On the principle of impedance-matching for underactuated wave energy harvesting systems

In recent years, the fundamental principle of impedance-matching (IM) has inspired a number of sophisticated, yet simple, control solutions for wave energy converters (WEC). Such controllers have the capability of maximising energy absorption from incoming waves with mild computational requirements, being often intuitive in their design, hence especially appealing for real-time industrial applications. Nonetheless, these control solutions are, to date, almost exclusively developed for single degree-of-freedom (DoF) (and hence fully actuated) WEC systems, hindering their application to realistic underactuated multi-DoF devices, i.e.harvesting systems where energy is extracted from only a handful of its total set of modes of motion. Motivated by this, we present, in this paper, a comprehensive derivation and discussion of the IM conditions for maximum energy absorption in underactuated multi-DoF WEC systems. In particular, we show that the IM principle for single-DoF devices can be effectively extended to underactuated multi-DoF systems, and that a set of optimality conditions can be explicitly derived. In addition, we discuss both the impact and use of this set of optimal conditions for control design and synthesis, hence effectively taking a fundamental step towards the general extension of current IM-based techniques to the case of underactuated multi-DoF devices.