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Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems

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Abstract

A new extension of the conventional adaptive fuzzy sliding mode control (AFSMC) scheme, for the case of under-actuated and uncertain affine multiple-input multiple-output (MIMO) systems, is presented. In particular, the assumption for non-zero diagonal entries of the input gain matrix of the plant is relaxed. In other words, the control effect of one actuator can propagate from a subgroup of canonical state equations to the rest of equations in an indirect sense. The asymptotic stability of the proposed AFSM control method is proved using a Lyapunov-based methodology. The effectiveness of the proposed method for the case of under-actuated systems is investigated in the presence of plant uncertainties and disturbances, through simulation studies.

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References

  1. H. G. Zhang, L. L. Cui, X. Zhang, Y. H. Luo. Data-driven robust approximate optimal tracking control for unknown general nonlinear systems using adaptive dynamic programming method. IEEE Transactions on Neural Networks, vol. 22, no. 12, pp. 2226–2236, 2011. DOI: 10.1109/TNN.2011.2168538.

    Article  Google Scholar 

  2. Y. P, Pan, J. Wang. Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Transactions on Industrial Electronics, vol. 59, no. 8, pp. 3089–3101, 2012. DOI: 10.1109/TIE.2011.2169636.

    Article  MathSciNet  Google Scholar 

  3. J. J. E. Slotine, W. P. Li. Applied Nonlinear Control, New Jersey: Prentice-Hall, 1991.

    MATH  Google Scholar 

  4. H. K. Khalil, Nonlinear Systems, 3rd ed., New Jersey, USA: Prentice-Hall, 2002.

    MATH  Google Scholar 

  5. A. Abrishamifar, A. Ahmad, M. Mobamadian. Fixed switching frequency sliding mode control for single-phase unipolar inverters. IEEE Transactions on Power Electronics, vol. 27, no. 5, pp. 2507–2514, 2012. DOI: 10.1109/TPEL.2011.2175249.

    Article  Google Scholar 

  6. T. Takagi, M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-15, no. 1, pp. 116–132, 1985. DOI: 10.1109/TSMC.1985.6313399.

    Article  MATH  Google Scholar 

  7. Y. C. Hsu, H. A. Malki. Fuzzy variable structure control for MIMO systems. In Proceedings of IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence, IEEE, Anchorage, AK, USA, pp. 280–285, 1998.

    Google Scholar 

  8. D. Pelusi. Optimization of a fuzzy logic controller using genetic algorithms. In Proceedings of IEEE International Conference on Intelligent Human-machine Systems and Cybernetics, IEEE, Zhejiang, China, pp. 143–146, 2011.

    Google Scholar 

  9. S. Kundu, D. R. Parhi. Reactive navigation of underwater mobile robot using ANFIS approach in a manifold manner. International Journal of Automation and Computing, vol. 14, no. 3, pp. 307–320, 2017. DOI: 10.1007/s11633-016-0983-5.

    Article  Google Scholar 

  10. A. Ishigame, T. Furukawa, S. Kawamoto, T. Taniguchi. Sliding mode controller design based on fuzzy inference for non-linear systems. In Proceedings of International Conference on Industrial Electronics, Control and Instrumentation, IEEE, Kobe, Japan, pp. 64–70, 1993.

    Google Scholar 

  11. M. Roopaei, M. Zolghadri Jahromi. Chattering-free fuzzy sliding mode control in MIMO uncertain systems. Nonlinear Analysis, vol. 71, no. 10, pp. 4430–4437, 2009. DOI: 10.1016/j.na.2009.02.132.

    Article  MathSciNet  MATH  Google Scholar 

  12. C. M. Lin, T. Y. Chen, W. Z. Fan, Y. F. Lee. Adaptive fuzzy sliding mode control for a two-link robot. In Proceedings of IEEE International Conference on Robotics and Biomimetics, IEEE, Shatin, China, pp. 581–586, 2005.

    Google Scholar 

  13. A. Poursamad, A. H. D. Markazi. Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems. Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 3100–3109, 2009. DOI: 10.1016/j.chaos.2009.04.044.

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Qiao, Q. M. Zhu, A. F. T. Winfield, C. Melhuish. Adaptive sliding mode control for MIMO nonlinear systems based on fuzzy logic scheme. International Journal of Automation and Computing, vol. 1, no. 1, pp. 51–62, 2004. DOI: 10.1007/s11633-004-0051-4.

    Article  Google Scholar 

  15. W. S. Lin, C. S. Chen. Robust adaptive sliding mode control using fuzzy modelling for a class of uncertain MIMO nonlinear systems. IEEE Proceedings–Control Theory and Applications, vol. 149, no. 3, pp. 193–202, 2002. DOI: 10.1049/ip-cta:20020236.

    Article  MathSciNet  Google Scholar 

  16. M. Khazaee, A. H. D. Markazi, S. T. Rizi, B. Seyfi. Adaptive fuzzy sliding mode control of input-delayed uncertain nonlinear systems through output-feedback. Nonlinear Dynamics, vol. 87, no. 3, pp. 1943–1956, 2017. DOI: 10.1007/s11071-016-3164-8.

    Article  MATH  Google Scholar 

  17. M. Benbrahim, N. Essounbouli, A. Hamzaoui, A. Betta. Adaptive type-2 fuzzy sliding mode controller for SISO nonlinear systems subject to actuator faults. International Journal of Automation and Computing, vol. 10, no. 4, pp. 335–342, 2013. DOI: 10.1007/s11633-013-0729-6.

    Article  Google Scholar 

  18. S. Moussaoui, A. Boulkroune. Stable adaptive fuzzy sliding-mode controller for a class of underactuated dynamic systems. Recent Advances in Electrical Engineering and Control Applications, M. Chadli, S. Bououden, I. Zelinka, Eds., Cham: Springer, 2017.

    Google Scholar 

  19. H. S. Haghighi, A. H. D. Markazi. Chaos prediction and control in MEMS resonators. Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 3091–3099, 2010. DOI: 10.1016/j.cnsns.2009.10.002.

    Article  Google Scholar 

  20. Y. T. Bai, P. Li. Adaptive fuzzy sliding mode control for electro-hydraulic position servo system. In Proceedings of Chinese Control and Decision Conference, IEEE, Xuzhou, China, pp. 3249–3253, 2010.

    Google Scholar 

  21. J. F. Wang, C. G. Wang, B. Feng, Y. X. Sun, J. Liu. Robust adaptive fuzzy sliding mode control of PM synchronous servo motor. In Proceedings of Chinese Control and Decision Conference, IEEE, Xuzhou, China, pp. 3419–3422, 2010.

    Google Scholar 

  22. S. M. Liu, L. Ding. Application of adaptive fuzzy sliding mode controller in PMSM servo system. In Proceedings of International Conference on Computing, Control and Industrial Engineering, IEEE, Wuhan, China, pp. 95–98, 2010.

    Google Scholar 

  23. A. Poursamad, A. H. Davaie-Markazi. Robust adaptive fuzzy control of unknown chaotic systems. Applied Soft Computing, vol. 9, no. 3, pp. 970–976, 2009. DOI: 10.1016/j.asoc.2008.11.014.

    Article  Google Scholar 

  24. T. Prestero. Verification of a Six-degree of Freedom Simulation Model for the REMUS Autonomous Underwater vehicle, Master dissertation, University of California, USA, 2001.

    Book  Google Scholar 

  25. D. P. Brutzman. A Virtual World for an Autonomous Underwater Vehicle, Ph. D. Dissertation, Naval Postgraduate School, USA, 1994.

    Google Scholar 

  26. T. I. Fossen. Guidance and Control of Ocean Vehicles, Chichester, UK: John Wiley and Sons, 1994.

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

    Amir Hossein Davaie Markazi, Mohammad Maadani, Seyed Hassan Zabihifar & Nafiseh Doost-Mohammadi

Authors
  1. Amir Hossein Davaie Markazi
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  2. Mohammad Maadani
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  3. Seyed Hassan Zabihifar
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  4. Nafiseh Doost-Mohammadi
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Corresponding author

Correspondence to Seyed Hassan Zabihifar.

Additional information

Recommended by Associate Editor Chandrasekhar Kambhampati

Amir Hossein Davaie Markazi received the Ph.D. degree in mechanical engineering from Mechanical Engineering Department, McGill university, Canada in 1995. He is a professor at Iran University of Since and Technology Iran. He is the Editor-in-Chief of International Journal of Engineering Science.

His research interests include adaptive fuzzy siding mode control (AFSMC), control of chaotic systems, control of parallel robots, networked control systems and wavelet pattern recognition.

Mohammad Maadani received the B. Sc. degree in mechanical engineering from Amirkabir University of Technology (Tehran Polytechnic), Iran in 2009, the M. Sc. degree in mechanical engineering from Iran University of Science and Technology, Iran in 2011.

His research interests include adaptive control, nonlinear dynamics and control.

Seyed Hassan Zabihifar received the B. Sc. and M. Sc. degrees in mechanical engineering and mechatronic respectively from Iran University of Since and Technology, Iran in 2012. He is currently a Ph.D. degree candidate in mechatronic and robotic systems in Bauman Moscow State Technical University (BMSTU), Russia.

His research interests include nonlinear control, adaptive fuzzy sliding mode, adaptive neural network, and optimal control.

Nafise Doost-Mohammadi received the M. Sc. degree in mechanical engineering from Iran University of Since and Technology, Iran in 2011.

Her research interests include nonlinear control, adaptive fuzzy sliding mode and fuzzy control systems.

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Markazi, A.H.D., Maadani, M., Zabihifar, S.H. et al. Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems. Int. J. Autom. Comput. 15, 364–376 (2018). https://doi.org/10.1007/s11633-017-1108-5

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  • DOI: https://doi.org/10.1007/s11633-017-1108-5

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