Convergence analysis of terminal ILC in the z domain

Abstract

This paper shows how we can apply z-transform theory to analyze the convergence of a terminal ILC algorithm. This approach uses an equivalent system viewed in the cycle domain and analyzes it with a z-transform. Then, conventional discrete time control is applied to the equivalent system. This control is viewed by the real system as a cycle-to-cycle control. Therefore, the stability analysis of the controlled equivalent system corresponds to convergence analysis used in TLC. Furthermore, a "dead beat" convergence is feasible and corresponds to the fastest convergence rate of the ILC algorithm.