Stability analysis of set-point-related indirect iterative learning control with PI-type local controller

The set-point-related (SPR) indirect iterative learning control (ILC) is used to update the set-point for a local controller. Working as a supervision module for the local controller, SPR indirect ILC can improve the tracking performance of the closed-loop system along the batch direction. In the previous works, the local controller was assumed to be P-type for simplicity. In this work, a more general form for the local controller, the PI-type controller, was studied. Based on a 2-dimensional (2D) Roesser´s system framework, a sufficient condition for asymptotical stability of multi-input multi-output linear batch processes under the SPR indirect ILC was derived in this paper. A numerical example was used to validate the proposed results.