An adaptive and energy-maximizing control of wave energy converters using an extremum-seeking approach

In this study is presented a systematical investigation on the feasibility of different extremum-seeking (ES) controls to improve the conversion efficiency of wave energy converters (WECs). The implemented schemes are model-free and adopt a continuous-time approach and are based on the sliding mode, relay, least-squares gradient, self-driving, and perturbation-based methods, and are used to improve the mean extracted power of a heaving point absorber subject to regular and irregular waves. This objective is achieved by optimizing the resistive and reactive coefficients of the power take-off (PTO) mechanism using the ES approach. The optimization results are verified against analytical solutions and the extremum of reference-to-output maps. The numerical results demonstrate that except for the self-driving ES algorithm, the other four ES schemes reliably converge for the two-parameter optimization problem, whereas the former is more suitable for optimizing a single-parameter. The results also show that for an irregular sea state, the sliding mode and perturbation-based ES schemes have better convergence to the optimum in comparison to other ES schemes considered here. The convergence of PTO coefficients towards the performance optimal values are tested for widely different initial values in order to avoid bias towards the extremum. We also demonstrate the adaptive capability of ES control by considering a case in which the ES controller adapts to the new extremum automatically amidst changes in the simulated wave conditions. Moreover, no explicit knowledge of (future) wave excitation forces is required in the algorithm, which implies that the model-free ES can be used as a causal controller for WECs. Our results demonstrate that the continuous-time and model-free ES method achieves the optimum within a single simulation, which contrasts with evolution-based optimization strategies that typically require a large number of (possibly expensive) function evaluations. The main contributions of this study consist in a wide overview of different ES techniques available in literature, some of which have not been tested for WEC devices before, using a continuous-time approach, for a submerged WEC. Also, a novel definition for the performance function is provided, in order to ensure the effectiveness of the control law among different sea states. The main advantages on using a model-free control law consist in the fact that there is no need to generate a model of the real device (which necessarily is a simplification of the actual device), therefore introducing an approximation on the description of the behavior of the WEC, especially when it comes to model the fluid-hull interaction. Also, a model-based control law should take into account the fact that the characteristics of the device may vary with time, due to the normal deterioration of materials in salt water, the growth of vegetation, or other reasons, and it is not possible to easily take into consideration these phenomena during the generation of the model. Another advantage of using an ES approach is that is not necessary to measure the parameters of the wave, since the force generated by the PTO can be obtained by measuring only the displacement and velocity of the buoy, which can be done much more easily. The main issue relative to the use of ES consists in the tuning of the controller parameters (although some of the methods used, such as the Sliding Mode ES, have a relatively low nu