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Über dieses Buch

This book systematizes recent research work on variable-structure control. It is self-contained, presenting necessary mathematical preliminaries so that the theoretical developments can be easily understood by a broad readership.

The text begins with an introduction to the fundamental ideas of variable-structure control pertinent to their application in complex nonlinear systems. In the core of the book, the authors lay out an approach, suitable for a large class of systems, that deals with system uncertainties with nonlinear bounds. Its treatment of complex systems in which limited measurement information is available makes the results developed convenient to implement. Various case-study applications are described, from aerospace, through power systems to river pollution control with supporting simulations to aid the transition from mathematical theory to engineering practicalities.

The book addresses systems with nonlinearities, time delays and interconnections and considers issues such as stabilization, observer design, and fault detection and isolation. It makes extensive use of numerical and practical examples to render its ideas more readily absorbed.

Variable-Structure Control of Complex Systems will be of interest to academic researchers studying control theory and its application in nonlinear, time-delayed an modular large-scale systems; the robustness of its approach will also be attractive to control engineers working in industries associate with aerospace, electrical and mechanical engineering.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
Complex control systems and some preliminary background knowledge of variable structure control are introduced in this chapter. Some of the sources of system complexity dealt with in this book are discussed. Specifically, the basic concepts and fundamental methodology of sliding mode control and decentralised control are provided. Core notions are clarified based on the authors’ many years of research in these areas. Several practical examples are introduced to illustrate complex systems.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 2. Mathematical Background

Abstract
This chapter presents the fundamental results which underpin the theoretical analysis presented in this book. Lipschitz functions, comparison functions, Lyapunov stability theory including uniform ultimate boundedness, the Razumikhin theorem, linear output sliding surface design, and the geometric structure of nonlinear systems are covered. Some preliminary mathematical results developed by the authors are also provided.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 3. Static Output Feedback Variable Structure Control

Abstract
Chapter 3 considers static output feedback controller design for both nonlinear systems and interconnected systems. For a class of fully nonlinear systems, a variable structure control based Lyapunov method is proposed to drive the system to a ‘small’ region of the origin and maintain motion in the region thereafter. Then, in the region, the nonlinear system is linearised and a sliding mode control is designed to stabilise the system asymptotically. Both the controllers combined to stabilise the system globally. For interconnected systems, decentralised control schemes are developed and output variables embedded in the nonlinear terms are separated and used in the control design to reduce conservatism. Case studies based on a mass–spring system, coupled inverted pendulums and a flight control system are provided to show the developed control methodologies.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 4. Dynamical Output Feedback Variable Structure Control

Abstract
The focus of this chapter is dynamical output feedback controller design for nonlinear systems with nonlinear disturbances using sliding mode techniques.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 5. Reduced-Order Compensator-Based Feedback Control of Large-Scale Systems

Abstract
This chapter continues to consider dynamical output feedback controller design. However, compared with Chap. 4, this chapter focuses on large-scale interconnected systems and uses reduced-order compensators in the feedback loop which is particularly important for large-scale systems to avoid ’the curse of dimensionality’. Sliding mode dynamics are established and the stability is analysed using an equivalent control approach and a local coordinate transformation. A robust decentralised output feedback sliding mode control scheme is synthesised such that the interconnected system can be driven to the predesigned sliding surface. This approach allows both the nominal isolated subsystem and the whole nominal system to be nonminimum phase. In a second approach, a similar structure is introduced to identify a class of nonlinear large-scale interconnected systems. By exploiting the system structure of similarity, the proposed nonlinear reduced-order control schemes allow more general forms of uncertainties. The study shows that similar structures can simplify the analysis and reduce computation. Case studies on the HIRM aircraft and coupled inverted pendula, and a numerical simulation example are provided, respectively, to illustrate the results developed.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 6. Delay Dependent Output Feedback Control

Abstract
This chapter considers complex control systems with time-delay under the assumption that the time-delay is precisely known. A Lyapunov–Razumikhin approach is employed to deal with time-delay throughout this chapter. All the developed results consider time-varying delay and there is no limitation on the rate of change of time-delay. This is in contrast with the Lyapunov–Krasovskii approach. Since the time-delay is precisely known, it can be used in both the controller and observer design, and the developed results have high robustness. Both static and dynamical output feedback control schemes are presented for complex time-delay systems. In addition, decentralised static output feedback sliding mode controllers are designed to stabilise a class of complex interconnected time-delay systems where delay exists in both the interconnections and the isolated subsystems. Numerical examples and a case study of river pollution control are provided to demonstrate the developed results.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 7. Delay Independent Output Feedback Control

Abstract
In Chap. 7, complex control systems with time-delay are considered. It is not required that the time-delay is known. A Lyapunov Razumikhin approach is used to deal with the time-delay throughout this chapter. All the developed results consider time-varying delay and there is no limitation on the rate of change of time-delay. A local stabilisation problem is considered for affine nonlinear control systems with uncertainties using a Lyapunov-based approach and sliding mode control techniques. It is not assumed that the nominal system is either linearisable or partially linearisable. Stabilisation of a class of large-scale systems with nonlinear interconnections is also considered. A decentralised static output feedback variable structure control is synthesised and a set of conditions is developed to guarantee that the considered large-scale interconnected systems are stabilised uniformly asymptotically. Examples are provided to demonstrate the theoretical results.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 8. Sliding Mode Observer-Based Fault Detection and Isolation

Abstract
This chapter considers fault detection and isolation (FDI) for nonlinear systems with uncertainties using particular sliding mode observers for which the parameters can be obtained using LMI techniques. A sliding mode observder-based approach is presented to estimate system faults using bounds on the uncertainty, and as a special case, a fault reconstruction scheme is available where the reconstructed signal can approximate the fault signal to any accuracy. Sensor FDI for nonlinear systems is considered where a nonlinear diffeomorphism is introduced to exploit the system structure and a simple filter is presented to ‘transform’ the sensor fault into a pseudo-actuator fault scenario. Both fault estimation and reconstruction are considered. Case studies on a robotic arm and a mass–spring system are given to demonstrate the effectiveness of the proposed schemes.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 9. Application of Decentralised Sliding Mode Control to Multimachine Power Systems

Abstract
This chapter provides a decentralised strategy for the excitation control problem of multimachine power systems formed from an interconnected set of lower order systems through a network transmission. Both mismatched uncertainties in the interconnections and parametric uncertainties in the direct axis transient short circuit time constants, which affect the subsystem input distribution matrix, are considered. The proposed approach can deal with interconnection terms and parametric disturbances with large magnitude. The results obtained hold in a large region of operation if the control gain is high enough. This allows the operating point of the multimachine power system to vary to satisfy different load demands. Simulations on a three-machine power system are presented.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Chapter 10. Concluding Remarks

Abstract
Some examples, as an echo of the discussion about the source of complexity in Chap. 1 at the beginning of the book, are presented to further confirm the complexity of the systems considered in this book. Some suggestions for future work are presented. It is shown that study of complex control systems is a long term task for researchers and control engineers.
Xing-Gang Yan, Sarah K. Spurgeon, Christopher Edwards

Backmatter

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