Linear Optimal Noncausal Control of Wave Energy Converters

This paper addresses the fundamental theoretical development of a linear optimal noncausal control for wave energy converters (WECs) in a closed analytic form. It is well known that the WEC control is a noncausal control problem, i.e., the future wave information contributes to the present control action. This paper provides a reliable, efficient, and simple linear optimal controller with guaranteed stability for the WEC control problem. The proposed WEC linear optimal control consists of a causal linear state feedback part and an anticausal linear feedforward part to incorporate the influence of future incoming waves. The stability of the closed-loop WEC control system with the proposed linear optimal controller is proven. The contribution of the noncausal term using wave prediction information to the optimal control and the energy output is analyzed quantitatively. The proposed linear controller can be more preferred when constraint satisfaction becomes a less important issue for mild sea states and some well-designed WECs with an ample operation range. The proposed optimal control strategy can be extended for a generic class of energy maximization problems. Numerical simulations are presented to justify the efficacy of the proposed WEC optimal control.