Conventional stages with rolling steel bearings exhibit friction and other mechanical nonlinearities; they are also dependent on servo-loop filters (including sluggish integrator terms) which all limit dynamics, throughput, and precision. In contrast, air bearings — those that carry loads on a layer of air — are nonfriction devices, so they can boost throughput 10 times versus rolling bearings.

Systems that make lots of small moves benefit most from the higher productivity of air-bearing ways. More specifically, small air-bearing stages can follow the rapid exponential decay of the proportional servo — down into noise — boosting throughput and accuracy. These stages are only limited by encoder resolution, amplifier linearity, and external vibration.

First some background: When a normal positioner makes large moves, profiling (the careful shaping of velocity as a function of time) minimizes higher derivatives and avoids exciting system resonances. However, move profiling is useless for small (under 100 µm) moves. Here, overall energy is very small, and the servo loop itself is a perfectly adequate trajectory shaper. The position servo loop functions as a low-pass filter, allowing a simple step-function position command. At time t = 0, we simply command the position loop to be at the destination. Despite step-command discontinuity, actual stage motion follows a smooth curve.

Sometimes a servosystem’s velocity profi le is shaped to make positioning more accurate. This approach is unhelpful for nanometer-scale moves.
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Where the goal is to minimize move and settle time, and make as many small moves per second as possible, tight settling tolerance is paramount. A move-and-settle time is meaningless without a definition of the settling window — the acceptable difference between target and actual position.

For example, in cutting-edge photonics-based alignment, this settling window may be as small as 10 to 20 nanometers. Following error — the difference between commanded and actual position — is zero just prior to the move.

Bandwidth

Servo bandwidth is critical to stage dynamics. Consider a servo system command with a small amplitude sine wave, and assume that we vary the frequency. Resulting amplitude versus frequency has a constant value from DC to a certain frequency; the amplitude peaks slightly (if properly tuned) and then declines as 1/f ². The point at which amplitude has fallen by 3 dB (which is also the point of a 90° phase relationship between the command and response) is the servo bandwidth of the servo system, and the most important predictor of dynamic response.

For small moves, despite the step-command discontinuity, actual stage motion follows a smooth curve. Here, commanded and actual position versus time is for a normalized small move.
Select figure to enlarge.

Normally, it's best to set servo bandwidth as high as possible, for highest rejection of outside perturbations, and greatest dynamic performance. The servo bandwidth is limited by a number of factors, but usually it is the phase lag from the first structural resonance that sets a practical limit. Why? Attempts to increase servo bandwidth beyond the limit set by structural resonances make positioners oscillate, with a poor prognosis for its service life.

The natural form for servo bandwidth is ω₀, expressed in radians per second, but the more familiar term for the servo bandwidth is f₀, expressed in Hertz. A conservative (and realistic) servo bandwidth value for either air or mechanical bearing stages is about 50 Hz.