Continuous fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems with matched and mismatched disturbances

Document Type : Article

Authors

Faculty of Electrical and Computer Engineering, Malek Ashtar University of Technology, Tehran, P.O. Box 15875-1774, Iran

Abstract

This paper investigates fixed-time nonsingular terminal sliding mode control of second-order nonlinear systems in the presence of matched and mismatched disturbances. Using estimation of the mismatched disturbance estimated by a fixed-time disturbance observer, a novel nonlinear dynamic sliding surface is designed. This estimation is utilized in designing a completely novel nonlinear dynamics sliding surface whereby the fixed-time convergence of the sliding motion is guaranteed in spite of mismatched disturbance. The convergence time of the closed-loop system including disturbance observer and control system is guaranteed to be uniform with respect to initial conditions. Moreover, the proposed controller avoids chattering phenomenon by producing a continuous control signal.

Keywords

References

References:
1. Jiang, T., Song, T., and Lin, D. "Integral sliding mode based control for quadrotors with disturbances: Simulations and experiments", International Journal of Control, Automation and Systems, 17, pp. 1987-1998 (2019).
2. Utkin, V., Guldner, J., and Shi, J., Sliding Mode Control in Electro-Mechanical Systems, Boca Raton, CRC Press (2009).
3. Drazenovic, B. "The invariance conditions in variable structure systems", Automatica, 5(3), pp. 287-295 (1969).
4. Shi, S.-L., Li, J.-X., and Fang, Y.-M. "Fractionaldisturbance- observer-based sliding mode control for fractional order system with matched and mismatched disturbances", International Journal of Control, Automation and Systems, 17(5), pp. 1184-1190 (2019).
5. Man, Z. and Yu, X. "Terminal sliding mode control design of mimo linear systems", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44(11), pp. 823-830 (1997).
6. Feng, Y., Yu, X., and Han, F. "On nonsingular terminal sliding-mode control of nonlinear systems", Automatica, 49(6), pp. 1715-1722 (2013).
7. Feng, Y., Yu, X., and Man, Z. "Non-singular terminal sliding mode control of rigid manipulators", Automatica, 38, pp. 2159-2167 (2002).
8. Yang, L. and Yang, J. "Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems", International Journal of Robust and Nonlinear Control, 21(16), pp. 1865-1879 (2011).
9. Yong-Zhi Sheng, Jie Geng, and Xiang-Dong Liu, et al. "Nonsingular finite-time second order sliding mode attitude control for reentry vehicle", International Journal of Control, Automation and Systems, 13(4), pp. 853-866 (2015).
10. Pukdeboon, C. and Siricharuanun, P. "Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking", International Journal of Control, Automation and Systems, 12(3), pp. 530-540 (2014).
11. Jun Yang, Shihua Li, Jinya Su, et al. "Continuous nonsingular terminal sliding mode control for systems withmismatched disturbances", Automatica, 49, pp. 2287-2291 (2013).
12. Bhat, S. and Bernstein, D. "Finite-time stability of continuous autonomous systems", SIAM Journal on Control and Optimization, 38(2), pp. 751-766 (2000).
13. Andrieu, V., Praly, L., and Astolfi, A. "Homogeneous approximation, recursive observer design, and output feedbak", SIAM Journal on Control and Optimization, 47(4), pp. 1814-1850 (2008).
14. Polyakov, A. and Fridman, L. "Srtability notions and Lyapunov functions for sliding mode control systems", Journal of Franklin Institute, 351(4), pp. 1831-1865 (2014).
15. Polyakov, A., Efimov, D., and Perruquetti, W. "Finitetime and fixed-time stabilization: Implicit Lyapunov function approach", Automatica, 51, pp. 332-340 (2015).
16. Polyakov, A. "Nonlinear feedback design of fixedtime stabilization of linear control systems", IEEE Transactions on Automatic Control, 57(8), pp. 2106- 2110 (2012).
17. Zou, Z. "Non-singular fixed-time terminal sliding mode control of non-linear systems", IET Control Theory and Applications, 9(4), pp. 545-552 (2014).
18. Khanzadeh, A. and Pourgholi, M. "Fixed-time leaderfollower consensus tracking of second-order multiagent systems with bounded input uncertainties using non-singular terminal sliding mode technique", IET Control Theory and Applications, 12(5), pp. 679-686 (2017).
19. Fu, J. and Wang, J. "Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties", Systems & Control Letters, 93, pp. 1-12 (2016).
20. Zou, Z. "Nonsingular fixed-time consensus tracking for second-order multi-agent networks", Automatica, 54, pp. 305-309 (2015).
21. Wei-Shun Sui, Guang-Ren Duan, Ming-Zhe Hou, et al. "Distributed fixed-time attitude synchronization control for multiple rigid spacecraft", International Journal of Control, Automation and Systems, 17(5), pp. 1117-1130 (2019).
22. Corradini, M.L. and Cristofaro, A. "Nonsingular terminal sliding-mode control of nonlinear planar systems with global fixed-time stability guarantees", Automatica, 95, pp. 561-565 (2018).
23. Rong Wu, Changzhu Wei, Feng Yang, et al. "Fixedtime disturbance observer based non-singular terminal sliding mode control for second-order uncertain systems", IET Control Theory and Applications, 12(18),pp. 2459-2467 (2018). 24. Wen-Hua Chen, Jun Yang, Lei Guo, et al. "Disturbance-observer-based control and related methods-An overview", IEEE Transactions on Industrial Electronics, 63(2), pp. 1083-1095 (2016).
25. Jun Yanga, Argyrios Zolotasb, Wen-Hua Chen, et al. "Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach", ISA Transactions, 50(3), pp. 389-396 (2011).
26. Mohamed, Y.A.-R.I. "Design and implementation of a robust current-control scheme for a PMSM vector drive with simple adaptive disturbance observer", IEEE Transactions on Industrial Electronics, 54(4), pp. 1981-1988 (2007).
27. Chang, J.-L. "Sliding mode control design for mismatched uncertain systems using output feedback", International Journal of Control, Automation and Systems, 14(2), pp. 579-586 (2016).
28. Chang, J.-L. and Wu, T.-C. "Disturbance observer based output feedback controller design for systems with mismatched disturbance", International Journal of Control, Automation and Systems, 16(4), p. 1775- 1782 (2018).
29. Ni, J., Liu, C., and Liu, H. "Continuous uniformly finite time exact disturbance observer based control for fixed-time stabilization of nonlinear systems with mismatched disturbances", PLoS One, 12(4), e0175645(2017).
30. Angulo, M.T., Moreno, J.A., and Fridman, L. "Robust exact uniformly convergent arbitrary order differentiator", Automatica, 49(8), pp. 2489-2495 (2013).
31. Shtessel, Y.B., Shkolnikov, I.A., and Levant, A. "Smooth second-order sliding modes: Missile guidance applications", Automatica, 43(8), pp. 1470-1476 (2007).
32. Ming You, Qun Zong, Bailing Tian, et al. "Comprehensive design of uniform robust exact disturbance observer and fixed-time controller for reusable launch vehicles", IET Control Theory and Applications, 12(5), pp. 638-648 (2017).
33. Bailing Tian, Hanchen Lu, Zongyu Zuo, et al. "Fixedtime stabilization of high-order integrator systems with mismatched disturbances", Nonlinear Dynamics, 94(4), pp. 2889-2899 (2018).
34. Li, S. and Tian, Y.-P. "Finite-time stability of cascaded time-varying systems", International Journal of Control, 80(4), pp. 646-657 (2007).
35. Jianguo, G. and Shengjiang, Y. "New fixed-time sliding mode control for a mismatched second-order system", Transactions of the Institute of Measurement and Control, 43(2), pp. 325-334 (2020).
Scientia Iranica
Volume 30, Issue 1
Transactions on Computer Science & Engineering and Electrical Engineering (D)
January and February 2023
Pages 142-153

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History

  • Receive Date: 05 June 2020
  • Revise Date: 13 April 2021
  • Accept Date: 05 July 2021

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