Souad TAHRAOUI, Abdelmadjid MEGHABBAR, Djamila BOUBEKEUR

Unknown input observer based on LMI for robust generation residuals

In this paper, a method of generating robust residuals of a linear system, subject to unknown inputs, is proposed. The impact of disturbances and uncertainty may create difficulties at the decision stage of diagnosis (false alarm); this has resulted in the use of a robust observer for the unknown inputs to ensure the robustness of the system based on the unknown input observer with an optimal decoupling approach, which has a sensitivity that is minimal to unknown inputs and maximal to faults. A generation of robust residuals is then transformed into a problem of robustness/sensitivity constraints (H∞ , H ) and then solved via a linear matrix inequality formulation by the solver CVX. An application for the method performance is also given.

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[1] Wang SH, Davison EJ, Dorato P. Observing the states of systems with immeasurable disturbances. IEEE T Automat Contr 1975; 20: 716-717.
[2] Viswanadham N, Srichander R. Fault detection using unknown input observers. Contr-Theor Adv Tech 1987; 3: 91-101.
[3] Golub GH, Van Loan CF. Matrix Computations Baltimore. Baltimore, MD, USA: Johns Hopkins University Press, 1991.
[4] Rambeaux F, Hamelin F, Sauter D. Optimal thresholding for robust fault detection of uncertain systems. Int J Robust Nonlin 2000; 10: 1155-1173.
[5] Ding SX, Jeinsch T, Frank PM, Ding EL. A unified approach to the optimization of fault detection systems. Int J Adapt Control 2000; 14: 725-745.
[6] Wang D, Lum KY. Adaptive unknown input observer approach for aircraft actuator fault detection and isolation. Int J Adapt Control 2007; 21: 31-48.
[7] Ding SX, Frank PP. An approach to the detection of multiplicative faults in uncertain dynamic systems. In: 41st IEEE Decision and Control Conference; 2002; Las Vegas, NV, USA. New York, NY, USA: IEEE. pp. 4371-4376.
[8] Jiang B, Chowdhury FN. Parameter fault detection and estimation of a class of nonlinear systems using observers. J Frankl Inst 2005; 342: 725-736.
[9] Johansson A, Bask M, Norlander T. Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty. Automatica 2006; 42: 1095-1106.
[10] Meseguer J, Puig V, Escobet T, Saludes J. Observer gain effect in linear interval observer-based fault detection. J Process Contr 2010; 20: 944-956.
[11] Khan AQ, Ding SX. Threshold computation for fault detection in a class of discrete-time nonlinear systems. Int J Adapt Control 2011; 25: 407-429.
[12] Chen J, Patton RJ. Robust Model-Based Fault Diagnosis for Dynamic Systems. Boston, MA, USA: Kluwer Academic Publishers, 1999.
[13] Mangoubi RS. Robust Estimation and Failure Detection: A Concise Treatment. 1st edition. Berlin, Germany: Springer, 1998.
[14] Rank ML, Niemann H. Norm based design of fault detectors. Int J Control 1999; 72: 773-795.
[15] Henry D, Zolghadri A. Design and analysis of robust residual generators for systems under feedback control. Automatica 2005; 41: 251-264.
[16] Henry D, Zolghadri A. Design of fault diagnosis filters: a multi-objective approach. Automatica 2005; 342: 421-446.
[17] Kiyak E, Kahvecioglu A, Caliskan F. Aircraft sensor and actuator fault detection isolation and accommodation. J Aerospace Eng 2011; 24: 46-58.
[18] Kiyak E, Cetin O, Kahvecioglu A. Aircraft sensor fault detection based on unknown input observers. Aircr Eng Aerosp Tec 2008; 80: 545-548.
[19] Hajiyev C, Caliskan F. Sensor and control surface/actuator failure detection and isolation applied to F-16 flight dynamic. Aircr Eng Aerosp Tec 2005; 77: 152-160.
[20] Patton RJ, Chen J, Lopez-Toribio CJ. Fuzzy observers for nonlinear dynamic systems fault diagnosis. In: 37th IEEE Decision and Control Conference; 1998; Tampa, FL, USA. New York, NY, USA: IEEE. pp 84-89.
[21] Fonod R, Henry D, Charbonnel C, Bornschlegl E. A class of nonlinear unknown input observer for fault diagnosis: application to fault tolerant control of an autonomous spacecraft. In: IEEE 2014 UKACC International Conference on Control; 911 July 2014; Loughborough, UK. New York, NY, USA: IEEE. pp. 13-18.
[22] Bagherpour E, Hairi-Yazdi MR. Disturbance decoupled residual generation with unknown input observer for linear systems. In: 2013 Control and Fault-Tolerant Systems Conference; 911 October; Nice, France.
[23] Hamdaoui R, Guesmi S, El Harabi R. UIO based robust fault detection and estimation. In: IEEE Control, Decision and Information Technologies Conference; 68 May 2013; Hammamet, Tunisia. New York, NY, USA: IEEE. pp.76-81.
[24] Toscano R. Commande et diagnostic des syst`emes dynamiques - Mod´elisation, analyse, commande par PID et par retour d´etat, diagnostic. Paris, France: Editions Ellipses, 2011 (in French).
[25] Sylvain Grenaille M, Henry D, Zolghadri A. Fault diagnosis in satellites using H∞ estimators. In: 2004 IEEE Systems, Man and Cybernetics Conference; 1013 October 2004; The Hague, the Netherlands. New York, NY,USA: IEEE. pp. 5195-5200.
[26] Ding X, Frank PM. Comparison of observer-based fault detection approaches. In: Proceedings of the IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes; 1994; Espoo, Finland. pp. 556-561.
[27] Courtine S. D´etection et localisation de d´efauts dans les entrainements ´electriques. Grenoble, France: Linstitut national polytechnique de Grenoble, 1997 (in French).