Trajectory tracking control for a floating ball into a magnetic system: an integral sliding mode approach

This study proposes a solution for a floating ball's trajectory tracking control problem in an exogenously and endogenously perturbed magnetic levitation system. This system consists of two electromagnets vertically arranged, one in front to the other, and the ball levitates in the gap between them. The controller inputs are the magnet's voltages, and we split its design into two parts. First, we design a controller, assuming the system is non-perturbed. Then, we incorporate an integral sliding mode to nullify the perturbations' undesirable effect. The proposed control approach can reject exogenous and endogenous perturbations almost immediately due to the integral controller action, avoiding using disturbance observers, which can be either finite or asymptotic provided the whole state is available, and the perturbation bound is known. We validate the performance of our approach through numerical simulations.