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Model predictive control (MPC) has achieved considerable success in the process industries, with its ability to deal with linear and nonlinear models, while observing system constraints and considering future behaviour. Given these characteristics, against the backdrop of the energy maximising control problem for Wave Energy Converters (WECs), with physical constraints on system variables and a non-causal optimal control solution it is, perhaps, natural to consider the application of MPC to the WEC problem. However, the WEC energy maximisation problem requires a significant modification of the traditional MPC objective function, resulting in a potentially non-convex optimisation problem. A variety of MPC formulations for WECs have been proposed, with variations in the WEC model, discretisation method, objective function and optimisation algorithm employed. This paper attempts to provide a critical comparison of the various WEC MPC algorithms, while also presenting WEC MPC algorithms within the broader context of other WEC "optimal" control schemes.

Abstract-A novel strategy for the real-time control of oscillating wave energy converters (WECs) is proposed. The controller tunes the oscillation of the system such that it is always in phase with the wave excitation force and the amplitude of the oscillation is within given constraints. Based on a nonstationary, harmonic approximation of the wave excitation force, the controller is easily tuned in real-time for performance and constraints handling, through one single parameter of direct physical meaning. The effectiveness of the proposed solution is assessed for a heaving system in one degree of freedom, in a variety of irregular (simulated and real) wave conditions. A performance close to reactive control and to model predictive control is achieved. Additional benefits in terms of simplicity and robustness are obtained.

The wave energy sector has made and is still doing a great effort in order to open up a niche in the energy market, working on several and diverse concepts and making advances in all aspects towards more efficient technologies. However, economic viability has not been achieved yet, for which maximisation of power production over the full range of sea conditions is crucial. Precise mathematical models are essential to accurately reproduce the behaviour, including nonlinear dynamics, and understand the performance of wave energy converters. Therefore, nonlinear models must be considered, which are required for power absorption assessment, simulation of devices motion and model-based control systems. Main sources of nonlinear dynamics within the entire chain of a wave energy converter-incoming wave trains, wave-structure interaction, power takeoff systems or mooring lines-are identified, with especial attention to the wave-device hydrodynamic interaction, and their influence is studied in the present paper for different types of converters. In addition, different approaches to model nonlinear wave-device interaction are presented, highlighting their advantages and drawbacks. Besides the traditional Navier-Stokes equations or potential flow methods, 'new' methods such as system-identification models, smoothed particle hydrodynamics or nonlinear potential flow methods are analysed.

A B S T R A C TWave Energy Converters (WECs) have to be controlled to ensure maximum energy extraction from waves while considering, at the same time, physical constraints on the motion of the real device and actuator characteristics. Since the control objective for WECs deviates significantly from the traditional reference ''tracking'' problem in classical control, the specification of an optimal control law, that optimises energy absorption under different sea-states, is non-trivial. Different approaches based on optimal control methodologies have been proposed for this energy-maximising objective, with considerable diversity on the optimisation formulation. Recently, a novel mathematical tool to compute the steady-state response of a system has been proposed: the moment-based phasor transform. This mathematical framework is inspired by the theory of model reduction by moment-matching and considers both continuous and discontinuous inputs, depicting an efficient and closed-form method to compute such a steady-state behaviour. This study approaches the design of an energy-maximising optimal controller for a single WEC device by employing the moment-based phasor transform, describing a pioneering application of this novel moment-matching mathematical scheme to an optimal control problem. Under this framework, the energy-maximising optimal control formulation is shown to be a strictly concave quadratic program, allowing the application of well-known efficient real-time algorithms. (N. Faedo). minimise the risk of damage, such an optimisation strategy must take into account the physical limitations of the whole conversion chain. Such an optimisation procedure can be achieved by designing an optimal controller that accomplishes such objectives.A considerable number of optimal control formulations and methods have been studied and developed to maximise the energy extraction process from WECs, with extensive reviews available, for example in Ringwood, Bacelli, and Fusco (2014). One particular popular wave energy control strategy is Model Predictive Control (MPC). The success of MPC on the energy-maximising control is mainly due to its ability to handle physical constraints systematically and within a finite horizon optimisation process. While MPC applied to WECs also involves a mathematical model, a typical receding horizon strategy, and can deal with system constraints, the objective function contrasts significantly with the one related to the usual set-point tracking objective. Rather, a converted energy-maximising objective, consistent with the definition https://doi.

For the research and development (R&D) of wave energy converters (WECs), numerical wave tanks (NWTs) provide an excellent numerical tool, enabling a cost-effective testbed for WEC experimentation, analysis and optimisation. Different methods for simulating the fluid dynamics and fluid structure interaction (FSI) within the NWT have been developed over the years, with increasing levels of fidelity, and associated computational expense. In the past, the high computational requirements largely precluded Computational Fluid Dynamics (CFD) from being applied to WEC analysis. However, the continual improvement and availability of high performance computing has led to the steady increase of CFD-based NWTs (CNWT) for WEC experiments. No attempt has yet been undertaken to comprehensively review CNWT approaches for WECs. This paper fills this gap and presents a thorough review of high-fidelity numerical modelling of WECs using CNWTs. In addition to collating the published literature, this review tries to make a step towards a best practice guideline for the applications of CFD in the field of wave energy.

Ringwood, John V., and Simon C. Malpas. Slow oscillations in blood pressure via a nonlinear feedback model. Am J Physiol Regulatory Integrative Comp Physiol 280: R1105-R1115, 2001.-Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species. sympathetic nervous system; baroreflex; stability; describing function; artificial neural network IT IS WELL ESTABLISHED that blood pressure in humans can contain a distinct oscillation at 0.1 Hz, often referred to as the Mayer wave (26,38). Experiments in a variety of animal models have shown that this oscillation is due to the action of the sympathetic nervous system on the vasculature. Although the oscillation in blood pressure is shifted to 0.4 Hz in the rat (7) and to 0.3 Hz in the rabbit (22), changes in the strength of this oscillation have been proposed to reflect changes in the mean level of sympathetic nerve activity (SNA) and/or baroreflex gain (6), raising the possibility that measurement of the strength of this oscillation may be used as a diagnostic measure of neural control of the cardiovascular system in humans (1,10,26).Current evidence favors the concept of feedback in the baroreflex loop as the origin for the 0.1-Hz oscillation in blood pressure (5,6,13,25,41). In this model, a change in blood pressure is sensed by the arterial barorece...

This study presents a methodology to assess the possible benefits of the combination of wind energy with the still unexploited, but quite significant in Ireland, wave energy. An analysis of the raw wind and wave resource at certain locations around the coasts of Ireland shows how they are very low correlated on the South and West Coast, where the waves are dominated by the presence of high energy swells generated by remote westerly wind systems. As a consequence, the integration of wind and waves in combined farms, at these locations, allows the achievement of a more reliable, less variable and more predictable electrical power production. The resulting benefits are particularly clear in the case of a relatively small and quite isolated electrical system such as the Irish one. Here, in fact, high levels of wind penetration strongly increase the requirement of surplus capacity and cause a much lower efficiency for conventional thermal plants.