Page 39 - Distributed model predictive control for plant-wide systems

Introduction 13

its corresponding subsystem’s cost function and the cost function of the subsystems directly
impacts on
∑
J (k)= J (k) (1.3)
i
j
j∈P i
where P ={j ∶ j ∈ P or j = i} is the set of subscripts of the downstream subsystems of
i −i
subsystem S , that is the region impacted on by subsystem S . The resulting control algorithm
i i
is termed as an impacted-region cost optimization-based DMPC (ICO-DMPC) [55–57] or
N-DMPC with communication constraints. It could achieve a better performance than the
first method, and its communication burden is much less than the second method. Clearly,
this coordination strategy as proposed in [19, 47, 54] and described in (1.3) is a preferable
method to trade off the communication burden and global performance.

Some other kinds of DMPC formulations are also available in [11, 13, 29, 46, 48, 51–54,
58–64]. Among them, the methods described in [52, 62] are proposed for a set of decoupled
subsystems, and the extension of [52] could handle systems with weakly interacting subsystem
dynamics [51]. There is no absolute priority among these different distributed predictives.
One could select different algorithms according to their purpose of employing the control
system.

1.5 About this Book
This book systematically introduces the distributed predictive control with different coordina-
tion strategies for the plant-wide system, including the system decomposition, classification of
distributed predictive control, unconstrained distributed predictive control, and the stabilized
distributed predictive control with different coordinating strategies for different purposes, as
well as the implementation examples of distributed predictive control. The major new con-
tribution of this book is to show how the DMPCs can be coordinated efficiently for different
control requirements, namely the network connectivity, error tolerance, performance of the
entire closed-loop system, calculation speed, etc. This book also describes how to design
DMPC. The latest theory and technologies of DMPC for coupling discrete-time linear sys-
tems are introduced in this book. The rest of this book is structured into four parts, as shown
in Figure 1.11, and are organized as follows.
In the first part, Chapters 2 and 4, we recall the main concepts and some fundamental
results of the predictive control for discrete-time linear systems. Some existing results about
the solution and the stability of the closed-loop system under the control of MPC are pro-
vided in this part. The system model, structure model, and some decomposition methods, e.g.,
the relative gain array (RGA), N-step accessible matrix-based decomposition, are also intro-
duced in this chapter to present how to divide the entire system into the interacted subsystems
according to the specific control requirements. Then some coordination strategies are intro-
duced according to the classification of coordination degree (the optimization index of each
subsystem-based MPC).
Our intent is to provide only the necessary background for the understanding of the rest of
the book.
In the second part, Chapters 5–7, the unconstrained DMPCs with different coordination
strategies are introduced for primary readers, since the major ideas and the characteristics of