Force-Limited Control of Wave Energy Converters using a Describing Function Linearization

TL;DR

This paper introduces a frequency domain linearization approach using describing functions to analyze force saturation effects in wave energy converters, enabling more efficient design and control insights.

Contribution

It presents a novel application of describing functions to approximate force saturation nonlinearities, facilitating analytical and graphical analysis of their impact on power generation.

Findings

Systems with specific impedance ratios are less sensitive to force limits

The method provides insights into the trade-offs between impedance matching and force saturation

Results are visualized with Smith charts for intuitive understanding

Abstract

Actuator saturation is a common nonlinearity. In wave energy conversion, force saturation conveniently limits drivetrain size and cost with minimal impact on energy generation. However, such nonlinear dynamics typically demand numerical simulation, which increases computational cost and diminishes intuition. This paper instead uses describing functions to approximate a force saturation nonlinearity as a linear impedance mismatch. In the frequency domain, the impact of controller impedance mismatch (such as force limit, finite bandwidth, or parameter error) on electrical power production is shown analytically and graphically for a generic nondimensionalized single degree of freedom wave energy converter in regular waves. Results are visualized with Smith charts. Notably, systems with a specific ratio of reactive to real mechanical impedance are least sensitive to force limits, a criteria which conflicts with resonance and bandwidth considerations. The describing function method shows promise to enable future studies such as large-scale design optimization and co-design.