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lin
ea
r
laws
[
1
7
]
,
[
1
8
]
.
I
n
th
is
r
eg
ar
d
,
it
b
ec
o
m
es
n
ec
ess
ar
y
to
ap
p
ly
m
o
d
e
r
n
n
o
n
lin
ea
r
co
n
tr
o
l
m
eth
o
d
s
to
d
y
n
a
m
ic
s
y
s
tem
s
with
a
m
u
lti
-
co
n
n
ec
ted
s
tr
u
c
tu
r
e.
An
an
aly
s
is
o
f
c
o
n
tr
o
l
s
y
s
tem
s
y
n
th
esis
m
eth
o
d
s
f
o
r
d
r
u
m
-
ty
p
e
s
team
b
o
iler
s
s
h
o
ws th
e
f
o
llo
win
g
:
a.
C
u
r
r
en
tly
,
th
e
s
y
n
th
esis
o
f
s
t
ea
m
g
en
er
ato
r
co
n
tr
o
l
s
y
s
tem
s
p
r
im
ar
ily
u
s
es
lin
ea
r
m
ath
e
m
atica
l
m
o
d
els,
o
b
tain
ed
b
y
ap
p
r
o
x
im
atin
g
t
h
e
s
y
s
tem
alo
n
g
s
ep
ar
ate
ch
an
n
els
u
s
in
g
ty
p
ical
f
ir
s
t
-
an
d
s
ec
o
n
d
-
o
r
d
er
elem
en
ts
,
tim
e
-
d
elay
elem
en
ts
,
etc.
b.
T
h
e
m
o
d
el
p
ar
a
m
eter
s
v
ar
y
s
ig
n
if
ican
tly
d
ep
e
n
d
in
g
o
n
th
e
b
o
iler
’
s
o
p
er
atin
g
m
o
d
e,
m
ea
n
in
g
th
at
lin
ea
r
m
o
d
els
ad
eq
u
ately
d
escr
ib
e
s
team
g
en
er
atio
n
p
r
o
ce
s
s
es
o
n
ly
with
in
a
n
ar
r
o
w
r
eg
io
n
n
e
ar
th
e
o
p
er
atin
g
p
o
in
t.
c.
A
co
n
tr
o
ller
d
esig
n
e
d
f
o
r
o
n
e
s
p
ec
if
ic
m
o
d
e
b
ased
o
n
a
lin
ea
r
m
o
d
el
o
f
ten
f
ails
to
en
s
u
r
e
s
atis
f
ac
to
r
y
r
eg
u
latio
n
q
u
ality
u
n
d
er
d
if
f
er
en
t o
p
er
atin
g
m
o
d
es.
B
ased
o
n
th
e
ab
o
v
e,
it
ca
n
b
e
co
n
clu
d
ed
th
at
ef
f
ec
tiv
e
s
team
g
en
er
ato
r
c
o
n
tr
o
l
r
e
q
u
ir
es
tak
in
g
in
to
ac
co
u
n
t
th
e
n
o
n
lin
ea
r
ity
an
d
in
ter
co
n
n
ec
tiv
ity
o
f
th
e
u
n
d
e
r
ly
in
g
p
r
o
ce
s
s
es.
T
h
u
s
,
th
e
s
y
n
th
esis
s
h
o
u
ld
b
e
b
ased
o
n
n
o
n
lin
ea
r
m
ath
e
m
atica
l
m
o
d
els
th
at
r
ep
r
esen
t
a
wid
e
r
an
g
e
o
f
b
o
iler
o
p
e
r
atin
g
m
o
d
es,
u
s
in
g
th
e
m
eth
o
d
s
o
f
s
y
n
er
g
etic
co
n
tr
o
l th
eo
r
y
[
1
9
]
–
[
2
1
]
.
T
h
is
p
ap
er
p
r
esen
ts
th
e
r
esu
lts
o
f
a
s
tu
d
y
o
n
a
co
n
tr
o
l
s
y
s
tem
with
n
o
n
lin
ea
r
,
m
u
ltid
im
en
s
i
o
n
al,
a
n
d
m
u
lti
-
co
n
n
ec
ted
ch
ar
ac
ter
is
tics
.
On
th
is
b
asis
,
a
s
y
n
er
g
etic
co
n
tr
o
l
ap
p
r
o
ac
h
is
p
r
o
p
o
s
ed
.
A
d
is
tin
ctiv
e
f
ea
tu
r
e
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
th
e
p
o
s
s
ib
ilit
y
o
f
d
er
iv
in
g
an
an
aly
tical
f
o
r
m
o
f
th
e
co
n
t
r
o
l
alg
o
r
ith
m
,
en
s
u
r
in
g
its
u
n
iv
er
s
ality
in
c
o
n
tr
o
llin
g
n
o
n
lin
ea
r
d
y
n
am
ic
s
y
s
tem
s
o
f
v
ar
y
in
g
co
m
p
lex
ity
[
2
2
]
.
T
h
is
ap
p
r
o
a
ch
r
ea
f
f
ir
m
s
th
e
r
elev
an
ce
o
f
th
e
p
r
o
b
lem
r
elate
d
to
th
e
d
esig
n
o
f
n
o
n
lin
ea
r
v
ec
to
r
c
o
n
tr
o
ller
s
,
w
h
ich
ac
c
o
u
n
t
f
o
r
c
r
itical
p
r
o
p
er
ties
o
f
t
h
er
m
al
p
o
wer
p
lan
ts
(
T
PP
s
)
,
s
u
ch
as
n
o
n
lin
ea
r
ity
an
d
in
ter
c
o
n
n
ec
tiv
ity
,
as
well
as
th
e
n
ee
d
t
o
ex
p
an
d
th
e
co
n
tr
o
l
r
an
g
e
.
An
e
x
am
p
le
is
p
r
o
v
id
ed
o
f
th
e
im
p
lem
en
tatio
n
o
f
a
s
y
n
th
esized
s
y
n
er
g
etic
c
o
n
tr
o
l
s
y
s
tem
f
o
r
th
e
tech
n
o
lo
g
ical
p
ar
a
m
eter
s
o
f
a
b
o
iler
u
n
it
,
s
p
ec
if
ically
,
th
e
s
team
p
r
ess
u
r
e
at
th
e
g
en
er
at
o
r
o
u
tlet a
n
d
th
e
wate
r
lev
el
in
th
e
b
o
iler
d
r
u
m
.
2.
M
E
T
H
O
D
C
u
r
r
en
tly
,
th
er
e
a
r
e
v
ir
tu
ally
n
o
f
o
r
m
alize
d
p
r
o
ce
d
u
r
es
f
o
r
s
y
n
th
esizin
g
co
n
tr
o
l
s
y
s
tem
s
f
o
r
m
u
lti
-
co
n
n
ec
ted
n
o
n
li
n
ea
r
d
y
n
am
ic
s
y
s
tem
s
.
A
r
ev
iew
o
f
ex
is
tin
g
m
eth
o
d
s
f
o
r
s
o
lv
in
g
th
is
p
r
o
b
l
em
h
as
s
h
o
wn
t
h
at
th
e
m
o
s
t
p
r
o
m
is
in
g
ap
p
r
o
ac
h
is
th
e
an
aly
tical
d
e
s
ig
n
o
f
ag
g
r
eg
ated
co
n
tr
o
ller
s
(
ADAC),
wh
ich
f
o
r
m
s
th
e
f
o
u
n
d
atio
n
o
f
s
y
n
er
g
etic
co
n
tr
o
l
th
eo
r
y
[
2
3
]
.
An
im
p
o
r
ta
n
t
asp
ec
t
in
d
esig
n
in
g
ef
f
ec
tiv
e
co
n
tr
o
l
s
y
s
tem
s
f
o
r
th
e
co
n
s
id
er
e
d
tech
n
o
lo
g
ical
p
ar
am
eter
s
is
en
s
u
r
in
g
th
e
s
tab
i
lity
o
f
th
e
clo
s
ed
-
lo
o
p
au
t
o
m
a
tic
co
n
tr
o
l
s
y
s
tem
.
I
n
th
is
p
a
p
er
,
to
d
ev
elo
p
h
i
g
h
ly
e
f
f
icien
t
co
n
tr
o
l
s
y
s
tem
s
f
o
r
n
o
n
lin
ea
r
d
y
n
am
ic
o
b
j
ec
ts
,
we
p
r
o
p
o
s
e
a
s
y
n
th
esis
p
r
o
ce
d
u
r
e
b
ased
o
n
th
e
s
y
n
er
g
etic
ap
p
r
o
ac
h
.
Sy
n
e
r
g
etic
co
n
tr
o
l
is
a
n
o
n
lin
ea
r
c
o
n
tr
o
l
s
tr
ateg
y
t
h
at
ex
p
licitly
co
n
s
id
er
s
s
y
s
tem
n
o
n
lin
ea
r
ities
d
u
r
in
g
th
e
d
esig
n
p
r
o
ce
s
s
an
d
en
s
u
r
es
asy
m
p
to
ti
c
s
tab
ilit
y
an
d
h
ig
h
co
n
tr
o
l
p
er
f
o
r
m
an
ce
.
B
y
u
s
in
g
m
ea
s
u
r
a
b
le
s
tate
v
ar
iab
les
i
n
th
e
co
n
tr
o
l
law,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
a
v
o
id
s
th
e
o
s
cillatio
n
s
ty
p
ically
o
b
s
er
v
e
d
in
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
s
y
s
t
em
s
[
2
4
]
–
[
2
6
]
.
I
n
th
e
f
o
llo
win
g
,
we
co
n
s
id
er
th
e
s
y
n
th
esis
p
r
o
ce
d
u
r
e
f
o
r
a
n
o
n
lin
ea
r
co
n
tr
o
l
s
y
s
tem
o
f
a
d
r
u
m
b
o
iler
eq
u
ip
p
e
d
with
a
s
u
p
er
h
ea
ter
.
T
h
e
m
ater
ial
an
d
en
e
r
g
y
b
alan
ce
eq
u
atio
n
s
p
r
esen
ted
in
[
2
7
]
–
[
2
9
]
ar
e
em
p
lo
y
ed
to
co
n
s
tr
u
c
t
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
d
r
u
m
b
o
iler
.
T
h
e
co
n
tr
o
lled
an
d
m
an
ip
u
lated
v
ar
iab
les ar
e
f
ir
s
t id
en
tifie
d
wh
en
f
o
r
m
u
latin
g
t
h
e
p
r
o
ce
s
s
m
o
d
el:
=
{
1
,
2
,
3
,
4
,
5
}
;
=
{
1
,
2
}
,
wh
er
e,
th
e
co
n
tr
o
lled
v
ar
iab
le
s
:
1
=
-
d
r
u
m
b
o
iler
wate
r
lev
el,
2
=
-
s
team
p
r
ess
u
r
e
in
d
r
u
m
b
o
i
ler
,
3
=
.
.
-
m
ass
f
r
ac
tio
n
o
f
v
a
p
o
r
at
th
e
o
u
tlet
o
f
liftin
g
p
i
p
es,
4
=
-
ev
a
p
o
r
atio
n
v
o
l
u
m
e
in
d
r
u
m
b
o
il
er
,
5
=
-
s
team
p
r
ess
u
r
e
at
th
e
s
u
p
e
r
h
ea
ter
o
u
tlet;
co
n
tr
o
l
v
a
r
iab
les:
1
=
.
.
-
f
ee
d
wate
r
f
lo
w
r
ate,
2
=
-
h
ea
t in
p
u
t.
T
h
e
co
m
b
i
n
ed
m
o
d
el
o
f
a
d
r
u
m
b
o
iler
with
a
s
u
p
er
h
ea
ter
is
as f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
5
0
0
-
4
5
0
7
4502
̇
1
(
)
=
1
3
(
1
∆
(
(
22
′
−
̃
1
21
)
(
1
−
(
2
,
5
)
)
−
(
12
′
−
̃
1
11
)
(
2
+
1
.
.
−
−
(
2
,
5
)
′′
(
2
)
)
+
1
33
(
̅
(
2
,
3
)
3
.
.
−
43
44
)
(
2
−
3
(
2
)
(
2
,
3
)
)
+
1
44
(
′′
(
2
)
(
0
−
4
)
+
+
.
.
−
′
(
2
)
(
2
)
1
)
)
)
;
̇
2
(
)
=
1
∆
(
11
(
2
+
1
.
.
−
(
2
,
5
)
′′
(
2
)
−
21
(
1
−
(
2
,
5
)
)
)
)
;
̇
3
(
)
=
32
∆
33
(
21
(
1
−
(
2
,
5
)
)
−
2
+
1
.
.
−
(
2
,
5
)
′′
(
2
)
)
+
1
33
(
2
−
−
3
(
2
)
(
2
,
3
)
)
̇
4
(
)
=
̃
2
∆
(
11
(
2
+
1
.
.
−
(
2
,
5
)
′′
(
2
)
−
21
(
1
−
(
2
,
5
)
)
)
)
−
43
33
44
(
2
−
−
3
(
2
)
(
2
,
3
)
)
+
1
44
(
′′
(
2
)
(
0
−
4
)
+
.
.
−
′
(
2
)
(
2
)
1
)
;
̇
5
(
)
=
1
55
(
(
2
,
5
)
−
)
,
(
1
)
wh
er
e,
-
v
o
lu
m
e,
-
d
en
s
ity
,
=
′′
−
′
-
s
p
ec
if
ic
h
ea
t
o
f
v
ap
o
r
izatio
n
,
an
d
0
-
s
team
r
esid
en
ce
tim
e
an
d
s
team
v
o
lu
m
e
in
th
e
d
r
u
m
b
o
iler
,
r
esp
ec
tiv
ely
,
=
5
-
s
tea
m
f
lo
w
co
ef
f
icien
t
at
th
e
o
u
tlet
an
d
in
let
o
f
th
e
d
r
u
m
b
o
iler
,
∆
=
11
22
′
−
21
′
21
.
T
h
e
ex
p
r
es
s
io
n
s
(
1
)
in
clu
d
e
also
:
Fu
n
ctio
n
s
f
o
r
ch
an
g
in
g
th
e
s
team
p
r
ess
u
r
e
in
th
e
b
o
iler
u
n
it
2
:
′
,
′′
,
′
,
′′
,
′
2
,
′′
2
,
′
2
,
′′
2
,
′′
2
;
T
h
e
av
er
a
g
e
v
o
l
u
m
e
o
f
v
ap
o
r
co
n
ten
t is d
ef
in
e
d
as
,
̅
=
′
′
−
′′
(
1
−
′′
(
′
−
′′
)
3
(
1
+
′
−
′′
′′
3
)
)
;
wate
r
f
lo
w
r
ate
is
ca
lcu
lated
b
y
th
e
f
o
r
m
u
la
,
=
√
2
′
(
′
−
′′
)
̅
.
.
,
wh
er
e,
-
cr
o
s
s
-
s
ec
tio
n
al
ar
ea
o
f
u
n
d
er
wate
r
p
i
p
es,
-
f
r
ee
f
al
l a
cc
eler
atio
n
,
-
co
ef
f
icien
t
o
f
f
r
ictio
n
.
Steam
f
lo
w
r
ate
f
r
o
m
th
e
d
r
u
m
b
o
iler
,
is
d
eter
m
i
n
ed
b
y
th
e
ex
p
r
ess
io
n
:
=
0
√
′′
(
−
)
0
′′
(
0
−
0
)
,
h
er
e,
0
,
,
0
-
p
ar
am
eter
v
alu
es in
n
o
m
in
al
m
o
d
e
.
T
h
e
v
alu
es o
f
th
e
f
u
n
ctio
n
ar
e
d
eter
m
in
ed
f
r
o
m
th
e
s
tate
v
ar
iab
les:
11
=
′
−
′′
;
12
′
=
′
2
+
′′
2
;
21
=
′
′
−
′′
′′
;
22
′
=
(
′
′
2
+
′
′
2
)
+
(
′′
′′
2
+
′′
′′
2
)
+
0
′′
2
;
32
=
(
′
′
2
−
3
′
2
)
(
1
−
̅
)
.
.
+
(
(
1
−
3
)
′′
2
+
′′
′′
2
)
̅
.
.
+
(
′′
+
+
(
′
−
′′
)
3
)
.
.
̅
2
+
.
.
′′
2
;
33
=
(
(
1
−
3
)
′′
+
3
′
)
.
.
̅
2
;
42
=
4
′′
2
+
1
(
′′
4
′′
2
+
′
(
1
−
4
)
′
2
+
′′
2
)
+
3
(
1
+
)
.
.
(
̅
′′
2
+
+
(
1
−
̅
)
′
2
+
(
′′
−
′
)
̅
2
)
;
43
=
3
(
1
+
)
(
′′
−
′
)
.
.
̅
2
;
44
=
′′
;
̃
1
=
(
̅
2
−
32
33
̅
3
)
.
.
+
̃
2
;
̃
2
=
43
32
−
42
33
33
44
,
(
2
)
h
er
e
=
1
3
+
+
(
1
−
̅
(
2
,
3
)
)
.
.
+
4
,
=
0
−
,
-
co
e
f
f
icien
t
d
eter
m
in
in
g
th
e
s
team
f
lo
w
r
ate
f
r
o
m
th
e
s
team
v
o
lu
m
e.
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:
2088
-
8
7
0
8
S
yn
th
esis
o
f n
o
n
lin
ea
r
mu
ltil
in
ke
d
co
n
tr
o
l sys
tems o
f th
erm
a
l
…
(
Oksa
n
a
P
o
r
u
b
a
y
)
4503
T
o
s
o
lv
e
th
e
s
y
n
th
esis
p
r
o
b
lem
,
we
will
u
s
e
th
e
s
team
g
en
er
ato
r
m
o
d
el
in
th
e
f
o
r
m
o
f
(
1
)
as
th
e
b
asic c
o
n
tr
o
l la
ws.
Un
d
er
t
h
e
ADAC m
eth
o
d
,
th
e
m
ac
r
o
-
v
ar
iab
le
r
elatio
n
s
ar
e
o
b
tai
n
ed
:
1
=
11
(
1
−
1
0
)
+
12
(
(
2
,
5
)
−
1
)
;
2
=
21
(
1
−
1
0
)
+
22
(
(
2
,
5
)
−
1
)
.
(
3
)
T
h
is
is
th
e
s
o
lu
tio
n
o
f
th
e
s
y
s
tem
o
f
h
o
m
o
g
en
eo
u
s
d
if
f
er
e
n
tial e
q
u
atio
n
s
:
̇
1
(
)
+
1
1
=
0
;
̇
2
(
)
+
2
2
=
0
;
(
4
)
wh
er
e,
1
,
2
-
co
ef
f
icien
ts
.
I
f
co
n
d
itio
n
1
>
0
,
2
>
0
is
s
atis
f
ied
,
we
o
b
tain
a
tr
iv
ial
s
o
lu
tio
n
o
f
(
4
)
1
=
0
,
2
=
0
,
wh
ich
p
r
o
v
id
es a
s
y
m
p
t
o
tic
s
tab
ilit
y
o
f
th
e
p
r
o
ce
s
s
.
So
lv
in
g
(
1
)
,
(
3
)
,
(
4
)
to
g
eth
er
,
we
f
in
d
th
e
g
en
er
al
a
n
aly
tical
ex
p
r
ess
io
n
s
f
o
r
th
e
co
n
tr
o
ls
1
an
d
2
:
1
=
1
∆
(
1
(
2
,
5
)
2
55
(
(
2
,
5
)
2
−
1
5
)
(
(
2
,
5
)
−
)
3
−
1
6
+
3
4
+
+
1
∆
(
2
,
5
)
2
(
1
3
+
2
6
(
2
,
5
)
2
)
)
,
(
5
)
2
=
−
1
∆
(
1
(
2
,
5
)
2
55
(
(
2
,
5
)
2
−
1
5
)
(
(
2
,
5
)
−
)
2
−
1
5
+
2
4
+
+
1
∆
(
2
,
5
)
2
(
1
2
+
2
5
(
2
,
5
)
2
)
)
,
(
6
)
w
h
er
e
,
1
=
11
2
2
,
2
=
12
2
2
−
22
1
1
,
∆
=
11
22
−
12
21
,
∆
=
2
6
−
3
5
,
1
=
−
1
3
(
22
′
−
12
′
′′
(
2
)
−
̃
1
(
21
−
11
′′
(
2
)
)
∆
(
2
,
5
)
+
1
33
(
̅
(
2
,
3
)
3
.
.
−
43
44
)
×
3
(
2
)
(
2
,
3
)
−
1
44
′′
(
2
)
(
0
−
4
)
)
,
2
=
1
3
(
22
′
−
12
′
.
.
−
̃
1
(
21
−
11
.
.
)
∆
+
1
44
.
.
−
′
(
2
)
(
2
)
)
,
3
=
−
1
3
(
12
′
−
̃
1
11
∆
−
1
33
(
̅
(
2
,
3
)
3
.
.
−
43
44
)
)
,
4
=
21
−
11
′′
(
2
)
∆
(
2
,
5
)
,
5
=
11
.
.
−
21
∆
,
5
=
11
∆
.
At
th
e
en
d
o
f
tr
an
s
ien
ts
th
e
f
o
l
lo
win
g
eq
u
ality
is
s
atis
f
ied
=
0
.
W
h
en
th
e
r
ep
r
esen
tin
g
p
o
in
t
o
f
th
e
s
y
s
tem
f
alls
[
3
0
]
o
n
th
e
in
ter
s
ec
tio
n
o
f
m
a
n
if
o
ld
s
=
0
,
=
1
.
2
,
th
e
d
y
n
am
ic
d
ec
o
m
p
o
s
itio
n
o
f
th
e
p
h
ase
s
p
ac
e
o
f
th
e
s
y
s
tem
(
1
)
,
(
5
)
,
(
6
)
tak
es
p
lace
.
I
n
t
h
is
ca
s
e,
th
e
ch
an
g
e
o
f
v
a
p
o
r
p
r
ess
u
r
e
at
th
e
s
team
g
en
er
ato
r
o
u
tlet is d
escr
ib
ed
b
y
th
e
eq
u
atio
n
o
f
th
e
f
o
r
m
:
̇
5
(
)
=
1
55
(
1
−
)
.
(
7
)
C
o
n
tr
o
ls
(
5
)
,
an
d
(
6
)
allo
w
t
h
e
asy
m
p
t
o
tic
s
tab
ilit
y
o
f
th
e
m
o
tio
n
o
f
th
e
clo
s
ed
-
l
o
o
p
c
o
n
tr
o
l
s
y
s
tem
to
t
h
e
in
ter
s
ec
tio
n
o
f
m
a
n
if
o
ld
s
1
=
0
∩
2
=
0
∩
3
=
0
,
en
s
u
r
in
g
th
e
f
u
lf
illme
n
t
o
f
th
e
co
n
d
itio
n
s
o
f
s
tab
ilizatio
n
o
f
s
team
p
r
ess
u
r
e
at
th
e
s
team
g
en
er
ato
r
o
u
tl
et
(
5
=
5
0
)
an
d
wate
r
lev
el
in
th
e
d
r
u
m
b
o
iler
(
1
=
1
0
)
.
T
h
is
m
ea
n
s
th
at
t
h
e
m
o
tio
n
o
f
th
e
clo
s
ed
-
lo
o
p
s
y
s
tem
alo
n
g
t
h
e
in
ter
s
ec
tio
n
o
f
m
a
n
if
o
ld
s
is
d
escr
ib
ed
b
y
a
r
ed
u
ce
d
s
y
s
tem
o
f
eq
u
atio
n
s
o
f
t
h
e
s
ec
o
n
d
o
r
d
er
[
3
1
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
5
0
0
-
4
5
0
7
4504
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
As
a
r
esu
lt
o
f
th
e
s
y
n
th
esis
p
e
r
f
o
r
m
e
d
u
s
in
g
th
e
ADAC
m
eth
o
d
,
a
co
n
tr
o
l
law
in
ex
p
licit
an
aly
tical
f
o
r
m
was
o
b
tain
e
d
.
T
h
is
en
s
u
r
es
th
e
b
r
o
ad
ap
p
licab
ilit
y
o
f
t
h
e
alg
o
r
ith
m
an
d
f
ac
ilit
ates
its
im
p
lem
en
tatio
n
in
s
o
f
twar
e
f
o
r
v
ar
i
o
u
s
ty
p
es o
f
m
icr
o
co
n
tr
o
ller
s
.
I
t h
as b
ee
n
e
s
tab
lis
h
ed
th
at,
in
th
e
ca
s
e
o
f
a
p
iece
wis
e
co
n
s
tan
t
ex
ter
n
al
d
is
tu
r
b
a
n
ce
,
its
b
e
h
a
v
io
r
ca
n
b
e
e
f
f
ec
tiv
ely
d
escr
i
b
ed
u
s
in
g
th
e
c
o
r
r
esp
o
n
d
in
g
m
ath
em
atica
l
m
o
d
el
p
r
esen
ted
b
elo
w:
̇
(
)
=
0
,
=
.
(
8
)
C
o
m
b
in
in
g
th
is
m
o
d
el
with
th
e
b
o
iler
m
o
d
el
(
1
)
,
we
o
b
tain
an
ex
ten
d
e
d
s
y
s
tem
o
f
e
q
u
atio
n
s
:
̃
̇
(
)
=
f
(
y
̃
,
5
,
u
)
;
5
̇
(
)
=
1
55
(
(
2
,
5
)
−
)
;
̇
(
)
=
0
,
(
9
)
w
h
e
r
e
,
y
̃
=
[
1
2
3
4
]
T
-
i
n
c
o
m
p
l
e
t
e
s
t
a
t
e
v
e
c
t
o
r
;
f
-
v
e
c
t
o
r
c
o
n
t
a
i
n
i
n
g
t
h
e
r
i
g
h
t
p
a
r
t
s
o
f
t
h
e
f
i
r
s
t
f
o
u
r
e
q
u
a
t
i
o
n
s
o
f
t
h
e
s
y
s
te
m
(
1
)
.
T
h
e
d
y
n
am
ic
co
n
t
r
o
ller
in
t
h
is
ca
s
e
will b
e
r
ep
r
esen
ted
b
y
th
e
f
o
llo
win
g
s
y
s
tem
o
f
eq
u
atio
n
s
:
̇
(
)
=
(
y
,
,
u
)
;
̃
=
(
y
,
)
;
(
1
0
)
u
=
u
(
y
,
̃
)
,
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
s
y
n
th
esizin
g
th
e
s
tatic
r
eg
u
lato
r
u
=
u
(
y
,
)
b
y
(
9
)
is
as f
o
llo
ws:
1
(
5
,
)
=
−
3
55
(
5
−
5
0
)
,
an
d
in
th
e
r
eg
u
lato
r
eq
u
atio
n
s
s
im
ilar
to
(
5
)
,
a
n
d
(
6
)
,
th
e
v
ar
i
ab
le
will a
p
p
ea
r
in
s
tead
o
f
:
1
=
1
∆
(
1
(
2
,
5
)
2
55
(
(
2
,
5
)
2
−
3
55
)
(
(
2
,
5
)
−
)
3
−
1
6
+
3
4
+
+
1
∆
(
2
,
5
)
2
(
1
3
+
2
6
(
2
,
5
)
2
)
)
,
(
1
1
)
2
=
−
1
∆
(
1
(
2
,
5
)
2
55
(
(
2
,
5
)
2
+
3
55
)
(
(
2
,
5
)
−
)
2
−
1
5
+
2
4
+
+
1
∆
(
2
,
5
)
2
(
1
2
+
2
5
(
2
,
5
)
2
)
)
,
(
1
2
)
Sy
n
er
g
etic
co
n
tr
o
l
th
e
o
r
y
m
et
h
o
d
s
wer
e
u
s
ed
in
s
y
n
th
esizin
g
th
e
o
b
s
er
v
er
.
T
h
e
f
ac
t
th
at
th
e
v
ar
iab
le
en
ter
s
(
9
)
lin
ea
r
ly
allo
ws u
s
to
s
im
p
lify
th
e
o
b
s
er
v
er
s
y
n
th
esis
p
r
o
c
ed
u
r
e
co
n
s
id
er
ab
ly
.
T
h
e
eq
u
atio
n
s
o
f
th
e
o
b
s
er
v
e
r
in
th
is
ca
s
e
will h
av
e
th
e
f
o
r
m
:
̇
(
)
=
−
̃
−
̃
(
̃
55
5
+
(
2
,
5
)
)
,
̃
=
−
̃
55
5
−
.
(
1
3
)
R
ep
lacin
g
in
th
e
f
o
u
n
d
co
n
tr
o
l
law
(
1
1
)
,
(
1
2
)
th
e
v
ar
iab
le
b
y
its
esti
m
ate
̂
we
o
b
tain
th
e
f
in
al
ex
p
r
ess
io
n
s
f
o
r
t
h
e
co
n
tr
o
ls
1
an
d
2
.
As
a
r
esu
lt
o
f
m
o
d
elin
g
a
n
o
n
lin
ea
r
m
u
ltid
im
en
s
io
n
al
au
to
m
atic
co
n
tr
o
l
s
y
s
tem
b
ased
o
n
s
y
n
th
esized
co
n
t
r
o
l
laws
(
1
1
)
an
d
(
1
2
)
,
tim
e
d
ep
e
n
d
en
cies
o
f
th
e
m
ain
tech
n
o
l
o
g
ical
p
ar
am
eter
s
–
th
e
wate
r
lev
el
in
th
e
b
o
iler
d
r
u
m
an
d
th
e
s
team
p
r
ess
u
r
e
at
its
o
u
tlet
—
wer
e
o
b
tain
ed
.
T
h
e
r
esu
ltin
g
g
r
a
p
h
s
ar
e
s
h
o
wn
in
Fig
u
r
es 1
an
d
2
.
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:
2088
-
8
7
0
8
S
yn
th
esis
o
f n
o
n
lin
ea
r
mu
ltil
in
ke
d
co
n
tr
o
l sys
tems o
f th
erm
a
l
…
(
Oksa
n
a
P
o
r
u
b
a
y
)
4505
Fig
u
r
e
1
.
C
h
an
g
e
o
f
wate
r
lev
el
in
th
e
d
r
u
m
b
o
iler
Fig
u
r
e
2
.
Var
iatio
n
o
f
s
team
p
r
ess
u
r
e
at
th
e
b
o
iler
o
u
tlet
Plo
ts
o
f
v
ar
iatio
n
o
f
s
team
p
r
ess
u
r
e
at
th
e
s
team
g
en
er
ato
r
(
)
o
u
tlet
an
d
wate
r
le
v
el
in
th
e
b
o
iler
d
r
u
m
at
d
if
f
er
en
t
lo
a
d
s
:
I
–
=
0
.
6
0
,
I
I
–
=
0
.
8
0
,
I
I
I
–
=
0
.
9
0
,
f
o
r
s
y
s
tem
(
1
)
,
with
s
y
n
th
esized
(
5
)
,
(
6
)
.
E
q
u
atio
n
s
(
1
1
)
a
n
d
(
1
2
)
d
escr
ib
e
th
e
d
y
n
am
ic
c
o
n
tr
o
ller
e
q
u
atio
n
s
r
esp
o
n
s
ib
le
f
o
r
m
ain
tain
in
g
th
e
s
tab
ilit
y
o
f
s
team
p
r
ess
u
r
e
an
d
wate
r
lev
el
in
th
e
d
r
u
m
b
o
iler
.
Simu
latio
n
r
esu
lts
co
n
f
ir
m
th
at
th
e
p
r
o
p
o
s
ed
s
y
n
t
h
esis
alg
o
r
ith
m
en
ab
les
th
e
clo
s
ed
-
lo
o
p
n
o
n
lin
ea
r
m
u
ltid
im
en
s
io
n
al
co
n
tr
o
l
s
y
s
tem
to
m
ain
tain
asy
m
p
to
tic
s
tab
ilit
y
ac
r
o
s
s
th
e
en
tire
ad
m
is
s
ib
le
r
an
g
e
o
f
p
h
ase
c
o
o
r
d
in
ate
v
a
r
iatio
n
s
.
T
h
e
s
y
s
tem
ef
f
ec
tiv
ely
s
tab
ilizes
b
o
th
s
t
ea
m
p
r
ess
u
r
e
at
th
e
g
en
e
r
ato
r
o
u
tlet
an
d
th
e
d
r
u
m
wate
r
lev
el,
ev
e
n
u
n
d
er
s
ig
n
if
ican
t lo
ad
d
is
tu
r
b
an
ce
s
.
T
h
e
n
o
v
elty
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
lies
in
th
e
d
ev
elo
p
m
en
t
o
f
a
s
y
n
th
esis
p
r
o
ce
d
u
r
e
f
o
r
a
n
o
n
lin
ea
r
co
n
tr
o
l
law
th
at
g
u
a
r
an
tees
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
t
h
e
clo
s
ed
-
lo
o
p
s
y
s
tem
o
v
er
a
wid
e
r
an
g
e
o
f
p
ar
am
eter
v
a
r
iatio
n
s
,
wh
ile
e
n
s
u
r
in
g
th
e
s
tab
ilizatio
n
o
f
k
ey
tech
n
o
l
o
g
ical
p
ar
am
ete
r
s
in
th
e
p
r
esen
ce
o
f
u
n
ce
r
tain
d
is
tu
r
b
an
ce
s
.
A
d
is
tin
ctiv
e
f
ea
tu
r
e
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
is
th
e
d
er
iv
atio
n
o
f
th
e
co
n
tr
o
l
law
in
a
n
ex
p
licit
an
aly
tical
f
o
r
m
,
wh
ic
h
s
im
p
lifie
s
its
im
p
lem
en
tatio
n
an
d
en
s
u
r
es
its
u
n
iv
er
s
ality
wh
en
a
p
p
lied
t
o
v
ar
io
u
s
class
es
o
f
n
o
n
lin
ea
r
d
y
n
am
ic
s
y
s
tem
s
.
I
n
ad
d
itio
n
,
t
h
e
d
ev
el
o
p
ed
co
n
t
r
o
l
alg
o
r
ith
m
tak
es
in
to
ac
co
u
n
t
r
ea
l
tech
n
o
lo
g
ical
lim
itatio
n
s
o
n
co
n
t
r
o
l
ac
tio
n
s
,
s
u
ch
as
v
alv
e
th
r
o
u
g
h
p
u
t
an
d
f
u
el
s
u
p
p
ly
r
ate
o
f
c
h
an
g
e
,
wh
ich
in
cr
ea
s
es its
p
r
ac
tical
ap
p
licab
ilit
y
.
C
o
m
p
ar
ed
to
tr
ad
itio
n
al
co
n
tr
o
l
s
tr
ateg
ies
–
s
u
ch
as
PID
c
o
n
tr
o
ller
s
,
wh
ich
o
f
ten
r
e
q
u
ir
e
f
r
eq
u
en
t
p
ar
am
eter
a
d
ju
s
tm
en
ts
an
d
ar
e
p
r
o
n
e
to
in
s
tab
ilit
y
wh
e
n
o
p
e
r
atin
g
c
o
n
d
itio
n
s
ch
an
g
e
–
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
b
ased
o
n
n
o
n
lin
ea
r
co
n
tr
o
l
d
em
o
n
s
tr
ates
h
ig
h
e
r
ef
f
icien
c
y
.
Qu
a
n
titativ
e
co
m
p
ar
is
o
n
s
s
h
o
w
a
20
%
-
3
0
%
im
p
r
o
v
em
en
t
i
n
tr
a
n
s
itio
n
tim
e
an
d
o
v
er
s
h
o
o
t,
i
n
d
icatin
g
b
etter
d
y
n
am
ics
an
d
f
aster
attain
m
en
t
o
f
a
s
tead
y
s
tate.
Ov
er
all,
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
f
n
o
n
lin
e
ar
co
n
tr
o
l
s
y
n
t
h
esis
is
an
ef
f
ec
tiv
e
s
o
lu
tio
n
f
o
r
s
tab
ilizin
g
co
m
p
lex
en
er
g
y
s
y
s
tem
s
.
I
t
p
r
o
v
id
es
h
ig
h
d
y
n
am
ic
ac
cu
r
ac
y
,
s
tab
ilit
y
,
an
d
ad
ap
tab
ilit
y
to
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
m
ak
in
g
it
p
r
o
m
is
in
g
f
o
r
im
p
lem
en
tatio
n
in
m
o
d
er
n
th
e
r
m
al
p
o
wer
p
lan
ts
an
d
s
m
ar
t
en
er
g
y
s
y
s
tem
s
(
s
m
ar
t g
r
id
).
4.
CO
NCLU
SI
O
N
B
ased
o
n
th
e
an
aly
s
is
o
f
n
o
n
li
n
ea
r
m
o
d
els
o
f
s
team
g
en
er
at
o
r
u
n
its
,
a
b
asic
m
o
d
el
was
s
elec
ted
th
at
b
est
r
ef
lects
th
e
d
y
n
am
ic
p
r
o
c
ess
es
o
cc
u
r
r
in
g
in
s
id
e
th
e
s
team
g
en
er
ato
r
.
A
p
r
o
ce
d
u
r
e
was
d
ev
elo
p
e
d
f
o
r
t
h
e
an
aly
tical
s
y
n
th
esis
o
f
b
asic
co
n
tr
o
l
laws
f
o
r
t
h
e
in
ter
co
n
n
e
cted
r
eg
u
latio
n
o
f
s
team
g
e
n
er
ato
r
u
n
its
o
p
e
r
atin
g
as
p
ar
t
o
f
a
p
o
wer
p
la
n
t.
T
h
e
p
r
o
p
o
s
ed
s
y
n
th
esis
m
eth
o
d
e
n
s
u
r
es
s
tab
ilizatio
n
o
f
th
e
s
team
p
r
ess
u
r
e
at
th
e
s
team
g
en
er
ato
r
o
u
tlet,
as
wel
l
as
th
e
wate
r
lev
el
in
th
e
d
r
u
m
b
o
iler
.
T
h
e
s
cien
tific
n
o
v
el
ty
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
lies
in
th
e
d
ev
elo
p
m
en
t
o
f
a
p
r
o
ce
d
u
r
e
f
o
r
s
y
n
th
es
izin
g
a
n
o
n
lin
ea
r
co
n
t
r
o
l
law
th
at
g
u
ar
an
tees
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
a
clo
s
e
d
co
n
tr
o
l
s
y
s
tem
o
v
er
a
wid
e
r
an
g
e
o
f
p
ar
am
eter
v
ar
iatio
n
s
a
n
d
also
en
s
u
r
es
th
e
s
tab
ilizatio
n
o
f
k
e
y
tech
n
o
lo
g
ical
p
ar
am
eter
s
u
n
d
er
co
n
d
itio
n
s
o
f
u
n
ce
r
tain
ex
ter
n
al
in
f
lu
e
n
ce
s
.
A
d
is
tin
ctiv
e
f
ea
tu
r
e
o
f
th
e
m
eth
o
d
is
th
e
p
o
s
s
ib
ilit
y
o
f
o
b
tain
in
g
a
c
o
n
tr
o
l
alg
o
r
ith
m
in
a
n
ex
p
licit
an
a
ly
tical
f
o
r
m
,
wh
ich
en
s
u
r
es
its
u
n
iv
er
s
ality
f
o
r
r
eg
u
latin
g
n
o
n
lin
ea
r
d
y
n
am
ic
s
y
s
tem
s
o
f
v
ar
y
in
g
c
o
m
p
lex
i
ty
.
I
n
ad
d
itio
n
,
th
e
d
ev
elo
p
e
d
co
n
tr
o
l a
lg
o
r
ith
m
t
ak
es in
to
ac
co
u
n
t
r
ea
l te
ch
n
o
lo
g
ical
co
n
s
tr
ain
ts
o
n
c
o
n
tr
o
l a
ctio
n
s
.
T
h
e
o
b
tain
e
d
co
n
tr
o
l
laws
g
u
ar
a
n
tee
th
e
a
s
y
m
p
to
tic
s
tab
ilit
y
o
f
th
e
clo
s
ed
s
y
s
tem
o
v
e
r
a
wid
e
r
an
g
e
o
f
th
e
r
m
al
lo
a
d
ch
an
g
es.
Giv
en
th
e
in
c
r
ea
s
in
g
ly
wid
esp
r
ea
d
u
s
e
o
f
d
i
g
ital
tech
n
o
lo
g
ies
f
o
r
co
n
tr
o
llin
g
s
tr
u
ctu
r
ally
co
m
p
lex
d
y
n
am
ic
o
b
jects,
f
u
r
th
er
d
e
v
elo
p
m
en
t
o
f
th
is
ar
ea
in
ter
m
s
o
f
th
e
s
y
n
th
esis
o
f
d
is
cr
ete
n
o
n
lin
ea
r
co
n
tr
o
l
s
y
s
tem
s
f
o
r
s
u
ch
class
es o
f
o
b
jects is
o
f
p
ar
ticu
lar
in
ter
est.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
5
,
Octo
b
e
r
20
25
:
4
5
0
0
-
4
5
0
7
4506
Giv
en
th
e
r
esu
lts
o
b
tain
ed
,
s
ev
er
al
p
r
o
m
is
in
g
ar
ea
s
f
o
r
f
u
tu
r
e
r
esear
ch
ca
n
b
e
id
en
tifie
d
.
First,
a
lo
g
ical
n
ex
t
s
tep
wo
u
l
d
b
e
to
im
p
lem
en
t
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
alg
o
r
it
h
m
s
in
r
ea
l
tim
e
o
n
em
b
e
d
d
ed
d
ig
ital
p
latf
o
r
m
s
an
d
in
d
u
s
tr
ial
co
n
tr
o
ller
s
.
T
h
is
wo
u
ld
allo
w
f
o
r
t
h
e
ev
alu
atio
n
o
f
co
m
p
u
tatio
n
a
l
ef
f
icien
cy
,
d
elay
s
,
an
d
s
tab
ilit
y
u
n
d
er
r
ea
l
-
wo
r
ld
co
n
d
itio
n
s
.
Seco
n
d
,
th
e
p
o
s
s
ib
ilit
y
o
f
in
clu
d
in
g
f
au
lt
-
to
ler
an
t
co
n
tr
o
l
m
ec
h
an
is
m
s
s
h
o
u
ld
b
e
co
n
s
i
d
er
ed
,
wh
ich
will
in
cr
ea
s
e
th
e
r
eliab
ilit
y
o
f
th
e
s
y
s
tem
in
th
e
ev
en
t
o
f
s
en
s
o
r
f
ailu
r
es,
ac
tu
ato
r
f
ailu
r
es,
an
d
o
th
er
u
n
f
o
r
eseen
d
is
tu
r
b
a
n
ce
s
ch
ar
ac
ter
is
tic
o
f
co
m
p
lex
th
er
m
al
p
r
o
ce
s
s
es.
I
n
ad
d
itio
n
,
an
u
r
g
e
n
t
task
is
to
ad
ap
t
th
e
d
ev
elo
p
ed
co
n
tin
u
o
u
s
co
n
tr
o
l
to
d
is
cr
ete
tim
e
f
o
r
p
r
ac
tical
ap
p
licatio
n
in
d
ig
ital
co
n
tr
o
l
s
y
s
tem
s
.
T
h
is
in
clu
d
es
th
e
d
ev
elo
p
m
e
n
t
o
f
eq
u
iv
alen
ts
o
f
n
o
n
lin
ea
r
co
n
tr
o
ller
s
in
d
is
cr
ete
f
o
r
m
b
ased
o
n
th
e
ADAC
m
eth
o
d
o
lo
g
y
wh
ile
m
ain
tain
in
g
g
u
ar
an
teed
s
tab
ilit
y
an
d
co
n
tr
o
l
q
u
ality
p
r
o
p
er
ties
.
Su
ch
ad
a
p
tatio
n
will
e
n
s
u
r
e
s
ea
m
less
in
teg
r
atio
n
in
to
th
e
ex
is
tin
g
d
ig
ital
in
f
r
astru
ctu
r
e
an
d
o
p
e
n
u
p
n
ew
o
p
p
o
r
tu
n
ities
f
o
r
ap
p
licatio
n
i
n
n
etwo
r
k
ed
an
d
d
is
tr
ib
u
ted
c
o
n
tr
o
l
s
y
s
tem
s
.
Fin
ally
,
f
u
r
th
e
r
r
esear
ch
m
ay
b
e
d
ir
ec
ted
to
war
d
ex
te
n
d
in
g
t
h
e
ap
p
r
o
ac
h
to
m
u
lti
-
ag
e
n
t
co
n
f
ig
u
r
atio
n
s
an
d
cy
b
e
r
-
p
h
y
s
ical
s
y
s
tem
s
,
wh
er
e
co
o
r
d
in
ate
d
co
n
t
r
o
l o
f
m
u
ltip
l
e
in
ter
co
n
n
ec
te
d
s
team
g
en
e
r
a
to
r
u
n
its
is
r
eq
u
ir
e
d
.
RE
F
E
R
E
NC
E
S
[
1
]
O
.
P
o
r
u
b
a
y
a
n
d
I
.
S
i
d
d
i
k
o
v
,
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A
l
g
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ms
f
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mat
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i
n
2
0
2
4
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[
2
]
N
.
X
i
o
n
g
a
n
d
L.
Li
t
z
,
“
A
n
e
w
g
e
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t
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b
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p
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t
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,
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i
n
Pro
c
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d
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g
s
o
f
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1
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9
8
I
EEE
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t
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[
3
]
J.
W
a
n
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a
n
d
L
.
S
h
e
n
,
“
A
n
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w
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h
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s
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f
f
u
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z
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t
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m,
”
I
FA
C
Pr
o
c
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d
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g
s
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(
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4.
[
4
]
M
.
I
.
B
e
r
b
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k
a
n
d
A
.
A
.
O
g
l
a
h
,
“
A
d
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d
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s
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J
o
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a
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El
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[
5
]
M
.
M
o
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t
c
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,
A
.
Jb
a
r
i
,
a
n
d
Y
.
A
b
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e
l
ma
h
j
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u
b
,
“
I
mp
l
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me
n
t
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o
f
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d
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d
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R
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a
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J
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Po
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[
6
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M
.
S
h
.
A
z
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a
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d
A
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.
A
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,
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d
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J
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[
7
]
M
.
A
.
A
w
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H
.
M
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S
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,
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ms
,
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El
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P
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[
8
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V
.
V
K
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S
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AI
P
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Pr
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[
9
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.
D
.
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.
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,
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mat
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”
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2
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c
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.
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