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An Introduction to Nonlinearity in Control Systems

An Introduction to Nonlinearity in Control Systems

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Author: Derek Atherton

Book Description Report this book

The book is concerned with the effects of nonlinearity in feedback control systems and techniques which can be used to design feedback loops containing nonlinear elements. After a short introductory chapter on nonlinearity and its possible effects the use of phase plane methods for nonlinear second order systems is discussed. The next three chapters cover the describing function method and its applications in the determination of limit cycles, stability analysis and the prediction of unique nonlinear behaviour such as jump resonance and subharmonic generation. The following chapter shows using the Tsypkin approach how in feedback loops with a relay nonlinearity any limit cycles and their stability can be found exactly. Examples are given which cover some unique forms of limit cycles such as limit cycles with a sliding mode and multipulse limit cycles, which can be caused by resonant plant transfer functions. In recent years with the advent of microprocessor controllers there has been considerable interest in techniques for controller tuning based on limit cycle data and this is the topic covered in the next chapter. The analyses used make use of both the describing function method and the Tsypkin method presented in the previous chapters. The next topic covered is absolute stability methods for a nonlinear feedback loop with a single nonlinearity with emphasis placed on frequency domain methods to allow comparison with describing function results. The final chapter covers some methods for the design of nonlinear systems. The material is of an introductory nature but hopefully gives an overview and provides a basic understanding of various topics, many developed in recent years, and several of which have entire textbooks devoted to them.

ABOUT THE AUTHOR

Derek Atherton

Professor Derek. P. AthertonBEng, PhD, DSc, CEng, FIET, FIEEE, HonFInstMC, Derek Atherton studied at the universities of Sheffield ( BEng 1956) and Manchester, obtaining a PhD in 1962 and DSc in 1975 from the latter. He spent the period from 1962 to 1980 teaching and doing research in Canada, first at McMaster University until 1964 and then at the University of New Brunswick. Whilst in Canada he served on several National Research Council committees including the Electrical Engineering Grants Committee. He took up the post of Professor of Control Engineering at the University of Sussex in 1980 and is currently retired but has an office at the university, gives some lectures, and has the title of Emeritus Professor and Associate Tutor. He has been active with many professional engineering bodies, serving as President of the Institute of Measurement and Control in 1990, President of the IEEE Control Systems Society in 1995, and as a member of the IFAC Council from 1990-96. He was an Editor of the IEE Proceedings on Control Theory and Applications (CTA) for several years until 2007 and was also formerly an editor for the IEE Control Engineering Book Series. He served EPSRC on research panels and as an assessor for research grants for many years and also served as a member of the Electrical Engineering Panel for the Research Assessment Exercise in 1992. His major research interests are in non-linear control theory, computer aided control system design, simulation and target tracking. He has written four books, is a co-author of two others [1-6] and has published more than 350 papers in Journals and Conference Proceedings. Professor Atherton has given invited lectures in many countries and supervised over 30 Doctoral students. 1. Atherton D P, Nonlinear Control Engineering: Describing Function Analysis and Design. London, Van Nostrand Reinhold, September 1975, 627 pages. (also abridged version) Atherton D P, Nonlinear Control Engineering. Van Nostrand Reinhold, 1982, student edition, 470 pages 2. Atherton D P, Stability of Nonlinear Systems. Research Studies Press, John Wiley,1981, 231 pages 3. Atherton, D.P. Control Engineering. 2009 Bookboon publications at www.bookboon.com 4. Furuta K, Sano A and Atherton D P State Variable Methods in Automatic Control. John Wiley, 1988, 212 pages. 5. Xue, D , Chen,Y and Atherton,D.P Linear Feedback Control; Analysis and Design with MATLAB SIAM books, Philadelphia, USA, 2007, pp354. 6. Atherton, D.P. An Introduction to Nonlinearity in Control Systems. 2011Bookboon publications at www.bookboon.com Derek P. Atherton.br />February 2012

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