Robust principal component analysis for iterative learning control of precision motion systems with non-repetitive disturbances

In precision motion systems, the same desired trajectory may have to be repeatedly followed. In such cases, iterative learning control (ILC) is a useful strategy to improve the tracking performance at every iteration cycle. The fundamental assumption is that the error is due to repetitive disturbances. In practice, however, non-repetitive disturbances may also be present, and non-repetitive and repetitive disturbances may possess common frequency components. If non-repetitive disturbance effects enter the learning loop, the performance of ILC may be degraded. This paper studies the problem of robust ILC in the presence of non-repetitive disturbances. An optimization based time-domain Q-filtering technique is presented to prevent non-repetitive disturbances from entering the ILC learning loop. More precisely, we apply the robust principal component analysis (RPCA) to filter out non-repetitive effects from the error signals. The effectiveness of the proposed method is demonstrated on a laboratory setup to emulate precision motion control stages of a wafer scanner. The method is also applicable to a broad class of precision motion systems.