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This paper derives a control law within the context of optimal control theory for a heaving wave energy converter (WEC) and presents its implementation procedure. The proposed control assumes the availability of measurements of pressure distribution on the buoy surface, buoy position, and buoy velocity. This control has two main characteristics. First, this control is derived based on a simple dynamic model. The forces on the WEC are modeled as one total force, and hence there is no need to compute excitation or radiation forces. Second, this control can be applied to both linear and nonlinear WEC systems. The derived control law is optimal, yet its implementation requires estimation of some force derivatives which render the obtained control force sub-optimal. Numerical testing demonstrates in this paper that the proposed simple model control can achieve levels of harvested energy close to the maximum theoretical limit predicted by singular arc control in the case of linear WEC systems. 

The model of a three-degree-of-freedom Wave Energy Converter can be simplified as a linear time-varying system. In this model, the heave mode parametrically excites the pitch mode, which in turn excites the surge mode. The heave mode, however, is independent to the other two modes when the motion is small. The purpose of this paper is to design a controller to maximize the energy harvested over a receding time horizon. We also want to demonstrate that, with proper design of the control, it is possible to exploit this nonlinear coupling between the modes so as to harvest more energy. The controller selected is the linear quadratic Gaussian optimal control. The prediction of excitation forces is constructed based on the estimation where the estimations are obtained by using extended Kalman Filter. The prediction of excitation force is fed into the controller to compute the time-varying linear quadratic optimal control. Constraints on the WEC motion are accounted for in computing the control. The results show that the energy captured by three-degree-of-freedom Wave Energy Converter is 3:56 times the energy extracted in heave mode only. Higher energy harvesting is demonstrated when the linear time-varying model is used in control design.