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Adaptive Fault Tolerant Control of Multi-time-scale Singularly Perturbed Systems

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Abstract

This paper studies the fault tolerant control, adaptive approach, for linear time-invariant two-time-scale and three-time-scale singularly perturbed systems in presence of actuator faults and external disturbances. First, the full order system will be controlled using ε-dependent control law. The corresponding Lyapunov equation is ill-conditioned due to the presence of slow and fast phenomena. Secondly, a time-scale decomposition of the Lyapunov equation is carried out using singular perturbation method to avoid the numerical stiffness. A composite control law based on local controllers of the slow and fast subsystems is also used to make the control law ε-independent. The designed fault tolerant control guarantees the robust stability of the global closed-loop singularly perturbed system despite loss of effectiveness of actuators. The stability is proved based on the Lyapunov stability theory in the case where the singular perturbation parameter is sufficiently small. A numerical example is provided to illustrate the proposed method.

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References

  1. P. Y. Kokotovic, H. K. Khalil, J. O’Reilly. Singular Perturbation Methods in Control-analysis and Design, USA Academic Press, 1999.

  2. H. K. Khalil. Output feedback control of linear two-timescale systems. IEEE Transactions on Automatic Control, vol. 32, no. 9, pp. 784–792, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  3. Z. Gajic, M. Lim. Optimal Control of Singularly Perturbed Linear Systems and Applications, New York, USA: Marcel Dekker, 2001.

    Book  MATH  Google Scholar 

  4. Z. H. Shao, M. E. Sawan. Stabilization of uncertain singularly perturbed systems. IEE Proceedings: Control Theory and Applications, vol. 153, no. 1, pp. 99–103, 2006.

    Article  Google Scholar 

  5. R. J. Patton. Fault-tolerant control systems: The 1997 situation. In Proceedings of the 3rd IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes, Kingston Upon Hull, UK, vol. 2, pp. 1033–1055, 1997.

    Google Scholar 

  6. H. Noura, D. Sauter, F. Hamelin, D. Theilliot. Fault tolerant control in dynamic systems: Application to a winding machine. IEEE Control Systems Magazine, vol. 20, no. 1, pp. 33–49, 2000.

    Article  Google Scholar 

  7. M. Y. Zhao, H. P. Liu, Z. J. Li, D. H. Sun. Fault tolerant control for networked control systems with packet loss and time delay. International Journal of Automation and Computing, vol. 8, no. 2, pp. 244–253, 2011.

    Article  Google Scholar 

  8. R. J. Veillette. Reliable linear-quadratic state-feedback control. Automatica, vol. 31, no. 1, pp. 137–143, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. H. Yang, S. Y. Zhang, J. Lam, J. L. Wang. Reliable control using redundant controllers. IEEE Transactions on Automatic Control, vol. 43, no. 11, pp. 1588–1593, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. Wang, G. Jin, J. Zhao. Robust fault-tolerant control for a class of switched nonlinear systems in lower triangular form. Asian Journal of Control, vol. 9, no. 1, pp. 68–72, 2007.

    Article  MathSciNet  Google Scholar 

  11. D. Ye, G. H. Yang. Adaptive fault-tolerant tracking control against actuator faults with application to flight control. IEEE Transactions on Control Systems Technology, vol. 14, no. 6, pp. 1088–1096, 2006.

    Article  Google Scholar 

  12. M. L. Corradini, G. Orlando. Actuator failure identification and compensation through sliding modes. IEEE Transactions on Control Systems Technology, vol. 15, no. 1, pp. 184–190, 2007.

    Article  Google Scholar 

  13. J. Stoustrup, D. Blondel. Fault tolerant control: A simultaneous stabilization result. IEEE Transactions on Automatic Control, vol. 49, no. 2, pp. 305–310, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. H. Yang, J. L. Wang, Y. C. Soh. Reliable H8 controller design for linear systems. Automatica, vol. 37, no. 5, pp. 717–725, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  15. R. J. Veillette, J. V. Medanic, W. R. Perkins. Design of reliable control systems. IEEE Transactions on Automatic Control, vol. 37, no. 3, pp. 290–304, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Tellili, M. N. Abdelkrim, M. Benrejeb. Reliable H8 control of multiple time scales singularly perturbed systems with sensor failure. International Journal of Control, vol. 80, no. 5, pp. 659–665, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. Bodson, J. E. Groszkiewicz. Multivariable adaptive algorithms for reconfigurable flight control. IEEE Transactions on Control Systems Technology, vol. 5, no. 2, pp. 217–229, 1997.

    Article  Google Scholar 

  18. G. Tao, S. M. Joshi, X. L. Ma. Adaptive state feedback and tracking control of systems with actuator failures. IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 78–95, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  19. X. N. Zhang, J. L. Wang, G. H. Yang. Adaptive faulttolerant tracking controller design against actuator stuck faults. In Proceedings of the 24th Chinese Control and Decision Conference, IEEE, Taiyuan, China, pp. 4098–4103, 2012.

    Google Scholar 

  20. B. K. Sahu, B. Subudhi. Adaptive tracking control of an autonomous underwater vehicle. International Journal of Automation and Computing, vol. 11, no. 3, pp. 299–307, 2014.

    Article  Google Scholar 

  21. P. Chandler, M. Pachter, M. Mears. System identification for adaptive and reconfigurable control. Journal of Guidance, Control, and Dynamics, vol. 18, no. 3, pp. 516–524, 1995.

    Article  Google Scholar 

  22. L. Smith, P. Chandler, M. Pachter. Regularization techniques for real-time identification of aircraft parameters. In Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA, New Orleans, USA, pp. 1466–1480, 1997.

    Google Scholar 

  23. G. Tao, X. D. Tang, S. H. Chen, J. T. Fei, S. M. Joshi. Adaptive failure compensation of two-state aircraft morphing actuators. IEEE Transactions on Control Systems Technology, vol. 14, no. 1, pp. 157–164, 2006.

    Article  Google Scholar 

  24. X. Z. Jin, G. H. Yang. Robust adaptive fault-tolerant compensation control with actuator failures and bounded disturbances. Acta Automatica Sinica, vol. 35, no. 3, pp. 305–309, 2009. (in Chinese)

    MathSciNet  Google Scholar 

  25. L. L. Fan, Y. D. Song. On fault-tolerant control of dynamic systems with actuator failures and external disturbances. Acta Automatica Sinica, vol. 36, no. 11, pp. 1620–1625, 2010.

    MathSciNet  Google Scholar 

  26. J. Wang, H. L. Pei, N. Z. Wang. Adaptive output feedback control using fault compensation and fault estimation for linear system with actuator failure. International Journal of Automation and Computing, vol. 10, no. 5, pp. 463–471, 2013.

    Article  MathSciNet  Google Scholar 

  27. P. Ioannou, P. Kokotovic. Decentralized adaptive control of interconnected systems with reduced-order models. Automatica, vol. 21, no. 4, pp. 401–412, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  28. K. B. Datta, A. RaiChaudhuri. H2/H8 control of singularly perturbed systems: The state feedback case. European Journal of Control, vol. 16, no. 1, pp. 54–69, 2010.

  29. H. K. Khalil, F. C. Chen. H8 control of two-time-scale systems. Systems Control Letter, vol. 19, no. 1, pp. 35–42, 1992.

  30. W. Tan, T. Leungs, Q. Tu. H8 control for singularly perturbed systems. Automatica, vol. 34, no. 2, pp. 255–260, 1998.

  31. D.S. Naidu. Singular Perturbation Methodology in Control Systems, England: Bath Press, 1988.

    Book  MATH  Google Scholar 

  32. S. Koskie, C. Coumarbatch, Z. Gajic. Exact slow-fast decomposition of the singularly perturbed matrix differential Riccati equation. Applied Mathematics and Computation, vol. 216, no. 5, pp. 1401–1411, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  33. H. Khalil, P. V. Kokotovic. Control strategies for decision makers using different models of the same system. IEEE Transactions on Automatic Control, vol. 23, pp. 289–298, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  34. G. S. Ladde, S. G. Rajalakshmi. Diagonalization and stability of multi-time-scale singularly perturbed linear systems. Applied Mathematics and Computation, vol. 16, pp. 115–140, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  35. Z. Gajic, M. Lim. Optimal control of singularly perturbed linear systems and applications, New York, USA: Marcel Dekker, 2001.

    Book  MATH  Google Scholar 

  36. S. M. Shahruz. H8 optimal compensators for singularly perturbed systems. In Procedings of IEEE Conference on decision and control, IEEE, Brighton, England, pp. 2397–2398, 1989.

    Google Scholar 

  37. S. R. Shimjith, A.P. Tiwari, B. Bandyopadhyay. Modeling and Control of a Large Nuclear Reactor–A Three-Time-Scale Approach. Berlin, Germany: Springer, 2013.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Research Unit MACS, University of Gabes, Gabes, Tunisia

    Adel Tellili, Nouceyba Abdelkrim, Amina Challouf & Mohamed-Naceur Abdelkrim

  2. Higher Institute of Industrial Systems at Gabes, University of Gabes, Gabes, Tunisia

    Nouceyba Abdelkrim & Amina Challouf

  3. Higher Institute of Technological Studies at Djerba, Djerba, Tunisia

    Adel Tellili

  4. National School of Engineers of Gabes, University of Gabes, Gabes, Tunisia

    Mohamed-Naceur Abdelkrim

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  1. Adel Tellili
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  2. Nouceyba Abdelkrim
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  3. Amina Challouf
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  4. Mohamed-Naceur Abdelkrim
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Correspondence to Adel Tellili.

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Recommended by Associate Editor Donghua Zhou

Adel Tellili graduated from the Technical University of Karlsruhe, Germany in 1994. He received the M. Sc. degree in automation from National School of Engineers of Sfax (ENIS), Tunisia in 2003, and the Ph.D. degree from the same school in 2007. He is currently an assistant professor at Higher Institute of Technological Studies, Tunisia. He is a member of the research unit Modeling, Analysis and Control of Systems (MACS).

His research interests include singularly perturbed systems, fault diagnosis and fault tolerant control.

Nouceyba Abdelkrim graduated from the National School of Engineers, Tunisia in 2009. She received the M. Sc. degree from the same school in 2011, and the Ph.D. degree from the same school in 2014. She is currently an assistant at Higher Institute of Industrial Systems of Gabes, Tunisia. She is a member of the research unit Modeling, Analysis and Control of Systems (MACS).

Her research interests include fault tolerant control, fault diagnosis, singularly perturbed systems and delayed systems.

Amina Challouf graduated from the National School of Engineers, Tunisia in 2006. She received the M. Sc. degree from the same school in 2008, and the Ph.D. degree from the same school in 2015. She is currently an assistant at Higher Institute of Industrial Systems of Gabes, Tunisia. She is a member of the research unit Modeling, Analysis and Control of Systems (MACS).

Her research interests include fault tolerant control, fault diagnosis and interconnected systems.

Mohamed Naceur Abdelkrim graduated from High School of Technical Education of Tunis, Tunisia in 1980. He received the M. Sc. degree from the same school in 1981 and the Ph.D. degree and “State Doctorate thesis” from the National School of Engineers of Tunis, Tunisia in 1984 and 2003. He is currently a professor of automatic control at the National School of Engineers of Gabes, Tunisia. He is also the head of the research unit Modeling, Analysis and Control of Systems (MACS).

His research interests include robust control, fault tolerant control and singularly perturbed systems.

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Tellili, A., Abdelkrim, N., Challouf, A. et al. Adaptive Fault Tolerant Control of Multi-time-scale Singularly Perturbed Systems. Int. J. Autom. Comput. 15, 736–746 (2018). https://doi.org/10.1007/s11633-016-0971-9

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