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Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control

Owens, D.H. and Chu, B. (2009) Modelling of non-minimum phase effects in discrete-time norm optimal iterative learning control. Research Report. ACSE Research Report no. 1005 . Automatic Control and Systems Engineering, University of Sheffield

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Abstract

The subject of this paper is the modelling of the in°uence of non-minimum phase discrete-time system dynamics on the performance of norm optimal iterative learning control (NOILC) algorithms with the intent of explaining the observed phenomenon and predicting its primary characteristics. It is established that performance in the presence of non-minimum phase plant zeros typically has two phases. These consist of an initial fast monotonic reduction of the L2 error norm (mean square error) followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over a finite number of trials is apparent convergence to a non-zero error. The source of this slow convergence is identified using the singular value distribution of the system's all pass component. A predictive model of the onset of slow convergence behavior is developed as a set of linear constraints and shown to be valid when the iteration time interval is sufficiently long. The results provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm and associated error time series are obtained for single-input single-output systems with several non-minimum phase zeros outside the unit circle using Lagrangian techniques. Numerical simulations are given to confirm the validity of the analysis.

Item Type: Monograph (Research Report)
Copyright, Publisher and Additional Information: The Department of Automatic Control and Systems Engineering research reports offer a forum for the research output of the academic staff and research students of the Department at the University of Sheffield. Papers are reviewed for quality and presentation by a departmental editor. However, the contents and opinions expressed remain the responsibility of the authors. Some papers in the series may have been subsequently published elsewhere and you are advised to cite the later published version in these instances.
Keywords: iterative learning control; non-minimum phase systems; singular value decomposition; all pass systems
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) > ACSE Research Reports
Depositing User: Miss Anthea Tucker
Date Deposited: 26 Oct 2012 15:54
Last Modified: 08 Feb 2013 17:40
Status: Published
Publisher: Automatic Control and Systems Engineering, University of Sheffield
URI: http://eprints.whiterose.ac.uk/id/eprint/74694

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