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From Continuous to Discrete Models of Linear Repetitive Processes

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Języki publikacji
EN
Abstrakty
EN
Differential linear repetitive processes are a distinct class of 2D linear systems which pose problems which cannot (except in a few very restrictive special cases) be solved by application for computer aided annalysis and simulation. One such problem area is the construction of accurate numerically well conditioned discrete approximations of the dynamics of differential processes which could, as one example of number of immediate applications areas, from the basis for digital implementation of control laws. In this paper, we undertake a detailed investigation of the critical problems which arise when attempting to construct usefull discrete approximations of the dynamics of differential linear repetitive processes and develop solutions to them. Numerical examples to support the results obtained are also given using a specially developed MATLAB based toolbox.
Rocznik
Strony
151--185
Opis fizyczny
Bibliogr. 33 poz., rys., tab.
Twórcy
autor
  • Department of Electronics and Computer Science, University of Zielona Góra, Poland
autor
  • Department of Electronics and Computer Science, University of Zielona Góra, Poland
  • Department of Control and Computation Engineering, University of Zielona Góra
autor
  • Department of Electronics and Computer Science, University of Southampton
autor
  • Department of Automatic Control and Systems Engineering, University of Sheffield, UK
Bibliografia
  • [1] N. Amann, D.H. Owens and E. Rogers: Iterative learning control using optimal feedback nad feedforward actions. Int. J. Control, 65(2), (1996), 277-293.
  • [2] S. Arimoto, S. Kawamura and F. Miyazaki: Bettering operation of robots by learning. J. Robotic Systems, 1(2), (1984), 123-140.
  • [3] CDC-98. Proc. IEEE Iterative Learning Control Workshop and Roundtable, Hyatt Regency Wstshore, Tampa, Florida, USA, (1998). See also special issue of Int. J. of Control, 73(10), (2000).
  • [4] Y. Chen and C. Wen: Iterative Learning Control, 248 Lecture Notes in Control and Information Science, Springer Verlag, Berlin, 1999.
  • [5] J.B. Edwards: Stability problems in the control of multipass processes. Proceedings of The Institution of Electrical Engineers, 121(11), (1974), 1425-1432.
  • [6] E. Fornasini and G. Marchesini: Doubly-indexed dynamical systems: State space models and structural properties. Mathematical Systems Theory, 12 (1978), 59-72.
  • [7] K. Gałkowski, E. Rogers, A. Gramacki, J. Gramacki and D.H. Owens: Stability and dynamic boundary condition decoupling analysis for a class of 2-D discrete linear systems. IEE Proceedings - Circuits, Devices and Systems, 148(3), 2001, 126-134.
  • [8] K. Gałkowski, E. Rogers and D.H. Owens: A new extended form of 1D state space model for discrete linear repetitive processes. Proc. 2nd Portuguese Conference on Automatic Control, 2 (1996), 419-423.
  • [9] K. Gałkowski, E. Rogers and D.H. Owens: Matrix rank based conditions for reachability/controllability of discrete linear repetitive processes. Linear Algebra and its Applications, (1998), 275-276, 201-224.
  • [10] A. Gramacki: Discretization of linear, differential repetitive processes. PhD thesis, Technical University of Zielona Gora, Computer Eng. and Electronics Dept., 1999. (in Polish).
  • [11] A. Gramacki: On a new method of discretization of differential linear repetitive processes. Bulletin of the Polish Academy of Science, Technical Sciences, 48(14), (2000), 539-560.
  • [12] A. Gramacki, K. Gałkowski, E. Rogers and D.H. Owens: Methods for the discretization of a class of 2D continuous-discrete linear systems. Proc. IEEE Conf. on Decision and Control, Phoenix, (1999).
  • [13] J. Gramacki: Methods of testing stability and stabilization of linear discrete repetitive processes. PhD thesis, Technical University of Zielona Gora, Computer Eng. and Electronics Dept., 1999. (in Polish).
  • [14] T. Kaczorek: Reduction of nD linear systems to 1D systems with variable structure. Bulletin Polish Academy of Science. Technical Sciences, Electronics and Electrotechnics, 35(11-12), (1987), 623-631.
  • [15] T. Kaczorek: Controllability and minimum energy control of 2D continuous-discrete linear systems. Applied Mathematics and Computer Science, 11, (1995), 5-21.
  • [16] J.E. Kurek: Discrete-time model for continuous-time repetitive system. Proc. Workshop on nD Systems, University of Zielona Góra, Poland, (2000).
  • [17] L. Lapidus and J.H. Seinfeld: Numerical solutions of ordinary differential equations. Academic Press, N.Y., 1971.
  • [18] NDS-2000. Proc. Second Int. Workshop on Multidimensional (ND) Systems. Technical University Press, Zielona Gora, Poland, (2000).
  • [19] G. Oriolo, S. Panzieri and G. Ulivi: Learning optimal trajectories for non-holonomic systems. Int. J. of Control, 73(10), (1988), 980-991.
  • [20] D.H. Owens: Stability of multipass processes. Proceedings of The Institution of Electrical Engineers, 124(11), (1977), 1079-1082.
  • [21] D.H. Owens, N. Amann, E. Rogers and M. French: Analysis of linear iterative learning control schemes - a 2-D systems/repetitive processes approach. Multidimensional Systems and Signal Processing, 11(1/2), (2000), 125-177.
  • [22] D.H. Owens and E. Rogers: Stability analysis for a class of 2D continuous-discrete linear systems with dynamic boundary conditions. Systems and Control Letters, 37, (1999), 55-60.
  • [23] W.A. Porter and J.L. Aravena: 1-D models for m-D processes. IEEE Trans. Circuits and Systems, CAS-3, (1984), 742-744.
  • [24] P.D. Roberts: Numerical investigation of a stability theorem arising from the 2-dimensional analysis of an iterative optimal control algorithm. Multidimensional Systems and Signal Processing, 11(1/2) (2000), 109-124.
  • [25] R.P. Roesser: A discrete state space model for linear image processing. IEEE Trans. Automatic Control, 20 (1975), 1-10.
  • [26] E. Rogers, K. Gałkowski and D.H. Owens: Systems Theory and Applications of Linear Repetitive Processes. Lecture Notes in Control and Information Science. Springer Verlag, Berlin, 2002. (to appear).
  • [27] E. Rogers, J. Gramacki, K. Gałkowski and D.H. Owens: Stability theory for a class of 2-D linear systems with dynamic boundary conditions. Proc. of the CDC-98, Tampa, USA, pages 2800-2805, 1998.
  • [28] E. Rogers and D.H. Owens: Stability analysis for linear repetitive processes, 175 Lecture Notes in Control and Information Science, Springer Verlag, Berlin, 1992.
  • [29] A.M. Schneider, J.T. Keneshige and F.D. Groutage: Higher order s-to-z mapping functions and their application in digitizing continuous–time filters. Proc. IEEE, 79(11), (1991), 1661-1674.
  • [30] L. F. Shampine and M. W. Reichelt: The MATLAB ODE suite. SIAM Journal on Scientific Computing, 18(1), (1997), 1-22.
  • [31] K.J. Smyth Computer aided analysis for linear repetitive processes. PhD thesis, University of Strathclyde, UK, 1992.
  • [32] Inc. The MathWorks. Using MATLAB, Version 5. 24 Prime Park Way, Natick, Massachusets 01760, 1998.
  • [33] M. Yamakita and K. Furuta Iterative generation of virtual reference for a manipulator. Robotica, 9 (1991), 71-80.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0002-0053
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