MATLAB® 实战：基于案例的先进鲁棒控制设计教程

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"《2005_Robust Control Design with MATLAB.pdf》是一本专门针对学习者讲解如何在实际情况下应用高级鲁棒控制设计方法的教材。该书将理论知识与实践案例相结合，旨在帮助读者掌握复杂控制系统的稳健设计技巧。书中采用MATLAB® Robust Control Toolbox 3、Control System Toolbox以及Simulink®进行教学，确保理论与软件工具的有效结合。作者们，来自斯特拉斯克莱德大学电子与电气工程系的教授们，强调了通过一系列具体实例来传授知识，如两轮自平衡机器人实验和柔性链接操纵器等复杂系统的设计。这些例子涵盖了从基础的实验室实验到工业级应用的广泛范围，使读者能够理解如何在动态环境中设计出具有鲁棒性的控制系统。在这个系列中，该书作为控制与信号处理高级教材的一部分，与诸如遗传算法、神经网络在动力学系统建模和控制中的应用、机器人操纵器模型与控制的第二版、工业系统中的故障检测与诊断、软计算技术以及统计信号处理等其他主题相互补充，共同构成了全面的控制与信号处理知识体系。读者不仅可以学到鲁棒控制理论，还能通过Matlab的实际操作练习，提升设计和分析复杂控制系统的能力，这对从事自动化、机器人技术、航空航天或任何依赖于精确控制的工程领域的专业人士来说，是一本极具价值的参考资料。此外，对于那些希望深入理解控制工程实践的学生和研究人员，这本书提供了宝贵的实践经验，帮助他们在面对不确定性和变化的环境时，构建出稳定且性能卓越的控制系统。"

Introduction

Robustness is of crucial importance in control-system design because real engi-

neering systems are vulnerable to external disturbance and measurement noise

and there are always diﬀerences between mathematical models used for design

and the actual system. Typically, a control engineer is required to design a

controller that will stabilise a plant, if it is not stable originally, and satisfy

certain performance levels in the presence of disturbance signals, noise inter-

ference, unmodelled plant dynamics and plant-parameter variations. These

design objectives are best realised via the feedback control mechanism, al-

though it introduces in the issues of high cost (the use of sensors), system

complexity (implementation and safety) and more concerns on stability (thus

internal stability and stabilising controllers).

Though always being appreciated, the need and importance of robustness

in control-systems design has been particularly brought into the limelight dur-

ing the last two decades. In classical single-input single-output control, robust-

ness is achieved by ensuring good gain and phase margins. Designing for good

stability margins usually also results in good, well-damped time responses, i.e.

good performance. When multivariable design techniques were ﬁrst developed

in the 1960s, the emphasis was placed on achieving good performance, and not

on robustness. These multivariable techniques were based on linear quadratic

performance criteria and Gaussian disturbances, and proved to be success-

ful in many aerospace applications where accurate mathematical models can

be obtained, and descriptions for external disturbances/noise based on white

noise are considered appropriate. However, application of such methods, com-

monly referred to as the linear quadratic Gaussian (LQG) methods, to other

industrial problems made apparent the poor robustness properties exhibited

by LQG controllers. This led to a substantial research eﬀort to develop a the-

ory that could explicitly address the robustness issue in feedback design. The

pioneering work in the development of the forthcoming theory, now known as

the H

∞

optimal control theory, was conducted in the early 1980s by Zames

[170] and Zames and Francis [171]. In the H

∞

approach, the designer from the

outset speciﬁes a model of system uncertainty, such as additive perturbation

4 1 Introduction

and/or output disturbance (details in Chapter 2), that is most suited to the

problem at hand. A constrained optimisation is then performed to maximise

the robust stability of the closed-loop system to the type of uncertainty cho-

sen, the constraint being the internal stability of the feedback system. In most

cases, it would be suﬃcient to seek a feasible controller such that the closed-

loop system achieves certain robust stability. Performance objectives can also

be included in the optimisation cost function. Elegant solution formulae have

been developed, which are based on the solutions of certain algebraic Riccati

equations, and are readily available in software packages such as Slicot [119]

and MATLAB



Despite the mature theory ([26, 38, 175]) and availability of software pack-

ages, commercial or licensed freeware, many people have experienced diﬃcul-

ties in solving industrial control-systems design problems with these H

∞

and

related methods, due to the complex mathematics of the advanced approaches

and numerous presentations of formulae as well as adequate translations of

industrial design into relevant conﬁgurations. This book aims at bridging the

gap between the theory and applications. By sharing the experiences in in-

dustrial case studies with minimum exposure to the theory and formulae, the

authors hope readers will obtain an insight into robust industrial control-

system designs using major H

∞

optimisation and related methods.

In this chapter, the basic concepts and representations of systems and

signals will be discussed.

1.1 Control-system Representations

A control system or plant or process is an interconnection of components to

perform certain tasks and to yield a desired response, i.e. to generate desired

signal (the output), when it is driven by manipulating signal (the input). A

control system is a causal, dynamic system, i.e. the output depends not only

the present input but also the input at the previous time.

In general, there are two categories of control systems, the open-loop sys-

tems and closed-loop systems. An open-loop system uses a controller or control

actuator to obtain the design response. In an open-loop system, the output

has no eﬀect on the input. In contrast to an open-loop system, a closed-loop

control system uses sensors to measure the actual output to adjust the input

in order to achieve desired output. The measure of the output is called the

feedback signal, and a closed-loop system is also called a feedback system.

It will be shown in this book that only feedback conﬁgurations are able to

achieve the robustness of a control system.

Due to the increasing complexity of physical systems under control and

rising demands on system properties, most industrial control systems are no

longer single-input and single-output (SISO) but multi-input and multi-output

(MIMO) systems with a high interrelationship (coupling) between these chan-

6 1 Introduction

1.2 System Stabilities

An essential issue in control-systems design is the stability. An unstable sys-

tem is of no practical value. This is because any control system is vulnerable

to disturbances and noises in a real work environment, and the eﬀect due

to these signals would adversely aﬀect the expected, normal system output

in an unstable system. Feedback control techniques may reduce the inﬂuence

generated by uncertainties and achieve desirable performance. However, an

inadequate feedback controller may lead to an unstable closed-loop system

though the original open-loop system is stable. In this section, control-system

stabilities and stabilising controllers for a given control system will be dis-

cussed.

When a dynamic system is just described by its input/output relation-

ship such as a transfer function (matrix), the system is stable if it generates

bounded outputs for any bounded inputs. This is called the bounded-input-

bounded-output (BIBO) stability. For a linear, time-invariant system mod-

elled by a transfer function matrix (G(s) in (1.2)), the BIBO stability is guar-

anteed if and only if all the poles of G(s) are in the open-left-half complex

plane, i.e. with negative real parts.

When a system is governed by a state-space model such as (1.1), a stability

concept called asymptotic stability can be deﬁned. A system is asymptotically

stable if, for an identically zero input, the system state will converge to zero

from any initial states. For a linear, time-invariant system described by a

model of (1.1), it is asymptotically stable if and only if all the eigenvalues of

the state matrix A are in the open-left-half complex plane, i.e. with positive

real parts.

In general, the asymptotic stability of a system implies that the system

is also BIBO stable, but not vice versa. However, for a system in (1.1), if

[A, B, C, D] is of minimal realisation, the BIBO stability of the system implies

that the system is asymptotically stable.

The above stabilities are deﬁned for open-loop systems as well as closed-

loop systems. For a closed-loop system (interconnected, feedback system), it is

more interesting and intuitive to look at the asymptotic stability from another

point of view and this is called the internal stability [20]. An interconnected

system is internally stable if the subsystems of all input-output pairs are

asymptotically stable (or the corresponding transfer function matrices are

BIBO stable when the state space models are minimal, which is assumed in

this chapter). Internal stability is equivalent to asymptotical stability in an

interconnected, feedback system but may reveal explicitly the relationship

between the original, open-loop system and the controller that inﬂuences the

stability of the whole system. For the system given in Figure 1.1, there are

two inputs r and d (the disturbance at the output) and two outputs y and u

(the output of the controller K).

The transfer functions from the inputs to the outputs, respectively, are

= GK(I + GK)

−1

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