Precision dynamics, stochastic modeling, and multivariable control of planar magnetic levitator

We have developed a high-precision magnetically levitated (Maglev) stage with large planar motion (50 mm×50 mm) capability. The key element of this stage is a linear motor capable of providing forces in both suspension and translation without contact. To deal with the dynamic coupling in the platen, we designed and implemented a multivariable linear quadratic regulator, and performed time-optimal control. In this paper, we address issues related to the stochastic modeling of the stage including transfer function identification and noise/disturbance analysis and prediction. Provided are recent test results on precision dynamics, such as fine settling, effect of optical table oscillation, and position ripple. We demonstrate how the performance of the current Maglev stage can be improved with these analyses and test results. The Maglev stage operates with positioning noise of 5 nm RMS in x and y, acceleration capabilities in excess of 2 g (20 m/s²), and closed-loop cross-over frequency of 100 Hz.