Realization of nonlinear composite systems

• Autorzy: Mullari T. , Kotta U. , Nomm S. , Tonso M.
• Języki publikacji: EN

Abstrakty

EN

The paper studies the realization problem for series and parallel connections of nonlinear single-input single-output systems, described by higher order differential equations. Necessary and sufficient conditions are given for the existence of the classical state space realization in both cases. It is proved that post- and parallel compensators are of no help in overcoming non-realizability. Results are illustrated by an example.

Słowa kluczowe

EN

nonlinear control systems; realization; composite systems

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2006
• Tom: Vol. 35, no 4
• Strony: 905--921
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Mullari T.

autor

Kotta U.

autor

Nomm S.

autor

Tonso M.

• Institute of Cybernetics at Tallin, University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia,

Bibliografia

• CROUCH, P. and LAMNABHI-LAGARRIGUE F. (1988) State space realizations of nonlinear systems defined by input-output differential equations. In A. Bensoussan and J. L. Lions, eds., Analysis and Optimization of Systems. In: Lecture Notes in Control and Information Sciences 111, 138-149.
• CROUCH, P., LAMNABHI-LAGARRIGUE, F. and PINCHON, D.(1995) A realization algorithm for input-output systems. International Journal of Control 62 (4).
• DELALEAU, E. and RUDOLPH, J. (1998) Control of flat systems by quasy-static feedback of generalised states. International Journal of Control 71 (5), 745-765.
• DELALEAU, E. and RESPONDEK. W. (1995) Lowering the orders of derivatives of controls in generalized state space systems. Journal of Mathematical Systems Estimation and Control 40, 127-132.
• GLAD, S.T. (1988) Nonlinear state-space and input-output descriptions using differential polynomials. In: A. Isidori J. Descusse, M. Fliess and P. Leborgne, eds., New Trends in Nonlinear Control Theory, 182-489, Springer-Verlag, New York.
• KAWSKI, M. (2000) Calculus of nonlinear interconnections with applications. In: Proc. of the 39th IEEE Conference on Decision and Control, 2, 1661-1666, Sydney, Australia.
• KOTTA, U. and MULLARI, T. (2005) Equivalence of different realizability conditions for nonlinear control systems described by a set of higher-order differential equations. European Journal of Control 3, 185 193.
• MOOG, C.H., ZHENG, Y.-F. and LIU, P. (2002) Input-output equivalence of nonlinear systems and their realizations. In: Proc. of the 15th IFAC World Congress, Barcelona.
• NIJMEIJER, H. and VAN DER SCHAFT, A. J. (1990) Nonlinear dynamical control systems. Springer, New York.
• NÕMM, S. (2003) Realization of interconnected input-output discrete-time systems. In: Proc. of the 42nd IEEE Conf. on Decision and Control, 1368-1373, Maui, Hawaii, USA.
• NÕMM, S., MOOG, C.H., KOTTA, Ü. and TÕNSO, M. (2004) Realization of nonlinear discrete-time composite systems. In: Proc. of the 2nd IFAC Symp. on System Structure and Control, 712-717, Oaxaca, Mexico.
• NÕMM, S., KOTTA, Ü. and TÕNSO, M. (2005) Realization of nonlinear discrete-time composite systems: computational aspects. In: P. Horacek et al., eds., Preprints of the 16th IFAC World Congress. Prague.
• RUDOLPH, J. (2000) Flatness based control by quasy-static feedback illustrated on a cascad of two chemical reactors. International Journal of Control 73 (2), 115-131.
• VAN DER SCHAFT, A.J. (1987) On realization of nonlinear systems described by higher-order differential equations. Mathematical Systems Theory 19, 239-275.
• VAN DER SCHAFT, A.J. (1990) Transformations and representations of nonlinear systems. In: K. Malanowski B. Jakubczyk and W. Respondek, eds., Perspectives in Control Theory, 297-314, Birkhäuser, Boston.
• SONTAG, E.D. and INGALLS B. (2002) A small-gain theorem with applications to input/output systems, incremental stability, detectability and interconnections. Journal of the Franklin Institute 339, 211-229.
• WILLEMS, C.J. (1997) On interconnections, control, and feedback. IEEE Transactions on Automatic Control 3, 326-339.