Observer design using a partial nonlinear observer canonical form

• Autorzy: Röbenack K. , Lynch A. F.
• Języki publikacji: EN

Abstrakty

EN

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the advantages of the approach relative to the existing nonlinear observer design methods. The advantages of the proposed method include a relatively simple design procedure which can be broadly applied.

Słowa kluczowe

EN

observer design; canonical form; detectability

PL

wzorzec projektowy; postać kanoniczna; wykrywalność

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2006
• Tom: Vol. 16, no 3
• Strony: 333--343
• Opis fizyczny: Bibliogr. 31 poz., wykr.

Twórcy

autor

Röbenack K.

• Technische Universität Dresden, Department of Mathematics, Institute of Scientific Computing, Mommsenstr. 13, D–01062 Dresden, Germany

autor

Lynch A. F.

• University of Alberta, Department of Electrical and Computer Engineering, Edmonton AB T6G 2V4, Canada

Bibliografia

• [1] Amicucci G. L. and Monaco S. (1998): On nonlinear detectability.- J. Franklin Inst. 335B, Vol. 6, pp. 1105-1123.
• [2] Bestle D. and Zeitz M. (1983): Canonical form observer design for non-linear time-variable systems.-Int. J. Contr., Vol. 38, No. 2, pp. 419-431.
• [3] Birk J. and Zeitz M. (1988): Extended Luenberger observer for non-linear multivariable systems.-Int. J. Contr., Vol. 47, No. 6, pp. 1823-1836.
• [4] Brunovsky P. (1970): A classification of linear controllable systems.- Kybernetica, Vol. 6, No. 3, pp. 173-188.
• [5] Gauthier J. P., Hammouri H. and Othman S. (1992): A simple observer for nonlinear systems - Application to bioreactors. - IEEE Trans. Automat. Contr., Vol. 37, No. 6, pp. 875-880.
• [6] Hermann R. and Krener A. J. (1977): Nonlinear controllability and observability. - IEEE Trans. Automat. Contr., Vol. AC-22, No.5, pp. 728-740.
• [7] Isidori A. (1995): Nonlinear Control Systems: An Introduction, 3-rd Edn. -London: Springer.
• [8] Jo N. H. and Seo J. H. (2002): Observer design for non-linear systems that are not uniformly observable.-Int. J. Contr., Vol. 75, No. 5, pp. 369-380.
• [9] Kazantzis N. and Kravaris C. (1998): Nonlinear observer design using Lyapunov's auxiliary theorem. - Syst. Contr. Lett., Vol. 34, pp. 241-247.
• [10] Keller H. (1986): Entwurf nichtlinearer Beobachter mittels Normalformen. - Düsseldorf: VDI-Verlag.
• [11] Krener A. and Xiao M. (2002): Nonlinear observer design in the siegel domain. - SIAM J. Contr. Optim., Vol. 41, No. 3, pp. 932-953.
• [12] Krener A., Hubbard M., Karaham S., Phelps A. and Maag B. (1991): Poincaré's linearization method applied to the design of nonlinear compensators. - Proc. Algebraic Computing in Control, Vol. 165 of Lecture Notes in Control and Information Science, Berlin: Springer, pp. 76-114.
• [13] Krener A. J. and Isidori A. (1983): Linearization by output injection and nonlinear observers. - Syst. Contr. Lett., Vol. 3, pp. 47-52.
• [14] Krener A. J. and Respondek W. (1985): Nonlinear observers with linearizable error dynamics. - SIAM J. Contr. Optim., Vol. 23, No. 2, pp. 197-216.
• [15] Lynch A. and Bortoff S. (2001): Nonlinear observers with approximately linear error dynamics: The multivariable case. - IEEE Trans. Automat. Contr., Vol. 46, No. 7, pp. 927-932.
• [16] Marino R. and Tomei P. (1995): Nonlinear Control Design: Geometric, Adaptive and Robust. - London: Prentice Hall.
• [17] Moore E. H. (1920): On the reciprocal of the general algebraic matrix. -Bull. Amer. Math. Soc., Vol. 26, pp. 394-395.
• [18] Mukhopadhyay B. K. and Malik O. P. (1972): Optimal control of synchronous-machine excitation by quasilinearisation techniques. -Proc. IEE, Vol. 119, No. 1, pp. 91-98.
• [19] Nijmeijer H. and van der Schaft A. J. (1990): Nonlinear Dynamical Control Systems. -New York: Springer.
• [20] Phelps A. R. (1991): On constructing nonlinear observers. - SIAM J. Contr. Optim., Vol. 29, No. 3, pp. 516-534.
• [21] Respondek W. (1986): Global aspects of linearization, equivalence to polynomial forms and decomposition of nonlinear control systems. - Proc. Algebraic and Geometric Methods in Nonlinear Control, Dordrecht: Reidel, pp. 257-284.
• [22] Respondek W., Pogromsky A. and Nijmeijer H. (2004): Time scaling for observer design with linearizable error dynamics.- Automatica, Vol. 40, No. 2, pp. 277-285.
• [23] Röbenack K. and Lynch A. F. (2004): High-gain nonlinear observer design using the observer canonical form. - J. Franklin Institute, submitted.
• [24] Rudolph J. and Zeitz M. (1994): A block triangular nonlinear observer normal form. - Syst. Contr. Lett., Vol. 23, pp. 1-8.
• [25] Schweitzer G., Bleuler H. and Traxler A. (1994): Active Magnetic Bearings. - Zürich: VDF .
• [26] Shim H., Son Y. I. and Seo J. H. (2001): Semi-global observer for multi-output nonlinear systems. - Syst. Contr. Lett., Vol. 42, No. 3, pp. 233-244.
• [27] Sontag E. D. and Wang Y. (1997): Output-to-state stability and detectability of nonlinear system. - Syst. Contr. Lett., Vol. 29, No. 5, pp. 279-290.
• [28] Wang Y. and Lynch A. (2005): Block triangular observer forms for nonlinear observer design.-Automatica, (submitted).
• [29] Wang Y. and Lynch A. (2006): A block triangular form for nonlinear observer design. - IEEE Trans. Automat. Contr., (to appear).
• [30] Xia X.-H. and GaoW.-B. (1988): Non-linear observer design by observer canonical form. - Int. J. Contr., Vol. 47, No. 4, pp. 1081-1100.
• [31] Xia X. H. and Gao W. B. (1989): Nonlinear observer design by observer error linearization.-SIAM J. Contr. Optim., Vol. 27, No. 1, pp. 199-216.