Self-Oscillations in Dynamic Systems: A New Methodology Via Two-Relay Controllers

ISBN-13: 9783319233024 / Angielski / Twarda / 2015 / 158 str.

Luis T. Aguilar; Igor Boiko; Leonid Fridman

Opis

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, Poincare 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.

Recenzje

"The book contains ten chapters presented in three parts. ... The intended audience for this book consists of mechanical and control scientists and engineers, as well as graduate and Ph.D. students interested in the theory of self-oscillation generation in underactuated dynamic systems." (Clementina D. Mladenova, Mathematical Reviews, June, 2016)

Spis treści

​Introduction.- Part I: Design of Self-Oscillations using Two-Relay Controller.- Describing Function-Based Design of TRC for Generation of Self-Oscillation.- Poincaré Maps Based Design.- Self-Oscillation via Locus of a Perturbed Relay System Design (LPRS).- Part II: Robustification of the Self-Oscillation Generated by Two-Relay Controller.- Robustification of the Self-Oscillation via Sliding Modes Tracking Controllers.- Output-Based Robust Generation of Self-Oscillations.- Part III: Applications.- Generating Self-Oscillations in Furuta Pendulum.- Three Link Serial Structure Underactuated Robot.- Generation of Self-Oscillations in Systems with Double Integrator.- Fixed-Phase Loop (FPL).- Appendix A: Describing Function.- Appendix B: The Locus of a Perturbed Relay System (LPRS).- Appendix C: Poincaré Map.- Appendix D: Output Feedback.- References.- Index.

Blurb

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.