HIGHER ORDER SLIDING MODE CONTROL FOR CONTINUOUS TIME NONLINEAR SYSTEMS BASED ON OPTIMAL CONTROL

Zhiyu Xi, Tim Hesketh

Abstract

This paper addresses higher order sliding mode control for continuous nonlinear systems. We propose a new method of reaching control design while the sliding surface and equivalent control can be designed conventionally. The deviations of the sliding variable and its high order derivatives from zero are penalized. This is realized by minimizing the amplitudes of the higher order derivatives of the sliding variable. An illustrative example— a field-controlled DC motor— is given at the end.

References

  1. Vadim I. Utkin (1992). Sliding Modes in Control and Optimization. Springer-Verlag New York, Inc.
  2. Vadim I. Utkin (1977). Variable Structure Systems with Sliding Modes. IEEE Transactions on Automatic Control, Volume AC-22, No. 2, April.
  3. S. V. Emeryanov, S. K. Korovin, and A. Levant (1996). Higher-order Sliding Modes in Control Systems. Computational Mathematics and Modeling, Vol. 7, No. 3.
  4. A. Levant (2007). Principles of 2-sliding mode design. Automatica Vol. 43, pp. 576 - 586.
  5. S. Laghrouche, F. Plestan, and A. Glumineau (2005). Multivariable practical higher order sliding mode control. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference.
  6. A.J. Koshkouei, K.J. Burnham and A.S.I. Zinober. Dynamic sliding mode control design. IEE Proceedings online no. 20055133.
  7. I. Boiko, L. Fridman, and I. M. Castellanos (2004). Analysis of second-order sliding-mode algorithms in the frequency domain. IEEE Transaction on Automatic Control, Vol. 49, No. 6, pp. 946-950, Jun.
  8. Vadim Utkin and Jingxin Shi(1996). Integral Sliding Mode in Systems Operating under Uncertainty Conditions. Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, December.
  9. S. K. Spurgeon (2004). Temperature Control of Industrial Process using a Variable Structure Design Philosophy. Transactions of the Institute of Measurement and Control
  10. R. R. Bitmead, M. Gevers, and V. Wertz (1990). Adaptive Optimal Control: The Thinking Man's GPC. Englewood Cliffs, NJ: Prentice-Hall.
  11. Raymond, A. DeCarlo, Stanislaw H. Zak, Gregory P. Matthews(1988). Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial. Proceedings of The IEEE, Vol. 76, No. 3, March.
  12. Christopher Edwards and Sarah K. Spurgeon (1998). Sliding Mode Control, Theory And Applications. CRC Press, Taylor & Francis Group.
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Paper Citation


in Harvard Style

Xi Z. and Hesketh T. (2009). HIGHER ORDER SLIDING MODE CONTROL FOR CONTINUOUS TIME NONLINEAR SYSTEMS BASED ON OPTIMAL CONTROL . In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-674-001-6, pages 54-59. DOI: 10.5220/0002168100540059


in Bibtex Style

@conference{icinco09,
author={Zhiyu Xi and Tim Hesketh},
title={HIGHER ORDER SLIDING MODE CONTROL FOR CONTINUOUS TIME NONLINEAR SYSTEMS BASED ON OPTIMAL CONTROL},
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2009},
pages={54-59},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002168100540059},
isbn={978-989-674-001-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - HIGHER ORDER SLIDING MODE CONTROL FOR CONTINUOUS TIME NONLINEAR SYSTEMS BASED ON OPTIMAL CONTROL
SN - 978-989-674-001-6
AU - Xi Z.
AU - Hesketh T.
PY - 2009
SP - 54
EP - 59
DO - 10.5220/0002168100540059