MATLAB在模型预测控制设计中的应用实践

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MPC

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"模型预测控制设计的MATLAB实现" 在工业控制领域，模型预测控制（Model Predictive Control，简称MPC）是一种广泛应用的先进控制策略，它利用数学模型预测系统未来行为，通过优化算法来确定最佳控制序列。MATLAB作为强大的数值计算和建模工具，被广泛用于MPC的设计和实现。本书《model prediction control system design and implementation using MATLAB》深入探讨了如何利用MATLAB进行MPC的开发。 MPC的核心在于其对未来多个时间步的预测能力，这使得控制器能够考虑到系统的动态行为和约束条件。在MATLAB环境中，可以方便地构建系统模型，如线性时不变（LTI）模型或非线性模型，并使用内置的优化工具箱来求解多步预测的优化问题。MATLAB的System Identification Toolbox可用于系统识别，从而获得准确的动态模型，而Control System Toolbox则提供了MPC算法的实现框架。该书可能涵盖了以下几个方面： 1. **系统建模**：详细介绍了如何使用MATLAB构建系统模型，包括离散时间模型、连续时间模型以及非线性模型的构建方法。 2. **MPC算法**：讲解了基本的线性MPC算法，如滚动优化、预测模型的更新、状态反馈和输出反馈的控制律设计等，并可能扩展到鲁棒MPC、自适应MPC和多变量MPC等高级主题。 3. **约束处理**：讨论了如何在优化过程中考虑系统和控制输入的约束，如边界限制、物理限制等，以确保控制策略的可行性和安全性。 4. **实时实施**：介绍了将MATLAB模型转换为实际硬件上的控制器，如利用Embedded Coder生成嵌入式代码，或者使用Simulink实时接口进行实时仿真和测试。 5. **应用案例**：书中很可能包含不同领域的应用实例，如化工过程控制、能源系统、机械动力系统等，以演示MPC在解决实际问题中的效果。 6. **MATLAB工具箱应用**：详细阐述了如何利用MATLAB的各种工具箱，如Simulink、Stateflow、Optimization Toolbox等，进行MPC的建模、仿真和优化。 7. **故障诊断与鲁棒性**：可能涉及系统健康监测、故障诊断技术，以及在不确定性和外部扰动下的鲁棒控制策略。通过学习这本书，读者将掌握使用MATLAB进行MPC设计的基本步骤和高级技巧，从而能够为各种复杂系统设计出高效、稳健的控制方案。对于从事控制工程、自动化及相关领域的研究人员和工程师来说，这是一份宝贵的参考资料。

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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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