Adaptive Fuzzy Type-3 Fractional-Order Sliding Mode Controller Without Reaching Phase for Underactuated Mechanical Systems

This paper presents a adaptive hybrid control strategy for underactuated mechanical systems (UMS). The proposed controller integrates fractional calculus, sliding mode control (SMC), and type-3 fuzzy logic control within a unified framework. A new time-varying switching surface is designed such that the sliding plane passes through the position defined by the system’s initial error conditions, thereby eliminating the reaching phase and reducing chattering. The fractional-order operator in the SMC acts as a tunable gain, allowing precise controller adjustment to optimize performance and improve the convergence rate. Moreover, an adaptive Type-3 fuzzy logic system is employed to approximate unknown uncertainties and external disturbances. The stability of the controller is established using Lyapunov theory. Finally, an underactuated crane system is used to validate the proposed approach. Simulation results demonstrate accurate trajectory tracking, effective distur bance rejection, fast convergence (2.98 s), and low tracking error (MSE = 0.00073), confirming the robust performance of the proposed method despite system underactuation.