Abstract
AbstractGrazing events may create coexisting attractors and cause complex dynamics in piecewise-smooth dynamical systems. This paper studies the control of grazing-induced multistability in a soft impacting oscillator by using the time-delayed feedback control. The control switches from one of the coexisting attractors to a desired one to suppress complex dynamics near grazing events. We use path-following (continuation) techniques for non-smooth dynamical systems to investigate robustness of the controller and the parameter dependence of the controlled system. In particular, several newly developed computational methods are used, including a numerical method for analysing non-smooth delay equations and a method for calculating the Lyapunov exponents and the grazing point estimation. Numerical simulations demonstrate that the delayed feedback controller is effective, and a proper selection of the control gain and delay time can simplify the complex dynamics of the system near grazing.
Funder
Engineering and Physical Sciences Research Council
University of Exeter
Horizon 2020
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Cited by
16 articles.
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