access icon free Backstepping active disturbance rejection control: a delayed activation approach

© The Institution of Engineering and Technology
Received 04/01/2017, Accepted 24/05/2017, Revised 19/04/2017, Published 31/05/2017

This study provides a solution to the problem of applying the active disturbance rejection control (ADRC) approach to the tracking control of pure feedback non-linear systems with large uncertainties. The design is based on the backstepping technique, and in each step two extended state observers (ESOs) are designed, one to approximate the derivative of the virtual control generated from the last step, while the other to estimate the system uncertainty. A key feature of the developed backstepping ADRC is that the activations of the ESOs are delayed successively. It is proved that under the new backstepping scheme, the closed-loop signals are guaranteed to be semi-globally uniformly ultimately bounded and the output tracking error can be made arbitrarily small.

Inspec keywords: delay systems; control nonlinearities; uncertain systems; state feedback; active disturbance rejection control; nonlinear control systems; closed loop systems; observers

Other keywords: extended state observers; output tracking error; delayed activation approach; pure feedback nonlinear systems; backstepping active disturbance rejection control; ESOs; tracking control; virtual control; closed-loop signals; ADRC approach; system uncertainty

Subjects: Distributed parameter control systems; Stability in control theory; Simulation, modelling and identification; Nonlinear control systems

References

    1. 1)
      • 18. Ran, M., Wang, Q., Dong, C.: ‘Active disturbance rejection control for uncertain nonaffine-in-control nonlinear systems’, IEEE Trans. Automat. Control, doi: 10.1109/TAC.2016.2641980.
    2. 2)
      • 9. Gao, Z.: ‘Scaling and bandwidth-parameterization based controller tuning’. Proc. American Control Conf., Denver, CO, 2003, pp. 4989–4996.
    3. 3)
      • 1. Han, J.: ‘Active disturbance rejection control technique-the technique for estimating and compensating the uncertainties’ (National Defense Industry Press, Beijing, 2008).
    4. 4)
      • 23. Guo, B.Z., Wu, Z.H.: ‘Active disturbance rejection control approach to output-feedback stabilization of lower triangular nonlinear systems with stochastic uncertainty’, Int. J. Robust Nonlin. Control, 2016, 26, (11), pp. 2314–2337.
    5. 5)
      • 7. Sun, G., Ren, X., Li, D.: ‘Neural active disturbance rejection output control of multimotor servomechanism’, IEEE Trans. Control Syst. Technol., 2015, 23, (2), pp. 746–753.
    6. 6)
      • 3. Zheng, Q., Dong, L., Lee, D.H., et al: ‘Active disturbance rejection control for MEMS gyroscopes’, IEEE Trans. Control Syst. Technol., 2009, 17, (6), pp. 1432–1438.
    7. 7)
      • 25. Freidovich, L.B., Khalil, H.K.: ‘Performance recovery of feedback-linearization-based designs’, IEEE Trans. Automat. Control, 2008, 53, (10), pp. 2324–2334.
    8. 8)
      • 27. Nazrulla, S., Khalil, H.K.: ‘Robust stabilization of non-minimum phase nonlinear systems using extended high-gain observers’, IEEE Trans. Automat. Control, 2011, 56, (4), pp. 802–813.
    9. 9)
      • 19. Li, S., Yang, J., Chen, W.H., et al: ‘Generalized extended state observer based control for systems with mismatched uncertainties’, IEEE Trans. Ind. Electron., 2012, 59, (12), pp. 4792–4802.
    10. 10)
      • 12. Guo, B.Z., Zhao, Z.L.: ‘On the convergence of an extended state observer for nonlinear systems with uncertainty’, Syst. Control Lett., 2011, 60, (6), pp. 420–430.
    11. 11)
      • 4. Li, S., Yang, X., Yang, D.: ‘Active disturbance rejection control for high pointing accuracy and rotation speed’, Automatica, 2009, 45, pp. 1854–1860.
    12. 12)
      • 17. Guo, B.Z., Wu, Z.H., Zhou, H.C.: ‘Active disturbance rejection control approach to output-feedback stabilization of a class of uncertain nonlinear systems subject to stochastic disturbance’, IEEE Trans. Automat. Control, 2016, 61, (6), pp. 1613–1618.
    13. 13)
      • 15. Ran, M., Wang, Q., Dong, C.: ‘Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control’, Automatica, 2016, 63, pp. 302–310.
    14. 14)
      • 13. Guo, B.Z., Zhao, Z.L.: ‘On convergence of the nonlinear active disturbance rejection control for MIMO systems’, SIAM J. Control Optim., 2013, 51, (2), pp. 1727–1757.
    15. 15)
      • 21. Yao, J., Jiao, Z., Ma, D.: ‘Extended-state-observer-based output feedback nonlinear robust control of hydraulic systems with backstepping’, IEEE Trans. Ind. Electron., 2014, 61, (11), pp. 6285–6293.
    16. 16)
      • 20. Xue, W., Huang, Y.: ‘On performance analysis of ADRC for a class of MIMO lower-triangular nonlinear uncertain systems’, ISA Trans., 2014, 53, pp. 955–962.
    17. 17)
      • 14. Jiang, T., Huang, C., Guo, L.: ‘Control of uncertain nonlinear systems based on observers and estimators’, Automatica, 2015, 59, pp. 35–47.
    18. 18)
      • 28. Lee, J., Mukherjee, R., Khalil, H.K.: ‘Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties’, Automatica, 54, pp. 146–157.
    19. 19)
      • 2. Han, J.: ‘From PID to active disturbance rejection control’, IEEE Trans. Ind. Electron., 2009, 56, (3), pp. 900–906.
    20. 20)
      • 8. Huang, Y., Xue, W.: ‘Active disturbance rejection control: methodology and theoretical analysis’, ISA Trans., 2014, 53, pp. 963–976.
    21. 21)
      • 11. Xue, W., Huang, Y.: ‘On frequency-domain analysis of ADRC for uncertain systems’. Proc. American Control Conf., Wanshington, DC, 2013, pp. 6637–6642.
    22. 22)
      • 16. Wang, Q., Ran, M., Dong, C.: ‘An analysis and design method for a class of nonlinear systems with nested saturations’, Int. J. Control, 2016, 89, (8), pp. 1711–1724.
    23. 23)
      • 26. Chakrabortty, A., Arcak, M.: ‘Rboust stabilization and performance recovery of nonlinear systems with unmodeled dynamics’, IEEE Trans. Automat. Control, 2009, 54, (6), pp. 1351–1356.
    24. 24)
      • 10. Zheng, Q., Gao, L., Gao, Z.: ‘On validation of extended state observer through analysis and experimentation’, J. Dyn. Syst. Meas. Control, 2012, 134, (2), pp. 024505.1–024505.6.
    25. 25)
      • 6. Zhao, L., Yang, Y., Xia, Y., et al: ‘Active disturbance rejection position control for a magnetic rodless pneumatic cylinder’, IEEE Trans. Ind. Electron., 2015, 62, (9), pp. 5838–5846.
    26. 26)
      • 22. Zhao, Z.L., Guo, B.Z.: ‘Active disturbance rejection control approach to stabilization of lower triangular systems with uncertainty’, Int. J. Robust Nonlin. Control, 2016, 26, pp. 2314–2337.
    27. 27)
      • 5. Sira-Ramírez, H., Linares-Flores, J., García-Rodríguez, C.et al.: ‘On the control of the permanent mangnet synchronous motor: an active disturbance rejection control approach’, IEEE Trans. Control Syst. Technol., 2014, 22, (5), pp. 2056–2063.
    28. 28)
      • 24. Guo, B.Z., Wu, Z.H.: ‘Output tracking for a class of nonlinear systems with mismatched uncertainties by active disturbance rejection control’, Syst. Control Lett., 2017, 100, pp. 21–31.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2016.1533
Loading

Related content

content/journals/10.1049/iet-cta.2016.1533
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading