An Introduction to Nonlinearity in Control Systems

Learn describing functions and relay methods for nonlinear control.

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اللغة

English

الصفحات

176

سنة النشر

2014

المؤلف

Derek Atherton

PDF: 3,99 €

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• Build intuition for why nonlinear feedback can behave differently than linear control.
• Learn phase-plane and describing-function methods for analyzing limit cycles.
• See how DF accuracy is assessed and why discontinuities and distortions matter.
• Study relay-based exact limit cycle analysis and practical controller tuning.
• Compare absolute stability criteria with DF-based predictions.

الوصف

This book provides an introduction to how nonlinear elements affect feedback control systems. It develops practical analysis tools and shows how nonlinear behavior can differ qualitatively from linear systems, including amplitude-dependent responses, limit cycles, and possible chaotic motion. After introducing the idea of nonlinearity and common forms found in control engineering, it develops the phase-plane method for second-order systems and then focuses on the describing function (DF) method—used to predict limit cycles, analyze their stability, and understand when DF predictions fail. The text extends DF ideas to sinusoid-plus-bias and multiple-sinusoid cases (including jump resonance). It then treats exact limit cycle analysis for relay systems, controller tuning from relay-produced limit cycles, and absolute stability results via frequency-domain criteria. Finally, it surveys design approaches for nonlinear control systems.

فهرس المحتويات

Preface

1 Introduction

2 The Phase Plane Method

3 The Describing Function

Preface
1 Introduction
2 The Phase Plane Method
3 The Describing Function
4 Stability and Limit Cycles using the DF
5 The SSDF and Harmonically Forced Systems
6 Limit cycles in relay systems
7 Controller Tuning from Relay Produced Limit Cycles
8 Absolute Stability Results
9 Design of Nonlinear Control Systems

معاينة

The book is intended to provide an introduction to the effects of nonlinear elements in feedback control systems. A central topic is the use of the Describing Function (DF) method since in combination with simulation it provides an excellent approach for the practicing engineer and follows on logically from a first course in classical control, such as the companion volume in this series. Some of the basic material on the topic can be found in my earlier book which is frequently referenced throughout the text.
The first chapter provides an introduction to nonlinearity from the basic definition to a discussion of the possible effects it can have on a system and the different behaviour that might be found, in particular when it occurs within a cascade system of elements or in a feedback loop. The final part of the chapter gives a brief overview of the contents of the book.

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