Radiation Force Modeling for a Wave Energy Converter Array

Salman Husain, Gordon G. Parker (), David Forehand and Enrico Anderlini
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Salman Husain: Mechanical Engineering—Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA
Gordon G. Parker: Mechanical Engineering—Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA
David Forehand: School of Engineering, The University of Edinburgh, Edinburgh EH8 9YL, UK
Enrico Anderlini: Department of Mechanical Engineering, University College London, London WC1E 6BT, UK

Energies, 2023, vol. 17, issue 1, 1-23

Abstract: The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, ν , of the radiation force transfer function matrix.

Keywords: ocean energy; radiation force; stability; passivity; positive-realness; marine structures; Wave Energy Converters (WEC) (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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