Up-wave surface elevation for smooth hydrodynamic control of wave energy conversion in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers-Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal, full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this non-causality and the non-causality of the exciting force impulse response function, the use of up-wave surface elevation has been suggested in the literature for synthesis of the necessary control forces. The overall formulation here draws on draws on this approach and leads to smooth control that is near-optimal given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. A predominantly heaving submerged device comprised of three vertically stacked discs driving a hydraulic cylinder is studied. Absorbed power performance with the present near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results are obtained for wave spectra at different significant wave heights and energy periods representing three locations along the U.S. coastline.