Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

López-Estrada, Francisco-Ronay; Ponsart, Jean-Christophe; Astorga-Zaragoza, Carlos-Manuel; Camas-Anzueto, Jorge-Luis; Theilliol, Didier

doi:10.1515/amcs-2015-0018

Abstract

This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H_∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

References

Aguilera-González, A., Astorga-Zaragoza, C.M., Adam-Medina, M., Theilliol, D., Reyes-Reyes, J. and Garcia-Beltrán, C.-D. (2013). Singular linear parameter-varying observer for composition estimation in a binary distillation column, IET Control Theory & Applications 7(3): 411-422.10.1049/iet-cta.2011.0469
Search in Google Scholar
Alcorta-García, E., Saucedo-Flores, S. and Díaz-Romero, D.A. (2014). Intelligent fault diagnosis in nonlinear systems, Intelligent Automation and Soft Computing 20(2): 201-212.10.1080/10798587.2013.861963
Search in Google Scholar
Astorga-Zaragoza, C.M., Theilliol, D., Ponsart, J.C. and Rodrigues, M. (2011). Observer synthesis for a class of descriptor LPV systems, American Control Conference, ACC 2011, San Francisco, CA, USA, pp. 722-726.
Search in Google Scholar
Blesa, J., Rotondo, D., Puig, V. and Nejjari, F. (2014). FDI and FTC of wind turbines using the interval observer approach and virtual actuators/sensors, Control Engineering Practice 24: 138-155.10.1016/j.conengprac.2013.11.018
Search in Google Scholar
Chadli, M., Abdo, A. and Ding, S.X. (2013a). H−/H∞ fault detection filter design for discrete-time Takagi-Sugeno fuzzy system, Automatica 49(7): 1996-2005.10.1016/j.automatica.2013.03.014
Search in Google Scholar
Chadli, M., Aouaouda, S., Karimi, H. and Shi, P. (2013b). Robust fault tolerant tracking controller design for a VTOL aircraft, Journal of the Franklin Institute 350(350): 2627-2645.10.1016/j.jfranklin.2012.09.010
Search in Google Scholar
Chadli, M. and Darouach, M. (2011). Robust admissibility of uncertain switched singular systems, International Journal of Control 84(10): 1587-1600.10.1080/00207179.2011.615865
Search in Google Scholar
Chen, J. and Patton, R.J. (1999). Robust Model-based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers, Norwell, MA.10.1007/978-1-4615-5149-2
Search in Google Scholar
Ding, S.X. (2008). Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms and Tools, Springer, Berlin/Heidelberg.
Search in Google Scholar
Duan, G.R. (2010). Analysis and Design of Descriptor Linear Systems, Springer, New York, NY.10.1007/978-1-4419-6397-0
Search in Google Scholar
Frank, P. (1996). Analytical and qualitative model-based fault diagnosis-a survey and some new results, European Journal of Control 2(1): 6-28.10.1016/S0947-3580(96)70024-9
Search in Google Scholar
Gertler, J. (1997). Fault detection and isolation using parity relations, Control Engineering Practice 5(5): 653-661.10.1016/S0967-0661(97)00047-6
Search in Google Scholar
Hamdi, H., Rodrigues, M., Mechmeche, C. and Braiek, N.B. (2012a). Robust fault detection and estimation for descriptor systems based on multi-models concept, International Journal of Control, Automation and Systems 10(6): 1260-1266.10.1007/s12555-012-0622-z
Search in Google Scholar
Hamdi, H., Rodrigues, M., Mechmeche, C. and Theilliol, D. (2012b). Fault detection and isolation for linear parameter varying descriptor systems via proportional integral observer, International Journal of Adaptive Control and Signal Processing 26(3): 224-240.10.1002/acs.1260
Search in Google Scholar
Hwang, I., Sungwan, K., Youdan, K. and Seah, C. (2010). A survey of fault detection, isolation, and reconfiguration methods, IEEE Transactions on Control Systems Technology 18(3): 636-653.10.1109/TCST.2009.2026285
Search in Google Scholar
Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2010). State estimation of Takagi-Sugeno systems with unmeasurable premise variables, IET Control Theory & Applications 4(5): 897.10.1049/iet-cta.2009.0054
Search in Google Scholar
Isermann, R. (1984). Process fault detection based on modeling and estimation methods-a survey, Automatica 20(4): 387-404.10.1016/0005-1098(84)90098-0
Search in Google Scholar
Kamidi, R. (2000). Controllability and observability of polytopic linear models, Technical report, Eindhoven University of Technology, Eindhoven.
Search in Google Scholar
Lendek, Z., Guerra, T.M., Babuˆska, R. and De Schutter, B. (2011). Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models, Studies in Fuzziness and Soft Computing, Vol. 262, Springer, Berlin/Heidelberg.
Search in Google Scholar
Lofberg, J. (2004). A toolbox for modeling and optimization in MATLAB, Proceedings of the Computer Aided Control System Design Conference, Taipei, Taiwan, pp. 284-289.
Search in Google Scholar
López-Estrada, F.-R., Ponsart, J., Theilliol, D. and Astorga-Zaragoza, C.-M. (2013). Fault estimation observer design for descriptor-LPV systems with unmeasurable gain scheduling functions, 2nd International Conference on Control and Fault-Tolerant Systems (SYSTOL), Nice, France, pp. 269-274.
Search in Google Scholar
López-Estrada, F.R., Ponsart, J.C., Theilliol, D., Astorga-Zaragoza, C.-M. and Aberkane, S. (2014a). Fault diagnosis based on robust observer for descriptor-LPV systems with unmeasurable scheduling parameters, 19th World Congress of the International Federation of Automatic Control, Cape Town, South Africa, pp. 1079-1084.10.3182/20140824-6-ZA-1003.00960
Search in Google Scholar
López-Estrada, F.-R., Ponsart, J., Theilliol, D. and Astorga-Zaragoza, C.-M. (2014b). Robust sensor FDI observer for polytopic descriptor-LPV systems with unmeasurable scheduling varying parameter, American Control Conference, Portland, OR, USA.10.1109/ACC.2014.6859513
Search in Google Scholar
Lunze, J., Blanke, M., Staroswiecki, M. and Kinnaert, M. (2006). Diagnosis and Fault-Tolerant Tolerant Control, Springer, Berlin/Heidelberg.
Search in Google Scholar
Martínez-Sibaja, A., Astorga-Zaragoza, C.M., Alvarado-Lassman, A., Posada-Gómez, R., Aguila-Rodríguez, G., Rodríguez-Jarquin, J. and Adam-Medina, M. (2011). Simplified interval observer scheme: A new approach for fault diagnosis in instruments, Sensors 11(1): 612-622.10.3390/s110100612327410722346593
Search in Google Scholar
Masubuchi, I., Kato, J., Saeki, M. and Ohara, A. (2004). Gain-scheduled controller design based on descriptor representation of LPV systems: Application to flight vehicle control, 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, The Bahamas, Vol. 1, pp. 815-820.
Search in Google Scholar
Montes de Oca, S., Puig, V. and Blesa, J. (2011). Robust fault detection based on adaptive threshold generation using interval LPV observers, International Journal of Adaptive Control and Signal Processing 26(3): 258-283.10.1002/acs.1263
Search in Google Scholar
Nagy-Kiss, A.M., Marx, B., Mourot, G., Schutz, G. and Ragot, J. (2011a). Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. application to a wastewater treatment plant, Journal of Process Control 21(7): 1105-1114.10.1016/j.jprocont.2011.05.001
Search in Google Scholar
Nagy Kiss, A.M., Marx, B., Mourot, G., Schutz, G. and Ragot, J. (2011b). State estimation of two-time scale multiple models. Application to wastewater treatment plant, Control Engineering Practice 19(11): 1354-1362.10.1016/j.conengprac.2011.07.009
Search in Google Scholar
Samy, I., Postlethwaite, I. and Gu, D.-W. (2011). Survey and application of sensor fault detection and isolation schemes, Control Engineering Practice 19(7): 658-674.10.1016/j.conengprac.2011.03.002
Search in Google Scholar
Theilliol, D. and Aberkane, S. (2011). Design of LPV observers with unmeasurable gain scheduling variable under sensors faults, IFAC World Congress, Milan, Italy, pp. 7613-7618.
Search in Google Scholar
Wang, J.L., Yang, G.-H. and Liu, J. (2007). An LMI approach to index and mixed fault detection observer design, Automatica 43(9): 1656-1665.
Search in Google Scholar
Xu, S. and Lam, J. (2006). Robust Control and Filtering of Singular Systems, Springer, Berlin/Heidelberg.
Search in Google Scholar
Yoneyama, J. (2009). H∞ filtering for fuzzy systems with immeasurable premise variables: An uncertain system approach, Fuzzy Sets and Systems 160(12): 1738-1748. 10.1016/j.fss.2008.09.012
Search in Google Scholar

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

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