Fractional-order iterative learning control for fractional-order systems with initialization non-repeatability

Xiaofeng Xu; Jinshui Chen; Jiangang Lu

doi:10.1016/j.isatra.2023.09.028

Fractional-order iterative learning control for fractional-order systems with initialization non-repeatability

ISA Trans. 2023 Dec:143:271-285. doi: 10.1016/j.isatra.2023.09.028. Epub 2023 Sep 27.

Authors

Xiaofeng Xu¹, Jinshui Chen², Jiangang Lu³

Affiliations

¹ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China. Electronic address: xxf_cse@zju.edu.cn.
² State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China. Electronic address: jschen@zju.edu.cn.
³ State Key Laboratory of Industrial Control Technology, College of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, China. Electronic address: lujg@zju.edu.cn.

PMID: 37827906
DOI: 10.1016/j.isatra.2023.09.028

Abstract

The effect of initialization non-repeatability on iterative learning control performance for fractional-order systems has not been sufficiently investigated. It is a hidden deficiency that leads directly to the breaking of perfect tracking conditions in both theoretical analysis and real-world applications. Therefore, under the framework of general fractional-order nonlinear systems, this paper proposes an open-close loop D^α-type iterative learning control scheme based on system preconditioning and strictly derives two convergence conditions. By applying the preconditioning optimization strategy based on the short-memory principle, the tracking error due to initialization nonrepetition can converge to any desired range. Compared with the existing results, the proposed iteration scheme fully considers the complexity of the initialization and initial conditions of fractional-order systems, and provides several practical preconditioning methods to improve the tracking efficiency. Two numerical examples are presented to validate the above conclusions.

Keywords: Fractional order system; Initialization; Iterative learning control; Preconditioning.