Skip to main content

Robust tracking of multi-variable linear systems under parametric uncertainty

  • Conference paper
  • First Online:
Nonlinear control in the Year 2000

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 258))

Abstract

In this article the robustness of tracking controllers acting on multivariable linear systems under parametric uncertainty is investigated. After a system transformation we design PID-like tracking controllers for the resulting subsystems taking nominal parameters into account. Robustness is studied under parametric uncertainty: it splits into the robust stability of an autonomous linear system and into the robust stability of the same autonomous system being perturbed by secalled “quasi-exogenous” signals. The article is concluded by a DC drive example.

This work was financially supported by the German Academic Exchange Service (DAAD)

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ackermann, J.(1993) Robust Control:Systems with Uncertain Physical Parameters. Springer-Verlag, London

    MATH  Google Scholar 

  2. Barmish, B. R.(1994) New Tools for Robustness of Linear Systems. Macmillan, New York

    MATH  Google Scholar 

  3. Bitauld, L., Fliess, M. and Lévine, J. (1997) Flatness based control synthesis of linear systems: an application to windshield wipers. Proceedings of ECC, Brussels

    Google Scholar 

  4. Delaeau, E. (1997) Suivi de trajectoires pour les systèmes linéaires. Actes Coll. Cetsis — Eea, Orsay, 149–154

    Google Scholar 

  5. Fliess, M. and Marquez, R. (2000) Continous-time linear predictive control and flatness: a module-theoretic setting with examples. Internat. J. Control 73, 606–623

    Article  MATH  MathSciNet  Google Scholar 

  6. Francis, B. A. (1977) The linear multivariable regulator problem. SIAM Contr. Opt. 15, 486–505

    Article  MathSciNet  Google Scholar 

  7. Frazer, R. and Duncan, W. (1929) On the criteria for the stability of small motions. In Proceedings of the Royal Society A 124, 642–654

    Article  Google Scholar 

  8. Hagenmeyer, V. (2000) Robust tracking of linear systems under parametric uncertainty. Proceedings of MTNS 2000, Perpignan

    Google Scholar 

  9. Hagenmeyer, V., Kohlrausch, P. and Delaleau, E. (2000) Flatness based control of the separately excited DC drive. In “Nonlinear Control in the Year 2000” (this very book), eds. Isidori, A., Lamnabhi-Lagarrigue, F. and Respondek, W., Springer-Verlag, London

    Google Scholar 

  10. Hunt, L. R., Meyer, G. and Su, R. (1996) Noncausal inverses for linear systems. IEEE Trans. Automat. Contr. 41, 608–611

    Article  MATH  MathSciNet  Google Scholar 

  11. Hunt, L. R., Meyer, G. and Su, R. (1997) Driven dynamics of time-varying linear systems. IEEE Trans. Automat. Contr. 42, 1313–1317

    Article  MATH  MathSciNet  Google Scholar 

  12. Hopp, T. H., and Schmitendorf, W. E.(1990) Design of a linear controller for robust tracking and model following. Trans. ASME, J. Dynamic Syst., Measurement, and Contr. 112, 552–558

    Article  Google Scholar 

  13. Kharitonov, V. L. (1978) Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial'nye Uravneniya 14, 2086–2088

    MATH  MathSciNet  Google Scholar 

  14. Kokotović, P., Khalil, H. K. and O'Reilly, J. (1986) Singular Perturbation Methods in Control: Analysis and Design. Academic Press, London

    MATH  Google Scholar 

  15. Leonhard, W. (1996) Control of Electrical Drives. Springer, Berlin

    Google Scholar 

  16. Luenberger, D. G.(1967) Canonical Forms for Linear Multivariable Systems. IEEE Trans. Automat. Contr., 290–293

    Google Scholar 

  17. Moore, R. E.(1979) Methods and Applications of Interval Analysis. SIAM, Philadelphia

    MATH  Google Scholar 

  18. Rugh, W. J. (1996) Linear System Theory (2nd edition). Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  19. Schmitendorf, W. E. and Barmish, B. R. (1986) Robust asymptotic tracking for linear systems with unknown parameters. Automatica 22, 335–360

    Article  Google Scholar 

  20. Schmitendorf, W. E. and Barmish, B. R. (1987) Guaranteed output stability for systems with constant disturbances. Trans. ASME, J. Dynamic Syst., Measurement, and Contr. 109, 186–189

    Article  MATH  Google Scholar 

  21. Schmitendorf, W. E. (1987) Methods for obtaining robust tracking control laws. Automatica 23, 675–677

    Article  MATH  Google Scholar 

  22. Sontag, E. D. (1998) Mathematical Control Theory (2nd edition). Springer-Verlag, New York

    MATH  Google Scholar 

  23. Walter, E. and Jaulin, L. (1994) Guaranteed Characterization of Stability Domains Via Set Inversion. IEEE Trans. Automat. Contr. 39, 886–889

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Alberto Isidori (Professor)Françoise Lamnabhi-Lagarrigue (Docteur D’état)Witold Respondek (Professor)

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London Limited

About this paper

Cite this paper

Hagenmeyer, V. (2001). Robust tracking of multi-variable linear systems under parametric uncertainty. In: Isidori, A., Lamnabhi-Lagarrigue, F., Respondek, W. (eds) Nonlinear control in the Year 2000. Lecture Notes in Control and Information Sciences, vol 258. Springer, London. https://doi.org/10.1007/BFb0110231

Download citation

  • DOI: https://doi.org/10.1007/BFb0110231

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-363-8

  • Online ISBN: 978-1-84628-568-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics