[论文解读] Global Iterative Sliding Mode Control of an Industrial Biaxial Gantry System for Contouring Motion Tasks

Wenxin Wang, Jun Ma+4 more|arXiv (Cornell University)|Mar 23, 2021

Iterative Learning Control Systems参考文献 41被引用 39

一句话总结

本文提出了一种全局迭代滑模控制（GISMC）方法，用于柔性连接的双轴龙门系统中的高精度轮廓跟踪。通过将自适应滑模控制与增量级联迭代学习律相结合，该方法抑制了抖振现象，并在无需事先知晓不确定性边界的情况下处理匹配与非匹配不确定性，实现了复杂轨迹下轮廓跟踪任务的快速收敛与高精度。

ABSTRACT

This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficulties in system identification, etc. To overcome the above-mentioned issues, this work investigates an intelligent model-free contouring control method for such a multi-axis motion stage. Essentially in the methodology developed here, it is firstly ensured that all the coupling, friction, nonlinearity, and disturbance (regarded as uncertain dynamics in each axis) are suitably posed as `uncertainties'. Then, a varying-gain sliding mode control method is proposed to adaptively compensate for the matched unknown dynamics in the time domain, while an iterative learning law is applied to suppress the undesirable effects (arising from the repetitive matched and unmatched uncertainties in the iteration domain). With this approach, the chattering that typically results from the overestimated control gains in the sliding mode control is thus suppressed during the iterations. To analyze the contouring performance and show the improved outcomes, rigorous proof is furnished on both the stability in the time domain and the convergence in the iteration domain; and the real-time experiments also illustrate that the requirements of precision motion control towards high-speed and complex-curvature references can be satisfied using the proposed method, without prior knowledge of the boundary to the unknown dynamics.

研究动机与目标

• 解决柔性连接双轴龙门系统中高精度轮廓跟踪的挑战，此类系统存在强耦合、由摩擦引起的间隙/死区以及非线性特性。
• 克服现有控制方法的局限性，这些方法需要精确的系统辨识或对不确定性边界有先验知识。
• 开发一种无模型控制策略，确保在时间和迭代域内对匹配与非匹配不确定性均具有鲁棒性。
• 在时间域实现全局稳定性，在迭代域实现全局收敛，以应对重复性轮廓跟踪任务。
• 通过迭代自适应抑制滑模控制中的抖振，避免控制增益的过度估计。

提出的方法

• 将每个轴的所有系统非线性、耦合效应、摩擦和扰动统一表述为‘不确定性’。
• 实施具有时变增益的自适应滑模控制（ASMC）组件，以实时补偿匹配的未知动态。
• 引入一种增量级联迭代学习律（ILL），以在迭代过程中抑制重复出现的匹配与非匹配不确定性。
• 采用两自由度（2-DOF）控制结构：ASMC用于实时鲁棒性，ILL用于迭代性能提升。
• 基于李雅普诺夫分析，对时间域和迭代域的稳定性和收敛性进行严格证明。
• 将控制框架与实际柔性连接双轴龙门系统上的实时实验相结合，以验证性能。

实验结果

研究问题

• RQ1 无模型控制策略是否能在无需系统辨识或不确定性边界先验知识的情况下，实现柔性连接双轴龙门系统中的高精度轮廓跟踪？
• RQ2 在迭代学习过程中，如何有效抑制滑模控制中的抖振，同时不牺牲鲁棒性？
• RQ3 所提出的全局迭代滑模控制（GISMC）方法在多大程度上能确保时间域的稳定性与迭代域的收敛性？
• RQ4 该方法在复杂高曲率参考轨迹（如心形线和圆形）上的表现如何？
• RQ5 该控制框架在实际应用中能否有效处理外部扰动和测量噪声？

主要发现

• 在任务1（圆形）中，所提出的GISMC方法在xy轴上实现了5.990 µm的均方根轮廓误差（RMSE），在任务2（心形线）中降低至6.540 µm，表明在复杂路径上具有高精度。
• 最大绝对轮廓误差（MaxAE）分别降低至16.80 µm（xy轴，任务1）和17.23 µm（xy轴，任务2），表明在高曲率运动下仍具鲁棒性。
• 滑动变量均方根值（RMSSV）在迭代过程中显著下降：xy轴从5.58×10⁻⁴降至3.38×10⁻⁴，表明滑动运动有效建立。
• 该方法有效抑制了抖振，表现为控制努力和滑动变量幅值随迭代减小，即使未对控制增益进行过度估计。
• 系统在额外外部扰动和测量噪声下仍保持一致性能，证实了强大的鲁棒性。
• 收敛性在六次迭代中得到验证：RMSE和RMSSV值在首次迭代后迅速下降，并以递减速率持续减小。