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access icon free Stabilisability analysis and design of UDE-based robust control

  • Author(s): Zhen Tian 1, 2 ; Qing-Chang Zhong 2 ; Beibei Ren 3 ; Jingqi Yuan 1
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  • Source: Volume 13, Issue 10, 02 July 2019, p. 1445 – 1453
    DOI:  10.1049/iet-cta.2018.6012 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 03/09/2018, Accepted 25/03/2019, Revised 01/03/2019, Published 27/03/2019

The uncertainty and disturbance estimator (UDE)-based robust control approach is widely investigated and applied due to its excellent performance and simple implementation. However, its stabilisability of unstable systems has not been documented. In this study, the sufficient and necessary stabilisability conditions of the UDE-based robust control are investigated. According to the stabilisability conditions, a systematical design method is presented for the reference model based on the controllable canonical transformation and pole placement. This is then applied to a magnetic levitation system (MagLev) subject to model uncertainties and external disturbance as an example. Simulation results are presented to illustrate the effectiveness of the proposed control approach with respect to matched uncertainties.

Inspec keywords: robust control; magnetic levitation; stability; uncertain systems; control system synthesis

Other keywords: pole placement; sufficient stabilisability conditions; control approach; systematical design method; controllable canonical transformation; necessary stabilisability conditions; UDE-based robust control; uncertainty

Subjects: Control system analysis and synthesis methods; Stability in control theory

References

    1. 1)
      • 7. Zhong, Q.C., Rees, D.: ‘Control of uncertain LTI systems based on an uncertainty and disturbance estimator’, J. Dyn. Syst. Meas. Control, 2004, 63, (2), pp. 905–910.
    2. 2)
      • 32. Kuperman, A., Arogeti, S., Brand, Z., et al: ‘Robust UDE-based control of active magnetic bearing for flywheel applications’. Proc. of 2012 Electrical Systems for Aircraft, Railway and Ship Propulsion, Bologna, Italy, October 2012, pp. 1–5.
    3. 3)
      • 26. Ren, B., Wang, Y., Zhong, Q.C.: ‘UDE-based control of variable-speed wind turbine systems’, Int. J. Control, 2017, 90, (1), pp. 121–136.
    4. 4)
      • 8. Ren, B., Zhong, Q.C., Dai, J.: ‘Asymptotic reference tracking and disturbance rejection of UDE-based robust control’, IEEE Trans. Ind. Electron., 2017, 64, (4), pp. 3166–3176.
    5. 5)
      • 18. Zhang, Q., Liu, H.T.: ‘UDE-based robust command filtered backstepping control for close formation flight’, IEEE Trans. Ind. Electron., 2018, 65, (11), pp. 8818–8827.
    6. 6)
      • 39. Yang, J., Zolotas, A., Chen, W.H., et al: ‘Robust control of nonlinear maglev suspension system with mismatched uncertainties via DOBC approach’, ISA Trans., 2011, 50, (3), pp. 389–396.
    7. 7)
      • 6. Han, J.: ‘From PID to active disturbance rejection control’, IEEE Trans. Ind. Electron., 2009, 126, (4), pp. 900–906.
    8. 8)
      • 9. Ren, B., Zhong, Q.C., Chen, J.: ‘Robust control for a class of nonaffine nonlinear systems based on the uncertainty and disturbance estimator’, IEEE Trans. Ind. Electron., 2015, 62, (9), pp. 5881–5888.
    9. 9)
      • 33. Zhong, Q.C., Kuperman, A., Stobart, R.: ‘Design of UDE-based controllers from their two-degree-of-freedom nature’, Int. J. Robust Nonlinear Control, 2011, 21, (17), pp. 1994–2008.
    10. 10)
      • 31. Raj, V.R., Poluru, V.S., Chandar, T.S.: ‘Robust control of electric motor drive based on UDE’, IFAC-Pap. Online, 2015, 48, (30), pp. 37–42.
    11. 11)
      • 16. Sanz, R., Garcia, P., Zhong, Q.C., et al: ‘Predictor-based control of a class of time-delay systems and its application to quadrotors’, IEEE Trans. Ind. Electron., 2017, 64, (1), pp. 459–469.
    12. 12)
      • 4. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: ‘Nonlinear and adaptive control design’ (Wiley, Hoboken, 1995).
    13. 13)
      • 10. Kuperman, A., Zhong, Q.C.: ‘UDE-based linear robust control for a class of nonlinear systems with application to wing rock motion stabilization’, Nonlinear Dyn., 2015, 81, (2), pp. 780–799.
    14. 14)
      • 37. Cervera, A., Ezra, O., Kuperman, A., et al: ‘Modelling and control of magnetic actuation systems based on sensorless displacement information’, IEEE Trans. Ind. Electron., 2019, 66, (6), pp. 4849–4859.
    15. 15)
      • 42. Yang, J., Li, S., Yu, X.: ‘Sliding mode control for systems with mismatched uncertainties via a disturbance observer’, IEEE Trans. Ind. Electron., 2013, 60, (1), pp. 160–169.
    16. 16)
      • 40. Ginoya, D., Gutte, C.M., Shendge, P.D., et al: ‘State-and-disturbance-observer-based sliding mode control of magnetic levitation systems’, Trans. Meas. Control, 2016, 38, (6), pp. 751–763.
    17. 17)
      • 15. Alshek, N., Bronshtein, S., Elkayam, M., et al: ‘Modified uncertainty and disturbance estimator for enhanced periodic signals suppress’, IEEE Trans. Ind. Electron., 2019, 66, (2), pp. 1246–1254.
    18. 18)
      • 30. Kodhanda, A., Kolhe, J.P., Zeru, T., et al:Robust aircraft control based on UDE theory', Proc. Inst. Mech. Eng. G, J. Aerosp. Eng., 2017, 231, (4), pp. 728–742.
    19. 19)
      • 1. Zhou, K., Doyle, J.C.: ‘Essentials of robust control’ (Prentice-Hall, Upper Saddle River, 1998).
    20. 20)
      • 19. Londhe, P., Dhadekar, D.D., Patre, B., et al: ‘Uncertainty and disturbance estimator based sliding mode control of an autonomous underwater vehicle’, Int. J. Dyn. Control, 2017, 5, (4), pp. 1122–1138.
    21. 21)
      • 29. Dai, J., Ren, B.: ‘UDE-based robust boundary control for an unstable parabolic PDE with unknown input disturbance’, Automatica, 2018, 93, pp. 363–368.
    22. 22)
      • 2. Zhou, K., Doyle, J.C.: ‘Robust and optimal control’ (Prentice-Hall, New Jersey, 1996).
    23. 23)
      • 5. Chen, W.H., Yang, J., Guo, L., Li, S.: ‘Disturbance-observer-based control and related methods: an overview’, IEEE Trans. Ind. Electron., 2016, 63, (2), pp. 1083–1095.
    24. 24)
      • 3. Utkin, V.I.: ‘Sliding modes in control and optimization’ (Springer, Science, 2013).
    25. 25)
      • 35. Khalil, H.K.: ‘Noninear systems’ (Prentice-Hall, New Jersey, 1996).
    26. 26)
      • 24. Zhong, Q.C., Wang, Y., Ren, B.: ‘UDE-based robust droop control of inverters in parallel operation’, IEEE Trans. Ind. Electron., 2017, 64, (9), pp. 7552–7562.
    27. 27)
      • 17. Dai, J., Ren, B., Zhong, Q.C.: ‘Uncertainty and disturbance estimator-based backstepping control for nonlinear systems with mismatched uncertainties and disturbances’, J. Dyn. Syst. Meas. Control, 2018, 140, (12), pp. 1–11.
    28. 28)
      • 27. Dong, Y., Ren, B.: ‘UDE-based variable impedance control of uncertain robot systems’, IEEE Trans. Syst. Man Cybern., 2017, PP, (99), pp. 1–12.
    29. 29)
      • 41. Jain, S., Mishra, J.P., Talange, D.B.: ‘Practical implementation of adaptive gain and variable gain super-twisting algorithms on the magnetic levitation system: a comparative study’. Proc. of 14th Int. Workshop on Variable Structure Systems (VSS), Nanjing, China, June 2016, pp. 28–33.
    30. 30)
      • 12. Sun, L., Li, D., Zhong, Q.C., et al: ‘Control of a class of industrial processes with time delay based on a modified uncertainty and disturbance estimator’, IEEE Trans. Ind. Electron., 2016, 63, (11), pp. 7018–7028.
    31. 31)
      • 21. Deepika, D., Kaur, S., Narayan, S.: ‘Uncertainty and disturbance estimator-based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control’, Chaos Solitons Fractals, 2018, 115, pp. 196–203.
    32. 32)
      • 13. Kuperman, A., Zhong, Q.C.: ‘Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator’, IEEE Trans. Ind. Electron., 2018, 65, (2), pp. 1439–1449.
    33. 33)
      • 28. Xu, Q.: ‘Precision motion control of piezoelectric nanopositioning stage with chattering-free adaptive sliding mode control’, IEEE Trans. Autom. Sci. Eng., 2017, 14, (1), pp. 238–248.
    34. 34)
      • 38. Goodall, R.: ‘Optimised configuration of sensing elements for control and fault tolerance applied to an electromagnetic suspension’. PhD Thesis, Lough borough University, 2009.
    35. 35)
      • 20. Zhu, Y., Zhu, S.: ‘Adaptive sliding mode control based on uncertainty and disturbance estimator’, Math. Probl. Eng., 2014, pp. 1–10.
    36. 36)
      • 14. Aharon, I., Shmilovitz, D., Kuperman, A.: ‘Uncertainty and disturbance estimator-based controllers under finite control bandwidth constraint’, Int. J. Robust Nonlinear Control, 2011, 21, (1), pp. 79–92.
    37. 37)
      • 43. Zheng, Q., Gao, Z.: ‘Predictive active disturbance rejection control for processes with time delay’, ISA Trans., 2014, 53, (4), pp. 873–881.
    38. 38)
      • 25. Wang, Y., Ren, B., Zhong, Q.C.: ‘Robust power flow control of grid-connected inverters’, IEEE Trans. Ind. Electron., 2016, 63, (11), pp. 6887–6897.
    39. 39)
      • 11. Sanz, R., Garcia, P., Albertos, P., et al: ‘Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator’, Int. J. Robust Nonlinear Control, 2017, 27, (10), pp. 1826–1840.
    40. 40)
      • 23. Gadelovits, S.Y., Zhong, Q.C., Kadirkamanathan, V., et al: ‘Uncertainty and disturbance estimator-based controller equipped with a time-delay filter to improve the voltage quality of inverters’, IEEE Trans. Ind. Electron., 2019, 66, (1), pp. 459–469.
    41. 41)
      • 36. Antsaklis, P.J., Michel, A.N.: ‘A linear systems primer’ (Birkhauser, Boston, 2007).
    42. 42)
      • 34. Francis, B.A., Wonham, W.M.: ‘The internal model principle of control theory’, Automatica, 1976, 12, (5), pp. 457–465.
    43. 43)
      • 22. Gadelovits, S.Y., Zhong, Q.C., Kadirkamanathan, V., et al: ‘UDE-based controller equipped with a multi-band-stop filter to improve the voltage quality of inverters’, IEEE Trans. Ind. Electron., 2017, 64, (9), pp. 7433–7443.
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