A fixed-time sliding mode control for uncertain magnetic levitation systems with prescribed performance and anti-saturation input

This paper proposes a novel control strategy for uncertain magnetic levitation (UML) systems. Our method is fundamentally based on terminal sliding mode (TSM) and prescribed performance (PP) control theory. In contrast to conventional TSM and PP methods, which heavily rely on a precise model of the dynamics, our approach breaks free from the constraint of requiring such precision. It employs a neural network (NN) to approximate unknown functions and the components that may cause singularities in the control input. Additionally, the dual PP functions designed in this novel approach not only effectively manage maximum overshoot but also ensure symmetric steady-state tracking error (SSTE) boundaries, rapidly minimizing errors to zero within a fixed time. Moreover, this approach reduces chattering. On the other hand, to mitigate the adverse impact of input saturation, a fixed-time auxiliary system (FTAS) is introduced into the control design. As a result of these proposals, the approach enables the attainment of multiple desired performance indicators within a predetermined domain and a fixed time, particularly under conditions of uncertainties and input saturation. These indicators include convergence, SSTE, and maximum overshoot. The stability of the proposed scheme has been rigorously established by applying the stable principles of Lyapunov theory and fixed-time control (FTC) theory. Experiments serve to validate the exceptional performance of the proposed strategy under a range of diverse operating conditions.