Optimisation-based tuning of nonlinear controllers for targeted dynamics: Methodology and a demonstrative wind energy case

Abstract

Tuning controllers for nonlinear systems remains a significant challenge due to their inherent complexity and the lack of systematic design methodologies. This study presents a practical, versatile, and robust optimisation-based procedure for tuning nonlinear controllers, including linear ones, offering a structured alternative to the traditional trial-and-error tuning strategies commonly used in practice. A key contribution of the proposed methodology is the explicit definition and achievement of target closed-loop dynamic behaviours in nonlinear systems, which is analogous to classical dynamics in linear control. By leveraging global optimisation techniques, the procedure systematically identifies controller parameters that minimise deviations from predefined dynamic targets while ensuring robustness and stability across a range of operating conditions. The approach addresses the nonlinear response of the controlled system and provides an intuitive and customisable framework for shaping closed-loop dynamics according to design objectives. The methodology is validated through its application to a wind turbine control problem, demonstrating its ability to tune both proportional–integral (PI) and super-twisting sliding mode controllers (SMC) effectively. The results highlight the sensitivity of nonlinear controllers to parameter selection and underscore the benefits of a systematic tuning approach in achieving consistent performance, preventing actuator saturation, and ensuring system longevity. This study offers a powerful and generalisable solution for tuning controllers in complex nonlinear systems, enabling practitioners to move beyond empirical tuning practice.