Receding-Horizon Pseudo-spectral Control of Wave Energy Converters Using Periodic Basis Functions

Power-maximizing control of wave energy converters (WECs) can be implemented within a receding-horizon (RH) framework, whereby the reference force or velocity trajectory is updated in real-time by a feed-forward control (FFC) algorithm. For the computation of optimal WEC trajectories and control forces, Fourier pseudo-spectral (PS) control, using periodic basis functions, is simple and computationally attractive, for both linear and non-linear WEC dynamics. However, the finite-length wave excitation signal, as seen by the FFC, is in general non-periodic. In this paper, it is shown that, despite the non-periodicity of the input wave signal, a simple Fourier PS method can be successfully used as an FFC algorithm, by applying suitable windowing functions to the input signal when necessary. Furthermore, a simple wave forecasting algorithm is introduced, solely based on past values of the wave excitation, and the impact of wave forecast errors on the controller performance is investigated. Overall, with or without forecast errors, the proposed approach allows for power absorption above 99% of the optimum, for a forecasting horizon of less than 30s for a linear WEC model, and less than 15s for a non-linear WEC model including a quadratic viscous drag term.