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Adaptive Recursive Terminal Sliding Mode Control for Uncertain Systems With Input Saturation Based on Positive Semi-definite Barrier Function

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Abstract

In this article, a novel positive semi-definite barrier function based adaptive recursive terminal sliding mode control for a class of uncertain nonlinear systems with actuator saturation is proposed. The method explicitly considers the actuator saturation and uncertainty, and achieves high-speed and high-precision control of the system with a lower amplitude adaptive gain, while without require the knowledge of the upper bound of the disturbance. First, in order to avoid the singularity problem and effectively improve the tracking accuracy, an error-based adaptive recursive terminal sliding surface is constructed; Then, a positive semi-definite barrier function, which realizes the adaptive adjustment of the controller gain in a lower amplitude mode is considered. It ensures that the sliding variable converges to a predefined region even when it is in the presence of actuator saturation and external disturbance. In addition, in order to prevent the problem of excessive positive semi-definite barrier function gain caused by sudden large disturbances, a modified barrier function gain form which can vary with the disturbance amplitude is also proposed, therefore the overestimation of the gain which may be difficult to achieve in reality is effectively avoided; Finally, the stability analysis of the above two control strategies is carried out in detail, and it is proved that both the systematic error and its derivative can converge to a predefined region in finite time. Numerical simulations show that in the presence of actuator saturation and external disturbances, the proposed control method not only improve the convergence performance and the control accuracy of the system, but also better prevent actuator saturation. The proposed method is also applied to a multi-cylinder hydraulic press servo system, and the results show its effectiveness.

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References

  1. V. I. Utkin, Sliding Modes in Control and Optimization, Springer Science & Business Media, 2017.

  2. X. Huang, C. Zhang, H. Lu, and M. Li, “Adaptive reaching law based sliding mode control for electromagnetic formation flight with input saturation,” Journal of the Franklin Institute, vol. 353, no. 11, pp. 2398–2417, 2016.

    Article  MathSciNet  Google Scholar 

  3. Z. Yu, Z. Liu, Y. Zhang, Y. Qu, and C.-Y. Su, “Distributed finite-time fault-tolerant containment control for multiple unmanned aerial vehicles,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 6, pp. 2077–2091, 2019.

    Article  MathSciNet  Google Scholar 

  4. H. Obeid, L. M. Fridman, S. Laghrouche, and M. Harmouche, “Barrier function-based adaptive sliding mode control,” Automatica, vol. 93, pp. 540–544, 2018.

    Article  MathSciNet  Google Scholar 

  5. A. Arbi, “Controllability of delayed discret Fornasini-Marchesini model via quantization and random packet dropouts,” Mathematical Modelling of Natural Phenomena, vol. 17, 2022.

  6. V. I. Utkin and A. S. Poznyak, “Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method,” Automatica, vol. 49, no. 1, pp. 39–47, 2013.

    Article  MathSciNet  Google Scholar 

  7. D. Y. Negrete-Chávez and J. A. Moreno, “Second-order sliding mode output feedback controller with adaptation,” International Journal of Adaptive Control and Signal Processing, vol. 30, no. 8–10, pp. 1523–1543, 2016.

    Article  MathSciNet  Google Scholar 

  8. Y. Chang, “Adaptive sliding mode control of multi-input nonlinear systems with perturbations to achieve asymptotical stability,” IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2863–2869, 2009.

    Article  MathSciNet  Google Scholar 

  9. F. Plestan, Y. Shtessel, V. Bregeault, and A. Poznyak, “New methodologies for adaptive sliding mode control,” International Journal of Control, vol. 83, no. 9, pp. 1907–1919, 2010.

    Article  MathSciNet  Google Scholar 

  10. G. Bartolini, A. Levant, F. Plestan, M. Taleb, and E. Punta, “Adaptation of sliding modes,” IMA Journal of Mathematical Control and Information, vol. 30, no. 3, pp. 285–300, 2013.

    Article  MathSciNet  Google Scholar 

  11. H. Obeid, L. Fridman, S. Laghrouche, and M. Harmouche, “Barrier adaptive first order sliding mode differentiator,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 1722–1727, 2017.

    Article  Google Scholar 

  12. L. Cao, Y. N. Pan, H. J. Liang, and T. W. Huang, “Observer-based dynamic event-triggered control for multi-agent systems with time-varying delay,” IEEE Transactions on Cybernetics, vol. 53, no. 5, pp. 3376–3387, 2023.

    Article  Google Scholar 

  13. H. Obeid, L. Fridman, S. Laghrouche, and M. Harmouche, “Barrier function-based adaptive integral sliding mode control,” Proc. of IEEE Conference on Decision and Control (CDC), pp. 5946–5950, 2018.

  14. H. J. Liang, L. Chen, Y. N. Pan, and H. K. Lam, “Fuzzy-based robust precision consensus tracking for uncertain networked systems with cooperative-antagonistic interactions,” IEEE Transactions on Fuzzy System, vol. 31, no. 4, pp. 1362–1376, 2023.

    Article  Google Scholar 

  15. J. Zheng, H. Wang, Z. Man, J. Jin, and M. Fu, “Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 4, pp. 1743–1752, 2014.

    Article  Google Scholar 

  16. Y. Feng, X. Yu, and Z. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 38, no. 12, pp. 2159–2167, 2002.

    Article  MathSciNet  Google Scholar 

  17. V. T. Haimo, “Finite time controllers,” SIAM Journal on Control and Optimization, vol. 24, no. 4, pp. 760–770, 1986.

    Article  MathSciNet  Google Scholar 

  18. K. Shao, J. Zheng, K. Huang, H. Wang, Z. Man, and M. Fu, “Finite-time control of a linear motor positioner using adaptive recursive terminal sliding mode,” IEEE Transactions on Industrial Electronics, vol. 67, no. 8, pp. 6659–6668, 2019.

    Article  Google Scholar 

  19. K. Shao, J. Zheng, R. Tang, X. Li, Z. Man, and B. Liang, “Barrier function based adaptive sliding mode control for uncertain systems with input saturation,” IEEE/ASME Transactions on Mechatronics, vol. 27, no. 6, pp. 4258–4268, 2022.

    Article  Google Scholar 

  20. K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, 2009.

    Article  MathSciNet  Google Scholar 

  21. Q. Hu, G. Ma, and L. Xie, “Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity,” Automatica, vol. 44, no. 2, pp. 552–559, 2008.

    Article  MathSciNet  Google Scholar 

  22. K. Shao, J. Zheng, H. Wang, X. Wang, R. Lu, and Z. Man, “Tracking control of a linear motor positioner based on barrier function adaptive sliding mode,” IEEE Transactions on Industrial Informatics, vol. 17, no. 11, pp. 7479–7488, 2021.

    Article  Google Scholar 

  23. H. Ma, W. Liu, Z. Xiong, Y. Li, Z. Liu, and Y. Sun, “Predefined-time barrier function adaptive sliding-mode control and uts application to piezoelectric actuators,” IEEE Transactions on Industrial Informatics, vol. 18, no. 12, pp. 8682–8691, 2022.

    Article  Google Scholar 

  24. F. Plestan, Y. Shtessel, V. Bregeault, and A. Poznyak, “New methodologies for adaptive sliding mode control,” International Journal of Control, vol. 83, no. 9, pp. 1907–1919, 2010.

    Article  MathSciNet  Google Scholar 

  25. J. Chao and A. Wu, Novel Control Scheme for Multi Cylinder Hydraulic Press, Journal of Huazhong University of Science and Technology (Natural Science Edition), 2013.

  26. E. Moulay and W. Perruquetti, “Finite time stability and stabilization of a class of continuous systems,” Journal of Mathematical Analysis and Applications, vol. 323, no. 2, pp. 1430–1443, 2006.

    Article  MathSciNet  Google Scholar 

  27. L. Yang and J. Yang, “Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 16, pp. 1865–1879, 2011.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin, China

    Chao Jia, Lijie Li & Xuanyue Shangguan

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  1. Chao Jia
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  2. Lijie Li
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  3. Xuanyue Shangguan
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Correspondence to Chao Jia.

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This work was supported by the National Natural Science Foundation of China under grants 62103298 and the Natural Science Foundation of Tianjin under grants 18JCYBJC87700; and the Training plan for young and middle-aged backbone innovative talents in colleges and universities in Tianjin.

Chao Jia received his B.E. and M.E. degrees from Tianjin University of Technology, Tianjin, China, in 2002 and 2008, respectively, and a Ph.D. degree from Tianjin University, Tianjin, China, in 2013. He joined the School of Electrical and Electronic Engineering, Tianjin University of Technology, China, in 2002, becoming an Associate Professor in 2013. He was a Visiting Scholar with Columbia University, NY, USA, from 2016 to 2017. His current research interests include nonlinear control, adaptive control, repetitive control, as well as their applications.

Lijie Li received his B.S. degree in antomation from Nantong Institute of Technology, Nantong, in 2020, and an M.E. degree in electronic engineering and automation from the School of Electrical Engineering and Antomation, Tianjin University of Technology, Tianjin, China, in 2023, respectively. His research interests include sliding-mode control, barrier function, input saturation, and finite-time control.

Xuanyue Shangguan received his B.S. degree from Tianjin Chengjian University majoring in electrical engineering and automation, Tianjin, in 2021, which he is pursuing a master’s degree. His research interests include super-twisting algorithm, multi-agent system, and nonlinear control for multi-cylinder hydraulic press.

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Jia, C., Li, L. & Shangguan, X. Adaptive Recursive Terminal Sliding Mode Control for Uncertain Systems With Input Saturation Based on Positive Semi-definite Barrier Function. Int. J. Control Autom. Syst. (2024). https://doi.org/10.1007/s12555-023-0368-9

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  • DOI: https://doi.org/10.1007/s12555-023-0368-9

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