Switched <img width="58" height="55" src="http://article.sciencepublishinggroup.com/journal/248/2481135/image001.png" /> Detection Filter Design for Nonlinear Systems

Zsolt Horváth; András Edelmayer

doi:doi:10.11648/j.ajmie.20190401.11

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Switched Detection Filter Design for Nonlinear Systems

Zsolt Horváth, András Edelmayer

Published in American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 1)

Received: 26 February 2019 Accepted: 3 April 2019 Published: 7 May 2019

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Abstract

This paper presents the application of the concept of detection filters to the detection of faults in nonlinear systems. The nonlinear dynamics in specific meaningful points of the operation is approximated by means of a matched array of linear systems. Then, linear filters are designed for each particular subsystem and a switching scheme is applied to carefully choose the most suitable filter regarding the operational characteristics of the plant in real time. Stability of the switching process is guaranteed by keeping the switching time between two consecutive switching large enough to ensure a proper falloff of filter transients. Therefore, apart from the solution of the standard linear-quadratic optimization problem represented by the detection filter design problem one has to derive sufficient conditions for the observation error dynamics to be globally asymptotically stable during switching. The goal is to find a common minimum of the switching time to each specific level calculated separately for every single filter that can be used as a restriction for the switching signal. The idea is demonstrated with the application to the detection of faults in the air path of a diesel engine. The results can be considered as the extension of the standard linear fault detection filtering problem to nonlinear systems.

Published in	American Journal of Mechanical and Industrial Engineering (Volume 4, Issue 1)
DOI	10.11648/j.ajmie.20190401.11
Page(s)	1-10
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Switched Linear System, Dwell Time, Switched Fault Detection Filter, MFARE

References

[1]	Boulkroune Boulaid, Djemili Issam, Aitouche Abdel, and Cocquempot Vincent. Robust nonlinear observer design for actuator fault detection in diesel engines. International Journal of Applied Mathematics and Computer Science. Vol. 23, No. 3, 2013, pp. 557–569.
[2]	Sangha, M. S, Yu, D. L., and Gomm, J. B. Sensor fault detection, isolation, accommodation and unknown fault detection in automotive engine using AI. International Journal of Engineering, Science and Technology. Vol.4, No.3, 2012, pp. 53-65.
[3]	Guermouche Mohamed, Benkaci Mourad, Hoblos Ghaleb and Langlois Nicolas. Sensor fault detection and isolation in diesel air path using fuzzy-ARTMAP neural network. IEEE 10th International Conference on Networking, Sensing and Control (ICNSC). Evry, France, 2013, pp.728-733.
[4]	Krishnaswami Venkat, Chun-L G., and Rizzoni Giorgio. Fault Detection in IC Engines using Nonlinear Parity Equations. Proceedings of the American Control Conference. Baltimore, Maryland, 1994, pp. 2001-2005.
[5]	Vanek Bálint, Szabó Zoltán, Edelmayer András, Bokor József. Geometric LPV fault detection filter design for commercial aircrafts. AIAA Guidance, Navigation and Control Conference. Portland, OR, United States, 2011.
[6]	Edelmayer András, Bokor József, Szabó Zoltán. A geometric view on inversion-based detection filter design in nonlinear systems. In Proceedings of the fifth IFAC symposium on fault detection, supervision and safety of technical processes. SAFEPROCESS, Washington, 2003, pp. 783-788.
[7]	Paxman Jonathan. Switching Controllers: Realization, Initialization and Stability. Ph.D Dissertation. University of Cambridge, 2003.
[8]	DeCarlo Raymond A., Branicky Michael, Pettersson Stefan and Lennartson Bengt. Perspectives and Results On the Stability and Stabilizability of Hybrid Systems. Proc. IEEE. Vol. 88, 2000, pp. 1069-1082.
[9]	Liberzon Daniel, A. Stephen Morse. Basic Problems in Stability and Design of Switched Systems. IEEE Contr. Syst. 1999, pp. 59-70.
[10]	João Pedro Hespanha, A. Stephen Morse. Stability of switched systems with average dwell-time. Proc. 38th Conf. Decision and Contr. 1999, pp. 2655-2660.
[11]	Alessandri Angelo, Coletta Paolo. Switching observers for continuous-time and discrete-time linear systems. In Proceedings of the American Control Conference Arlington. 2001.
[12]	Johansson Mikael. Piecewise Linear Control Systems: A computational Approach. Springer Verlag. Heidelberg, 2003.
[13]	Colaneri Patrizio. Analysis and control of linear switched system. Lecture notes. Politecnico Di Milano, 2009.
[14]	Horváth Zsolt, Edelmayer András. Robust Model-Based Detection of Faults in the Air Path of Diesel Engines. Acta Universitatis Sapientiae Electrical and Mechanical Engineering. Vol.7, 2015, pp. 5-22.
[15]	Edelmayer András, Bokor József, Keviczky László. An H∞ Filtering Approach to Robust Detection of Failures in Dynamical Systems. In Proc. 33th Annual Decision and Control, Conf. Buena Vista, USA, 1994, pp. 3037-3039.
[16]	Edelmayer András, Bokor József, Keviczky László. An H∞ Filter Design for Linear Systems: Comparison of two Approaches. IFAC 13th Triennial World Congress. San Francisco, USA, 1996.
[17]	Edelmayer András. Fault detection in dynamic systems: From state estimation to direct input reconstruction. Universitas-Győr Nonprofit Kft. Győr, 2012.
[18]	Horváth Zsolt, Edelmayer András. Solving of the Modified Filter Algebraic Riccati Equation for H-infinity fault detection filtering. Acta Universitatis Sapientiae Electrical and Mechanical Engineering. Vol. 9, 2017, pp. 57-77.
[19]	Geromel Jose C., Colaneri Patrizio. H∞ and Dwell Time Specifications of Switched Linear Systems. Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, 2008.
[20]	See supplementary material at http://home.deib.polimi.it/prandini/file/2015_06_16%20hybrid%20systems_2.pdf.
[21]	Chen Weitian, Saif Mehrdad. Observer design for linear switched control systems. American Control Conference Proceedings of the 2004. 0-7803-8335-4, Boston, 2004.
[22]	Horváth Zsolt, Csomós Petra. A Switched Linear System Approach to the Modeling of the Air Path of Diesel Engines. Proc. of the 14th ICCMSE International Conference of Computational Methods in Sciences and Engineering. Thessaloniki, 2018.
[23]	See supplementary material at https://de.mathworks.com/help/robust/ref/mincx.html.
[24]	Gahinet Pascal, Nemirovski Arkadi, Laub Alan J. and Chilali Mahmoud. LMI Control Toolbox for Use with Matlab. The MathWorks Inc. Natick, 1995.
[25]	Boyd Stephen, Laurent El Ghaoui, Feron Erik and Balakrishnan Venkataramanan. Linear Matrix Inequalities in System and Control Theory. SIAM. Philadelphia, 1994.
[26]	See supplementary material at https://de.mathworks.com/help/robust/ref/feasp.html.
[27]	Guang-Ren Duan, Hai-Hua Yu. LMIs in Control Systems: Analysis, Design and Applications. CRC Press. Boca Raton, 2013.
[28]	Horváth Zsolt, Edelmayer András. An algorithm for the calculation of the dwell time constraint for switched H-infinity filters. Acta Universitatis Sapientiae, Electrical and Mechanical Engineering. Vol. 10, 2018, pp. 57-77.
[29]	Horváth Zsolt, Edelmayer András. Determining the common minimum dwell time for switched H∞ fault detection filtering. Przeglad Elektrotechniczny. 2018.
[30]	Jankovic Mrdjan, Kolmanovsky Ilya. Robust Nonlinear Controller for Turbocharged Diesel Engines. Proceedings of the American Control Conference. Philadelphia, PA, 1998.
[31]	Horváth Zsolt, Edelmayer András. LTI-modelling of the Air Path of Turbocharged Diesel Engine for Fault Detection and Isolation. Invited paper in: Mechanical Engineering Letters. Vol. 14, ISSN 2060-3789, Gödöllő, 2016, pp. 172-188.

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APA Style

Zsolt Horváth, András Edelmayer. (2019). Switched Detection Filter Design for Nonlinear Systems. American Journal of Mechanical and Industrial Engineering, 4(1), 1-10. https://doi.org/10.11648/j.ajmie.20190401.11

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ACS Style

Zsolt Horváth; András Edelmayer. Switched Detection Filter Design for Nonlinear Systems. Am. J. Mech. Ind. Eng. 2019, 4(1), 1-10. doi: 10.11648/j.ajmie.20190401.11

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AMA Style

Zsolt Horváth, András Edelmayer. Switched Detection Filter Design for Nonlinear Systems. Am J Mech Ind Eng. 2019;4(1):1-10. doi: 10.11648/j.ajmie.20190401.11

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@article{10.11648/j.ajmie.20190401.11,
  author = {Zsolt Horváth and András Edelmayer},
  title = {Switched  Detection Filter Design for Nonlinear Systems},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajmie.20190401.11},
  url = {https://doi.org/10.11648/j.ajmie.20190401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190401.11},
  abstract = {This paper presents the application of the concept of  detection filters to the detection of faults in nonlinear systems. The nonlinear dynamics in specific meaningful points of the operation is approximated by means of a matched array of linear systems. Then, linear  filters are designed for each particular subsystem and a switching scheme is applied to carefully choose the most suitable filter regarding the operational characteristics of the plant in real time. Stability of the switching process is guaranteed by keeping the switching time between two consecutive switching large enough to ensure a proper falloff of filter transients. Therefore, apart from the solution of the standard linear-quadratic optimization problem represented by the  detection filter design problem one has to derive sufficient conditions for the observation error dynamics to be globally asymptotically stable during switching. The goal is to find a common minimum of the switching time to each specific  level calculated separately for every single filter that can be used as a restriction for the switching signal. The idea is demonstrated with the application to the detection of faults in the air path of a diesel engine. The results can be considered as the extension of the standard linear  fault detection filtering problem to nonlinear systems.},
 year = {2019}
}

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TY  - JOUR
T1  - Switched  Detection Filter Design for Nonlinear Systems
AU  - Zsolt Horváth
AU  - András Edelmayer
Y1  - 2019/05/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmie.20190401.11
DO  - 10.11648/j.ajmie.20190401.11
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20190401.11
AB  - This paper presents the application of the concept of  detection filters to the detection of faults in nonlinear systems. The nonlinear dynamics in specific meaningful points of the operation is approximated by means of a matched array of linear systems. Then, linear  filters are designed for each particular subsystem and a switching scheme is applied to carefully choose the most suitable filter regarding the operational characteristics of the plant in real time. Stability of the switching process is guaranteed by keeping the switching time between two consecutive switching large enough to ensure a proper falloff of filter transients. Therefore, apart from the solution of the standard linear-quadratic optimization problem represented by the  detection filter design problem one has to derive sufficient conditions for the observation error dynamics to be globally asymptotically stable during switching. The goal is to find a common minimum of the switching time to each specific  level calculated separately for every single filter that can be used as a restriction for the switching signal. The idea is demonstrated with the application to the detection of faults in the air path of a diesel engine. The results can be considered as the extension of the standard linear  fault detection filtering problem to nonlinear systems.
VL  - 4
IS  - 1
ER  -

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Author Information

Zsolt Horváth

School of Postgraduate Studies of Multidisciplinary Sciences, Faculty of Technical Sciences, Széchenyi István University, Gy?r, Hungary
András Edelmayer

Department of Informatics Engineering, Faculty of Technical Sciences, Széchenyi István University, Gy?r, Hungary; Systems and Control Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary

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APA Style

Zsolt Horváth, András Edelmayer. (2019). Switched Detection Filter Design for Nonlinear Systems. American Journal of Mechanical and Industrial Engineering, 4(1), 1-10. https://doi.org/10.11648/j.ajmie.20190401.11

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ACS Style

Zsolt Horváth; András Edelmayer. Switched Detection Filter Design for Nonlinear Systems. Am. J. Mech. Ind. Eng. 2019, 4(1), 1-10. doi: 10.11648/j.ajmie.20190401.11

Copy | Download

AMA Style

Zsolt Horváth, András Edelmayer. Switched Detection Filter Design for Nonlinear Systems. Am J Mech Ind Eng. 2019;4(1):1-10. doi: 10.11648/j.ajmie.20190401.11

Copy | Download

@article{10.11648/j.ajmie.20190401.11,
  author = {Zsolt Horváth and András Edelmayer},
  title = {Switched  Detection Filter Design for Nonlinear Systems},
  journal = {American Journal of Mechanical and Industrial Engineering},
  volume = {4},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajmie.20190401.11},
  url = {https://doi.org/10.11648/j.ajmie.20190401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmie.20190401.11},
  abstract = {This paper presents the application of the concept of  detection filters to the detection of faults in nonlinear systems. The nonlinear dynamics in specific meaningful points of the operation is approximated by means of a matched array of linear systems. Then, linear  filters are designed for each particular subsystem and a switching scheme is applied to carefully choose the most suitable filter regarding the operational characteristics of the plant in real time. Stability of the switching process is guaranteed by keeping the switching time between two consecutive switching large enough to ensure a proper falloff of filter transients. Therefore, apart from the solution of the standard linear-quadratic optimization problem represented by the  detection filter design problem one has to derive sufficient conditions for the observation error dynamics to be globally asymptotically stable during switching. The goal is to find a common minimum of the switching time to each specific  level calculated separately for every single filter that can be used as a restriction for the switching signal. The idea is demonstrated with the application to the detection of faults in the air path of a diesel engine. The results can be considered as the extension of the standard linear  fault detection filtering problem to nonlinear systems.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Switched  Detection Filter Design for Nonlinear Systems
AU  - Zsolt Horváth
AU  - András Edelmayer
Y1  - 2019/05/07
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmie.20190401.11
DO  - 10.11648/j.ajmie.20190401.11
T2  - American Journal of Mechanical and Industrial Engineering
JF  - American Journal of Mechanical and Industrial Engineering
JO  - American Journal of Mechanical and Industrial Engineering
SP  - 1
EP  - 10
PB  - Science Publishing Group
SN  - 2575-6060
UR  - https://doi.org/10.11648/j.ajmie.20190401.11
AB  - This paper presents the application of the concept of  detection filters to the detection of faults in nonlinear systems. The nonlinear dynamics in specific meaningful points of the operation is approximated by means of a matched array of linear systems. Then, linear  filters are designed for each particular subsystem and a switching scheme is applied to carefully choose the most suitable filter regarding the operational characteristics of the plant in real time. Stability of the switching process is guaranteed by keeping the switching time between two consecutive switching large enough to ensure a proper falloff of filter transients. Therefore, apart from the solution of the standard linear-quadratic optimization problem represented by the  detection filter design problem one has to derive sufficient conditions for the observation error dynamics to be globally asymptotically stable during switching. The goal is to find a common minimum of the switching time to each specific  level calculated separately for every single filter that can be used as a restriction for the switching signal. The idea is demonstrated with the application to the detection of faults in the air path of a diesel engine. The results can be considered as the extension of the standard linear  fault detection filtering problem to nonlinear systems.
VL  - 4
IS  - 1
ER  -

Copy | Download