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New design of active disturbance rejection control for nonlinear uncertain systems with unknown control input gain

Abstract

The paper considers the control problem for uncertain nonlinear systems with unknown control input gain. Based on the information of control direction rather than the nominal value of control input gain, a new active disturbance rejection control design is proposed. In the proposed design, the extended state observer (ESO) is constructed to estimate the total disturbance containing the uncertainty of control input. Via the estimations from ESO, the control input is generated by a designed dynamical system, which can force the actual input to track the ideal input. Moreover, for a wide class of nonlinear uncertainties, the transient performance of the proposed design is investigated. The theoretical results show that the tracking and estimating errors, as well as the difference between the actual and ideal inputs, can be sufficiently small by tuning the parameter of ESO despite various uncertainties. The experiment of a permanent magnet linear synchronous motor servo system illustrates the effectiveness of the proposed design.

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References

  1. Gao Z. On the centrality of disturbance rejection in automatic control. ISA Trans, 2014, 53: 850–857

    Article  Google Scholar 

  2. Zhao C, Guo L. PID controller design for second order nonlinear uncertain systems. Sci China Inf Sci, 2017, 60: 022201

    MathSciNet  Article  Google Scholar 

  3. Liu K Z, Yao Y. Robust Control. New York: Wiley, 2016

    Book  Google Scholar 

  4. Liu L. Analysis and Design of Sliding Mode Control Systems. Beijing: Science Press, 2017

    Google Scholar 

  5. Li S, Yang J, Chen W H, et al. Disturbance Observer-Based Control: Methods and Applicaitons. Boca Raton: CRC Press, 2014

    Google Scholar 

  6. Sun J, Yang J, Zheng W X, et al. GPIO-based robust control of nonlinear uncertain systems under time-varying disturbance with application to DC-DC converter. IEEE Trans Circ Syst II, 2016, 63: 1074–1078

    Google Scholar 

  7. Liu R J, She J H, Wu M, et al. Robust disturbance rejection for a fractional-order system based on equivalent-input-disturbance approach. Sci China Inf Sci, 2018, 61: 070222

    MathSciNet  Article  Google Scholar 

  8. Han J. From PID to active disturbance rejection control. IEEE Trans Ind Electron, 2009, 56: 900–906

    Article  Google Scholar 

  9. Chen S, Bai W Y, Hu Y, et al. On the conceptualization of total disturbance and its profound implications. Sci China Inf Sci, 2020, 63: 129201

    MathSciNet  Article  Google Scholar 

  10. Yuan Y, Cheng L, Wang Z D, et al. Position tracking and attitude control for quadrotors via active disturbance rejection control method. Sci China Inf Sci, 2019, 62: 010201

    Article  Google Scholar 

  11. Sun J, Pu Z, Yi J. Conditional disturbance negation based active disturbance rejection control for hypersonic vehicles. Control Eng Practice, 2019, 84: 159–171

    Article  Google Scholar 

  12. Su J, Ma H, Qiu W, et al. Task-independent robotic uncalibrated hand-eye coordination based on the extended state observer. IEEE Trans Syst Man Cybern B, 2004, 34: 1917–1922

    Article  Google Scholar 

  13. Texas Instruments. Technical Reference Manual, TMS320F28069M, TMS320F28068M InstaSPINTMMOTION Software. Literature Number: SPRUHJ0A, 2013

  14. Madonski R, Stanković M, Shao S, et al. Active disturbance rejection control of torsional plant with unknown frequency harmonic disturbance. Control Eng Practice, 2020, 100: 104413

    Article  Google Scholar 

  15. Chen Z, Qin B, Sun M, et al. Q-learning-based parameters adaptive algorithm for active disturbance rejection control and its application to ship course control. Neurocomputing, 2020, 408: 51–63

    Article  Google Scholar 

  16. Xia Y, Dai L, Fu M, et al. Application of active disturbance rejection control in tank gun control system. J Franklin Institute, 2014, 351: 2299–2314

    MathSciNet  Article  Google Scholar 

  17. Sun L, Shen J, Hua Q, et al. Data-driven oxygen excess ratio control for proton exchange membrane fuel cell. Appl Energy, 2018, 231: 866–875

    Article  Google Scholar 

  18. Sun L, Jin Y, You F. Active disturbance rejection temperature control of open-cathode proton exchange membrane fuel cell. Appl Energy, 2020, 261: 114381

    Article  Google Scholar 

  19. Yang X, Huang Y. Capabilities of extended state observer for estimating uncertainties. In: Proceedings of the 2009 American Control Conference, St Louis, 2009. 3700–3705

  20. Guo B Z, Zhao Z L. On the convergence of an extended state observer for nonlinear systems with uncertainty. Syst Control Lett, 2011, 60: 420–430

    MathSciNet  Article  Google Scholar 

  21. Zheng Q, Chen Z, Gao Z. A practical approach to disturbance decoupling control. Control Eng Practice, 2009, 17: 1016–1025

    Article  Google Scholar 

  22. Li J, Xia Y, Qi X, et al. Robust absolute stability analysis for interval nonlinear active disturbance rejection based control system. ISA Trans, 2017, 69: 122–130

    Article  Google Scholar 

  23. Xue W, Huang Y. Performance analysis of 2-DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances. Int J Robust Nonlin Control, 2018, 28: 1456–1473

    MathSciNet  Article  Google Scholar 

  24. Shao S, Gao Z. On the conditions of exponential stability in active disturbance rejection control based on singular perturbation analysis. Int J Control, 2017, 90: 2085–2097

    MathSciNet  Article  Google Scholar 

  25. Zhao Z L, Guo B Z. A novel extended state observer for output tracking of MIMO systems with mismatched uncertainty. IEEE Trans Automat Contr, 2018, 63: 211–218

    MathSciNet  Article  Google Scholar 

  26. Chen S, Xue W, Huang Y. On active disturbance rejection control for nonlinear systems with multiple uncertainties and nonlinear measurement. Int J Robust Nonlin Control, 2020, 30: 3411–3435

    MathSciNet  Article  Google Scholar 

  27. Chen S, Huang Y, Zhao Z L. The necessary and sufficient condition for the uncertain control gain in active disturbance rejection control. 2020. ArXiv:2006.11731

  28. Lee J, Mukherjee R, Khalil H K. Output feedback performance recovery in the presence of uncertainties. Syst Control Lett, 2016, 90: 31–37

    MathSciNet  Article  Google Scholar 

  29. Yi B, Lin S, Yang B, et al. Performance recovery of a class of uncertain non-affine systems with unmodelled dynamics: an indirect dynamic inversion method. Int J Control, 2018, 91: 266–284

    MathSciNet  Article  Google Scholar 

  30. Ran M, Wang Q, Dong C. Active disturbance rejection control for uncertain nonaffine-in-control nonlinear systems. IEEE Trans Automat Contr, 2017, 62: 5830–5836

    MathSciNet  Article  Google Scholar 

  31. Yoo D, Yau S S T, Gao Z. Optimal fast tracking observer bandwidth of the linear extended state observer. Int J Control, 2007, 80: 102–111

    MathSciNet  Article  Google Scholar 

  32. Zhao Z L, Jiang Z P. Semi-global finite-time output-feedback stabilization with an application to robotics. IEEE Trans Ind Electron, 2019, 66: 3148–3156

    Article  Google Scholar 

  33. Ting C S, Lieu J F, Liu C S, et al. An adaptive FNN control design of PMLSM in stationary reference frame. J Control Autom Electr Syst, 2016, 27: 391–405

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundations of China (Grant Nos. 62003202, 61973202, 61903085), Fundamental Research Funds for the Central Universities (Grant No. GK202003008), National Key R & D Program of China (Grant No. 2018YFA0703800), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2019A1515111070), China Postdoctoral Science Foundation (Grant No. 2020M672965), and State Key Laboratory of Synthetical Automation for Process Industries and the National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences.

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Correspondence to Zhi-Liang Zhao.

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Chen, S., Chen, Z., Huang, Y. et al. New design of active disturbance rejection control for nonlinear uncertain systems with unknown control input gain. Sci. China Inf. Sci. 65, 142201 (2022). https://doi.org/10.1007/s11432-020-3121-3

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  • DOI: https://doi.org/10.1007/s11432-020-3121-3

Keywords

  • uncertain system
  • active disturbance rejection control
  • control input gain