Data-Driven Time-Delay Iterative Learning Control of Unknown Disturbances for Image-Based Piezoelectric Systems

Abstract

A data-driven time-delay iterative learning control (TDILC) is proposed to reject unknown time-varying disturbances for image-based piezoelectric systems with large time delays, in which the delay-based robust filter is iteratively optimized online to act as a flexible notch filter, resulting in significant attenuation at the disturbance frequencies. To overcome multi-variable coupling in this optimization process, a cyclic coordinate descent (CCD) algorithm with bounded parameter intervals is incorporated. Furthermore, a fractional-order operator is employed to reshape the time-delay notch filter, and a parallel-cascade composite filtering architecture is developed. This architecture not only alleviates the non-causality issue in the high-frequency range but also significantly improves the suppression of wideband disturbances. Rigorous theoretical analysis demonstrates the stability and convergence of the proposed method. Experimental results in an image-based piezoelectric positioning system validate that the proposed method significantly enhances the system’s robustness against unknown disturbances in large-delay environments. Note to Practitioners—Significant time delays pose an inevitable challenge in precision positioning systems, severely limiting control bandwidth and potentially leading to system instability. Traditional compensation methods typically rely on system models and struggle to effectively suppress unknown disturbances. To address these problems, a data-driven time-delay iterative learning control (TDILC) is proposed. This approach utilizes measured data to iteratively optimize the robust delay-based filter online, allowing it to operate as a dynamic notch filter to suppress unknown disturbances. The delay variables are updated sequentially within bounded intervals based on a cyclic coordinate descent (CCD) approach to achieve decoupling. Furthermore, a parallel-cascade composite filtering architecture is designed to enhance the suppression of high-frequency and wideband disturbances. However, due to the fundamental waterbed effect, high-order filtering under extreme conditions often compromises notch depth while amplifying noise. Future research will investigate predictive control to further alleviate the performance trade-off. Ultimately, the proposed framework can be generalized to other precision automation systems with time delays.