I
A
E
S
I
n
t
e
r
n
at
io
n
al
Jou
r
n
al
of
A
r
t
if
ic
ia
l
I
n
t
e
ll
ig
e
n
c
e
(
I
J
-
AI
)
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
, pp.
2979
~
2990
I
S
S
N
:
2252
-
8938
,
D
O
I
:
10.11591/
ij
a
i.
v
14
.i
4
.pp
2979
-
2990
2979
Jou
r
n
al
h
om
e
page
:
ht
tp
:
//
ij
ai
.
ia
e
s
c
or
e
.c
om
O
p
t
i
m
i
z
at
i
on
c
on
t
r
ol
d
e
si
g
n
an
d
s
i
m
u
l
at
i
on
of
f
u
r
n
ac
e
-
f
i
r
e
d
b
oi
l
e
r
e
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t
p
r
e
ss
u
r
e
:
l
e
ve
r
agi
n
g d
i
sr
u
p
t
i
ve
t
e
c
h
n
ol
ogy
G
an
iy
at
A
b
io
d
u
n
S
al
aw
u
,
G
le
n
B
r
ig
h
t
D
e
pa
r
t
m
e
nt
of
M
e
c
ha
ni
c
a
l
E
ngi
ne
e
r
i
ng, F
a
c
ul
t
y of
E
ngi
ne
e
r
i
ng,
U
ni
ve
r
s
i
t
y of
K
w
a
Z
u
-
L
u N
a
t
a
l
, D
ur
ba
n, S
out
h A
f
r
i
c
a
A
r
t
ic
le
I
n
f
o
A
B
S
T
R
A
C
T
A
r
ti
c
le
h
is
to
r
y
:
R
e
c
e
iv
e
d
J
ul
11, 2024
R
e
vi
s
e
d
J
un 18, 2025
A
c
c
e
pt
e
d
J
ul
10, 2025
The
efficient
operation
of
furnace
-
fired
drum
boilers
is
critically
dependent
on
the
precise
control
of
downstream
exit
pressure,
especially
in
the
presence
of
stochastic
heat
fluctuations.
This
paper
presents
a
sto
chastic
control
approach
for
regulati
ng
the
downstream
exit
pressure
in
a
fu
rnace
-
fired
boiler
subject
to
random
heat
fluctuations.
A
stochastic
model
of
the
boiler
dynamics
is
developed,
incorporating
heat
transfer
and
com
bustion
uncertainties.
By
leveraging
disruptive
technology,
such
as
the
mo
del
predictive
control
(MPC),
strategies
were
designed
to
optimi
ze
the
downstream
exit
pressure
in
real
-
time,
and
minimizing
deviations
fr
om
the
set
point.
Simulation
studies
demonstrated
the
effectiveness
of
the
proposed
approach
in
maintai
ning
a
stable
exit
pressure
despite
random
heat
fluctuatio
ns.
Results
show
significant
improvement
s
in
boiler
perfor
mance
and
efficiency
compared
to
traditional
proportional
integral
derivative
(PID)
control.
The
proposed
stochast
ic
control
strategy
offers
a
promisi
ng
s
o
lution
for
reliable
and
efficient
operation
of
furnace
-
fired
boilers
under
un
certain
conditi
ons.
K
e
y
w
o
r
d
s
:
D
is
r
upt
iv
e
t
e
c
hnol
ogy
D
ow
ns
tr
e
a
m
e
xi
t
pr
e
s
s
ur
e
F
ur
na
c
e
-
f
ir
e
d boil
e
r
M
ode
l
pr
e
di
c
ti
ve
c
ont
r
ol
M
ode
ll
in
g a
nd s
im
ul
a
ti
on
R
a
ndom he
a
t
f
lu
c
tu
a
ti
ons
S
to
c
ha
s
ti
c
c
ont
r
ol
This is an
open
acce
ss artic
le unde
r the
CC BY
-
SA
license.
C
or
r
e
s
pon
di
n
g A
u
th
or
:
G
a
ni
ya
t
A
bi
odun S
a
la
w
u
D
e
pa
r
tm
e
nt
of
M
e
c
ha
ni
c
a
l
E
ngi
ne
e
r
in
g, F
a
c
ul
ty
of
E
ngi
ne
e
r
in
g, U
ni
ve
r
s
it
y of
K
w
a
Z
u
-
L
u N
a
ta
l
D
ur
ba
n, S
out
h A
f
r
ic
a
E
m
a
il
:
S
a
la
w
ug@
ukz
n.a
c
.z
a
1.
I
N
T
R
O
D
U
C
T
I
O
N
T
he
a
dv
e
nt
of
a
dva
n
c
e
d
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
te
c
hnol
ogi
e
s
ha
s
i
nt
r
oduc
e
d
tr
a
ns
f
or
m
a
ti
ve
c
a
pa
bi
li
ti
e
s
w
it
hi
n
th
e
th
e
r
m
a
l
pow
e
r
ge
ne
r
a
ti
on
dom
a
in
,
pa
r
ti
c
ul
a
r
ly
a
c
r
os
s
in
dus
tr
ia
l
m
a
nuf
a
c
tu
r
in
g
e
nvi
r
onm
e
nt
s
[
1]
,
[
2
]
.
L
e
ve
r
a
gi
ng
s
ta
te
-
of
-
th
e
-
a
r
t
de
s
ig
n
m
e
th
odol
ogi
e
s
,
h
ig
h
-
pe
r
f
or
m
a
nc
e
m
a
te
r
ia
ls
,
a
nd
s
ophi
s
ti
c
a
te
d
a
ut
om
a
ti
on
f
r
a
m
e
w
or
ks
,
m
ode
r
n
boi
le
r
s
ys
te
m
s
now
e
xhi
bi
t
e
nha
nc
e
d
ope
r
a
ti
ona
l
r
e
li
a
bi
li
ty
a
nd
th
e
r
m
a
l
e
f
f
ic
ie
nc
y
[
3]
.
T
he
in
te
gr
a
ti
on
of
hi
gh
-
e
f
f
ic
ie
nc
y
bur
ne
r
s
,
e
qui
ppe
d
w
it
h
c
lo
s
e
d
-
lo
op
c
ont
r
ol
s
ys
te
m
s
,
f
a
c
il
it
a
te
s
pr
e
c
is
e
m
odul
a
ti
on
of
c
om
bus
ti
on
p
a
r
a
m
e
te
r
s
,
t
he
r
e
by
opt
im
iz
in
g
he
a
t
r
e
le
a
s
e
pr
of
il
e
s
a
nd
im
pr
ovi
ng
ove
r
a
ll
e
ne
r
gy
c
onve
r
s
io
n
e
f
f
ic
ie
nc
y
[
4]
,
[
5
]
.
T
he
s
e
in
nova
ti
ons
a
r
e
f
ur
th
e
r
c
om
pl
e
m
e
nt
e
d
by
e
m
be
dde
d
r
e
a
l
-
ti
m
e
m
oni
to
r
in
g
a
r
c
hi
te
c
tu
r
e
s
a
nd
A
I
-
dr
iv
e
n
pr
e
di
c
ti
ve
m
a
in
te
na
nc
e
a
lg
or
it
hm
s
,
w
hi
c
h
c
ol
le
c
ti
ve
ly
r
e
duc
e
uns
c
he
dul
e
d
dow
nt
im
e
s
,
e
na
bl
e
c
ond
it
io
n
-
ba
s
e
d
s
e
r
vi
c
in
g,
a
nd
e
xt
e
nd
s
y
s
te
m
li
f
e
c
yc
le
[
6]
–
[
8]
.
F
ur
na
c
e
-
f
i
r
e
d
boi
le
r
s
a
r
e
e
xt
e
ns
iv
e
ly
de
pl
oy
e
d
a
c
r
os
s
th
e
r
m
a
l
pow
e
r
s
ta
ti
ons
a
nd
pr
oc
e
s
s
in
dus
tr
ie
s
,
w
he
r
e
th
e
y
s
e
r
ve
a
s
pr
im
a
r
y
s
our
c
e
s
of
s
a
tu
r
a
te
d
or
s
upe
r
he
a
te
d
s
te
a
m
f
or
e
le
c
tr
ic
it
y
ge
ne
r
a
ti
on,
pr
oc
e
s
s
he
a
ti
ng,
a
nd
th
e
r
m
oc
he
m
ic
a
l
ope
r
a
ti
ons
[
9]
,
[
10]
.
N
one
th
e
le
s
s
,
th
e
s
e
s
ys
te
m
s
r
e
m
a
in
s
us
c
e
pt
ib
le
to
s
to
c
ha
s
ti
c
th
e
r
m
a
l
pe
r
tu
r
ba
ti
ons
a
r
is
in
g
f
r
om
f
ue
l
qua
li
ty
i
nc
ons
is
te
nc
i
e
s
,
c
om
bus
ti
on
in
s
t
a
bi
li
ti
e
s
,
a
nd
dyna
m
ic
va
r
ia
ti
ons
in
c
onve
c
ti
ve
a
nd
r
a
di
a
ti
ve
he
a
t
tr
a
ns
f
e
r
r
a
te
s
.
S
uc
h
th
e
r
m
a
l
di
s
tu
r
ba
nc
e
s
c
a
n
m
a
ni
f
e
s
t
a
s
pr
e
s
s
ur
e
in
s
ta
bi
li
ti
e
s
a
t
th
e
dow
ns
tr
e
a
m
e
xi
t,
a
dve
r
s
e
ly
a
f
f
e
c
ti
n
g
s
ys
te
m
pe
r
f
or
m
a
nc
e
,
ope
r
a
ti
ona
l
s
a
f
e
ty
,
a
nd
th
e
r
m
a
l
r
e
gul
a
ti
on
[
11]
,
[
12]
.
T
he
dow
ns
tr
e
a
m
e
xi
t
pr
e
s
s
ur
e
is
a
c
r
it
ic
a
l
p
a
r
a
m
e
te
r
in
boi
le
r
ope
r
a
ti
on,
a
s
it
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
:
2979
-
2990
2980
di
r
e
c
tl
y
a
f
f
e
c
ts
s
te
a
m
qu
a
li
ty
,
tu
r
bi
ne
pe
r
f
or
m
a
nc
e
,
a
nd
ove
r
a
ll
pl
a
nt
e
f
f
ic
ie
nc
y
[
13]
,
[
14]
.
T
he
in
te
gr
a
ti
on
of
di
s
r
upt
iv
e
te
c
hnol
ogi
e
s
,
s
u
c
h
a
s
m
a
c
hi
ne
le
a
r
ni
ng
a
lg
or
it
hm
s
,
a
dva
nc
e
d
s
e
n
s
or
s
,
a
nd
r
e
a
l
-
ti
m
e
da
ta
a
na
ly
ti
c
s
,
pr
ovi
de
s
s
ol
ut
io
ns
to
th
e
s
e
f
lu
c
tu
a
ti
ons
.
A
dva
nc
e
d
s
e
ns
or
s
c
a
n
e
f
f
e
c
ti
ve
ly
m
oni
to
r
th
e
boi
le
r
c
ondi
ti
ons
w
it
h
a
hi
ghe
r
pr
e
c
is
io
n
r
a
te
,
w
hi
le
th
e
im
p
le
m
e
nt
a
ti
on
of
m
a
c
hi
ne
le
a
r
ni
ng
a
lg
or
it
hm
s
a
s
s
is
ts
in
a
na
ly
z
in
g
th
is
da
ta
a
nd f
ur
th
e
r
pr
e
di
c
ti
ng a
nd a
dj
us
ti
ng t
o pote
nt
ia
l
di
s
tu
r
ba
nc
e
s
[
14]
, [
15]
.
T
h
e
i
nt
e
g
r
a
t
io
n
o
f
r
e
a
l
-
ti
m
e
d
a
t
a
a
n
a
ly
ti
c
s
f
a
c
i
li
t
a
t
e
s
r
a
pi
d,
da
t
a
-
dr
iv
e
n
d
e
c
i
s
i
on
-
m
a
k
i
ng
,
e
n
a
b
li
n
g
d
y
n
a
m
ic
o
pt
im
i
z
a
ti
o
n
o
f
b
oi
l
e
r
op
e
r
a
ti
o
n
s
a
n
d
c
o
n
s
i
s
t
e
n
t
r
e
g
u
l
a
t
io
n
o
f
s
t
e
a
m
q
u
a
l
it
y.
T
h
e
s
e
c
a
p
a
bi
li
ti
e
s
s
i
g
ni
f
i
c
a
n
tl
y
im
pr
ov
e
th
e
o
p
e
r
a
t
io
n
a
l
e
f
f
ic
i
e
n
c
y,
r
e
s
p
o
n
s
i
v
e
n
e
s
s
,
a
n
d
s
a
f
e
ty
m
a
r
gi
n
s
of
f
u
r
n
a
c
e
-
f
ir
e
d
bo
il
e
r
s
y
s
t
e
m
s
,
s
up
p
or
t
in
g
m
or
e
r
e
s
il
i
e
n
t
a
n
d
s
u
s
t
a
i
n
a
b
l
e
p
o
w
e
r
g
e
n
e
r
a
t
io
n
a
n
d
in
du
s
tr
i
a
l
a
p
p
li
c
a
t
io
n
s
[
1
6]
.
A
c
r
i
ti
c
a
l
p
e
r
f
or
m
a
n
c
e
p
a
r
a
m
e
te
r
i
n
th
e
s
e
s
y
s
t
e
m
s
i
s
t
he
do
w
n
s
tr
e
a
m
e
xi
t
p
r
e
s
s
ur
e
,
w
hi
c
h
m
u
s
t
be
m
a
i
nt
a
i
n
e
d
w
i
th
i
n
o
p
ti
m
a
l
li
m
i
t
s
t
o
e
n
s
ur
e
s
t
a
b
l
e
t
h
e
r
m
o
dy
n
a
m
i
c
o
p
e
r
a
t
i
on
a
nd
e
f
f
ic
i
e
nt
e
n
e
r
gy
c
on
v
e
r
s
io
n.
G
iv
e
n
t
h
e
pr
e
s
e
n
c
e
of
r
a
nd
om
d
i
s
t
ur
b
a
n
c
e
s
s
t
e
m
m
i
ng
f
r
om
c
om
b
u
s
t
io
n
v
a
r
i
a
bi
li
ty
,
th
e
r
m
a
l
in
s
t
a
b
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it
i
e
s
,
a
n
d
f
lu
c
tu
a
ti
ng
h
e
a
t
tr
a
n
s
f
e
r
c
h
a
r
a
c
t
e
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i
s
ti
c
s
,
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o
nv
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on
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o
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a
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h
or
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in
m
a
n
a
g
in
g
t
hi
s
u
nc
e
r
t
a
i
nt
y
.
S
t
o
c
h
a
s
ti
c
c
on
tr
o
l
t
e
c
hn
iq
u
e
s
pr
ov
id
e
a
r
o
bu
s
t
f
r
a
m
e
w
or
k f
or
t
a
c
k
li
ng
t
he
s
e
c
h
a
l
l
e
ng
e
s
b
y
e
x
p
li
c
i
tl
y
m
o
d
e
l
in
g
s
y
s
t
e
m
d
yn
a
m
i
c
s
a
nd
d
i
s
tu
r
b
a
nc
e
s
a
s
s
to
c
h
a
s
t
i
c
pr
o
c
e
s
s
e
s
.
T
h
i
s
a
pp
r
o
a
c
h
e
n
a
b
le
s
r
e
a
l
-
ti
m
e
o
pt
im
iz
a
ti
on
of
d
ow
n
s
t
r
e
a
m
pr
e
s
s
ur
e
r
e
gu
l
a
t
io
n,
e
n
s
ur
in
g
a
d
a
pt
i
v
e
c
o
nt
r
ol
pe
r
f
or
m
a
n
c
e
un
d
e
r
u
n
c
e
r
ta
i
n
a
n
d
ti
m
e
-
v
a
r
y
in
g
c
on
di
ti
o
n
s
.
T
hi
s
r
e
s
e
a
r
c
h
a
i
m
s
to
a
d
v
a
n
c
e
d
e
v
e
l
op
m
e
n
t
of
i
nt
e
l
li
g
e
nt
s
t
oc
h
a
s
t
i
c
c
on
tr
ol
s
tr
a
te
g
ie
s
s
pe
c
if
ic
a
ll
y
d
e
s
i
gn
e
d
f
o
r
f
ur
n
a
c
e
-
f
i
r
e
d
b
o
il
e
r
s
,
w
it
h
o
bj
e
c
t
iv
e
o
f
e
nh
a
n
c
i
ng
s
y
s
t
e
m
r
e
li
a
bi
li
t
y
,
op
e
r
a
ti
o
na
l
e
f
f
i
c
i
e
n
c
y,
a
n
d
r
e
s
i
li
e
nc
e
t
o
pr
o
c
e
s
s
v
a
r
ia
b
il
it
y.
M
a
in
ta
in
in
g
a
s
ta
bl
e
dow
ns
tr
e
a
m
e
xi
t
pr
e
s
s
ur
e
is
e
s
s
e
nt
ia
l
to
e
ns
ur
e
r
e
li
a
bl
e
a
nd
e
f
f
ic
ie
nt
boi
le
r
ope
r
a
ti
on. S
to
c
ha
s
ti
c
c
ont
r
ol
m
e
th
ods
of
f
e
r
a
pr
om
is
in
g a
ppr
oa
c
h t
o m
a
na
ge
unc
e
r
ta
in
ty
a
nd opti
m
iz
e
s
ys
te
m
pe
r
f
or
m
a
nc
e
unde
r
r
a
ndom
di
s
tu
r
ba
nc
e
s
.
B
y
m
ode
ll
in
g
th
e
boi
le
r
dyna
m
ic
s
a
nd
he
a
t
f
lu
c
tu
a
ti
ons
a
s
s
to
c
ha
s
ti
c
pr
oc
e
s
s
e
s
,
s
to
c
h
a
s
ti
c
c
ont
r
ol
s
tr
a
te
gi
e
s
c
a
n
be
de
s
ig
ne
d
to
opt
im
iz
e
th
e
dow
ns
tr
e
a
m
e
xi
t
pr
e
s
s
ur
e
in
r
e
a
l
-
ti
m
e
.
T
hi
s
r
e
s
e
a
r
c
h
a
im
s
to
c
ont
r
ib
ut
e
to
th
e
de
ve
lo
pm
e
nt
of
a
dva
nc
e
d
c
ont
r
ol
s
tr
a
te
gi
e
s
f
or
f
ur
na
c
e
-
f
ir
e
d boil
e
r
s
, e
na
bl
in
g i
m
pr
ove
d pe
r
f
or
m
a
nc
e
a
nd e
f
f
ic
i
e
nc
y i
n t
he
f
a
c
e
of
unc
e
r
ta
in
ty
.
2.
L
I
T
E
R
A
T
U
R
E
R
E
V
I
E
W
T
he
ope
r
a
ti
on
a
nd
c
ont
r
ol
of
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
s
pl
a
y
a
pi
vo
ta
l
r
ol
e
in
va
r
io
us
in
dus
tr
ia
l
s
e
c
to
r
s
,
pr
im
a
r
il
y
due
to
th
e
ir
in
f
lu
e
nc
e
on
e
ne
r
gy
e
f
f
ic
ie
nc
y,
ope
r
a
ti
ona
l
s
a
f
e
ty
,
a
nd
r
e
gul
a
to
r
y
c
om
pl
ia
nc
e
[
10]
,
[
14
]
.
O
ve
r
ti
m
e
,
c
ont
r
ol
m
e
th
odol
ogi
e
s
f
or
th
e
s
e
s
ys
te
m
s
ha
ve
e
vol
ve
d
c
ons
id
e
r
a
bl
y
f
r
om
r
udi
m
e
nt
a
r
y
m
a
nua
l
in
te
r
ve
nt
io
ns
to
f
ul
ly
a
ut
om
a
te
d,
in
te
ll
ig
e
nt
s
ys
te
m
s
dr
iv
e
n
by
a
dva
nc
e
s
in
c
ont
r
ol
th
e
or
y
a
n
d
c
om
put
a
ti
ona
l
te
c
hnol
ogy
[
15]
,
[
16]
.
T
r
a
di
ti
ona
ll
y,
p
r
opor
ti
o
na
l
in
te
gr
a
l
de
r
iv
a
ti
ve
(
P
I
D
)
c
ont
r
ol
le
r
s
ha
ve
be
e
n
th
e
c
or
ne
r
s
to
ne
of
boi
le
r
c
ont
r
ol
s
tr
a
te
gi
e
s
,
va
lu
e
d
f
or
t
he
ir
s
im
pl
ic
it
y,
e
a
s
e
of
im
pl
e
m
e
nt
a
ti
on,
a
nd
e
f
f
e
c
ti
ve
ne
s
s
in
m
a
in
ta
in
in
g
s
e
tp
oi
nt
s
und
e
r
r
e
la
ti
ve
ly
s
ta
bl
e
c
ondi
ti
ons
.
H
ow
e
v
e
r
,
th
e
in
he
r
e
nt
non
-
li
ne
a
r
it
ie
s
a
nd
s
to
c
ha
s
ti
c
di
s
tu
r
ba
nc
e
s
pr
e
s
e
nt
in
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
ope
r
a
ti
ons
o
f
te
n
c
ha
ll
e
nge
th
e
r
obus
tn
e
s
s
a
nd
a
da
pt
a
bi
li
ty
of
P
I
D
-
ba
s
e
d
c
ont
r
ol
f
r
a
m
e
w
or
ks
[
17]
.
E
m
pi
r
ic
a
l
s
tu
di
e
s
s
uc
h
a
s
th
os
e
by
[
17]
,
[
18
]
r
e
ve
a
l
th
a
t
w
hi
le
P
I
D
c
ont
r
ol
le
r
s
a
r
e
c
om
pe
te
nt
in
m
a
na
gi
ng
s
te
a
dy
-
s
ta
te
ope
r
a
ti
ons
,
th
e
ir
r
e
s
pons
iv
e
ne
s
s
di
m
in
is
he
s
s
ig
ni
f
ic
a
nt
ly
i
n t
he
pr
e
s
e
n
c
e
of
r
a
pi
d dyna
m
ic
va
r
ia
ti
ons
a
nd unc
e
r
ta
in
ty
.
T
o
ov
e
r
c
om
e
th
e
s
e
li
m
i
t
a
t
io
n
s
,
c
o
nt
e
m
p
or
a
r
y
r
e
s
e
a
r
c
h
h
a
s
s
hi
f
t
e
d
t
o
w
a
r
d
a
d
va
n
c
e
d
c
o
nt
r
ol
p
a
r
a
di
gm
s
s
u
c
h
a
s
m
o
d
e
l
pr
e
di
c
ti
v
e
c
o
nt
r
o
l
(
M
P
C
)
.
M
P
C
i
s
pa
r
t
ic
u
la
r
l
y
a
d
v
a
n
t
a
g
e
ou
s
d
u
e
t
o
it
s
pr
e
di
c
ti
v
e
c
a
p
a
bi
l
it
i
e
s
,
w
h
i
c
h
a
ll
o
w
f
or
pr
o
a
c
ti
v
e
d
e
c
i
s
i
on
-
m
a
k
i
ng
b
a
s
e
d
o
n
f
ut
ur
e
s
y
s
t
e
m
be
h
a
v
i
or
.
M
o
r
e
o
ve
r
,
it
s
i
nh
e
r
e
nt
a
bi
li
ty
t
o
h
a
n
dl
e
m
u
lt
iv
a
r
i
a
b
l
e
c
o
nt
r
o
l
pr
o
bl
e
m
s
w
it
h
i
n
pu
t
a
n
d
ou
tp
ut
c
on
s
t
r
a
i
nt
s
m
a
k
e
s
i
t
w
e
l
l
-
s
ui
te
d
f
or
c
om
pl
e
x
t
h
e
r
m
a
l
s
y
s
t
e
m
s
[
19
]
–
[
2
1]
.
N
e
v
e
r
th
e
l
e
s
s
,
d
e
pl
oy
m
e
n
t
of
M
P
C
in
f
ur
n
a
c
e
-
f
ir
e
d
bo
il
e
r
s
y
s
t
e
m
s
i
s
n
o
t
w
i
th
ou
t
c
h
a
l
le
n
g
e
s
.
E
f
f
e
c
ti
v
e
i
m
p
le
m
e
n
t
a
t
io
n
n
e
c
e
s
s
i
t
a
t
e
s
t
h
e
d
e
ve
lo
p
m
e
n
t
of
h
i
gh
-
f
i
d
e
l
it
y
d
yn
a
m
i
c
m
od
e
l
s
a
n
d
im
p
o
s
e
s
c
o
n
s
id
e
r
a
bl
e
c
om
pu
t
a
t
io
n
a
l
d
e
m
a
nd
s
,
a
s
n
ot
e
d
i
n
[
1
7]
.
D
e
s
pi
t
e
th
e
s
e
h
ur
d
l
e
s
,
p
ot
e
nt
ia
l
of
M
P
C
to
s
i
gn
if
i
c
a
nt
ly
e
n
h
a
n
c
e
c
o
nt
r
o
l
pr
e
c
i
s
io
n
a
n
d
a
d
a
p
t
a
b
il
it
y
ju
s
ti
f
i
e
s
i
t
s
c
on
ti
nu
e
d
e
x
p
lo
r
a
ti
o
n
in
b
o
il
e
r
p
r
o
c
e
s
s
a
u
to
m
a
ti
o
n.
R
obus
t
c
ont
r
ol
m
e
th
ods
ha
ve
be
e
n
de
ve
lo
pe
d
to
m
a
in
ta
in
pe
r
f
or
m
a
nc
e
de
s
pi
te
unc
e
r
ta
in
ti
e
s
a
nd
di
s
tu
r
ba
nc
e
s
. R
obus
t
c
ont
r
ol
t
e
c
hni
que
s
, s
uc
h a
s
H
-
in
f
in
it
y
(
H
∞
)
c
ont
r
ol
, ha
ve
be
e
n a
ppl
ie
d t
o
boi
le
r
s
ys
te
m
s
to
e
nha
nc
e
th
e
ir
r
e
s
il
ie
nc
e
.
H
ow
e
ve
r
,
P
ur
s
e
th
e
t
al
.
[
22]
pr
ovi
de
d
a
c
om
pr
e
he
n
s
iv
e
ove
r
vi
e
w
of
r
obus
t
c
ont
r
ol
de
s
ig
n,
e
m
pha
s
iz
in
g
it
s
a
ppl
ic
a
bi
li
ty
in
s
ys
te
m
s
w
it
h
s
ig
ni
f
ic
a
nt
pa
r
a
m
e
te
r
va
r
ia
ti
ons
a
nd
e
xt
e
r
na
l
di
s
tu
r
ba
nc
e
s
.
S
im
il
a
r
ly
,
a
da
pt
iv
e
c
ont
r
ol
te
c
hni
qu
e
s
a
dj
us
t
th
e
c
ont
r
ol
le
r
pa
r
a
m
e
te
r
s
in
r
e
a
l
-
ti
m
e
ba
s
e
d
on
obs
e
r
ve
d
s
y
s
te
m
be
ha
vi
or
.
A
ls
o,
R
ut
kow
s
ki
a
nd
S
z
c
z
ygi
e
ł
[
23]
il
lu
s
tr
a
te
d
th
e
e
f
f
e
c
ti
ve
ne
s
s
of
a
d
a
pt
iv
e
c
ont
r
ol
i
n m
a
na
gi
ng s
ys
te
m
s
w
it
h va
r
yi
ng dyna
m
ic
s
, a
c
om
m
on
s
c
e
na
r
io
i
n f
ur
na
c
e
-
f
ir
e
d boil
e
r
s
.
G
iv
e
n
th
e
s
to
c
ha
s
ti
c
n
a
tu
r
e
of
he
a
t
f
lu
c
tu
a
ti
on
s
i
n
f
ur
n
a
c
e
-
f
ir
e
d
boi
l
e
r
s
,
s
to
c
ha
s
ti
c
c
ont
r
ol
m
e
th
ods
ha
ve
a
l
s
o
b
e
e
n
e
x
pl
or
e
d
.
T
he
s
e
m
e
t
hod
s
e
xpl
ic
i
tl
y
a
c
c
ount
f
or
th
e
r
a
ndo
m
ne
s
s
in
s
y
s
te
m
in
put
s
a
nd
di
s
tu
r
b
a
nc
e
s
.
R
e
s
e
a
r
c
h
by
D
u
a
n
e
t
al
.
[
1
7]
,
on s
to
c
ha
s
ti
c
s
ys
t
e
m
s
pr
ovi
de
d
f
ound
a
ti
on
a
l
c
onc
e
pt
s
f
or
a
ppl
yi
n
g
s
to
c
ha
s
ti
c
c
ont
r
ol
in
i
ndu
s
tr
ia
l
pr
o
c
e
s
s
e
s
.
M
or
e
r
e
c
e
nt
s
tu
di
e
s
,
s
uc
h
a
s
th
o
s
e
by
[
11]
,
[
24]
,
[
25]
,
h
a
ve
de
ve
l
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O
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s
imul
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fi
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(
G
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2981
pr
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to
l
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s
of
di
f
f
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e
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m
e
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F
or
in
s
ta
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c
e
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a
c
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m
bi
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of
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e
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D
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a
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d c
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ui
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ta
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m
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xt
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put
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ti
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a
l
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m
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b
e
f
e
a
s
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f
or
a
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a
p
pl
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ti
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s
.
T
h
is
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im
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tu
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s
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s
ti
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t
f
lu
c
t
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ti
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n
s
.
3.
M
E
T
H
O
D
I
n
t
hi
s
r
e
s
e
a
r
c
h
,
t
he
p
e
r
f
o
r
m
a
n
c
e
a
nd
r
e
li
a
bi
li
ty
of
f
ur
n
a
c
e
-
f
ir
e
d
b
oi
l
e
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s
un
de
r
s
to
c
h
a
s
ti
c
h
e
a
t
f
lu
c
tu
a
ti
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s
w
a
s
e
nh
a
n
c
e
d b
y d
e
ve
l
op
in
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n o
pt
i
m
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e
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c
on
tr
ol
d
e
s
ig
n.
T
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a
ppr
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a
c
h
le
ve
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a
ge
s
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d
va
nc
e
d c
on
tr
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s
tr
a
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gi
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s
i
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e
gr
a
t
e
d
w
it
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s
to
c
h
a
s
ti
c
m
o
de
l
s
,
b
y
ut
il
i
z
i
ng
m
od
e
r
n
c
om
pu
ta
t
io
na
l
te
c
h
ni
qu
e
s
,
a
nd
s
i
m
ul
a
t
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n
s
t
udi
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s
.
T
h
e
m
e
th
od
i
nv
ol
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s
c
r
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a
ti
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a
c
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n
s
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th
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m
a
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c
a
l
m
o
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l
of
t
he
boi
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s
y
s
t
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m
,
c
a
p
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i
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t
he
ke
y
dy
na
m
i
c
s
a
nd
u
nc
e
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t
a
i
nt
i
e
s
pr
e
s
e
nt
in
s
u
c
h
s
ys
te
m
s
.
T
h
e
f
ol
lo
w
in
g
i
s
a
d
e
t
a
il
e
d
de
s
c
r
i
pt
i
on
of
th
e
te
c
hn
iq
u
e
s
u
s
e
d
:
‒
E
ne
r
gy
ba
la
nc
e
e
qua
ti
ons
:
th
e
e
ne
r
gy
f
lo
w
th
r
ough
a
boi
le
r
s
ys
te
m
in
vol
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s
he
a
t
in
put
f
r
om
f
ue
l
c
om
bus
ti
on,
he
a
t
lo
s
s
e
s
to
th
e
s
ur
r
oundings
,
a
nd
he
a
t
e
x
c
ha
nge
s
be
twe
e
n
di
f
f
e
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e
nt
c
om
pone
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, s
uc
h
a
s
th
e
f
ur
na
c
e
a
nd
w
a
te
r
in
th
e
dr
um
.
T
he
e
ne
r
gy
ba
la
nc
e
is
e
xpr
e
s
s
e
d
by
di
f
f
e
r
e
nt
ia
l
e
qua
ti
ons
th
a
t
de
s
c
r
ib
e
t
he
s
y
s
te
m
'
s
t
ot
a
l
e
ne
r
gy c
h
a
nge
ove
r
t
im
e
, a
c
c
ount
in
g
f
or
va
r
io
us
e
ne
r
gy s
our
c
e
s
a
nd l
os
s
e
s
.
‒
M
a
s
s
ba
la
n
c
e
e
qua
ti
ons
:
th
e
m
a
s
s
ba
la
nc
e
e
qua
ti
on
s
in
a
boi
le
r
s
ys
te
m
e
n
s
ur
e
th
e
c
ons
e
r
va
ti
on
of
m
a
s
s
by t
r
a
c
ki
ng t
he
f
lo
w
r
a
te
s
of
w
a
te
r
a
nd s
te
a
m
. T
he
w
a
te
r
e
nt
e
r
i
ng t
he
boi
le
r
i
s
c
onve
r
te
d i
nt
o
s
te
a
m
, a
nd
th
e
pr
in
c
ip
le
of
c
ons
e
r
va
ti
on e
ns
ur
e
s
t
ha
t
th
e
m
a
s
s
of
w
a
te
r
e
nt
e
r
in
g e
qua
ls
t
he
m
a
s
s
of
w
a
te
r
a
nd s
te
a
m
e
xi
ti
ng,
a
c
c
ount
in
g
f
or
a
ny
a
c
c
um
ul
a
ti
on.
T
hi
s
ba
la
n
c
e
i
s
m
ode
le
d
us
in
g
di
f
f
e
r
e
nt
ia
l
e
qua
ti
ons
th
a
t
de
s
c
r
ib
e
t
he
r
a
te
of
m
a
s
s
c
ha
nge
i
n di
f
f
e
r
e
nt
s
ys
t
e
m
c
om
pone
nt
s
.
‒
P
r
e
s
s
ur
e
dyna
m
ic
s
:
e
f
f
ic
ie
nt
m
ode
li
ng
of
pr
e
s
s
ur
e
b
e
ha
vi
or
i
n
a
boi
le
r
dr
um
is
e
s
s
e
nt
ia
l
f
or
s
a
f
e
a
nd
e
f
f
ic
ie
nt
ope
r
a
ti
on,
a
s
pr
e
s
s
ur
e
is
c
lo
s
e
ly
li
nke
d
to
te
m
pe
r
a
tu
r
e
a
nd
vol
um
e
,
f
lu
c
tu
a
ti
ng
w
it
h
c
ha
nge
s
in
he
a
t
in
put
a
nd
s
te
a
m
pr
oduc
ti
on.
T
he
dyna
m
ic
s
of
p
r
e
s
s
ur
e
a
r
e
de
s
c
r
ib
e
d
us
in
g
di
f
f
e
r
e
nt
ia
l
e
qua
ti
ons
th
a
t
c
onne
c
t
pr
e
s
s
ur
e
,
te
m
pe
r
a
tu
r
e
,
a
nd
vol
um
e
,
of
te
n
in
c
or
por
a
ti
ng
nonl
in
e
a
r
it
ie
s
to
s
im
ul
a
te
r
e
a
l
-
w
or
ld
be
ha
vi
or
a
c
c
ur
a
te
ly
a
nd pr
e
di
c
t
pr
e
s
s
ur
e
c
ha
nge
s
ove
r
t
im
e
i
n r
e
s
pons
e
t
o he
a
t
in
put
va
r
ia
ti
ons
.
‒
S
to
c
ha
s
ti
c
he
a
t
in
put
:
to
r
e
pr
e
s
e
nt
r
a
ndom
va
r
ia
ti
ons
in
h
e
a
t
s
u
ppl
y
to
th
e
boi
le
r
,
pr
oba
bi
li
s
ti
c
m
e
th
ods
a
r
e
us
e
d
to
m
ode
l
unc
e
r
ta
in
ti
e
s
s
uc
h
a
s
f
ue
l
qua
li
ty
,
c
om
bus
ti
on
e
f
f
ic
ie
nc
y,
a
nd
e
nvi
r
onm
e
nt
a
l
c
ondi
ti
ons
.
T
he
he
a
t
in
put
is
tr
e
a
te
d
a
s
a
s
to
c
ha
s
ti
c
pr
oc
e
s
s
,
w
he
r
e
r
a
ndom
va
r
ia
bl
e
s
w
it
h
de
f
in
e
d
pr
oba
bi
li
ty
di
s
tr
ib
ut
io
ns
r
e
p
r
e
s
e
nt
th
e
s
e
unc
e
r
ta
in
ti
e
s
.
T
e
c
hni
que
s
li
ke
M
ont
e
C
a
r
lo
s
im
ul
a
ti
ons
a
r
e
a
ppl
ie
d t
o a
s
s
e
s
s
t
h
e
i
m
pa
c
t
of
t
he
s
e
va
r
ia
ti
ons
on boil
e
r
pe
r
f
or
m
a
nc
e
.
‒
A
dva
nc
e
d
c
ont
r
ol
s
tr
a
te
gi
e
s
:
to
de
s
ig
n
c
ont
r
ol
s
y
s
te
m
s
th
a
t
a
d
a
pt
to
unc
e
r
ta
in
ti
e
s
a
nd
nonl
in
e
a
r
it
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s
in
boi
le
r
ope
r
a
ti
on,
r
obus
t
a
nd
a
da
pt
iv
e
c
ont
r
ol
te
c
hni
que
s
a
r
e
us
e
d.
R
obu
s
t
c
ont
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ol
e
ns
ur
e
s
s
y
s
te
m
s
ta
bi
li
ty
de
s
pi
te
va
r
ia
ti
ons
in
f
a
c
to
r
s
li
ke
he
a
t
in
put
,
w
hi
le
a
da
pt
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e
c
ont
r
ol
a
dj
us
ts
pa
r
a
m
e
te
r
s
in
r
e
a
l
-
ti
m
e
to
opt
im
iz
e
pe
r
f
o
r
m
a
nc
e
.
T
he
s
e
s
tr
a
te
gi
e
s
e
m
pl
oy
a
l
gor
it
hm
s
th
a
t
a
c
c
ount
f
or
th
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s
ys
te
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'
s
s
to
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s
ti
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a
nd
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in
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r
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s
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u
s
in
g
m
e
th
ods
s
uc
h
a
s
M
P
C
,
H
-
in
f
in
it
y
c
ont
r
o
l,
or
a
da
pt
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e
f
il
te
r
in
g.
‒
S
im
ul
a
ti
on
s
tu
di
e
s
:
th
e
pr
opos
e
d
c
ont
r
ol
de
s
ig
n
a
nd
m
a
th
e
m
a
ti
c
a
l
m
ode
ls
w
e
r
e
va
li
da
te
d
th
r
ough
s
im
ul
a
ti
ons
unde
r
va
r
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s
c
e
na
r
io
s
,
in
c
lu
di
ng
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
ons
.
N
um
e
r
ic
a
l
m
e
th
ods
w
e
r
e
us
e
d
to
s
ol
ve
th
e
di
f
f
e
r
e
nt
ia
l
e
qua
ti
ons
f
or
boi
le
r
dyna
m
ic
s
,
a
nd
s
c
e
na
r
io
a
na
ly
s
is
te
s
te
d
s
y
s
te
m
pe
r
f
or
m
a
nc
e
unde
r
di
f
f
e
r
e
nt
ope
r
a
ti
ng
c
ondi
ti
ons
,
in
c
lu
di
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e
xt
r
e
m
e
he
a
t
va
r
ia
bi
li
ty
.
S
i
m
ul
a
ti
ons
,
c
onduc
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d
us
in
g
to
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s
li
ke
M
A
T
L
A
B
a
nd
S
im
ul
in
k,
a
ll
ow
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d
f
or
vi
s
ua
li
z
a
ti
on
a
nd
a
na
ly
s
is
.
T
hi
s
in
te
gr
a
te
d
a
ppr
oa
c
h,
c
om
bi
ni
ng
e
ne
r
gy
a
nd
m
a
s
s
ba
la
n
c
e
e
qua
ti
ons
,
pr
e
s
s
ur
e
dyna
m
ic
s
,
s
to
c
ha
s
ti
c
he
a
t
in
put
m
ode
li
ng,
a
nd
a
dva
nc
e
d
c
ont
r
ol
s
tr
a
te
gi
e
s
,
opt
im
iz
e
d
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
pe
r
f
or
m
a
nc
e
a
nd
de
ve
lo
pe
d a
r
obus
t
s
y
s
te
m
c
a
pa
bl
e
of
ha
ndl
in
g r
e
a
l
-
w
or
ld
unc
e
r
ta
in
ti
e
s
.
3.1.
M
at
h
e
m
at
ic
al
m
od
e
ll
in
g
A
c
om
pr
e
he
ns
iv
e
m
a
th
e
m
a
ti
c
a
l
m
ode
l
of
t
he
boi
le
r
s
ys
te
m
i
s
d
e
ve
lo
pe
d, i
nc
or
por
a
ti
ng t
he
dyna
m
ic
s
of
he
a
t
tr
a
ns
f
e
r
, f
lu
id
f
lo
w
, a
nd pr
e
s
s
ur
e
c
ha
nge
s
.
T
he
m
ode
l
in
c
lu
de
s
a
s
f
ol
lo
w
s
:
‒
E
ne
r
gy
ba
la
nc
e
e
qua
ti
ons
:
th
e
s
e
e
qua
ti
ons
a
c
c
ount
f
or
th
e
h
e
a
t
in
put
,
he
a
t
lo
s
s
,
a
nd
he
a
t
e
xc
ha
nge
w
it
hi
n t
he
boi
le
r
c
om
pone
nt
s
.
‒
M
a
s
s
ba
la
nc
e
e
qua
ti
ons
:
th
e
s
e
e
qu
a
ti
ons
de
s
c
r
ib
e
th
e
f
lo
w
r
a
te
s
of
w
a
te
r
a
nd
s
te
a
m
,
e
ns
ur
in
g
th
e
c
ons
e
r
va
ti
on of
m
a
s
s
.
‒
P
r
e
s
s
ur
e
dyna
m
ic
s
:
r
e
la
ti
ons
hi
p
s
be
twe
e
n pr
e
s
s
ur
e
, t
e
m
pe
r
a
tu
r
e
, a
nd volum
e
i
n t
he
dr
um
a
r
e
m
ode
le
d t
o
c
a
pt
ur
e
pr
e
s
s
ur
e
f
lu
c
tu
a
ti
ons
a
c
c
ur
a
te
ly
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
:
2979
-
2990
2982
‒
S
to
c
ha
s
ti
c
he
a
t
in
put
:
th
e
he
a
t
in
put
is
m
ode
ll
e
d
a
s
a
s
to
c
ha
s
ti
c
pr
oc
e
s
s
,
us
in
g
pr
oba
bi
li
s
ti
c
m
e
th
ods
to
r
e
pr
e
s
e
nt
r
a
ndom va
r
ia
ti
ons
i
n he
a
t
s
uppl
y due
t
o f
a
c
to
r
s
l
ik
e
f
u
e
l
qua
li
ty
a
nd c
om
bus
ti
on c
ondi
ti
ons
.
3.
1
.1.
F
u
r
n
ac
e
T
he
f
ur
na
c
e
is
w
he
r
e
th
e
f
ue
l
is
c
om
bu
s
te
d
to
ge
ne
r
a
te
he
a
t.
T
he
e
ne
r
gy
ba
la
nc
e
f
or
th
e
f
ur
na
c
e
c
a
n
be
e
xpr
e
s
s
e
d a
s
gi
ve
n i
n
(
1
)
.
=
+
(
1)
W
he
r
e
is
th
e
he
a
t
in
put
f
r
om
th
e
c
om
bus
ti
on
of
f
ue
l
;
is
th
e
he
a
t
tr
a
ns
f
e
r
r
e
d
to
th
e
w
a
te
r
a
nd
s
te
a
m
in
t
he
boi
le
r
;
a
nd
is
t
he
he
a
t
lo
s
t
to
t
he
s
ur
r
oundings
(
e
.g. t
hr
ou
gh t
he
boi
le
r
w
a
ll
s
, f
lu
e
ga
s
e
s
)
.
3.
1
.2.
D
r
u
m
T
he
dr
um
is
w
he
r
e
th
e
pha
s
e
c
ha
ng
e
of
w
a
te
r
to
s
te
a
m
o
c
c
ur
s
.
T
he
e
ne
r
gy
ba
la
nc
e
f
or
th
e
dr
um
is
gi
ve
n i
n
(
2
)
.
=
,
−
,
(
2
)
W
he
r
e
is
th
e
m
a
s
s
of
w
a
te
r
in
th
e
d
r
um
;
is
th
e
s
pe
c
if
ic
he
a
t
c
a
pa
c
it
y
of
w
a
te
r
;
is
th
e
r
a
te
of
c
ha
nge
of
w
a
te
r
te
m
pe
r
a
tu
r
e
;
,
is
th
e
he
a
t
in
put
to
th
e
dr
u
m
f
r
om
th
e
f
u
r
na
c
e
;
a
nd
,
is
th
e
he
a
t
tr
a
ns
f
e
r
f
r
om
t
he
dr
um
t
o pr
oduc
e
s
te
a
m
.
3.
1
.
3
.
Wat
e
r
/s
t
e
am
p
at
h
w
ays
T
he
w
a
te
r
a
nd
s
te
a
m
p
a
th
w
a
ys
in
vol
ve
h
e
a
t
tr
a
ns
f
e
r
f
r
om
th
e
w
a
te
r
to
s
te
a
m
.
T
he
e
ne
r
gy
b
a
la
nc
e
c
a
n be
e
xpr
e
s
s
e
d a
s
gi
ve
n i
n (
3)
. W
a
te
r
t
o s
te
a
m
c
onve
r
s
io
n:
ℎ
=
ℎ
+
,
(
3
)
W
he
r
e
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
w
a
te
r
;
ℎ
is
th
e
s
p
e
c
if
ic
e
nt
ha
lp
y
of
w
a
te
r
;
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
s
te
a
m
;
ℎ
is
t
he
s
pe
c
if
ic
e
nt
ha
lp
y of
s
te
a
m
;
a
nd
,
is
t
he
he
a
t
lo
s
s
i
n
w
a
te
r
-
to
-
s
te
a
m
c
onve
r
s
io
n pr
oc
e
s
s
.
3.
1
.
4
.
H
e
at
e
xc
h
an
ge
w
it
h
in
b
oi
le
r
T
he
he
a
t
e
x
c
ha
nge
w
it
hi
n t
he
boi
le
r
i
s
a
s
gi
ve
n i
n
(
4
)
.
,
=
(
−
)
(
4
)
W
he
r
e
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
w
a
te
r
;
is
th
e
s
pe
c
if
ic
he
a
t
c
a
pa
c
it
y
of
w
a
te
r
;
is
th
e
out
le
t
te
m
pe
r
a
tu
r
e
of
w
a
te
r
/s
te
a
m
;
a
nd
is
t
he
i
nl
e
t
te
m
pe
r
a
tu
r
e
of
w
a
te
r
.
3.
1
.
5
.
O
ve
r
al
l
e
n
e
r
gy b
al
an
c
e
C
om
bi
ni
ng
th
e
a
bove
c
om
pone
nt
s
,
th
e
ove
r
a
ll
e
n
e
r
gy
ba
la
nc
e
e
qua
ti
on
f
or
th
e
boi
le
r
s
ys
t
e
m
c
a
n
be
w
r
it
te
n a
s
gi
ve
n i
n
(
5
)
.
−
=
+
ℎ
(
5
)
W
he
r
e
is
t
he
t
ot
a
l
he
a
t
in
put
f
r
om
f
ue
l
c
om
bus
ti
on
;
I
nc
lu
de
s
a
ll
f
or
m
s
of
he
a
t
lo
s
s
(
to
s
ur
r
oundings
,
in
e
f
f
ic
ie
nc
ie
s
)
;
r
e
pr
e
s
e
nt
s
t
he
c
h
a
nge
i
n i
nt
e
r
na
l
e
ne
r
gy of
w
a
t
e
r
i
n t
he
dr
um
;
a
nd
ℎ
is
t
he
he
a
t
r
e
qui
r
e
d t
o c
onve
r
t
w
a
te
r
t
o s
te
a
m
.
S
to
c
ha
s
ti
c
he
a
t
in
put
:
to
a
c
c
ount
f
or
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
o
ns
,
th
e
he
a
t
in
put
c
a
n
be
m
ode
ll
e
d
a
s
gi
ve
n i
n (
6)
.
=
̅
+
(
)
(
6
)
W
he
r
e
̅
is
th
e
a
ve
r
a
ge
he
a
t
in
put
;
a
nd
(
)
is
a
s
to
c
ha
s
ti
c
te
r
m
r
e
pr
e
s
e
nt
in
g
r
a
ndom
f
lu
c
tu
a
ti
ons
in
he
a
t
in
put
, w
hi
c
h c
a
n be
m
ode
ll
e
d us
in
g
s
to
c
ha
s
ti
c
pr
oc
e
s
s
e
s
.
3.2.
M
as
s
b
al
an
c
e
e
q
u
at
io
n
s
f
or
a
f
u
r
n
ac
e
-
f
ir
e
d
d
r
u
m
b
oi
le
r
T
he
m
a
s
s
ba
la
nc
e
e
qua
ti
on
s
f
or
a
f
ur
na
c
e
-
f
ir
e
d
dr
um
boi
le
r
in
vol
ve
tr
a
c
ki
ng
th
e
f
lo
w
r
a
te
s
of
w
a
te
r
a
nd s
te
a
m
t
o e
ns
ur
e
c
ons
e
r
va
ti
on of
m
a
s
s
t
hr
oughout t
he
s
ys
te
m
.
T
he
f
ol
lo
w
in
g
a
r
e
t
he
de
ta
il
e
d m
a
s
s
ba
la
nc
e
e
qua
ti
ons
f
or
t
he
ke
y c
om
pone
nt
s
of
t
he
boi
le
r
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
at
io
n c
ont
r
ol
de
s
ig
n and
s
imul
at
io
n of
f
ur
nac
e
-
fi
r
e
d boi
le
r
e
x
it
…
(
G
ani
y
at
A
bi
odun Salaw
u
)
2983
3.2.1.
D
r
u
m
m
a
s
s
b
al
an
c
e
T
he
dr
um
is
w
he
r
e
w
a
te
r
is
c
onve
r
te
d
in
to
s
te
a
m
.
T
he
m
a
s
s
ba
la
nc
e
e
qua
ti
on
f
or
th
e
dr
u
m
c
a
n
be
w
r
it
te
n a
s
(
7)
.
(
,
+
,
)
=
̇
,
−
̇
,
(
7
)
W
he
r
e
,
is
th
e
m
a
s
s
of
w
a
te
r
in
th
e
dr
um
;
,
is
th
e
m
a
s
s
of
s
te
a
m
in
th
e
dr
um
;
̇
,
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
w
a
te
r
e
nt
e
r
in
g t
he
dr
um
;
a
nd
̇
,
is
t
he
m
a
s
s
f
lo
w
r
a
te
of
s
te
a
m
l
e
a
vi
ng t
he
dr
um
.
A
s
s
um
in
g s
te
a
dy
-
s
ta
te
c
ondi
ti
ons
w
h
e
r
e
t
he
a
c
c
um
ul
a
ti
on t
e
r
m
.
(
,
+
,
)
=
0
̇
,
=
̇
,
(
8
)
3.2.2.
Wat
e
r
/f
e
e
d
w
at
e
r
m
as
s
b
al
an
c
e
T
he
f
e
e
dw
a
te
r
s
y
s
te
m
s
uppl
ie
s
w
a
te
r
to
th
e
dr
um
.
T
he
m
a
s
s
ba
la
nc
e
e
qua
ti
on
f
or
th
e
f
e
e
dw
a
te
r
s
ys
te
m
a
s
in
(
9)
.
̇
,
=
̇
,
+
̇
(
9
)
W
he
r
e
̇
,
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
f
e
e
d
w
a
te
r
e
nt
e
r
in
g
th
e
s
ys
te
m
;
̇
,
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
f
e
e
d
-
w
a
te
r
e
nt
e
r
in
g
th
e
dr
um
;
a
nd
̇
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
bl
ow
dow
n,
w
hi
c
h
is
w
a
te
r
r
e
m
ove
d
to
c
ont
r
ol
t
he
c
onc
e
nt
r
a
ti
on of
i
m
pur
it
ie
s
.
3.2.
3
.
S
t
e
am
m
as
s
b
al
an
c
e
T
he
s
te
a
m
s
ys
t
e
m
in
vol
ve
s
th
e
ge
ne
r
a
ti
on
a
nd
ut
il
iz
a
ti
on
o
f
s
t
e
a
m
.
T
he
m
a
s
s
ba
la
nc
e
e
qua
ti
on
f
or
th
e
s
te
a
m
s
y
s
te
m
a
s
in
(
10)
.
̇
,
=
̇
,
+
̇
,
(
10
)
W
he
r
e
̇
,
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
s
te
a
m
ge
ne
r
a
te
d
in
th
e
dr
um
;
̇
,
is
th
e
m
a
s
s
f
lo
w
r
a
te
of
s
t
e
a
m
e
xi
ti
ng t
he
s
ys
te
m
(
to
t
ur
bi
ne
)
;
a
nd
̇
,
is
t
he
m
a
s
s
f
lo
w
r
a
te
of
s
te
a
m
l
os
t
th
r
ough le
a
ks
.
3.2.
4
.
O
ve
r
al
l
m
as
s
b
al
an
c
e
C
om
bi
ni
ng
th
e
m
a
s
s
ba
la
nc
e
e
qua
ti
ons
f
or
th
e
dr
um
,
f
e
e
dw
a
te
r
,
a
nd
s
te
a
m
s
ys
te
m
s
e
n
s
ur
e
s
th
e
c
ons
e
r
va
ti
on
of
m
a
s
s
th
r
oughout
th
e
e
nt
ir
e
boi
le
r
s
y
s
te
m
.
T
he
ove
r
a
ll
m
a
s
s
ba
la
n
c
e
c
a
n
be
e
xpr
e
s
s
e
d
a
s
f
ol
lo
w
s
:
̇
,
=
̇
,
+
̇
̇
,
=
̇
,
̇
,
=
̇
,
̇
,
=
̇
,
+
̇
,
F
or
a
s
im
pl
if
ie
d, s
te
a
dy
-
s
ta
te
a
na
ly
s
i
s
w
it
hout
c
ons
id
e
r
in
g bl
ow
dow
n a
nd l
e
a
ks
, gi
ve
a
s
i
n (
11)
.
̇
,
=
̇
,
(
11
)
T
he
s
e
e
qua
ti
on
s
e
n
s
ur
e
th
a
t
th
e
m
a
s
s
f
lo
w
r
a
te
s
of
w
a
te
r
a
n
d
s
te
a
m
a
r
e
ba
la
n
c
e
d
th
r
oughout
th
e
s
ys
te
m
, m
a
in
ta
in
in
g c
ons
e
r
va
ti
on of
m
a
s
s
. T
he
y f
or
m
t
he
ba
s
is
f
or
a
na
ly
z
in
g t
he
boi
le
r
'
s
pe
r
f
or
m
a
nc
e
a
nd f
o
r
de
s
ig
ni
ng
c
ont
r
ol
s
tr
a
te
gi
e
s
to
r
e
gul
a
te
f
lo
w
r
a
te
s
a
nd
m
a
in
ta
in
s
ys
te
m
s
ta
bi
li
ty
unde
r
va
r
yi
ng
ope
r
a
ti
ona
l
c
ondi
ti
ons
.
T
h
e
c
om
pl
e
te
S
im
ul
in
k
m
ode
l
of
th
e
f
ur
na
c
e
-
f
ir
e
boi
le
r
is
a
s
s
how
n
in
F
ig
ur
e
1.
T
he
M
A
T
L
A
B
/
S
im
ul
in
k
m
ode
l
of
a
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
is
di
vi
de
d
in
to
th
r
e
e
ke
y
f
ig
ur
e
s
th
a
t
r
e
pr
e
s
e
nt
di
f
f
e
r
e
nt
a
s
pe
c
ts
of
th
e
s
ys
te
m
’
s
ope
r
a
ti
on.
F
ig
ur
e
1(
a
)
f
oc
u
s
e
s
on
th
e
w
a
te
r
f
lo
w
s
ubs
y
s
te
m
,
s
ho
w
in
g
how
w
a
te
r
e
nt
e
r
s
t
he
boi
le
r
, unde
r
goe
s
he
a
t
e
xc
ha
nge
, a
nd i
s
r
e
gul
a
te
d t
o m
a
in
ta
in
c
ons
is
te
nt
i
nput
f
or
s
te
a
m
ge
ne
r
a
ti
on.
F
ig
ur
e
1(
b)
m
ode
ls
th
e
s
te
a
m
f
lo
w
s
ubs
ys
te
m
,
de
ta
il
in
g
how
s
te
a
m
is
ge
ne
r
a
te
d,
c
ont
r
ol
le
d
f
or
pr
e
s
s
ur
e
s
ta
bi
li
ty
,
a
nd
r
e
le
a
s
e
d
f
r
om
th
e
s
y
s
te
m
.
F
in
a
ll
y,
F
ig
ur
e
1(
c
)
pr
e
s
e
nt
s
th
e
in
te
gr
a
te
d
boi
le
r
s
ys
te
m
,
c
om
bi
ni
ng
bot
h
w
a
te
r
a
nd
s
te
a
m
s
ub
s
ys
te
m
s
to
m
a
in
ta
in
m
a
s
s
a
nd
e
n
e
r
gy
ba
la
nc
e
s
,
w
hi
le
in
c
or
por
a
ti
ng
a
dva
n
c
e
d
c
ont
r
ol
s
tr
a
te
gi
e
s
li
ke
M
P
C
to
opt
im
iz
e
pe
r
f
or
m
a
nc
e
.
T
oge
t
he
r
,
th
e
s
e
f
ig
ur
e
s
pr
ovi
de
a
c
om
pr
e
he
ns
iv
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
:
2979
-
2990
2984
s
im
ul
a
ti
on
of
th
e
boi
le
r
’
s
dyna
m
ic
be
ha
vi
or
,
a
ll
ow
in
g
f
or
a
n
a
ly
s
is
a
nd
c
ont
r
ol
unde
r
va
r
yi
ng
ope
r
a
ti
ona
l
c
ondi
ti
ons
.
(
a
)
(
b)
(
c
)
F
ig
ur
e
1. M
A
T
L
A
B
S
im
ul
in
k m
ode
l
of
a
f
ur
na
c
e
f
ir
e
d
boi
le
r
of
(
a
)
s
ub
-
s
ubm
ode
l
of
i
nt
e
r
na
l
s
te
a
m
vol
um
e
te
m
pe
r
a
tu
r
e
r
e
gul
a
ti
on, (
b)
s
ubm
ode
l
of
s
te
a
m
vol
um
e
a
nd t
e
m
pe
r
a
tu
r
e
r
e
gul
a
ti
on, a
nd (
c
)
m
ode
l
of
t
he
f
ur
na
c
e
f
ir
e
d boil
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
at
io
n c
ont
r
ol
de
s
ig
n and
s
imul
at
io
n of
f
ur
nac
e
-
fi
r
e
d boi
le
r
e
x
it
…
(
G
ani
y
at
A
bi
odun Salaw
u
)
2985
3.
3
.
P
ar
am
e
t
e
r
e
s
t
im
at
io
n
S
ys
te
m
id
e
nt
if
ic
a
ti
on
te
c
hni
que
w
a
s
e
m
pl
oye
d
to
e
s
ti
m
a
te
t
he
pa
r
a
m
e
te
r
s
of
th
e
m
a
th
e
m
a
ti
c
a
l
m
ode
l.
T
hi
s
pr
oc
e
s
s
in
vol
ve
s
two
m
a
in
s
te
ps
.
F
ir
s
t,
da
ta
c
ol
l
e
c
ti
on
is
c
a
r
r
ie
d
out
by
c
ol
le
c
ti
ng
ope
r
a
ti
ona
l
da
ta
f
r
om
th
e
boi
le
r
,
in
c
lu
di
ng
te
m
pe
r
a
tu
r
e
,
pr
e
s
s
ur
e
,
f
lo
w
r
a
te
s
,
a
nd
he
a
t
in
put
.
S
e
c
ond,
pa
r
a
m
e
te
r
f
it
ti
ng
is
pe
r
f
or
m
e
d
us
in
g
opt
im
iz
a
ti
on
a
lg
or
it
h
m
s
to
f
it
th
e
m
ode
l
pa
r
a
m
e
te
r
s
w
it
h
th
e
c
ol
le
c
te
d
da
ta
,
e
ns
ur
in
g
th
e
m
ode
l
a
c
c
ur
a
te
ly
r
e
f
le
c
ts
t
he
r
e
a
l
s
ys
te
m
be
h
a
vi
or
.
3.4. Con
t
r
ol
s
t
r
at
e
gy d
e
s
ig
n
3.4.1. Cont
r
ol
ob
j
e
c
t
iv
e
s
T
he
pr
im
a
r
y
obj
e
c
ti
ve
is
to
m
a
in
ta
in
s
ta
bl
e
e
xi
t
pr
e
s
s
ur
e
w
it
hi
n
de
s
ir
e
d
li
m
it
s
,
m
in
im
iz
e
th
e
im
pa
c
t
of
s
to
c
ha
s
ti
c
h
e
a
t
f
lu
c
tu
a
ti
ons
,
a
nd
opt
im
iz
e
f
ue
l
e
f
f
ic
ie
nc
y.
T
h
e
f
or
e
m
os
t
goa
l
of
th
e
s
ys
te
m
i
s
to
e
n
s
ur
e
th
a
t
th
e
e
xi
t
pr
e
s
s
ur
e
r
e
m
a
in
s
c
ons
is
te
nt
ly
w
it
hi
n t
he
de
s
ir
e
d ope
r
a
ti
ona
l
r
a
nge
. M
a
in
ta
in
in
g s
ta
bl
e
e
xi
t
pr
e
s
s
ur
e
i
s
c
r
it
ic
a
l
to
th
e
ove
r
a
ll
pe
r
f
o
r
m
a
nc
e
a
nd
s
a
f
e
ty
of
th
e
r
m
a
l
o
r
f
lu
id
s
ys
te
m
s
,
a
s
f
lu
c
tu
a
ti
ons
c
a
n
le
a
d
to
m
e
c
ha
ni
c
a
l
s
tr
e
s
s
,
r
e
duc
e
d
s
ys
t
e
m
li
f
e
s
pa
n,
or
ope
r
a
ti
ona
l
in
e
f
f
ic
ie
nc
ie
s
.
T
he
r
e
f
or
e
,
pr
e
c
is
e
c
ont
r
ol
m
e
c
ha
ni
s
m
s
m
u
s
t
be
im
pl
e
m
e
nt
e
d
to
m
oni
to
r
a
nd
r
e
gul
a
te
th
e
pr
e
s
s
ur
e
out
put
unde
r
va
r
yi
ng
lo
a
d
a
nd
de
m
a
nd c
ondi
ti
ons
.
A
not
he
r
im
por
ta
nt
obj
e
c
ti
ve
is
to
m
in
im
iz
e
th
e
in
f
lu
e
nc
e
of
r
a
ndom
or
unpr
e
di
c
ta
bl
e
he
a
t
f
lu
c
tu
a
ti
ons
,
w
hi
c
h
c
a
n
a
r
is
e
due
to
e
xt
e
r
na
l
e
nvi
r
onm
e
nt
a
l
f
a
c
to
r
s
,
va
r
ia
bl
e
in
put
s
our
c
e
s
,
or
s
ys
te
m
dyna
m
ic
s
.
T
he
s
e
s
to
c
ha
s
ti
c
he
a
t
va
r
ia
ti
ons
c
a
n
di
s
r
upt
th
e
r
m
a
l
s
ta
bi
li
ty
,
a
f
f
e
c
t
pr
oc
e
s
s
c
ons
i
s
te
nc
y,
a
nd
le
a
d
to
une
ve
n
e
ne
r
gy
di
s
tr
ib
ut
io
n.
B
y
r
e
duc
in
g
th
e
i
m
pa
c
t
of
s
uc
h
di
s
tu
r
ba
nc
e
s
,
th
e
s
ys
te
m
c
a
n
ope
r
a
te
m
or
e
r
e
li
a
bl
y a
nd r
e
s
pond mor
e
e
f
f
e
c
ti
ve
ly
t
o r
e
a
l
-
ti
m
e
c
ha
nge
s
.
F
in
a
ll
y,
th
e
s
ys
te
m
a
im
s
to
e
nha
nc
e
ove
r
a
ll
f
ue
l
e
f
f
ic
ie
nc
y
b
y
opt
im
iz
in
g
th
e
e
ne
r
gy
c
onve
r
s
io
n
pr
oc
e
s
s
.
E
f
f
ic
ie
nt
f
ue
l
us
a
ge
not
onl
y
lo
w
e
r
s
ope
r
a
ti
ona
l
c
os
ts
but
a
ls
o
r
e
duc
e
s
e
m
is
s
io
ns
a
nd
s
uppor
ts
s
us
ta
in
a
bl
e
e
ne
r
gy
pr
a
c
ti
c
e
s
.
A
c
hi
e
vi
ng
th
is
r
e
qui
r
e
s
in
te
ll
ig
e
n
t
c
ont
r
ol
s
tr
a
te
gi
e
s
th
a
t
ba
la
nc
e
th
e
r
m
a
l
in
put
w
it
h
e
ne
r
gy
de
m
a
nd,
e
ns
ur
in
g
m
in
im
a
l
w
a
s
te
w
hi
le
m
a
in
ta
in
in
g
pe
r
f
or
m
a
nc
e
a
nd
r
e
gul
a
to
r
y
c
om
pl
ia
nc
e
.
T
oge
th
e
r
,
th
e
s
e
obj
e
c
ti
ve
s
s
uppor
t
a
hi
gh
-
pe
r
f
or
m
a
nc
e
,
e
ne
r
gy
-
c
ons
c
io
us
s
y
s
te
m
c
a
pa
bl
e
of
a
da
pt
in
g
to
dyna
m
ic
c
ondi
ti
ons
.
3.4.2. M
od
e
l
p
r
e
d
ic
t
iv
e
c
on
t
r
ol
A
n
M
P
C
s
tr
a
te
gy
is
de
s
ig
ne
d
to
ha
ndl
e
s
to
c
h
a
s
ti
c
di
s
tu
r
ba
nc
e
s
a
nd
m
a
in
ta
in
d
e
s
ir
e
d
pr
e
s
s
ur
e
le
v
e
ls
a
s
gi
ve
n i
n t
he
M
A
T
L
A
B
c
ode
.
‒
M
P
C
f
or
m
ul
a
ti
on:
t
he
obj
e
c
ti
ve
f
unc
ti
on, p
r
e
di
c
ti
on hor
iz
on, a
nd c
ons
tr
a
in
ts
f
or
t
he
M
P
C
pr
obl
e
m
w
e
r
e
de
f
in
e
d.
T
he
obj
e
c
ti
ve
f
unc
ti
on
a
im
s
to
m
in
im
iz
e
th
e
de
vi
a
ti
on
of
th
e
e
xi
t
pr
e
s
s
ur
e
f
r
om
th
e
s
e
t
-
poi
nt
w
hi
le
c
ons
id
e
r
in
g c
ont
r
ol
e
f
f
or
t.
‒
S
ta
te
-
s
pa
c
e
r
e
pr
e
s
e
nt
a
ti
on:
c
onve
r
t
th
e
boi
le
r
m
ode
l
in
to
a
s
ta
te
-
s
pa
c
e
f
or
m
s
ui
ta
bl
e
f
or
M
P
C
de
s
ig
n.
‒
O
pt
im
iz
a
ti
on
a
lg
or
it
hm
:
a
n
opt
im
iz
a
ti
on
a
lg
or
it
hm
w
a
s
im
pl
e
m
e
nt
e
d
to
s
ol
ve
th
e
M
P
C
pr
obl
e
m
in
r
e
a
l
-
ti
m
e
, a
dj
us
ti
ng c
ont
r
ol
i
nput
s
ba
s
e
d on pr
e
di
c
te
d
s
ys
te
m
be
h
a
vi
our
.
3.5. S
im
u
la
t
io
n
s
t
u
d
y
I
n t
hi
s
s
tu
dy, t
he
pe
r
f
or
m
a
nc
e
of
M
P
C
s
tr
a
te
gy w
a
s
i
nve
s
ti
ga
te
d, f
or
m
a
na
gi
ng t
he
e
xi
t
pr
e
s
s
ur
e
of
a
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
unde
r
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
ons
. T
he
s
ys
t
e
m
w
a
s
m
ode
le
d
us
in
g
c
om
pr
e
he
n
s
iv
e
e
n
e
r
gy
a
nd
m
a
s
s
ba
la
nc
e
e
qua
ti
ons
,
in
c
or
por
a
ti
ng
s
to
c
ha
s
ti
c
e
le
m
e
n
ts
to
s
im
ul
a
te
r
a
ndom
h
e
a
t
in
put
va
r
ia
ti
ons
.
M
A
T
L
A
B
/S
im
ul
in
k
w
a
s
u
s
e
d
to
m
ode
l
th
e
boi
le
r
s
ys
t
e
m
a
nd
i
m
pl
e
m
e
nt
c
ont
r
ol
a
lg
or
it
hm
s
.
T
he
s
im
ul
a
ti
on
s
w
e
r
e
c
onduc
te
d
us
in
g
M
A
T
L
A
B
/S
im
ul
in
k,
a
nd
va
r
io
us
ope
r
a
ti
ng
s
c
e
na
r
io
s
w
e
r
e
a
na
ly
z
e
d
to
e
va
lu
a
te
th
e
e
f
f
e
c
ti
ve
ne
s
s
of
t
he
c
ont
r
ol
s
tr
a
te
gy.
4.
R
E
S
U
L
T
S
A
N
D
D
I
S
C
U
S
S
I
O
N
4.1. S
im
u
la
t
io
n
r
e
s
u
lt
s
S
im
ul
a
ti
on
w
a
s
c
a
r
r
ie
d
out
in
M
A
T
L
A
B
e
nvi
r
onm
e
nt
.
T
he
M
P
C
s
tr
a
te
gy
de
m
ons
tr
a
te
d
e
xc
e
ll
e
nt
pr
e
s
s
ur
e
s
ta
bi
li
ty
,
m
a
in
ta
in
in
g
th
e
e
xi
t
pr
e
s
s
ur
e
w
it
hi
n
±1.5%
of
th
e
s
e
t
-
poi
nt
de
s
pi
te
s
ig
ni
f
ic
a
nt
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
ons
.
T
h
e
pr
e
di
c
ti
ve
na
tu
r
e
of
M
P
C
a
ll
ow
e
d
it
to
a
nt
ic
ip
a
te
di
s
tu
r
ba
nc
e
s
a
nd
a
dj
u
s
t
c
ont
r
ol
a
c
ti
ons
pr
oa
c
ti
ve
ly
a
s
s
how
n
in
F
ig
ur
e
2,
w
hi
c
h
is
th
e
f
e
e
d
w
a
te
r
a
c
tu
a
ti
on
s
ig
na
l
in
kg/
s
a
nd
th
e
he
a
t
a
c
tu
a
ti
on s
ig
na
l
in
F
ig
ur
e
3.
F
ig
ur
e
4
s
how
s
th
e
h
e
a
t
di
s
tu
r
ba
nc
e
in
k
J
. T
he
di
s
tu
r
ba
nc
e
va
r
ie
s
by a
s
m
uc
h
a
s
50%
of
th
e
nom
in
a
l
he
a
t
va
lu
e
.
F
ig
ur
e
5
s
how
s
th
e
c
or
r
e
s
ponding
dr
um
pr
e
s
s
ur
e
in
kP
a
.
T
he
pr
e
s
s
ur
e
va
r
ie
s
by
a
bout
1%
of
th
e
nom
in
a
l
va
lu
e
e
ve
n t
hough the
di
s
tu
r
ba
nc
e
i
s
r
e
la
ti
ve
ly
l
a
r
ge
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
-
8938
I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
:
2979
-
2990
2986
F
ig
ur
e
2. F
e
e
d w
a
te
r
a
c
tu
a
ti
on s
ig
na
l
F
ig
ur
e
3
.
H
e
a
t
a
c
tu
a
ti
on s
ig
na
l
in
kJ
T
he
M
P
C
e
xhi
bi
te
d
a
r
a
pi
d
r
e
s
pon
s
e
ti
m
e
,
s
ta
bi
li
z
in
g
pr
e
s
s
ur
e
f
lu
c
tu
a
ti
ons
w
it
hi
n
5
s
e
c
onds
of
di
s
tu
r
ba
nc
e
ons
e
t.
T
he
opt
im
iz
a
ti
on
a
lg
or
it
hm
e
f
f
ic
ie
nt
ly
a
d
ju
s
te
d
c
ont
r
ol
a
c
ti
ons
ba
s
e
d
on
f
ut
ur
e
s
ta
t
e
pr
e
di
c
ti
ons
.
M
P
C
im
pr
ove
d
f
ue
l
e
f
f
ic
ie
nc
y
by
a
ppr
oxi
m
a
te
ly
6%
c
om
pa
r
e
d
to
tr
a
di
ti
ona
l
P
I
D
c
ont
r
ol
.
I
ts
a
bi
li
ty
to
opt
im
iz
e
th
e
c
om
bus
ti
on
pr
oc
e
s
s
a
nd
r
e
duc
e
unn
e
c
e
s
s
a
r
y
f
ue
l
us
a
ge
w
a
s
e
vi
d
e
nt
.
M
P
C
w
a
s
r
obus
t
to
m
ode
r
a
te
s
to
c
ha
s
ti
c
di
s
tu
r
ba
nc
e
s
but
s
how
e
d
s
om
e
pe
r
f
or
m
a
nc
e
de
gr
a
da
ti
on
unde
r
e
xt
r
e
m
e
f
lu
c
tu
a
ti
ons
.
I
ts
r
e
li
a
nc
e
on
a
c
c
ur
a
te
pr
e
di
c
ti
ons
a
nd
m
ode
l
f
id
e
li
ty
li
m
it
s
it
s
r
obus
tn
e
s
s
in
hi
ghl
y
unp
r
e
di
c
ta
bl
e
e
nvi
r
onm
e
nt
s
.
T
he
s
tu
dy
und
e
r
s
c
or
e
s
th
e
im
por
ta
nc
e
of
e
m
pl
oyi
ng
c
ont
r
ol
s
tr
a
te
gy
f
or
m
a
na
gi
ng
e
xi
t
pr
e
s
s
ur
e
in
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
s
.
M
P
C
c
ont
r
ol
s
tr
a
te
gy
s
ig
ni
f
ic
a
nt
ly
im
pr
ove
d
s
ys
te
m
pe
r
f
or
m
a
nc
e
by
e
nha
nc
in
g pr
e
s
s
ur
e
s
ta
bi
li
ty
, r
e
s
pons
e
t
im
e
, f
ue
l
e
f
f
ic
ie
nc
y,
a
nd
r
obus
tn
e
s
s
t
o di
s
tu
r
ba
nc
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
A
r
ti
f
I
nt
e
ll
I
S
S
N
:
2252
-
8938
O
pt
imi
z
at
io
n c
ont
r
ol
de
s
ig
n and
s
imul
at
io
n of
f
ur
nac
e
-
fi
r
e
d boi
le
r
e
x
it
…
(
G
ani
y
at
A
bi
odun Salaw
u
)
2987
F
ig
ur
e
4. H
e
a
t
di
s
tu
r
ba
nc
e
F
ig
ur
e
5. D
r
um
pr
e
s
s
ur
e
4.2. Dis
c
u
s
s
io
n
o
f
f
in
d
in
gs
T
he
r
e
s
e
a
r
c
h
pr
e
s
e
nt
e
d
in
th
is
pa
pe
r
de
m
ons
tr
a
te
s
th
e
e
f
f
ic
a
c
y
of
a
s
to
c
ha
s
ti
c
c
ont
r
ol
s
tr
a
te
gy,
s
pe
c
if
ic
a
ll
y
M
P
C
,
in
m
a
na
gi
ng
th
e
dow
ns
tr
e
a
m
e
xi
t
pr
e
s
s
ur
e
o
f
f
ur
na
c
e
-
f
i
r
e
d
dr
um
boi
le
r
s
unde
r
c
ondi
ti
ons
of
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
ons
.
T
hi
s
s
e
c
ti
on
de
lv
e
s
in
to
th
e
im
pl
ic
a
ti
ons
of
th
e
f
in
di
ngs
,
th
e
a
dva
nt
a
ge
s
a
nd
li
m
it
a
ti
ons
of
th
e
pr
opos
e
d
a
ppr
oa
c
h,
c
om
pa
r
is
ons
w
it
h
tr
a
di
ti
ona
l
c
ont
r
ol
m
e
th
ods
,
a
nd
th
e
br
oa
d
e
r
im
pa
c
t
on i
ndus
tr
ia
l
boi
le
r
ope
r
a
ti
on.
4.2.1. S
ig
n
if
ic
an
c
e
of
t
h
e
r
e
s
u
lt
s
T
he
s
im
ul
a
ti
on
r
e
s
ul
ts
s
how
th
a
t
th
e
M
P
C
s
tr
a
te
gy
s
ig
ni
f
ic
a
nt
ly
im
pr
ove
s
th
e
s
ta
bi
li
ty
a
nd
pe
r
f
or
m
a
nc
e
of
f
ur
na
c
e
-
f
ir
e
d
d
r
um
boi
le
r
s
c
om
pa
r
e
d
to
tr
a
di
t
io
na
l
P
I
D
m
e
th
ods
.
M
P
C
e
nha
nc
e
s
pr
e
s
s
ur
e
s
ta
bi
li
ty
by
m
a
in
ta
in
in
g
th
e
e
xi
t
pr
e
s
s
ur
e
c
lo
s
e
to
th
e
s
e
t
poi
nt
,
e
ve
n
w
it
h
r
a
ndom
he
a
t
in
put
f
lu
c
tu
a
ti
ons
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2252
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I
nt
J
A
r
ti
f
I
nt
e
ll
,
V
ol
.
14
, N
o.
4
,
A
ugus
t
2025
:
2979
-
2990
2988
e
ns
ur
in
g
e
f
f
ic
ie
nt
a
nd
s
a
f
e
boi
le
r
ope
r
a
ti
on.
I
t
a
ls
o
opt
im
iz
e
s
r
e
a
l
-
ti
m
e
c
ont
r
ol
a
c
ti
on
s
,
im
pr
ovi
ng
f
ue
l
e
f
f
ic
ie
nc
y
a
nd
r
e
duc
in
g
op
e
r
a
ti
ona
l
c
os
t
s
.
A
ddi
ti
ona
ll
y,
M
P
C
'
s
in
c
or
por
a
ti
on
of
s
to
c
ha
s
ti
c
m
ode
li
ng
m
a
k
e
s
th
e
s
ys
te
m
r
obu
s
t
to
unc
e
r
ta
in
ti
e
s
in
he
a
t
tr
a
n
s
f
e
r
a
nd
c
om
bus
ti
on,
w
hi
c
h
is
e
s
s
e
nt
ia
l
in
unpr
e
di
c
ta
bl
e
in
dus
tr
ia
l
e
nvi
r
onm
e
nt
s
.
4.2.2. Ad
van
t
age
s
ove
r
t
r
ad
it
io
n
al
P
I
D
c
on
t
r
ol
T
he
r
e
s
e
a
r
c
h
d
e
m
ons
tr
a
te
s
th
a
t
M
P
C
s
ig
ni
f
ic
a
nt
ly
out
p
e
r
f
or
m
s
tr
a
di
ti
ona
l
P
I
D
c
ont
r
ol
in
f
ur
na
c
e
-
f
ir
e
d
dr
um
boi
le
r
s
.
M
P
C
’
s
pr
e
di
c
ti
ve
c
a
pa
bi
li
ti
e
s
a
ll
ow
it
to
a
nt
ic
ip
a
te
a
nd
m
a
na
ge
s
to
c
ha
s
ti
c
he
a
t
f
lu
c
tu
a
ti
ons
,
w
hi
le
it
s
a
bi
li
ty
to
opt
im
iz
e
m
ul
ti
pl
e
va
r
ia
bl
e
s
,
li
ke
pr
e
s
s
ur
e
s
ta
bi
li
ty
a
nd
f
ue
l
e
f
f
ic
ie
nc
y,
e
n
s
ur
e
s
upe
r
io
r
pe
r
f
or
m
a
nc
e
.
U
nl
ik
e
P
I
D
,
w
hi
c
h
r
e
qui
r
e
s
c
om
pl
e
x
t
uni
ng,
M
P
C
is
a
da
pt
iv
e
,
a
dj
us
ti
ng
to
va
r
yi
ng
ope
r
a
ti
ng
c
ondi
ti
ons
w
it
hout
f
r
e
que
nt
r
e
tu
ni
ng.
T
h
e
s
e
be
ne
f
it
s
r
e
s
ul
t
in
im
pr
ove
d
s
ta
bi
li
ty
,
f
ue
l
e
f
f
ic
ie
nc
y,
a
nd r
obus
tn
e
s
s
, m
a
ki
ng
M
P
C
t
he
i
de
a
l
c
ont
r
ol
s
tr
a
te
gy f
or
i
ndus
tr
ia
l
boi
le
r
s
ys
te
m
s
.
4.2.3. L
im
it
at
io
n
s
an
d
c
h
al
le
n
ge
s
M
P
C
r
e
qui
r
e
s
th
e
s
ol
ut
io
n
of
opt
im
iz
a
ti
on
p
r
obl
e
m
s
a
t
e
a
c
h
c
ont
r
ol
s
te
p,
w
hi
c
h
c
a
n
be
c
om
put
a
ti
ona
ll
y
in
te
ns
iv
e
.
I
n
r
e
a
l
-
ti
m
e
a
ppl
ic
a
ti
on
s
,
th
is
c
oul
d
pos
e
c
ha
ll
e
nge
s
,
p
a
r
ti
c
ul
a
r
ly
in
s
y
s
te
m
s
w
it
h
li
m
it
e
d
c
om
put
a
ti
ona
l
r
e
s
our
c
e
s
.
T
he
a
dopt
io
n
of
M
P
C
in
in
dus
tr
ia
l
s
e
tt
in
gs
m
a
y
in
vol
ve
s
ig
ni
f
ic
a
nt
upf
r
ont
c
os
ts
,
in
c
lu
di
ng
s
of
twa
r
e
,
ha
r
dw
a
r
e
,
a
nd
tr
a
in
in
g.
W
hi
le
th
e
s
e
c
os
ts
m
a
y
be
of
f
s
e
t
by
lo
ng
-
te
r
m
s
a
vi
ngs
in
f
ue
l
a
nd
m
a
in
te
na
n
c
e
,
th
e
y
c
oul
d
be
a
ba
r
r
ie
r
to
a
dopt
io
n
f
or
s
om
e
or
ga
ni
z
a
ti
ons
.
A
ls
o,
th
e
e
f
f
e
c
ti
ve
ne
s
s
of
M
P
C
is
hi
ghl
y
de
pe
nd
e
nt
on
th
e
a
c
c
ur
a
c
y
of
th
e
unde
r
ly
in
g
m
a
th
e
m
a
ti
c
a
l
m
ode
ls
.
I
na
c
c
ur
a
te
or
ove
r
ly
s
im
pl
if
ie
d
m
ode
ls
c
oul
d
le
a
d
to
s
ubopti
m
a
l
c
ont
r
ol
a
c
ti
ons
,
unde
r
m
in
in
g
th
e
pot
e
nt
ia
l
be
ne
f
it
s
o
f
th
e
a
ppr
oa
c
h.
4.2.4. Com
p
ar
is
on
w
it
h
t
r
ad
it
io
n
al
c
on
t
r
ol
m
e
t
h
od
s
W
hi
le
tr
a
di
ti
ona
l
P
I
D
c
ont
r
ol
ha
s
be
e
n
th
e
in
dus
tr
y
s
ta
nda
r
d
f
or
de
c
a
de
s
due
to
it
s
s
im
pl
ic
it
y
a
nd
e
a
s
e
of
im
pl
e
m
e
nt
a
ti
on,
it
ha
s
li
m
it
a
ti
ons
in
de
a
li
ng
w
it
h
th
e
c
om
pl
e
x,
nonl
in
e
a
r
dyna
m
ic
s
of
f
ur
na
c
e
-
f
ir
e
d
boi
le
r
s
,
pa
r
ti
c
ul
a
r
ly
unde
r
s
to
c
h
a
s
ti
c
c
ondi
ti
ons
.
T
he
c
om
p
a
r
is
on
be
twe
e
n
P
I
D
a
nd
M
P
C
c
ont
r
ol
s
tr
a
te
gi
e
s
r
e
ve
a
ls
th
a
t
th
e
P
I
D
c
ont
r
ol
le
r
s
r
e
a
c
t
to
di
s
tu
r
ba
nc
e
s
ba
s
e
d
on e
r
r
or
c
or
r
e
c
ti
on,
w
hi
c
h
c
a
n
le
a
d
to
os
c
il
la
ti
ons
a
nd i
ns
ta
bi
li
ty
i
n s
ys
te
m
s
w
it
h hi
gh l
e
ve
ls
of
unc
e
r
ta
in
ty
. M
P
C
,
on t
he
ot
he
r
ha
nd,
pr
oa
c
ti
ve
ly
a
dj
us
ts
c
ont
r
ol
a
c
ti
ons
ba
s
e
d
on
pr
e
di
c
te
d
f
ut
ur
e
s
ta
te
s
,
r
e
duc
in
g
th
e
li
ke
li
hood
of
os
c
il
la
ti
ons
.
T
he
s
ys
te
m
e
f
f
ic
ie
nc
y
is
a
ls
o
hi
gh
w
it
h
M
P
C
'
s
a
bi
li
ty
to
opt
im
iz
e
c
ont
r
ol
a
c
ti
ons
f
or
f
ue
l
e
f
f
ic
ie
nc
y
a
nd
pr
e
s
s
ur
e
s
ta
bi
li
ty
le
a
d
s
to
m
or
e
e
f
f
ic
ie
nt
s
ys
te
m
ope
r
a
ti
on c
om
pa
r
e
d t
o P
I
D
, w
hi
c
h m
a
y not be
a
bl
e
t
o ba
la
nc
e
t
he
s
e
obj
e
c
ti
ve
s
a
s
e
f
f
e
c
ti
ve
ly
.
4.2.5. B
r
oad
e
r
i
m
p
ac
t
on
i
n
d
u
s
t
r
ia
l
b
oi
le
r
op
e
r
at
io
n
T
he
a
dopt
io
n
of
M
P
C
a
s
a
c
ont
r
ol
s
tr
a
te
gy
in
in
dus
tr
ia
l
boi
l
e
r
s
ha
s
th
e
pot
e
nt
ia
l
to
br
in
g
a
bout
s
ig
ni
f
ic
a
nt
ope
r
a
ti
ona
l
im
pr
ove
m
e
nt
s
a
c
r
os
s
a
w
id
e
r
a
nge
of
a
p
pl
ic
a
ti
ons
:
‒
S
c
a
la
bi
li
ty
:
th
e
c
ont
r
ol
s
tr
a
te
gy
d
e
ve
lo
pe
d
in
th
is
r
e
s
e
a
r
c
h
c
a
n
be
s
c
a
le
d
to
la
r
ge
r
a
nd
m
or
e
c
om
pl
e
x
boi
le
r
s
ys
te
m
s
. T
hi
s
s
c
a
la
bi
li
ty
ope
ns
up oppor
tu
ni
ti
e
s
f
or
i
ts
a
ppl
ic
a
ti
on i
n va
r
io
us
i
ndus
tr
ie
s
, i
nc
lu
di
n
g
pow
e
r
ge
ne
r
a
ti
on, c
he
m
ic
a
l
pr
oc
e
s
s
in
g, a
nd ma
nuf
a
c
tu
r
in
g, w
h
e
r
e
boi
le
r
s
ys
te
m
s
pl
a
y
a
c
r
it
ic
a
l
r
ol
e
.
‒
E
nha
nc
e
d
r
e
li
a
bi
li
ty
:
by
m
a
in
ta
in
in
g
s
ta
bl
e
op
e
r
a
ti
on
unde
r
v
a
r
yi
ng
c
ondi
ti
ons
,
M
P
C
c
a
n
r
e
duc
e
th
e
li
ke
li
hood
of
unpl
a
nne
d
s
hut
dow
ns
a
nd
e
qui
pm
e
nt
f
a
il
ur
e
s
.
T
h
is
e
nha
nc
e
d
r
e
li
a
bi
li
ty
is
a
ke
y
f
a
c
to
r
in
r
e
duc
in
g m
a
in
te
na
nc
e
c
o
s
ts
a
nd downtim
e
i
n i
ndus
tr
ia
l
ope
r
a
ti
o
ns
.
‒
E
nvi
r
onm
e
nt
a
l
im
pa
c
t:
im
pr
ove
d
f
ue
l
e
f
f
ic
ie
nc
y
not
onl
y
r
e
duc
e
s
ope
r
a
ti
ona
l
c
os
ts
but
a
ls
o
c
ont
r
ib
ut
e
s
to
e
nvi
r
onm
e
nt
a
l
s
us
ta
in
a
bi
li
ty
by
lo
w
e
r
in
g
gr
e
e
nhous
e
ga
s
e
m
is
s
io
ns
.
T
hi
s
is
pa
r
ti
c
ul
a
r
ly
r
e
le
va
nt
in
in
dus
tr
ie
s
w
he
r
e
boi
le
r
s
a
r
e
a
m
a
jo
r
s
our
c
e
of
e
m
is
s
io
ns
.
4.3. F
u
t
u
r
e
r
e
s
e
ar
c
h
d
ir
e
c
t
io
n
s
T
he
pr
om
is
in
g r
e
s
ul
ts
of
t
hi
s
s
tu
dy
s
ugge
s
t
s
e
ve
r
a
l
a
v
e
nue
s
f
or
f
ut
ur
e
r
e
s
e
a
r
c
h:
‒
I
nt
e
gr
a
ti
on
w
it
h
in
te
r
ne
t
o
f
th
in
gs
(
I
oT
)
a
nd
pr
e
di
c
ti
ve
m
a
in
te
na
nc
e
:
f
ut
ur
e
r
e
s
e
a
r
c
h
c
oul
d
e
xpl
or
e
th
e
in
te
gr
a
ti
on
of
M
P
C
w
it
h
I
oT
-
ba
s
e
d
m
oni
to
r
in
g
a
nd
pr
e
di
c
ti
v
e
m
a
in
te
na
nc
e
s
ys
te
m
s
.
T
hi
s
in
te
gr
a
ti
on
w
oul
d
e
na
bl
e
r
e
a
l
-
ti
m
e
pe
r
f
or
m
a
nc
e
m
oni
to
r
in
g
a
nd
e
a
r
ly
de
te
c
ti
on
of
pot
e
nt
ia
l
i
s
s
ue
s
,
f
ur
th
e
r
e
nha
nc
in
g t
he
r
e
li
a
bi
li
ty
a
nd e
f
f
ic
ie
nc
y of
boi
le
r
s
ys
te
m
s
.
‒
E
xpl
or
a
ti
on
of
a
lt
e
r
na
ti
ve
c
ont
r
ol
s
tr
a
te
gi
e
s
:
w
hi
le
M
P
C
ha
s
s
how
n
s
ig
ni
f
ic
a
nt
a
dva
nt
a
ge
s
,
f
ut
ur
e
r
e
s
e
a
r
c
h
c
oul
d
in
ve
s
ti
ga
te
ot
he
r
a
dva
nc
e
d
c
ont
r
ol
s
tr
a
te
gi
e
s
,
s
uc
h
a
s
a
da
pt
iv
e
or
f
uz
z
y
lo
gi
c
c
ont
r
ol
,
to
de
te
r
m
in
e
i
f
t
he
y of
f
e
r
a
ddi
ti
ona
l
be
ne
f
it
s
or
a
r
e
be
tt
e
r
s
ui
te
d t
o s
pe
c
if
ic
a
ppl
ic
a
ti
ons
.
‒
L
ong
-
te
r
m
f
ie
ld
t
r
ia
ls
:
w
hi
le
s
im
ul
a
ti
on
s
tu
di
e
s
pr
ovi
de
va
lu
a
bl
e
in
s
ig
ht
s
,
lo
ng
-
te
r
m
f
ie
ld
tr
ia
ls
in
r
e
a
l
in
dus
tr
ia
l
s
e
tt
in
gs
w
oul
d
be
ne
c
e
s
s
a
r
y
to
f
ul
ly
va
li
da
te
th
e
e
f
f
e
c
ti
ve
ne
s
s
a
nd
r
obus
tn
e
s
s
of
th
e
pr
opos
e
d
c
ont
r
ol
s
tr
a
te
gy unde
r
a
c
tu
a
l
ope
r
a
ti
ng c
ondi
ti
ons
.
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