A generic linear non-causal optimal control framework integrated with wave excitation force prediction for multi-mode wave energy converters with application to M4

Abstract

The multi-float multi-mode wave energy converter (M-WEC) M4 has essentially linear hydrodynamics characteristics in operational and even extreme waves. This is in contrast to point-absorber and most raft-type devices where nonlinear effects and associated losses are significant. The control problem now involves a large number of degrees of freedom. Energy maximizing control of wave energy converters (WECs) is a non-causal control problem. This paper aims to propose a complete self-contained noncausal optimal control framework by combining a linear non-causal optimal control (LNOC) algorithm with an autoregressive (AR) model as the wave excitation force predictor and a Kalman Filter with random walk wave model (KFRW) as the wave excitation force estimator. The efficacy of the proposed framework together with its enabling components is demonstrated numerically using irregular waves. The proposed framework has low computational load, which enables its real-time implementation on standard computational hardware. Furthermore, the wave force prediction does not require deployment and maintenance of expensive hardware, which helps to reduce the unit cost of the generated electricity.

Non-causal Linear Optimal Control With Adaptive Sliding Mode Observer for Multi-Body Wave Energy Converters

“…Firstly, perfect prediction of wave forces is assumed to demonstrate the performance degradation influenced by the length of prediction horizon; secondly, with a suitably chosen prediction horizon, several cases considering prediction errors are simulated to show the influences on control performance by the prediction error. We choose the values of significant wave height, the peakedness factor and the peak period as H s = 0.04 m, γ = 1 and T p = 1.8 s as suggested in [16], [22]. Since a 1:40 scaled model of M4 is used in simulation, the corresponding actual wave height is scaled to 1.6 m and the corresponding actual peak period is scaled to 11.4 s. A wide range of sea states are tested in Simulation Sets 2 & 3.…”

“…Since the prediction errorw k,np is not available, we prove that the proposed control policy (15) enables the ideal model (16) involving unavailable information to be approximated by the nominal model (17) which only uses known but inaccurate information.…”

“…The wave prediction methods are mainly divided into two categories: 1) deterministic prediction methods that are based on the measurements at multiple nearby locations around the WECs, such as the deterministic sea wave prediction (DSWP) [12] and 2) statistical methods based on the analysis of the past measurement data using statistical models, such as the Auto-Regressive (AR) model [13]- [16]. In comparison, deterministic methods provide a much longer and reliable prediction horizon of wave profiles but at an increased cost of measurement hardware installation and maintenance.…”

“…To estimate the excitation force in realtime, extended Kalman filter (EKF) [13], [19], unknown input observer [20] and adaptive sliding mode observer (ASMO) [21] have been proposed to cope with uncertainties with acceptable estimation error. Based on the historical estimations, AR and EKF have been applied to predict incoming excitation forces [13]- [16].The proposed NLOC+ASMO has its roots in the recent techniques developed in [5], [18], [21]. The enhanced robustness to prediction error is achieved by fusing the following enabling technologies within one framework: 1) an ASMO to estimate current excitation force in realtime with explicitly formulated boundary of estimation error, 2) an online-updated AR model to predict the incoming excitation force using a set of latest historical estimation data with explicitly formulated boundary of prediction error, 3) a real-time sliding mode compensator to mitigate the estimation and prediction error, and 4) the NLOC control strategy [5] to determine optimal control input based on improved accuracy of the estimated and predicted wave excitation forces.…”

“…The state-space modeling and the non-causal LOC design of M4 have been proposed in [22], which verifies the effectiveness of the non-causal LOC being applied in M-WECs. Based on this work, a generic non-causal LOC integrated with excitation force prediction has been proposed in [16], which applies extended Kalman Filter (EKF) to estimate and predict the wave excitation force, while the control degradation by the prediction error is presented in [16]. Thus this paper can also be seen as an extension of these works by improving these existing WEC control methods.…”