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SD-TCSs Control Deriving from Fractional-order Sliding Mode and Fuzzy-compensator

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  • Intelligent Control and Applications
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Abstract

Uncertainty and disturbance (UAD) always exist and influence negatively on technical systems. Focusing on improving the effectiveness of smart dampers (SDs)-based semi-active train-car suspensions (SD-TCSs), we present the fuzzy-compensator-enhanced fractional-derivative (FD) order sliding control of a class of SD-TCSs subjected to UAD, in which the disturbance time-varying rate (DTVR) may be high but bounded. To reduce uncertainty related to the mathematical model error, we propose a fractional derivative (FD)-based sliding mode controller (FDSMC) for specifying the main control signal. Whereas, to estimate the compensation for external disturbance, first, we utilize the well-known DO to build an initial framework of the compensator. To avoid conflict between the update-laws of the DO and FDSMC, as well as to make the system dynamic response converge stably to the desired state even if the DTVR increasing but bounded, constraints along with a fuzzy-based adjusting mechanism are then discovered. Thus, we obtain an improved DO (imDO), update-laws of the imDO and FDSMC, and their combination model (imDO-FDSMC) of the proposed controller. The survey results reflect the positive capability of the method.

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References

  1. S. D. Nguyen, W. H. Kim, J. H. Park, and S. B. Choi, “A new fuzzy sliding mode controller for vibration control systems using integrated-structure smart dampers,” Smart Materials and Structures, vol. 26, pp. 1–16, 2017.

    Article  Google Scholar 

  2. S. D. Nguyen, S. B. Choi, and T. I. Seo, “Adaptive fuzzy sliding control enhanced by compensation for explicitly unidentified aspects,” International Journal of Control, Automation, and Systems, vol. 15, pp. 2906–2920, 2017.

    Article  Google Scholar 

  3. Y. Qin, F. Zhao, Z. Wang, L. Gu, and M. Dong, “Comprehensive analysis for influence of controllable damper time delay on semi-active suspension control strategies,” Journal of Vibration and Acoustics, vol. 139, no. 3, p. 031006, 2017.

    Article  Google Scholar 

  4. S. D. Nguyen and T. I. Seo, “Establishing ANFIS and the use for predicting sliding control of active railway suspension systems subjected to uncertainties and disturbances,” International Journal of Machine Learning and Cybernetics, vol. 9, no. 5, pp. 853–865, 2016.

    Article  Google Scholar 

  5. W. H. Chen, “Nonlinear disturbance observer-enhanced dynamic inversion control of missiles,” Journal of Guidance, Control, and Dynamics, vol. 26, no. 1, pp. 161–166, 2003.

    Article  Google Scholar 

  6. S. D. Nguyen, B. D. Lam, and S. B. Choi, “Smart dampers-based vibration control — Part 2: Fractional-order sliding control for vehicle suspension system,” Mechanical Systems and Signal Processing, vol. 148, p. 107145, 2020.

    Article  Google Scholar 

  7. A. C. Norelys, A. D. M. Manuel, and A. G. Javier, “Lyapunov functions for fractional order systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2951–2957, 2014.

    Article  MathSciNet  Google Scholar 

  8. S. D. Nguyen, B. D. Lam, and V. H. Ngo, “Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions,” Nonlinear Dynamics, vol. 101, pp. 795–821, 2020.

    Article  Google Scholar 

  9. C. Li and W. Deng, “Remarks on fractional derivatives,” Applied Mathematics and Computation, vol. 187, pp. 777–784, 2007.

    Article  MathSciNet  Google Scholar 

  10. A.-J. Muñoz-Vázquez, V. Parra-Vega, A. Sánchez-Orta, and G. Romero-Galván, “Quadratic Lyapunov functions for stability analysis in fractional-order systems with not necessarily differentiable solutions,” Systems & Control Letters, vol. 116, pp. 15–19, 2018.

    Article  MathSciNet  Google Scholar 

  11. A.-J. Muñoz-Vázquez, V. Parra-Vega, and A. Sánchez-Orta, “Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems,” Transactions of the Institute of Measurement and Control, vol. 41, no. 6, pp. 1627–1639, 2019.

    Article  Google Scholar 

  12. H. You, Y. Shen, H. Xing, and S. Yang, “Optimal control and parameters design for the fractional-order vehicle suspension system,” Journal of Low Frequency Noise, Vibration and Active Control, vol. 37, no. 3, pp. 456–467, 2018.

    Article  Google Scholar 

  13. P. Wang, Q. Wang, X. Xu, and N. Chen, “Fractional critical damping theory and its application in active suspension control,” Shock and Vibration, vol. 2017, Article ID 2738976, 2017.

  14. Z. Zhu, Y. Pan, Q. Zhou, and C. Lu, “Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 5, pp. 1273–1283, 2021.

    Article  Google Scholar 

  15. W. Wang, H. Liang, Y. Pan, and T. Li, “Prescribed performance adaptive fuzzy containment control for nonlinear multiagent systems using disturbance observer,” IEEE Transactions on Cybernetics, vol. 50, no. 9, pp. 3879–3891, 2020.

    Article  Google Scholar 

  16. S. D. Nguyen, S. B. Choi, and T. I. Seo, “Recurrent mechanism and impulse noise filter for establishing ANFIS,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 985–997, 2017.

    Article  Google Scholar 

  17. S. P. Utkarsh, D. C. Sushant, P. D. Shendge, and S. B. Phadke, “Linear disturbance observer based sliding mode control for active suspension systems with non-ideal actuator,” Journal of Sound and Vibration, vol. 442, no. 3, pp. 428–444, 2018.

    Google Scholar 

  18. F. J. Lin, K. K. Shyu, and R. J. Wai, “Recurrent fuzzy neural network sliding mode controlled motor toggle servomechanism,” IEEE/ASME Transactions on Mechatronics, vol. 6, no. 4, pp. 453–466, 2001.

    Article  Google Scholar 

  19. S. Roy, S. B. Roy, J. Lee, and S. Baldi, “Overcoming the under- and over-estimation problems in adaptive sliding mode control,” IEEE/ASME Transactions on Mechatronics, vol. 24, no. 5, pp. 2031–2039, 2019.

    Article  Google Scholar 

  20. S. Kurode, S. K. Spurgeon, B. Bandyopadhyah, and P. S. Gandhi, “Sliding mode control for slosh-free motion using a nonlinear sliding surface,” IEEE/ASME Transactions on Mechatronics, vol. 18, no. 2, pp. 714–724, 2013.

    Article  Google Scholar 

  21. Y. F. Li, B. Eriksson, and J. Wikander, “Sliding mode control of two-mass positioning systems,” Proc. of the 14th IFAC Triennial World Congress, Oxford, pp. 151–156, 1999.

  22. J. J. Kim, J. J. Lee, K. B. Park, and M. J. Youn, “Design of a new time-varying sliding surface for robot manipulator using variable structure controller,” Electronics Letters, vol. 29, no. 2, pp. 195–196, 1993.

    Article  Google Scholar 

  23. S. Tokat, M. S. Fadali, and O. Eray, “A classification and overview of sliding mode controller sliding surface design methods,” Studies in Sysems, Decision and Control, vol. 24, pp. 417–439, 2015.

    Article  MathSciNet  Google Scholar 

  24. S. D. Nguyen, D. Jung, and S. B. Choi, “A robust vibration control of a magnetorheological damper based railway suspension using a novel adaptive type-2 fuzzy sliding mode controller,” Shock and Vibration, vol. 2017, Article ID 7306109, 2017.

  25. X. Lei, High Speed Railway Track Dynamics: Models, Algorithms and Applications, Science Press, Beijing, Springer Nature Singapore Pte Ltd., pp. 271–280, 2017.

    Book  Google Scholar 

  26. W. Gong and Z. Cai, “Differential evolution with ranking-based mutation operators,” IEEE Transactions on Cybernetics, vol. 43, no. 6, pp. 2066–2081, 2013.

    Article  Google Scholar 

  27. W. Sun, Z. Zhao, and H. Gao, “Saturated adaptive robust control for active suspension systems,” IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3889–3896, 2013.

    Article  Google Scholar 

  28. C. Hua, J. Chen, Y. Li, and L. Li, “Adaptive prescribed performance control of half-car active suspension system with unknown dead-zone input,” Mechanical Systems and Signal Processing, vol. 111, pp. 135–148, 2018.

    Article  Google Scholar 

  29. H. Zhang, E. Wang, F. Min, R. Subash, and C. Su, “Skyhook-based semi-active control of full-vehicle suspension with magneto-rheological dampers,” Chinese Journal of Mechanical Engineering, vol. 26, no. 3, pp. 498–505, 2013.

    Article  Google Scholar 

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Authors and Affiliations

  1. Division of Computational Mechatronics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Sy Dzung Nguyen

  2. Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Sy Dzung Nguyen

  3. Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Vien Quoc Nguyen

Authors
  1. Sy Dzung Nguyen
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  2. Vien Quoc Nguyen
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Correspondence to Sy Dzung Nguyen.

Additional information

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.01-2019.328.

Sy Dzung Nguyen received his M.E. degree in manufacturing engineering from Ho Chi Minh City University of Technology (HCMUT) — VNU in 2001, a Ph.D. degree in applied mechanics in 2011 from HCMUT. He was a postdoctoral fellow at Inha University, Korea, 2011–2012, at Incheon National University, Korea, 2015–2016. He is currently a Head of Division of Computational Mechatronics (DCME), Institute for Computational Science (INCOS), Ton Duc Thang University (TDTU), Vietnam. His research interests include artificial intelligence and its applications to nonlinear adaptive control, system identification, and managing structure damage. Dr. Nguyen has been the main author of plenty of ISI papers in these fields.

Vien Quoc Nguyen received his B.E. and M.E. degrees in automatic control engineering from Ho Chi Minh City University of Technology (HCMUT), Vietnam, in 1998 and 2003. He received a Ph.D. degree in mechanical engineering in 2010 from Inha University, Korea. He is currently with the Mechatronic Division, Faculty of Mechanical Engineering at Industrial University of Ho Chi Minh City, Vietnam. His research interests include nonlinear adaptive control, vibration control, smart materials, and their applications.

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Nguyen, S.D., Nguyen, V.Q. SD-TCSs Control Deriving from Fractional-order Sliding Mode and Fuzzy-compensator. Int. J. Control Autom. Syst. 20, 1745–1755 (2022). https://doi.org/10.1007/s12555-020-0115-4

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  • DOI: https://doi.org/10.1007/s12555-020-0115-4

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