iv
en
b
y
(
1
2
)
.
3
(
)
=
∏
2
(
)
ℎ
,
=
1
,
2
,
3
,
4
,
5
(
1
2
)
iv
)
L
ay
er
4
-
o
u
t
p
u
t la
y
er
:
i
t c
o
n
s
is
ts
o
f
a
lin
ea
r
n
eu
r
o
n
,
a
n
d
its
o
u
tp
u
t is ex
p
r
ess
ed
as
(
1
3
)
.
4
(
)
=
∑
4
3
(
)
ℎ
=
1
=
1
,
2
,
.
.
.
,
25
(
1
3
)
W
ith
4
is
th
e
co
n
n
ec
tio
n
weig
h
t
b
etwe
en
lay
er
3
a
n
d
la
y
er
4
.
T
h
e
o
u
tp
u
t
o
f
t
h
is
lay
er
also
r
ep
r
esen
ts
th
e
o
u
tp
u
t o
f
th
e
R
FNNI
, a
s
ex
p
r
ess
ed
in
(
1
4
)
.
1
4
(
)
=
(
)
=
̂
[
1
(
)
,
2
(
)
]
ℎ
1
(
)
,
2
(
)
(
10
)
(
1
4
)
Fig
u
r
e
4
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
R
FNN
I
T
h
e
p
u
r
p
o
s
e
o
f
th
e
o
n
lin
e
t
r
a
in
in
g
alg
o
r
ith
m
in
R
FNNI
is
to
ad
ap
tiv
ely
tu
n
e
t
h
e
n
etwo
r
k
weig
h
ts
an
d
th
e
f
u
zz
y
lay
e
r
-
d
e
p
en
d
e
n
t f
u
n
ctio
n
p
ar
am
eter
s
to
m
in
im
ize
th
e
co
s
t f
u
n
ctio
n
,
as d
ef
in
e
d
in
(
1
5
)
.
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tan
t
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d
th
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ad
ju
s
tab
le
p
ar
am
eter
in
th
e
R
FN
N
I
tr
ain
in
g
,
r
esp
ec
tiv
ely
.
T
h
e
g
r
a
d
ien
t
o
f
Z(.
)
in
(
1
5
)
an
d
th
e
weig
h
t
o
f
ea
ch
R
FNNI
n
etwo
r
k
lay
er
ar
e
d
eter
m
in
e
d
in
r
ef
er
en
ce
[
1
7
]
.
Ad
d
itio
n
ally
,
to
p
r
ed
ict
th
e
o
u
tp
u
t
(
)
o
f
th
e
p
lan
t
m
o
d
el,
th
e
R
FNNI
m
u
s
t
a
ls
o
co
m
p
u
te
th
e
J
ac
o
b
ian
(
)
(
)
,
wh
ich
is
ess
en
tial
f
o
r
th
e
o
n
lin
e
tr
ain
in
g
o
f
th
e
SNA
-
PID
co
n
tr
o
ller
.
T
h
e
J
ac
o
b
ian
in
f
o
r
m
atio
n
is
d
ef
in
ed
in
(
1
7
)
,
r
ef
er
r
in
g
to
[
1
7
]
,
[
1
9
]
.
(
)
(
)
=
1
4
=
∑
{
4
3
.
3
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=
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4
.
{
3
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25
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25
=
1
=
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4
.
{
∑
3
2
.
2
}
=
∑
4
.
{
∑
3
2
.
(
−
2
)
[
1
(
)
−
]
(
)
2
}
(
1
7
)
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
4
.
1
.
Dia
g
ra
m
o
f
SNA
–
P
I
D
–
RF
NNI c
o
ntr
o
ller
A
b
lo
ck
d
ia
g
r
am
o
f
th
e
co
n
tr
o
l
s
y
s
tem
d
ev
elo
p
ed
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
is
p
r
esen
ted
in
Fig
u
r
e
5
[
2
0
]
,
[
2
1
]
.
B
ased
o
n
(
3
)
a
n
d
(
4
)
,
th
e
m
ath
e
m
atica
l
d
escr
ip
tio
n
f
o
r
t
h
e
b
all
a
n
d
b
ea
m
s
etu
p
is
estab
lis
h
ed
.
T
h
e
p
ar
am
eter
s
o
f
th
e
SNA
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PID
co
n
tr
o
ller
a
r
e
s
elec
ted
b
y
a
tr
ial
-
an
d
-
er
r
o
r
m
eth
o
d
,
as
d
escr
ib
e
d
in
[
4
]
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
R
FNNI
s
et
co
n
s
is
ts
o
f
4
m
ain
lay
er
s
: in
p
u
t,
f
u
zz
if
icatio
n
,
r
u
le,
an
d
d
ef
u
zz
if
icatio
n
.
T
h
e
r
ec
o
g
n
itio
n
s
et
s
u
p
p
o
r
ts
o
n
lin
e
ad
ju
s
tm
en
t
th
r
o
u
g
h
b
ac
k
p
r
o
p
a
g
atio
n
g
r
ad
ien
t.
I
t o
u
tp
u
ts
th
e
o
u
tp
u
t
s
ig
n
a
l
o
f
th
e
o
b
ject
as
well
as
th
e
J
ac
o
b
ian
d
er
iv
ativ
e
to
d
eter
m
i
n
e
th
e
in
f
lu
en
ce
le
v
el
o
f
th
e
i
n
p
u
t
o
n
th
e
o
u
tp
u
t,
s
er
v
in
g
th
e
tr
ain
i
n
g
o
f
ad
a
p
tiv
e
co
n
tr
o
l.
Fig
u
r
e
5
.
SNA
-
PID
-
R
FNNI
co
n
tr
o
ller
d
iag
r
am
[
1
9
]
,
[
2
2
]
4
.
2
.
Resul
t
s
a
nd
co
m
pa
riso
n
T
h
e
b
ea
m
an
d
b
all
s
y
s
tem
,
u
s
in
g
th
e
SNA
-
PID
-
R
FNNI
alg
o
r
ith
m
,
is
s
im
u
lated
with
f
ix
ed
p
ar
am
eter
p
o
s
itio
n
s
o
f
2
4
cm
an
d
2
8
cm
(
s
tep
f
u
n
ctio
n
)
an
d
ze
r
o
n
o
is
e
f
o
r
th
e
o
u
tp
u
t
r
esp
o
n
s
es
in
Fig
u
r
es
6
an
d
7
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
b
all
m
o
v
es
an
d
s
tay
s
at
th
e
d
esire
d
p
o
s
itio
n
.
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o
n
tin
u
e
u
s
in
g
th
e
SNA
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PID
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R
F
NNI
alg
o
r
ith
m
to
s
im
u
late
with
f
ix
ed
p
ar
am
eter
p
o
s
itio
n
s
o
f
3
0
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d
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5
cm
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co
n
s
tan
t
f
u
n
ct
io
n
)
with
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n
o
is
e
o
f
0
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0
0
0
0
1
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o
r
th
e
o
u
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t
r
esp
o
n
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es
in
Fig
u
r
es
8
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d
9
.
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h
e
r
e
s
u
lts
s
h
o
w
th
at
th
e
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all
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its
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o
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itio
n
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alth
o
u
g
h
th
e
r
e
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a
s
lig
h
t o
s
cillatio
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ar
o
u
n
d
t
h
e
eq
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i
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r
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m
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o
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n
t.
T
h
e
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ea
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d
b
all
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y
s
tem
u
s
in
g
th
e
PID
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d
th
e
SNA
-
P
I
D
-
R
FNNI
alg
o
r
ith
m
is
s
im
u
lated
with
f
ix
ed
p
ar
a
m
eter
p
o
s
itio
n
s
o
f
2
6
cm
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s
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f
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n
ctio
n
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ze
r
o
n
o
is
e
f
o
r
th
e
o
u
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u
t
r
esp
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n
s
es
in
Fig
u
r
e
1
0
,
wit
h
f
ix
ed
p
ar
a
m
eter
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o
s
itio
n
s
o
f
3
2
cm
(
co
n
s
tan
t
f
u
n
ctio
n
)
with
n
o
is
e
eq
u
al
to
0
.
0
0
0
0
1
f
o
r
th
e
o
u
tp
u
t
r
esp
o
n
s
es
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I
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t J Ar
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I
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8
9
3
8
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o
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a
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a
n
d
b
ea
m
s
ystem
u
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S
N
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P
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mb
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w
ith
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r
r
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1207
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Fig
u
r
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1
1
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n
Fig
u
r
e
1
0
,
b
o
th
th
e
SNA
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PID
-
R
FN
NI
an
d
PID
co
n
tr
o
ller
s
r
etu
r
n
th
e
b
all
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th
e
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ce
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o
s
itio
n
.
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e
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n
tr
o
ller
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u
s
es
lar
g
e
o
s
cillatio
n
s
an
d
h
ig
h
er
in
itial
o
v
er
s
h
o
o
t,
wh
ile
th
e
SNA
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PID
-
R
F
NNI
co
n
tr
o
ller
p
r
o
v
id
es
a
s
m
o
o
th
e
r
r
esp
o
n
s
e,
s
h
o
r
ter
r
ec
o
v
er
y
tim
e,
an
d
les
s
o
s
cillatio
n
.
W
h
en
d
is
tu
r
b
an
ce
s
ar
e
p
r
esen
t
(
Fig
u
r
e
1
1
)
,
th
e
d
if
f
er
en
ce
b
ec
o
m
es
m
o
r
e
p
r
o
n
o
u
n
ce
d
.
T
h
e
PID
c
o
n
tr
o
ller
co
n
tin
u
es
to
ex
h
ib
it
lar
g
e
o
v
er
s
h
o
o
ts
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d
p
r
o
l
o
n
g
e
d
s
ettlin
g
tim
es.
I
n
co
n
tr
ast,
th
e
SNA
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PID
-
R
FNN
I
m
ain
tain
s
a
r
esp
o
n
s
e
clo
s
e
to
th
e
r
e
f
er
en
ce
p
o
s
itio
n
with
f
ewe
r
o
s
cillatio
n
s
an
d
im
p
r
o
v
ed
n
o
is
e
im
m
u
n
ity
.
Fig
u
r
e
6
.
T
r
an
s
ien
t r
esp
o
n
s
e
o
f
SNA
-
PID
-
R
FNNI
with
r
=2
4
cm
Fig
u
r
e
7
.
T
r
an
s
ien
t r
esp
o
n
s
e
o
f
SNA
-
PID
-
R
FNNI
with
r
=2
8
cm
Fig
u
r
e
8
.
T
r
an
s
ien
t r
esp
o
n
s
e
o
f
SNA
-
PID
-
R
FNNI
with
r
=3
0
cm
Fig
u
r
e
9
.
T
r
an
s
ien
t r
esp
o
n
s
e
o
f
SNA
-
PID
-
R
FNNI
with
r
=3
5
cm
Fig
u
r
e
1
0
.
Po
s
itio
n
r
esp
o
n
s
e
with
r
=2
6
cm
Fig
u
r
e
1
1
.
Po
s
itio
n
r
esp
o
n
s
e
with
r
=3
2
cm
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
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n
t J Ar
tif
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n
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l.
15
,
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.
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,
Ap
r
il
20
26
:
1
2
0
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2
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0
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d
er
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n
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n
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e
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r
e
1
2
)
,
b
o
th
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PID
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R
FNN
I
an
d
PID
co
n
tr
o
ller
s
ac
h
iev
e
ze
r
o
co
n
v
er
g
en
ce
e
r
r
o
r
s
.
Ho
w
ev
er
,
th
e
SNA
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PID
-
R
FNN
I
co
n
tr
o
ller
g
iv
es
s
m
o
o
t
h
er
a
n
d
f
aster
s
tab
ilit
y
,
with
s
m
aller
o
s
cillatio
n
am
p
litu
d
e
af
ter
th
e
tr
an
s
ien
t
p
er
io
d
.
Me
a
n
wh
ile,
u
n
d
e
r
th
e
co
n
d
itio
n
o
f
n
o
is
e
(
Fig
u
r
e
1
3
)
,
th
e
PID
co
n
tr
o
ller
clea
r
ly
d
e
m
o
n
s
tr
ates
th
e
in
f
lu
en
ce
o
f
n
o
is
e,
ex
h
ib
itin
g
s
tr
o
n
g
o
s
cillatio
n
er
r
o
r
s
an
d
s
lo
w
s
tab
ilizatio
n
.
I
n
co
n
tr
ast,
th
e
S
NA
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PID
-
R
FNN
I
co
n
tr
o
ller
s
till
m
ain
tain
s
g
o
o
d
s
tab
ilit
y
,
m
i
n
o
r
er
r
o
r
s
,
a
n
d
less
o
s
cillatio
n
.
T
h
e
J
ac
o
b
s
ig
n
al
o
f
th
e
SNA
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PID
-
R
FNNI
co
n
tr
o
ller
u
n
d
er
n
o
is
e
-
f
r
ee
an
d
n
o
is
e
co
n
d
itio
n
s
is
s
h
o
wn
in
Fig
u
r
es 1
4
an
d
1
5
[
2
3
]
–
[
2
5
]
.
Fig
u
r
e1
2
.
E
r
r
o
r
o
f
two
co
n
tr
o
l
ler
s
with
r
=2
6
cm
Fig
u
r
e1
3
.
E
r
r
o
r
o
f
two
co
n
tr
o
l
ler
s
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[
1
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T.
Tr
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p
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[
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]
V.
-
H.
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Tr
a
n
e
t
a
l
.
,
“
B
a
c
k
st
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p
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c
o
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b
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o
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/
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1
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5
.
[
3
]
C
.
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.
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5
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A
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m
s
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st
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m,”
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n
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o
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[
6
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N
.
S
.
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