Robust Excitation Force Estimation and Prediction for Wave Energy Converter M4 Based on Adaptive Sliding-Mode Observer

Abstract

The wave excitation force estimation and prediction play an important role in improving the performance of causal and noncausal controllers for wave energy converters (WECs). This article proposes a robust adaptive sliding-mode observer (ASMO) to estimate the wave excitation force subject to unknown disturbances and parametric uncertainties for a multimotion multifloat WEC, called M4. Both the convergence time and the estimation error can be explicitly bounded within expected limits by tuning the ASMO parameters, which are essentially beneficial for causal controllers to maintain the control performance. A fixed-time convergent sliding variable is designed to drive the estimation error into a small region within a fixed time. Due to the adaptive law, the overall system is proven to be finite-time stable, which allows explicit formulations of the convergence time and the estimation error. Moreover, based on the wave force estimation by the ASMO, an improved auto-regressive (AR) model whose coefficients are updated by online training is developed to predict the wave excitation force. The prediction errors can also be explicitly estimated to achieve guaranteed control performance for the noncausal controller requiring future excitation force. From the comparison based on a realistic sea wave gathered from Cornwall, U.K., it can be found that compared with the conventional Kalman filter, the ASMO achieves a smaller steady-state estimation error and has satisfactory robustness performance against 30% model mismatch.