Page 185 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Information Structure Constraints 159

From the simulation, the networked MPC scheme can work as well as the centralized MPC
method. In addition, the design parameters for each subsystem such as prediction horizon, con-
trol horizon, weighting matrices, etc. can all be designed and tuned separately, which provides
more flexibility for the analysis and applications. Notice that each subsystem is not necessary
limited to SISO case and also it can be MIMO subsystem, whose dimension is still much lower
than that of the whole system.

7.4 Conclusion
In this chapter, the noniterative distributed MPC algorithm based on neighborhood optimiza-
tion is present and the condition of closed-loop stability is given for local MPCs tuning. In the
procedure of resolving optimal solution, each subsystem only communicates with its neigh-
bors, which is rather easy to fulfill the network requirements. Moreover, the discussion of
the performance of proposed methodology and the application of N-DMPC to ACC test rig
prove that the proposed method guarantees an improving performance of entire system with
relative relaxed communication requirements. Further investigation will focus on designing
stable distributed MPC with constraints and global performance improvement for this class of
large-scale systems.
In addition, regarding the network capacity, an iterative networked DMPC method based
on neighborhood optimization is developed for a class of serially connected processes. The
state-space model for each subsystem is developed directly from step responses without fur-
ther identification. It is not necessary to identify the structure of the subsystem during the
modeling, and the more flexible error correction is naturally derived by employing the pre-
dictive state observer. Neighborhood optimization employs a cooperative strategy so that the
whole control performance can be efficiently improved. Regarding the network capacity, an
iterative algorithm for networked MPC is presented with one situation that it is possible for
each subsystem to exchange information several times during it solves its local optimization
problem. The computational convergence of the iteration based N-MPC algorithm and the
nominal stability are derived for distributed control systems without the control and output
constraints. In addition, when convergent condition is satisfied, the solution to the local opti-
mization problems collectively is proved to equal the Nash optimality. An illustrative example
and the simulation study of the fuel feed flow control for the walking beam reheating furnace
if presented to verify the efficiency of the proposed networked MPC algorithms.

Appendix
Appendix A. Proof of Lemma 7.1

The proof is stated by writing, for i = 1, … , n,the h-ahead predictions at time k based on the
information computed at time k − 1 of the interaction vectors (9) (10) and by representing
them in a stacked form for h = 1, … , P.The last P − M − 1 samples of the stacked control
action predictions U (k, P|k − 1)(j = 1, 2, … , n), that are not contained in U (k − 1, M|k − 1),
j
j
are assumed equal to the last element of U (k − 1, M|k − 1). By definitions (14–18) and
j
Table 7.1, this implies that relations (7.23) hold.