Bi-Layer Model Predictive Control with Extended Horizons for Multi-Axis Underactuated Wave Energy Converters

In the field of wave energy, multi-axis wave energy converters (WECs) have emerged as a research priority owing to their enhanced energy absorption, leading to increased computational complexity. Conventional model predictive control (MPC) approaches have demonstrated limitations in the trade-off between real-time requirements and control performance. This paper proposes a bi-layer MPC strategy, including a long-term energy maximization layer and a short-term trajectory-tracking layer. First, a multi-axis underactuated WEC (MU-WEC) is proposed, which incorporates an inertial cable-driven parallel mechanism to absorb energy from multiple directions. In addition, a control-oriented dynamic model of a MU-WEC is established. Then, a bi-layer MPC strategy is proposed, which decouples computationally intensive optimization processes from time-sensitive real-time control, alleviating the computational burden significantly. Therefore, the upper layer achieves enhanced control performance by enabling extended prediction horizons, whereas the lower layer serves to ensure real-time requirements. Moreover, numerical simulations under irregular wave conditions demonstrate the performance of the proposed bi-layer MPC: under different waves, bi-layer MPC improves energy absorption by 127–311% over conventional MPC. This performance enhancement stems from the 5 times extension of the prediction horizon enabled by the reduced computational burden.