Chaotic behavior and memory-dependent dynamics in fractional-order brushless DC motors (FOBLDCMs) pose significant challenges for robust and stable control design, particularly when physical constraints such as actuator saturation and rate limitations are present. Existing control frameworks often neglect these nonlinear limitations, resulting in performance degradation and potential instability in practical applications. Motivated by these challenges, this paper presents a comprehensive Lyapunov-based stability and control synthesis framework for FOBLDCMs within the fractional-order (FO) range 0 < v < 1. The proposed methodology employs indirect, direct, and composite Lyapunov functions to derive sufficient stability conditions under four scenarios: unconstrained input, saturation- only, rate-limited-only, and combined constraints. For each case, a family of stabilizing controllers is designed to explicitly handle the respective limitations. To the best of our knowledge, this is the first study to rigorously address both saturation and rate limitations in the control design of FO chaotic systems. Numerical simulations confirm that the proposed controllers significantly improve performance over existing methods. Specifically, the unconstrained controller achieves a notable reduction in control energy (from 2.72 × 105 to 1.83 × 105), a 26.3% decrease in maximum control effort, and enhanced or comparable tracking accuracy, as indicated by lower ISE and RMSE values. These results highlight the robustness and practical applicability of the proposed control framework for real-world FO electromechanical systems.

Keywords