This article presents a universal method of precise synchronization control for linear-motor-driven systems. The control method named cross-coupled second-order discrete-time fractional-order sliding mode control contains a cross-coupled control strategy to reduce the incoordination among driving linear motors. It also includes the second-order structure and fractional-order sliding mode surface to reduce the chattering phenomenon and improve the dynamic performance simultaneously, so that the precision is further enhanced. In particular, a universal definition of synchronization error is presented so that a better synchronization control performance can be achieved, especially in multidimensional systems. It is also compatible well with the contouring control, which extends the application further. Moreover, the stability of the controller is analyzed in this article. Finally, the proposed control method is conducted in simulations and experiments under various tasks, whose results have proved its effectiveness and advantages over conventional methods.

中文翻译：

---

通过交叉耦合的二阶离散分数阶滑模进行精确的线性电动机同步控制

本文提出了一种用于线性电动机驱动系统的精确同步控制的通用方法。称为交叉耦合二阶离散时间分数阶滑模控制的控制方法包含一种交叉耦合控制策略，可减少驱动线性电动机之间的不协调。它还包括二阶结构和分数阶滑模表面，以减少颤动现象并同时提高动态性能，从而进一步提高了精度。特别地，提出了同步误差的通用定义，以便可以实现更好的同步控制性能，尤其是在多维系统中。它也与轮廓控制非常兼容，从而进一步扩展了应用范围。而且，本文分析了控制器的稳定性。最后，该控制方法在各种任务下的仿真和实验中进行，其结果证明了其有效性和与常规方法相比的优势。