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

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.