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In this study, we address the issue of real-time energy-maximising control for wave energy converters (WECs), by proposing a receding-horizon optimal control framework based on the concept of a moment . This approach is achieved by extending the so-called moment-based framework, recently published in the WEC literature, to effectively solve the associated optimal control problem within a finite time-horizon, allowing for real-time performance, and a straightforward inclusion of the wave excitation force $\mathcal {F}_e$ estimation and forecasting requirements, which are intrinsic to the wave energy control application. We present a case study, based on a CorPower-like device, subject to both state and input constraints. We show that the proposed strategy can perform almost identically to the ideal performance case, where full knowledge of $\mathcal {F}_e$ over the time-horizon is assumed available. Moreover, a sensitivity analysis is provided, addressing the impact of wave excitation force estimation and forecasting errors in the computation of the moment-based control input. Two main conclusions can be drawn from this analysis: Forecasting mismatch has a negligible impact on the overall performance of the strategy, while potential differences arising from estimating $\mathcal {F}_e$ , in particular, phase errors, can substantially impact total energy absorption.

A Linear Time Invariant (LTI) energy-maximising control strategy for Wave Energy Converters (WECs) is proposed in this paper. Using the fundamental requirement of impedance-matching, the controller is tuned to maximise the energy obtained under polychromatic wave excitation. Given the LTI nature of the proposed controller, the design and implementation procedure is significantly simpler than well-established energy-maximising controllers, including state-of-the-art numerical optimisation routines, which are predominant in this field. Additionally, a LTI constraint handling mechanism is provided. The effectiveness of both the LTI control strategy and the constraint handling mechanism are assessed using regular and irregular waves in unconstrained and constrained cases. The resulting performance is compared to those obtained using existing WEC optimal control strategies. Finally, the benefits, in terms of power production, for both the controller and the constraint handling mechanism are explicitly highlighted by means of an application case.

For wave energy converter control applications, autoregressive (AR) models have been proposed as a simple wave forecasting method, solely based on measured or estimated values of the past wave elevation (or excitation force) signal. Using offline-filtered wave time series, AR models can achieve accurate forecasts several wave periods into the future. In this paper, the AR method is examined from the broader perspective of linear, Gaussian processes. In particular, assuming Gaussian waves and perfect knowledge of the wave spectrum, it is possible to derive a theoretically-optimal wave elevation predictor. It is shown that, in realistic situations, AR models can achieve a performance comparable to the theoretically optimal, spectrum-based predictor, both in simulated wave time series and using actual wave elevation records.

Considering the Wave Star wave energy converter (WEC), which is a standard point absorber prototype, this study addresses the complete energy maximising control design procedure. The WEC model is obtained using system identification routines. Then, using the identified model, a LTI energy maximising control strategy, recently presented in the literature, is designed. Additionally, for the wave excitation force estimation, a standard Kalman filter with a harmonic oscillator is considered. Finally, for the assessment of the performance of the complete system, the controller and estimator are implemented in the numerical WEC simulation environment WEC-Sim. The system is tested under realistic conditions and satisfying performance of the LTI controller is shown. Thus, through a non-conventional approach, and considering a realistic software environment, a novel energy maximising controller is implemented, obtaining results which indicate the feasibility of the approach.

Due to the inherent relevance of passive (physically representative) models for control, state‐estimation, and motion simulation in the field of marine systems, in this paper, an optimisation‐based approach to passivation of linear time‐invariant (LTI) systems is proposed with application to physically consistent dynamical modelling of marine structures. In particular, the presented strategy is based upon the introduction of a suitably designed perturbation, computed via minimisation of a linear objective subject to a specific set of linear matrix inequalities (LMIs). The performance of the passivation technique is showcased in terms of two case studies: An offshore platform, with a frequency‐domain response computed by means of hydrodynamic codes, and a 1:20 scale wave energy converter (WEC), is characterised in terms of real experimental data.

When it comes to parameterisation of dynamical models for arrays of Wave Energy Converters (WECs), the most used approach, within the wave energy literature, provides a state-space representation whose order (dimension) increases quadratically with the number of devices composing the WEC array. This represents a major drawback for key WEC design elements, such as motion simulation and unknown input estimation, being the latter essential to effectively maximise energy extraction from ocean waves. We present herein a multi-input, multi-output (MIMO) parameterisation strategy based on a system-theoretic interpretation of moments. The state-space representations computed with this moment-based approach exactly match the steady-state behaviour of the target WEC system at specific (user-selected) interpolation points, providing efficient low dimensional models that can accurately represent the input-output dynamics of WEC arrays. Moreover, we show that there exists an intrinsic connection between wave excitation force estimation strategies and the moment-based parameterisation method proposed in this paper. We exploit this mathematical correlation to provide low order models that deliver the same degree of wave excitation force estimation accuracy to that obtained by implementing the currently-used parameterisation methods, with mild computational requirements. The performance of the strategy is analysed in terms of a case study, considering a WEC array composed of state-of-the-art CorPower-like devices, for both WEC motion simulation and wave excitation force estimation scenarios.

The implementation of energy-maximizing control systems (EMCSs) can significantly increase the efficiency and economic viability of resonant wave-energy converters (WECs). To achieve optimal control and drive the WEC into resonance with the incoming wave field, knowledge of the wave excitation force is required. In operational conditions, this quantity is immeasurable and, thus, has to be estimated. This article presents a critical comparison of the available excitation force estimators found in the literature. A reference measurement of the excitation force is determined using computational fluid dynamics (CFD) simulation, allowing an absolute comparison of the different estimation strategies. The estimators are compared based on the required input data, achieved accuracy, computational delay, and estimation time. In total, 11 estimation strategies are compared, with three, in particular, emerging with relatively superior performance.

The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which involves a convolution product. The convolution term, which accounts for the radiation forces, represents a computational and representational drawback both for simulation, and analysis/design of control strategies. Several studies attempt to find a suitable finite parametric form that approximates the radiation impulse response, to express the equation of motion in the time-domain by a state-space representation. Ideally, this approximated parametric model should behave as closely as possible to the system under analysis, particularly at key frequencies, such as the resonant frequency of the device. This study presents a method to obtain a parametric model of both the force-to-motion dynamics and/or the radiation force convolution term, based on moment-matching. Recent advances in moment-matching, allow the computation of a model that exactly matches the frequency response of the original system at the chosen frequencies, while enforcing specific physical properties of the device, depicting a robust and efficient method to compute a state-space representation for the dynamics of a WEC. The potential of the algorithm is illustrated by numerical examples, and the approximation error is shown to be monotonically decreasing with increasing model order.

The motion of a Wave Energy Converter (WEC) can be described in terms of a particular integro-differential equation, which involves a convolution product accounting for the radiation forces. This convolution term has a computational and a representational drawback both for simulation, and for analysis/design of control strategies. This study presents an application case of a method to obtain a parametric model of the force-to-motion dynamics and/or the radiation force convolution term, based on recent advances in moment-matching. This allows the computation of a model that exactly matches the frequency response of the original system at a chosen set of frequencies, while enforcing specific physical properties of the device.