Fractional Super-Twisting/Terminal Sliding Mode Protocol for Nonlinear Dynamical Model: Applications on Hovercraft/Chaotic Systems

Fractional terminal and super-twisting as two types of fractional sliding mode controller are addressed in the present paper. The proposed methodologies are planned for both the nonlinear fractional-order chaotic systems and the nonlinear factional model of Hovercraft. The suggested procedure guarantees the asymptotic stability of fractional-order chaotic systems based on Lyapunov stability theorem, by presenting a set of fractional-order laws. Compared to the previous studies that concentrate on sliding mode controllers with unwanted chattering phenomena, the proposed methodologies deal with chattering reduction of terminal sliding mode controller/super twisting to converge to desired value in finite time, consequently. The main advantages of the offered controllers are 1) closed-loop system stability, 2) robustness against external disturbances and uncertainties, 3) finite time zero-convergence of the output tracking error, and 4) chattering phenomena reduction. Finally, the simulation results show the performance of the approaches both on the chaotic and Hovercraft models.