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Repetitive Control Compensator Design for Frequency Response near Singularities
Author(s)
Longman, Richard W.
Date Issued
December 1, 2021
Type
Article
Abstract
Repetitive control (RC) aims to achieve zero error from a feedback control system that is subject to a periodic disturbance of known period, or that is executing a periodic command. It can be used in spacecraft for jitter mitigation, for creating active vibration isolation mounts that theoretically can produce complete cancellation of periodic jitter. RC is a feedback loop around an existing feedback control system that adjusts the control system’s command aiming for that command that produces zero error. The design requires creating a compensator that cancels the phase lag through the feedback controller within a tolerance of less that ±90 degrees. The phase behavior of digital systems is presented in detail, exhibiting the possibility of step discontinuities in phase that approach ± 90 degrees. The issue of whether stable RC systems can be designed for sample rates near such discontinuities is addressed. It is shown in numerical studies that compensators that use as few as 2 or 4 gains times previously recorded errors can be sufficient for not only stability, but can give rather fast convergence to zero error for nearly all frequencies except approaching Nyquist frequency. For systems with even pole excess, there can be a different kind of phase singularity that occurs as the sample rate tends to infinity. When designing for fast sample rate it is best to use a larger set of gains to obtain good convergence rate for all frequencies except approaching Nyquist. It was expected that these discontinuities might make it hard to design the RC compensators, but the results indicate that the singularities do not cause serious difficulty in RC design.
Citation
Journal of the Astronautical Sciences, 68(4), 916-945, 2021