Self-Oscillations in Dynamic Systems

A New Methodology via Two-Relay Controllers

  • Luis T. Aguilar
  • Igor Boiko
  • Leonid Fridman
  • Rafael Iriarte

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
    Pages 1-16
  3. Design of Self-Oscillations Using Two-Relay Controller

    1. Front Matter
      Pages 17-17
    2. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 19-37
    3. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 39-52
    4. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 53-64
  4. Robustification of Self-Oscillations Generated by Two-Relay Controller

    1. Front Matter
      Pages 65-65
    2. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 67-80
    3. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 81-88
  5. Applications

    1. Front Matter
      Pages 89-89
    2. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 91-98
    3. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 99-107
    4. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 109-119
    5. Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte
      Pages 121-135
  6. Back Matter
    Pages 137-158

About this book

Introduction

This monograph presents a simple and efficient two-relay control algorithm for generation of self-excited oscillations of a desired amplitude and frequency in dynamic systems. Developed by the authors, the two-relay controller consists of two relays switched by the feedback received from a linear or nonlinear system, and represents a new approach to the self-generation of periodic motions in underactuated mechanical systems.


The first part of the book explains the design procedures for two-relay control using three different methodologies – the describing-function method, Poincaré maps, and the locus-of-a perturbed-relay-system method – and concludes with stability analysis of designed periodic oscillations.


Two methods to ensure the robustness of two-relay control algorithms are explored in the second part, one based on the combination of the high-order sliding mode controller and backstepping, and the other on higher-order sliding-modes-based reconstruction of uncertainties and their compensation where Lyapunov-based stability analysis of tracking error is used. Finally, the third part illustrates applications of self-oscillation generation by a two-relay control with a Furuta pendulum, wheel pendulum, 3-DOF underactuated robot, 3-DOF laboratory helicopter, and fixed-phase electronic circuits.


Self-Oscillations in Dynamic Systems will appeal to engineers, researchers, and graduate students working on the tracking and self-generation of periodic motion of electromechanical systems, including non-minimum-phase systems. It will also be of interest to mathematicians working on analysis of periodic solutions.

Keywords

Nonlinear systems Self-excited oscillations Two-relay controller Underactuated mechanical systems Variable structure systems

Authors and affiliations

  • Luis T. Aguilar
    • 1
  • Igor Boiko
    • 2
  • Leonid Fridman
    • 3
  • Rafael Iriarte
    • 4
  1. 1.CITEDIInstituto Politecnico NacionalTijuanaMexico
  2. 2.Department of Electrical EngineeringThe Petroleum InstituteAbu DhabiUnited Arab Emirates
  3. 3.Division de Ingenieria ElectricaUniversidad Nacional Autonoma de MexicoMexico CityMexico
  4. 4.Division de Ingenieria ElectricaUniversidad Nacional Autonoma de MexicoMexico CityMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-23303-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-23302-4
  • Online ISBN 978-3-319-23303-1
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • About this book