Abstract

This paper proposes the extension of generalized internal model control (GIMC) based diagnosis and fault tolerant control to singularly perturbed system. This control method consists of two parts: a controller which guaranties nominal performance and works in the fault free case and a robustness controller to compensate the fault when a sensor failure is detected. This work describes the way to design such controllers for singularly perturbed systems so that the performance with the nominal controller may be guaranteed in the case of sensor failure.

References

• H. K. , Khalil, ''Stabilization of multiparameter singularly perturbed systems'', IEEE Trans. on Automatic Control, vol. AC-24, No. 5, pp. 790-791, October 1979.
• H. K. Khalil,'' Output feedback control of linear two-time-scale systems'', IEEE Transactions on Automatic Control, Vol. AC-32, No. 9, pp. 784-792, 1987.
• E. H. Abed,'' Decomposition and stability of multiparameter singular perturbation problems'', IEEE transactions on Automatic Control, AC 31, pp. 925-934, 1986.
• P. Y. Kokotovic, H. K. Khalil, and J. O'Reilly, Singular perturbation methods in control: analysis and design, Academic press, Harcourt Brace Jovanovich publishers, 1986.
• Z. Gajic, and M. Lim. Optimal control of singularly perturbed linear systems and applications Marcel Dekker, Inc. , New York, Basel, 2001.
• A. Tellili, M. N. Abdelkrim and M. Benrejeb. '' On the fault diagnosis of uncertain singularly perturbed systems'', to appear in Journal of Systems and Control Engineering.
• A. Tellili, M. N. Abdelkrim and M. Benrejeb. ''Sensor fault diagnosis of singularly perturbed systems applied to F-8 flight dynamic'', 16th IFAC symposium on Automatic Control in Aerospace, IFAC-ACA'2004, June 14-18 2004, Saint Petersburg, Russia.
• H. Oloomi, M. Saif and B. Shafai, ''On the well posedness of singularly perturbed fault detection filters'', in proceedings of the 2004 American Control Conference, Boston Massachusetts, June 30-july 2, 2004, pp. 5676-5677.
• M. Blanke, M. Staroswiecki, and N. E. Wu, ''Concepts and methods in fault-tolerant control'', Proceedings of American Control Conference, June 2001, Washington.
• M. Blanke, M. Kinneaert, J. Lunze, M. Staroswiecki, Diagnosis and fault tolerant control, Springer, 2003.
• H. Noura, Méthodes d'accommodation aux défauts : théorie et application. Habilitation à diriger des recherches, université Henri poincaré, Nancy 1, 26 mars 2002, France.
• R. J. Patton, '' Fault-tolerant control systems : the 1997 situation'', Safe'process, united kingdom, August 1997, pp. 1033-1055, 1997.
• H. Noura, D. Sauter, F. Hamelin, and D. Theilliot, ''Fault tolerant control in dynamic systems : Application to a winding machine'', IEEE control Systems Magazine, Vol. 20, No. 1, pp. 33-49, 2000.
• J. Stoustrup, and D. Blondel, ''Fault tolerant control : A simultaneous stabilization result'', IEEE transactions on automatic control, Vol. 49, No. 2, pp. 305-310, 2004.
• F. Liao, J. L. Wang, and G. –H Yang,''Reliable robust flight tracking control : An LMI approach '', IEEE transactions on control systems technology , Vol. 10, No. 1, pp. 76-89, 2002.
• R. J. Veillette, J. V. Medani? and W. R. Perkins, '' Design of reliable control systems '', IEEE Transactions on Automatic Control, Vol. 37, No. 3, pp. 290-304, 1992.
• R. J. Veillette, ''Reliable linear-quadratic state-feedback control'', Automatica, Vol. 31, pp. 137-143, 1995.
• G. -H. Yang, S. -Y. Zhang, J. Lam, and J. L. Wang, ''Reliable control using redundant controllers'', IEEE Transactions on Automatic Control, Vol. 43, No. 11, pp. 1588-1593, 1998.
• G. -H. Yang, J. L. Wang, and Y. C. Soh, ''Reliable H? controller design for linear systems'', Automatica, Vol. 37, pp. 717-725, 2001.
• Y. W. Liang, D. C. Liaw, and T. C. Lee, ''Reliable Control of Nonlinear Systems'', IEEE Transactions on Automatic Control, Vol. 45, No. 4, pp. 706-710, April 2000.
• A. Tellili and M. N. Abdelkrim. '' Reliable H? controller design for singularly perturbed systems with sensor failure'', In Proceedings of IEEE International Conference on Industrial Technology, IEEE-ICIT'04, pp. 1636-1641, december 8-10 2004, Hammamet, Tunisia.
• A. Tellili, M. N. Abdelkrimad and M. Benrejeb. '' Reliable H? control of multiple time scales singularly perturbed systems with sensor failure'', to appear in International Journal of Control.
• Y. Li, J. L. Wang, and G. H. Yang, ''Reliable linear-quadratic control for singularly perturbed systems'', International Journal of Systems Science , Vol. 33, N°12, pp. 949-958, 2002.
• K. Zhou, and Z. Ren. ''A new controller architecture for high performance, robust and fault-tolerant control'', IEEE Transactions on Automatic control, Vol. 46, No. 10, October 2001, pp. 1613-1618.
• D. Campos-Delgado and K. Zhou, ''Reconfigurable fault tolerant control using GIMC structure'', IEEE Transactions on Automatic control, Vol. 48, No. 5, May 2003, pp. 832-838.
• Kokotovic, P. V. and Yakel, R. A. (1972). Singular perturbation of linear regulators: basic theorems. IEEE Trans. On automatic control, vol. AC-17, N°1 Fev. 1972, pp. 29-37.
• Abdelkrim, M. N. and Benrejeb. M. A near robust H? control for simplified models of weakly coupled systems and singularly perturbed systems. Annales Maghrébines de l'Ingénieur, vol. 15, N°1, 2003, pp. 7-37.