Towards the Optimal Control of an Active Mechanical Motion Rectifier Power Take-Off Using Dynamic Programming

This paper presents a numerical method to approximately solve a challenging optimal control problem arising from a new mechanical power take-off design. The active mechanical motion rectifier design, while possessing great potential for converting energy from an oscillating mechanical structure, poses a complex control problem where the switching times and control variables need to be optimized simultaneously subject to implicit constraints from rectification requirements. A novel method is proposed to approximate the optimal solution based on dynamic programming (DP) techniques. By discretizing the state space and the control horizon, a new multi-step forward dynamic programming scheme is proposed to efficiently incorporate the switching time decisions into the conventional optimization of control variables. The proposed method is flexible enough to accommodate nonlinear dynamics and complex dynamic constraints. A numerical example demonstrated the effectiveness of the proposed method by controlling the active mechanical motion rectifier power take-off for an ocean wave energy converter.