Skip to main content
SpringerLink
Log in

An Internal-Model Controller for a Class of Single-Input Single-Output Nonlinear Systems: Stability and Robustness

  • Published:
Dynamics and Control

Abstract

A controller design procedure for a class of nonlinear systems is presented. The structure of the control system corresponds to the so-called internal-model controller that, for linear systems, has exhibited good performance and stability robustness with respect to disturbances and to uncertainty in the plant parameters. The systems involved are single-input single-output and fully linearizable by coordinates transformation and state feedback. It is shown that the plant output converges to a constant reference, even under the presence of constant disturbances and parameter uncertainties, provided the closed-loop system has an asymptotically stable equilibrium point placed anywhere. This scheme does not need an explicit design of a nonlinear observer; instead, it uses the state of a plant model. A conservative stability robustness margin is estimated by applying standard results of Lyapunov theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alvarez, J. and Alvarez, J., “Tracking and regulation reference model control of nonlinear systems,” in Proc. of the IFAC Int. Symp. on Nonlinear Control Systems Design, Capri, Italy, pp. 466–471, 1989.

  2. Alvarez, J., “Stability and robustness of an internal-model controller for a class of nonlinear system,” in Preprints of the Nonlinear Control Systems Design Symp., Tahoe City, CA, USA, pp. 765–770, 1995.

  3. Arkun, Y. and Calvet, J. P., “Robust stabilization of input/output linearizable systems under uncertainty and disturbances,” AIChE Journal, vol. 38, pp. 1145–1156, 1992.

    Google Scholar 

  4. Bartusiak, R. D., Georgakis, C., and Reilly, M. J., “Nonlinear feedforward/feedback control structures designed by reference system synthesis,” Chem. Eng. Sci.,vol.44, pp. 1837, 1989.

    Google Scholar 

  5. Calvet, J., and Arkun, Y., “Feedforward and feedback linearization of nonlinear systems and its implementation using internal model control (IMC),” Ind. Eng. Chem. Res.,vol. 27, pp. 1822, 1988.

    Google Scholar 

  6. Castillo, B. and Alvarez, J., “Identification and bilinear control of a binary distillation column,” Int. J. of Systems Sci., vol. 18, pp. 2209–2228, 1987.

    Google Scholar 

  7. Cho, Y.M., Rajamani, R. “A systematic approach to adaptive observer synthesis for nonlinear systems”, IEEE Trans. on Automatic Control, vol. 42, pp. 534–537, 1997.

    Google Scholar 

  8. Doyle III, F. J., Packard, A. K., and Morari, M., “Robust controller design for a nonlinear CSTR,” Chemical Engineering Science, vol. 44, pp. 1929–1947, 1989.

    Google Scholar 

  9. Economou, C. G., Morari, M., and Palsson, B. O., “Internal model control, 5. Extension to nonlinear systems,” Ind. Eng. Chem. Proc. Des. and Dev., vol. 25, pp. 403, 1986.

    Google Scholar 

  10. España, M. D., “Bilinear modeling of distillation columns,” Ph. D. dissertation (in French), INPG, Grenoble, France, 1977.

    Google Scholar 

  11. Henson, M. A. and Seborg, D. E., “An internal model control strategy for nonlinear systems,” AIChE J., vol. 37, pp. 1065–1081, 1991.

    Google Scholar 

  12. Isidori, A. Nonlinear Control Systems,Springer Verlag, London, 3th Ed., 1995.

    Google Scholar 

  13. Khalil, H. K. “Robust servomechanism output feedback controllers for feedback linearizable systems,” Automatica,vol. 30, pp. 1587–1599, 1994.

    Google Scholar 

  14. Khalil, H. K. Nonlinear Systems,Prentice Hall, 2nd Ed., Upper Saddle River, NJ, 1996.

    Google Scholar 

  15. Kravaris, C. and Palanki, S., “Robust nonlinear state feedback under structured uncertainty,” AIChE Journal, vol. 34, pp. 1119–1127, 1988.

    Google Scholar 

  16. Michel, A. and Wang, K., Qualitative Theory of Dynamical Systems, Marcel Dekker, Inc., New York, 1995.

    Google Scholar 

  17. Morari, M. and Zafiriou, E., Robust Process Control,Prentice Hall, 1989.

  18. Pilyugin, S. Y. Introduction to structurally stable systems of differential equations,Birkhäuser Verlag, Basel, 1992.

    Google Scholar 

  19. Schoenwald, D. A. and Ozguner, U., “Robust stabilization of nonlinear systems with parametric uncertainty,” IEEE Trans. on Automatic Control, vol. 39, pp. 1751–1755, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Scientific Research and Advanced Studies Center of Ensenada (CICESE), Km. 107 Carretera Tijuana-Ensenada, 22860, Ensenada, BC, México

    Joaquin Alvarez & Salvador Zazueta

Authors
  1. Joaquin Alvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Salvador Zazueta
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alvarez, J., Zazueta, S. An Internal-Model Controller for a Class of Single-Input Single-Output Nonlinear Systems: Stability and Robustness. Dynamics and Control 8, 123–144 (1998). https://doi.org/10.1023/A:1008286412428

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008286412428

Search

Navigation