Fractional-Proportional-Type Iterative Learning Control With a Novel Gain Selection Rule

This article proposes a novel gain selection scheme for fractional-proportional-type ILC, aiming to achieve faster convergence rates while maintaining high tracking precision. The convergence of tracking errors to adjustable limit cycles is demonstrated, and a recursive computation method is provided for these limit cycles. Furthermore, the bounds of the limit cycles are estimated in detail, and both local and global convergence rates are thoroughly analyzed. A systematic performance comparison of different gain selection rules, including tracking precision and convergence rate, is conducted. Two multistage update schemes are established through combining different gain selections to accelerate convergence quantitatively, resulting in faster convergence rates compared to the common PTUR while preserving final zero-error tracking performance. Moreover, the switching iteration of the proposed multistage schemes can be independent of system matrices. Numerical simulations and experiments are presented to validate the theoretical findings.