Advertisement

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

  • Mojtaba Hashemi
  • Ali Kamali EgoliEmail author
  • Mahyar Naraghi
Article
  • 2 Downloads

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.

Keywords

Integrated design linear matrix inequality observer-based fault tolerant saturated linear system 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [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.CrossRefGoogle Scholar
  2. [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.MathSciNetCrossRefGoogle Scholar
  3. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [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.CrossRefGoogle Scholar
  6. [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.CrossRefGoogle Scholar
  7. [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. [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. [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.CrossRefGoogle Scholar
  10. [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.MathSciNetCrossRefGoogle Scholar
  11. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [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.CrossRefGoogle Scholar
  13. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [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.CrossRefGoogle Scholar
  15. [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.CrossRefGoogle Scholar
  16. [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.CrossRefzbMATHGoogle Scholar
  17. [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. [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.MathSciNetCrossRefGoogle Scholar
  19. [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.CrossRefzbMATHGoogle Scholar
  20. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    T. Hu and Z. Lin, Control systems with actuator saturation: analysis and design, Springer Science & Business Media, September 2001.CrossRefGoogle Scholar
  24. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, vol. 15, Siam, June 1994.CrossRefzbMATHGoogle Scholar
  28. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [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. [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.CrossRefGoogle Scholar
  31. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [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.CrossRefGoogle Scholar
  33. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [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.CrossRefGoogle Scholar
  35. [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.CrossRefzbMATHGoogle Scholar
  36. [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.CrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Mojtaba Hashemi
    • 1
  • Ali Kamali Egoli
    • 1
    Email author
  • Mahyar Naraghi
    • 1
  1. 1.School of Mechanical EngineeringAmirKabir UniversityTehranIran

Personalised recommendations