Iterative Learning Control -- Deep Dive

TL;DR

This paper compares different methods for analyzing the stability and convergence of Iterative Learning Controllers (ILC), including eigenvalue analysis, Z-transform, and convergence criteria, using various learning functions.

Contribution

It systematically applies multiple stability and convergence tests to ILC systems and evaluates their consistency and effectiveness.

Findings

All three methods provide consistent stability assessments.

Two-term and three-term learning functions improve convergence.

Different tests may vary in sensitivity to system parameters.

Abstract

The stability and convergence of an Iterative Learning Controller (ILC) may be assessed either by directly iterating the equations for a variety of inputs, or by finding the eigenvalues of the iterated system, or by forming the Z-transform and applying pole-zero or equivalent root locus. Two often-used criteria are (i) Asymptotic Convergence (AC) of the difference vectors, and (ii) mono-tonic convergence (MC) of the vector norm. The latter (MC) has a Z- domain counterpart. In this paper we apply all three methods and both convergence tests to a simple plant with an ILC wrapper. One, two and three-term learning functions are used. We can then ask the questions: do all the tests work, and do they agree on the stability?