Real-Time Implementation of the Prescribed Performance Tracking Control for Magnetic Levitation Systems

Abstract

For magnetic levitation systems subject to dynamical uncertainty and exterior perturbations, we implement a real-time Prescribed Performance Control (PPC). A modified function of Global Fast Terminal Sliding Mode Manifold (GFTSMM) based on the transformed error of the novel PPC is introduced; hence, the error variable quickly converges to the equilibrium point with the prescribed performance, which means that maximum overshoot and steady-state of the controlled errors will be in a knowledge-defined boundary. To enhance the performance of Global Fast Terminal Sliding Mode Control (GFTSMC) and to reduce chattering in the control input, a modified third-order sliding mode observer (MTOSMO) is proposed to estimate the whole uncertainty and external disturbance. The combination of the GFTSMC, PPC, and MTOSMO generates a novel solution ensuring a finite-time stable position of the controlled ball and the possibility of performing different orbit tracking missions with an impressive performance in terms of tracking accuracy, fast convergence, stabilization, and chattering reduction. It also possesses a simple design that is suitable for real-time applications. By using the Lyapunov-based method, the stable evidence of the developed method is fully verified. We implement a simulation and an experiment on the laboratory magnetic levitation model to demonstrate the improved performance of the developed control system.