Page 153 - Distributed model predictive control for plant-wide systems

Networked Distributed Predictive Control with Information Structure Constraints 127

In the previous chapters, two classes of distributed MPCs for the large-scale systems as
described above were presented.

1. Distributed algorithms where each local controller minimizes following the local optimiza-
tion objective
P M
∑ ‖ d ‖ 2 ∑ 2
J (k)= ‖y (k + l) − y (k + l)‖ + ‖ Δu (k + l − 1) ‖ (7.4)
i
i
i
i
‖ ‖Q i ‖ ‖R i
l=1 l=1
When computing the optimal solution, each local controller exchanges estimation states
with its neighbors; therefore, it improves the performance of the closed-loop subsystem.
2. Distributed algorithms where each local controller minimizes a global cost function
m
∑
J(k)= J (k) (7.5)
i
i=1
This strategy could achieve a good performance closing to the centralized MPC under the
condition that the global information is available to each subsystem-based MPC and there
are more communication resources.
In this chapter, a method based on the neighborhood optimization is proposed for the
large-scale system in which each subsystem interacts with each other by both inputs and
states. The goal of it is to achieve a significantly improving performance of the entire system
with little increase of the network resources comparing to the (1) strategy when the global
information is not available and the communication resources are limited.

7.2.2 DMPC Formulation
The proposed control architecture is based on a set of independent MPC controllers C , i =
i
1, 2, … , m, for each subsystem S . Each controller could exchange information with its neigh-
i
bors through a network. To discuss the control methodology proposed in this chapter, the sim-
plifying hypothesis of accessible local states x (k) and Assumption 1 are considered. Moreover,
i
Definition 1 and notations listed in Table 7.1 are defined to describe the proposed methodology
clearly.

Assumption 7.1
(a) Controllers are synchronous.
(b) Controllers communicate only once within a sampling time interval.
(c) Communication cannel introduces a delay of a single sampling time interval.

This set of assumptions is not restrictive. The controllers are synchronous is not so strong
because the sampling interval is usually rather long compared to the computational time in
process control. The assumption (b) of single information exchange with a sampling time
interval is due to the necessity of minimizing the amount of data exchange through the network.
In real situations, an instantaneous data transfer is not possible; therefore, assumption (c) of
unit delay is required.