Page 180 - Distributed model predictive control for plant-wide systems

154 Distributed Model Predictive Control for Plant-Wide Systems

with the proposed networked MPC scheme, first of all divide the whole process into two sub-
systems, they are
1
Subsystem 1 ∶ y = u
1 1
10 s + 1
1.5
Subsystem 2 ∶ y = u 2
2
9 s + 1
The local performance index for each subsystem is
P M
∑ 2 ∑ 2
J (k)= ‖ r (k + s) − ̂y (k + s|k) ‖ + ‖ Δu (k + h − 1|k) ‖
i
i
i
‖ i
‖
‖Q i
‖R i
s=1 h=1
With regard to neighborhood optimization, the new performance index for each subsystem is
J (k)= J (k)+ J (k)
1
i
2
The tuning parameters for each subsystem are set with P = 8, M = 2, Q = 10, R = 1(i = 1, 2)
i i
using sampling time of 1 s, and = 0.01(i = 1, 2). MATLAB-based simulation results are car-
i
ried out to evaluate the proposed networked MPC interactive algorithm (shown in Figure 7.11)
through performance comparisons with decentralized MPC (shown in Figure 7.9) and dis-
tributed MPC with Nash optimization (shown in Figure 7.10). Set points step from 0 to 1
for the first subsystem and from 1 to 0 for the second subsystem at the time 20 s shown as
the dotted lines in figures. As can be seen, system outputs are divergent and fluctuant under
the decentralized MPC, while system outputs under the networked MPC Algorithm 7.1 with
neighborhood optimization reach the set-points in a very shorter time exhibiting a very smaller
overshoots than that of the distributed MPC with Nash optimization under similar conditions.
In addition, the iteration based networked MPC scheme with neighborhood optimization can
work as well as the centralized MPC method.
Performance index comparisons are shown for these three schemes in Figure 7.12.
Simulation results demonstrate that the control performance with decentralized MPC (shown
as dotted line) is worse than the distributed MPC with Nash optimization (shown as dashed
line) and the proposed networked MPC with neighborhood optimization (shown as solid
line), and the networked MPC with neighborhood optimization can efficiently improve the
control performance.

7.3.6.2 Walking Beam Reheating Furnace System
Walking beam reheating furnace is one of the most important equipment in steel rolling
industry. The structure of a walking beam reheating furnace is depicted in Figure 7.13. As
seen in the figure, the reheating furnace consists of three chambers: preheating, heating, and
soaking zones. Billets are fed to the furnace and move forward a step at every interval, it
will be heated to the specified temperature at the exit of the furnace for metallurgical quality
and for hot rolling [109]. If furnace temperature is too high, the billets in the furnace will be
overheated. Otherwise, it cannot be heated to the desired temperature. So it is important to
control the fuel feed flow appropriately for each zone in order to heat billets to the desired
temperature with minimum energy consumption.