Abstract
In this work, the optimal power-maximising control problem is considered for the CETO 6 wave energy device, which consists of a fully-submersed cylindrical buoy, moving in its six hydrodynamic degrees of freedom, and attached to the seabed by means of three tether lines, each of which is equipped with a translational power take-off (PTO) system. A spectral control approach is employed, whereby the wave excitation, control input and buoy dynamics are approximated by means of Fourier series. Several scenarios are investigated in terms of PTO efficiency, which the proposed control approach is able to take into account. Viscous forces are modelled by means of a quadratic drag term, handled through an iterative control-statistical linearisation procedure. The power flow in individual PTOs is examined: assuming ideal PTO efficiency, achieving optimal power absorption requires the exchange of large amounts of reactive power, even more spectacularly than in WECs with a single DoF. However, in the presence of realistic constraints onto tether tension and with non-ideal PTO efficiency, those effects are practically eliminated. Finally, the interplay between control results and kinematic non-linearities is discussed- which, in contrast to hydrodynamic non-linearities, are rarely addressed in the WEC control literature. To that end, linear optimal control solutions, computed offline via the proposed spectral method, are used to control a numerically simulated model of the system where kinematic relations, between the buoy motion and tether motion and forces, exhibit substantial non-linear behavior.