Fixed-time fractional-order terminal sliding mode control of linear magnetic levitation stages for CNC machine tools

A non-singular fractional-order terminal sliding mode control method based on a fixed-time extended state observer (NFTSMC-FTESO) is proposed to address the susceptibility of linear magnetic levitation platform for computer numerical control (CNC) machine tools to nonlinearities, strong coupling, and other uncertainty perturbations. First, a novel FTESO is constructed to estimate the lumped perturbation of the system and compensate it into the control law to reduce the system chattering, and the observer converges quickly and does not need to know the upper bound of the perturbation derivatives compared with the conventional ESO. Second, a novel fixed-time FTSMC is designed using fixed-time theory and fractional-order differential calculus theory to improve the dynamic tracking performance of the system by adjusting the fractional-order operator to ensure that the system variables converge to the equilibrium point more quickly. Then, the proposed composite control strategy is proved to be globally fixed-time convergent and the convergence time is independent of the initial conditions using Lyapunov functions. Finally, the proposed control strategy is applied to a linear magnetic levitation platform for CNC machine tools and the effectiveness of the proposed method is verified. Compared with the traditional SMC and the new ESO based on NTSMC (NTSMC-NESO), the proposed control strategy improves the levitation accuracy by 50% with the steady state error within 4 μ m. This method improves the machining accuracy of CNC machine tools and meets the needs of precision manufacturing.