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T
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i
s
w
e
ll
k
n
o
w
n
f
o
r
its
r
o
b
u
s
t
n
es
s
ag
ai
n
s
t
u
n
ce
r
ta
in
tie
s
an
d
e
x
t
er
n
al
d
is
tu
r
b
a
n
ce
s
[
1
2
]
,
b
u
t
co
n
v
en
tio
n
al
SM
C
is
af
f
ec
ted
b
y
c
h
atter
in
g
,
w
h
ic
h
d
eg
r
ad
es
tr
ac
k
in
g
ac
cu
r
ac
y
,
i
n
d
u
ce
s
m
ec
h
a
n
ical
v
ib
r
atio
n
s
,
a
n
d
in
cr
ea
s
es
t
h
er
m
al
lo
s
s
e
s
in
p
o
w
er
elec
tr
o
n
ic
co
m
p
o
n
e
n
ts
[
1
3
]
.
T
o
o
v
er
co
m
e
th
e
s
e
is
s
u
e
s
,
th
is
p
ap
er
p
r
o
p
o
s
es
an
ad
ap
tiv
e
f
u
zz
y
s
l
id
in
g
m
o
d
e
co
n
tr
o
l
(
A
FS
MC)
w
it
h
an
ex
p
o
n
e
n
tial
r
ea
ch
in
g
la
w
(
E
R
L
)
an
d
m
in
i
m
u
m
p
ar
a
m
eter
lear
n
in
g
(
MP
L
)
f
o
r
liq
u
id
lev
el
co
n
tr
o
l
o
f
a
co
u
p
led
-
tan
k
s
y
s
te
m
,
ai
m
i
n
g
to
r
ed
u
ce
tr
an
s
ie
n
t ti
m
es,
s
tead
y
-
s
tate
er
r
o
r
,
ch
atter
in
g
e
f
f
ec
ts
,
an
d
o
n
l
in
e
co
m
p
u
tatio
n
al
b
u
r
d
en
.
T
h
e
r
em
ai
n
d
er
o
f
th
i
s
p
ap
er
i
s
o
r
g
an
ized
as
f
o
llo
w
s
.
Se
ctio
n
2
p
r
esen
ts
t
h
e
m
at
h
e
m
atica
l
m
o
d
el
o
f
th
e
co
u
p
led
-
ta
n
k
s
y
s
te
m
.
Se
ctio
n
3
d
escr
ib
es
th
e
d
esig
n
o
f
th
e
p
r
o
p
o
s
ed
A
FS
M
C
-
E
R
L
-
MP
L
co
n
tr
o
ller
.
Sectio
n
4
d
is
cu
s
s
e
s
th
e
s
i
m
u
la
tio
n
r
esu
l
ts
a
n
d
p
er
f
o
r
m
a
n
ce
e
v
alu
a
tio
n
,
an
d
s
ec
tio
n
5
co
n
cl
u
d
es th
e
p
ap
er
.
2.
M
AT
H
E
M
A
T
I
CAL M
O
DE
L
O
F
T
H
E
CO
UP
L
E
D
-
T
AN
K
SYST
E
M
T
h
e
co
u
p
led
-
tan
k
s
y
s
te
m
co
m
p
r
is
es t
w
o
ta
n
k
s
ar
r
an
g
ed
in
s
er
ies,
as ill
u
s
tr
ated
in
Fi
g
u
r
e
1
[
1
4
]
,
[
1
5
]
.
L
et
1
an
d
2
d
en
o
te
th
e
liq
u
id
le
v
els
i
n
T
an
k
1
an
d
T
an
k
2
,
r
esp
ec
tiv
el
y
,
w
h
ile
1
an
d
2
r
ep
r
esen
t
th
e
ir
co
r
r
esp
o
n
d
in
g
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
s
.
T
h
e
in
ter
co
n
n
ec
ti
n
g
f
lo
w
b
et
w
ee
n
t
h
e
t
w
o
tan
k
s
is
d
e
n
o
ted
b
y
3
.
T
h
e
v
ar
iab
les
1
an
d
2
co
r
r
esp
o
n
d
to
th
e
p
u
m
p
i
n
f
lo
w
r
ates
to
T
an
k
1
an
d
T
an
k
2
,
r
esp
ec
ti
v
el
y
,
w
h
er
ea
s
1
an
d
2
in
d
icate
t
h
e
o
u
t
f
lo
w
r
ate
s
f
r
o
m
ea
ch
ta
n
k
.
Fig
u
r
e
1.
S
y
s
te
m
co
n
f
i
g
u
r
atio
n
an
d
s
tr
u
ctu
r
e
o
f
t
h
e
co
u
p
led
-
tan
k
p
r
o
ce
s
s
Ass
u
m
in
g
t
h
at
t
h
e
i
n
f
lo
w
r
ate
s
1
an
d
2
ar
e
f
ix
ed
,
th
e
s
y
s
te
m
r
ea
ch
es
s
tead
y
-
s
tate
liq
u
id
lev
el
s
1
an
d
2
.
S
m
al
l
v
ar
iatio
n
s
i
n
t
h
e
in
f
lo
w
s
,
r
ep
r
esen
ted
b
y
1
an
d
2
,
in
d
u
ce
co
r
r
esp
o
n
d
in
g
p
er
tu
r
b
atio
n
s
i
n
th
e
liq
u
id
lev
el
s
,
d
en
o
ted
as
ℎ
1
an
d
ℎ
2
[
1
6
]
,
[
1
7
]
.
T
h
e
d
y
n
a
m
ic
b
eh
av
io
r
o
f
th
e
s
y
s
te
m
is
r
ep
r
esen
ted
b
y
th
e
tr
an
s
f
er
f
u
n
c
tio
n
i
n
(
1
)
[
1
8
]
:
ℎ
2
(
)
1
(
)
=
1
2
1
2
2
+
(
1
+
2
)
+
(
1
−
12
21
)
(
1
)
w
h
er
e
,
1
=
1
1
2
√
1
+
3
2
√
1
−
2
,
2
=
2
2
2
√
2
+
3
2
√
1
−
2
,
1
=
1
1
2
√
1
+
3
2
√
1
−
2
,
2
=
1
2
2
√
1
+
3
2
√
1
−
2
,
12
=
3
2
√
1
−
2
1
2
√
1
+
3
2
√
1
−
2
,
21
=
3
2
√
1
−
2
2
2
√
1
+
3
2
√
1
−
2
,
1
,
2
,
3
ar
e
p
r
o
p
o
r
tio
n
alit
y
co
n
s
tan
ts
.
W
ith
in
th
e
p
lan
t
m
o
d
el,
th
e
v
al
v
e
(
p
u
m
p
ac
tu
ato
r
)
is
a
p
p
r
o
x
im
a
ted
as
a
g
ain
ele
m
en
t,
w
h
o
s
e
d
y
n
a
m
ics ar
e
ch
ar
ac
ter
ized
b
y
th
e
d
if
f
er
en
t
ial
eq
u
atio
n
p
r
ese
n
ted
in
(
2
)
[
1
9
]
:
(
)
+
(
)
=
(
)
(
2
)
w
h
er
e
,
is
t
h
e
ti
m
e
co
n
s
ta
n
t
o
f
th
e
v
al
u
e/p
u
m
p
ac
t
u
ato
r
,
(
)
is
t
h
e
ti
m
e
-
v
ar
y
i
n
g
i
n
p
u
t
f
lo
w
r
at
e,
an
d
(
)
is
th
e
co
m
p
u
ted
o
r
co
m
m
a
n
d
ed
f
lo
w
r
ate.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
A
d
a
p
tive
fu
z
z
y
s
lid
in
g
mo
d
e
c
o
n
tr
o
l wi
th
ex
p
o
n
en
tia
l rea
c
h
in
g
la
w
a
n
d
MPL
meth
o
d
…
(
Th
a
n
h
Tu
n
g
P
h
a
m
)
709
Def
i
n
e
th
e
s
tate
v
ar
iab
le
s
as (
3
)
an
d
(
4
)
:
ℎ
2
(
)
=
1
(
)
(
3
)
̇
1
(
)
=
2
(
)
(
4
)
Su
b
s
ti
tu
t
in
g
(
3
)
an
d
(
4
)
in
to
(
1
)
,
w
e
h
a
v
e
(
5
)
:
̇
2
(
)
=
−
1
−
12
21
1
2
1
(
)
−
1
+
2
1
2
2
(
)
+
1
2
1
2
1
(
)
(
5
)
D
ef
i
n
e
:
(
)
=
−
1
−
12
21
1
2
1
(
)
−
1
+
2
1
2
2
(
)
(
6
)
T
h
e
s
p
ac
e
s
tate
o
f
th
e
co
u
p
led
-
ta
n
k
s
y
s
te
m
a
s
(
7
)
an
d
(
8
)
:
{
̇
1
(
)
=
2
(
)
̇
2
(
)
=
(
)
+
1
2
1
2
(
)
+
(
)
(
7
)
ℎ
2
(
)
=
1
(
)
(
8
)
w
h
er
e
,
(
)
=
[
1
(
)
2
(
)
]
is
th
e
s
tate
v
ec
to
r
o
f
t
h
e
s
y
s
te
m
,
1
(
)
=
(
)
is
th
e
co
n
tr
o
l
in
p
u
t,
(
)
is
th
e
d
is
tu
r
b
an
ce
,
|
(
)
|
≤
.
3.
DE
S
I
G
N
T
H
E
AF
SM
C
-
E
RL
-
M
P
L
M
E
T
H
O
D
T
h
e
o
v
er
all
s
tr
u
ctu
r
e
o
f
th
e
p
r
o
p
o
s
ed
A
FS
MC
-
E
R
L
-
MP
L
c
o
n
tr
o
l
s
tr
ateg
y
i
s
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
is
b
lo
ck
d
iag
r
a
m
s
h
o
w
s
t
h
e
clo
s
ed
-
lo
o
p
co
n
f
i
g
u
r
atio
n
,
in
w
h
ic
h
th
e
r
e
f
er
en
ce
s
ig
n
al
i
s
co
m
p
ar
ed
w
it
h
th
e
m
ea
s
u
r
ed
o
u
tp
u
t
to
p
r
o
d
u
ce
th
e
tr
ac
k
in
g
er
r
o
r
u
s
ed
b
y
th
e
co
n
tr
o
ller
.
B
ased
o
n
th
i
s
er
r
o
r
s
i
g
n
al,
th
e
AFSM
C
-
E
R
L
-
MP
L
al
g
o
r
ith
m
co
m
p
u
t
es
t
h
e
co
n
tr
o
l
i
n
p
u
t
to
r
e
g
u
l
ate
th
e
co
u
p
led
-
ta
n
k
s
y
s
te
m
d
y
n
a
m
ics,
en
s
u
r
i
n
g
ac
cu
r
ate
liq
u
id
-
le
v
el
tr
ac
k
i
n
g
an
d
r
o
b
u
s
t
d
is
t
u
r
b
an
ce
r
ej
ec
tio
n
.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
th
e
AFSM
C
-
E
R
L
-
MP
L
m
et
h
o
d
as
Fig
u
r
e
2
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
a
m
o
f
t
h
e
A
F
SMC
-
E
R
L
-
MP
L
3
.
1
.
Desig
n t
he
S
M
C
ba
s
ed
o
n t
he
E
RL
T
h
e
s
lid
in
g
s
u
r
f
ac
e
is
f
o
r
m
u
lat
ed
as in
(
9
)
[
2
0
]
,
[
2
1
]
:
=
+
̇
(9
)
w
h
er
e
t
h
e
co
ef
f
icie
n
t
is
s
elec
ted
to
s
atis
f
y
th
e
Hu
r
w
i
tz
s
tab
ilit
y
co
n
d
itio
n
w
i
th
>
0
.
T
h
e
tr
ac
k
in
g
er
r
o
r
is
d
ef
in
ed
i
n
(
1
0
)
[
2
2
]
as:
=
ℎ
2
−
ℎ
2
(
1
0
)
w
h
er
e
,
ℎ
2
d
en
o
tes
th
e
d
esire
d
l
iq
u
id
lev
el,
an
d
ℎ
2
r
e
p
r
esen
ts
th
e
ac
tu
al
liq
u
id
lev
el
o
f
th
e
co
u
p
led
-
tan
k
s
y
s
te
m
.
T
ak
i
n
g
t
h
e
d
er
iv
ati
v
e
o
f
(
1
0
)
,
w
e
h
a
v
e
(
1
1
)
an
d
(
1
2
)
:
̇
=
ℎ
̇
2
−
ℎ
̇
2
(
1
1
)
̈
=
ℎ
̈
2
−
ℎ
̈
2
(
1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
24
,
No
.
2
,
A
p
r
il
20
26
:
7
0
7
-
71
6
710
T
ak
in
g
t
h
e
d
er
iv
ati
v
e
o
f
(
9
)
,
w
e
h
av
e
(
1
3
)
:
̇
=
̇
+
̈
(
1
3
)
Su
b
s
ti
tu
t
in
g
(
7
)
an
d
(
1
2
)
in
to
(
1
3
)
,
w
e
h
a
v
e
(
1
4
)
:
̇
=
̇
+
(
)
+
1
2
1
2
+
(
)
−
ℎ
̈
2
(
1
4
)
T
h
e
SMC
b
ased
o
n
th
e
E
R
L
i
s
(
1
5
)
[
2
0
]
,
[
2
3
]
:
=
1
2
1
2
[
−
̇
−
(
)
+
ℎ
̈
2
(
)
−
(
)
−
]
(
1
5
)
w
h
er
e
,
>
0
,
>
0
.
No
w
,
̇
=
−
(
)
−
+
(
)
,
s
o
if
w
e
d
esi
g
n
≥
,
>
0
,
w
e
h
a
v
e
(
1
6
)
:
̇
=
(
−
(
)
−
+
(
)
)
=
−
|
|
−
2
+
(
)
≤
0
(
1
6
)
T
h
e
co
m
p
o
n
en
t
(
)
i
n
(
1
5
)
is
v
er
y
d
i
f
f
icu
lt
to
m
ea
s
u
r
e
in
ac
tu
a
l
co
n
tr
o
l.
T
h
u
s
,
th
e
f
u
zz
y
s
y
s
t
e
m
(
FS
)
w
it
h
th
e
MP
L
m
eth
o
d
is
u
s
ed
i
n
th
i
s
s
t
u
d
y
to
ap
p
r
o
x
i
m
ate
t
h
is
co
m
p
o
n
en
t
[
2
1
]
,
[
2
2
]
.
3
.
2
.
Uncer
t
a
inty
a
pp
ro
x
i
m
a
t
io
n us
ing
a
n F
S
I
n
th
i
s
s
ec
t
io
n
,
t
h
e
u
n
k
n
o
w
n
n
o
n
li
n
ea
r
f
u
n
ctio
n
(
)
is
ap
p
r
o
x
im
ated
b
y
a
n
FS
̂
(
)
to
i
m
p
le
m
e
n
t
f
ee
d
b
ac
k
co
n
tr
o
l.
B
ased
o
n
th
e
u
n
i
v
er
s
al
ap
p
r
o
x
i
m
atio
n
t
h
e
o
r
em
,
t
h
e
f
u
zz
y
m
o
d
eli
n
g
p
r
o
ce
d
u
r
e
is
d
ev
elo
p
ed
th
r
o
u
g
h
t
h
e
f
o
llo
w
i
n
g
s
tep
s
[
1
3
]
.
First,
f
o
r
t
h
e
in
p
u
t
v
ar
iab
le
s
1
an
d
2
,
th
e
co
r
r
esp
o
n
d
in
g
f
u
zz
y
s
ets
1
1
an
d
2
2
ar
e
d
ef
in
ed
,
w
h
er
e
=
1
,
2
,
…
,
5
.
Seco
n
d
,
a
to
tal
o
f
∏
=
1
=
1
×
2
=
25
f
u
zz
y
r
u
les
ar
e
co
n
s
tr
u
cted
to
f
o
r
m
th
e
FS
̂
(
∣
)
,
ex
p
r
ess
ed
b
y
r
u
les o
f
th
e
f
o
r
m
:
(
1
)
:
i
f
1
is
1
1
an
d
…
an
d
2
is
2
1
th
en
̂
is
1
⋮
(
25
)
:
i
f
1
is
1
5
an
d
…
an
d
2
is
2
5
th
en
̂
is
25
(
1
7
)
w
h
er
e
,
=
1
,
2
,
.
.
.
,
5
,
=
1
,
2
,
1
=
2
=
5
.
Fin
all
y
,
t
h
e
o
u
tp
u
t o
f
th
e
FS
is
o
b
tain
ed
u
s
i
n
g
s
tan
d
ar
d
f
u
zz
y
in
f
er
e
n
ce
m
ec
h
a
n
is
m
s
:
̂
(
|
)
=
∑
∑
̄
1
2
(
∏
(
)
2
=
1
)
5
2
=
1
5
1
=
1
∑
∑
(
∏
(
)
2
=
1
)
5
2
=
1
5
1
=
1
(
1
8
)
w
h
er
e
,
(
)
is
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
f
.
L
et
̄
1
2
b
e
a
f
r
ee
p
ar
am
eter
b
elo
n
g
i
n
g
to
th
e
ad
m
is
s
ib
le
s
et
̂
∈
(
25
)
.
A
co
lu
m
n
v
ec
to
r
(
)
is
th
en
i
n
tr
o
d
u
ce
d
,
en
ab
li
n
g
(
1
8
)
to
b
e
r
ew
r
itte
n
in
t
h
e
co
m
p
ac
t
f
o
r
m
g
i
v
e
n
b
y
(
1
9
)
:
̂
(
|
)
=
̂
(
)
(
1
9
)
w
h
er
e
,
=
[
1
2
]
,
(
)
is
th
e
∏
=
1
=
1
×
2
=
25
th
e
d
i
m
e
n
s
io
n
al
co
lu
m
n
v
ec
to
r
,
an
d
1
,
2
d
en
o
te
th
e
co
r
r
esp
o
n
d
in
g
ele
m
e
n
ts
[
2
4
]
.
1
2
(
)
=
∏
(
)
2
=
1
∑
∑
(
∏
(
)
2
=
1
)
2
2
=
1
1
1
=
1
(
2
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
A
d
a
p
tive
fu
z
z
y
s
lid
in
g
mo
d
e
c
o
n
tr
o
l wi
th
ex
p
o
n
en
tia
l rea
c
h
in
g
la
w
a
n
d
MPL
meth
o
d
…
(
Th
a
n
h
Tu
n
g
P
h
a
m
)
711
T
h
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
n
ee
d
to
b
e
s
elec
ted
ac
co
r
d
in
g
to
ex
p
er
ien
ce
.
Mo
r
eo
v
er
,
all
th
e
s
tates
m
u
s
t
b
e
k
n
o
w
n
.
3
.
3
.
Desig
n o
f
t
he
AF
SM
C
-
E
RL
-
M
P
L
Ass
u
m
e
th
at
t
h
e
o
p
ti
m
al
p
ar
a
m
eter
v
ec
to
r
is
d
ef
in
ed
as i
n
(
2
1
)
[
2
5
]
:
∗
=
∈
[
|
̂
(
|
∈
)
−
(
)
|
]
(
2
1
)
w
h
er
e
,
Ω
d
en
o
tes
th
e
ad
m
i
s
s
ib
le
s
et
o
f
,
i.e
.
,
∈
Ω
.
A
cc
o
r
d
in
g
l
y
,
th
e
n
o
n
li
n
ea
r
f
u
n
ctio
n
ca
n
b
e
ex
p
r
ess
ed
as [
2
5
]
:
=
∗
(
)
+
(
2
2
)
w
h
er
e
r
ep
r
esen
ts
th
e
in
p
u
t
v
e
cto
r
o
f
th
e
FS
,
(
)
is
th
e
f
u
zz
y
b
a
s
is
v
ec
to
r
,
an
d
d
en
o
tes
th
e
ap
p
r
o
x
i
m
atio
n
er
r
o
r
,
w
h
ich
i
s
b
o
u
n
d
ed
b
y
≤
.
T
h
e
FS
is
em
p
lo
y
ed
to
ap
p
r
o
x
i
m
ate
t
h
e
u
n
k
n
o
w
n
f
u
n
cti
o
n
.
T
h
e
in
p
u
t
o
f
th
e
FS
is
s
elec
ted
as
=
[
1
2
]
,
an
d
th
e
co
r
r
esp
o
n
d
in
g
FS
o
u
t
p
u
t is g
iv
e
n
i
n
(
2
3
)
[
1
2
]
,
[
1
6
]
:
̂
(
|
)
=
̂
(
)
(
2
3
)
Usi
n
g
MP
L
,
d
ef
i
n
e
=
‖
∗
‖
2
,
w
h
er
e
is
a
p
o
s
itiv
e
co
n
s
tan
t,
an
d
let
̂
b
e
an
esti
m
atio
n
o
f
.
T
h
e
FS
MC
-
E
R
L
-
MP
L
co
n
tr
o
ller
is
d
esig
n
ed
as (
2
4
)
:
=
1
2
1
2
[
−
1
2
̂
+
ℎ
̈
2
−
̇
−
(
)
−
]
(
2
4
)
w
h
er
e
,
≥
+
,
>
0
.
T
h
en
w
e
h
av
e
(
2
5
)
:
̇
=
+
1
2
1
2
+
−
ℎ
̈
2
+
̇
=
̂
(
)
+
−
1
2
̂
−
(
)
−
+
(
2
5
)
T
h
e
L
y
ap
u
n
o
v
f
u
n
ct
io
n
is
d
e
f
i
n
ed
as (
2
6
)
[
1
6
]
,
[
2
4
]
:
=
1
2
2
+
1
2
̃
2
(
2
6
)
w
h
er
e
,
>
0
,
̃
=
̂
−
.
Su
b
s
ti
tu
t
in
g
(
2
5
)
in
to
th
e
d
er
iv
ati
v
e
o
f
(
2
6
)
,
w
e
h
a
v
e
(
2
7
)
:
̇
=
̇
+
1
̃
̂
̇
=
(
̂
(
)
+
−
1
2
̂
−
(
)
−
+
)
+
1
̃
̂
̇
≤
1
2
2
+
1
2
+
−
1
2
2
̂
−
|
|
−
2
+
+
1
̃
̂
̇
=
−
1
2
2
̃
+
1
2
+
−
|
|
−
2
+
+
1
̃
̂
̇
=
̃
(
−
1
2
2
+
1
̂
̇
)
+
1
2
−
2
+
−
|
|
+
≤
̃
(
−
1
2
2
+
1
̂
̇
)
+
1
2
−
2
(
2
7
)
T
h
e
ad
ap
tiv
e
la
w
is
d
esi
g
n
ed
as (
2
8
)
:
̂
̇
=
2
2
−
̂
(
2
8
)
w
h
er
e
>
0
T
h
en
w
e
h
av
e
(
2
9
)
:
̇
≤
−
̃
̂
+
1
2
−
2
≤
−
2
(
̃
2
−
2
)
+
1
2
−
2
=
−
2
̃
2
−
2
+
(
2
2
+
1
2
)
(
2
9
)
Def
i
n
e
=
2
,
th
en
w
e
h
a
v
e
(
3
0
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6930
T
E
L
KOM
NI
K
A
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l
C
o
n
tr
o
l
,
Vo
l.
24
,
No
.
2
,
A
p
r
il
20
26
:
7
0
7
-
71
6
712
̇
≤
−
̃
2
−
2
+
(
2
2
+
1
2
)
=
−
2
(
1
2
̃
2
+
1
2
2
)
+
(
2
2
+
1
2
)
=
−
2
+
(
3
0
)
w
h
er
e
=
2
2
+
1
2
.
B
y
ap
p
l
y
i
n
g
L
e
m
m
a
1
.
3
,
th
e
s
o
lu
tio
n
o
f
t
h
e
d
if
f
er
e
n
tial i
n
eq
u
alit
y
̇
≤
−
2
+
is
o
b
tain
ed
as (
3
1
)
:
̇
≤
2
+
(
(
0
)
−
2
)
−
2
(
3
1
)
T
h
en
,
→
∞
=
2
=
2
2
+
1
2
2
=
2
+
1
4
=
2
2
+
1
4
=
2
2
+
1
4
(
3
2
)
Fro
m
th
e
ab
o
v
e
-
m
en
t
io
n
ed
,
w
e
ca
n
d
is
ce
r
n
t
h
at
th
e
o
v
er
lap
p
r
ec
is
io
n
d
ep
en
d
s
o
n
an
d
.
4.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
Fig
u
r
e
3
p
r
esen
ts
t
h
e
M
A
T
L
A
B
/Si
m
u
li
n
k
s
c
h
e
m
a
tic
o
f
t
h
e
p
r
o
p
o
s
ed
A
FS
M
C
-
E
R
L
-
M
P
L
co
n
tr
o
l
s
tr
ateg
y
.
T
h
e
p
ar
am
eter
s
o
f
th
e
co
u
p
led
-
ta
n
k
s
y
s
te
m
ar
e
p
r
esen
ted
as
[
1
]
:
1
=
2
=
32
(
cm
3
),
1
=
2
=
14
.
3
(
c
m
3/2
/
s
)
,
3
=
20
(
cm
3
/2
/s
)
,
=
1
(
s
)
,
=
300
(
cm
3
/s
)
,
1
=
7
.
445
,
2
=
6
.
2
,
1
=
0
.
23267
,
2
=
0
.
1939
,
12
=
0
.
6453
,
an
d
21
=
0
.
5378
.
=
0
.
35
,
=
12
,
=
2
,
=
25
,
an
d
(
)
=
(
)
.
T
h
ese
ar
e
th
e
p
ar
am
eter
s
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
.
Fig
u
r
e
4
d
ep
icts
th
e
s
y
s
te
m
r
esp
o
n
s
e
an
d
tr
ac
k
i
n
g
er
r
o
r
o
b
tain
ed
u
s
i
n
g
th
e
AFSM
C
-
E
RL
-
MP
L
co
n
tr
o
ller
f
o
r
a
r
ef
er
en
ce
le
v
e
l
o
f
9
c
m
.
A
s
o
b
s
er
v
ed
,
t
h
e
a
ctu
al
liq
u
id
lev
el
ac
c
u
r
atel
y
f
o
llo
w
s
t
h
e
d
esire
d
tr
aj
ec
to
r
y
,
ac
h
iev
i
n
g
a
r
is
e
ti
m
e
o
f
6
.
1
9
1
8
s
,
a
s
ettlin
g
ti
m
e
o
f
1
1
.
2
5
5
3
s
,
ze
r
o
p
er
ce
n
t
o
v
er
s
h
o
o
t,
an
d
co
n
v
er
g
e
n
ce
o
f
th
e
s
tead
y
-
s
t
ate
er
r
o
r
to
ze
r
o
.
T
h
ese
p
er
f
o
r
m
a
n
ce
in
d
ice
s
ar
e
s
u
m
m
ar
i
ze
d
in
T
a
b
le
1
an
d
co
m
p
ar
ed
w
i
th
t
h
o
s
e
o
f
th
e
P
I
D
FL
co
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ates
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ated
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ati
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e
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g
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ate
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RE
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NC
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S
[
1
]
A
.
M
u
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.
[
2
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,
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0
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7
.
[
3
]
S
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Y
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,
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.
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.
[
4
]
P
.
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.
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.
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d
J.
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n
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.
[
5
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D
.
M
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h
,
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.
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,
a
n
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.
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h
,
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.
[
6
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S
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K
u
mar
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d
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.
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l
,
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.
[
7
]
A
.
N
.
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a
,
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.
K
.
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MA
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C
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0
6
0
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0.
[
8
]
S
.
Y
.
S
i
m,
S
.
L
.
K
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k
,
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n
d
K
.
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h
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n
.
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