Nonlinear modelling and control of wave energy conversion systems: An LPV and robust control approach

The emission of pollutants and global warming caused by the consumption of fossil fuels has led researchers to find sustainable alternatives. In recent years, wave energy has gained increasing attention among researchers due to its high potential compared to other renewable energy sources. Nevertheless, wave energy converters (WECs) have yet to take significant steps toward commercialisation. Achieving this goal requires the development of control strategies that minimise the cost of delivered energy, while ensuring the robustness of the device. Throughout the thesis, the two main elements of a suitable energy-maximising control technology are discussed. The first one involves modelling the wave energy conversion systems, by exploiting the physical phenomena affecting these devices, to derive a control-oriented dynamical model, that describes the motion of the converter. The second element is the Optimal Control Problem (OCP), which serves as the foundation for WEC control. Thus, the OCP is solved in real-time to compute the corresponding control action subject to a set of constraints, defined according to the physical limits of the device, with the objective of maximising the energy extracted from ocean waves. Furthermore, this work proposes the use of a Linear Parameter-Varying (LPV) framework for WEC systems. LPV systems are characterised by a closed-form representation of a system in terms of a set of scheduling parameters, allowing the inclusion of dynamic behaviours which are often neglected in linear models. A realistic wave excitation input, modelled using the JONSWAP spectrum, is employed to validate the LPV model. This validation demonstrates the capacity of the LPV model to represent key nonlinearities, while retaining sufficient simplicity to facilitate analysis and control design. To further advance the framework, the nonlinear system is reformulated in a Linear Fractional Transformation (LFT) form. This transformation enables a robust control strategy designed to address both parametric uncertainties, such as variations in system parameters due to environmental changes, and non-parametric uncertainties, which may arise from unmodelled dynamics or sensor dynamics. This methodology guarantees an acceptable level of performance even in the presence of significant uncertainty, thereby enhancing the reliability of WEC operation under varying ocean conditions.