Skip to main content
SpringerLink
Log in

A QFT Procedure for Generating Design Frequencies and Bounds of Guaranteed Accuracy

  • Published:
Reliable Computing

Abstract

In this paper, a QFT procedure is presented to systematically determine the following (i) the set of design frequency intervals from a given design frequency range, (ii) the controller bounds of prescribed accuracy at each design frequency interval, and (iii) the controller phase intervals for efficient bound generation at each design frequency interval. The procedure is given for the robust gain-phase margin specifications, based on several new results derived in the paper in the interval analysis framework. The procedure is demonstrated on a significant practical problem concerning the longitudinal motion of an aircraft.

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. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.

    Google Scholar 

  2. Ballance, D. J. and Gawthrop, P. J.: Control System Design via a Quantitative Feedback Theory Approach, in: Proc. IEEE Conference on Control'91, volume 1, Edinburgh, 1991, pp. 476-480.

    Google Scholar 

  3. Balance, D. J. and Hughes, G.: A Survey of Template Generation Methods for Quantitative Feedback Theory, in: UKACC International Conference on Control'96, volume 1, Atlanta, 1996, pp. 172-174.

    Google Scholar 

  4. Borghesani, C., Chait, Y., and Yaniv, O.: The Quantitative Feedback Theory Toolbox for MATLAB, 1995.

  5. Chait, Y., Borghesani, C., and Zheng, Y.: Single Loop QFT Design for Robust Performance in the Presence of Non-Parametric Uncertainties, Trans. Of the ASME Journal of Dynamic Systems, Measurement, and Control 117 (1995), pp. 420-424.

    Google Scholar 

  6. Chait, Y. and Hollot, C. V.: A Comparison Between H-Infinity Methods and QFT for a SISO Plant with both Parametric Uncertainty and Performance Specifications, in: Nwokah, O. D. I. (ed.), Recent Developments in Quantitative Feedback Theory, 1990. pp. 33-40.

  7. Chait, Y. and Yaniv, O.: Direct Control Design in Sampled-Data Uncertain Systems, Automatica 29 (2) (1993), pp. 365-372.

    Google Scholar 

  8. Chait. Y. and Yaniv, O.: Multi-Input/Single-Output Computer-Aided Control Design Using Quantitative Feedback Theory, International Journal of Robust and Nonlinear Control 3 (1) (1993), pp. 47-54.

    Google Scholar 

  9. Chen, W. and Balance, D. J.: Plant Template Generation for Uncertain Plants in QFT, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 121 (1999), pp. 359-364.

    Google Scholar 

  10. East, D. J.: A New Approach to Optimum Loop Synthesis, International Journal of Control 34 (4) (1981), pp. 731-748.

    Google Scholar 

  11. Horowitz, I. M.: Quantitative Feedback Design Theory (QFT), QFT Publications, Boulder, Colorado, 1993.

    Google Scholar 

  12. Horowitz, I. M.: Survey of Quantitative Feedback Theory (QFT), International Journal of Control 53 (2) (1991), pp. 255-291.

    Google Scholar 

  13. Horowitz, I. M.: Synthesis of Feedback Systems, Academic Press, New York, 1963.

    Google Scholar 

  14. Jayasuriya, S.: Frequency Domain Design for Robust Performance Under Parametric, Unstructure, or Mixed Uncertainties, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 115 (1993), pp. 439-451.

    Google Scholar 

  15. Kearfott, R. B.: Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, 1996.

    Google Scholar 

  16. Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, Ch.: PASCAL-XSC Language Reference with Examples, Springer-Verlag, Berlin, Hidelberg, 1993.

    Google Scholar 

  17. Longdon, L. and East, D. J.: A Simple Geometrical Technique for Determining Loop Frequency Bounds Which Achieve Prescribed Sensitivity Specifications, International Journal of Control 30 (1) (1979), pp. 153-158.

    Google Scholar 

  18. Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.

    Google Scholar 

  19. Moore, R. E.: Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979.

    Google Scholar 

  20. Nataraj, P. S. V.: A MATLAB Based Toolbox for Synthesis of Lumped Linear and Nonlinear and Distributed Systems, in: IEEE/IFAC Symposium on Computer Aided Control System Design, Tucson, 1994. pp. 513-518.

  21. Nataraj, P. S. V. and Sardar, G.: Computation of QFT Bounds for Robust Sensitivity and Gain-Phase Margin Specifications, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 122 (2000), pp. 528-534.

    Google Scholar 

  22. Nataraj, P. S. V. and Sardar, G.: Template Generation for Continuous Transfer Functions Using Interval Analysis, Automatica 36 (2000), pp. 111-119.

    Google Scholar 

  23. Nataraj, P. S. V. and Sheela, S. A Procedure for Extraction of Boundary Rectangles from Interval Templates of Plants, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control, under review.

  24. Nordgren, R. E., Nwokah, O. D. I., and Franchek, M. A.: New Formulations for Quantitative Feedback Theory, Int. J. of Robust and Nonlinear Control 4 (1994), pp. 47-64.

    Google Scholar 

  25. Nwokah, O. D. I., Jayasuriya, S., and Chait, Y.: Parametric Robust Control by Quantiative Feedback Theory, AIAA Journal of Guidance and Control 5 (1992), pp. 207-214.

    Google Scholar 

  26. Rodrigues, J. M., Chait, Y., and Hollot, C. V.: An Efficient Algorithm for Computing QFT Bounds, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 119 (3) (1997), pp. 548-552. 27._ Rump, S. M.: INTLAB-Interval Laboratory, in: Csendes, T. (ed.), Developments in Reliable Computing, Kluwer Academic Publishers, 1999.

    Google Scholar 

  27. Thompson, D. F.: Gradient Formulations for Sensitivity-Based QFT Performance Bounds, in: Proc. of ACC, Seattle, 1996, pp. 3975-3976.

  28. Thomspon, D. F. and Nwokah, O. D. I.: Analytical Loop Shaping Methods in Quantitative Feedback Theory, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 116 (1994), pp. 169-177.

    Google Scholar 

  29. Wang, G. C., Chen, C. W., and Wang, S. H.: Equation for Loop Bound in Quantitative Feedback Theory, in: Proc. IEEE Conf. Decision and Control, England, 1991, pp. 2968-2969.

  30. Yaniv, O.: QFT Software, Israel, 1990.

  31. Yaniv, O. and Horowitz, I.: Quantitative Feedback Theory-Reply to Criticisms, International Journal of Control 40 (1987), pp. 945-962.

    Google Scholar 

  32. Zhao, Y. and Jayasuriya, S.: An H-Infinity Formulation of Quantitative Feedback Theory, Trans. of the ASME Journal of Dynamic Systems, Measurement, and Control 120 (3) (1998), pp. 305-313.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Systems and Control Engineering, IIT Bombay, 400 076, India

    Paluri S. V. Nataraj & Suresh Mandir Sheela

Authors
  1. Paluri S. V. Nataraj
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suresh Mandir Sheela
    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

Nataraj, P.S.V., Sheela, S.M. A QFT Procedure for Generating Design Frequencies and Bounds of Guaranteed Accuracy. Reliable Computing 8, 427–451 (2002). https://doi.org/10.1023/A:1021331309574

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021331309574

Keywords

Search

Navigation