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Self-Oscillations in Dynamic Systems: A New Methodology Via Two-Relay Controllers by Luis T. Aguilar

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

by Luis T. Aguilar
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Book cover type: Paperback
  • ISBN13: 9783319365374
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Birkhauser
  • Publication Date:
  • Pages: 158
  • Original Price: EUR 49.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 257 grams
  • BISAC Subject(s): System Theory, Automation, and Industrial Design / Product

From the Back Cover

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.

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