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Robust control of distributed parameter mechanical systems using a multidimensional systems approach

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Języki publikacji
EN
Abstrakty
EN
The unique characteristic of a repetitive processes is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration. On each pass an output, termed the pass profile is produced which acts as on forcing function, and hence contributes to, the dynamics of the next pass profile. This leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations that increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by application of standard linear systems control laws and instead they must be treated as two-dimensional (2D) systems where information propagation in two independent directions, termed passto-pass and along the pass respectively, is the defining feature. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control law design algorithms are developed for discrete linear repetitive processes where a plane, or rectangle, of information is propagated in the pass-to-pass direction. The possible use of such a model in the control of distributed parameter systems has been investigated in previous work and this paper considers an extension to allow for uncertainty in the model description.
Rocznik
Strony
67--75
Opis fizyczny
Bibliogr. 20 poz., rys., tab.
Twórcy
autor
autor
autor
autor
  • Institute of Control and Computation Engineering, University of Zielona Góra, 50 Podgórna St., 65-246 Zielona Góra, Poland, k.galkowski@issi.uz.zgora.pl
Bibliografia
  • [1] R.P. Roesser, “A discrete state-space model for linear image processing”, IEEE Trans. on Automatic Control 20, (1), 1–10 (1975).
  • [2] E. Fornasini and G. Marchesini, “Doubly indexed dynamical systems: state-space models and structural properities”, Theory of Computing Systems 12, (1), 59–72 (1978).
  • [3] C. Du and L. Xie, “Stability analysis and stabilization of uncertain two-dimensional discrete systems: an LMI approach”, IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications 46, 1371–1374 (1999).
  • [4] H.D. Tuan, P. Apkarian, and T.Q. Nguyen, “Robust mixed H2/H1 filtering of 2-D systems”, IEEE Trans. on Signal Processing 50 (7), 1759–1771 (2002).
  • [5] E. Rogers, K. Gałkowski, and D.H. Owens, “Control systems theory and applications for linear repetitive processes”, in: Lecture Notes in Control and Information Sciences, vol. 349, Springer-Verlag, Berlin, 2007.
  • [6] H-S. Ahn, Y. Chen, and K.L. Moore, “Iterative learning control: brief survey and categorization”, IEEE Trans. on Systems Man and Cybernetics C 37 (6), 1109–1121 (2007).
  • [7] P.D. Roberts, “Numerical investigations of a stability theorem arising from 2-dimensional analysis of an iterative optimal control algorithm”, Multidimensional Systems and Signal Processing 11 (1/2), 109–124 (2000).
  • [8] Ł. Hładowski, Z. Cai, K. Gałkowski, E. Rogers, C.T. Freeman, and P.L. Lewin, “Using 2D systems theory to design output signal based iterative learning control laws with experimental verification”, Proc. 47th IEEE Conf. on Decision and Control 1, 3026–3031 (2008).
  • [9] Ł. Hładowski, K. Gałkowski, Z. Cai, E. Rogers, C.T. Freeman, and P.L. Lewin, “Experimentally supported 2D systems based iterative learning control law design for error convergence and performance”, Control Engineering Practice 18 (4), 339–348 (2010).
  • [10] J. Wood, U. Oberst, E. Rogers, and D.H. Owens, “A behavioural approach to the pole structure of one-dimensional and multidimensional linear systems”, SIAM J. on Control and Optimization 38,(2), 627–661 (2000).
  • [11] H. Pillai, J. Wood, and E. Rogers, “On the homomorphisms of n-D behaviors”, IEEE Trans. on Circuits and Systems Part I: Fundamental Theory and Applications 49 (6), 732–742 (2002).
  • [12] G.E. Dullerud and R. D’Andrea, “Distributed control of heterogeneus systems”, IEEE Trans. Automatic Control 49 (12), 2113–2128 (2004).
  • [13] P. Augusta and Z. Hur´ak, “Multidimensional transfer function model of a deformable mirror in adaptive optics systems”, pp. 1556–1561, Int. Symposium on Mathematical Theory of Networks and Systems, Kyoto, 2006.
  • [14] S. Timoshenko and S. Woinowski-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1959.
  • [15] J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks, London, 1989.
  • [16] B. Cichy, P. Augusta, E. Rogers, K. Gałkowski, and Z. Hurak, “On the control of distributed parameter systems using a multidimensional systems setting”, Mechanical Systems and Signal Processing 22, 1566–1581 (2008).
  • [17] P.I. Belly, The Design and Construction of Large Optical Telescopes, Springer-Verlag, Berlin, 2003.
  • [18] K.L. Moore, M. Ghosh, and Y. Chen, “Spatial-based iterative learning control for motion control applications”, Mechanica 42 (2), 167–175 (2007).
  • [19] K.L. Moore and Y.Q. Chen, “Iterative learning approach to a diffusion control problem in an irrigation application”, Proc. IEEE Int. Conf. on Mechatronics and Automation 1, 1329–1334 (2006).
  • [20] H. Zhao, Passive, Iterative, and Repetitive Control for Flexible Distributed Parameter Systems, Ph.D. Dissertation, The Pennsylvania State University, USA, 2005.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG8-0020-0007
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