Novel LQR and Economic MPC Strategies for Energy Harvesting in Wave Energy Converters

In this paper, we propose two novel control strategies for energy harvesting and constraint satisfaction in wave energy converters (WEC). The first strategy is based on a Linear Quadratic Regulator (LQR) with a non-standard cost function designed to directly maximize the electrical power generated by the electromechanical actuator, leveraging the system's steady-state response to the wave signal for power computation. The second strategy employs a non-causal Economic Model Predictive Control (EMPC) law, also based on the same non-standard cost, to balance energy harvesting and heave position constraints. The analysis considers two scenarios: an ideal case with perfect wave signal prediction and a non-ideal case with imperfect wave signal prediction. Unlike other MPC strategies developed for WECs, the proposed EMPC strategy incorporate several distinctive features, including the inclusion of generator dynamics in the objective function for power maximization without external tuning parameters, the use of control input current rather than control input force, the integration of short-term wave prediction information to enhance control performance, recursive feasibility and the satisfaction of heave position constraints. The proposed strategies demonstrate versatility, offering potential extensions to a broader class of energy maximization problems. Their effectiveness is validated through numerical simulations using a point absorber as a case study and a comparative analysis with the linear non-causal optimal control (LNOC) strategy.