A Geometrical Interpretation of Force and Position Constraints in the Optimal Control of Wave Energy Devices
Bacelli, Giorgio and Ringwood, John (2011) A Geometrical Interpretation of Force and Position Constraints in the Optimal Control of Wave Energy Devices. Proceedings of the 9th European Wave and Tidal Energy Conference (EWTEC) .
Physical constraints need to be considered in the design of control systems for an oscillating body Wave Energy Converter (WEC). In the case of a hydraulic Power Take Off (PTO) unit, such constraints include the length of the stroke of a hydraulic piston or the maximum pressure permitted in the hydraulic circuit. In the paper, two types of WEC are considered: A 1-body point absorber oscillating in heave and a 2-body point absorber also oscillating in heave. A procedure for the analysis of the constraints is presented. It provides sufficient conditions for the satisfaction of both constraints and/or the violation of at least one constraint. The procedure is based on the discretization of the equations of motion of the WECs by approximating the forces and the velocities with a linear combination of basis functions. A special case is presented in which truncated Fourier series are used for the approximation. It is shown that the constraints can be interpreted as a geometrical object in a finite dimensional vector space, and that the study of sufficient conditions for the satisfaction of both constraints and for sufficient conditions for the violation of at least one constraint can be seen as the study of the intersection between these geometrical objects. It is also shown that the method allows the study of the effect of constraints on the amount of produced energy.
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