An Improved Levant Tracking Differentiator Based on Prescribed Performance and Its Applications in the Control of Magnetic Levitation Ball System

This paper proposes an improved active disturbance rejection control (IADRC) scheme for a magnetic levitation ball system to enhance performance under scenarios of internal parameter perturbations and external disturbances. Firstly, a mathematical model of a magnetic levitation ball system is established. Then, following the basic framework and design steps of ADRC, an improved Levant tracking differentiator based on a prescribed performance function and adaptive control is designed, which employs a Sigmoid function to suppress chattering, and its stability is proved using Lyapunov stability theory. Secondly, a nonlinear extended state observer is designed. Thirdly, according to the characteristics of the robust integral term, disturbances can be better suppressed. Therefore, the nonlinear error feedback control law is replaced with a robust integral control law of the error sign. These three components are combined to form an improved active disturbance rejection controller, and the whole closed-loop stability of the overall system is also demonstrated via Lyapunov stability theory. The simulation results show that the performance of the improved Levant tracking differentiator is significantly enhanced, and the proposed improved ADRC strategy offers better tracking performance and stronger disturbance rejection capability.