Optimal Performance Tradeoffs in Repetitive Control: Experimental Validation on an Active Air Bearing Setup

Abstract

In repetitive control, the bode sensitivity integral dictates a tradeoff between improved suppression of periodic disturbances and degraded performance for non-periodic inputs. This paper experimentally demonstrates the implications of this tradeoff by applying a recently developed repetitive controller design approach to reduce the error motion of the spindle's axis of rotation on an active air bearing setup. This design methodology translates the performance tradeoff into tradeoff curves between a non-periodic and periodic performance index, of which the practical relevance is illustrated by the obtained experimental results. Second, the relation is investigated between these two performance indices and the adaptive performance of the repetitive controller during large variations of the spindle's rotational speed setpoint. The experiments suggest that, although defined for steady state, the two performance indices also relate to the adaptive performance of the repetitive controller.