Control of a MIMO Magnetic Levitation System using Exponential Control Barrier Function

Abstract

This work presents the control of a magnetic levitation system. The system is constituted by a Y shape metal plate that must be levitated by electromagnetic attractive forces. The system is nonlinear, open loop unstable and Multiple-Input/Multiple-Output (MIMO), whose inputs are represented by attractive forces generated from three electromagnets and outputs are represented by three plate positions. The proposed control structure uses Quadratic Programming (QP) to combine performance/stability objectives, represented by an arbitrary nominal control law, and safety constraints, represented by Control Barrier Functions (CBFs). The arbitrary nominal control law applied is determined by feedback linearization. Multiple safety constraints with relative-degree greater than one were applied. One way to deal with this is to use Exponential Control Barrier Functions (ECBFs). The results of this control structure applied to the magnetic levitation system are obtained through numerical simulations and indicate that performance/stability objectives are reached and safety constraints are respected.