A Linear Time Invariant (LTI) energy-maximising control strategy for Wave Energy Converters (WECs) is proposed in this paper. Using the fundamental requirement of impedancematching, 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.

The design of controllers for wave energy devices has evolved from early monochromatic impedance-matching methods to complex numerical algorithms that can handle panchromatic seas, constraints, and nonlinearity. However, the potential high performance of such numerical controller comes at a computational cost, with some algorithms struggling to implement in real-time, and issues surround convergence of numerical optimisers. Within the broader area of control engineering, practitioners have always displayed a fondness for simple and intuitive controllers, as evidenced by the continued popularity of the ubiquitous PID controller. Recently, a number of energy-maximising wave energy controllers have been developed based on relatively simple strategies, stemming from the fundamentals behind impedance-matching. This paper documents this set of (5) controllers, which have been developed over the period 2010–2020, and compares and contrasts their characteristics, in terms of energy-maximising performance, the handling of physical constraints, and computational complexity. The comparison is carried out both analytically and numerically, including a detailed case study, when considering a state-of-the-art CorPower-like device.

Spectral and Pseudospectral methods have been widely considered in diverse optimal control applications, usually where energy optimisation is required. Although such methods are a good way to ensure a good balance between performance and computational effort, in most of the literature, nominal mathematical models are considered without taking into account possible dynamic deviations from the nominal case.The main aim of this study is to propose a novel framework where spectral and pseudospectral problems include some structured uncertainty, achieving robust optimal control designs guaranteeing the 'best worst-case performance'. In this paper, the objective function used for optimisation is inspired by wave energy converters. Two solution methodologies are developed. Firstly, an analytical solution, for circular and convex polytopic uncertainty boundaries, is proposed. Then, a numerical formulation is introduced to consider uncertainty sets of arbitrary shape, adding the ability to consider physical system constraints. Finally, an application example shows the benefit of this new control formulation.

The ARG algorithm was successfully validated in a pilot clinical trial, encouraging further tests with a larger number of patients and in outpatient settings.