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In the paper, the computationally effective MATLAB based stability tests for discrete linear repetitive processes (DLRP) are presented. Despite the clear 2D character of repetitive processes, due to the finite pass length, asymptotic stability may be characterized in term of equivalent 1D state space model, and hence all well known standard stability tests for the discrete case may be adopted here. However, the presence of so-called dynamic initial conditions (also known as dynamic boundary conditions), which play an essential role in many various applications, e.g. in Iterative Learning Control(ILC) schemes, requires adopting these tests to the (dense) matrices of a large, sometimes enormously, dimension. The results are illustrated by simulation material.
Słowa kluczowe
Rocznik
Tom
Strony
513--537
Opis fizyczny
8 rys., 2 tabele, bibliogr. 25 poz.
Twórcy
autor
- Department of Computer Science and Electronics, Technical University of Zielona Góra, ul.Podgórna 50, 65-246 Zielona Góra, Poland (Wydział Informatyki i Elektroniki Politechniki Zielonogórskiej), J.Gramacki@iie.pz.zgora.pl
Bibliografia
- [1] R. L. Burden, J. D. Faires Numerical analysis, Brooks/Cole, 6-th edition, 1998.
- [2] J. B. Edwards, Stability problems in the control of multipass processes, Proc. IEEE, 121, 11, (1974) 1425-1432.
- [3] D. K. Faddeev, V. N. Faddeeva, Computational methods of linear algebra, Freeman, San Francisco 1963.
- [4] E. Fornasini, G. Marchesini, Doubly indexed dynamical systems: state models and structural properties, Math. Systems Theory, 12 (1978) 59-72.
- [5] K. Gałkowski, E. Rogers, A. Gramacki, J. Gramacki, D. H. Owens, Controlling of dynamics of discrete linear repetitive processes by rejecting the effects of dynamic pass initial conditions, Proceedings of NDS-98, Zielona Góra/Łagów, Poland, (1998) 63-68.
- [6] K. Gałkowski, E. Rogers, J. Gramacki, A. Gramacki, D. H. Owens, Higher order discretization methods for a class of 2D continuous-discrete linear systems, IEE Proceedings-Circuits, Devices and Systems 146, 6, (1999) 315-320.
- [7] K. Gałkowski, E Rogers, A. Gramacki, J. Gramacki, D. H. Owens, Higher order discretiation of differential linera repetitive processes, 14th IFAC World Congress, Beijing, P.R. China, 1999.
- [8] K. Gałkowski, E. Rogers, D. H. Owens, A new state-space model for linear discrete multipass processes, Bull. Pol. Ac.: Tech., 44, 1, (1996) 87-98.
- [9] K. Gałkowski, E. Rogers, D. H. Owens, Basic systems theory for discrete linear repetitive processes using 2d Roesser model interpretations, Applied Mathematics and Computer Science, 7, 1, (1997) 101-116.
- [10] K. Gałkowski, E. Rogers, D. H. O wens, Analysis of linear repetitive processes with dynamic boundary conditions, technical report, Dept. Electronics and Computer Science, University of Southampton, UK 1998.
- [11] K. Gałkowski, D. Rogers, D. H. Owens, Matrix rank based conditions for reachability/controllability of discrete linear repetitive processes, Linear Algebra and its Applications, 275-276 (1998) 201-224.
- [12] J. Gramacki, Methods of testing stability and stabilization of linear discrete repetitive processes (in Polish), PhD thesis, Technical University of Zielona Góra, Poland 1999.
- [13] N. J. Higham, Accuracy and stability of numerical algorithms, SIAM 1996.
- [14] T. Kaczorek, Reduction of nd linear systems to 1d systems with variable structure, Bull. Pol. Ac.: Tech., 35, 11-12, (1987) 623-631.
- [15] T. Kaczorek, Straight line reachability of Roesser model, IEEE Trans. Automat. Contr., AC-32, 7, (1987) 637-639.
- [16] T. Kaczorek, Singular 2d continuous-discrete lincar systems, Bull. Pol. Ac: Tech., 42 (1994) 417-122.
- [17] T. Kaczorek, When does the local controllability of the genar model of 2d linear systems imply its local reachabilily? Systems and Control Letters, 23 (1994) 445-152.
- [18] J. Klamka, Controllability of 2-d continuous-discrete abstract linear systems, Proc. European Contr. Conf., Rome, 3 (1995) 2208-2213.
- [19] W. A. Porter, J. L. Aravena, 1d models for m-d processes, IEEE Trans. Circuits and Systems, CAC-31 (1984) 742-744.
- [20] P. D. Roberts, Computing the stability of iterative optimal iterative learning control schemes through the use of two-dimensional systems theory, Proceedings of UKACC International Conference Control 96, 2 (1996) 981-986.
- [21] P. Rocha, Stability of discrete non-unit memory linear repetitive processes – a two-dimensional systems interpretation, Int. J. Control, 63, 3, (1996) 457-482.
- [22] R. P. Roesser, A discrete state space model for linear “age processing, IEEE Trans. Automatical Control, 20 (1975) 1-10.
- [23] E. Rogers, D. H. Owens, Stability analysis for linear repetitive processes, Lecture Notes in Control and Information Sciences Series, Springer-Verlag, 175 (1992).
- [24] E. Rogers, J. Gramacki, K. Gałkowski, D. H. Owens, Stability theory for a class of 2d linear systems with dynamic boundary conditions, Proceedings of the 37-th CDC-98, Tampa, USA (1998) 2800-2805.
- [25] E. Rogers, K. Gałkowski, D. H. Owens, Control systems theory for linear repetitive processes – recent progress and open research problems, Applied Mathematics and Computer Science, 7, 4, (1997) 737-774.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG1-0011-0098
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