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

Robust energy-maximising control of wave energy systems under input uncertainty

Motivated by the ubiquitous presence of input uncertainty in the wave energy control problem, we propose, in this paper, a robust energy-maximising framework which explicitly considers potential wave excitation force deviations in the computation of the optimal control law, while systematically respecting state and input constraints. In particular, this is achieved by a suitable moment-based characterisation for the input uncertainty, taking into consideration an appropriate convex uncertainty set. The concept of moments is combined with well-known robust optimisation principles, by proposing a worst-case performance approach. We show that this novel moment-based robust optimal control framework always admits a unique global energy-maximising solution, hence leading to a computationally efficient robust solution. The performance of the proposed controller is illustrated by means of a case study, considering a heaving point absorber WEC

Empowering wave energy with control technology: Possibilities and pitfalls

With an increasing focus on climate action and energy security, an appropriate mix of renewable energy technologies is imperative. Despite having considerable global potential, wave energy has still not reached a state of maturity or economic competitiveness to have made an impact. Challenges include the high capital and operational costs associated with deployment in the harsh ocean environment, so it is imperative that the full energy harnessing capacity of wave energy devices, and arrays of devices in farms, is realised. To this end, control technology has an important role to play in maximising power capture, while ensuring that physical system constraints are respected, and control actions do not adversely affect device lifetime. Within the gamut of control technology, a variety of tools can be brought to bear on the wave energy control problem, including various control strategies (optimal, robust, nonlinear, etc.), data-based model identification, estimation, and forecasting. However, the wave energy problem displays a number of unique features which challenge the traditional application of these techniques, while also presenting a number of control ‘paradoxes’. This review articulates the important control-related characteristics of the wave energy control problem, provides a survey of currently applied control and control-related techniques, and gives some perspectives on the outstanding challenges and future possibilities. The emerging area of control co-design, which is especially relevant to the relatively immature area of wave energy system design, is also covered

Model Predictive Energy-Maximising Tracking Control for a Wavestar-Prototype Wave Energy Converter

To date, one of the main challenges in the wave energy field is to achieve energy-maximizing control in order to reduce the levelized cost of energy (LCOE). This paper presents a model predictive velocity tracking control method based on a hierarchical structure for a Wavestar-like deivce in the WEC-SIM benchmark. The first part of the system structure aims to estimate the wave excitation moment (WEM) by using a Kalman filter. Then, an extended Kalman filter (EKF) is chosen to obtain the amplitude and angular frequency of the WEM in order to compute the reference velocity. Following this, a low-level model predictive control (MPC) method is designed to ensure the wave energy converter (WEC) tracks the optimal reference velocity for maximum energy extraction from irregular waves. Two Gaussian Process (GP) models are considered to predict the future wave excitation moment and future reference velocity, which are needed in MPC design. The proposed strategy can give a new vision for energy-maximizing tracking control based on MPC

Energy-maximising moment-based constrained optimal control of ocean wave energy farms

Successful commercialisation of wave energy technology inherently incorporates the concept of an array of wave energy converters (WECs). These devices, which constantly interact via hydrodynamic effects, require optimised control that can guarantee maximum energy extraction from incoming ocean waves while ensuring, at the same time, that any physical limitations associated with device and actuator systems are being consistently respected. This paper presents a moment-based energy-maximising optimal control framework for WECs arrays subject to state and input constraints. The authors develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable quadratic program (QP), which can be efficiently solved using state-of-the-art solvers. Moreover, the authors show that this QP is always concave, i.e. existence and uniqueness of a globally optimal solution is guaranteed under this moment-based framework. The performance of the proposed strategy is demonstrated through a case study, where (state and input constrained) energy-maximisation for a WEC farm composed of CorPower-like WEC devices is considered

Towards data-driven and data-based control of wave energy systems: Classification, overview, and critical assessment

Currently, a significant effort in the world research panorama is focused on finding efficient solutions to a carbon-free energy supply, wave energy being one of the most promising sources of untapped renewable energy. However, wave energy is not currently economic, though control technology has been shown to significantly increase the energy capture capabilities. Usually, the synthesis of a wave energy control strategy requires the adoption of control-oriented models, which are prone to error, particularly arising from unmodelled hydrodynamics, given the complexity of the hydrodynamic interactions between the device and the ocean. In this context, data-driven and data-based control strategies provide a potential solution to some of these issues, using real-time data to gather information about the system dynamics and performance. Thus motivated, this study provides a detailed analysis of different approaches to the exploitation of data in the design of control philosophies for wave energy systems, establishing clear definitions of data-driven and data-based control in this field, together with a classification highlighting the various roles of data in the control synthesis process. In particular, we investigate intrinsic opportunities and limitations behind the use of data in the process of control synthesis, providing a comprehensive review together with critical considerations aimed at directly contributing towards the development of efficient data-driven and data-based control systems for wave energy devices

Nonlinear energy-maximising optimal control of wave energy systems: A moment-based approach

Linear dynamics are virtually always assumed when designing optimal controllers for wave energy converters (WECs), motivated by both their simplicity and computational convenience. Nevertheless, unlike traditional tracking control applications, the assumptions under which the linearization of WEC models is performed are challenged by the energy-maximizing controller itself, which intrinsically enhances device motion to maximize power extraction from incoming ocean waves. \GSIn this article, we present a moment-based energy-maximizing control strategy for WECs subject to nonlinear dynamics. We develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable nonlinear program, which can be efficiently solved using state-of-the-art nonlinear programming solvers. Moreover, we show that the objective function belongs to a class of generalized convex functions when mapped to the moment domain, guaranteeing the existence of a global energy-maximizing solution and giving explicit conditions for when a local solution is, effectively, a global maximizer. The performance of the strategy is demonstrated through a case study, where we consider (state and input-constrained) energy maximization for a state-of-the-art CorPower-like WEC, subject to different hydrodynamic nonlinearities

Model reduction by moment matching: beyond linearity a review of the last 10 years

We present a review of some recent contributions to the theory and application of nonlinear model order reduction by moment matching. The tutorial paper is organized in four parts: 1) Moments of Nonlinear Systems; 2) Playing with Moments: Time-Delay, Hybrid, Stochastic, Data-Driven and Beyond; 3) The Loewner Framework; 4) Applications to Optimal Control and Wave Energy Conversion

Energy-maximising tracking control for a nonlinear heaving point absorber system commanded by second order sliding modes

Energy-maximising control has proven to be of fundamental aid in the pathway towards commercialisation of wave energy conversion technology. The WEC control problem is based upon the design of a suitable control law capable of maximising energy extraction from the wave resource, while effectively minimising any risk of component damage. A particularly well-established family of WEC controllers is based upon a composite structure, where an optimal velocity reference is generated via direct optimal control procedures, followed by a suitable tracking control strategy. This paper presents the design and synthesis of a second order sliding mode controller to attain a reference tracking for a wave energy system. The presented approach can inherently handle parameter uncertainty in the model, which is ubiquitous within hydrodynamic modelling procedures. Furthermore, the proposed sliding mode controller has relatively mild computational requirements, and finite-time convergence to the designed surface, hence being an ideal candidate for real-time energy-maximising control of WEC systems. Copyright (C) 2022 The Authors

The wave energy converter control competition (WECCCOMP): Wave energy control algorithms compared in both simulation and tank testing

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial