Fault Estimator Design using Data Driven H∞ Technique

Abstract

Abstract: In this paper, a data driven method for fault estimation in control systems is proposed. The fault estimation problem is formulated as a time domain control problem and the H technique is applied for solving it. The mathematical model is assumed to be unknown and only input/output (I/O) data are used for detector design. Minimizing the fault estimation error is considered as the fault detection performance measure. Also, since the estimated fault plays the role of a virtual control input, a cost is defined on it to avoiding the H control problem being singular. These measures are achieved by tuning a scalar parameter and some weighting matrices. An easily implementable design algorithm summarizes the methodology presented in the paper. The proposed algorithm is applied to a numerical example in order to illustrate its effectiveness.

Keywords


[1] I. Hwang, S. Kim, and Ch.E. Seah, “A Survey of fault detection, isolation, and reconfiguration methods,” IEEE Transaction on Control Systems Technology, vol. 18, no. 3, 2010.
[2] H. Wang, C. T. Y. Chai, J. L. Ding, and M. Brown, “Data driven fault diagnosis and fault tolerant control: some advances and possible new directions,” Acta Automation Sinica, vol. 35, no. 6, 2009.
[3] R. J. Patton, and J. Chen, “Robust model-based fault diagnosis for dynamic systems,” Kluwer Academic Publishers, 1999.
[4] S. X. Ding, Model-based Fault Diagnosis Techniques-design Schemes, Algorithms and Tools, 2nd ed., Springer-Verlag, 2013.
[5] محمدجواد خسروجردی و مهدی علیاری شوره­دلی، روش­های تشخیص و جبران­سازی عیب در سیستم­های کنترل، انتشارات دانشگاه صنعتی سهند، 1395.
[6] Z. S. Hou, and Z. Wang, “From model-based control to data driven control: survey, classification and perspective,” Information Science, vol. 235, pp. 1-35, 2013.

[7] سعید هاشمی‌نژاد، سیدقدرت­اله سیف­السادات، مرتضی رزاز و محمود جورابیان، «دسته‌بندی خطا و شناسایی فازهای تحت خطا در سیستم‌های قدرت با استفاده از تئوری امواج سیار و سیستم فازی،» مجلهمهندسیبرقدانشگاهتبریز، دوره 45 ، شماره 4، صفحه 223-233، 1394.

[8] علیرضا رضائی، ابوالقاسم اسدالله راعی و سعید شیری قیداری، «یادگیری رفتار مقاوم در مقابل تغییرات محیطی و خرابی حسگرهای روبات سیار، با استفاده از شبکه بیزین پویای مبتنی بر داده،» مجلهمهندسیبرقدانشگاهتبریز، دوره 43 ، شماره 1، صفحه 27-38، 1392.

[9] حسین مرادی فراهانی و جواد عسگری، «طراحی کنترل‌کننده عصبی-فازی نوع-2،» مجلهمهندسیبرقدانشگاهتبریز، دوره ۴۳، شماره ۱، صفحه 63-73، 1392.

[10] علی حسامی نقشبندی، شورش شکوهی و حسن بیورانی، «کـاربرد کنترل­کننده فازی - عصبی در پایداری ولتاژ و فرکانس ریز شبکه­های جزیره­ای،» مجلهمهندسیبرقدانشگاهتبریز، دوره ۴۱ ، شماره2، صفحه41-50، 1390.

[11] P. V. Overshee, B. D. Moor, “A unifying theorem for three subspace identification algorithms,” Automatica, vol. 31, pp. 1853-1864, 1995.
[12] P. Zhang, and S. X. Ding, “A Model-free approach to fault detection of continuous-time systems based on time domain data,” International Journal of Automation and Computing, pp. 189-194, 2007.
[13] A. S. Naik, Subspace-based Data-driven Designs of Fault Detection Systems, PhD Thesis, 2010.
[14] M. H. Palanthandalam, and D. S. Brenstain, “A subspace algorithm for simultaneous identification and input reconstruction,” International Journal of Control and Signal Processing, vol. 23, pp. 1053-1069, 2009.
[15] Y. Wang, G. Bingzhao, and H. Chen, “Data-driven design of parity space-based FDI system for AMT vehicles,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 1, 2015.
[16] S. X. Ding, S. Yin, Y. Wang, Y. Yang, and B. Ni, “Data-driven design of observers and its applications,” Proceedings of the 18th IFAC World Congress, 2011.
[17] S. Yin, G. Wang, and H. R. Karimi, “Data-driven design of robust fault detection system for wind turbines,” Original Research Article Mechatronics, vol. 24, no. 4, pp. 298-306, 2014.
[18] S. Yin, H. Luo, and S. X. Ding, “Real-time implementation of fault-tolerant control systems with performance optimization,” IEEE Transactions of Industrial Electronics, vol. 61, no. 5, 2014.
[19] W. Li, H. Raghavan, and S. Shah, “Subspace identification of continuous time models for process fault detection and isolation,” Journal of Process Control, pp. 407-421, 2003.
[20] J. Dong, and M. Verhaegen, “Identification of fault estimation filter from I/O data for systems with stable inversion,” IEEE Transaction on Automatic Control, vol. 57, no. 6, 2012.
[21] S. X. Ding, “Data-driven design of monitoring and diagnosis systems for dynamic processes: A review of subspace technique based schemes and some recent results,” Journal of Process Control, vol. 24, pp. 431-449, 2014.
[22] S. X. Ding, Data-driven Design of Fault Diagnosis and Fault-tolerant Control Systems, Springer-Verlag, London, 2014.
[23] B. R. Woodley, J. P. How, and R. L. Kosut, “Subspace based direct adaptive H control,” International Journal of Adaptive Control and Signal Processing, vol. 915, 535-561, 2001.
[24] S. Yin, Wang, and H. R. Karimi, “Data-driven design of robust fault detection system for wind turbines,” Original Research Article Mechatronics, vol. 24, no. 4, pp. 298-306, 2014.
[25] S. Joe Qin, “An overview of subspace identification,” Computers and Chemical Engineering, vol. 30, pp. 1502-1513, 2006.
[26] V. Overschee, and B. D.  Moor, Subspace Identification for Linear Systems: Theory, Implementation, Application, Kluwer Academic Publishers, 1999.
[27] K. H. Johnsson, “The quadruple-tank process: a multi variable laboratory process with an adjustable zero,” IEEE Transaction on Control Systems Technology, vol. 8, no. 3, pp. 456-465, 2000.
[28] M. J. Khosrowjerdi, R. Nikoukhah, and N. Safari-Shad, “Fault detection in a mixed H2/H∞ setting,” IEEE Transactions on Automatic Control, vol. 50, no. 7, 2005.
[29] V. Kirubakarana, T. K. Radhakrishnana, and N. Sivakumaranb, “Distributed multi parametric model predictive control design for a quadruple tank process,” Measurement, vol. 47, pp. 841-854, 2014.
[30] P. P. Biswas, R. Srivastava, S. Ray, and A. N.  Samanta, “Sliding mode control of quadruple tank process,” Mechatronics, vol. 19, no. 4, pp. 548-561, 2009.