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Backstepping control based on disturbance observer and equilibrium manifold linearization model for power-line inspection robots

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Abstract

In this paper, a backstepping controller based on equilibrium manifold linearization (EMI) model and a finite time disturbance observer is proposed for power line inspection (PLI) robots. Firstly, the state equations of PLI robot are established, and the nonlinear system model is linearized at the nominal equilibrium point. Then, the EMI model is established to expand the working range of the controlled system. In this paper, a finite time disturbance observer is used to observe and compensate the external disturbance of the PLI robot system to ensure that the observation error approaches zero in a finite time. Finally, a backstepping controller is designed based on the EMI model and finite time disturbance observer. The simulation results show the disturbance approximation ability and control effectiveness of the control scheme.

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References

  1. Zhang A, Lai X, Wu M et al (2017) Nonlinear stabilizing control for a class of underactuated mechanical systems with multi degree of freedoms. Nonlinear Dyn 89(3):2241–2253

    Article  MathSciNet  MATH  Google Scholar 

  2. Xu Y, Zhu Q, Xie J et al (2019) Intelligent charging dock and interface design of overhead distribution line inspection robot. Electrotechnical 01:49–52

    Google Scholar 

  3. Xia YF, Song XM, Jia ZD et al (2018) Research status and prospect of transmission line condition based maintenance technology based on line inspection robot. High Volt Apparatus 54(07):53–63

    Google Scholar 

  4. Meng XL (2018) Design and research on control circuit of flying-slip line inspection robot. Technol Innov Appl 17:91–93

    Google Scholar 

  5. Yang K, Tang X, Qin Y et al (2021) Comparative study of trajectory tracking control for automated vehicles via model predictive control and robust H-infinity state feedback control. Chin J Mech Eng 34(1):1–14

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Wang Z, Wang XH, Xia JW et al (2020) Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems. Sci China Technol Sci 63(9):1854–1862

    Article  Google Scholar 

  8. Markazi AHD, Maadani M, Zabihifar SH et al (2018) Adaptive fuzzy sliding mode control of under-actuated nonlinear systems. Int J Autom Comput 15(3):364–376

    Article  Google Scholar 

  9. Zhuang H, Sun Q, Chen Z et al (2021) Active disturbance rejection control for attitude control of missile systems based on back-stepping method. Int J Control Autom Syst 19(11):3642–3656

    Article  Google Scholar 

  10. Sun H, Li S, Yang J et al (2014) Non-linear disturbance observer-based back-stepping control for airbreathing hypersonic vehicles with mismatched disturbances. IET Control Theory Appl 8(17):1852–1865

    Article  Google Scholar 

  11. Xing H, Zhong X, Li J (2015) Linear extended state observer based back-stepping control for uncertain SISO nonlinear systems. Int J Innov Comput Information Control 11(4):1411–1419

    Google Scholar 

  12. Li YZ, Zhao KG (2011) Adaptive back-stepping control of permanent magnetic synchronous motor based on slide mode observer International Conference Measuring Technology and Mechatronics Automation IEEE

  13. Li Y, Qiang S, Zhuang X et al (2004) Robust and adaptive backstepping control for nonlinear systems using RBF neural networks. IEEE Trans Neural Netw 15(3):693–701

    Article  Google Scholar 

  14. Tong S, Wang T, Li Y et al (2013) A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control. IEEE Trans Fuzzy Syst 21(2):314–327

    Article  Google Scholar 

  15. Cao L, Zhang D, Zhang A (2020) Back-stepping control for flexible air-breathing hypersonic vehicles based on uncertainty and disturbance estimator. J Beijing Inst Technol 29(4):504–513

    Google Scholar 

  16. Liu XF, Zhao L (2012) Approximate nonlinear modeling of aircraft engine surge margin based on equilibrium manifold expansion. Chin J Aeronaut 25(5):663–674

    Article  Google Scholar 

  17. Pakmehr M, Fitzgerald N, Feron EM et al (2014) Gain scheduled control of gas turbine engines: stability and verification. J Eng Gas Turbines Power 136(3):31201–31201

    Article  Google Scholar 

  18. Daren Y, Tao C, Wen B (2005) Equilibrium manifold linearization model for normal shock position control systems. J Aircr 42(5):1344–1347

    Article  Google Scholar 

  19. Tao C, Daren Y, Wen B et al (2007) Gain scheduling control of nonlinear shock motion based on equilibrium manifold linearization model. Chin J Aeronaut 20(6):481–487

    Article  Google Scholar 

  20. Chengkun LV, Chang J, Yu D (2021) Feedback linearized sliding mode control of turbofan engine based on multiple input multiple output equilibrium manifold expansion model. Propuls Technol 42(08):1681–1689

    Google Scholar 

  21. Zhang J, Liu X, Xia Y et al (2016) Disturbance observer-based integral sliding-mode control for systems with mismatched disturbances. IEEE Trans Industr Electron 63(11):7040–7048

    Article  Google Scholar 

  22. He W, Yan Z, Sun C et al (2017) Adaptive neural network control of a flapping wing micro aerial vehicle with disturbance observer. IEEE Transactions Cybern 47(10):3452–3465

    Article  Google Scholar 

  23. Yaping Li, Fang W, Chao Z (2020) Filtering backstepping control of hypersonic vehicle with full state constraints. Acta Aeronautica Sinica 41(11):109–120

    Google Scholar 

  24. Wei C, Jinjie Q, Ming S (2020) Position backstepping control for disturbance estimation and compensation of permanent magnet linear motor. Control Decis Making 35(06):1409–1414

    Google Scholar 

  25. Xue YL, Jiang CS, Zhu L (2008) Trajectory linearization control of a class of RBF neural network disturbance observer. Syst Eng Electron Technol 30(3):522–526

    Google Scholar 

  26. Wang JH, Hu JB, Zhang L et al (2018) Inverse terminal sliding mode flight control based on sliding mode disturbance observer. Syst Eng Electron Technol 40(6):1345–1350

    Google Scholar 

  27. Li FB, Huang PM, Yang CH et al (2021) Sliding mode control design of aircraft electric braking system based on nonlinear disturbance observer. J Automation 47(11):2557–2569

    Google Scholar 

  28. Dian S, Chen L, Hoang S et al (2017) Dynamic balance control based on an adaptive gain-scheduled backstepping scheme for power-line inspection robots. IEEE/CAA J Automatica Sinica 6(1):198–208

    Article  Google Scholar 

  29. Liu L, Shao N, Gao J, Song H (2021) Displacement tracking dynamic surface backstepping control of permanent magnet linear synchronous motor based on fixed time disturbance observer. High Tech Commun 31(06):671–679

    Google Scholar 

  30. Liu L, Shao N, Gao J et al (2021) Displacement tracking dynamic surface backstepping control of permanent magnet linear synchronous motor based on fixed time disturbance observer. High Tech Commun 31(06):671–679

    Google Scholar 

  31. Cruz-Zavala E, Moreno JA, Fridman LM (2011) Uniform robust exact differentiator. IEEE Trans Autom Control 56(11):2727–2733

    Article  MathSciNet  MATH  Google Scholar 

  32. Krantz SG, Parks HR (2002) The implicit function theorem: history, theory, and applications. Birkhauser, Boston, MA

  33. Stilwell DJ, Rugh WJ (1999) Interpolation of observer state feedback controllers for gain scheduling. IEEE Trans Autom Control 44(6):1225–1229

    Article  MathSciNet  MATH  Google Scholar 

  34. Zhang J, Sun C, Zhang R, et al (2013) Adaptive backstepping controller design for reentry attitude of near space hypersonic vehicle[C]//International Conference on Intelligent Science and Big Data Engineering. Springer, Berlin, Heidelberg, 642–648

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Author information

Authors and Affiliations

  1. Business School of Hohai University, Nanjing, China

    Beining Chen

  2. College of Mechanical and Electrical Engineering, Hohai University, Nanjing, China

    Yanbo Feng

  3. Hohai-Lille College, Nanjing, China

    Yuhan Cao

Authors
  1. Beining Chen
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  2. Yanbo Feng
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  3. Yuhan Cao
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Contributions

For research articles with several authors, a short paragraph specifying their individual contributions must be provided. BC is mainly responsible for thesis writing, control design. YF is mainly responsible for simulation research. YC is responsible for the editing, proofreading and revision of the article.

Corresponding author

Correspondence to Beining Chen.

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The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Chen, B., Feng, Y. & Cao, Y. Backstepping control based on disturbance observer and equilibrium manifold linearization model for power-line inspection robots. Int. J. Dynam. Control 11, 3124–3135 (2023). https://doi.org/10.1007/s40435-022-01032-1

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  • DOI: https://doi.org/10.1007/s40435-022-01032-1

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