Work-loop techniques for optimising nonlinear forced oscillators

TL;DR

This paper introduces work-loop techniques to optimize nonlinear forced oscillators, enabling the bypass of traditional restrictions on resonant states, with applications in biomimetic propulsion systems like flapping-wing micro-air-vehicles.

Contribution

It presents novel work-loop methods and theoretical results that reveal non-uniqueness in resonant optimization problems, aiding system design and control.

Findings

Non-unique solutions in resonant optimization problems.

Derived bounds for optimal elasticity and frequency regions.

Practical implications for biomimetic propulsion system design.

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.