Non-Causal Linear Optimal Control of Wave Energy Converters With Enhanced Robustness By Sliding Mode Control - Engineering Assignment Help

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Abstract—Sea wave energy converter control is a non-causal optimal control problem, and the control performance relies on the accuracy of wave prediction information. However, the existing wave prediction methods, such as Auto-Regressive (AR) method, extended Kalman Filter (EKF), Artificial neural network and deterministic sea wave prediction (DSWP), inevitably introduce prediction errors. This paper presents a robust non-causal linear optimal control of wave energy converters to explicitly cope with the prediction error of sea wave prediction and simultaneously compensate the modeling uncertainty caused by wave force approximations.

This is achieved by designing a non-causal linear optimal control (LOC) to maximize the energy output and a sliding mode control (SMC) to compensate for unmodeled WEC dynamics and wave prediction error. The parameters of both SMC and non-causal LOC are calculated offline, which significantly enhances the real-time implementation of the proposed controller with the reasonably low computational load. Simulation results demonstrate the efficacy of the proposed control strategy. 

Introductions

Sea waves provide an enormous source of renewable energy with high energy density and continuous power supply [1], [2]. To harness wave energy [3], many wave energy converters (WECs) have been developed, including oscillating water columns, overtopping WECs, point absorbers and attenuators. It has also been recognized that WEC control is a non-causal optimal control problem, which means the current control decision is based on the prediction of the incoming sea waves [4]. Recent studies show that wave prediction can play an important role in improving WEC control performance and maintaining safe operations compared to the counterpart of causal control, see [5]–[9].

Index Terms—Non-causal control, Sliding mode control, Wave Energy Converters, Prediction error, Modelling uncertainty developed and applied to the WEC non-causal control problem. One class of prediction approaches are based on statistical methods, such as the Auto-Regressive (AR) prediction method [10] and the extended Kalman Filters (EKF) [11]. Artificial neural network (ANN) has also been used to forecast the short-term wave forces [12], [13]. Another class of prediction is based on the measurements of sea wave elevations at multiple upstream locations with certain distances away from the WEC, such 

Y. Zhang is a postdoctoral researcher with Queen Mary University of London, UK, E1 4NS.

G. Li, the corresponding author, is with Queen Mary University of London, UK, E1 4NS.

as the deterministic sea wave prediction (DSWP) [14], which provides long and reliable wave prediction but at the cost of installation of extra more expensive hardware for wave measurements. 

The accuracy of wave prediction methods is a key factor influencing WEC control performance. With inaccurate pre dictions of the wave excitation force or the wave elevation, the control performance can be degraded as shown in [15]– [17]. However, the prediction error has not been explicitly compensated for. 

Sliding mode control (SMC) is a nonlinear control strategy that has unique advantages in coping with model uncertainties and disturbances [18], [19], and has been widely applied in aerospace engineering [20], marine engineering [21] and permanent magnet synchronous motor system [22], etc. To maximize the energy output subject to prediction errors and modelling uncertainties, this paper proposes an SMC based non-causal linear optimal control (LOC) strategy to maximize the energy output and simultaneously enhance the robustness by explicitly compensating the prediction error and the modelling uncertainty. The main novelties and contributions of the paper are summarized as follows: 

• The wave prediction error and the modelling uncertainty are explicitly handled; 

• Robust WEC control performance can be significantly recovered subject to large prediction errors and even in the absence of wave prediction; 

• The proposed controller is computationally inexpensive so that it can be efficiently implemented in real-time;

• The tuning procedure is simple since the approach only has two tuning parameters. 

Although the proposed controller can be applied to a wide variety of WEC devices, we select a particular WEC, called point absorber, as a case study for demonstration purpose. The schematic diagram of the point absorber is shown in Fig. 1. The proposed controller consists of a non-causal LOC and an additional term of SMC. 

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