Prescribed-time fixed-time integral sliding mode control of magnetic levitation systems under matched and mismatched uncertainties

Abstract

This paper proposes a prescribed-time fixed-time integral sliding mode controller for a nonlinear magnetic levitation system subject to matched and mismatched uncertainties. The proposed method combines nonlinear feedback linearization, an integral sliding manifold, and a fixed-time reaching law with an explicit designer-adjustable upper convergence bound. Compared with conventional proportional-integral sliding mode control, the proposed reaching law employs two homogeneous nonlinear terms to accelerate convergence both far from and near the sliding manifold. Compared with discrete quasi-sliding approaches, the continuous-time formulation preserves exact sliding motion in the ideal case, while a saturation-based implementation is introduced to attenuate chattering. New lemmas and theorems are developed to prove fixed-time convergence of the sliding variable, exponential stability of the nominal sliding dynamics, and input-to-state stability under bounded mismatched disturbances. Comparative simulations against feedback linearization control, proportional-integral sliding mode control, adaptive fast terminal sliding mode control, fractional-order sliding mode control, and multirate output-feedback discrete-time sliding mode control demonstrate faster convergence, lower tracking error, smaller control energy, and improved robustness.