A robust trajectory tracking controller for a magnetic system: A sliding mode-based approach

Abstract

A robust control strategy is developed to address the position trajectory tracking problem in a perturbed magnetic levitation system. The system consists of two electromagnets, each controlled by its respective input voltage. To enhance the model’s complexity, perturbations are introduced into the electrical and mechanical subsystems. The controller design begins under the assumption of a disturbance-free system. Subsequently, an integral sliding mode controller (ISMC) is incorporated to compensate for matching disturbances initially excluded from the model, and a super-twisting observer (STO) is employed to estimate and reject disturbances affecting the mechanical dynamics. The proposed control strategy enforces the convergence of two invariant manifolds to the origin. The first manifold ensures the asymptotic convergence of the position-tracking error to zero, while the second stabilizes the magnetic system and prevents magnetic flux saturation and singularities. The stability properties of the closed-loop system are rigorously analyzed using Lyapunov-based methods, ensuring robustness against bounded disturbances. Numerical simulations are conducted to evaluate the performance of the control scheme, demonstrating its efficacy in achieving precise trajectory tracking and disturbance rejection under the imposed perturbations.