In this paper, an accurate, large range, two-axis compliant positioning system is described and the performance of the implemented control system is analysed. The characteristics of two independently controlled axes are designed to be nominally identical and orthogonal. Both the kinematic and the kinetostatic cross-coupling interactions between the axes are statically analysed. The movement of each system axis can be modelled with linear equations when assuming a small motion range, upper bounded by about 0.2 mm. To achieve high-performance over the full permissible motion range (i.e., for movements up to ± 1 mm), the non-linearity due to stiffness has been considered and modelled to implement the controller. The control system is based on both a PID feedback controller and a force feed-forward controller based on a non-linear model. For sinusoidal or triangular reference signals, a repetitive controller (RC) based on a linear system model is added in parallel to improve system performances. Various dynamic tests have been performed, and the obtained simulation and experimental results are discussed. A suitable application of the designed RC is shown to significantly improve the accuracy of the system especially at the higher frequencies selected, thus allowing the accurate tracking of movements up to 50 Hz. The adopted encoder (with a resolution of 5 nm) allows the relative accuracy of the system to be of the order of a few percent for displacements of up to ± 1 mm from the null position.

本文描述了一种精确的，大范围的，两轴兼容的定位系统，并分析了所实现的控制系统的性能。两个独立控制的轴的特性设计为名义上相同且正交。静态地分析了轴之间的运动学和运动学上的交叉耦合。当假设较小的运动范围（上限约0.2 mm）时，可以使用线性方程式对每个系统轴的运动进行建模。为了在整个允许的运动范围内（即，对于最大±1 mm的运动）实现高性能，已经考虑并建模了由于刚度引起的非线性，以实现控制器。该控制系统基于PID反馈控制器和基于非线性模型的力前馈控制器。对于正弦或三角形参考信号，并行添加基于线性系统模型的重复控制器（RC）以提高系统性能。已经进行了各种动态测试，并讨论了获得的仿真和实验结果。已显示设计的RC的适当应用可以显着提高系统的精度，尤其是在所选的较高频率下，从而可以精确跟踪高达50 Hz的运动。所采用的编码器（分辨率为5 nm）使系统从零位到最大偏移量为±1 mm时的相对精度约为百分之几。并对获得的仿真结果和实验结果进行了讨论。已显示设计的RC的适当应用可以显着提高系统的精度，尤其是在所选的较高频率下，从而可以精确跟踪高达50 Hz的运动。所采用的编码器（分辨率为5 nm）使系统从零位到最大偏移量为±1 mm时的相对精度约为百分之几。并对获得的仿真结果和实验结果进行了讨论。已显示设计的RC的适当应用可以显着提高系统的精度，尤其是在所选的较高频率下，从而可以精确跟踪高达50 Hz的运动。所采用的编码器（分辨率为5 nm）使系统从零位到最大偏移量为±1 mm时的相对精度约为百分之几。