Model Predictive Control of parametric excited pitch-surge modes in wave energy converters

For a heave-pitch-surge three-degrees-of-freedom wave energy converter, the heave mode is usually decoupled from the pitch-surge modes for small motions. The pitch-surge modes are usually coupled and are parametrically excited by the heave mode, depending on the buoy geometry. In this paper, a Model Predictive Control is applied to the parametric excited pitch-surge motion, while the heave motion is optimized independently. The optimality conditions are derived, and a gradient-based numerical optimization algorithm is used to search for the optimal control. Numerical tests are conducted for regular and Bretschneider waves. The results demonstrate that the proposed control can be implemented to harvest more than three times the energy that can be harvested using a heave-only wave energy converter. The energy harvested using a parametrically excited model is higher than that is harvested when using a linear model.