Linear Repetitive Process Control Theory Applied to a Physical Example

• Autorzy: Gałkowski K. , Rogers E. , Paszke W. , Owens D. H.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

repetitive dynamics; metal rolling; LMIs; delay differential system; stability

PL

dynamika powtarzalna; walcowanie metali; układ różniczkowy

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 1
• Strony: 87--99
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Gałkowski K.

• Institute of Control and Computation Engineering, University of Zielona Góra, 65–246 Zielona Góra, ul. Podgórna 50, Poland

autor

Rogers E.

• Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, U.K.

autor

Paszke W.

• Institute of Control and Computation Engineering, University of Zielona Góra, 65–246 Zielona Góra, ul. Podgórna 50, Poland

autor

Owens D. H.

• Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, U.K.

Bibliografia

• [1] Agathoklis P. and Foda S. (1989): Stability and the matrix Lyapunov equation for delay differential systems. — Int. J. Contr., Vol. 49, No. 2, pp. 417–432.
• [2] Agathoklis P., Jury E.I. and Mansour M. (1982): The margin of stability of 2-D linear systems. — IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-30, No. 6, pp. 869–873.
• [3] Amann N., Owens D.H. and Rogers E. (1998): Predictive optimal iterative learning control. — Int. J. Contr., Vol. 69, No. 2, pp. 203–226.
• [4] Barnett S. (1983): Polynomials and Linear Control Systems. — New York: Marcel Dekker.
• [5] Boyd S., Ghaoui L.E., Feron E. and Balakrishnan V. (1994): Linear Matrix Inequalities in Systems and Control Theory. — Philadelphia: SIAM.
• [6] Byrnes C.I. Spong M.W. and Tarn T.J. (1984): A several complex variable approach to feedback stabilization of linear delay-differential systems. — Math. Syst. Theory, Vol. 17, pp. 97–133.
• [7] Edwards J.B. (1974): Stability problems in the control of multipass processes. — Proc. IEE, Vol. 121, No. 11, pp. 1425–1431.
• [8] Foda S. and Agathoklis P. (1989): Stability of differential multipass processes. — Electronics Lett., Vol. 24, No. 16, pp. 1016.
• [9] Fornasini E. and Marchesini G. (1978): Doubly-indexed dynamical systems: state space models and structural properties. — Math. Syst. Theory, Vol. 12, pp. 59–72.
• [10] Gałkowski K., Rogers E., Gramacki A., Gramacki J. and Owens D.H. (2001): Stability and dynamic boundary condition decoupling analysis for a class of 2-D discrete linear systems. — Proc. IEE, Vol. 148, No. 3, pp. 126–131.
• [11] Gałkowski K., Paszke W., Sulikowski B., Rogers E. and Owens D.H. (2002a): LMI based stability analysis and controller design for a class of 2D continuous-discrete linear systems. — Proc. Amer. Contr. Conf., Anchorage, pp. 29–34.
• [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.
• [13] Hale J. (1977): Theory of Functional Differential Equations. — New York: Springer.
• [14] Herz D., Jury E.I. and Zeheb E. (1984): Simplified analytic stability test for systems with commensurate delays. — Proc. IEE, Part D, Contr. Theory Applic., Vol. 131, No. 1, pp. 52–56.
• [15] Kaczorek T. (1995): Generalized 2-D continuous-discrete linear systems with delay. — Appl. Math. Comput. Sci., Vol. 5, No. 3, pp. 439–454.
• [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 model for linear image processing. — IEEE Trans. Automat. Control, Vol. AC-20, No. 1, pp. 1–10.
• [18] Rogers E. and Owens D.H. (1992): Stability Analysis for 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.