Fractional impulsive controller design of fractional-order fuzzy systems with average dwell-time strategy and its application to wind energy systems

Govindasamy Narayanan, M. Syed Ali, Sangtae Ahn, Young Hoon Joo, Rajagopal Karthikeyan, Grienggrai Rajchakit

Abstract: Highlights•This study aims to design a fractional impulsive controller scheme and investigate the stabilization problems of T–S fuzzy modeling for FOPMSG-based WES, considering both smooth and non-smooth air gap junctions.•The study reveals significant findings from the derived FO impulsive equations, showing that the effect of fractional impulsive control on FOPMSG-based WESs depends not only on the impulsive functions but also on the order of the fractional systems.•By constructing a Lyapunov functional in the fractional domain and utilizing an average impulsive interval, impulsive controller design, and novel sufficient conditions, the exponential stability of the FOPMSG model with smooth air gap is established through verifiable algebraic inequality conditions.•In the case of non-smooth air gap junctions, for the FOPMSG-based WES subject to parameter perturbations and disturbances, we derive an adaptive impulsive controller that combines the advantages of both control methods. The proposed adaptive impulsive control for the FOPMSG model can handle both continuous and discontinuous dynamics, demonstrating strong robustness and improving practical significance by adaptively adjusting the designed parameters, making it more effective than traditional controllers.•Finally, the proposed control method for the FOPMSG-based WES is validated through numerical simulations, with a comparison to the FO Chua’s circuit system demonstrating its higher effectiveness and highlighting the superiority of the proposed method.