Actuator fault diagnosis for flat systems: a constraint satisfaction approach

• Autorzy: Seydou R. , Raissi T. , Zolghadri A. , Efimov D.
• Języki publikacji: EN

Abstrakty

EN

This paper describes a robust set-membership-based Fault Detection and Isolation (FDI) technique for a particular class of nonlinear systems, the so-called flat systems. The proposed strategy consists in checking if the expected input value belongs to an estimated feasible set computed using the system model and the derivatives of the measured output vector. The output derivatives are computed using a numerical differentiator. The set-membership estimator design for the input vector takes into account the measurement noise thereby making the consistency test robust. The performances of the proposed strategy are illustrated through a three-tank system simulation affected by actuator faults.

Słowa kluczowe

EN

fault detection; input observer; flat systems; consistency techniques

PL

detekcja uszkodzeń; technika zgodności

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2013
• Tom: Vol. 23, no. 1
• Strony: 171--181
• Opis fizyczny: Bibliogr. 63 poz., rys., tab., wykr.

Twórcy

autor

Seydou R.

• Automatic Control Group, IMS-Lab, Bordeaux University, 351 cours de la libération, 33405 Talence cedex, France

autor

Raissi T.

• CEDRIC-Lab, National Conservatory of Arts and Crafts, 292, rue Saint-Martin, 75141 Paris, France

autor

Zolghadri A.

• Automatic Control Group, IMS-Lab, Bordeaux University, 351 cours de la libération, 33405 Talence cedex, France

autor

Efimov D.

• Non-A Project INRIA-LNE, Parc scientifique de la haute borne 40, Av. Halley, Bât. A, Park Plaza, 59650 Villeneuve d’Ascq, France

Bibliografia

• [1] Akhenak, A., Chadli, M., Maquin, D. and Ragot, J. (2003). Sliding mode multiple observer for fault detection and isolation, 42nd IEEE Conference on Decision and Control, Maui, HI, USA, Vol. 1, pp. 953–958.
• [2] Arangú, M. and Salido, M. (2011). A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems, International Journal of Applied Mathematics and Computer Science 21(4): 733–744, DOI: 10.2478/v10006-011-0058-2.
• [3] Berdjag, D., Christophe, C., Cocquempot, V. and Jiang, B. (2006). Nonlinear model decomposition for robust fault detection and isolation using algebraic tools, International Journal of Innovative Computing, Information & Control 2(6): 1337–1354.
• [4] Bernard, O. and Gouzé, J. (2004). Closed loop observers bundle for uncertain biotechnological models, Journal of Process Control 14(7): 765–774.
• [5] Besançon, G. and Zhang, Q. (2002). Further developments on nonlinear adaptive observers with application in fault detection, IFAC World Congress, Barcelona, Spain, Vol. 15, Part 1, pp. 19–22.
• [6] Bokor, J. and Balas, G. (2004). Detection filter design for LPV systems: A geometric approach, Automatica 40(3): 511–518.
• [7] Bokor, J. and Szab, Z. (2009). Fault detection and isolation in nonlinear systems, Annual Reviews in Control 33(2): 113–123.
• [8] Caccavale, F. and Villani, L. (2004). An adaptive observer for fault diagnosis in nonlinear discrete-time systems, American Control Conference, Boston, MA, USA, Vol. 3, pp. 2463–2468.
• [9] Chen, J. and Patton, R. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA.
• [10] Chen, W., Saif, M. and Soh, Y. (2000). A variable structure adaptive observer approach for actuator fault detection and diagnosis in uncertain nonlinear systems, American Control Conference, Chicago, IL, USA, Vol. 4, pp. 2674–2678.
• [11] Corless, M. and Tu, J. (1998). State and input estimation for a class of uncertain systems, Automatica 34(6): 757–764.
• [12] De Persis, C. and Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control 46(6): 853–865.
• [13] De Persis, C. and Isidori, A. (2002). On the design of fault detection filters with game-theoretic-optimal sensitivity, International Journal of Robust and Nonlinear Control 12(8): 729–747.
• [14] Ding, S. (2008). Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, Springer, Heidelberg/Berlin.
• [15] Ding, X. and Frank, P.M. (1993). An adaptive observer-based fault detection scheme for nonlinear dynamic systems, 12th IFAC World Congress, Sydney, Australia, Vol. 6, pp. 307–310.
• [16] Edwards, C. and Spurgeon, S.K. (2000). A sliding mode observer based FDI scheme for the ship benchmark, European Journal of Control 6(4): 341–356.
• [17] Fagarasana, I., Ploix, S. and Gentil, S. (2004). Causal fault detection and isolation based on a set-membership approach, Automatica 40(12): 2099–2110.
• [18] Fliess, M., Levine, J., Martin, P. and Rouchon, P. (1992). Sur les systmes non linaires diffrentiellement plats, Comptes rendus de l’Acadmie des sciences, Srie 1: Mathmatiques 315(5): 619–624.
• [19] Gouzé, J., Rapaport, A. and Hadj-Sadok, M. (2000). Interval observers for uncertain biological systems, Ecological Modelling 133(1–2): 46–56.
• [20] Grenaille, S., Henry, D. and Zolghadri, A. (2008). A method for designing fault diagnosis filters for LPVpolytopic systems, Journal of Control Science and Engineering (1): 1–11.
• [21] Ha, Q. and Trinh, H. (2004). State and input simultaneous estimation for a class of nonlinear systems, Automatica 40(10): 1779–1785.
• [22] Hakiki, K., Mazari, B., Liazid, A. and Djaber S. (2006). Fault reconstruction using sliding mode observers, American Journal of Applied Sciences 3(1): 1669–1674.
• [23] Hansen, R. (2004). Global Optimization Using Interval Analysis, 2nd Edn., CRC, New York, NY.
• [24] Henry, D. and Zolghadri, A. (2004). Robust fault diagnosis in uncertain linear parameter-varying systems, IEEE International Conference on Systems, Man and Cybernetics, The Hague, The Netherlands, Vol. 6, pp. 5165–5170.
• [25] Hermann, R. and Krener, A.J. (1977). Nonlinear controllability and observability, IEEE Transactions on Automatic Control 22(5): 728–740.
• [26] Hwang, I., Kim, S., Kim, Y. and Seah, C.E. (2010). A survey of fault detection, isolation, and reconfiguration methods, IEEE Transactions on Control Systems Technology 18(3): 636–653.
• [27] Ingimundarson, A., Bravo, J., Puig, V., Alamo, T. and Guerra, P. (2009). Robust fault detection using zonotope-based set-membership consistency test, International Journal of Adaptive Control and Signal Processing 23(4): 311–330.
• [28] Isermann, R. and Ball, P. (1997). Trends in the application of model-based fault detection and diagnosis of technical processes, Control Engineering Practice 5(5): 709–719.
• [29] Jaulin, L. (2013). Combining interval analysis with flatness theory for state estimation of sailboat robots, Mathematics in Computer Sciences 6(4): 347–359.
• [30] Jaulin, L., Kieffer, M., Didrit, O. and Walter, E. (2001). Applied Interval Analysis, Springer, London.
• [31] Jaulin, L. and Walter, E. (1993). Set inversion via interval analysis for nonlinear bounded-error estimation, Automatica 29(4): 1053–1064.
• [32] Jiang, B., Staroswiecki, M. and Cocquempot, V. (2004). Fault estimation in nonlinear uncertain systems using robust/sliding-mode observers, IEE Proceedings Control Theory and Applications 151(1): 29–37.
• [33] Join, C., Sira-Ramirez, H. and Fliess, M. (2005). Control of an uncertain three-tank system via on-line parameter identification and fault detection, IFAC World Congress, Prague, Czech Republic.
• [34] Kabore, R. and Wang, H. (2001). Design of fault diagnosis filters and fault-tolerant control for a class of nonlinear systems, IEEE Transactions on Automatic Control 46(11): 1805–1810.
• [35] Korbicz, J., Kościelny, J.M., Kowalczuk, Z. and Cholewa, W. (Eds.) (2004). Fault Diagnosis: Models, Artificial Intelligence, Applications, Springer-Verlag, Berlin/Heidelberg.
• [36] Krantz, S. and Parks, H. (Eds.) (2002). The Implicit Function Theorem: History, Theory, and Applications, Birkhäuser, Boston, MA.
• [37] Lalami, A. and Combastel, C. (2006). Generation of set membership tests for fault diagnosis and evaluation of their worst case sensitivity, 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Beijing, China, pp. 569–574.
• [38] Levant, A. (1998). Robust exact differentiation via sliding mode technique, Automatica 34(3): 379–384.
• [39] Levant, A. (2001). Higher order sliding modes and arbitrary order exact robust differentiation, European Control Conference, Porto, Portugal, pp. 996–1001.
• [40] Levant, A. (2003). Higher-order sliding modes, differentiation and output-feedback control, International Journal of Control 76(9): 924–941.
• [41] Liu, Y. (2009). Robust adaptive observer for nonlinear systems with unmodeled dynamics, Automatica 45(8): 1891–1895.
• [42] Moisan, M., Bernard, O. and Gouzé, J. (2009). Near optimal interval observers bundle for uncertain bioreactors, Automatica 45(1): 291–295.
• [43] Moisan, M. and Bernard, O. (2006). Robust interval observers for uncertain chaotic systems, 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 3712–3717.
• [44] Moore, R. (1966). Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ.
• [45] Neumaier, A. (2004). Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13: 271–369.
• [46] Orani, N., Pisano, A. and Usai, E. (2009). Fault detection and reconstruction for a three-tank system via high-order sliding-mode observer, IEEE Multi-conference on Systems and Control (MSC), Saint-Petersburg, Russia, pp. 1714–1719.
• [47] Poulsen, N. and Niemann, H. (2008). Active fault diagnosis based on stochastic tests, International Journal of Applied Mathematics and Computer Science 18(4): 487–496, DOI: 10.2478/v10006-008-0043-6.
• [48] Puig, V. (2010). Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies, International Journal of Applied Mathematics and Computer Science 20(4): 619–635, DOI: 10.2478/v10006-010-0046-y.
• [49] Puig, V., Quevedo, J., Escobet, T. and Stancu, R. (2003). Robust fault detection using linear interval observers, Proceedings of the 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, SAFEPROCESS 2003, Washington, DC, USA, pp. 609–614.
• [50] Ragot, J., Maquin, D. and Adrot, O. (2006). Parameter uncertainties characterisation for linear models, Computer Journal: 16–20.
• [51] Raissi, T., Videau, G. and Zolghadri, A. (2010). Interval observer design for consistency checks of nonlinear continuous-time systems, Automatica 46(3): 518–527.
• [52] Sontag, E. and Wang, Y. (1991). I/O equations for nonlinear systems and observation spaces, 30th IEEE Conference on Decision and Control, Brighton, UK, pp. 720–725.
• [53] Stancu, A., Puig, V., Cuguer, P. and Quevedo, J. (2005). Benchmarking on approaches to interval observation applied to robust fault detection, in C. Jermann, A. Neumaier and D. Sam (Eds.), Global Optimization and Constraint Satisfaction, Lecture Notes in Computer Science, Vol. 3478, Springer, Berlin/Heidelberg, pp. 336–336.
• [54] Theilliol, D., Noura, H. and Ponsart, J. (2002). Fault diagnosis and accommodation of a three-tank system based on analytical redundancy, ISA Transactions 41(3): 365–382.
• [55] Waltz, D.L. (1975). Generating semantic descriptions from drawings of scenes with shadows, in P.H. Winston (Ed.), The Psychology of Computer Vision, McGraw-Hill, New York, NY, pp. 19–91.
• [56] Wang, H. (2003). Fault diagnosis and fault tolerant control for non-Gaussian stochastic systems with random parameters, in F. Caccavale and L. Villani (Eds.), Fault Diagnosis and Fault Tolerance for Mechatronic Systems: Recent Advances, Springer Tracts in Advanced Robotics, Vol. 1, Springer, Berlin/Heidelberg, pp. 59–84.
• [57] Wang, H. and Daley, S. (1996). Actuator fault diagnosis: An adaptive observer-based technique, IEEE Transactions on Automatic Control 41(7): 1073–1078.
• [58] Wang, H., Huang, Z. and Daley, S. (1997). On the use of adaptive updating rules for actuator and sensor fault diagnosis, Automatica 33(2): 217–225.
• [59] Wang, H. and Lin, W. (2000). Applying observer based FDI techniques to detect faults in dynamic and bounded stochastic distributions, International Journal of Control 73(15): 1424–1436.
• [60] Wang, H. and Noriega, R. (2001). Fault diagnosis for unknown non-linear systems via neural networks and its comparisons and combinations with recursive least-squares based techniques, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 215(3): 261–278.
• [61] Yan, X. and Edwards, C. (2008). Adaptive sliding-mode-observer-based fault reconstruction for nonlinear systems with parametric uncertainties, IEEE Transactions on Industrial Electronics 55(11): 4029–4036.
• [62] Zhang, Q., Basseville, M. and Benveniste, A. (1998). Fault detection and isolation in nonlinear dynamic systems: A combined inputoutput and local approach, Automatica 34(11): 1359–1373.
• [63] Zolghadri, A., Henry, D. and Monsion, M. (1996). Design of nonlinear observers for fault diagnosis: A case study, Control Engineering Practice 4(11): 1535–1544.