Systems and Control PDF

PREFACE

This book is about modeling, analysis, and control of dynamical systems. Its objective is to familiarize the reader with the basics of dynamical system theory while, at the same time, equipping him or her with the tools necessary for control system design. The emphasis is on the design in order to show how dynamical system theory fits into practical applications. Various methods of a controller design are discussed.

This text can be used in a variety of ways. It is suitable for a senior- or graduate-level course on systems and control. The text can also be used in an introductory course on nonlinear systems. Finally, it can be used in an introductory course to modern automatic control. No special background is necessary to read this text beyond basic differential equations and elements of linear algebra. The book is also suitable for self-study. To accomplish this goal, the required mathematical techniques and terminology are reviewed in the Appendix. Depending on the background, the reader may refer to the material in the Appendix as needed.

Whenever one wishes to analyze a problem arising in the "real" world, the first order of business is the construction of a mathematical model of the problem. In this book we discuss mathematical modeling of problems from mechanical and electrical engineering, as well as from physics and biology. Constructing models of dynamical systems using a linguistic description that employs IF–THEN rules is also considered. Two main types of dynamical systems are common in applications: those for which the time variable is discrete and those for which the time variable is continuous. When the time variable is discrete, the dynamics of such systems are often modeled using difference equations. In the case when the time is continuous, ordinary differential equations are frequently chosen for modeling purposes. Both types of models are considered in the book. Nonlinear systems are emphasized to acknowledge the critical role that nonlinear phenomena play in science and technology. The models presented are the ones that can be used to design controllers. These models are constructed from the control engineering point of view. Most of the time, engineers develop models of man-made objects. This is in contrast with physicists, who are more interested in modeling nature. Models in the last chapter of this book, however, are of interest to engineers, physicists, or biologists. This chapter is an invitation to control engineering of the future where control designers will be challenged to tackle highly complex, nonlinear, dynamical systems using multidisciplinary tools.

This book is about modeling, analysis, and control of dynamical systems. Its objective is to familiarize the reader with the basics of dynamical system theory while, at the same time, equipping him or her with the tools necessary for control system design. The emphasis is on the design in order to show how dynamical system theory fits into practical applications. Various methods of a controller design are discussed. This text can be used in a variety of ways. It is suitable for a senior- or graduate-level course on systems and control. The text can also be used in an introductory course on nonlinear systems. Finally, it can be used in an introductory course to modern automatic control. No special background is necessary to read this text beyond basic differential equations and elements of linear algebra. The book is also suitable for self-study. To accomplish this goal, the required mathematical techniques and terminology are reviewed in the Appendix. Depending on the background, the reader may refer to the material in the Appendix as needed. Whenever one wishes to analyze a problem arising in the "real" world, the first order of business is the construction of a mathematical model of the problem. In this book we discuss mathematical modeling of problems from mechanical and electrical engineering, as well as from physics and biology. Constructing models of dynamical systems using a linguistic description that employs IF–THEN rules is also considered. Two main types of dynamical systems are common in applications: those for which the time variable is discrete and those for which the time variable is continuous. When the time variable is discrete, the dynamics of such systems are often modeled using difference equations. In the case when the time is continuous, ordinary differential equations are frequently chosen for modeling purposes. Both types of models are considered in the book. Nonlinear systems are emphasized to acknowledge the critical role that nonlinear phenomena play in science and technology. The models presented are the ones that can be used to design controllers. These models are constructed from the control engineering point of view. Most of the time, engineers develop models of man-made objects. This is in contrast with physicists, who are more interested in modeling nature. Models in the last chapter of this book, however, are of interest to engineers, physicists, or biologists. This chapter is an invitation to control engineering of the future where control designers will be challenged to tackle highly complex, nonlinear, dynamical systems using multidisciplinary tools.

As can be concluded from the above remarks, the scope of the book is quite broad. This is in order to show the multidisciplinary role of nonlinear dynamics and control. In particular, neural networks, fuzzy systems, and genetic algorithms are presented and a self-contained introduction to chaotic systems is provided. Lyapunov's stability theory and its extensions are used in the analysis of dynamical system models. The objective of the stability analysis is to determine the system behavior without solving the differential, or difference, equations modeling the system. In fact, the Lyapunov theory is used as a unifying medium for different types of dynamical systems analyzed. In particular, optimal, fuzzy, sliding mode, and chaotic controllers are all constructed with the aid of the Lyapunov method and its variants. Furthermore, a class of neural networks is analyzed using Lyapunov's method. Classical methods and the techniques of postmodern control engineering, such as fuzzy logic, neural networks, and genetic algorithms, are presented in a unified fashion. It is shown how these new tools of a control engineer supplement the classical ones.

In addition to worked examples, this book also contains exercises at the end of each chapter. A number of solved problems, as well as the exercises, require the use of a computer. Although there are now many quality software packages available that could be used with this book, MATLAB* was chosen because it appears to be the most widely used math-tools program in engineering circles, and it is also popular among science students. Student editions ofMATLAB and SIMULINK are sufficient for the worked examples and exercises in this book. The solutions manual, with complete solutions to all the exercises in the book, is available from the publisher to the instructors who adopt this book for their courses.

There is a companion web site for this book, where the current errata are available as well as the MATLAB m-files of examples solved in the text. The URL of the site is http://dynamo.ecn.purdue.edu/~zak/systems/Index.html.