Iterative learning control for linear discrete-time systems with unknown high-order internal models

An online identification method is presented for the iterative learning control (ILC) problem of linear discrete-time systems with unknown high-order internal models (HOIMs). The reference is generated by a known HOIM, and the HOIMs of the initial state and the exogenous disturbances are unknown. First, the case with known HOIMs is first considered, where the 2-D H
_∞
based ILC design method is introduced. Then, the case with unknown HOIMs is further discussed, where an online identification and ILC algorithm is presented. In this situation, it is shown that the tracking error inherits the unknown augmented HOIM that denotes an aggregation of all unknown HOIMs. Based on this, the least squares estimation method with an arithmetic mean filter is utilized to identify the unknown augmented HOIM. After that, the 2-D H
_∞
based ILC law is designed for the identified unknown augmented HOIM. It is worth noting that the online identification and ILC algorithm is robust to the imperfect identification for the unknown augmented HOIM. Finally, a microscale robotic deposition system with invariant or slowly varying HOIMs is given to illustrate the efficiency of the proposed online algorithm.