Descriptor Approach in Design of Discrete-Time Fault Estimators

WSEAS Transactions on Systems and Control

Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 13, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 13, 2018

Descriptor Approach in Design of Discrete-Time Fault Estimators

AUTHORS: Dušan Krokavec, Anna Filasová

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ABSTRACT: Design conditions for linear discrete-time fault estimators are given in the paper, formulated by using the descriptor approach as a set of linear matrix inequalities in the bounded real lemma structures. Combining the state and the fault adapting equations, it is demonstrated that the conditions can be obtained for three basic fault estimator structures, when taking into design the constrain implying from the fault timedifference norm boundary. The result is illustrated by a numerical example.

KEYWORDS: Discrete-time linear systems, state observers, discrete-time fault estimation, linear matrix inequalities, bounded real lemma.

REFERENCES:

[1] S. Ding, Model-based Fault Diagnosis Techniques. Design Schemes, Algorithms, and Tools, Berlin, Springer, 2013.

[2] A. Filasová, D.Gontkovič and D. Krokavec, Observer-based fault estimation for linear systems with distributed time delay, Archives of Control Sciences, Vol. 23, No. 2, 2013, pp. 169-186.

[3] A. Filasová and D. Krokavec, H∞ control of discrete-time linear systems constrained in state by equality constraints, International Journal of Applied Mathematics and Computer Science, Vol. 22, No. 3, 2012, pp. 551-560, 2012.

[4] S. He, Fault estimation for T-S fuzzy Markovian jumping systems based on the adaptive observer, International Journal of Control, Automation and Systems, Vol. 12, No. 5, pp. 2014, 977-985.

[5] Q. Jia, W. Chen, Y. Zhang, and Y. Jiang, Robust fault reconstruction in discrete-time Lipschitz nonlinear systems via Eulerapproximate proportional integral observers, Mathematical Problems in Engineering, Vol. 2015, ID 741702, 2015, 14p.

[6] B. Jiang and F.N. Chowdhury, Fault estimation and accommodation for linear MIMO discretetime systems, IEEE Transactions on Control Systems Technology, Vol. 13, No. 3, 2005, pp. 493-499.

[7] A. Khedher, K. Benothman, M. Benrejeb, and D. Maquin, Adaptive observer for fault estimation in nonlinear systems described by a Takagi-Sugeno model, Proceedings of the 18th Mediterranean Conference on Control and Automation MED'10, Marrakech, Morocco, 2010, pp.261-266.

[8] D. Krokavec and A. Filasová, Design of PD observer-based fault estimator for a class of Takagi-Sugeno descriptor systems, IFACPapersOnLine, Vol. 48, No. 11, 2015, pp. 754- 759.

[9] D. Krokavec and A. Filasová, Improved LMI design conditions for discrete-time fault estimation, Procedings of the 14th European Workshop on Advanced Control and Diagnosis, ACD 2017, Bucharest, Romania, 2017, 6p.

[10] M.S. Mahmoud and Y. Xia, Analysis and Synthesis of Fault-Tolerant Control Systems, Chichester, John Wiley & Sons, 2014.

[11] R.J. Patton and S. Klinkhieo, Actuator fault estimation and compensation based on an augmented state observer approach, Proceedings of the Joint 48th IEEE Conference Decision and Control and 28th Chinese Control Conferemce, Shanghai, China, 2009, pp. 8482-8487.

[12] F. Shi and R.J. Patton, Simultaneous state and fault estimation for descriptor systems using an augmented PD observer, IFAC Proceedings Volumes, Vol. 47, No 3, 2014, pp. 8006-8011.

[13] S.M. Tabatabaeipour and T. Bak, Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems, Journal of the Franklin Institute, Vol. 35, No. 1, 2014, pp. 277-295.

[14] Z. Wang, M. Rodrigues, D. Theilliol, and Y. Shen, Fault estimation filter design for discretetime descriptor systems, IET Control Theory & Applications, Vol. 9, No. 10, 2015, pp. 1587- 1594.

[15] M. Witczak, D. Zegar, and M. Pazera, Design of an adaptive sensor and actuator fault estimation scheme with a quadratic boundedness approach, Advanced and intelligent Computations in Diagnosis and Control, Z. Kowalczuk (Ed.), Cham, Springer, 2016, pp. 49-59.

[16] A.G. Wu and G.R. Duan, Design of PD observers in descriptor linear systems, International Journal of Control, Automation and Systems, Vol. 5, No. 1, 2007, pp. 93-98.

[17] S. Xu and C. Yang, Stabilization of discretetime singular systems. A matrix inequalities approach, Automatica, Vol. 35, No. 9, 1999, pp. 1613-1617.

[18] F. Zhang, G. Liu, and L. Fang, Actuator fault estimation based on adaptive H∞ observer technique, Proceedings of the IEEE International Conference on Mechatronics and Automation, Changchun, China, 2009, pp. 352-357.

[19] K. Zhang and B. Jiang, Analysis and design of adaptive fault estimation for time-varying delay systems, Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008, pp. 38- 42.

[20] K. Zhang, B. Jiang, and V. Cocquempot, Adaptive observer-based fast fault estimation, International Journal of Control, Automation and Systems, Vol. 6, No. 3, 2008, pp. 320-326.

[21] K. Zhang, B. Jiang, and P. Shi, Observer-based Fault Estimation and Accomodation for Dynamic Systems, Berlin, Springer, 2013.

[1] S. Ding, Model-based Fault Diagnosis Techniques. Design Schemes, Algorithms, and Tools, Berlin, Springer, 2013.

[2] A. Filasová, D.Gontkovič and D. Krokavec, Observer-based fault estimation for linear systems with distributed time delay, Archives of Control Sciences, Vol. 23, No. 2, 2013, pp. 169-186.

[3] A. Filasová and D. Krokavec, H∞ control of discrete-time linear systems constrained in state by equality constraints, International Journal of Applied Mathematics and Computer Science, Vol. 22, No. 3, 2012, pp. 551-560, 2012.

[4] S. He, Fault estimation for T-S fuzzy Markovian jumping systems based on the adaptive observer, International Journal of Control, Automation and Systems, Vol. 12, No. 5, pp. 2014, 977-985.

[5] Q. Jia, W. Chen, Y. Zhang, and Y. Jiang, Robust fault reconstruction in discrete-time Lipschitz nonlinear systems via Eulerapproximate proportional integral observers, Mathematical Problems in Engineering, Vol. 2015, ID 741702, 2015, 14p.

[6] B. Jiang and F.N. Chowdhury, Fault estimation and accommodation for linear MIMO discretetime systems, IEEE Transactions on Control Systems Technology, Vol. 13, No. 3, 2005, pp. 493-499.

[7] A. Khedher, K. Benothman, M. Benrejeb, and D. Maquin, Adaptive observer for fault estimation in nonlinear systems described by a Takagi-Sugeno model, Proceedings of the 18th Mediterranean Conference on Control and Automation MED'10, Marrakech, Morocco, 2010, pp.261-266.

[8] D. Krokavec and A. Filasová, Design of PD observer-based fault estimator for a class of Takagi-Sugeno descriptor systems, IFACPapersOnLine, Vol. 48, No. 11, 2015, pp. 754- 759.

[9] D. Krokavec and A. Filasová, Improved LMI design conditions for discrete-time fault estimation, Procedings of the 14th European Workshop on Advanced Control and Diagnosis, ACD 2017, Bucharest, Romania, 2017, 6p.

[10] M.S. Mahmoud and Y. Xia, Analysis and Synthesis of Fault-Tolerant Control Systems, Chichester, John Wiley & Sons, 2014.

[11] R.J. Patton and S. Klinkhieo, Actuator fault estimation and compensation based on an augmented state observer approach, Proceedings of the Joint 48th IEEE Conference Decision and Control and 28th Chinese Control Conferemce, Shanghai, China, 2009, pp. 8482-8487.

[12] F. Shi and R.J. Patton, Simultaneous state and fault estimation for descriptor systems using an augmented PD observer, IFAC Proceedings Volumes, Vol. 47, No 3, 2014, pp. 8006-8011.

[13] S.M. Tabatabaeipour and T. Bak, Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems, Journal of the Franklin Institute, Vol. 35, No. 1, 2014, pp. 277-295.

[14] Z. Wang, M. Rodrigues, D. Theilliol, and Y. Shen, Fault estimation filter design for discretetime descriptor systems, IET Control Theory & Applications, Vol. 9, No. 10, 2015, pp. 1587- 1594.

[15] M. Witczak, D. Zegar, and M. Pazera, Design of an adaptive sensor and actuator fault estimation scheme with a quadratic boundedness approach, Advanced and intelligent Computations in Diagnosis and Control, Z. Kowalczuk (Ed.), Cham, Springer, 2016, pp. 49-59.

[16] A.G. Wu and G.R. Duan, Design of PD observers in descriptor linear systems, International Journal of Control, Automation and Systems, Vol. 5, No. 1, 2007, pp. 93-98.

[17] S. Xu and C. Yang, Stabilization of discretetime singular systems. A matrix inequalities approach, Automatica, Vol. 35, No. 9, 1999, pp. 1613-1617.

[18] F. Zhang, G. Liu, and L. Fang, Actuator fault estimation based on adaptive H∞ observer technique, Proceedings of the IEEE International Conference on Mechatronics and Automation, Changchun, China, 2009, pp. 352-357.

[19] K. Zhang and B. Jiang, Analysis and design of adaptive fault estimation for time-varying delay systems, Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008, pp. 38- 42.

[20] K. Zhang, B. Jiang, and V. Cocquempot, Adaptive observer-based fast fault estimation, International Journal of Control, Automation and Systems, Vol. 6, No. 3, 2008, pp. 320-326.

[21] K. Zhang, B. Jiang, and P. Shi, Observer-based Fault Estimation and Accomodation for Dynamic Systems, Berlin, Springer, 2013.

WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 13, 2018, Art. #53, pp. 481-490

Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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