Page 163 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Information Structure Constraints 137

It should be noticed that each controller only communicates with its neighbors and its neigh-
bors’ neighbors in ND-MPC. Moreover, if each controller communicates with its neighbors
twice within a sampling time interval, the information of its neighbors’ neighbors can be
obtained from its neighbors. That means only the information exchanging among neighbor-
hood is required using this method. Thus, if one subsystem fails, the other subsystem unrelated
to S can be run normally. The communication loads related to S are that S get its future states
i i i
to its neighbors and sent its neighbor’s states and inputs to its neighbors. This means that the
maximum communication loads is
( )
m
∑ ∑
n Pn + Pn (7.41)
i xi xj
i=1 j∈N i
In Equation (7.41), some information is calculated repeatedly; thus, Equation (7.41) is the
maximum communication burden using ND-MPC. The required physical connections equal
the number of nonzero elements in A subtract the rank of A.
Since the computational burden mainly comes from the complexity of the inversion algo-
rithm, the computational burden is similar to (a little more than) that of the method proposed in
[46]. The memory required is a little larger than that in [46] since the system matrice’s dimen-
sion of each subsystem’s states evolution equation is larger than that in [46]. However, the
memory is not a problem with the modern computer technology. The efficiency of this method
will be validated in the next section.

7.2.6 Numerical Validation

To illustrate the performance of the proposed method, application of this method to the accel-
erated cooling process (ACC) test rig is performed in one steel company in Shanghai, China.

7.2.6.1 Process Description
The ACC process, simplified in Figure 7.1, is used to cool a metal plate from initial temper-
◦
◦
ature around 750–800 C down to final temperature in the range of 450–560 C. A constant
cooling curve of plate is required in ACC, which helps a lot to strongly improve the mechan-
ical characteristics of the corresponding products. The cooling area is partitioned into three
sections: air cooling section, water cooling section, and re-reddening section, labeled A, B,
and C, respectively. Fifteen cooling header units are uniformly spaced along section B. The
number of cooling header units in operation (N) and the water flux of each cooling unit (F) can
be adjusted separately. The temperature drop is caused by the heat radiation in sections A and
C, and caused by both radiation and water cooling in section B [102, 103]. Four pyrometers
T − T are located in the positions of 13.5 m, 58.6 m, 89 m, and 109.5 m, respectively. The
P1 P4
temperatures of the plate inside cooling section are measured by soft sensors.
The control objective is to control the location-dependent temperatures at loca-
d
tion l , l , … , l n to be consistent with the reference temperature denoted with y =
2
1
[ d d d ] T
y y ··· y through adjusting the flux of each water cooling header unit and plate
1 2 m
velocity. (l is the location of T ; l , i = 1, 2, … , 15, is the entry of the ith cooling header
0
i
P1
unit; l m−1 is the exit of section B; and l is the location of T .)
m
P3