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Sliding Mode Control with Adaptive Fuzzy Immune Feedback Reaching Law

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  • Control Theory and Applications
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Abstract

In this paper, a novel adaptive fuzzy immune feedback reaching law (AFIFRL) based sliding mode control (SMC) strategy is proposed for uncertain nonlinear systems with time-varying disturbances. First, a nonlinear immune feedback reaching law (IFRL) inspired by biological immune feedback regulation mechanism is designed to alleviate chattering effect without losing the robustness against disturbances. Second, an improved IFRL is developed in a thin boundary layer to enhance tracking performance. Then, the applied fuzzy controller adjusts the boundary layer online to further improve control performance despite large system uncertainties and disturbances. Furthermore, an adaptive law is employed to estimate the unknown bound of uncertainties, which can effectively attenuate chattering and minimize control effort. The stability analysis is derived by Lyapunov stability theorem. Finally, numerical simulations are conducted to evidence the effectiveness and superiority of the proposed AFIFRL based SMC scheme.

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References

  1. V. I. Utkin, “Sliding mode control design principles and applications to electric drives,” IEEE Trans, on Industrial Electronics, vol. 40, no. 1, pp. 23–36, February 1993.

    Google Scholar 

  2. L. Li, L. Sun, S. Zhang, and Q. Yang, “Speed tracking and synchronization of multiple motors using ring coupling control and adaptive sliding mode control,” ISA Transactions, vol. 58, pp. 635–649, September 2015.

    Google Scholar 

  3. A. Saghaflnia, H. W. Ping, M. N. Uddin, and K. S. Gaeid, “Adaptive fuzzy sliding-mode control into chattering-free IM drive,” IEEE Trans, on Industry Applications, vol. 51, no. 1, pp. 692–701, January 2015.

    Google Scholar 

  4. A. Benamor and H. Messaoud, “Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input,” ISA Transactions, vol. 79, pp. 1–12, August 2018.

    Google Scholar 

  5. K. Erbatur and O. Kaynak, “Use of adaptive fuzzy systems in parameter tuning of sliding-mode controllers,” IEEE/ASME Trans, on Mechatronics, vol. 6, no. 4, pp. 474–482, December 2011.

    Google Scholar 

  6. F. Cupertino, D. Naso, E. Mininno, and B. Turchiano, “Sliding-mode control with double boundary layer for robust compensation of payload mass and friction in linear motors,” IEEE Trans, on Industry Applications, vol. 45, no. 5, pp. 1688–1696, September 2009.

    Google Scholar 

  7. W. Sun, S. F. Su, G. Dong, and W. Bai, “Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints,” IEEE Trans, on Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2019.2898204

    Google Scholar 

  8. W. Sun, S. F. Su, Y. Wu, J. Xia, and V. T. Nguyen, “Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints,” IEEE Trans, on Cybernetics, 2019. DOI: 10.1109/TCYB.2018.2890256

    Google Scholar 

  9. R. Shahnazi, H. M. Shanechi, and N. Pariz, “Position control of induction and DC servomotors: A novel adaptive fuzzy PI sliding mode control,” IEEE Trans, on Energy Conversion, vol. 23, no. 1, pp. 138–147, March 2008.

    Google Scholar 

  10. R. J. Wai and K. H. Su, “Adaptive enhanced fuzzy sliding-mode control for electrical servo drive,” IEEE Trans, on Industrial Electronics, vol. 53, no. 2, pp. 569–580, April 2006.

    Google Scholar 

  11. O. Barambones and P. Alkorta, “Position control of the induction motor using an adaptive sliding-mode controller and observers,” IEEE Trans, on Industrial Electronics, vol. 61, no. 12, pp. 6556–6565, December 2014.

    Google Scholar 

  12. T. X. Dinh and K. K. Ahn, “Radial basis function neural network based adaptive fast nonsingular terminal sliding mode controller for piezo positioning stage,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2892–2905, December 2017.

    Google Scholar 

  13. S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, November 2005.

    MathSciNet  MATH  Google Scholar 

  14. R. Ma, G. Zhang, and O. Krause, “Fast terminal sliding-mode finitetime tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems,” International Journal of Robust and Nonlinear Control, vol. 28, no. 2, pp. 625–639, January 2018.

    MathSciNet  MATH  Google Scholar 

  15. X. Liu, S. Qi, R. Malekain, and Z. Li, “Observer-based composite adaptive dynamic terminal sliding-mode controller for nonlinear uncertain SISO systems,” International Journal of Control, Automation and Systems, vol. 17, no. 1, pp. 94–106, January 2019.

    Google Scholar 

  16. F. Hamerlain, K. Achour, T. Floquet, and W. Perruquetti, “Trajectory tracking of a car-like robot using second order sliding mode control,” Proc. of European Control Conference, IEEE, Kos, pp. 4932–4936, July 2007.

    Google Scholar 

  17. G. Bartolini, A. Ferrara, E. Usai, and V. I. Utkin, “On multi-input chattering-free second-order sliding mode control,” IEEE Trans, on Automatic Control, vol. 45, no. 9, pp. 1711–1717, September 2000.

    MathSciNet  MATH  Google Scholar 

  18. L. Li, L. Sun, and S. Zhang, “Mean deviation coupling synchronous control for multiple motors via second-order adaptive sliding mode control,” ISA Transactions, vol. 62, pp. 222–235, May 2016.

    Google Scholar 

  19. J. Yang, S. Li, J. Su, and X. Yu, “Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances,” Automatica, vol. 49, no. 7, pp. 2287–2291, July 2013.

    MathSciNet  MATH  Google Scholar 

  20. J. Yang, S. Li, and X. Yu, “Sliding-mode control for systems with mismatched uncertainties via a disturbance observer,” IEEE Trans, on Industrial Electronics, vol. 60, no. 1, pp. 160–169, January 2013.

    Google Scholar 

  21. L. Tao, Q. Chen, and Y. Nan, “Disturbance-observer based adaptive control for second-order nonlinear systems using chattering-free reaching law,” International Journal of Control, Automation and Systems, vol. 17, no. 2, pp. 356–369, February 2019.

    Google Scholar 

  22. N. Adhikary and C. Mahanta, “Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the cartpendulum system,” ISA Transactions, vol. 52, no. 6, pp. 870–880, November 2013.

    Google Scholar 

  23. R. J. Wai, “Fuzzy sliding-mode control using adaptive tuning technique,” IEEE Trans, on Industrial Electronics, vol. 54, no. 1, pp. 586–594, February 2007.

    Google Scholar 

  24. H. T. Yau and C. L. Chen, “Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems,” Chaos, Solitons and Fractals, vol. 30, no. 3, pp. 709–718, November 2006.

    Google Scholar 

  25. A. Saghaflnia, H. W. Ping, and M. N. Uddin, “Fuzzy sliding mode control based on boundary layer theory for chattering-free and robust induction motor drive,” International Journal of Advanced Manufacturing Technology, vol. 71, no. 1–4, pp. 57–68, March 2014.

    Google Scholar 

  26. S. J. Huang and W. C. Lin, “Adaptive fuzzy controller with sliding surface for vehicle suspension control,” IEEE Trans, on Fuzzy Systems, vol. 11, no. 4, pp. 550–559, August 2003.

    Google Scholar 

  27. S. J. Huang, K. S. Huang, and K. C. Chiou, “Development and application of a novel radial basis function sliding mode controller,” Mechatronics, vol. 13, no. 4, pp. 313–329, May 2003.

    Google Scholar 

  28. K. H. Cheng, C. F. Hsu, C. M. Lin, T. T. Lee, and C. Li, “Fuzzyneural sliding-mode control for DC-DC converters using asymmetric gaussian membership functions,” IEEE Trans, on Industrial Electronics, vol. 54, no. 3, pp. 1528–1536, June 2007.

    Google Scholar 

  29. D. Dasgupta, “Advances in artificial immune systems,” IEEE Computational Intelligence Magazine, vol. 1, no. 4, pp. 40–49, November 2006.

    Google Scholar 

  30. D. Dasgupta, “An overview of artificial immune systems and their applications,” Artificial Immune Systems and Their Applications, Springer, Berlin, Heidelberg, 1993, pp. 3–21.

    MATH  Google Scholar 

  31. L. N. D. Castro and J. Timmis, Artificial Immune Systems: A New Computational Intelligence Approach, Springer Science and Business Media, 2002.

    MATH  Google Scholar 

  32. D. Dasgupta, S. H. Yu, and F. Nino, “Recent advances in artificial immune systems: models and applications,” Applied Soft Computing, vol. 11, no. 2, pp. 1574–1587, March 2011.

    Google Scholar 

  33. G. C. Silva, W. M. Caminhas, and R. M. Palhares, “Artificial immune systems applied to fault detection and isolation: a brief review of immune response-based approaches and a case study,” Applied Soft Computing, vol. 57, pp. 118131, August 2017.

    Google Scholar 

  34. D. A. B. Fernandes, M. M. Freire, P. A. P. Fazendeiro, and P. R. M. Inacio, “Applications of artificial immune systems to computer security: a survey,” Journal of Information Security and Applications, vol. 35, pp. 138–159, August 2017.

    Google Scholar 

  35. C. C. Wu and B. S. Chen, “Key immune events of the pathomechanisms of early cardioembolic stroke: multi-database mining and systems biology approach,” International Journal of Molecular Sciences, vol. 17, no. 3, March 2016.

    Google Scholar 

  36. X. Li, J. Liu, and L. Yang, “Sliding mode control of grid chaotic oscillation based on immune algorithm,” Applied Mathematics and Information Sciences, vol. 8, no. 4, pp. 1967–1971, July 2014.

    Google Scholar 

  37. H. N. Esfahani, V. Azimirad, A. Eslami, and S. Asadi, “An optimal sliding mode control based on immune-wavelet algorithm for underwater robotic manipulator,” Proc. of 21st Iranian Conference on Electrical Engineering (ICEE), IEEE, Mashhad, pp. 1–6, May 2013.

    Google Scholar 

  38. R. R. Sumar, A. A. Rodrigues Coelho, and L. S. Coelho, “Use of an artificial immune network optimization approach to tune the parameters of a discrete variable structure controller,” Expert Systems with Applications, vol. 36, no. 3, pp. 5009–5015, April 2009.

    Google Scholar 

  39. W. Gao and J. C. Hung, “Variable structure control of nonlinear systems: a new approach,” IEEE Trans, on Industrial Electronics, vol. 40, no. 1, pp. 45–55, February 1993.

    Google Scholar 

  40. H. Du, X. Yu, M. Z. Q. Chen, and S. Li, “Chattering-free discrete-time sliding mode control,” Automatica, vol. 68, pp. 87–91, June 2016.

    MathSciNet  MATH  Google Scholar 

  41. C. Xiu and P. Guo, “Global terminal sliding mode control with the quick reaching law and its application,” IEEE Access, vol. 6, pp. 49793–49800, 2018.

    Google Scholar 

  42. S. Lin and W. Zhang, “Chattering reduced sliding mode control for a class of chaotic systems,” Nonlinear Dynamics, vol. 93, no. 4, pp. 2273–2282, September 2018.

    MATH  Google Scholar 

  43. Y. Chen, Y. Wei, and Y. Wang, “On 2 types of robust reaching laws,” International Journal of Robust and Nonlinear Control, vol. 28, no. 6, pp. 2651–2667, April 2018.

    MathSciNet  MATH  Google Scholar 

  44. Z. Yang, D. Zhang, X. Sun, and X. Ye, “Adaptive exponential sliding mode control for a bearingless induction motor based on a disturbance observer,” IEEE Access, vol. 6, pp. 35425–35434, 2018.

    Google Scholar 

  45. C. J. Fallaha, M. Saad, H. Y. Kanaan, and K. Al-Haddad, “Sliding-mode robot control with exponential reaching law,” IEEE Trans, on Industrial Electronics, vol. 58, no. 2, pp. 600–610, February 2011.

    Google Scholar 

  46. L. Xiong, P. Li, H. Li, and J. Wang, “Sliding mode control of DFIG wind turbines with a fast exponential reaching law,” Energies, vol. 10, no. 11, November 2017.

    Google Scholar 

  47. Y. Liu, Z. Wang, L. Xiong, J. Wang, X. Jiang, G. Bai, et al, “DFIG wind turbine sliding mode control with exponential reaching law under variable wind speed,” International Journal of Electrical Power and Energy Systems, vol. 96, pp. 253–260, March 2018.

    Google Scholar 

  48. S. M. Mozayan, M. Saad, H. Vahedi, H. Firtin-Blanchette, and M. Soltani, “Sliding mode control of PMSG wind turbine based on enhanced exponential reaching law,” IEEE Trans, on Industrial Electronics, vol. 63, no. 10, pp. 6148–6159, October 2016.

    Google Scholar 

  49. L. Tao, Q. Chen, Y. Nan, and C. Wu, “Double hyperbolic reaching law with chattering-free and fast convergence,” IEEE Access, vol. 6, pp. 27717–27725, 2018.

    Google Scholar 

  50. J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Hoboken, NJ, 1991.

    MATH  Google Scholar 

  51. A. Leibowitz and E. L. Schiffrin, “Immune mechanisms in hypertension,” Current Hypertension Reports, vol. 13, no. 6, pp. 465–472, December 2011.

    Google Scholar 

  52. K. Erbatur and B. Calli, “Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot,” Soft Computing, vol. 13, no. 11, pp. 1099–1111, September 2009.

    MATH  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, China

    Chenchen Sun, Guofang Gong & Huayong Yang

Authors
  1. Chenchen Sun
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  2. Guofang Gong
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Correspondence to Guofang Gong.

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Recommended by Associate Editor Hongyi Li under the direction of Editor Euntai Kim. This work is supported by the National Key R&D Program of China [No. 2017YFB1302604 and 2017YFB1302602]; the National Basic Research Program (973 Program) of China [No. 2013CB035400]; the National High Technology Research and Development Program (863 Program) of China [No. 2012AA041803]

Chenchen Sun received her M.S. degree in mechatronic engineering from Zhejiang Sci-Tech University, Hangzhou, China, in 2010. She is currently working toward a Ph.D. degree at Zhejiang University, Hangzhou, China. Her current research interests include electro-hydraulic driving system of tunneling boring machines, synchronous control, and mechatronic systems design.

Huayong Yang received his Ph.D. degree in Philosophy from the University of Bath, Bath, U.K., in 1988. He is currently the “Cheung Kong Scholar” Chair Professor at Zhejiang University, Hangzhou, China. From 1997 to 2001, he was the Director of the State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University. Since 2000, he has been the Director of the National Engineering Research Center of Electrohydraulic Control, Zhejiang University. He is the Editor of the Chinese Journal of Mechanical Engineering. His current research interests include motion control and energy saving of mechatronic systems, micro-fluidic devices and systems, and R&D of fluid power components. Prof. Yang is a Fellow of the Chinese Mechanical Engineering Society. He is the recipient of the National Scientific and Technological Progress Prize (first class) and National Scientific and Technological Progress Prize (second class). He has also received the National Outstanding Researcher of the Natural Science Foundation of China Award.

Guofang Gong received his Ph.D. degree in mechanical engineering from China University of Mining and Technology, Beijing, China, in 2000. Prof. Gong is a Doctoral Tutor at the Institute of Mechatronics and Control Engineering, Zhejiang University. He has implemented 1 project from National Natural Science Foundation, 1 project from National Technology Support Project, and 3 projects from 863 Hi-tech Project. He has authored or coauthored more than 100 journal and conference papers. His current research interests include design and analysis of electro-hydraulic control systems, hydraulic brake, and slurry shield.

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Sun, C., Gong, G. & Yang, H. Sliding Mode Control with Adaptive Fuzzy Immune Feedback Reaching Law. Int. J. Control Autom. Syst. 18, 363–373 (2020). https://doi.org/10.1007/s12555-019-0285-0

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