Geodesic
H−/H∞ fault detection observer design for a polytopic LPV system using the relative degree
International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 1, pp. 83-95.

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This paper proposes an H−/H∞ fault detection observer method by using generalized output for a class of polytopic linear parameter-varying (LPV) systems. As the main contribution, with the aid of the relative degree of output, a new output vector is generated by gathering the original output and its time derivative, and it is feasible to consider H− actuator fault sensitivity in the entire frequency for the new system. In order to improve actuator and sensor fault sensitivity as well as guarantee robustness against disturbances, simultaneously, an H−/H∞ fault detection observer is designed for the new LPV polytopic system. Besides, the design conditions of the proposed observer are transformed into an optimization problem by solving a set of linear matrix inequalities (LMIs). Numerical simulations are provided to illustrate the effectiveness of the proposed method.
Keywords: fault detection observer, polytopic LPV system, relative degree of output, actuator fault detection, sensor fault detection
Mots-clés : detekcja uszkodzeń, urządzenie wykonawcze, czujnik detekcji 
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Zhou, M.; Rodrigues, M.; Shen, Y.; Theilliol, D. H−/H∞ fault detection observer design for a polytopic LPV system using the relative degree. International Journal of Applied Mathematics and Computer Science, Tome 28 (2018) no. 1, pp. 83-95. http://geodesic.mathdoc.fr/item/IJAMCS_2018_28_1_a5/

[1] Apkarian, P. and Tuan, A.H.D. (2000). Parameterized LMIs in control theory, SIAM Journal on Control and Optimization 38(4): 1241–1264.

[2] Armeni, S., Casavola, A. and Mosca, E. (2009). Robust fault detection and isolation for LPV systems under a sensitivity constraint, International Journal of Adaptive Control and Signal Processing 23(1): 55–72.

[3] Balas, G., Bokor, J. and Szabo, Z. (2002). Failure detection for LPV system—a geometric approach, Proceedings of the American Control Conference, Anchorage, AK, USA, pp. 4421–4426.

[4] Bara, G., Daafouz, J., Kratz, F. and Ragot, J. (2001). Parameter dependent state observer design for affine LPV systems, International Journal of Control 74(17): 1601–1611.

[5] Bokor, J. (2007). Geometric theory and control of linear parameter varying systems, Proceedings of the 4th International Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, pp. 163–170.

[6] Bokor, J. and Balas, G. (2004). Detection filter design for LPV systems—A geometric approach, Automatica 40(3): 511–518.

[7] Cai, X.J. and Wu, F. (2010). Robust fault detection and isolation for parameter-dependent LFT systems, International Journal of Robust and Nonlinear Control 20(7): 764–776.

[8] Casavola, A., Famularo, D., Franze, G. and Sorbara, M. (2007). A fault-detection filter design method for linear-parameter varying systems, IMecheE I: Journal of Systems and Control Engineering 221(6): 865–873.

[9] Chadli, M., Abdo, A. and Ding, S.X. (2013). H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system, Automatica 49(7): 1996–2005.

[10] Chen, J.L., Cao, Y.Y. and Zhang, W.D. (2015). A fault detection observer design for LPV systems in finite frequency domain, International Journal of Control 88(3): 571–584.

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

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

[13] Estrada, F.R.L., Ponsart, J.C., Theilliol, D. and Astorga-Zaragoza, C.M. (2015). Robust H−/H∞ fault detection observer design for descriptor-LPV systems with unmeasurable gain scheduling functions, International Journal of Control 88(11): 2380–2391.

[14] Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge based redundancy: A survey and some new results, Automatica 26(3): 459–474.

[15] Gahinet, P., Apkarian, P. and Chilaly, M. (1996). Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control 41(3): 436–442.

[16] Garcia, G. and Bernussou, J. (1995). Pole assignment for uncertain systems in a specified disk by state feedback, IEEE Transactions on Automatic Control 40(1): 184–190.

[17] Grenaille, S., Henry, D. and Zolghadri, A. (2008). A method for designing fault diagnosis filters for LPV polytopic systems, Journal of Control Science and Engineering 2008: 1–11.

[18] Henry, D. (2008). Fault diagnosis of the microscope satellite actuators using H∞/H− filters, AIAA Journal of Guidance, Control and Dynamics 31(3): 699–711.

[19] Henry, D. (2012). Structured fault detection filters for LPV systems modelled in an LFR manner, International Journal of Adaptive Control and Signal Processing 26(3): 190–207.

[20] Henry, D., Cieslak, J. and Efimov, D. (2015a). H∞/H−LPV solutions for fault detection of aircraft actuator faults: Bridging the gap between theory and practice, International Journal of Robust and Nonlinear Control 25(5): 649–672.

[21] Henry, D., Cieslak, J., Zolghadri, A. and Efimov, D. (2014). A non-conservative H−/H∞ solution for early and robust fault diagnosis in aircraft control surface servo-loops, Control Engineering Practice 31: 183–199.

[22] Henry, D., LePeuvedic, C., Strippoli, L. and Ankersen, F. (2015b). Robust model-based fault diagnosis of truster faults in spacecraft, International Symposium on Fault Detection, Supervision and Safety for Technical Processes, Paris, France, pp. 1078–1083.

[23] Hou, M. and Patton, R.J. (1996). An LMI approach to H−/H∞ fault detection observers, Proceedings of the UKACC International Conference on Control, Exeter, UK, pp. 305–310.

[24] Huang, D., Duan, Z.S. and Hao, Y.Q. (2017). An iterative approach to H−/H∞ fault detection observer design for discrete-time uncertain systems, Asian Journal of Control 19(1): 1–14.

[25] Ichalal, D., Marx, B., Maquin, D. and Ragot, J. (2016). Actuator fault diagnosis: H∞ framework with relative degree notion, International Conference on Intelligent Control and Automation Science, Reims, France, pp. 327–332.

[26] Isidori, A. (1995). Nonlinear Control Systems, Communications and Control Engineering, Springer, London.

[27] Iwasaki, T., Hara, S. and Fradkov, A.L. (2005). Time domain interpretations of frequency domain inequalities on (semi) finite ranges, Systems Control Letters 54(7): 681–691.

[28] Jia, Q., Chen, W., Zhang, Y. and Chen, X. (2015). Fault reconstruction and accommodation in linear parameter-varying systems via learning unknown-input observers, Journal of Dynamic Systems, Measurement and Control 137(6): 061008(1)–061008(9).

[29] Li, X.J. and Yang, G.H. (2014). Fault detection in finite frequency domain for Takagi–Sugeno fuzzy systems with sensor faults, IEEE Transactions on Cybernetics 44(8): 1446–1458.

[30] Liu, J., Wang, J.L. and Yang, G.H. (2005). An LMI approach to minimum sensitivity analysis with application to fault detection, Automatica 41(11): 1995–2004.

[31] Millerioux, G., Rosier, L., Bloch, G. and Daafouz, J. (2004). Bounded state reconstruction error for LPV systems with estimated parameters, IEEE Transactions on Automatic Control 49(8): 1385–1389.

[32] Rodrigues, M., Habib, H., Theilliol, D., Mechmeche, C. and Braiek, N.B. (2015). Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems, International Journal of Robust and Nonlinear Control 25(5): 673–688.

[33] Rodrigues, M., Hamdi, H., Braiek, N.B. and Theilliol, D. (2014). Observer-based fault tolerant control design for a class of LPV descriptor systems, Journal of the Franklin Institute 351(6): 3104–3125.

[34] Tanaka, K. and Wang, H.O. (2001). Fuzzy Control Systems Design and Analysis, John Wiley Son, New York, NY.

[35] Vanek, B., Edelmayer, A., Szabo, Z. and Bokor, J. (2014). Bridging the gap between theory and practice in LPV fault detection for flight control actuators, Control Engineering Practice 31: 171–182.

[36] Varga, A. (2008). On parametric solution of fault detection problems, Proceedings of the 18th IFAC World Congress, Milan, Italy, pp. 6697–6702.

[37] Varga, A. and Ossmann, D. (2014). LPV model-based robust diagnosis of flight actuator faults, Control Engineering Practice 31: 135–147.

[38] Wang, H. and Yang, G.H. (2008). A finite frequency domain approach to fault detection observer design for linear continuous-time systems, Asian Journal of Control 10(5): 559–568.

[39] Wang, Z.H., Rodrigues, M., Theilliol, D. and Shen, Y. (2015a). Actuator fault estimation observer design for discrete-time linear parameter-varying descriptor systems, International Journal of Adaptive Control and Signal Processing 29(1): 242–258.

[40] Wang, Z.H., Rodrigues, M., Theilliol, D. and Shen, Y. (2015b). Fault estimation filter design for discrete-time descriptor systems, IET Control Theory Applications 9(10): 1587–1594.

[41] Wei, X. and Verhaegen, M. (2008). Mixed H−/H∞ fault detection observer design for LPV systems, Proceedings of the 47th Conference on Decision and Control, Cancun, Mexico, pp. 1073–1078.

[42] Wei, X. and Verhaegen, M. (2011). LMI solutions to the mixed H−/H∞ fault detection observer design for linear parameter-varying systems, International Journal of Adaptive Control and Signal Processing 25(2): 114–136.

[43] Yin, S., Gao, H.J., Qiu, J.B. and Kaynak, O. (2017). Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults, Automatica 76: 282–292.