Fixed-time disturbance observer-based funnel control for controllable excitation linear synchronous motor with state constraints

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This paper proposes a fixed-time disturbance observer-based funnel control method for a controllable excitation linear synchronous motor (CELSM) with state constraints and disturbances. This approach simultaneously resolves the issues of prescribed tracking performance and state constraints, taking into account disturbances. We employ a fixed-time disturbance observer (DO) to estimate both matched and mismatched disturbances. Additionally, we design a modified funnel variable to confine the tracking error within a prescribed region and the singularity problem is avoided. An integral barrier Lyapunov function (iBLF) is utilized to directly tackle state constraints. Furthermore, we employ a fixed-time differentiator (FTD) to address the “explosion of complexity” issue in backstepping control. Theoretical analysis demonstrates that the tracking error asymptotically converges to the origin within a prescribed region while satisfying state constraints. Finally, simulation results demonstrate the efficacy of the proposed method.