doi: 10.17586/2226-1494-2022-22-3-472-479

Adaptive control of nonlinear plant with unmatched parametric uncertainties and input saturation

A. V. Pashenko, D. N. Gerasimov, A. V. Paramonov, V. O. Nikiforov

Read the full article  ';
Article in Russian

For citation:
Pashenko A.V., Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Adaptive control of nonlinear plant with unmatched parametric uncertainties and input saturation. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2022, vol. 22, no. 3, pp. 472–479 (in Russian). doi: 10.17586/2226-1494-2022-22-3-472-479

The problem of adaptive control of a parametrically uncertain nonlinear plant presented in a state-feedback form with unmatched uncertainties and input constraint is considered. The solution is based on adaptive backstepping procedure, in which the virtual controls includes the high-order time derivatives of adjustable parameters calculated with the use of an adaptation algorithm with improved parametric convergence. Analytical design of control with compensation for the influence of input constraints is performed using of a special filter. The approach presented in this paper allows one to design an adaptive controller that ensures the boundedness for all signals in the closed-loop system and provides tracking of the reference signal. Simulation results presented in the MATLAB/Simulink environment illustrate the performance of the presented approach and the acceleration of parametric convergence with an increase of the adaptation coefficient. The plant considered in this work describes a wide class of systems, such as various manipulation robots, technological processes, electromagnetic levitation systems, chemical processes, etc. The proposed control algorithm considers natural for practical applications input constraints and significantly reduces the influence of the regulator parameters tuning speed on the control system transient processes.

Keywords: adaptive control, backstepping, nonlinear object, input saturation, input constraint, improved parametric tuning

Acknowledgements. The reported study was funded by RFBR according to the research project № 20-31-90103.

  1. Kanellakopoulos I., Kokotovic P.V., Morse A.S. Systematic design of adaptive controllers for feedback linearizable systems. IEEE Transactions on Automatic Control, 1991, vol. 36, no. 11, pp. 1241–1253.
  2. Krstić M., Kanellakopoulos I., Kokotović P.V. Adaptive nonlinear control without overparametrization. Systems & Control Letters, 1992, vol. 19, no. 3, pp. 177–185.
  3. Krstic M., Kanellakopoulos I., Kokotovic P.V. Nonlinear and Adaptive Control Design. John Wiley & Sons, Inc., 1995, 563 p.
  4. Nikiforov V.O., Voronov K.V. Adaptive backstepping with a high-order tuner. Automatica, 2001, vol. 37, no. 12, pp. 1953–1960.
  5. Morse A.S. High-order parameter tuners for the adaptive control of linear and nonlinear systems. Systems, Models and Feedback: Theory and Applications, 1992, pp. 339–364.
  6. Ortega R. On Morse's new adaptive controller: parameter convergence and transient performance. IEEE Transactions on Automatic Control, 1993, vol. 38, no. 8, pp. 1191–1202.
  7. Gerasimov D.N., Pashenko A.V., Nikiforov V.O. Improved adaptive servotracking for a class of nonlinear plants with unmatched uncertainties. IFAC-PapersOnLine, 2020, vol. 53, no. 2, pp. 3835–3840.
  8. Gerasimov D.N., Pashenko A.V., Nikiforov V.O. Improved adaptive compensation of unmatched multisinusoidal disturbances in uncertain nonlinear plants. Proc. of the American Control Conference (ACC 2020), 2020, pp. 626–632.
  9. Nikiforov V.O., Gerasimov D., Pashenko A. Modular adaptive backstepping design with a high-order tuner. IEEE Transactions on Automatic Control, 2022, vol. 67, no. 5, pp. 2663–2668
  10. Kreisselmeier G. Adaptive observers with exponential rate of convergence. IEEE Transactions on Automatic Control, 1977, vol. 22, no. 1, pp. 2–8.
  11. Wen C., Zhou J., Liu Z., Su H. Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance. IEEE Transactions on Automatic Control, 2011, vol. 56, no. 7, pp. 1672–1678.
  12. Gao Y.-F., Sun X.-M., Wen C., Wang W. Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Transactions on Automatic Control, 2017, vol. 62, no. 5, pp. 2498–2504.
  13. Min H., Xu S., Ma Q., Zhang B., Zhang Z. Composite-observer-based output-feedback control for nonlinear time-delay systems with input saturation and its application. IEEE Transactions on Industrial Electronics, 2018, vol. 65, no. 7, pp. 5856–5863.
  14. Zhou J., Wen C. Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations. Springer, 2008, 241 p.
  15. Gerasimov D., Nikiforov V. On key properties of the Lion’s and Kreisselmeier’s adaptation algorithms. International Journal of Adaptive Control and Signal Processing, 2021, in press.
  16. Kaczorek T. Externally and internally positive time-varying linear systems. Proc. of the 2002 American Control Conference, 2002, vol. 6, pp. 4638–4641.
  17. Kaczorek T., Sajewski L. The Realization Problem for Positive and Fractional Systems. Springer International Publishing, 2014, 590 p.
  18. Ortega R., Nikiforov V., Gerasimov D. On modified parameter estimators for identification and adaptive control. A unified framework and some new schemes. Annual Reviews in Control, 2020, vol. 50, pp. 278–293.
  19. Nikiforov V.O., Gerasimov D.N. Adaptive Regulation: Reference Tracking and Disturbance Rejection. Springer-Verlag, 2022, in press.
  20. Ioannou P.A., Sun J. Robust Adaptive Control. V. 1. Upper Saddle River, NJ, PTR Prentice-Hall, 1996, 825 p.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2022 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.