Active fault tolerant control of nonlinear systems: the cart-pole example

Bonfe, M. ; Castaldi, P. ; Mimmo, N. ; Simani, S.

International Journal of Applied Mathematics and Computer Science, Tome 21 (2011) no. 3, pp. 441-455.

Résumé

This paper describes the design of fault diagnosis and active fault tolerant control schemes that can be developed for nonlinear systems. The methodology is based on a fault detection and diagnosis procedure relying on adaptive filters designed via the nonlinear geometric approach, which allows obtaining the disturbance de-coupling property. The controller reconfiguration exploits directly the on-line estimate of the fault signal. The classical model of an inverted pendulum on a cart is considered as an application example, in order to highlight the complete design procedure, including the mathematical aspects of the nonlinear disturbance de-coupling method based on the nonlinear differential geometry, as well as the feasibility and efficiency of the proposed approach. Extensive simulations of the benchmark process and Monte Carlo analysis are practical tools for assessing experimentally the robustness and stability properties of the developed fault tolerant control scheme, in the presence of modelling and measurement errors. The fault tolerant control method is also compared with a different approach relying on sliding mode control, in order to evaluate benefits and drawbacks of both techniques. This comparison highlights that the proposed design methodology can constitute a reliable and robust approach for application to real nonlinear processes.

Détail

Keywords: fault detection, fault isolation, nonlinear filter, nonlinear geometric approach, fault tolerant control, cart pole nonlinear model
Mots-clés : detekcja uszkodzeń, lokalizacja uszkodzeń, filtracja nieliniowa, sterowanie tolerujące uszkodzenia

Bibliographie

[1] Baldi, P., Castaldi, P. and Simani, S. (2010). Fault diagnosis and control reconfiguration in Earth satellite model engines, Proceedings of the 9th UKACC International Conference on Control (CONTROL 2010), Coventry, UK, pp. 1-6.

[2] Benini, B., Castaldi, P. and Simani, S. (2009). Fault Diagnosis for Aircraft System Models: An Introduction from Fault Detection to Fault Tolerance, 1st Edn., VDM Verlag Dr. Muller, Saarbrucken.

[3] Bertoni, G., Bertozzi, N., Castaldi, P. and Simani, S. (2010a). A nonlinear guidance and active fault tolerant control system for a fixed wing unmanned aerial vehicle, Proceedings of the 2010 American Control Conference-ACC2010, Baltimore, MD, USA, pp. 1-6.

[4] Bertoni, G., Castaldi, P., Mimmo, N. and Simani, S. (2010b). Active fault tolerant control system for a high accuracy planet-image satellite, Proceedings of the 18th IFAC Symposium on Automatic Control in Aerospace-ACA2010, Nara, Japan, pp. 1-6.

[5] Blanke, M., Kinnaert, M., Lunze, J. and Staroswiecki, M. (2006). Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin.

[6] Bonfè, M., Castaldi, P., Geri, W. and Simani, S. (2007). Nonlinear actuator fault detection and isolation for a general aviation aircraft, Space Technology-Space Engineering, Telecommunication, Systems Engineering and Control 27(2-3): 107-113.

[7] Castaldi, P., Geri, W., Bonfè, M., Simani, S. and Benini, M. (2010). Design of residual generators and adaptive filters for the FDI of aircraft model sensors, Control Engineering Practice 18(5): 449-495, DOI:10.1016/j.conengprac.2008.11.006.

[8] Chen, J. and Patton, R. J. (1999). Robust Model-Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA.

[9] De Persis, C. and Isidori, A. (2001). A geometric approach to non-linear fault detection and isolation, IEEE Transactions on Automatic Control 45(6): 853-865.

[10] Ding, S. X. (2008). Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, 1st Edn., Springer, Berlin/Heidelberg.

[11] Edwards, C. (2004). A practical method for the design of sliding mode controllers using linear matrix inequalities, Automatica 40(10): 1761-1769.

[12] Edwards, C., Lombaerts, T. and Smaili, H. (Eds.) (2010). Fault Tolerant Flight Control: A Benchmark Challenge, 1st Edn., Lecture Notes in Control and Information Sciences, Vol. 399, Springer, Heidelberg/Berlin.

[13] Edwards, C. and Spurgeon, S. (1998). Sliding Mode Control: Theory and Applications, 1st Edn., Taylor Francis, London.

[14] Ioannou, P. and Sun, J. (1996). Robust Adaptive Control, PTR Prentice-Hall, Upper Saddle River, NJ.

[15] Isermann, R. (2005). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, 1st Edn., Springer-Verlag, Heidelberg/Berlin,.

[16] Kaboré, P., Othman, S.,McKenna, T. and Hammouri, H. (2000). An observer-based fault diagnosis for a class of nonlinear systems-Application to a free radical copolymerization reaction, International Journal of Control 73(9): 787-803.

[17] Kaboré, P. 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.

[18] Korbicz, J., Koscielny, J. M., Kowalczuk, Z. and Cholewa, W. (Eds.) (2004). Fault Diagnosis: Models, Artificial Intelligence, Applications, 1st Edn., Springer-Verlag, Heidelberg/Berlin.

[19] Li, H., Zhao, Q. and Yang, Z. (2007). Reliability modeling of fault tolerant control systems, International Journal of Applied Mathematics and Computer Science 17(4): 491-504, DOI: 10.2478/v10006-007-0041-0.

[20] Mahmoud, M., Jiang, J. and Zhang, Y. (2003). Active Fault Tolerant Control Systems, Springer-Verlag, Heidelberg/Berlin.

[21] Marcos, A., Ganguli, S. and Balas, G. J. (2005). An application of H infinity fault detection and isolation to a transport aircraft, Control Engineering Practice 13(1): 105-119.

[22] Noura, H., Theilliol, D., Ponsart, J.-C. and Chamseddine, A. (2009). Fault-tolerant Control Systems: Design and Practical Applications, 1st Edn. Advances in Industrial Control, Vol. 1, Springer, London.

[23] Rodrigues, M., Theilliol, D., Aberkane, S. and Sauter, D. (2007). Fault tolerant control design for polytopic LPV systems, International Journal of Applied Mathematics and Computer Science 17(1): 27-37, DOI: 10.2478/v10006-007-0004-5.

[24] Simani, S., Fantuzzi, C. and Patton, R. J. (2003). Model-Based Fault Diagnosis in Dynamic Systems Using Identification Techniques, Advances in Industrial Control, Vol. 1, Springer-Verlag, London.

[25] Slotine, J.-J. and Sastry, S. (1983). Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators, International Journal of Control 38(2): 465-492.

[26] Su, C.-Y. and Stepanenko, Y. (1994). Adaptive sliding mode control of robot manipulators: General sliding manifold case, Automatica 30(9): 1497-1500.

[27] Theilliol, D., Join, C. and Zhang, Y. (2008). Actuator fault tolerant control design based on a reconfigurable reference input, International Journal of Applied Mathematics and Computer Science 18(4): 553-560, DOI: 10.2478/v10006-008-0048-1.

[28] Utkin, V. (1977). Variable structure systems with sliding mode, IEEE Transactions on Automatic Control AC-22(2): 212-222.

[29] Utkin, V. (1992). Sliding Modes in Control Optimization, Springer-Verlag, Heidelberg/Berlin.

[30] Utkin, V. I., Guldner, J. and Shi, J. (1999). Sliding Mode Control in Electromechanical Systems, 1st Edn., Series in Systems Control Engineering, Taylor Francis, London.

[31] Witczak, M. (2007). Modelling and Estimation Strategies for Fault Diagnosis of Non-Linear Systems: From Analytical to Soft Computing Approaches, 1st Edn., Lecture Notes in Control Information Sciences, Vol. 354, Springer-Verlag, Berlin/Heidelberg.

[32] Zhang, Y. and Jiang, J. (2008). Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control 32(2): 229-252.