Work-loop techniques for optimising nonlinear forced oscillators
Abstract
Linear and nonlinear resonant states can be restrictive: they exist at particular discrete states in frequency and/or elasticity, under particular (e.g., simple-harmonic) waveforms. In forced oscillators, this restrictiveness is an obstacle to system design and control modulation: altering the system elasticity, or modulating the response, would both appear to necessarily incur a penalty to efficiency. In this work, we describe an approach for bypassing this obstacle. Using novel work-loop techniques, we prove and illustrate how certain classes of resonant optimisation problem lead to non-unique solutions. In a structural optimisation context, several categories of energetically-optimal elasticity are non-unique. In an optimal control context, several categories of energetically-optimal frequency are non-unique. For these classes of non-unique optimum, we can derive simple bounds defining the optimal region. These novel theoretical results have practical implications for the design and control of a range of biomimetic propulsion systems, including flapping-wing micro-air-vehicles: using these results, we can generate efficient forms of wingbeat modulation for flight control.
Cite
@article{arxiv.2206.09859,
title = {Work-loop techniques for optimising nonlinear forced oscillators},
author = {Arion Pons and Tsevi Beatus},
journal= {arXiv preprint arXiv:2206.09859},
year = {2022}
}