Abstract
This paper deals with the issues of sensor fault estimation, actuator fault detection and isolation for a class of uncertain nonlinear systems. By taking the sensor fault vector as a part of an extended state vector, the original system with sensor faults, actuator faults and unknown inputs is transformed into an augmented singular system which is just with actuator faults and unknown inputs. For the constructed singular system, a robust sliding-mode observer is developed to simultaneously estimate the states and sensor faults of original system, and the observer gain matrices are computed in terms of linear matrix inequalities by solving an optimization problem. Then an actuator fault detector is designed to detect actuator faults when ones occur, and multiple observers used as actuator fault isolators are proposed to identify which actuator is with fault. Finally, a simulation example is given to illustrate the effectiveness of the proposed methods.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
H. Wang, Z. J. Huang, and S. Dalay, “On the use of adaptive updating rules for actuator and sensor fault diagnosis,” Automatica, vol. 33, no. 2, pp. 217–225, 1997.
H. Ye, G. Wang, and S. X. Ding, “A new parity space approach for fault detection based on stationary wavelet transform,” IEEE Trans. on Automatic Control, vol. 49, no. 2, pp. 281–287, 2004.
Z. Zhang and M. I. Jaimoukha, “On-line fault detection and isolation for linear discrete-time uncertain systems,” Automatica, vol. 50, no. 2, pp. 513–518, 2014.
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. 351, no. 1, pp. 277–295, 2014.
H. M. Odendaal and T. Jones, “Actuator fault detection and isolation: an optimized parity space approach,” Control Engineering Practice, vol. 26, pp. 222–232, 2014.
S. J. Yoo, “Fault detection and accommodation of a class of nonlinear systems with unknown multiple time-delayed faults,” Automatica, vol. 50, no. 1, pp. 255–261, 2014.
L. Chen, M. Zhong, and M. Zhang, “H ∞ fault detection for linear singular systems with time-varying delay,” International Journal of Control, Automation, and Systems, vol. 9, no. 1, pp. 9–14, 2011.
C. Edwards, S. K. Spurgeon, and R. J. Patton, “Sliding mode observers for fault detection and isolation,” Automatica, vol. 36, no. 4, pp. 541–553, 2000.
C. P. Tan and C. Edwards, “Robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade,” IEEE Trans. on Automatic Control, vol. 55, no. 4, pp. 855–867, 2010.
W. Chen and M. Saif, “Actuator fault diagnosis for uncertain linear systems using a high-order slidingmode robust differentiator (HOSMRD),” International Journal of Robust and Nonlinear Control, vol. 18, no. 4–5, pp. 413–426, 2008.
W. Chen and M. Saif, “Actuator fault diagnosis for a class of nonlinear systems and its application to a laboratory 3D crane,” Automatica, vol. 47, no. 7, pp. 1435–1442, 2011.
K. C. Veluvolu and Y. C. Soh, “Fault reconstruction and state estimation with sliding mode observers for Lipschitz non-linear systems,” IET Control Theory and Applications, vol. 5, no. 11, pp. 1255–1263, 2011.
K. C. Veluvolu, M. Y. Kim, and D. Lee, “Nonlinear sliding mode high-gain observers for fault estimation,” International Journal of Systems Science, vol. 42, no. 7, pp. 1065–1074, 2011.
R. Raoufi, H. J. Marquez, and A. S. I. Zinober, “H ∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis,” International Journal of Robust and Nonlinear Control, vol. 20, no. 16, pp. 1785–1801, 2010.
Z. Wang, Y. Shen, and X. Zhang, “Actuator fault estimation for a class of nonlinear descriptor systems,” International Journal of Systems Science, vol. 45, no. 3, pp. 487–496, 2014.
X. Zhang, M. M. Polycarpou, and T. Parisini, “Fault diagnosis of a class of nonlinear uncertain systems with Lipschitz nonlinearities using adaptive estimation,” Automatica, vol. 46, no. 2, pp. 290–299, 2010.
X. Zhang, “Sensor bias fault detection and isolation in a class of nonlinear uncertain systems using adaptive estimation,” IEEE Trans. on Automatic Control, vol. 56, no. 5, pp. 1220–1226, 2011.
D. Wang and K.-Y. Lum, “Adaptive unknown input observer approach for aircraft actuator fault detection and isolation,” International Journal of Adaptive Control and Signal Processing, vol. 21, no. 1, pp. 31–48, 2007.
K. Zhang, B. Jiang, and V. Cocquempot, “Adaptive observer-based fast fault estimation,” International Journal of Control, Automation, and Systems, vol. 6, no. 3, pp. 320–326, 2008.
X.-J. Li and G.-H. Yang, “Adaptive fault detection and isolation approach for actuator stuck faults in closed-loop systems,” International Journal of Control, Automation, and Systems, vol. 10, no. 4, pp. 830–834, 2012.
D. J. Lee, Y. Park, and Y. S. Park, “Robust H ∞ sliding mode descriptor observer for fault and output disturbance estimation of uncertainty systems,” IEEE Trans. on Automatic Control, vol. 57, no. 11, pp. 2928–2012, 2012.
Z. Gao and S. X. Ding, “Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems,” Automatica, vol. 43, no. 5, pp. 912–920, 2007.
M. Corless and J. Tu, “State and input estimation for a class of uncertain systems,” Automatica, vol. 34, no. 6, pp. 757–764, 1998.
M. Darouach, L. Boutat-Baddas, and M. Zerrougui, “H ∞ observers design for a class of nonlinear singular systems,” Automatica, vol. 47, no. 11, pp. 2517–2525, 2011.
W. Chen and M. Saif, “Observer-based strategies for actuator fault detection, isolation and estimation for certain class of uncertain nonlinear systems,” IET Control Theory and Applications, vol. 1, no. 6, pp. 1672–1680, 2007.
K. Kalsi, J. Lian, S. Hui, and S. H. Zak, “Slidingmode observers for systems with unknown inputs: A high-gain approach,” Automatica, vol. 46, no. 2, pp. 347–353, 2010.
J. Yang, F. Zhu, and W. Zhang, “Sliding-mode observers for nonlinear systems with unknown inputs and measurement noise,” International Journal of Control, Automation and Systems, vol. 11, no. 5, pp. 903–910, 2013.
H. R. Karimi, M. Zapateiro, and N. Luo, “A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed timevarying delays and nonlinear perturbations,” Journal of the Franklin Institute, vol. 347, no. 6, pp. 957–973, 2010.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Guang-Hong Yang under the direction of Editor Duk-Sun Shim.
This work is supported by the National Nature Science Foundation of China (61403129). This work is also supported by the Doctoral Fund Program of Henan Polytechnic University (B2015-30), the Fund of Key Laboratory of Control Engineering of Henan Province (KG2014-08), the Project of Henan Province Science and Technology Agency (142102210048), and the Program of Natural Science of Henan Provincial Education Department (13B413028 and 13B413035).
Junqi Yang received his Ph.D. degree in Control Theory and Control Engineering from Tongji University, Shanghai, China, in 2013. He is currently an Associate Professor of Henan Polytechnic University. His research interests include modelbased fault detection, fault-tolerant control and switched system.
Fanglai Zhu received his Ph.D. degree in Control Theory and Control Engineering from Shanghai Jiao Tong University in 2001. Now he is a professor of Tongji University, China. His research interests include nonlinear observer design, system identification, and model-based fault detection and isolation.
Xin Wang received his Ph.D. degree from East China University of Science and Technology in 2005. He is professor of Henan Polytechnic University. His research interests include fault diagnosis, signal processing and electrical drive.
Xuhui Bu received his Ph.D. degree in Control Theory and Application from Beijing Jiaotong University, Beijing, China, in 2011. He is currently an Associate Professor in Henan Polytechnic University, JiaoZuo, China. His research is mainly related to data-driven control, iterative learning control, traffic control, etc.
Rights and permissions
About this article
Cite this article
Yang, J., Zhu, F., Wang, X. et al. Robust sliding-mode observer-based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems. Int. J. Control Autom. Syst. 13, 1037–1046 (2015). https://doi.org/10.1007/s12555-014-0159-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-014-0159-4