Receding Horizon Pseudo-Spectral Control for Energy Maximization of a 1/25th Scale Hinge-Barge Wave Energy Converter

This paper addresses the real-time optimal control of a1/25thscale three-body hinge-barge wave energy device. The objective of the control is to maximize the power extracted by the device under given constraints on the maximum displacements,velocities and control forces. An optimal pseudo-spectral control based on the Half-Range Chebyshev-Fourier basis functions is presented. HRCF basis functions are well suited for the approximation of non-periodic signals, allowing the representation of both the transient and steady-state response of the device.A reduced equivalent dynamic model of the device, which is computationally more advantageous than a full dynamic model,is obtained for the optimal control problem formulation. Results show that pseudo-spectral control outperforms a simple control strategy based on the optimal constant passive damping for both monochromatic and polychromatic waves

Modeling and Control of a Multibody Hinge-BargeWave Energy Converter

Wave Energy Converters (WECs) are devices used to extract energy from the waves. The particular WEC considered in this thesis is a three-body hinge-barge WEC, which is an articulated floating structure composed of 3 rectangular bodies interconnected by hinges, and it operates longitudinally to the direction to the incoming wave. The relative motion between each pair of bodies drives a Power Take-Off (PTO) system, which extracts the energy from the waves. The objective of this thesis is to increase the energy that can be extracted by a three-body hinge-barge WEC using an optimal control strategy, which computes the optimal loads applied by the PTOs driven by the relative motion between the bodies. The optimal control is formulated in the time domain, and computes the PTO loads in a coordinated way, so that the total energy extracted by the device is maximized. The optimal control strategy is formulated for a three-body hinge-barge WEC that is equipped with either passive or active PTOs. In this thesis, an optimal control strategy, for the maximization of the energy extracted by a three-body hinge-barge WEC, is derived with Pseudo-Spectral (PS) methods, which are a subset of the class of techniques used for the discretisation of integral and partial differential equations known as mean weighted residuals. In particular, PS methods based on Fourier basis functions, are used to derive an optimal control strategy, for a finite time horizon. Therefore, an optimal control strategy, with PS methods based on Fourier basis functions, cannot be applied for realtime control of the WEC, as Fourier basis functions can only represent the steady-state response of the WEC. However, PS methods based on Fourier basis functions provide a useful framework for the evaluation of the achievable power absorption performance of the WEC, with both active and passive PTOs. The Receding Horizon (RH) real-time optimal control of a three-body hingebarge WEC is derived with PS methods based on Half-Range Chebyshev-Fourier (HRCF) basis functions. The RH optimal real-time controller, with PS methods based on HRCF basis functions, maximizes the energy extracted by the WEC at each time step over a moving control horizon. In contrast to Fourier basis functions, HRCF basis functions are well suited for the approximation of non-periodic signals, allowing the representation of both the transient and steady-state response of the WEC. The optimal control strategy, with PS methods based on either Fourier or HRCF basis functions, is based on a dynamic model of the device, which is derived with two different modeling methodologies, that can be also applied to other types of multiple body WECs. The modeling methodologies are validated against wave-tank tests carried out on a 1/7th scale two-body hingebarge device, and a 1/25th and 1/20th scale three-body hinge-barge device

Optimal control and model reduction for wave energy systems: A moment-based approach

Following the sharp increase in the price of traditional fossil fuels, in combination with issues of security of supply, and pressure to honor greenhouse gas emission limits, much attention has turned to renewable energy sources in recent years. Ocean wave energy is a massive and untapped resource, which can make a valuable contribution towards a sustainable, global, energy mix. Despite the fact that ocean waves constitute a vast resource, wave energy converters (WECs) have yet to make significant progress towards commercialisation. One stepping stone to achieve this objective is the availability of appropriate control technology, suchthatenergyconversionisperformedaseconomicallyaspossible,minimisingthedelivered energy cost, while also maintaining the structural integrity of the device, minimising wear on WEC components, and operating across a wide range of sea conditions. Suitable energy-maximising control technology depends upon the availability of two fundamental ‘pieces’: A control-oriented dynamical model, describing the motion of the WEC, and a model-based optimal control framework, able to efficiently compute the corresponding energy-maximising control law, subject to a set of constraints, defined according to the physical limitations of the device. FollowingtherequirementsforsuccessfulWECcontrol,andbothusingandextendingkeytools arising from the framework of model reduction by moment-matching, this thesis presents two main contributions. Firstly, this monograph proposes a comprehensive moment-based model reduction framework, tailored for WEC systems, addressing linear and nonlinear model reduction cases, providing a systematic method to compute control-oriented models from complex target structures. These approximating models inherit steady-state response characteristics of the target system, via the proposed moment-matching reduction framework. Secondly, by recognising that, besides being a powerful model reduction tool, the parameterisation of the steady-state response of a system in terms of moment-based theory can be explicitly used to transcribe the energy-maximising control problem to a finite-dimensional nonlinear program, a comprehensive moment-based optimal control framework, tailored for WEC systems, is proposed. This framework considers both linear and nonlinear optimal control cases, while also including robust solutions with respect to both system, and input uncertainty, providing an efficient method to compute the energy-maximising control law for WECs, under different modelling assumptions. Throughout this thesis both model reduction, and optimal control frameworks, are presented for a general class of WEC devices, and their performance is analysed via multiple case studies, considering different devices, under different sea state conditions