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Integrated Fault Tolerant Control for Saturated Systems with Additive Faults: A Comparative Study of Saturation Models

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Abstract

In this paper, the integrated design problem of Fault Estimation (FE) and Fault Tolerant Control (FTC) for saturated systems is considered. The system suffers from input saturation and L2-bounded disturbances. To design an adaptive observer-based FE, the actuator output measurements are not used, when the actuator is saturated, there exist new interactions between FE and FTC. In such a case the separation principle for FE and FTC design does not hold anymore. In this paper, a method is introduced for integrated design of FE and FTC, which guarantees boundedness stability of such a system. To extract sufficient conditions for stability and minimum L2-gain performance for disturbance rejection, the Modified Sector Condition (MSC) is employed for saturation modeling. Also, Quadratic Polytopic Differential Inclusion (QPDI) approach is developed for the comparative study. All conditions are cast as Linear Matrix Inequality(LMIs) that can be evaluated in a single step. In a numerical example, the feasibility of the introduced method for stability guarantee is demonstrated and performance characteristics of FE and FTC in disturbance rejection are compared for both modeling approaches.

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References

  1. Y. Zhang and J. Jiang, “Bibliographical review on reconfigurable fault-tolerant control systems,” Annual Reviews in Control, vol. 32, no. 2, pp. 229–252, December 2008.

    Article  Google Scholar 

  2. H. Karimi, M. Chadli, and P. Shi, “Fault detection, isolation, andtolerant control of vehicles using soft computing methods,” IET Control Theory & Applications, vol. 8, no. 9, pp. 655–657, June 2014.

    Article  MathSciNet  Google Scholar 

  3. J. Lan and R. J. Patton, “A new strategy for integration of fault estimation within fault-tolerant control,” Automatica, vol. 69, no. 14, pp. 48–59, March 2016.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. Zhang, B. Jiang, and P. Shi, “Observer-based integrated robust fault estimation and accommodation design for discrete-time systems,” International Journal of Control, vol. 83, no. 6, pp. 1167–1181, Jan. 2010.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Fan, Y. Zhang, and Z. Zheng, “Adaptive observer-based integrated fault diagnosis and fault-tolerant control systems against actuator faults and saturation,” Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 4, pp. 41–48, February 2013.

    Article  Google Scholar 

  6. J. Fan, Y. Zhang, and Z. Zheng, “Observer-based reliable stabilization of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances,” ISA transactions, vol. 52, no. 6, pp. 730–737, November 2013.

    Article  Google Scholar 

  7. J. Fan, Y. Zhang, and Z. Zheng, “Integrated adaptive fault diagnosis and state-feedback control for systems with constant actuator faults and control input constraints,” in ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications (MESA11), Washington, DC, December 2011.

    Google Scholar 

  8. D. Tan and R. J. Patton, “Integrated fault estimation and fault tolerant control: A joint design,” IFACPapersOnLine, vol. 48, no. 21, pp. 517–522, November 2015.

    Google Scholar 

  9. J. Zhang, W.-B. Xie, M.-Q. Shen, and L. Huang, “State augmented feedback controller design approach for ts fuzzy system with complex actuator saturations,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 2395–2405, October 2017.

    Article  Google Scholar 

  10. M. Rehan, M. Tufail, C. K. Ahn, and M. Chadli, “Stabilisation of locally lipschitz non-linear systems under input saturation and quantisation,” IET Control Theory & Applications, vol. 11, no. 9, pp. 1459–1466, June 2017.

    Article  MathSciNet  Google Scholar 

  11. D. Saifia, M. Chadli, H. R. Karimi, and S. Labiod, “Fuzzy control for electric power steering system with assist motor current input constraints,” Journal of the Franklin Institute, vol. 352, no. 2, pp. 562–576, February 2015.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Wang, H. Jing, J. Wang, M. Chadli, and N. Chen, “Robust output-feedback based vehicle lateral motion control considering network-induced delay and tire force saturation,” Neurocomputing, vol. 214, pp. 409–419, November 2016.

    Article  Google Scholar 

  13. B. Shen, H. Tan, Z. Wang, and T. Huang, “Quantized/ saturated control for sampled-data systems under noisy sampling intervals: A confluent vandermonde matrix approach,” IEEE transactions on automatic control, vol. 62, no. 9, pp. 4753–4759, March 2017.

    Article  MathSciNet  MATH  Google Scholar 

  14. Y. Zhang and J. Jiang, “Fault tolerant control system design with explicit consideration of performance degradation,” IEEE Transactions on Aerospace and Electronic Systems, vol. 39, no. 3, pp. 838–848, September 2003.

    Article  Google Scholar 

  15. J. Jiang and Y. Zhang, “Accepting performance degradation in fault-tolerant control system design,” IEEE transactions on control systems technology, vol. 14, no. 2, pp. 284–292, February 2006.

    Article  Google Scholar 

  16. D. Theilliol, C. Join, and Y. Zhang, “Actuator fault tolerant control design based on a reconfigurable reference input,” International Journal of Applied Mathematics and Computer Science, vol. 18, no. 4, pp. 553–560, December 2008.

    Article  MATH  Google Scholar 

  17. J. Fan, Z. Zheng, and Y. Zhang, “Fault-tolerant control for output tracking systems subject to actuator saturation and constant disturbances: an lmi approach,” in AIAA Guidance, Navigation, and Control Conference, p. 6411. July 2011.

    Google Scholar 

  18. J. Lan, R. J. Patton, and X. Zhu, “Integrated fault-tolerant control for a 3-dof helicopter with actuator faults and saturation,” IET Control Theory & Applications, vol. 11, no. 14, pp. 2232–2241, September 2017.

    Article  MathSciNet  Google Scholar 

  19. S. Tarbouriech, G. Garcia, J. M. G. da Silva Jr, and I. Queinnec, Stability and stabilization of linear systems with saturating actuators, Springer Science & Business Media, March 2011.

    Book  MATH  Google Scholar 

  20. D. W. Kim, “Further refinement on controller design for linear systems with input saturation,” Automatica, vol. 77, no. 77, pp. 14–17, March 2017.

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Tarbouriech, C. Prieur, and J. G. Da Silva, “Stability analysis and stabilization of systems presenting nested saturations,” IEEE Transactions on Automatic Control, vol. 51, no. 8, pp. 1364–1371, August 2006.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Tarbouriech and F. Gouaisbaut, “Control design for quantized linear systems with saturations,” IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1883–1889, December 2012.

    Article  MathSciNet  MATH  Google Scholar 

  23. T. Hu and Z. Lin, Control systems with actuator saturation: analysis and design, Springer Science & Business Media, September 2001.

    Book  Google Scholar 

  24. Y. Li and Z. Lin, “Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback,” Automatica, vol. 49, no. 3, pp. 821–828, March 2013.

    Article  MathSciNet  MATH  Google Scholar 

  25. J. Lan and R. J. Patton, “A decoupling approach to integrated fault-tolerant control for linear systems with unmatched non-differentiable faults,” Automatica, vol. 89, pp. 290–299, March 2018.

    Article  MathSciNet  MATH  Google Scholar 

  26. K. Zhang, B. Jiang, X.-G. Yan, and Z. Mao, “Incipient sensor fault estimation and accommodation for inverter devices in electric railway traction systems,” International Journal of Adaptive Control and Signal Processing, vol. 31, no. 5, pp. 785–804, September 2017.

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, vol. 15, Siam, June 1994.

    Book  MATH  Google Scholar 

  28. J. G. Da Silva and S. Tarbouriech, “Antiwindup design with guaranteed regions of stability: an lmi-based approach,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 106–111, March 2005.

    Article  MathSciNet  MATH  Google Scholar 

  29. 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, June 2008.

    Google Scholar 

  30. Y. Wei, J. Qiu, P. Shi, and M. Chadli, “Fixed-order piecewise-affine output feedback controller for fuzzyaffine-model-based nonlinear systems with time-varying delay,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 64, no. 4, pp. 945–958, December 2017.

    Article  Google Scholar 

  31. M. Chadli, A. Abdo, and S. X. Ding, “H-/h fault detection filter design for discrete-time takagi-sugeno fuzzy system,” Automatica, vol. 49, no. 7, pp. 1996–2005, July 2013.

    Article  MathSciNet  MATH  Google Scholar 

  32. Y. Wei, J. Qiu, and H.-K. Lam, “A novel approach to reliable output feedback control of fuzzy-affine systems with time-delays and sensor faults,” IEEE Transactions on Fuzzy Systems, vol. 25, no. 6, pp. 1808–1823, November 2017.

    Article  Google Scholar 

  33. S. Cao and Y. Zhao, “Anti-disturbance fault-tolerant attitude control for satellites subject to multiple disturbances and actuator saturation,” Nonlinear Dynamics, vol. 89, no. 4, pp. 2657–2667, June 2017.

    Article  MathSciNet  MATH  Google Scholar 

  34. S. Cao, Y. Zhao, and J. Qiao, “Adaptive fault tolerant attitude control based on a disturbance observer for satellites with multiple disturbances,” Transactions of the Institute of Measurement and Control, vol. 38, no. 6, pp. 722–731, December 2016.

    Article  Google Scholar 

  35. T. Hu, Z. Lin, and B. M. Chen, “An analysis and design method for linear systems subject to actuator saturation and disturbance,” Automatica, vol. 38, no. 2, pp. 351–359, February 2002.

    Article  MATH  Google Scholar 

  36. T.-G. Park, “Designing fault detection observers for linear systems with mismatched unknown inputs,” Journal of Process Control, vol. 23, no. 8, pp. 1185–1196, September 2013.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, AmirKabir University, 424 Hafez Ave, Tehran, Iran

    Mojtaba Hashemi, Ali Kamali Egoli & Mahyar Naraghi

Authors
  1. Mojtaba Hashemi
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  2. Ali Kamali Egoli
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  3. Mahyar Naraghi
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Corresponding author

Correspondence to Ali Kamali Egoli.

Additional information

Recommended by Associate Editor M. Chadli under the direction of Editor Guang-Hong Yang.

Mojtaba Hashemi received the BSc degree in Mechanical Engineering from KNTU University in 2008 and his M.S. degree in Dynamic system and control from Sharif Univ. of Technology, Tehran, Iran in 2011. He is currently a Ph.D student in Amirkabir Univ. His research interests include Robust control, Fault Estimation, and Fault Tolerant.

Ali Kamali Egoli received the BSc from the Mechanical Engineering Department of Amirkabir University of Technology, Tehran, Iran, 2004, and his M.S. degree in 2006 and the Ph.D. degree in Dynamic system and control from Sharif univ. of Technology, Tehran, Iran in 2011. He is currently an Assistant Professor in mechanical engineering department in Amirkabir univ. His research interests include Robust control, nonlinear control, and fault tolerant control.

Mahyar Naraghi received his BSc from the Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA, in 1981, his MS from the Department of Mechanical Engineering, Tarbiat Modarres University, Tehran, Iran, in 1989, and his Ph.D. degree from the Department of Mechanical Engineering, University of Ottawa, Canada, in 1996. He is currently an Associated Professor in the mechanical engineering department in Amirkabir Univ. His research interests are in robotics and control, including both the theoretical and experimental studies.

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Hashemi, M., Egoli, A.K. & Naraghi, M. Integrated Fault Tolerant Control for Saturated Systems with Additive Faults: A Comparative Study of Saturation Models. Int. J. Control Autom. Syst. 17, 1019–1030 (2019). https://doi.org/10.1007/s12555-018-0270-z

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  • DOI: https://doi.org/10.1007/s12555-018-0270-z

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