Journal
JOURNAL OF PROCESS CONTROL
Volume 24, Issue 12, Pages 86-94Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.jprocont.2014.10.001
Keywords
Iterative learning control; Monotone convergence; Discrete frequency-domain spectrum; Fourier series; Parseval's Energy Equality
Funding
- National Natural Science Foundation of China [F010114-60974140, 61273135]
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On the basis that a Dirichlet-type signal over a finite time period can be expanded in a Fourier series consisting of fundamental-frequency sinusoidal and cosine waves plus a sequence of higher-frequency harmonic waves, this paper investigates the convergence characteristics of the first- and second-order proportional-derivative-type iterative learning control schemes for repetitive linear time-invariant systems in discrete spectrum. By deriving the properties of the Fourier coefficients in a complex form with respect to the linear time-invariant dynamics and adopting Parseval's Energy Equality, the average energy of the tracking error signal over the finite operation time interval is converted into a quarter of a summation of the fundamental spectrum plus the harmonic spectrums. By means of analyzing the feature of discrete frequency-wise spectrum of the tracking error, sufficient and necessary conditions for monotone convergence with respect to the first-order iterative learning control scheme is deduced together with convergence of the second-order learning scheme is discussed. Numerical simulations manifest the validity and the effectiveness. (C) 2014 Elsevier Ltd. All rights reserved.
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