Global Fast Terminal Sliding Mode Control of Magnetic Levitation System Based on Improved Extended State Observer

To address the issues of high-frequency chattering and insufficient steady-state accuracy in global fast terminal sliding mode control (GFTSMC) for strongly nonlinear and highly uncertain maglev systems, this paper proposes an improved extended state observer-based global fast terminal integral sliding mode control (IESO-GFTISMC) method. The method introduces an integral term of clearance error into the GFTSMC sliding surface to establish a dynamic compensation mechanism, thereby enhancing the system's steady-state accuracy. Simultaneously, by designing a continuously differentiable function (NFAL) to reconstruct the extended state observer and replacing the conventional non-smooth S function (Sign) in sliding surface design, the proposed method improves disturbance estimation capability and effectively suppresses chattering. Finally, the finite-time convergence characteristics of the system are rigorously proven using Lyapunov stability theory, supported by comprehensive simulation analysis and experimental validation. Experimental results demonstrate that under a +/- 2 V step disturbance, the proposed IESO-GFTISMC reduces maximum overshoot by 40% and shortens settling time by 30% compared with GFTSMC and its integral-enhanced variant global fast terminal integral sliding mode control (GFTISMC). In high-disturbance physical experiments, when GFTSMC becomes unstable and GFTISMC exhibits 1.3 mm fluctuation amplitude with 0.2 mm chattering, IESO-GFTISMC compresses the peak-to-valley fluctuation difference to 0.45 mm (65.4% reduction) and sharply diminishes chattering amplitude by 70% to 0.06 mm. The experiments confirm that IESO-GFTISMC significantly surpasses baseline methods across three critical metrics: overshoot suppression rate (+40%), response speed (+30%), and steady-state accuracy (+81.5%), substantially enhancing both dynamic response and robustness of the maglev system.