Dynamics and control of the UNCC/MIT sub-atomic measuring machine

This paper reports on the design, modeling, implementation, and experimental results for the control of our Sub-Atomic Measuring Machine (SAMM), which has been jointly developed by UNC-Charlotte and MIT. This machine is intended for measuring features on planar substrates with a work volume of 25 mm x 25 mm x 100 mum, with subatomic resolution. The machine uses four linear motors to control motion in six degrees of freedom and provide magnetic suspension. We derive the commutation law for these linear motors based on a least self-heating condition. We also present modeling of the stage motion in six degrees-of-freedom and our controller design using state-space methods. The experimentally-demonstrated RMS stage positioning noise is 0.12 nm in x, 0.082 nm in y, 1.45 nm in z, 22 nrad in theta (x), 18 nrad in theta (y), and 2.7 nrad in theta (z) over a 25 second measurement.