Practical Predefined-Time Fractional-Order Sliding Mode Control for Quadrotors with Variable Exponential Coefficients

This article addresses the trajectory tracking control problem for quadrotor unmanned aerial vehicles (UAVs) subject to complex external disturbances and parameter uncertainties. To balance disturbance rejection with control signal smoothness, a practical predefined-time control scheme incorporating variable exponent coefficients (VEC) is proposed. First, a variable exponent practical predefined-time disturbance observer (VEC-PPTDO) is designed to dynamically estimate and compensate for unknown aerodynamic disturbances. Additionally, a practical predefined-time fractional-order sliding mode control (VEC-PPTFOSMC) scheme is developed, which fuses fractional-order calculus with VEC reaching laws to accelerate convergence and mitigate high-frequency chattering. Based on Lyapunov stability theory, the practical predefined-time stability of the entire closed-loop system is rigorously proven. Finally, comparative simulations under severe stochastic disturbances validate the proposed framework. Quantitative results demonstrate that the proposed scheme achieves a steady-state convergence time of 0.95 s. Compared to the integer-order benchmarks, the proposed method reduces the convergence time by an average of 15.2%, while decreasing the root mean square error (RMSE) and integral absolute error (IAE) by an average of 13.4% and 14.5%, respectively. Consequently, the proposed architecture enhances the dynamic tracking precision, control efficiency, and operational robustness of the quadrotor system.