Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems
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发布时间：2025-04-30
发布时间：2025-04-30
论文名称：Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems
发表刊物：Advances in Difference Equations
摘要：For discrete-time iterative learning control systems, the discrete Fourier transform (DFT) is a powerful technique for frequency analysis, and Toeplitz matrices are a typical tool for the system input-output transmission. This paper first exploits z-transform and DFT-based frequency properties for iterative learning control systems and studies the convergence property of a Toeplitz matrix to the power of iteration index. The exploitation exhibits that for the finite-length discrete-time iterative learning control systems, the time-domain convolution theorem for the z-transform and DFT is no longer true, and the Toeplitz matrix to the power of iteration index converges if and only if the identical diagonal element lies in the unit circle. Then, by considering the DFT to a finite-length sequence as a linear transform, it is easy to equivalently reform the input-output equation of linear discrete time-invariant and time-varying ILC systems as an algebraic discrete-frequency equation. Thus the derivative-type (D-type) iterative learning control (ILC) converges in a discrete-frequency domain if and only if it converges in a discrete-time domain. Numerical simulations are carried out to exhibit the validity and effectiveness.
合写作者：Xiaohui Li, Xiaoe Ruan
卷号：2019（59）
页面范围：1-22
是否译文：否
发表时间：2019-02-12