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Invariant manifold based nonsingular terminal sliding mode control for systems with multi-source disturbances via output-feedback

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Abstract

This paper proposes an invariant manifold based nonsingular terminal sliding mode control (NTSMC) approach for systems subject to multi-source disturbances to achieve finite-time tracking in the case of only output measurement. By utilizing the invariant manifold, the mismatched disturbances are transferred into the lumped matched disturbance. A universal finite-time observer (UFTO) is designed to estimate the errors between actual states and their desired values, the steady-state of the control input as well as the lumped disturbance. Introducing the estimations, a nonsingular terminal sliding mode controller is constructed. Based on Lyapunov’s theory, the rigorous stability analysis for the closed-loop system is given. Compared with the existing output-feedback sliding mode control (SMC), the proposed approach enables finite-time tracking in the presence of unknown derivatives of the reference signal and multi-source disturbances without requiring additional tracking differentiators. The proposed approach is applied to the DC–DC buck converter system, and simulation results verify the effectiveness of the proposed control strategy.

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References

  1. Sira-Ramírez H, Aguilar-Orduña M, Zurita-Bustamante E (2019) On the sliding mode control of mimo nonlinear systems: an input–output approach. Int J Robust Nonlinear Control 29(3):715–735

    Article  MathSciNet  Google Scholar 

  2. Obeid H, Laghrouche S, Fridman L (2021) Dual layer barrier functions based adaptive higher order sliding mode control. Int J Robust Nonlinear Control 31(9):3795–3808

    Article  MathSciNet  Google Scholar 

  3. Hu J, Tan G, Liu L (2023) A new result on H\(\infty\) state estimation for delayed neural networks based on an extended reciprocally convex inequality. IEEE Trans Circuits Syst II: Express Briefs. https://doi.org/10.1109/TCSII.2023.3323834

    Article  Google Scholar 

  4. Polyakov A (2019) Sliding mode control design using canonical homogeneous norm. Int J Robust Nonlinear Control 29(3):682–701

    Article  MathSciNet  Google Scholar 

  5. Lin W-J, Tan G, Wang Q-G, Yu J (2023) Fault-tolerant state estimation for Markov jump neural networks with time-varying delays. IEEE Trans Circuits Syst II: Express Briefs. https://doi.org/10.1109/TCSII.2023.3332390

    Article  Google Scholar 

  6. Dong Y, Chen J (2021) Nonlinear observer-based approach for cooperative control of networked rigid spacecraft systems. Automatica 128:109552

    Article  MathSciNet  Google Scholar 

  7. Wang Y, Yuan Y, Liu J (2021) Finite-time leader-following output consensus for multi-agent systems via extended state observer. Automatica 124:109133

    Article  MathSciNet  Google Scholar 

  8. Esteban FD, Serra FM, De Angelo CH, Montoya OD (2023) Nonlinear control for a DC–DC converter with dual active bridges in a DC microgrid. Int J Electr Power Energy Syst 146:108731

    Article  Google Scholar 

  9. Zhang L, Wang Z, Li S, Ding S, Du H (2020) Universal finite-time observer based second-order sliding mode control for DC–DC buck converters with only output voltage measurement. J Frankl Inst 357(16):11863–11879

    Article  MathSciNet  Google Scholar 

  10. Zhang L, Yang J, Li S (2021) A model-based unmatched disturbance rejection control approach for speed regulation of a converter-driven DC motor using output-feedback. IEEE/CAA J Autom Sin 9(2):365–376

    Article  MathSciNet  Google Scholar 

  11. Yeh Y-L (2022) Output feedback sliding-mode control based on dynamic-gain observer for non-minimum phase systems. J Frankl Inst 359(17):9886–9901

    Article  MathSciNet  Google Scholar 

  12. Zhang J, Shi D, Xia Y (2021) Design of sliding mode output feedback controllers via dynamic sliding surface. Automatica 124:109310

    Article  MathSciNet  Google Scholar 

  13. Wang H, Zhang Z, Tang X, Zhao Z, Yan Y (2022) Continuous output feedback sliding mode control for underactuated flexible-joint robot. J Frankl Inst 359(15):7847–7865

    Article  MathSciNet  Google Scholar 

  14. Mishra JP, Kurode SR (2014) Output-feedback control for stabilization of slosh using higher order sliding modes. IFAC Proc Vol 47(1):1003–1010

    Article  Google Scholar 

  15. Feng J, Gao S, Zhao D, Yan X, Spurgeon SK (2020) Dynamic output feedback sliding mode control for non-minimum phase systems with application to an inverted pendulum. IFAC-PapersOnLine 53(2):5165–5170

    Article  Google Scholar 

  16. Hao L-Y, Zhang Y-Q, Li H (2021) Fault-tolerant control via integral sliding mode output feedback for unmanned marine vehicles. Appl Math Comput 401:126078

    MathSciNet  Google Scholar 

  17. Liu H, Khalil HK (2019) Output feedback stabilization using super-twisting control and high-gain observer. Int J Robust Nonlinear Control 29(3):601–617

    Article  MathSciNet  Google Scholar 

  18. Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9–10):924–941

    Article  MathSciNet  Google Scholar 

  19. Tang J, Dang Z, Deng Z, Li C (2022) Adaptive fuzzy nonlinear integral sliding mode control for unmanned underwater vehicles based on ESO. Ocean Eng 266:113154

    Article  Google Scholar 

  20. Zhuang H, Sun Q, Chen Z, Jiang Y (2020) Back-stepping sliding mode control for pressure regulation of oxygen mask based on an extended state observer. Automatica 119:109106

    Article  MathSciNet  Google Scholar 

  21. Yue J, Liu L, Peng Z, Wang D (2023) Wave-filtering finite-time self-learning extended state observers for robotic surface vehicles. Ocean Eng 275:113900

    Article  Google Scholar 

  22. Yang X, Yao J, Deng W (2021) Output feedback adaptive super-twisting sliding mode control of hydraulic systems with disturbance compensation. ISA Trans 109:175–185

    Article  PubMed  Google Scholar 

  23. Rabiee H, Ataei M, Ekramian M (2019) Continuous nonsingular terminal sliding mode control based on adaptive sliding mode disturbance observer for uncertain nonlinear systems. Automatica 109:108515

    Article  MathSciNet  Google Scholar 

  24. Dong R-Q, Wu A-G, Zhang Y, Duan G-R, Li B (2022) Anti-unwinding terminal sliding mode attitude tracking control for rigid spacecraft. Automatica 145:110567

    Article  MathSciNet  Google Scholar 

  25. Zhang J, Shi D, Xia Y (2021) Design of sliding mode output feedback controllers via dynamic sliding surface. Automatica 124:109310

    Article  MathSciNet  Google Scholar 

  26. Komurcugil H (2013) Non-singular terminal sliding-mode control of DC–DC buck converters. Control Eng Pract 21(3):321–332

    Article  MathSciNet  Google Scholar 

  27. Zhou M, Su H, Zhou H, Wang L, Liu Y, Yu H (2022) Full-order terminal sliding-mode control for soft open point. Energies 15(14):4999

    Article  Google Scholar 

  28. Zuo Z, Tie L (2016) Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int J Syst Sci 47(6):1366–1375

    Article  MathSciNet  Google Scholar 

  29. Isidori A, Byrnes CI (1990) Output regulation of nonlinear systems. IEEE Trans Autom Control 35(2):131–140

    Article  MathSciNet  Google Scholar 

  30. Zhang L, Yang J, Li S, Yu X (2020) Invariant manifold based output-feedback sliding mode control for systems with mismatched disturbances. IEEE Trans Circuits Syst II: Express Briefs 68(3):933–937

    Google Scholar 

  31. Du H, Qian C, Yang S, Li S (2013) Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems. Automatica 49(2):601–609

    Article  MathSciNet  Google Scholar 

  32. Rabiee H, Ataei M, Ekramian M (2019) Continuous nonsingular terminal sliding mode control based on adaptive sliding mode disturbance observer for uncertain nonlinear systems. Automatica 109:108515

    Article  MathSciNet  Google Scholar 

  33. Wang J, Li S, Yang J, Wu B, Li Q (2015) Extended state observer-based sliding mode control for PWM-based DC–DC buck power converter systems with mismatched disturbances. IET Control Theory Appl 9(4):579–586

    Article  MathSciNet  CAS  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China under Grants 62273254 and 62273199.

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Authors and Affiliations

  1. School of Control Science and Engineering, Tiangong University, Tianjin, 300387, China

    Yunjun Chen, Rui You & Lu Zhang

  2. Tianjin Key Laboratory of Intelligent Control of Electrical Equipment, Tiangong University, Tianjin, 300387, China

    Yunjun Chen, Rui You & Lu Zhang

Authors
  1. Yunjun Chen
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  2. Rui You
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  3. Lu Zhang
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Correspondence to Lu Zhang.

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Technical Editor: Adriano Almeida Gonçalves Siqueira.

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Chen, Y., You, R. & Zhang, L. Invariant manifold based nonsingular terminal sliding mode control for systems with multi-source disturbances via output-feedback. J Braz. Soc. Mech. Sci. Eng. 46, 161 (2024). https://doi.org/10.1007/s40430-024-04737-w

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  • DOI: https://doi.org/10.1007/s40430-024-04737-w

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