Leonid Fridman

Igor Boiko

Luis T. Aguilar

Rafael Iriarte

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.

A New Methodology via Two-Relay Controllers

Self-Oscillations in Dynamic Systems

Jaime Moreno

The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union – México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled "Automatization and Monitoring of Energy Production Processes via Sliding Mode Control". The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engineering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks.

Rafael Iriarte

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