Iterative Learning Control for Linear Discrete-Time Systems with Unknown High-Order Internal Models: A Time-Frequency Analysis Approach

作者：Zhu, Qiao; Xu, Jian-Xin; Huang, Deqing^*; Hu, Guang-Di

来源：Asian Journal of Control, 2018, 20(1): 370-385.

DOI：10.1002/asjc.1552

• Iterative learning control
• linear discrete-time system
• high-order internal model
• random bounded disturbance
• time-frequency analysis approach

This work focuses on the iterative learning control (ILC) for linear discrete-time systems with unknown initial state and disturbances. First, multiple high-order internal models (HOIMs) are introduced for the reference, initial state, and disturbances. Both the initial state and disturbance consist of two components, one strictly satisfies HOIM and the other is random bounded. Then, an ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For all known HOIMs, an ILC design criterion is introduced to achieve satisfactory tracking performance based on the 2-D H theory. Next, the case with unknown HOIMs is discussed, where a time-frequency-analysis (TFA)-based ILC algorithm is proposed. In this situation, it is shown that the tracking error inherits the unknown augmented HOIM that is an aggregation of all unknown HOIMs. Then, a TFA-based method, e.g., the short-time Fourier transformation (STFT), is employed to identify the unknown augmented HOIM, where the STFT could ignore the effect of the random bounded initial state and disturbances. A new ILC law is designed for the identified unknown augmented HOIM, which has the ability to reject the unknown the initial state and disturbances that strictly satisfy HOIMs. Finally, a gantry robot system with iteration-invariant or slowly-varying frequencies is given to illustrate the efficiency of the proposed TFA-based ILC algorithm.

• 出版日期2018-1
• 单位西南交通大学