FREQUENCY DOMAIN PREDICTION OF FINAL ERROR DUE TO QUANTIZATION IN LEARNING AND REPETITIVE CONTROL

摘要

Repetitive control is a field that creates controllers that eliminate the effects of periodic disturbances on a feedback control system. The methods have applications in spacecraft problems to isolate fine pointing equipment from periodic vibration disturbances such as slight imbalances in momentum wheels or cryo pumps. In engineering applications, noise goes into the control algorithm and is acted upon as if it will repeat in the next period, and since it does not repeat, the algorithm amplifies the noise. A previous paper developed methods to analyze the amount of amplification of plant and measurement noise in steady state for any chosen control law. However, experiments on a robot at NASA Langley Research Center demonstrated that quantization effects from analog to digital and digital to analog converters, can have a substantial effect on the final error level reached by a repetitive or learning control law. This paper makes use of the typical model of quantization effects as noise, which is the only reasonably easily used quantization model. The extent of the usefulness of this noise model is investigated. It is noted that the threshold effects of quantization in learning are not captured by the model. Previous work is extended to include quantization noise influence on the final error level after learning is complete. For the results to be accurate, the statistical assumptions of the quantization noise model must be satisfied. In numerical investigations, when the measurement noise level is roughly comparable to or larger than the quantization level, the statistical assumptions are satisfied.