Non‐Fragile Saturation Controller for Fractional‐Order Permanent Magnet Synchronous Generator With Fuzzy Quantized Mechanism

ABSTRACT The main objective of this study is to develop a non‐fragile saturation controller for a fractional‐order (FO) permanent magnet synchronous generator (PMSG) and utilize a fuzzy quantized mechanism. To this end, first, fractional‐order control is introduced into the non‐linear PMSG model to improve the convergence rate beyond the existing integer‐order control techniques. Next, the non‐linear PMSG model is converted to linear sub‐models using the Takagi‐Sugeno (T‐S) fuzzy method. Utilizing refined sector conditions, we conduct a theoretical analysis of the Mittag‐Leffler (M‐L) stabilization for the resultant closed‐loop systems. This analysis employs certain inequality techniques applied to the M‐L function and FO Lyapunov theory. Moreover, based on the polytopic representation approach, sufficient conditions ensuring M‐L stabilization are established by a closed‐loop system. Furthermore, we have devised two separate convex optimization approaches to effectively reduce the actuator costs and expand the admissible initial region (AIR). Finally, the method proposed in this study demonstrates the superiority and efficiency of the derived results.