Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

Szathys Songschon; Richard Longman

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 169-177
  • ISSN: 1641-876X

Abstract

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In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction between these conditions is of no practical significance. In ILC satisfying this frequency condition is important for good learning transients, even though the true stability boundary is very different.

How to cite

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Songschon, Szathys, and Longman, Richard. "Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 169-177. <http://eudml.org/doc/207632>.

@article{Songschon2003,
abstract = {In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction between these conditions is of no practical significance. In ILC satisfying this frequency condition is important for good learning transients, even though the true stability boundary is very different.},
author = {Songschon, Szathys, Longman, Richard},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {iterative learning control; monotonic convergence; stability; repetitive control; stability boundary; frequency domain; monotonic decay condition},
language = {eng},
number = {2},
pages = {169-177},
title = {Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control},
url = {http://eudml.org/doc/207632},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Songschon, Szathys
AU - Longman, Richard
TI - Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 169
EP - 177
AB - In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction between these conditions is of no practical significance. In ILC satisfying this frequency condition is important for good learning transients, even though the true stability boundary is very different.
LA - eng
KW - iterative learning control; monotonic convergence; stability; repetitive control; stability boundary; frequency domain; monotonic decay condition
UR - http://eudml.org/doc/207632
ER -

References

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