Nonlinear dynamic analysis and control synthesis for the Swinging Omnidirectional (SWINGO) Wave Energy Converter

We introduce, in this paper, an analysis of the dynamics of the Swinging Omnidirectional (SWINGO) wave energy converter. Such a device is an inertial reacting Wave Energy Converter (WEC), that exploits the dynamics of a gyropendulum mechanism which, being excited by the wave-induced whirling motion (i.e. coupling between pitch and roll on a floater), can successively activate an electric generator connected to the grid. In particular, we apply the harmonic balance method, tuned to the system fundamental harmonic, to identify the effect of nonlinearities on the SWINGO dynamics and their impact on energy production. Furthermore, we present the so-called van der Pol plane to assess the stability properties of the system. The SWINGO model is derived via a Lagrangian approach formulated with respect to quasi-coordinates. We demonstrate that multi-stability behaviour can be found for this nonlinear system, completely absent in its associated linearisation. Finally, we synthesise so-called ‘passive’ (i.e. proportional) energy-maximising controllers by leveraging the Harmonic Balance (HB) procedure, providing control parameters which are effectively tuned by exploiting the presented nonlinear description of SWINGO.