Disturbance Rejection Control for Magnetic Levitation System With Nondifferentiable Uncertainties and Measurement Noise

This article investigates the disturbance rejection control problem of a magnetic levitation system (MLS) in the presence of nondifferentiable uncertainties and measurement noise. In practical applications, disturbances often include abrupt or discontinuous changes, making them nondifferentiable. This article models such uncertainties as a total disturbance, further divided into two components: a bounded nondifferentiable signal and a differentiable signal. By leveraging this decomposition, we derive an extended state-space model for the MLS, where the differentiable component is treated as an extended state. To estimate both the extended state and the system state, we propose a high-order low-pass filter-based extended state observer (LPFESO). The high-order filter enhances the accuracy of state estimation by filtering the system output. In addition, an output feedback controller (FC) with disturbance compensation is designed based on the internal model (IM) principle. The stability of the proposed LPFESO is rigorously demonstrated. Comparative experimental results are presented to validate the superiority and effectiveness of the proposed approach in enhancing the noisy system's disturbance rejection capability.