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

In this paper, we systematically investigate the feasibility of different extremum-seeking (ES) control schemes to improve the conversion efficiency of wave energy converters (WECs). Continuous-time and model-free ES schemes based on the sliding mode, relay, least-squares gradient, self-driving, and perturbation-based methods 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

Extremum-seeking control for periodic steady-state response optimization

Extremum-seeking control is a powerful adaptive technique to optimize steady-state system performance. To this date, extremum-seeking control has mainly been used to optimize plants with constant steady-state outputs, whereas the case in which the steady-state outputs are time varying, has received less attention. We propose an extremum-seeking scheme for the optimization of nonlinear plants with periodic steady-state outputs. Extremum-seeking control in this setting is relevant in e.g. the scope of tracking and disturbance rejection problems. We show that under certain assumptions the proposed extremum-seeking controller design guarantees that for an arbitrarily large set of initial conditions the steady-state performance of the plant converges arbitrarily close to its optimal value

Extremum-seeking control for periodic steady-state response optimization

Extremum-seeking control is a powerful adaptive technique to optimize steady-state system performance. To this date, extremum-seeking control has mainly been used to optimize plants with constant steady-state outputs, whereas the case in which the steady-state outputs are time varying, has received less attention. We propose an extremum-seeking scheme for the optimization of nonlinear plants with periodic steady-state outputs. Extremum-seeking control in this setting is relevant in e.g. the scope of tracking and disturbance rejection problems. We show that under certain assumptions the proposed extremum-seeking controller design guarantees that for an arbitrarily large set of initial conditions the steady-state performance of the plant converges arbitrarily close to its optimal value