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Fig. 1.
The input-output relationships of a circulating fluidized bed boiler
Fig. 1 shows the bed temperature is influenced by the feeding coal amount,
the primary air and the secondary air. On the other hand, the three inputs can
also influence the pressure and temperature of steam, flue gas oxygen content.
As pointed out by [11], the response time delay from fuel to the steam pressure
is about 45s, and the rise time is about 350s. Thus, the circulating fluidized bed
boiler is also a large time delay system subjected to physical constraints from
feeding coal, primary air and secondary air.
From the process, the temperature control of a CFB boiler is a zone control.
That is, the bed temperature is allowed to fluctuate within a threshold range
of settings which can ensure the burn rate without coking risks. Similarly, the
main steam pressure, temperature, and flue gas oxygen content are also allowed
to fluctuate around the set values.
2.2 Dynamic Matrix Control[12]
Dynamic matrix control (DMC) is one of model predictive control (MPC) algo-
rithms. Since the circulating fluidized bed boiler is a constrained multi-variable
system with large time delay, DMC can be used as a better choice of control
strategy.
Suppose there are
m
outputs,
p
inputs.
a
ij
is model vector from
u
j
to
y
i
.
The control horizon and predictive horizon of DMC are denoted as
M
and
P
,
respectively. Then, dynamic matrix is
⎡
⎤
a
ij
(1)
0
⎡
⎤
⎣
.
⎦
.
.
.
A
11
···
A
1
m
⎣
.
.
⎦
A
=
,
A
ij
=
a
ij
(
M
)
···
a
ij
(1)
.
.
A
p
1
···
A
pm
a
ij
(
P
)
···
a
ij
(
P
−
M
+1)
y
M
(
k
)is the predictive output at time
k
and
y
P
0
(
k
) is the reference of system
output when
Δ
u
(
k
)=0.Thus,
y
M
(
k
)=
y
P
0
(
k
)+
A
Δ
u
(
k
). The optimized
performance of Dynamic Matrix Control is
2
Q
+
2
R
Δu
M
min
ω
(
k
)
−
y
P
0
(
k
)
−
AΔu
M
(
k
)
Δu
M
(
k
)
(1)
s.t.
Δu
M,
min
≤
Δu
M
(
k
)
≤
Δu
M,
max
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