Essentials of Non-linear Control Theory

by J.R. Leigh

Overview

The book is concerned with understanding the structure of nonlinear dynamic systems within a control engineering context After a discussion of theoretical foundations, the development moves to specific techniques (describing function method, phase plane portrait, linearisation methods). The treatment then becomes oriented to qualitative analysis and maintains this emphasis to the end of the book. The broad aim is to develop methods that will allow the topology of system behaviour to be visualised. The main tools are Lyapunov methods, extending to include recent work on system decomposition. A bibliography lists both earlier seminal and recent literature to allow the reader to follow up particular aspects.

Product Details

ISBN-13:	9780906048962
Publisher:	The Institution of Engineering and Technology
Publication date:	06/30/1983
Series:	Control, Robotics and Sensors
Pages:	104
Product dimensions:	6.14(w) x 9.21(h) x (d)

About the Author

Professor J.R. Leigh was educated at Sheffield City Grammar School and at Cambridge and London Universityies from which he holds higher degrees in both Control Engineering and Pure Mathematics. He has worked in both small and large organisations on the development and application of control systems. Previous posts include Senior Systems Engineer - United Steel Companies, and Head, Control Systems Section - British Steel Corporation Engineering Laboratory. In his current appointment at the Polytechnic of Central London, his research and teaching interests are centred around the modelling and computer control of industrial processes. Among his recent publications are the books, 'Functional Analysis and Linear Control Theory' (Academic Press, 1980), and 'Applied Control Theory' (IEE Control Engineering Series, Number 18, 1982). He is a Fellow of the Institution of Electrical Engineers and a Member of its Computing and Control Divisional Board. He is a Fellow of the Institute of Mathematics and its Applications and a Member of the London Mathematical Society.

Table of Contents

• Chapter 1: Initial orientation
• Chapter 2: Dynamic Systems - definitions and notation
• Chapter 3: The describing function method
• Chapter 4: The phase plane portrait
• Chapter 5: Linearisation
• Chapter 6: Determination of the qualitative behaviour of a nonlinear second-order system by linearisation (Lyapunov's first method)
• Chapter 7: Lyapunov's second or direct method
• Chapter 8: Envelope methods - the Popov and circle criteria for graphical analysis of a single feedback loop containing a nonlinear element
• Chapter 9: Limit cycles and relaxation oscillations
• Chapter 10: Liénard's equation
• Chapter 11: Gradient systems and system decomposition