Optimal Control of Nonlinear Wave Energy Converters In Heave for Maximum Power Extraction

The marine renewable energy community is interested in maximizing the power generated by nonlinear wave energy converters. Optimal control methods provide a tool to achieve this aim and can also help to inform the buoy design. An energy-optimal control law for a class of non-linear buoy models is derived and is shown to be singular. The solution approach is illustrated using an hourglass-shaped buoy having a cubic, hydrostatic nonlinearity. The optimal control law is only valid on singular arcs, and a method to search for these arcs is presented. Two singular arcs are found for the hourglass buoy model and analyzed. Neither is likely optimal thus, finding the energy-optimal singular arc is left for future work.