Skip to main content

Theory and method for designing feedback controllers of siso descriptor systems with H-optimal sensitivity

  • Linear Systems
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 111))

Abstract

In this paper, some frequency characteristics of SISO descriptor systems are first investigated after the brief introduction of the H-optimal sensitivity theory. Then a new frequency domain method for designing the feedback controllers of SISO descriptor systems, which can eliminate the impulsive modes, stabilize the systems and obtain the minimal sensitivity, is proposed. Furthermore, a practical sub-optimal design method is given. At last, an example is discussed to demonstrate the designing procedure.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Zames and B.A. Francis, "Feedback, minimax sensitivity, and optimal robustness", IEEE Trans. Automat. Contr., vol. AC-28, pp. 585–601, 1983.

    Google Scholar 

  2. G. Zames, "Feedback and optimal sensitivity: Model reference transformation multiplicative seminorms, and approximate inverse", IEEE Trans. Automat. Contr., vol. AC-26, pp. 301–320, 1981.

    Google Scholar 

  3. D.L.Xu and J.B.Yang, "A new frequency design method — an introduction to H-optimal method". Proc. of the 3th. National Conf. for Youth on Systems and Control, Lanzhou, China, Aug. 1987 (in Chinese).

    Google Scholar 

  4. H. Kwakernaak, "Minimax frequency domain performance and robustness optimization of linear feedback systems", IEEE Trans. Automat. Contr., vol. AC-30, pp.994–1004, 1985.

    Google Scholar 

  5. W.W.Rogsinski and H.S.Shapiro, "On certain extremum problems for analytic function", Acta Math., vol.90, pp. 287–318

    Google Scholar 

  6. B.A. Francis and G. Zames, "On H-optimal sensitivity theory for SISO feedback systems", IEEE Trans. Automat. Contr., vol. AC-29, pp. 9–16, 1984.

    Google Scholar 

  7. G.Zames, A.Tannenbaum and C.Foias, "Optimal H interpolation: A new approach", Proc. IEEE Conf. on Decision and Control, Athens, Greece, WP1, Dec. 1986.

    Google Scholar 

  8. M.G.Safonof, "Future direction in L-robust control theory", the same as [7].

    Google Scholar 

  9. H. Kimura, "Robust stabilizability for a class of transfer function", IEEE Trans. Automat. Contr., vol.AC-29, pp. 788–793, 1984.

    Google Scholar 

  10. C.A. Desoer, R.W. Liu, J. Murray, and R. Saeks, "Feedback system design: The fractional representation approach to analysis and synthesis", IEEE Trans. Automat. Contr., vol. AC-25, pp. 399–412, 1980.

    Google Scholar 

  11. J.J. Bongiorno and D.C. Youla, "On the design of single-loop single-input-output feedback control systems in the complex frequency domain", IEEE Trans. Automat. Contr., vol. AC-22, pp. 416–423, 1977.

    Google Scholar 

  12. Y.Y.Wang, "Feedback control of descriptor dynamic systems", Ph.D. Dissertation, Shanghai Jiao Tong University, China. 1987 (in Chinese).

    Google Scholar 

  13. H.H. Rosenbrock, "Structure properties of linear dynamic systems", Int. J. Contr., vol.20, pp. 191–202, 1974.

    Google Scholar 

  14. J.D. Cobb, "Feedback and poles placement in descriptor variable systems", Int. J. Contr., vol.33, pp. 1135–1146, 1981.

    Google Scholar 

  15. S.Z. Chen, "Feedback and poles placement of descriptor systems", Control Theory & Applications, vol.2, pp. 10–18, Mar. 1985 (in Chinese).

    Google Scholar 

  16. Z.W.Fei, "Structure analysis, poles placement and reduced order observer design". Master Dissertation, Shanghai Jiao Tong University, 1985 (in Chinese).

    Google Scholar 

  17. Y.Y.Wang, Z.J.Zhang, "Feedback control and poles placement for descriptor systems", Acta Automation Sinica, to appear (in Chinese).

    Google Scholar 

  18. L.Y.Dai and C.Z.Wang, "The regular dynamic compensator of structure stability for descriptor systems", Proc. of National Academic Conf. on Control Theory and Applications pp.36–40, 1985 (in Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Bensoussan J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Xu, DL., Yang, JB., Shi, SJ. (1988). Theory and method for designing feedback controllers of siso descriptor systems with H-optimal sensitivity. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042206

Download citation

  • DOI: https://doi.org/10.1007/BFb0042206

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19237-4

  • Online ISBN: 978-3-540-39161-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics