Stochastic control of wave energy converters with constrained displacements for optimal power absorption

• Published in: Applied ocean research 2019-08, Vol.89, p.1-11
• Main Authors: Sun, Tao, Nielsen, Søren R.K., Basu, Biswajit
• Format: Article
• Language: English
• Subjects: Control; Displacement; Displacement constraints; Handling; Heave point absorber; Nonlinear programming; Optimal power take-off; Wave energy; Wave power devices
• ISSN: 0141-1187; 1879-1549
• DOI: 10.1016/j.apor.2019.04.022

•A semi-analytical solution is derived for optimal control of PTO of a heave point absorber with constrained displacements.•The control laws in constrained and unconstrained states turn out to be an open-loop and a closed loop type respectively.•Algorithms have been devised to estimate the wave load and predict the future velocity.•The theory has been validated against numerical solutions obtained by nonlinear programming. An semi-analytical solution is derived for the optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the displacement. At first the control force is derived during states, where the displacement constraint is active. This results in an open-loop control law dependent on the external wave load on the absorber. Next, the analytical solution for the optimal control in the unconstrained state is indicated, which turns out to be of the closed loop type with feedback from the present displacement and acceleration and from future velocities. The derived control law contains an undetermined constant, which is calibrated at the interface to the previous constrained state. The approach requires the estimation of the wave load during the constrained states, and the prediction of the future velocity response during unconstrained states. An algorithm has been devised in the paper for handling these problems. The theory has been validated against numerical solutions obtained by nonlinear programming.