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Sliding mode tracking control of systems with unstable zero dynamics

  • Heon-Sul Jeong
  • Vadim I. Utkin
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 247)

Abstract

In this paper, a sliding mode tracking control methodology, based on the block control principle, for an arbitrary reference signal of multivariable systems with unstable zero dynamics is developed. The proposed approach does not require an exosystem and is applicable to any relative degree systems. It is shown that the two step design procedure of the sliding mode theory is applicable to provide tracking without an error. Nonlinear systems reducable to a regular form can also be incorporated in this approach. As an illustrative example, tracking controller for EGR/VGT diesel engine was designed which is a 7th order 2-input 2-output nonminimum phase system.

Keywords

Diesel Engine Slide Mode Control Regular Form Output Tracking Nonminimum Phase 
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References

  1. 1.
    Francis B. A., Wonham W. M., “The internal model principle of control theory”, Automatica, vol. 12, pp.457–465, 1976zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Wonham W. M., Linear Multivariable Control: A Geometric Approach, 3rd ed., Springer-Verlag, 1985Google Scholar
  3. 3.
    Byrnes C. I., Isidori A., “Output regulation of nonlinear systems”, IEEE Transactions on Automatic Control, Vol. 35, pp.131–140, 1990zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gopalswamy S., Hedrick J. K., “Tracking nonlinear non-minimum phase systems using sliding control”, Int. J. Control, vol. 57, no.5, pp.1141–1158, 1993zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Shtessel Y. B., Tournes C., “Nonminimum phase output tracking in dynamic sliding manifolds with application to aircraft control”, Proc. of the 35th Conference on Decision and Control, Kobe, Japan, Dec., 1996Google Scholar
  6. 6.
    Devasia S., Chen D., Paden B., “Nonlinear inversion-based output tracking”, IEEE Transactions on Automatic Control, Vol. 41, no. 7, pp. 930–942, 1996zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Hunt L. R., Meyer G., “Stable inversion for nonlinear systems”, Automatica, vol. 33, no. 8, pp. 1549–1554, 1997zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Lanari L., Wen J., “Feedforward calculation in tracking control of flexible robots”, Proc. of IEEE Conference on Decision and Control, pp.1403–1408, Brighton, England, 1991Google Scholar
  9. 9.
    Drakunov S. V., Izosimov D. B., Luk'yanov A. G., Utkin V. A., Utkin V. I., “Block control principle I & II”, Avtomatika i Telemekhanika, No. 5, pp. 38–47, May, 1990, No. 6, pp. 20–31, June, 1990Google Scholar
  10. 10.
    Luk'yanov A. G., Utkin V. I., “Methods of reducing equations for dynamic systems to a regular form”, Avtomatika i Telemekhanika, No. 4, pp. 5–13, April, 1981Google Scholar
  11. 11.
    Hale J. K., Ordinary Differential Equations, vol. 21, New York: Wiley-Interscience, 1980Google Scholar
  12. 12.
    Utkin V. I., Sliding Modes in Control and Optimization, Springer-Verlag, 1992Google Scholar
  13. 13.
    Brewer J. W., “Kronecker products and Matrix Calculus in System Theory”, IEEE Transactions on Circuits and Systems, vol. CAS-25, no. 9, pp. 772–781, Sep. 1978CrossRefMathSciNetGoogle Scholar
  14. 14.
    Isidori A., Nonlinear Control Systems, 2nd Ed., Springer-Verlag, 1989Google Scholar
  15. 15.
    Hahn W., Stability of Motion, Spinger-Verlag, 1967Google Scholar
  16. 16.
    Luk'yanov A. G., ‘Optimal Nonlinear Block-Control Method”, Proc. of the 2md European Control Conference, Groningen, 1853–1855, 1993Google Scholar
  17. 17.
    Luk'yanov A. G., Dodds S. J., “Sliding Mode Block Control of Uncertain Nonlinear Plants”, Proc. IFAC World Congr.Google Scholar
  18. 18.
    Moody J., “Variable Geometry Turbocharging with Electronic Control”, SAE Paper 860107, 1986Google Scholar
  19. 19.
    Kolmanovsky I., Moraal P., van Nieuwstadt M., and Stefanopoulou A., “Issues in Modelling and Control of Intake Flow in Variable Geometry Turbocharged Engines”, in System Modelling and Optimization, Addison Wesley Longman, to appearGoogle Scholar
  20. 20.
    Utkin, V. I., Chang, H., Kolmanovsky, I., and Chen, D., 1998, “Sliding Mode Control Design based on Block Control Principle,” The Fourth International Conference on Motion and Vibration Control (MOVIC), Zurich, Switzerland, August 25–28.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Heon-Sul Jeong
    • 1
  • Vadim I. Utkin
    • 2
  1. 1.Kunsan National University, KunsanChonbukKorea
  2. 2.The Ohio State UniversityColumbus

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