Fixed-time disturbance observer based on fractional-order state observer and super-twisting sliding mode control for a class of second-order of slotless self-bearing motor

This paper proposes a new fixed-time disturbance observer (FTDOB) based on the fractional-order state observer (FOSOB) and a super-twisting sliding-mode control (STSMC) for a slotless self-bearing motor (SSBM). First, the slotless self-bearing motor with fully embedded disturbances and uncertainties is analyzed, the imperfection of the perturbation sources. Second, a fractional-order state observer was designed to estimate the velocities and accelerations of movement on x - , y - , and ω - axes, respectively. Third, a new concept of fixed-time disturbance observer was proposed for estimating the perturbations on three axes of the bearing motor system. Fourth, the super-twisting sliding-mode control was designed to control the positions and the rotational speed of the bearing motor system. Final, the stability of the proposed algorithms was theoretically verified via the Lyapunov condition. To visually present the effectiveness and originality of the proposed theories, the MATLAB simulation was used to show that the proposed control system consisted small overshoots, small settling times, and stable tracking error values in narrow gaps around zero.