High-Precision Control of Ball-Screw-Driven Stage Based on Repetitive Control Using $n$-Times Learning Filter

This paper presents a novel learning control method for ball-screw-driven stages. In recent years, many types of friction models that are based on complicated equations have been studied. However, it is difficult to treat friction models with equations because the level of precision that is associated with real friction characteristics and parameter tuning are difficult to achieve. In contrast, repetitive perfect tracking control (RPTC) is a repetitive control technique that achieves high-precision positioning. In this paper, we propose the use of RPTC with n-times learning filter. The n-times learning filter has a sharper rolloff property than conventional learning filters. With the use of the n-times learning filter, the proposed RPTC can converge tracking errors n times faster than the RPTC with the conventional learning filter. Simulations and experiments with a ball-screw-driven stage show the fast convergence of the proposed RPTC. Finally, the proposed learning control scheme is combined with data-based friction compensation, and the effectiveness of this combination is verified for the x-y stage of a numerically controlled machine tool.