State feedback sliding mode control without chattering by constructing Hurwitz matrix for AUV movement

  • Huan-Yin ZhouEmail author
  • Kai-Zhou Liu
  • Xi-Sheng Feng


This paper presents a new method to eliminate the chattering of state feedback sliding mode control (SMC) law for the mobile control of an autonomous underwater vehicle (AUV) which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by Lyapunov function and the robust character is validated by the Matlab platform of one AUV model.


Autonomous underwater vehicle (AUV) state feedback sliding mode control (SMC) switching manifold Hurwitz matrix Matlab platform Lyapunov function 


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  1. [1]
    T. I. Fossen. Guidance and Control of Ocean Vehicles, USA: John Wiley and Sons, 1994.Google Scholar
  2. [2]
    M. Wang, B. Chen, X. P. Liu, P. Shi. Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems. Fuzzy Sets and Systems, vol. 159, no. 8, pp. 949–967, 2008.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    S. Y. Liu, D. W. Wang, E. Poh. Output feedback control design for station keeping of AUVs under shallow water wave disturbances. International Journal of Robust and Nonlinear Control, vol. 19, no. 13, pp. 1447–1470, 2009.MathSciNetCrossRefGoogle Scholar
  4. [4]
    W. M. Bessa, M. S. Dutra, E. Kreuzer. Depth control of remotely operated underwater vehicles using an adaptive fuzzy sliding mode controller. Robotics and Autonomous Systems, vol. 56, no. 8, pp. 670–677, 2008.CrossRefGoogle Scholar
  5. [5]
    W. M. Bessa, M. S. Dutra, E. Kreuzer. An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles. Robotics and Autonomous Systems, vol. 58, no. 1, pp. 16–26, 2010.CrossRefGoogle Scholar
  6. [6]
    Y. F. Peng. Robust intelligent sliding mode control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems. Chaos, Solitons & Fractals, vol. 39, no. 1, pp. 150–167, 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Y. Zheng, G. M. Dimirovski, Y. W. Jing, M. Y. Yang. Discrete-time sliding mode control of nonlinear systems. In Proceedings of American Control Conference, IEEE, New York, USA, pp. 3825–3830, 2007.CrossRefGoogle Scholar
  8. [8]
    I. Masahiro, T. Nobutaka, K. Takayuki. Adaptive force control for unknown environment using sliding mode controller with variable hyperplane. JSME International Journal, Series C, vol. 46, no. 3, pp. 967–972, 2003.CrossRefGoogle Scholar
  9. [9]
    J. Fei. Model reference adaptive sliding mode control for a flexible beam. Advances in Modeling and Analysis C, vol. 62, no. 1–2, pp. 84–97, 2007.Google Scholar
  10. [10]
    H. K. Lam, F. H. F. Leung. Fuzzy rule-based combination of linear and switching state-feedback controllers. Fuzzy Sets and Systems, vol. 156, no. 2, pp. 153–184, 2005.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    X. Y. Luo, Z. H. Zhu, X. P. Guan. Chattering reduction adaptive sliding-mode control for nonlinear time-delay systems. Control and Decision, vol. 24, no. 9, pp. 1429–1435, 2009. (in Chinese)Google Scholar
  12. [12]
    T. S. Jimnez, J. M. Spiewak, P. Froisse, B. Jouvencel. A robust control algorithm for AUV: Based on a high order sliding mode. In Proceedings of Ocean_04: Bridges Across the Oceans, IEEE, vol. 1, pp. 276–281, 2004.Google Scholar
  13. [13]
    M. S. Mahmoud. State-feedback stabilization of linear systems with input and state delays. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 223, no. 4, pp. 557–565, 2009.CrossRefGoogle Scholar
  14. [14]
    M. Wu, Y. H. Lan, J. H. She, Y. He. H state feedback robust repetitive control for uncertain linear systems. Control Theory and Applications, vol. 25, no. 3, pp. 427–433, 2008. (in Chinese)zbMATHCrossRefGoogle Scholar
  15. [15]
    J. M. Daly, D. W. L. Wang. Output feedback sliding mode control in the presence of unknown disturbances. Systems and Control Letters, vol. 58, no. 3, pp. 188–193, 2009.MathSciNetzbMATHCrossRefGoogle Scholar
  16. [16]
    C. Z. Huang, Y. Bai, X. J. Liu. H state feedback control for a class of networked cascade control systems with uncertain delay. IEEE Transactions on Industrial Informatics, vol. 6, no. 1, pp. 62–72, 2010.CrossRefGoogle Scholar
  17. [17]
    H. B. Ma, Q. Y. Feng. Fixed-frequency PWM sliding-mode control of buck switching converter based on precise feedback linearization. Electric Power Automation Equipment, vol. 29, no. 8, pp. 28–32, 2009. (in Chinese)MathSciNetGoogle Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.State Key Laboratory of Robotics, Shenyang Institute of AutomationChinese Academy of SciencesShenyangPRC
  2. 2.School of ElectricEast China Institute of TechnologyFuzhouPRC
  3. 3.Graduate School of the Chinese Academy of SciencesBeijingRRC

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