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

• Published in: Communications in nonlinear science & numerical simulation Vol. 140; p. 108394
• Main Authors: Narayanan, G., Ali, M. Syed, Ahn, Sangtae, Joo, Young Hoon, Karthikeyan, Rajagopal, Rajchakit, Grienggrai
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2025
• Subjects: Adaptive law; Caputo fractional derivative; Fractional impulsive controller; Takagi–Sugeno fuzzy; Wind energy system; Takagi–Sugeno fuzzy; Wind energy system; Caputo fractional derivative; Fractional impulsive controller; Adaptive law
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2024.108394

In this study, the issue of adaptive impulsive control of a permanent magnet synchronous generator (PMSG)-based wind energy system (WES) with an average dwell-time strategy is investigated using a Takagi–Sugeno (T–S) fuzzy model described by fractional-order differential equations. A T–S fuzzy model is employed to describe the nonlinear fractional-order PMSG (FOPMSG) model, an average dwell time, an average impulsive condition, a Lyapunov function, and a less conservative algebraic inequality criterion that guarantees stabilization for the considered nonlinear system. First, the mathematical model of the FOPMSG in the n−m reference frame is transformed into a dimensionless chaotic system through affine transformation and time scale transformation. Then, the stabilization problem of the nonlinear chaotic FOPMSG model is considered to validate the proposed sufficient conditions, leading to the derivation of a new stability criterion for the FOPMSG model, instead of addressing the general problem to validate the proposed result. Subsequently, the desired control gains can be obtained to ensure the stabilization of the addressed closed-loop system. By combining adaptive and impulsive control, the model under consideration can be stabilized for any target dynamics. Finally, we demonstrate the efficiency and feasibility of the suggested approach through numerical simulations and comparative results. •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.