Skip to main content

Robust Linear Multivariable Regulators under Perturbations of Physical Parameters

  • Chapter
Book cover New Trends in Systems Theory

Part of the book series: Progress in Systems and Control Theory ((PSCT,volume 7))

  • 440 Accesses

Abstract

In this paper the robust output regulation problem is solved for linear timeinvariant systems whose matrices are assumed to depend on some parameters, each of which possibly affects all the elements of the matrices describing the system, thus playing the role of a “physical” parameter. The robustness here obtained is the preservation of the output regulation property under perturbations of such parameters. Both the conditions for the existence of a solution and a design procedure of the compensator are given.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Basile, G., G. Marro and A. Piazzi, “Revisiting the regulator problem in the geometric approach. Part II-Asymptotic tracking and regulation in the presence of disturbances”, J. of Optimization Theory and Applications, 53, 1 (1987).

    Article  Google Scholar 

  2. Bengston, G. “Output regulation and internal models-A frequency domain approach”, Automatica, 13, 333–345 (1977).

    Article  Google Scholar 

  3. Davison, E.J. “The robust control of a servomechanism problem for linear time-invariant multivariate systems”, IEEE Trans. Aut. Control, AC-21, 25–34 (1976).

    Article  Google Scholar 

  4. Davison, E.J. and A. Goldenberg, “Robust control of a general servomechanism problem: the servo compensator”, Automatica ,11,461–471 (1975).

    Article  Google Scholar 

  5. Desoer, C.A. and Y.T. Wang “Linear time-invariant robust servomechanism problem: a self-contained exposition”, in Control and Dynamic Systems , (C.T. Leondes, Ed.), Academic Press, 81–129,1980.

    Google Scholar 

  6. Francis, B.A. “The linear multivariable regulator problem”, SIAM J. Control, 15,486–505 (1977).

    Article  Google Scholar 

  7. Francis, B.A. and W.M. Wonham, “The internal model principle for linear multivariable regulators”, Appl. Math. Opt., 2, 170–194 (1975).

    Article  Google Scholar 

  8. Francis, B.A. and W.M. Wonham, “The internal model principle of control theory”, Automatica, 12, 457–465 (1976).

    Article  Google Scholar 

  9. Grasselli, O.M., “Steady-state output insensitivity to step-wise disturbances and parameter variations”, System Science, 2, 13–28 (1976).

    Google Scholar 

  10. Grasselli, O.M. and F. Nicolò, “Modal synthesis of astatic multivariable regulation systems”, Proc. 2nd IFAC Symp. on Multiv. Tech. Control Syst., Dusseldorf, paper 1.1.4 (1971).

    Google Scholar 

  11. Grasselli, O.M. and F. Nicolo “Multivariable control systems with a structural steady-state signal in variance” Proc. 3rd IFAC Symp. on Sensitivity, Adaptivity and Optimality, Ischia (Italy),85–90 (1973).

    Google Scholar 

  12. Grasselli, O.M. and F. Nicold,, “Steady-state invariant control systems under polynomial disturbances”, Ricerche di Automatica, 4,105–141 (1973).

    Google Scholar 

  13. Grasselli, O.M. and F. Nicold,, “Steady-state invariant control systems under disturbances satisfying differential equations”, J. Franklin Inst., 301,287–305 (1976).

    Article  Google Scholar 

  14. Kimura, H. and Y. Tanaka, Minimal-time minimal order dead-beat regulator with internal stability, IEEE Trans. Aut. Control, AC-26, 1276–1282 (1981).

    Article  Google Scholar 

  15. Kučera, V. and M. Sebek, “On deadbeat controllers”JEEE Trans. Aut. Control, AC-29, 719–722 (1984).

    Google Scholar 

  16. Marro, G. “System and Control Theory” (in Italian), Chap 9, Zanichelli, Bologna, 1989

    Google Scholar 

  17. Staats, P.W. Jr and J.P. Pearson, “Robust solution of the linear servomechanism problem”, Automatica, 13,125–138 (1977).

    Article  Google Scholar 

  18. Wolovich, W.A “Deadbeat error control of discrete multivariable systems” ,Int. J. Control, 37, 567–582 (1983).

    Article  Google Scholar 

  19. Wonham, W. M.“Linear Multivariable Control-A Geometric Approach”, Springer-Verlag, 1974.

    Google Scholar 

  20. Young, P.C. and J.C. Willems. An approach to the linear multivariable servomechanism problem, Int. J. Control, 15, 961–979 (1972).

    Article  Google Scholar 

  21. Grasselli, O.M., A. Isidori and F. Nicolò, “Output regulation of a class of bilinear systems under constant disturbances”, Automatica, 15,189–195 (1979).

    Article  Google Scholar 

  22. Grasselli, O.M. and F. Lampariello, “Dead-beat control of linear periodic discrete-time systems”, Int. J. Control, 33, 1091–1106 (1981).

    Article  Google Scholar 

  23. Grasselli, O.M. and T. Leo, “Multivariable Control Systems” (in Italian), Pitagora, Bologna, 1979.

    Google Scholar 

  24. Davison, E.J. and S.H. Wang, “Properties and calculation of transmission zeros of linear multivariable systems”, Automatica , 10,643–658 (1974).

    Article  Google Scholar 

  25. Grasselli, O.M. and S. Longhi, “Robust linear multivariable regulators under perturbation of physical parameters”, Rap.Int.90.03, Dip. di Ingegn. Elettronica, Seconda Univ. di Roma “Tor Vergata”, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media New York

About this chapter

Cite this chapter

Grasselli, O.M., Longhi, S. (1991). Robust Linear Multivariable Regulators under Perturbations of Physical Parameters. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_38

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0439-8_38

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6760-7

  • Online ISBN: 978-1-4612-0439-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics