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.
