Page 73 - Distributed model predictive control for plant-wide systems

4

Structure Model and System

Decomposition

4.1 Introduction

In design distributed control, it is usual to represent the whole system as a collection of
interconnected subsystems. The types or forms of the subsystem model are very important
for the design of distributed predictive control. Different presentations of subsystem models
may cause different designs of MPC and, consequently, may cause different characteristics
of designed DMPC. Thus, the existing model formulation for the subsystem, including the
state evolution models, the interacting models (input interacting model and state interaction
model), etc., is introduced first. We also give some interpretation of how to transfer the
presentation of these models among each other.
In addition, how to divide the large-scale system into many subsystems is another very
important problem. In certain cases, the decomposition of a large-scale system can be derived
directly from the physical description of the problem, which suggests a “natural” grouping
of the state variables. More often than not, however, the only information that we have about
the system dynamics comes from a mathematical model whose properties provide little or no
insight into how the subsystems should be chosen. In order to deal with such problems in
a systematic manner, one obviously needs to introduce the decomposition algorithms that are
based on the structure of the underlying equations. Thus, in addition to the mathematic models,
the structure models are also introduced here to analyze the logical relationship between each
subsystem and to help modeling the mathematic model. The structure is an important supple-
mentary of mathematic model, and it is also an important approach for directly looking into
the mechanisms of large-scale distributed systems. Here, the function of the structure model
in system decomposition, the adjacent matrices, input–output accessibility, and the structure
controllability are introduced to investigate the characteristics of the system.
Finally, we refer to the traditional methods used for the MIMO system. Here, we briefly
introduce the classic RGA method. The RGA is widely used in designing and analyzing a
MIMO control scheme for a process in steady state. The RGA provides a quantitative approach
to the analysis of the interactions between the controls and the output, and thus provides a
method of pairing manipulated and controlled variables to generate a control scheme.

Distributed Model Predictive Control for Plant-Wide Systems, First Edition. Shaoyuan Li and Yi Zheng.
© 2015 John Wiley & Sons (Asia) Pte Ltd. Published 2015 by John Wiley & Sons (Asia) Pte Ltd.