Dual IM‐based ILC scheme for linear discrete‐time systems with iteration‐varying reference

Abstract

A novel iterative learning control (ILC) scheme is proposed to improve the convergence rate of ILC by ensuring the convergence in both the time and iteration domains simultaneously. First, an iteration‐varying reference is generated by a high‐order IM (HOIM) along the iteration axis, and is approximated by an HOIM along the time axis. Then, the HOIM‐based repetitive control (RC) and ILC design methods are introduced, which can update the input along the time and iteration axes, respectively. Motivated by the separately tracking abilities of the HOIM‐based RC and ILC in the time and iteration domains, a new ILC scheme is proposed by incorporating both the time‐domain and iteration‐domain HOIMs of the reference. The new ILC scheme is the combination of the HOIM‐based RC and ILC, which can update the input along both the time and iteration axes. The new ILC scheme consists of two loops: (i) the HOIM‐based ILC loop can learn the control input from previous iterations and (ii) the HOIM‐based RC loop can learn the control input from previous times at the current iteration. Moreover, the new ILC scheme is established on a dual‐HOIM (DHOIM) that is the assembly of the two HOIMs of the reference. In consequence, the new ILC scheme is named as DHOIM‐based repetitive ILC (RILC). On rthe basis of the two‐dimensional theory, a DHOIM‐based RILC design criterion is presented. Meanwhile, it is shown that the convergence rate of the proposed DHOIM‐based RILC scheme outperforms that of traditional ILC schemes. Finally, a microscale robotic deposition system is given to illustrate the efficiency of the proposed RILC scheme.