Online feedforward parameter learning with robustness to set-point variations

High-tech motion system development is driven by increasingly accurate and fast positioning requirements. Feedforward compensation together with high bandwidth feedback control are essential to achieve these ever tightening performance demands. In particular, online adaptation of the feedforward parameters, to correct for small position dependencies and slow variations, is crucial to approach zero error tracking. The aim of this paper is a framework that provides robust recursive learning of feedforward parameters for any bounded reference trajectory. The convergence of the parameter learning strategy exploits the difference in time-scale between the parameter variation rate and the bandwidth of the servo controlled system. This enables to describe a servo-error-based objective function for varying trajectories as a static sector bounded nonlinearity. Subsequently, the circle criterion is employed to derive stability guarantees on the learning with explicit robustness to reference trajectory variation. A numerical case study demonstrates that a significant performance improvement can be achieved.