Sinopsis
Robustness is of crucial importance in control-system design because real engineering 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 interference, unmodelled plant dynamics and plant-parameter variations. These design objectives are best realised via the feedback control mechanism, although 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 during the last two decades. In classical single-input single-output control, robustness 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 successful 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, commonly 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 theory 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 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 chosen, 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 closedloop 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 MATLABr .
Despite the mature theory ([26, 38, 175]) and availability of software packages, commercial or licensed freeware, many people have experienced difficulties 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 industrial case studies with minimum exposure to the theory and formulae, the authors hope readers will obtain an insight into robust industrial controlsystem designs using major H∞ optimisation and related methods. In this chapter, the basic concepts and representations of systems and signals will be discussed.
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 systems 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.
Content
- Introduction
- Modelling of Uncertain Systems
- Robust Design Specifications
- H∞ Design
- H∞ Loop-shaping Design Procedures
- μ-Analysis and Synthesis
- Lower-order Controllers
- Robust Control of a Mass-Damper-Spring System
- A Triple Inverted Pendulum Control-system Design
- Robust Control of a Hard Disk Drive
- Robust Control of a Distillation Column
- Robust Control of a Rocket
- Robust Control of a Flexible-Link Manipulator
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