Hybrid Optimal Control for an Active Mechanical Motion Rectifier for Wave Energy Converters via Separation Principle

The wave energy field is characterised by its continuous growth and development in research and technology. Over recent decades, different application issues have hindered the worldwide implementation of wave energy devices, and only a few have reached the commercialisation stage. Some of these inherent challenges have driven the creation of innovative wave energy system designs. In particular, active mechanical motion rectification (AMMR) is a novel proposal to rectify the energy flux in wave energy devices. The objective of active rectification is twofold. On the one hand, it increases the overall system efficiency by achieving a higher average output velocity in the generator. On the other hand, the AMMR introduces a new variable in the control design: A switching law to connect and disconnect the generator from the wave capture structure. Thus, the control design possesses two degrees of freedom, significantly increasing the complexity of the energy-maximising power take-off control problem. In this paper, the problem of designing an optimal control philosophy for an AMMR-based wave capture system is addressed. The problem is solved by proving that, a separation principle applies, and that the optimal control solution over a fixed interval, is independent of the optimal switching sequence selection. To illustrate the utility of the analytical results, a numerical example for a flap-type wave energy converter, utilising an AMMR-based power take-off, is presented.