H_/H fault detection observer design for a polytopic LPV system using the relative degree

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Abstract

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.

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

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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).

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.

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.

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.

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.

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.

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

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.

Varga, A. (2008). On parametric solution of fault detectionproblems, Proceedings of the 18th IFAC World Congress, Milan, Italy, pp. 6697-6702.

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

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.

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.

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.

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.

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.

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.

International Journal of Applied Mathematics and Computer Science

Journal of the University of Zielona Góra

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IMPACT FACTOR 2017: 1.694
5-year IMPACT FACTOR: 1.712

CiteScore 2017: 2.20

SCImago Journal Rank (SJR) 2017: 0.729
Source Normalized Impact per Paper (SNIP) 2017: 1.604

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