On the Robust Control of Systems Preceded by Differential Equation-Based Hysteresis Nonlinearities

  • Ying Feng
  • Juan Du
  • Chun-Yi Su
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6424)

Abstract

In this paper, a robust control approach for a class of nonlinear systems preceded by unknown hysteresis nonlinearities is addressed. Due to the complexity of the hysteresis characteristics, the hysteresis can not be linearized directly, and the effects caused by the hysteresis will degrade the system performance. Therefore, it is necessary to design an effective controller mitigating the negative effects. In this paper, the unknown hysteresis is represented by a differential equation-based hysteresis model - Duhem model. By exploring the characteristics of the Duhem model, the developed robust controller ensures the global stability of the system without constructing the hysteresis inverse. The effectiveness of the proposed control approach is demonstrated through a simulation example.

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References

  1. 1.
    Bessa, W.M.: Some remarks on the boundedness and convergence properties of smooth sliding mode controllers. International Journal of Automation and Computing 6(2), 154–158 (2009)CrossRefGoogle Scholar
  2. 2.
    Brokate, M., Sprekels, J.: Hysteresis and Phase Transitions. Springer, Berlin (1996)CrossRefMATHGoogle Scholar
  3. 3.
    Chen, X., Hisayama, T., Su, C.-Y.: Adaptive control for continuous-time systems preceded by hysteresis. IEEE Trans. Automat. Contr. 53(4), 1019–1025 (2008)CrossRefGoogle Scholar
  4. 4.
    Chua, L.O., Stromsmoe, K.A.: Mathematical model for dynamic hysteresis loops. Int. J. Engng. Sci. 9, 435–450 (1971)CrossRefGoogle Scholar
  5. 5.
    Coleman, B.D., Hodgdon, M.L.: On a class of constitutive relations for ferromagnetic hysteresis. Arch. Rational Mech. Anal., 375–396 (1987)Google Scholar
  6. 6.
    Duhem, P.: Die dauernden Aenderungen und die Thermodynamik. I, Z. Phys. Chem. 22, 543–589 (1897)Google Scholar
  7. 7.
    Feng, Y., Hu, Y.-M., Rabbath, C.A., Su, C.-Y.: Robust adaptive control for a class of perturbed strict-feedback nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. International Journal of Control 81(11), 1699–1708 (2008)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Krasnosel’skii, M.A., Pokrovskii, A.V.: Systems with Hysteresis. Springer, New York (1989)CrossRefMATHGoogle Scholar
  9. 9.
    Klein, O., Krejci, P.: Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations. Nonlinear Analysis: Real World Applications 4(5), 755–785 (2003)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Krejci, P., Kuhnen, K.: Inverse control of systems with hysteresis and creep. IEE Proc.-Control Theory and Applications 148(3), 185–192 (2001)CrossRefGoogle Scholar
  11. 11.
    Liu, S., Huang, T., Yen, J.: Tracking control of shape-memory-alloy actuators based on self-sensing feedback and inverse hysteresis compensation. Sensor 10, 112–127 (2010)CrossRefGoogle Scholar
  12. 12.
    Macki, J.W., Nistri, P., Zecca, P.: Mathematical models for hysteresis. SIAM Review 35(1), 94–123 (1993)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Mayergoyz, I.D.: Mathematical Models of Hysteresis. Springer, New York (1991)CrossRefMATHGoogle Scholar
  14. 14.
    Oh, J., Bernstein, D.S.: Semilinear Duhem model for rate-independent and rate-dependent hysteresis. IEEE Trans, Automat. Contr. 50(5), 631–645 (2005)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Oh, J., Bernstein, D.S.: Piecewise linear identification for the rate-independent and rate-dependent Duhem hysteresis models. IEEE Trans. Automat. Contr. 52(3), 576–582 (2007)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Slotine, J.J.E., Li, W.: Applied Nonlinear Control. China Machine Press (2004)Google Scholar
  17. 17.
    Shyu, K.K., Liu, W.J., Hsu, K.C.: Decentralised variable structure control of uncertain large-scale systems containing a dead-zone. IEE Proc. Control Theory Appl. 150(5), 467–475 (2003)CrossRefGoogle Scholar
  18. 18.
    Su, C.-Y., Stepanenko, Y., Svoboda, J., Leung, T.P.: Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Automat. Contr. 45(12), 2427–2432 (2000)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Feng, Y., Hu, Y.-M., Rabbath, C.A., Su, C.-Y.: Robust adaptive control for a class of perturbed strict-feedback nonlinear systems with unknown Prandtl-Ishlinskii hysteresis. International Journal of Control 81(11), 1699–1708 (2008)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Tan, X., Baras, J.S.: Modeling and Control of Hysteresis in Magnetostrictive Actuators. Automatica 40(9), 1469–1480 (2004)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Tan, X., Baras, J.S.: Adaptive identification and control of hysteresis in smart materials. IEEE Trans, Automat. Contr. 50(16), 827–839 (2005)MathSciNetMATHGoogle Scholar
  22. 22.
    Tao, G., Kokotović, P.V.: Adaptive control of plants with unknown hysteresis. IEEE Trans. Automat. Contr. 40, 200–212 (1995)CrossRefMATHGoogle Scholar
  23. 23.
    Visintin, A.: Differential Models of Hysteresis. Springer, New York (1994)CrossRefMATHGoogle Scholar
  24. 24.
    Wang, Q., Su, C.-Y.: Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations. Automatica 42(5), 859–867 (2006)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Zhou, J., Wen, C.-Y., Zhang, Y.: Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Automat. Contr. 49(10), 1751–1757 (2004)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ying Feng
    • 1
    • 2
  • Juan Du
    • 1
  • Chun-Yi Su
    • 2
  1. 1.College of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.Department of Mechanical and Industrial EngineeringConcordia UniversityMontrealCanada

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