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[
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I
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16
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4
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Dec
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20
25
:
2389
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9
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[
1
8
]
.
I
n
th
e
s
tirr
ed
h
ea
tin
g
tan
k
s
y
s
tem
,
th
e
ad
a
p
tiv
e
PID
a
p
p
r
o
ac
h
ca
n
h
an
d
le
tem
p
e
r
atu
r
e
f
l
u
ctu
atio
n
s
ca
u
s
ed
b
y
th
e
ad
d
itio
n
o
r
r
e
m
o
v
al
o
f
wate
r
u
n
d
er
s
tead
y
-
s
tate
[
1
9
]
,
[
2
0
]
.
R
esear
ch
s
h
o
ws
th
at
u
s
in
g
a
d
ap
tiv
e
PID
in
s
tirr
ed
tan
k
h
ea
te
r
s
y
s
tem
s
ca
n
r
ed
u
ce
tem
p
er
atu
r
e
f
lu
ctu
atio
n
s
b
y
u
p
to
3
0
%
co
m
p
a
r
ed
to
co
n
v
en
tio
n
al
m
eth
o
d
s
,
esp
ec
ially
d
u
r
in
g
d
is
tu
r
b
an
ce
s
lik
e
th
e
a
d
d
itio
n
o
r
r
em
o
v
al
o
f
f
lu
id
[
2
1
]
,
[
2
2
]
.
Fu
r
th
er
m
o
r
e,
s
tu
d
ies
[
1
8
]
,
[
2
3
]
ex
p
lain
th
at
ap
p
l
y
in
g
ad
ap
tiv
e
PID
co
n
tr
o
ller
s
to
s
tirr
ed
tan
k
h
ea
ter
s
im
p
r
o
v
es
r
esp
o
n
s
e
to
tem
p
er
atu
r
e
ch
a
n
g
es
an
d
d
is
tu
r
b
an
ce
s
,
en
h
an
cin
g
s
tab
ilit
y
an
d
co
n
tr
o
l
ef
f
icien
cy
.
T
h
e
r
esu
lt
[
2
4
]
-
[
2
6
]
also
in
d
icate
s
th
at
th
e
ad
ap
tiv
e
P
I
D
s
y
s
tem
in
s
tirr
ed
tan
k
h
e
ater
s
ac
h
iev
es
h
ig
h
ac
cu
r
ac
y
an
d
ef
f
icien
c
y
i
n
d
eter
m
in
in
g
h
e
at
f
lu
x
,
m
a
k
in
g
it
ef
f
ec
tiv
e
in
tem
p
er
atu
r
e
co
n
tr
o
l
in
r
esp
o
n
s
e
to
s
y
s
tem
co
n
d
itio
n
ch
a
n
g
es.
Desp
ite
th
e
p
r
o
g
r
ess
m
ad
e,
g
a
p
s
r
em
ain
,
s
u
ch
as
o
p
tim
izin
g
ad
ap
tiv
e
alg
o
r
ith
m
s
f
o
r
s
y
s
tem
s
with
u
n
p
r
ed
ictab
le
d
y
n
am
ic
d
is
tu
r
b
an
ce
s
an
d
ex
p
lo
r
in
g
m
o
r
e
co
m
p
lex
ad
ap
ti
v
e
alg
o
r
ith
m
s
to
m
an
a
g
e
d
y
n
am
ic
d
is
tu
r
b
an
ce
s
in
th
er
m
al
s
y
s
tem
s
[
2
2
]
,
[
2
7
]
-
[
2
9
]
.
T
h
is
s
tu
d
y
aim
s
to
o
p
tim
ize
h
ea
ter
p
o
wer
co
n
tr
o
l
with
ad
ap
ti
v
e
PID
to
m
ain
tain
s
tead
y
-
s
tate
s
tab
ilit
y
,
im
p
r
o
v
e
r
esp
o
n
s
e
to
d
is
tu
r
b
a
n
ce
s
,
en
h
a
n
ce
en
e
r
g
y
ef
f
ici
en
cy
,
an
d
m
i
n
im
ize
o
v
er
s
h
o
o
t
a
n
d
a
d
ju
s
tm
en
t
tim
e.
T
h
e
s
tirr
ed
tan
k
h
ea
te
r
s
y
s
tem
ca
n
b
e
m
o
d
eled
as
a
co
n
tin
u
o
u
s
s
tirr
ed
ta
n
k
with
i
n
let
an
d
o
u
tlet
f
l
o
ws
[
1
9
]
,
[
2
1
]
,
[
2
7
]
,
[
3
0
]
.
I
n
p
o
wer
elec
t
r
o
n
ics
an
d
d
r
iv
e
s
y
s
tem
s
(
PE
DS)
,
ef
f
ec
tiv
e
th
er
m
al
m
an
ag
e
m
en
t
is
ess
en
tial
f
o
r
en
s
u
r
in
g
d
e
v
ice
p
er
f
o
r
m
a
n
ce
an
d
lo
n
g
ev
ity
.
I
t
r
eq
u
ir
es
th
e
ca
p
ab
ilit
y
to
r
ea
ch
a
tar
g
et
te
m
p
er
atu
r
e
with
l
o
w
o
v
er
s
h
o
o
t
an
d
to
r
ejec
t
d
is
tu
r
b
an
ce
s
r
ap
id
ly
.
T
h
is
ex
p
e
r
im
en
tal
s
tu
d
y
em
p
lo
y
s
a
s
tirr
ed
-
wat
er
lo
o
p
with
v
alv
e
-
in
d
u
ce
d
i
n
f
lo
w
d
is
tu
r
b
a
n
ce
s
an
d
f
o
c
u
s
es
o
n
PID
-
b
ased
h
ea
t
er
p
o
wer
c
o
n
tr
o
l
t
o
ass
ess
th
e
s
y
s
tem
’
s
ca
p
ab
ilit
y
to
m
ain
tain
tem
p
er
at
u
r
e
s
tab
ilit
y
.
T
h
e
r
esu
lts
p
r
o
v
id
e
p
r
ac
tical
in
s
ig
h
ts
f
o
r
th
e
r
m
al
-
co
n
tr
o
l
d
esig
n
in
PEDS
ap
p
licatio
n
s
.
I
n
th
is
wa
y
,
t
h
e
s
y
s
tem
is
ex
p
ec
ted
to
p
r
o
v
id
e
m
o
r
e
ac
cu
r
ate
an
d
s
tab
le
tem
p
er
atu
r
e
co
n
tr
o
l
in
in
d
u
s
tr
ial
ap
p
licatio
n
s
,
as we
ll a
s
im
p
r
o
v
e
p
er
f
o
r
m
an
ce
a
n
d
o
p
er
atio
n
al
e
f
f
icien
cy
i
n
h
ea
ti
n
g
s
y
s
tem
s
.
2.
M
E
T
H
O
D
2
.
1
.
E
x
perim
ent
a
l set
-
up
T
h
is
s
tu
d
y
u
s
es
a
1
2
0
L
s
tirr
e
d
h
ea
tin
g
tan
k
with
an
in
let
ex
p
a
n
s
io
n
tan
k
a
n
d
L
ab
VI
E
W
-
b
ase
d
ad
ap
tiv
e
PID
co
n
tr
o
l,
in
s
u
lated
b
y
1
-
in
ch
g
lass
wo
o
l
an
d
alu
m
in
u
m
f
o
il
(
Fig
u
r
e
1
)
.
A
1
5
0
W
ag
itato
r
en
s
u
r
es
wate
r
h
o
m
o
g
en
izatio
n
,
e
n
ab
lin
g
ac
c
u
r
ate
r
ea
d
in
g
s
f
r
o
m
1
2
K
-
ty
p
e
th
er
m
o
co
u
p
les.
Me
an
wh
ile,
a
2
5
L
ex
p
a
n
s
io
n
tan
k
wit
h
a
s
o
len
o
id
v
alv
e
r
eg
u
lates 1
0
L
f
lo
w
e
v
er
y
5
m
in
u
tes to
m
ain
tain
2
6
.
6
–
2
7
.
5
°C
.
S
i
m
u
l
t
a
n
e
o
u
s
l
y
,
t
h
e
s
y
s
te
m
d
r
a
i
n
s
1
0
L
o
f
w
a
t
e
r
t
o
k
e
e
p
th
e
t
o
t
a
l
v
o
l
u
m
e
a
t
1
2
0
L
,
as
s
h
o
w
n
i
n
F
i
g
u
r
e
2
.
T
e
m
p
e
r
a
t
u
r
e
c
o
n
t
r
o
l
i
s
a
c
h
i
e
v
e
d
b
y
c
o
m
p
a
r
i
n
g
t
h
e
m
e
a
s
u
r
e
d
t
e
m
p
e
r
a
t
u
r
e
w
it
h
th
e
s
e
t
p
o
i
n
t
,
w
h
i
c
h
r
a
n
g
e
s
f
r
o
m
5
0
°
C
t
o
9
5
°C
.
T
h
e
e
r
r
o
r
(
o
r
d
i
f
f
e
r
e
n
c
e
)
i
s
c
al
cu
l
a
t
e
d
a
n
d
p
r
o
c
e
s
s
e
d
b
y
t
h
e
a
d
a
p
t
i
v
e
P
I
D
s
y
s
t
e
m
,
w
h
i
c
h
t
h
e
n
d
e
t
e
r
m
i
n
es
t
h
e
c
o
n
t
r
o
l
p
a
r
a
m
e
t
e
r
s
k
p
,
k
i
,
a
n
d
k
d
.
T
h
e
P
I
D
s
y
s
te
m
o
u
t
p
u
t
is
c
o
n
v
e
r
t
e
d
i
n
t
o
a
d
i
g
it
al
s
i
g
n
a
l
,
w
h
i
c
h
c
o
n
t
r
o
ls
t
h
e
p
o
w
e
r
o
f
f
o
u
r
h
e
a
t
e
r
s
t
h
r
o
u
g
h
a
N
a
t
i
o
n
a
l
I
n
s
t
r
u
m
e
n
ts
p
o
w
e
r
c
o
n
t
r
o
l
m
o
d
u
l
e
.
A
s
i
l
i
c
o
n
-
c
o
n
t
r
o
ll
e
d
r
e
c
ti
f
i
e
r
(
SC
R
)
e
n
s
u
r
es
t
h
a
t
s
u
f
f
i
c
i
e
n
t
p
o
we
r
i
s
s
u
p
p
l
ie
d
t
o
m
ai
n
t
a
i
n
t
h
e
s
et
p
o
i
n
t
t
e
m
p
e
r
a
t
u
r
e
.
Fig
u
r
e
1
.
Ad
a
p
tiv
e
co
n
tr
o
l sy
s
tem
test
s
etu
p
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
mp
leme
n
ta
tio
n
o
f
A
d
a
p
tive
P
I
D
co
n
tr
o
l fo
r
ma
in
ta
in
in
g
te
mp
era
tu
r
e
s
ta
b
ilit
y
…
(
P
r
icyli
a
V
a
len
tin
a
)
2391
Fig
u
r
e
2
.
E
x
p
er
im
e
n
tal
f
ac
ilit
y
(
a)
(
b
)
Fig
u
r
e
3
.
PID
ad
a
p
tiv
e
co
n
tr
o
l
s
y
s
tem
p
r
o
g
r
am
:
(
a)
wir
in
g
b
l
o
ck
d
iag
r
am
an
d
(
b
)
f
r
o
n
t p
a
n
el
2
.
2
.
P
I
D
co
ntr
o
ller
m
o
dellin
g
I
n
L
a
b
VI
E
W
,
th
e
PID
co
n
tr
o
l
is
en
h
an
ce
d
with
ad
ap
tiv
e
co
n
tr
o
l
u
s
in
g
th
e
g
ain
s
ch
ed
u
lin
g
to
o
l
k
it
with
in
th
e
PID
to
o
lk
it.
T
h
e
au
t
o
tu
n
in
g
f
ea
tu
r
e
is
u
s
ed
t
o
d
ete
r
m
in
e
th
e
o
p
tim
al
PID
p
ar
am
e
ter
s
in
itially
,
wh
ile
th
e
ad
ap
ti
v
e
co
n
tr
o
l
au
to
m
ati
ca
lly
ad
ju
s
ts
th
e
P
I
D
p
a
r
am
e
ter
s
d
u
r
in
g
t
h
e
ex
p
er
im
en
t
t
o
m
ain
tain
s
y
s
tem
s
tab
ilit
y
,
ev
en
in
th
e
p
r
esen
ce
o
f
ex
ter
n
al
d
is
tu
r
b
a
n
ce
s
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
m
ath
e
m
atica
l
m
o
d
el
f
o
r
co
n
v
en
tio
n
al
PID
co
n
tr
o
l is as
(
1
)
:
(
)
=
(
)
+
∫
(
)
(
)
+
0
(
)
(
)
(
1
)
W
h
er
e:
=
(
2
)
=
∙
(
3
)
T
h
e
ad
ap
tiv
e
PID
co
n
tr
o
l
s
y
s
tem
,
en
h
an
ce
d
with
ad
ap
tiv
e
c
o
n
tr
o
l
lo
g
ic,
u
s
es
th
e
g
ain
s
ch
ed
u
lin
g
m
eth
o
d
to
u
p
d
ate
th
e
p
ar
am
eter
s
Kp
,
Ki,
an
d
Kd
as f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2389
-
2
3
9
9
2392
(
+
1
)
=
(
)
+
(
)
(
−
1
)
(4
)
(
+
1
)
=
(
)
+
(
)
∫
(
)
0
(5
)
(
+
1
)
=
(
)
+
(
)
(
)
(6
)
W
h
er
e
,
,
an
d
ar
e
th
e
ad
ap
tati
o
n
f
ac
t
o
r
s
in
th
e
a
d
ap
tiv
e
co
n
tr
o
l
lo
g
ic.
B
ased
o
n
th
ese
e
q
u
atio
n
s
,
th
e
m
ath
em
atica
l m
o
d
el
o
f
th
e
Ad
ap
tiv
e
PID
co
n
tr
o
l sy
s
tem
b
ec
o
m
es:
(
)
=
(
)
(
)
+
(
)
∫
(
)
(
)
+
0
(
)
(
)
(
)
(
8
)
(
)
=
(
)
(
)
+
(
)
∑
(
)
∆
=
0
+
(
)
(
)
−
(
−
1
)
∆
(
)
(
9
)
B
ased
o
n
Fi
g
u
r
e
3
,
t
h
e
g
ai
n
s
ch
ed
u
l
in
g
m
et
h
o
d
i
n
ad
ap
ti
v
e
c
o
n
tr
o
l
d
y
n
a
m
i
ca
l
ly
a
d
j
u
s
ts
t
h
e
c
o
n
t
r
o
l
p
a
r
a
m
e
te
r
s
,
en
s
u
r
i
n
g
s
y
s
t
em
s
t
ab
i
lit
y
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e
v
e
n
i
n
t
h
e
p
r
ese
n
c
e
o
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d
is
t
u
r
b
a
n
ce
s
.
T
h
e
L
a
b
V
I
E
W
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b
as
ed
ad
a
p
ti
v
e
P
I
D
s
y
s
te
m
u
s
es
p
r
im
a
r
y
PI
D
to
o
ls
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d
a
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o
l
e
n
o
id
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al
v
e
c
o
n
t
r
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l
s
c
h
e
m
at
ic
,
w
it
h
a
f
r
o
n
t
p
a
n
el
f
o
r
r
e
al
-
ti
m
e
p
ar
am
ete
r
an
d
te
m
p
e
r
a
tu
r
e
m
o
n
it
o
r
in
g
t
o
e
n
s
u
r
e
u
s
a
b
ili
ty
an
d
e
f
f
e
cti
v
e
v
is
u
al
iz
ati
o
n
.
T
h
e
s
et
u
p
u
s
es
a
h
ea
te
d
wa
te
r
ta
n
k
,
K
-
t
y
p
e
th
e
r
m
o
c
o
u
p
les
,
N
I
9
2
1
4
f
o
r
te
m
p
er
at
u
r
e
ac
q
u
is
it
io
n
,
N
I
9
2
6
3
f
o
r
SC
R
p
h
ase
c
o
n
t
r
o
l,
a
n
d
r
ea
l
-
tim
e
p
a
r
a
m
e
te
r
t
u
n
i
n
g
in
L
a
b
VI
E
W
.
G
ai
n
s
ch
ed
u
l
in
g
is
c
h
o
s
e
n
f
o
r
i
ts
r
e
al
-
ti
m
e
p
a
r
a
m
et
er
a
d
ju
s
t
m
e
n
t
,
m
i
n
i
m
i
zi
n
g
o
v
e
r
s
h
o
o
t
w
h
i
le
m
ai
n
t
ai
n
i
n
g
f
ast
r
es
p
o
n
s
e
,
o
f
f
er
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n
g
s
i
m
p
le
r
an
d
m
o
r
e
r
o
b
u
s
t
c
o
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tr
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l
th
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n
f
u
z
zy
lo
g
i
c
o
r
n
e
u
r
a
l
n
et
wo
r
k
s
.
T
h
e
t
h
e
r
m
al
m
o
d
e
l
ap
p
l
ies
e
n
er
g
y
b
al
an
ce
f
o
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co
n
d
u
cti
o
n
,
c
o
n
v
ec
ti
o
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,
a
n
d
r
a
d
i
ati
o
n
,
s
h
o
wi
n
g
d
is
t
u
r
b
a
n
ce
e
f
f
e
cts
a
n
d
h
i
g
h
li
g
h
ti
n
g
SC
R
-
b
ase
d
p
o
w
er
c
o
n
t
r
o
l
f
o
r
im
p
r
o
v
ed
r
es
o
l
u
ti
o
n
a
n
d
e
f
f
ici
en
c
y
[
3
1
]
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
T
em
pera
t
ure
co
ntr
o
l sy
s
t
em
re
s
po
ns
e
I
n
cr
ea
s
in
g
s
et
p
o
in
ts
ca
u
s
e
a
d
ap
tiv
e
PID
p
ar
am
ete
r
s
to
r
e
q
u
ir
e
g
r
ea
ter
co
n
tr
o
l
e
f
f
o
r
t,
with
h
ig
h
e
r
p
o
wer
an
d
s
tr
o
n
g
e
r
ad
ju
s
tm
e
n
ts
n
ee
d
ed
to
r
ea
ch
an
d
s
tab
ilize
tem
p
er
atu
r
es.
C
o
n
s
eq
u
en
tly
,
th
e
P,
I
,
an
d
D
p
ar
am
eter
s
in
cr
ea
s
e
to
co
r
r
ec
t
er
r
o
r
s
,
r
esp
o
n
d
to
te
m
p
er
atu
r
e
ch
an
g
es,
an
d
m
in
im
ize
r
ap
i
d
f
lu
ctu
atio
n
s
,
k
ee
p
in
g
o
v
er
s
h
o
o
t
with
in
lim
its
.
T
ab
le
1
s
h
o
ws
th
at
ad
ap
tiv
e
PID
p
ar
am
eter
s
ar
e
s
m
aller
with
o
u
t
d
is
tu
r
b
an
ce
s
,
wh
ile
d
is
tu
r
b
an
ce
s
r
eq
u
ir
e
f
aster
r
es
p
o
n
s
es,
lead
in
g
t
o
lar
g
er
p
ar
a
m
eter
s
to
m
ain
tain
s
tab
ilit
y.
T
ab
le
1
.
Ad
a
p
tiv
e
PID
p
ar
am
e
ter
s
f
r
o
m
th
e
e
x
p
er
im
e
n
tal
r
esu
lts
an
d
ch
ar
ac
ter
is
tics
p
ar
am
eter
s
o
f
t
em
p
er
atu
r
e
with
d
is
tu
r
b
an
ce
Te
mp
e
r
a
t
u
r
e
S
e
t
P
o
i
n
t
(
°
C)
P
a
r
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me
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e
r
A
P
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D
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t
h
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st
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r
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n
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s
P
a
r
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me
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e
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P
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D
w
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t
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o
u
t
D
i
st
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r
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n
c
e
s
R
i
se
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me
(
sec
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n
d
s)
O
v
e
r
sh
o
o
t
(
%)
Lo
w
P
o
i
n
t
(
°
C)
B
a
c
k
t
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st
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a
d
y
(
sec
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n
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)
k
p
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50
2
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9
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1
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0
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0
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9
3
.
0
1
1
9
Fig
u
r
e
4
s
h
o
ws
th
at
th
e
o
v
er
s
h
o
o
t
is
s
m
aller
with
o
u
t
d
is
tu
r
b
an
ce
s
.
T
h
is
o
cc
u
r
s
b
ec
au
s
e
t
h
e
ad
ap
tiv
e
PID
co
n
tr
o
l
ac
ce
ler
ates
th
e
s
y
s
tem
’
s
ad
ju
s
tm
en
t.
I
n
t
h
e
d
is
tu
r
b
ed
e
x
p
er
im
e
n
t,
th
e
PID
s
y
s
tem
h
as
n
o
t
f
u
lly
ad
ap
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,
r
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in
a
n
ex
ce
s
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iv
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in
itial
r
esp
o
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s
e
an
d
a
l
ar
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o
v
e
r
s
h
o
o
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I
n
co
n
tr
ast,
in
th
e
u
n
d
is
tu
r
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e
d
ex
p
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im
en
t,
th
e
s
y
s
tem
b
en
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i
ts
f
r
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m
d
ata
m
em
o
r
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,
allo
win
g
ad
ap
tiv
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co
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tr
o
l to
r
esp
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n
d
m
o
r
e
ac
cu
r
ately
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d
m
in
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ize
er
r
o
r
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.
Fig
u
r
e
5
s
h
o
ws
th
at
th
e
s
tead
y
-
s
tate
er
r
o
r
is
lar
g
er
in
d
is
tu
r
b
ed
ex
p
er
i
m
en
ts
d
u
e
to
r
a
p
id
tem
p
er
atu
r
e
c
h
an
g
es
t
h
at
h
in
d
er
ac
cu
r
ate
ad
ap
tiv
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PID
p
o
wer
ad
ju
s
tm
en
t.
Fo
r
in
s
tan
ce
,
wh
en
c
o
ld
er
wate
r
r
ep
lace
s
d
r
ain
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d
wate
r
,
t
h
e
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tem
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o
m
es
u
n
s
tab
le.
T
h
e
v
ar
y
in
g
h
ea
t
d
e
m
an
d
m
ak
es
it
d
if
f
icu
lt
to
m
ain
tain
th
e
s
et
p
o
in
t te
m
p
er
atu
r
e.
W
h
en
th
e
ad
ap
tiv
e
PID
f
ails
to
ad
ju
s
t p
ar
am
eter
s
,
h
ea
ter
o
u
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u
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o
t f
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lly
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t a
n
d
in
cr
ea
s
in
g
s
tead
y
-
s
tate
er
r
o
r
.
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I
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2088
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ates
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tem
r
eq
u
ir
e
d
2
0
1
s
ec
o
n
d
s
to
r
esto
r
e
th
e
tem
p
er
atu
r
e
to
th
e
s
et
p
o
in
t v
al
u
e.
Fig
u
r
e
6
s
h
o
ws
th
e
Ad
ap
tiv
e
PID
h
o
ld
in
g
tem
p
er
atu
r
e
b
e
f
o
r
e
th
e
s
et
p
o
in
t
to
en
h
an
ce
s
ta
b
ilit
y
an
d
p
r
ev
en
t
o
v
er
s
h
o
o
t
b
y
d
is
s
ip
atin
g
r
esid
u
al
h
ea
t.
B
ased
o
n
T
a
b
le
2
,
h
i
g
h
er
s
et
p
o
in
ts
s
ig
n
if
ican
tly
in
cr
ea
s
e
r
is
e
tim
e,
s
h
o
win
g
g
r
ea
ter
en
er
g
y
d
em
an
d
a
n
d
r
ev
ea
lin
g
h
ea
ter
ef
f
icien
cy
o
r
co
n
tr
o
l
lim
i
tatio
n
s
at
elev
ated
tem
p
er
atu
r
es.
Ov
e
r
s
h
o
o
t
s
tay
s
lo
w
ac
r
o
s
s
all
tem
p
er
at
u
r
es
b
u
t
p
ea
k
s
n
o
n
lin
ea
r
ly
at
m
id
-
r
an
g
e,
with
th
e
h
ig
h
est
v
alu
e
o
f
0
.
1
2
%
at
6
5
°C
.
I
n
co
n
tr
ast,
at
a
h
ig
h
er
tem
p
er
at
u
r
e,
s
u
ch
as
9
0
°C
,
th
e
o
v
er
s
h
o
o
t
is
m
u
ch
lo
wer
(
0
.
0
2
%).
T
h
is
p
atter
n
in
d
icate
s
th
at
,
d
esp
ite
ef
f
ec
tiv
e
c
o
n
tr
o
l
,
n
o
n
lin
ea
r
f
ac
to
r
s
af
f
ec
t
th
er
m
al
r
esp
o
n
s
e,
y
et
th
e
s
y
s
tem
s
till
o
p
er
ates w
ith
s
tab
l
e
p
er
f
o
r
m
an
ce
.
Fig
u
r
e
4
.
Ov
e
r
s
h
o
o
t a
n
d
er
r
o
r
s
tead
y
-
s
tate
p
r
o
f
iles
Fig
u
r
e
5
.
C
h
ar
ac
ter
is
tics
o
f
te
m
p
er
atu
r
e
with
d
is
tu
r
b
an
ce
0
900
1800
2700
3600
4500
5400
6300
7200
20
30
40
50
60
70
80
90
100
Temperature,
T
(
°
C)
Ti
m
e,
t
(s)
T
sv
=
50
°
C
T
sv
=
75
°
C
T
sv
=
55
°
C
T
sv
=
80
°
C
T
sv
=
60
°
C
T
sv
=
85
°
C
T
sv
=
65
°
C
T
sv
=
90
°
C
T
sv
=
70
°
C
T
sv
=
95
°
C
Ri
se
ti
me
ove
r
shoot
B
a
c
k to st
e
a
dy
low point
Perf
orm
anc
e
of the
hea
ting control s
yste
m
unde
r disturbance
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
4
,
Dec
em
b
er
20
25
:
2389
-
2
3
9
9
2394
Fig
u
r
e
6
.
C
h
ar
ac
ter
is
tics
o
f
te
m
p
er
atu
r
e
with
o
u
t d
is
tu
r
b
a
n
ce
T
ab
le
2
.
T
em
p
er
atu
r
e
p
r
o
f
iles
with
o
u
t d
is
tu
r
b
an
ce
Te
mp
e
r
a
t
u
r
e
se
t
p
o
i
n
t
(
°
C)
R
i
se
t
i
me
(
sec
o
n
d
s)
O
v
e
r
sh
o
o
t
(
%)
Te
mp
e
r
a
t
u
r
e
se
t
p
o
i
n
t
(
°
C)
R
i
se
t
i
me
(
sec
o
n
d
s)
O
v
e
r
sh
o
o
t
(
%)
50
6
1
3
0
,
0
6
75
1
3
6
7
0
.
0
9
55
8
3
2
0
.
0
9
80
1
4
9
3
0
.
0
7
60
9
8
9
0
.
0
8
85
1
6
4
1
0
.
0
5
65
1
1
5
2
0
.
1
2
90
1
7
3
9
0
.
0
2
70
1
1
9
5
0
.
0
4
95
1
9
0
8
0
.
1
1
3
.
2
.
H
ea
t
a
bs
o
rpt
io
n a
na
ly
s
is
T
h
e
ad
ap
tiv
e
PID
co
n
tr
o
l
ad
ju
s
ts
p
ar
am
eter
s
to
r
ea
ch
th
e
s
et
p
o
in
t,
ca
u
s
in
g
p
o
wer
f
lu
ctu
ati
o
n
s
wh
ile
wate
r
tem
p
er
atu
r
e
s
tab
ilizes
g
r
ad
u
ally
d
u
r
in
g
tr
a
n
s
ien
ts
.
I
n
s
tead
y
s
tate,
h
ea
ter
p
o
we
r
s
tab
i
lizes
as
th
e
s
y
s
tem
r
ea
ch
es
eq
u
ilib
r
iu
m
,
with
f
ew
er
h
ea
ter
s
ac
tiv
e
at
lo
wer
s
et
p
o
in
ts
,
as
s
h
o
wn
in
Fig
u
r
e
7
.
T
o
m
ain
tain
th
e
s
et
p
o
in
t
tem
p
er
at
u
r
e,
th
e
a
d
ap
tiv
e
PID
s
y
s
tem
ty
p
ically
ac
tiv
ates
two
o
r
th
r
ee
h
ea
te
r
s
in
r
esp
o
n
s
e
to
d
is
tu
r
b
an
ce
s
.
E
v
en
with
d
is
tu
r
b
a
n
ce
s
,
s
tead
y
-
s
tate
h
ea
t
lo
s
s
is
m
in
im
al,
y
ield
in
g
co
n
s
tan
t
wate
r
tem
p
er
atu
r
e
an
d
s
tab
le
p
o
wer
,
wh
ile
tr
a
n
s
ien
ts
f
o
r
ce
h
ea
ter
s
to
wo
r
k
h
ar
d
e
r
with
g
r
ea
ter
lo
s
s
.
Fig
u
re
7
s
h
o
ws
p
o
wer
f
lu
ct
u
atio
n
s
with
s
h
ar
p
v
ar
iatio
n
s
as
th
e
h
ea
te
r
r
esp
o
n
d
s
to
t
em
p
er
atu
r
e
ch
an
g
es,
r
em
ain
in
g
s
tab
le
at
l
o
wer
tem
p
er
atu
r
es
b
u
t
in
cr
ea
s
i
n
g
n
o
tab
ly
at
9
0
°C
an
d
9
5
°C
.
T
h
is
p
atter
n
s
h
o
ws
d
is
tu
r
b
an
ce
ef
f
ec
ts
,
wh
er
e
th
e
h
ea
ter
ad
ju
s
ts
p
o
wer
to
m
ain
tain
th
e
s
et
p
o
in
t,
with
ad
ap
tiv
e
PID
in
cr
ea
s
in
g
p
o
wer
a
n
d
s
witch
in
g
o
f
f
m
o
r
e
h
ea
ter
s
at
h
ig
h
er
s
et
p
o
in
ts
.
T
h
e
s
y
s
tem
tu
r
n
s
o
f
f
all
f
o
u
r
h
ea
ter
s
to
m
ain
tain
s
tab
ilit
y
u
p
to
8
0
°C
,
b
u
t o
n
l
y
two
h
ea
ter
s
ar
e
tu
r
n
ed
o
f
f
at
8
5
°C
an
d
9
5
°C
s
et
p
o
in
ts
.
Fig
u
r
e
8
s
h
o
ws
h
ea
ter
p
o
wer
p
r
o
f
iles
with
o
u
t
d
is
tu
r
b
an
ce
s
,
wh
er
e
p
o
wer
is
m
o
r
e
s
tab
le
with
s
m
o
o
th
er
f
lu
ctu
atio
n
s
an
d
r
em
ain
s
lo
w
at
5
0
–
5
5
°C
.
As
th
e
s
et
p
o
in
t
r
is
es
f
r
o
m
7
0
°C
to
9
5
°C
,
p
o
wer
u
s
ag
e
in
cr
ea
s
es
with
s
lig
h
t
f
lu
ctu
atio
n
s
to
m
ai
n
tain
th
e
tem
p
e
r
atu
r
e
at
t
h
e
s
et
p
o
in
t.
Av
e
r
ag
e
p
o
wer
r
e
q
u
ir
em
en
ts
f
o
r
ea
c
h
s
et
p
o
in
t
ca
n
b
e
an
aly
ze
d
f
r
o
m
s
t
ea
d
y
-
s
tate
h
ea
ter
p
atter
n
s
with
o
u
t
d
is
tu
r
b
an
ce
s
.
W
ater
d
is
ch
ar
g
e
d
is
tu
r
b
an
ce
s
ca
u
s
e
h
ea
t f
lu
ctu
atio
n
s
,
r
eq
u
ir
i
n
g
ex
tr
a
p
o
wer
t
o
r
eh
ea
t in
c
o
m
in
g
r
ep
lace
m
e
n
t w
ater
.
T
h
is
e
f
f
ec
t
is
r
ef
lecte
d
in
t
h
e
h
ig
h
er
v
alu
es
o
f
q
electric
an
d
q
loss
co
m
p
ar
e
d
to
th
e
r
esu
lt
s
f
r
o
m
t
h
e
u
n
d
is
tu
r
b
ed
e
x
p
er
im
e
n
ts
,
p
ar
ticu
lar
ly
at
h
ig
h
er
tem
p
er
atu
r
es,
as
s
h
o
wn
in
Fig
u
r
es
9
an
d
1
0
.
B
ased
o
n
Fig
u
r
e
9
,
th
e
v
al
u
es
o
f
q
electric
an
d
q
absorb
in
cr
ea
s
e
with
th
e
r
i
s
e
in
s
et
p
o
in
t
tem
p
er
atu
r
e.
T
h
e
s
y
s
tem
ef
f
icien
cy
r
an
g
es
f
r
o
m
7
7
.
2
1
%
to
8
0
.
0
9
%,
with
th
e
h
ig
h
est
v
alu
e
o
f
8
0
.
0
9
%
ac
h
iev
ed
at
8
0
°C
.
Desp
ite
h
ig
h
er
h
ea
t
lo
s
s
at
elev
ated
tem
p
er
atu
r
es,
s
y
s
tem
ef
f
icien
cy
r
em
ain
s
s
tab
le
an
d
is
o
p
tim
al
ar
o
u
n
d
8
0
°C
.
T
h
is
in
d
icate
s
th
e
h
ea
tin
g
s
y
s
tem
ef
f
ec
tiv
ely
c
o
n
v
er
ts
elec
tr
ica
l
en
e
r
g
y
in
to
h
ea
t,
th
o
u
g
h
e
f
f
icien
cy
d
r
o
p
s
s
l
ig
h
tly
to
7
9
.
8
2
%
at
85
–
9
5
°C
d
u
e
to
i
n
cr
ea
s
ed
h
ea
t lo
s
s
an
d
r
ed
u
ce
d
p
er
f
o
r
m
a
n
c
e.
Fig
u
r
e
1
0
s
h
o
ws
th
at
elec
tr
ic
p
o
wer
(
q
electric
)
an
d
h
ea
t
lo
s
s
(
q
loss
)
s
h
o
w
a
s
h
a
r
p
in
c
r
ea
s
in
g
tr
en
d
.
E
f
f
icien
cy
s
lig
h
tly
d
ec
r
ea
s
e
s
with
r
is
in
g
s
et
p
o
in
t
tem
p
er
at
u
r
e,
r
em
ain
in
g
ar
o
u
n
d
7
9
%.
Hig
h
er
tem
p
e
r
atu
r
es
d
em
an
d
m
o
r
e
p
o
wer
an
d
g
en
er
ate
g
r
ea
ter
lo
s
s
,
th
o
u
g
h
ef
f
icie
n
cy
is
n
o
t
s
ig
n
if
ican
tly
af
f
ec
ted
.
I
n
cr
ea
s
ed
en
er
g
y
co
n
s
u
m
p
tio
n
an
d
h
ig
h
er
h
ea
t
l
o
s
s
in
th
e
d
is
tu
r
b
ed
e
x
p
er
im
e
n
t
r
esu
l
t
f
r
o
m
wate
r
d
is
ch
ar
g
e
d
is
r
u
p
tin
g
th
e
r
m
al
s
tab
ilit
y
in
th
e
h
ea
tin
g
tan
k
.
Sy
s
tem
ef
f
icien
cy
in
th
e
d
is
tu
r
b
ed
ex
p
er
im
en
t
is
lo
wer
an
d
m
o
r
e
f
lu
ctu
atin
g
,
in
d
icatin
g
a
m
o
r
e
o
p
tim
al
o
p
e
r
atio
n
u
n
d
e
r
u
n
d
is
tu
r
b
ed
co
n
d
it
io
n
s
with
o
u
t
en
er
g
y
lo
s
s
f
r
o
m
wate
r
r
ep
lace
m
en
t.
W
ater
d
is
ch
ar
g
e
d
is
tu
r
b
an
ce
s
in
cr
ea
s
e
elec
tr
ical
e
n
er
g
y
co
n
s
u
m
p
tio
n
an
d
h
ea
t
l
o
s
s
wh
ile
r
ed
u
ci
n
g
s
y
s
tem
0
900
1800
2700
3600
4500
5400
6300
7200
20
30
40
50
60
70
80
90
100
Temperature,
T
(
°
C)
Ti
m
e,
t
(s)
T
sv
=
50
°
C
T
sv
=
75
°
C
T
sv
=
55
°
C
T
sv
=
80
°
C
T
sv
=
60
°
C
T
sv
=
85
°
C
T
sv
=
65
°
C
T
sv
=
90
°
C
T
sv
=
70
°
C
T
sv
=
95
°
C
ove
r
shoot
Ri
se
ti
me
S
tea
dy
-
state
Perf
orm
anc
e
of the
hea
ting control s
yste
m
w
ithout
dis
turbances
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
I
mp
leme
n
ta
tio
n
o
f
A
d
a
p
tive
P
I
D
co
n
tr
o
l fo
r
ma
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I
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DATA AV
AI
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[
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wh
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RE
F
E
R
E
NC
E
S
[
1
]
A
.
C
.
To
r
r
e
z
a
n
e
t
a
l
.
,
“
C
o
n
t
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s
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t
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
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lec
&
Dr
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s
t
I
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N:
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mp
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(
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2397
[
2
]
N
.
H
.
A
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mi
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,
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[
3
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.
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.
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ć
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l
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T
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H
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,
”
2
0
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9
.
[
4
]
Y
.
F
.
Z
h
a
n
g
,
M
.
Li
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n
d
J.
M
.
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n
Pr
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c
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,
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.
[
5
]
A
.
TT,
O
.
A
O
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a
n
d
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.
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,
“
M
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