Abstract

This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive manufacturing processes as an important RPC problem, in which each iteration is a layer of deposition, encourages the revisit to large transient growth. Using time-bounded convolution operations, we show here new results for bounding large transient growth with causal ILC and RPC systems. The results show surprising new insights, such as guaranteed convergence, an exponential relationship between peak transient growth and time-length of the iteration, and faster than exponential convergence. The so-called λ -norm, classically used in ILC analysis, is reconsidered with respect to the new results.

Department(s)

Mechanical and Aerospace Engineering

Second Department

Mathematics and Statistics

Comments

National Science Foundation, Grant DMS-2111421

International Standard Serial Number (ISSN)

0743-1619

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Jan 2024

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