  In this work, we present a novel MPC-integrated multiphase IB framework that
can compute the optimal energy-maximizing control force on-the-fly by
dynamically interacting with a high-fidelity numerical wave tank (NWT). Due to
the requirement of solving a constrained optimization problem at each time step
of the IB simulation, the MPC algorithm utilizes a low-dimensional dynamical
model of the device that is based on the linear potential theory (LPT). The
multiphase IB solver, on the other hand, is based on the high-dimensional
fictitious domain Brinkman penalization (FD/BP) method, which fully-resolves
the hydrodynamic nonlinearities associated with the wave-structure interaction
(WSI). A time-series forecasting auto-regressive model is implemented that
predicts wave heights to estimate the future wave excitation/Froude- Krylov
forces for the MPC algorithm. Moreover, we also experiment with non-linear
Froude-Krylov (NLFK) forces for the first time in an MPC formulation. Under
varying sea conditions, the predictions of the MPC-integrated multiphase IB
solver are compared to the widely popular LPT-based solvers. Overall, six
WSI/MPC solver combinations are compared for a heaving vertical cylinder. We
also determine the pathway of energy transfer from the waves to the power
take-off (PTO) system and verify the relationships using IB simulations.
Additionally, three different sea states are simulated within the IB simulation
to test the adaptive capability of MPC for WECs. MPC is demonstrated to adapt
to changing sea conditions and find the optimal solution for each sea state.
