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Robust Flatness-based Multi-controllers Approach

Unité de Recherche LA.R.A Automatique, Ecole Nationale d’Ingénieurs de Tunis
B.P. 37, le Belvédère, 1002 Tunis, TUNISIE

Mounir AYADI
Unité de Recherche LA.R.A Automatique, Ecole Nationale d’Ingénieurs de Tunis
B.P. 37, le Belvédère, 1002 Tunis, TUNISIE

Unité de Recherche LA.R.A Automatique, Ecole Nationale d’Ingénieurs de Tunis
B.P. 37, le Belvédère, 1002 Tunis, TUNISIE

Pierre BORNE
LAGIS, &EACUTEcole Centrale de Lille
B.P. 48, Villeneuve d’Ascq, 59651 Lille, FRANCE

Abstract: In this paper, a robust fault tolerant control reconfiguration is proposed. For identified models whose parameters change according to operating conditions, it is convenient to design a reconfiguration control strategy. This approach switches on-line the right controller to achieve the same performances for a given objective. This reconfiguration strategy is based on robust flatness-based switching control and developed in discrete-time framework in order to track a reference trajectory starting from a flat output variable. For each model, a corresponding flatness-based controller is designed and consequently, a multi-controller structure is obtained. The switching process is based on the minimization of a criterion. The performances obtained by switching in terms of tracking trajectory and disturbance fault rejection are discussed in this paper. The stability of the corresponding switched discrete-time linear systems is given.

Keywords: Flatness, tracking trajectory, robustness, switching, multi-controllers, reconfiguration.

>Full text
Hajer GHARSALLAOUI, Mounir AYADI, Mohamed BENREJEB, Pierre BORNE, Robust Flatness-based Multi-controllers Approach, Studies in Informatics and Control, ISSN 1220-1766, vol. 19 (4), pp. 357-368, 2010.

1. Introduction

Associated with the increasing demands for higher system performance and product quality on the one side and more cost efficiency in the other side, the complexity and the automation degree of technical processes are continuously growing. However, conventional feedback control design for a complex system may result in an unsatisfactory performance, or even in instability, in the event of malfunctions in actuators, sensors or other system components. In order to overcome these limitations, modern complex systems use sophisticated controllers which are developed with fault accommodation and tolerance capabilities, in order to meet reliability and performance requirements.

Originated in the early 70’s, the model-based reconfiguration control technique is a kind of active approaches to achieve fault tolerant control for dynamic systems which has been developed remarkably since then. Its efficiency in detecting faults in a system has been demonstrated by a great number of successful applications in industrial processes and automatic control systems.

Although developed for different purposes by means of different techniques, all model-based fault tolerant control system are common in the explicit use of a process model, based on which algorithms are implemented for processing data that are on-line collected and recorded during the system operation.

In this way, general multiple model-based control approaches have been developed in last decade, [3]-[5]-[8]-[10]-[21]. Thus, in the literature, there are many strategies that take in consideration the multi-models methods used for reconfiguration of control law and diagnosis purposes, [7]-[14]-[18]-[20]-[22]. Furthermore, Multiple Models (MM) method is proposed in [16]. In addition, controller switching approach represents a class of active fault tolerant control detailed in [17]. Moreover, Multiple Models Switching and Tuning (MMST) approach that concerns more particularly the reconfigurable control method is proposed in [4]-[9]-[19]-[20]-[24]-[25]-[26].

In this paper, for a Single Input Single Output (SISO) nonlinear process with multiple operating modes, a robust control reconfiguration strategy, based on switching control, is used to ensure stability and desired performances. The multi-model flatness-based control is based on switching between identified operating modes. The minimization of criterion value, based on a difference between the estimated output of each model and the real system output, is generated.

The LMI tools which are based on quadratic Lyapunov criteria in order to guaranty the stability of the global system are used. The performances obtained by switching in terms of tracking trajectory and disturbance rejection are discussed in this paper and the stability of the corresponding switched discrete-time linear systems is given. The case of thermal process is studied.


  1. Ayadi, M., Contribution à la commande des systèmes linéaires plats de dimension finie, Thèse de Doctorat, Institut National Polytechnique de Toulouse, 2002.
  2. Ayadi, M., J. Haggège, S. Bouallègue, M. Benrejeb, A Digital Flatness Control System of a DC Motor, Studies in Informatics and Control, Vol. 17, 2008, pp. 205-224.
  3. Benrejeb, M., M. Gasmi, P. Borne, New Stability Conditions for TS Fuzzy Continuous Nonlinear Models. Nonlinear Dynamics and Systems Theory. Vol. 5, 2005, pp. 369-376.
  4. Blanke, M., M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control, Springer, London, 2006.
  5. Borne, P., Multimodel Analysis and Control of Complex Systems, 1st Sino-French Symposium on Sensory Evaluation and Intelligent Technique, Shangai, 2003.
  6. Borne, P., G. Dauphin-Tanguy, J. P. Richard, F. Rotella, I. Zambettakis, Commande et optimisation des processus, Edition Technip, Paris, 1990.
  7. Charbonnaud, P., J. F. Carrilo, S. Médar, Robust Control Reconfiguration of a Thermal Process with Multiple Operating Modes, IEEE Transactions on Control Systems Technology, Vol. 11, 2003 pp. 529-538.
  8. Delmotte, F. P. Borne, A General Scheme for Multi-model Controller Using Trust, Mathematics and Computers in Simulation, Vol. 41, 1996, pp. 173-186.
  9. Ding, X. S., Model-based Fault Diagnosis Techniques Design Schemes, Algorithm, and Tools, Springer, London, 2003.
  10. Duviella, E., P. Chiron, P. Charbonnaud, Networked Hydrographical Systems: A Reactive Control Strategy Integrating Time Transfer Delays, Studies in Informatics and Control, Vol. 17, 2008, pp.153-168.
  11. ElGhaoui, L., S. Niculescu, Advances in Linear Matrix Inequality methods in control, Philadelphia, 2000.
  12. Fliess, M., J. Lévine, Ph. Martin P. Rouchon, On differentially flat non linear systems, IFAC Symposium NOLLOS’92, 1992, pp. 408-412.
  13. Gharsallaoui, H., M. Ayadi, M. Benrejeb, P. Borne, Flatness-based Control and Conventional RST Polynomial Control of a Thermal Process, International Journal of Computers, Communications & Control, Vol. 4, 2009, pp. 27-41.
  14. Gharsallaoui, H., M. Ayadi, M. Benrejeb, P. Borne, Flatness-based Switching Control, 12th LSS 2010 IFAC Symposium on Large Scale Systems: Theory and Applications, Lille, 2010.
  15. Landau, I. D., R. Lozano, M. M’saad, Adaptive Control, Springer-Verlag, London, 1998.
  16. Lemos, J., L. Ratos, J. Marques, Switching Reconfigurable Control Based on Hidden Markov models, American Control Conference, San Diego, 1999.
  17. Mahmoud, M., J. Jiang, Y. Zhang, Stochastic Stability Analysis of Fault Tolerant Control Systems in the Presence of Noise, IEEE Transactions on Automatic Control, Vol. 11, 2001, pp. 1810-1815.
  18. Médar, S., P. Charbonnaud, F. Nouredine, Active Fault Accommodation of a Three Tank System via Switching Control, IFAC World Congress, Barcelona, 2002.
  19. Mendoza, J. E., L. A. Villaleiva, M. A. Castro, E. A. Lopez, Multi-objective Evolutionary Algorithms for Decision-Making in Reconfiguration Problems Applied to the Electric Distribution Networks, Studies in Informatics and Control, Vol. 18, 2009, pp. 325-336.
  20. Narendra, K. S., O. A. Driollet, M. Feiler, K. George, Adaptive Control using Multiple Models, Switching and Tuning, International Journal of Adaptive Control and Signal Processing, Vol. 17, 2003, pp. 87-102.
  21. Patton, R. J., Fault-tolerant Control: the 1997 Situation, Preprints of IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, Kingston upon Hull, UK, 1997.
  22. Rodrigues, M., Diagnostic et commande active tolérante aux défauts appliqués aux systèmes décrits par des multi-modèles linéaires, Thèse de Doctorat, Université Henri Poincaré, Nancy 1, 2005.
  23. Rotella, F., F. Carillo, M. Ayadi, Digital Flatness Based Robust Controller Applied to A Thermal Process, IEEE International Conference on Control Applications, Mexico, 2001, pp. 936-941.
  24. Steffen, T., Control Reconfiguration of Dynamical Systems, Springer, 2005.
  25. Staroswiecki, M., Fault Tolerant Control: The Pseudo-Inverse Method Revisited, Proceedings of the 16th IFAC World Congress, Prague, 2005.
  26. Zhang, Y., J. Jiang, Bibliographical Review on Reconfigurable Fault-tolerant Control Systems, Proceeding of the SAFEPROCESS: 5th IFAC Symposium on Detection and Safety for Technical Processes, Washington, 2003.