Commande par platitude de systèmes multi-entrées multi-sorties non stationnaires

ABSTRACT. This paper deals with a flatness-based control method of linear time-varying (LTV) multi-input multi-output (MIMO) system, developed in order to ensure the tracking of a reference trajectory. Polynomial two-degree-of-freedom controller can then be designed with the use of an exact observer and without resolving the generalized Bezout’s equation in LTV framework. The proposed approach is applied to nonlinear systems using its linearizations around given trajectories. The approach is illustrated with the control of the satellite SPOT-5.

[1]  F. Rotella,et al.  Commande des systèmes par platitude , 2007, Automatique et ingénierie système.

[2]  Y. Mutoh,et al.  Stability of the observer-based pole placement for discrete time-varying non-lexicographically-fixed systems , 2012, Proceedings of 2012 UKACC International Conference on Control.

[3]  Mohamed Benrejeb,et al.  Linear time-varying flatness-based control of Anti-lock Brake System (ABS) , 2012, International Multi-Conference on Systems, Sygnals & Devices.

[4]  Naoto Kimura,et al.  Observer-based pole placement for non-lexicographically-fixed linear time-varying systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[5]  Bogdan Marinescu,et al.  Output feedback pole placement for linear time-varying systems with application to the control of nonlinear systems , 2010, Autom..

[6]  J. Lévine Analysis and Control of Nonlinear Systems: A Flatness-based Approach , 2009 .

[7]  Mounir Ayadi,et al.  Polynomial controller design based on flatness , 2001, Kybernetika.

[8]  Philippe Martin,et al.  Dynamic feedback transformations of controllable linear time-varying systems , 2001 .

[9]  Oliver Montenbruck,et al.  Satellite Orbits: Models, Methods and Applications , 2000 .

[10]  Philippe Martin,et al.  A Lie-Backlund approach to equivalence and flatness of nonlinear systems , 1999, IEEE Trans. Autom. Control..

[11]  Michael Valásek,et al.  Pole placement for linear time-varying non-lexicographically fixed MIMO systems , 1999, Autom..

[12]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[13]  M. Fliess,et al.  Sur les systèmes non linéaires différentiellement plats , 1992 .

[14]  B. Shafai,et al.  Minimal order observer design for linear time varying multivariable systems , 1984, The 23rd IEEE Conference on Decision and Control.

[15]  Thomas Kailath,et al.  Linear Systems , 1980 .

[16]  A. Stubberud,et al.  Canonical forms for multiple-input time-variable systems , 1969 .

[17]  L. Silverman,et al.  Controllability and Observability in Time-Variable Linear Systems , 1967 .