Constrained optimal stochastic control of non-linear wave energy point absorbers

•The nonlinear buoyancy force of a wave energy absorber with a controller is modeled.•Constrains on the motion of the absorber and on the control force are modeled.•A sub-optimal controller is proposed which is causal and is close to optimal controller.•Optimal values of the controller parameters for various constrains are obtained.

The paper deals with the stochastic optimal control of a wave energy point absorber with strong nonlinear buoyancy forces using the reactive force from the electric generator on the absorber as control force. The considered point absorber has only one degree of freedom, heave motion, which is used to extract energy. Constrains are enforced on the control force to prevent large structural stresses in the floater at specific hot spots with the risk of inducing fatigue damage, or because the demanded control force cannot be supplied by the actuator system due to saturation. Further, constraints are enforced on the motion of the floater to prevent it from hitting the bottom of the sea or to make unacceptable jumps out of the water. The applied control law, which is of the feedback type with feedback from the displacement, velocity, and acceleration of the floater, contains two unprovided gain parameters, which are chosen so the mean (expected value) of the power outtake in the stationary state is optimized. In order to ensure accuracy of the results for each configuration of the controller Monte Carlo simulations have been carried out for various sea-states and the final results have been presented in the paper. The effect of nonlinear buoyancy force – in comparison to linear buoyancy force – and constraints of the controller on the power outtake of the device have been studied in details and supported by numerical simulations.