Modeling and control of a six degree-of-freedom magnetic/fluidic motion control stage

In this paper we describe a six degree of freedom positioning stage for fine motion control. The stage achieves a 6 σ positioning noise of 0.3 nm at a 1 Hz measuring bandwidth and a controller bandwidth of 5 Hz. Total travel is within a cube of 100 μm. The single moving element is immersed in oil, forming squeeze film dampers between itself and the frame. This design results in a highly overdamped and vibration resistant system. Twelve electromagnets provide the forces necessary to suspend and servo the platen while six capacitance probes sense the position. We perform all of the controls digitally, using a PC-based digital signal processing board. The controller performs two functions that are essential to achieving 0.3 nm positioning resolution. First, it uses a detailed model of the stage in a feedback linearization scheme that linearizes and decouples the degrees of freedom. Second, it uses a combination of a digital filter and an estimator to reduce the effect of measurement noise by about two orders of magnitude. The end result is a stage that is suitable for positioning a sample with better than atomic resolution. Envisioned applications of the stage include producing the scanning motions required in scanned probe microscopy or as a motion control stage for integrated circuit metrology