A decoupled inversion-based iterative control approach to multi-axis precision positioning: 3-d nanopositioning example

This article proposes the multi-axis inversion-based (MAIIC) approach. System inverse provides a nature avenue to utilize the priori knowledge of system dynamics in iterative learning control, resulting in rapid convergence as well as exact tracking (for nonminimum-phase systems). The benefits of system inverse, however, are not fully exploited in time-domain ILCs due to the lack of uncertainty quantification. This critical limit was removed in the inversion-based iterative control (IIC) techniques through a frequency-domain formulation. The existing IIC techniques, however, is limited to single-input-single-output (SISO) systems, and the time-domain properties of the IIC techniques are not clear. The contribution of this article is: First, the IIC technique is extended from SISO systems to multi-input-multi-output systems, and the convergence condition is analyzed. Secondly, the time-domain properties of the MAIIC law are discussed. It is shown that the set of tractable frequencies is characterized by the bounds of system uncertainty that are quantifiable in practices, and the truncated MAIIC input-output convergences to the neighborhood of the desired input-output truncated in time, where arbitrarily small tracking error can be obtained by having a large enough truncation time. The proposed MAIIC technique is illustrated in a 3-D nanopositioning experiment using piezoelectric actuators.