High-Precision Triaxial Contouring Control for Magnetic Levitation Planar Motor Based on Online Enhanced Newton-Robust Repetitive Learning Compensation

This article presents an enhanced Newton contouring error estimation (CEE) algorithm and a robust repetitive learning-based online compensation method to address the challenge of achieving high-precision triaxial contouring trajectory tracking in a magnetic levitation planar motor (MLPM). First, the static decoupling control of redundant actuator MLPM motion control and the primary factors contributing to contouring error are introduced. Second, to address the conflict between real-time computation and accuracy in CEE, an enhanced Newton’s method incorporating the Steffensen’s acceleration algorithm is proposed. Subsequently, through repetitive learning control, online compensation for the contouring error of the reference trajectory is achieved. A learning law incorporating PD+phase angle-lead compensation is utilized to broaden the bandwidth of the learning law and enhance the system's tracking performance. Furthermore, a multiple input-multiple output linear extended state observer (MIMO LESO) is employed to mitigate low-frequency crosstalk, thrust fluctuations, and uncertainties in the reference model, thereby enhancing the robustness of the system. Finally, the contouring error obtained through the enhanced Newton’s method and tangential analytical method is utilized as the compensation value, respectively. In comparison with MIMO LESO-based axis-independent control, cross-coupling control, the proposed repetitive learning control algorithm demonstrates superior contouring tracking performance under high-speed trajectories with large curvatures.