Design and hybrid control of a two-axis flexure-based positioning system

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.