Optimal control of an array of non-linear wave energy point converters

• Sub-optimal causal feedback control of displacement, velocity and acceleration vectors.
• Controllers force vector dependent on velocity in the stationary state.
• Absorption of energy ensured at any time.
• Proposed controller is shown to be optimal under mono-chromatic excitation.
• The control strategy and related optimization for non-linear point absorbers are elaborated.

The paper deals with the optimal feedback control and sub-optimal causal feedback control of an array of wave energy point absorbers using the reactive forces from the power take-off systems on the point absorbers as control forces. The dynamic coupling of the absorbers via the radiation wave forces and control forces are taken into account. Assuming linear wave mechanics the optimal control law is shown to be a non-causal feedback controller with feedback from measurement of the displacement, velocity, and acceleration of all floaters. i.e no wave load estimation or prediction is assumed. The control law will be optimal for any 2D or 3D irregular sea-state, as well as during the transient phase. To circumvent the non-causality problem related to the optimal controller law, a causal closed loop controller is suggested based on a slightly modified optimal control law. The controller contains an undetermined symmetric positive definite gain matrix. Since, the response of the array is narrow-banded at optimal control, this matrix has been chosen as the radiation damping matrix at the peak angular frequency. The causal controller is optimal under monochromatic wave excitation and close to optimal for irregular sea-states.