Linear repetitive process control theory applied to a physical example

Krzysztof Gałkowski; Eric Rogers; Wojciech Paszke; David Owens

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 1, page 87-99
  • ISSN: 1641-876X

Abstract

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In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.

How to cite

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Gałkowski, Krzysztof, et al. "Linear repetitive process control theory applied to a physical example." International Journal of Applied Mathematics and Computer Science 13.1 (2003): 87-99. <http://eudml.org/doc/207627>.

@article{Gałkowski2003,
abstract = {In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.},
author = {Gałkowski, Krzysztof, Rogers, Eric, Paszke, Wojciech, Owens, David},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {repetitive dynamics; metal rolling; LMIs; delay differential system; stability; linear matrix inequality; 2D linear systems; models},
language = {eng},
number = {1},
pages = {87-99},
title = {Linear repetitive process control theory applied to a physical example},
url = {http://eudml.org/doc/207627},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Gałkowski, Krzysztof
AU - Rogers, Eric
AU - Paszke, Wojciech
AU - Owens, David
TI - Linear repetitive process control theory applied to a physical example
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 1
SP - 87
EP - 99
AB - In the case of linear dynamics, repetitive processes are a distinct class of 2D linear systems with uses in areas ranging from long-wall coal cutting and metal rolling operations to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them for onward translation into efficient routinely applicable controller design algorithms for applications domains. In this paper, we introduce the dynamics of these processes by outlining the development of models for various metal rolling operations. These models are then used to illustrate some recent results on the development of a comprehensive control theory for these processes.
LA - eng
KW - repetitive dynamics; metal rolling; LMIs; delay differential system; stability; linear matrix inequality; 2D linear systems; models
UR - http://eudml.org/doc/207627
ER -

References

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  12. Gałkowski K., Rogers E., Xu S., Lam J. and Owens D.H. (2002b): LMIs-a fundamental tool in analysis and controller design for discrete linear repetitive processes. - IEEE Trans. Circ. Syst., Part 1, Fund. Theory Appl., Vol. 49, No. 6, pp. 768-778. 
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  16. Roberts P.D. (2000): Stability analysis of iterative optimal control algorithms modelled as linear repetitive processes. - Proc. IEE, Part D, Vol. 147, No. 3, pp. 229-238. 
  17. Roesser R.P. (1975): A discrete state space modelfor linear image processing. - IEEE Trans. Automat. Control, Vol. AC-20, No. 1, pp. 1-10. Zbl0304.68099
  18. Rogers E. and Owens D.H. (1992): Stability Analysisfor Linear Repetitive Processes. - Berlin: Springer. 
  19. Rogers E., Gałkowski K. and Owens D.H. (2003): Control Systems Theory and Applications for Linear Repetitive Processes. - Berlin: Springer (to appear). 
  20. Smyth K.J. (1992): Computer Aided Analysis for Linear Repetitive Processes. - Ph.D. Thesis, Department of Mechanical Engineering, University of Strathclyde. 

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