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

System inversion provides a nature avenue to utilize the priori knowledge of system dynamics in iterative learning control, resulting in rapid convergence and exact tracking (for nonminimum-phase systems). The benefits of system inversion, however, are not fully exploited in the time-domain ILC approach due to the lack of uncertainty quantification. This critical limit was alleviated in the frequency-domain formulated inversion-based iterative control (IIC) techniques. The existing IIC techniques, however, are for single-input–single-output (SISO) systems only, and the time-domain properties of the IIC techniques are unclear. The contributions of the proposed multi-axis inversion-based iterative control (MAIIC) approach are twofold: First, the IIC technique is extended from SISO systems to multi-input–multi-output systems and is easy to implement in practice. The iterative control law is optimized by using the quantification of the system uncertainty. Secondly, the time-domain properties of the MAIIC law are discussed. The proposed MAIIC technique is illustrated through 3D nanopositioning experiments using piezoelectric actuators. The experimental results clearly demonstrated that by using the proposed technique, precision tracking in all 3D axes can be achieved in the presence of a pronounced cross-axis dynamics coupling effect.