Advertisement

Sliding mode control with gain scheduled hyperplane for LPV plant

  • Kenzo Nonami
  • Selim Sivrioglu
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 247)

Abstract

This study presents sliding mode hyperplane design for a class of linear parameter-varying (LPV) plants, the state-space matrices of which are an affine function of time-varying physical parameters. The proposed hyperplane, involving a linear matrix inequality (LMI) approach, has continuous dynamics due to scheduling parameters and provides stability and robustness against parametric uncertainties. We have designed a time-varying hyperplane for a rotor-magnetic bearing system with a gyroscopic effect, which can be considered an LPV plant due to parameter dependence on rotational speed. The obtained hyperplane is continuously scheduled with respect to rotational speed. We successfully carried out experiments using a commercially available turbomolecular pump system and results were reasonable and good.

Keywords

Linear Matrix Inequality Slide Mode Control Sliding Mode Gain Schedule Unbalance Mass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V.I., Utkin, “Sliding Modes in Control Optimization,” Springer-Verlag, 1992.Google Scholar
  2. 2.
    K. Nonami, H. Tian, “Sliding Mode Control,” Corona Publication, 1994(in Japanese).Google Scholar
  3. 3.
    K.D. Young, V.I., Utkin, U. Ozguner, “A Control Engineer's Guide to Sliding Mode Control” Procs. IEEE International Workshop on VSS, p.1–14, Tokyo, 1996.Google Scholar
  4. 4.
    K. J. Astrom and B. Wittenmark, “Adaptive Control,” Reading, MA: Addison-Weslay, 1989.Google Scholar
  5. 5.
    H.K Khalil, “Nonlinear Systems,” Second Edition, Prentice Hall, 1997.Google Scholar
  6. 6.
    J. Shamma and M. Athans, “Guaranteed properties of gain scheduled control of linear parameter-varying plants,” Automatica, vol.27, no.3, pp.559–564, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    P. Apkarian, P. Gahinet, “A Convex Characterization of Gain Scheduled H Controllers,” IEEE. Trans. on Automatic Control, vol.40, pp.853–863, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    P. Apkarian, P. Gahinet, G. Becker, “Self-scheduled H Control of Linear Parameter-varying Systems: a Design Example,” Automatica, vol.31-9, pp.1251–1261, 1995.CrossRefMathSciNetGoogle Scholar
  9. 9.
    S. Boyd, L. E. Ghaoui, E. Feron, V. Balakrishnan, “Linear Matrix Inequalities in System and Control Theory,” SIAM Publication, 1994.Google Scholar
  10. 10.
    P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, “LMI Control Toolbox, For Use with MATLAB,” Mathworks, 1995.Google Scholar
  11. 11.
    D. Young, U. Ozguner, “Frequency Shaping Compensator Design for Sliding Mode Control,” Int. J. Control, vol.57, No.5, pp.1005, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    K. Nonami, H. Nishimura, H. Tian, “H /μ Control-based Frequency-shaped Sliding Mode Control for Flexible Structures,” JSME International Journal, Series C, vol.39, No.3, pp. 493–501, 1996.Google Scholar
  13. 13.
    P. Gahinet, P. Apkarian, M. Chilali, “Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty,” IEEE. Trans. on Automatic Control, vol.41, pp.436–442, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    G. Schweitzer, H. Bleuler, A. Traxler, “Active Magnetic Bearings,” vdf Hochschuverlag AG an der ETH Zurich, 1994.Google Scholar
  15. 15.
    K. Nonami, H. Ueyama and Y. Segawa, “H Control of Milling AMB Spindle,” JSME International Journal, vol.39, no.3, pp.502–508, 1996.Google Scholar
  16. 16.
    K. Nonami, T. Ito, “μ Synthesis of Flexible Rotor Bearing Systems,” IEEE. Trans. on Control Systems Technology, vol.4, No.5, pp.503–512, 1996.CrossRefGoogle Scholar
  17. 17.
    S. Sivrioglu, K. Nonami, “LMI Approach to Gain Scheduled H Control Beyond PID Control for Gyroscopic Rotor-Magnetic Bearing System,” Proc. of the 35th CDC, pp.3694–3699, 1996.Google Scholar
  18. 18.
    J.C. Doyle, B.A. Francis, A.R. Tannenbaum, “Feedback Control Theory,” Macmillan Publishing Company, 1992.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Kenzo Nonami
    • 1
  • Selim Sivrioglu
    • 1
  1. 1.Department of Electronics and Mechanical EngineeringChiba UniversityChibaJapan

Personalised recommendations