Encoder Dynamic Error and Moving Period Error: Evaluation for Production Velocities

Why dynamic error is a different quantity

A static calibration measures position error when nothing is moving: the axis settles at each target, the reference reads, the error is recorded. Dynamic error asks a harder question—while the carriage is sweeping past a point at feed rate, how far is the reported position from the truth at that instant? The answer involves every static effect plus a set of terms that only exist in motion: finite bandwidth in the readhead and interpolation electronics, phase lag between scale signal and counted position, vibration excited by the drive and modulating the scale gap, and, on the control side, tracking lag that pulls reported position away from commanded position during the move.

Moving period error deserves its own name because of how it manifests. Sub-divisional error, the cyclic error within each scale signal period, is usually characterized statically, where it appears as a clean periodic ripple. At speed the same mechanism produces an error whose amplitude and phase depend on velocity: interpolation filters introduce speed-dependent phase shift, and signal imbalance combines with counting dynamics so the ripple can double in amplitude or shift in phase relative to the static case. A stage whose static SDE is a comfortable 15 nanometres can exhibit moving period error of double that at production velocity, on top of tracking error from the servo.

Measuring error while the axis is moving

The measurement method must keep up with the axis. A laser interferometer can measure continuously during motion, but at speed its own error sources sharpen: deadpath error grows with any drift between setup and measurement, atmospheric compensation lags, and beam jitter from stage vibration adds apparent displacement. A calibrated two-dimensional grid encoder measures both axes simultaneously at high velocity with excellent bandwidth, which makes it the preferred reference for scanning-stage work, within the limits of its calibrated area. Dynamic circle tests exercise coordinated motion at process speeds and are unmatched as a screening tool, though they attribute error to the machine as a whole rather than to the encoder.

For moving period error specifically, on-axis analysis is powerful: recording the encoder's own fine-phase or interpolation diagnostics while the axis runs at constant velocity reveals the periodic component directly against signal period. Whatever the method, three disciplines apply—sampling bandwidth well above the fastest error frequency of interest, environmental conditions recorded, and repeat runs overlaid to prove the measurement itself is repeatable at speed.

• Sampling rate at least five to ten times the highest error frequency of interest
• Reference instrument bandwidth stated alongside its calibration
• Constant-velocity segments isolated for periodic-error spectral analysis
• Repeat runs overlaid to separate machine error from measurement noise

Separating encoder error from servo error

At velocity, reported position deviates from commanded position for two distinct reasons. The servo loop lags: a tracking error that grows with acceleration and depends entirely on controller tuning, feedforward quality and loop bandwidth. The encoder also errs: its own dynamic terms described above. Both appear on the same position trace, and conflating them wastes everyone's time—the stage builder tunes the servo while the encoder supplier checks a static report, and neither finding explains the process problem.

Clean separation is procedural. Step and ramp responses quantify the tracking component and its dependence on feedforward. On-axis periodic analysis isolates encoder-periodic error. A grid encoder or moving interferometer references true motion independently of the encoder under test. A specification that simply says 'dynamic accuracy' invites this confusion; one that defines tracking error, moving period error and total error-at-velocity as separate line items lets each be verified against its own limit and owned by its own supplier.

Writing dynamic error into a specification

A usable dynamic specification names the velocities—at minimum creep, production feed and rapid traverse—and states an error envelope at each. It defines the measurement method or accepts a proposed one with its bandwidth, requires the periodic-error spectrum at process speed, and fixes the responsibility split between servo tracking and encoder-intrinsic terms. Compensation state must be declared, because an error map calibrated statically can behave differently once velocity-dependent phase shifts move the periodic components it was meant to cancel.

The return on this paperwork is direct. Scanning processes—writing, inspection, metrology—spend their time in motion, so their quality is governed by error at speed, not error at rest. A stage qualified dynamically at process velocity delivers contour quality that a statically certified stage cannot promise, and when something drifts in production, the archived dynamic baseline turns 'the machine feels worse' into a measured delta with a date and a spectrum.