Energy maximising robust control for spectral and pseudospectral methods with application to wave energy systems

Abstract

Spectral and Pseudospectral methods have been widely considered in diverse optimal control applications, usually where energy optimisation is required. Although such methods are a good way to ensure a good balance between performance and computational effort, in most of the literature, nominal mathematical models are considered without taking into account possible dynamic deviations from the nominal case. The main aim of this study is to propose a novel framework where spectral and pseudospectral problems include some structured uncertainty, achieving robust optimal control designs guaranteeing the ‘best worst-case performance’. In this paper, the objective function used for optimisation is inspired by wave energy converters. Two solution methodologies are developed. Firstly, an analytical solution, for circular and convex polytopic uncertainty boundaries, is proposed. Then, a numerical formulation is introduced to consider uncertainty sets of arbitrary shape, adding the ability to consider physical system constraints. Finally, an application example shows the benefit of this new control formulation.

Keywords:

• Control
• robust
• spectral
• pseudospectral
• optimisation
• energy maximising

Acknowledgements

Thanks to Eng. Nicolás Faedo for the continuous discussion during this study.

Disclosure statement

No potentsial conflict of interest was reported by the authors.

ORCID

Demián Garcia-Violini http://orcid.org/0000-0002-3131-7575

John V. Ringwood https://orcid.org/0000-0003-0395-7943

Notes

1 The proposed framework is an intermediate step in a number of implementable feedforward control strategies such as, for example, strategies based on receding horizon control (Bacelli & Ringwood, 2015; Genest & Ringwood, 2017).

2 Note that this is a relatively standard assumption in the WEC control literature (Faedo et al., 2017).

Additional information

Funding

This material is based upon works supported by Science Foundation Ireland under [grant no. 13/IA/1886].