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

This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. Then, a new ILC scheme, a special high-order ILC (HO-ILC), is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. Next, more iteration-varying factors are further considered. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H∞H∞ performance is studied. In consequence, an ILC design criterion is presented to achieve perfect tracking and 2-D H∞H∞ performance. For comparison, the monotone convergence based ILC design method is extended to the situation with more iteration-varying factors. Utilizing information provided by the multiple HOIMs, it is verified that HO-ILC outperforms low-order ILC (LO-ILC) in presence of iteration-varying factors. Meanwhile, the 2-D H∞H∞ based ILC is shown to be superior to the monotone convergence based ILC. Finally, a microscale robotic deposition system with iteration-varying factors is given to illustrate the advantage of the proposed 2-D H∞H∞ based ILC.