Modelling and control of wave energy converters with nonlinearities: An LPV and robust control approach

This work presents a linear parameter-varying (LPV) framework for the modelling and control of a wave energy converter (WEC) system, explicitly addressing the nonlinear hydrodynamic effects that are critical for accurate representation of the dynamics of the system. Among these effects, viscous drag, for example, is a significant contributor to the nonlinear behaviour of WECs, particularly under realistic operational conditions. By incorporating this nonlinear behaviour directly into the LPV definition, the proposed framework provides a systematic approach to bridge the gap between traditional control-oriented models, which often oversimplify these phenomena, and the complex nonlinear dynamics of practical systems. The methodology begins with the definition of a quasi-LPV system to represents the nonlinear dynamics of the WEC. The nonlinear contributions, including those stemming from viscous drag, are embedded into the parameter-varying structure, enhancing the ability of the model to capture the true behaviour of the system. 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 design that leverages the flexibility of the LFT representation to incorporate structured uncertainties. The control strategy is 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. The proposed robust control loop operates as a reference-tracking energy-maximising framework. The reference signal, representing an optimal velocity trajectory, is generated externally and provides a target for the control system to follow. Weighted transfer functions are used within the control design to ensure both performance optimisation and robustness to uncertainties. This approach highlights one of the key strengths of the methodology: its ability to guarantee an acceptable level of performance even in the presence of significant uncertainty, thereby enhancing the reliability of WEC operation under varying ocean conditions. Simulation results validate the proposed approach, showcasing its ability to maximise energy extraction while effectively managing the nonlinearities and uncertainties inherent to WEC systems. The incorporation of viscous drag into the LPV model proves crucial in capturing the complex dynamics of the system, ensuring that the control strategy is well-tuned to the actual behaviour of the device. Furthermore, the robust control design demonstrates strong performance across a range of scenarios, highlighting its potential for real-world implementation. This work provides a comprehensive framework for integrating nonlinear hydrodynamic effects into WEC models and emphasises the critical role of robust control in achieving reliable and efficient operation. By addressing key challenges in modelling and control, the presented methodology contributes to advancing the practical deployment of wave energy systems, establishing the way for more effective utilisation of renewable ocean energy resources.