"MATLAB实现模型预测算法：MPC和工业控制领域的新进展"

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模型预测控制（MPC）是一种用于工业控制的先进算法，它能够对系统的未来行为进行预测，并基于这些预测进行最优化控制。使用MATLAB实现模型预测算法是目前的一种常见做法，它能够提供灵活性和高效性，使得工程师可以更加方便地进行模型预测控制系统的设计和实现。《模型预测算法的实现 Using MATLAB》这本书是一本红皮的大厚书，内容涵盖了模型预测控制算法的实现和应用。该书共有400页，作者细致地介绍了使用MATLAB进行模型预测算法的各个方面，包括其理论基础、实际实现和工程应用等。通过学习这本书，读者可以深入了解模型预测控制算法的内部原理和实际操作方法，从而为工程实践提供指导和帮助。《模型预测算法的实现 Using MATLAB》是“Advances in Industrial Control”系列的一部分，该系列还包括其他与工业控制相关的书籍，如《数字控制器的实现》、《工业过程的监控级优化》、《柴油船舶推进系统的鲁棒控制》等。这些书籍都是由知名的专家学者撰写，涵盖了工业控制领域的前沿理论和实践经验，为工程技术人员提供了宝贵的学习资源和参考资料。在《模型预测算法的实现 Using MATLAB》中，作者对MPC算法进行了深入的介绍，并结合MATLAB软件提供了大量的实例和仿真结果。读者可以通过学习该书，掌握MPC算法的基本原理和实际应用技巧，从而为自己在工业控制领域的工作和研究提供有力支持。除了介绍MPC算法的基本概念和实现方法，该书还对工程实际中常见的问题进行了深入的分析和讨论。比如在工业控制系统中，经常会遇到模型的不确定性、测量噪声和外部干扰等问题，作者们特别介绍了如何通过MPC算法进行鲁棒控制，以应对这些问题。此外，书中还介绍了MPC算法在多变量系统和非线性系统中的应用，使得读者能够更加全面地了解MPC算法的潜力和局限性。值得一提的是，书中还对MPC算法的参数调整和性能优化进行了详细的介绍。MPC算法的性能很大程度上取决于模型的准确性和控制器参数的选择，作者们针对这一问题提出了许多实用的建议和方法。通过学习这些内容，读者能够更好地应用MPC算法解决实际工程中的控制问题，提升系统的稳定性和性能。总的来说，《模型预测算法的实现 Using MATLAB》这本书全面而深入地介绍了MPC算法的理论基础和工程应用，具有很高的实用价值。作为工业控制领域的经典著作之一，它为工程技术人员提供了学习和研究的重要参考资料，对于推动工业控制技术的发展具有重要意义。希望更多的工程师和研究人员能够通过学习这本书，深入了解MPC算法的精髓，为工业控制系统的设计和应用贡献自己的力量。

xvi Preface

system is not necessarily stable, and if it is too large, the predictive control

system will encounter a numerical stability problem. To overcome this prob-

lem, in Chapter 4, we propose the use of an exponentially weighted moving

horizon window in model predictive control design. Within this framework,

the numerical ill-conditioning problem is resolved by a simple modiﬁcation

of the design model. Equally important are an asymptotic stability result

for predictive control designed using inﬁnite horizon with exponential data

weighting and a modiﬁcation of the weight matrices, as well as a result that

establishes the predictive control system with a prescribed degree of stability.

Analytical and numerical results are used in this chapter to show the equiv-

alence between the new class of discrete-time predictive control systems and

the classical discrete-time linear quadratic regulators (DLQR) without con-

straints. When constraints are present, the optimal solutions are obtained by

minimizing the exponentially weighted cost subject to transformed inequality

constraints.

Chapters 6 to 8 will introduce the continuous-time predictive control re-

sults. To prepare the background, in Chapter 5, we will discuss continuous-

time orthonormal basis functions and their applications in dynamic system

modelling. Laguerre functions and Kautz functions are special classes of or-

thonormal basis functions. Both sets of functions possess simple Laplace trans-

forms, and can be compactly represented by state-space models. The key prop-

erty is that when using the orthonormal functions, modelling of the impulse

response of a stable system, which has a bounded integral squared value,

will have a guaranteed convergence as the number of terms used increases.

This forms the fundamental principle of the model predictive control design

methods presented in this book.

After introducing the background information, in Chapter 6, we begin with

the topics in continuous-time model predictive control (CMPC). It is natural

that when the design model is embedded with integrators, the derivative of the

control signal should be modelled by the orthonormal basis functions, not the

control signal itself. With this as a start point, systematically, we will cover the

principles of continuous-time predictive control design, and the solutions of

the optimal control problem. It shows that when constraints are not involved

in the design, the continuous-time model predictive control scheme becomes

a state feedback control system, with the gain being chosen from minimizing

a ﬁnite prediction horizon cost. The continuous-time Laguerre functions and

Kautz functions discussed in Chapter 5 are utilized in the design of continuous-

time model predictive control.

In Chapter 7, we introduce continuous-time model predictive control with

constraints. Similar to the discrete-time case, we will ﬁrst formulate the con-

straints for the continuous-time predictive control system, and present the

numerical solution of the constrained control problem using a quadratic pro-

gramming procedure. Because of the nature of the continuous-time formu-

lation such as fast sampling, there might be computational delays when a

quadratic programming procedure is used in the solution of the real-time op-

Preface xvii

timization problem. In general terms, we discuss the real-time implementation

of continuous-time model predictive control in the presence of constraints in

this chapter too.

The numerical instability problem discussed in the discrete-time case, also

occurs in the continuous-time algorithms that is shown by a numerical example

in Chapter 8. In a similar spirit to previous chapters, Chapter 8 proposes the

use of exponential data weighting in the design of continuous-time model

predictive control systems. This essentially transforms the original state and

derivative of the control variables into exponentially weighted variables for the

optimization procedure. With a simple modiﬁcation on the weight matrices,

asymptotic stability is established for model predictive control systems with

inﬁnite prediction horizon. Similarly, a prescribed degree of stability can also

be obtained. Without constraints, analytical and numerical results are used

to demonstrate the equivalence between the continuous-time model predictive

controllers and the classical linear quadratic regulators (LQR). Constraints are

imposed on the transformed variables.

In a general framework of state feedback control, an observer is often

needed for its implementation. The design of an observer is a separate task

from the design of predictive controller. The role of an observer is to ensure

small errors between the estimated and the actual state variables. However,

if one faces many inputs and many outputs in a system, tuning of an ob-

server’s dynamics may not be a trivial task. The classical predictive control

systems, such as dynamic matrix control (DMC) and generalized predictive

control (GPC), have directly utilized plant input and output signals in the

closed-loop feedback control, hence avoiding observers in their implementa-

tion. In Chapter 9, we will link the predictive control systems designed using

the framework of state space to the classical predictive control systems. The

key to the link is to choose the state variables to be identical to the feed-

back variables that have been used in the classical predictive control systems.

Once the state-space model is formulated, the framework from the previous

chapters is naturally extended to the classical predictive control systems, pre-

serving all the advantages of a state-space design, including stability analysis,

exponential data weighting and LQR equivalence. In addition, because of the

utilization of plant input and output signals in the implementation, the pre-

dictive controller can be represented in a transfer function form, allowing a

direct frequency response analysis of the system to obtain critical informa-

tion, such as gain and phase margins. It is worthwhile to point out that the

discrete-time single-input and single-output predictive controller is very sim-

ple and easy for implementation. Simplicity as a feature of the algorithms

remains when they are extended to multi-input and multi-output systems.

Diﬀerent from discrete-time, in the continuous-time design, an implementa-

tion ﬁlter is required, and the poles of the ﬁlter become part of the desired

closed-loop poles when we choose to optimize the output errors in the design.

Chapter 10 presents three diﬀerent implementation procedures for model

predictive control systems. The ﬁrst implementation is based on a (low-cost)

xviii Preface

micro-controller for controlling a DC motor. In this application, the MAT-

LAB design programs are utilized to calculate the predictive controller gain

and the previous MATLAB closed-loop simulation program is converted to a

C program for real-time implementation on the micro-controller. The second

implementation is based on MATLAB Real-time Workshop and xPC target.

This application is very useful for those who are not familiar with C lan-

guage because the MATLAB Real-time Workshop and xPC target perform

the conversion from MATLAB programs to C programs through their com-

pilers in a systematic way. With these tools, we only need to create MATLAB

embedded functions for the real-time applications. The third implementation

uses the platform of a real-time PC-based supervisory control and data ac-

quisition (SCADA) system. A pilot food extrusion plant is controlled by the

continuous-time predictive controller developed in Chapter 6. The previous

MATLAB closed-loop simulation program for a continuous-time system is

converted to C program for this real-time implementation.

Acknowledgements

There are two aspects that have motivated me in the writing of this book.

The excitement of ﬁtting together the work I have been doing over the years

into a book is my ﬁrst motivation. The second is that I need to express my

gratitude to those who helped me over the years. With this book, I have the

opportunity to formally thank so many colleagues and friends.

My ﬁrst gratitude goes to Professor Graham C. Goodwin who was the

Director of the Center for Integrated Dynamics and Control, University of

Newcastle, Australia where I worked from February 1998 to February 2002.

His encouragement and help since November 1997 are gratefully acknowl-

edged. My special thanks go to Dr Robert Snow, who was previously the

Dean of Engineering, RMIT University, Australia and who had helped me

tremendously during my early years in RMIT.

My thanks go to Professor Michael Johnson who is a joint editor of the

Advances in Industrial Control Book series by Springer. Professor Michael

Johnson provided me with the opportunity to write this book and very valu-

able feedback towards its improvement. His encouragement is very much ap-

preciated.

Over the years, numerous people have helped me and worked with me in

various stages of my career. I would like to thank Professor Peter Gawthrop

(Glasgow, UK), Professor David Owens (Sheﬃeld, U.K), Professor Eric Rogers

(Southampton, UK), Professor Peter Young (Lancaster, UK), Professor Hugues

Garnier (Nancy, France), Professor Alex Penlidis (Waterloo, Canada), Pro-

fessor Rick Middleton (Newcastle, Australia), Professor Xinghou Yu (RMIT

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