Improving the Computational Performance of Nonlinear Pseudospectral Control of Wave Energy Converters

Abstract

The optimal control problem for a one-degree of freedom wave energy converter (WEC) with dynamical nonlinearities and constraints is formulated in the frequency-domain. The formulation adopted corresponds to a Fourier pseudospectral framework but, in contrast to previous similar approaches found in WEC control literature, it is shown that control force and velocity variables can be eliminated, using a frequency-domain transcription of the nonlinear dynamical equations, thus, resulting in fewer variables and elimination of the equality constraints. Furthermore, it is shown how the gradient and Hessian of the cost function and constraints can be explicitly calculated, which can be used to improve convergence within gradient-based optimisation techniques. The benefits of the proposed developments are illustrated by means of numerical experiments, for a flap-type WEC with viscous drag, under various constraint configurations. The techniques presented are formulated in a generic way, allowing for easy result transposition to a variety of nonlinear WEC models.