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Parametric robust control by quantitative feedback theory

  • Osita Nwokah
  • Suhada Jayasuriya
  • Yossi Chait
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 170)

Abstract

The problem of performance robustness, especially in the face of significant parametric uncertainty, has been increasingly recognized as a predominant issue of engineering significance in many design applications. Quantitative feedback theory (QFT) is very effective for dealing with this class of problems even when there exist hard constraints on closed loop response. In this paper, SISO-QFT is viewed formally as a sensitivity constrained multi objective optimization problem which can be used to set up a constrained H minimization problem whose solution provides an initial guess at the QFT solution. In contrast to the more recent robust control methods where phase uncertainty information is often neglected, the direct use of parametric uncertainty and phase information in QFT results in a significant reduction in the cost of feedback. An example involving a standard problem is included for completeness.

Keywords

Parametric uncertainty QFT robust control 

List of Symbols Used

L

Banach space of essentially bounded Baire functions

H

Banach space of bounded analytic functions

RH

Banach space of bounded analytic functions with elements from the ring of stable, proper real rational functions

Unit of RH

An element of RH whose inverse ∈ RH

e,r

relative degree of transfer function

SISO

single input, single output

MIMO

multi-input, multi-output

ω,λ

radian frequency

Θ

compact parameter space with elements α

QFT

Quantitative Feedback Theory

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6. References

  1. 1.
    D'Azzo, J. J., Houpis, C. H., Linear Control System Analysis and Design, 5th Edition, McGraw Hill, New York, 1988.Google Scholar
  2. 2.
    Gera, A., Horowitz, I. M., Optimization of the Loop Transfer Function, International J. Control 31, 389–398, 1980.Google Scholar
  3. 3.
    Robinson, E. A., Random Wavelets and Cybernetic Systems, Hafner Publishers, New York 1962.Google Scholar
  4. 4.
    Thompson, D. F., Optimal and Sub-optimal Loop Shaping in Quantitative Feedback Theory, Ph. D. Thesis, Purdue University, August 1990.Google Scholar
  5. 5.
    Nwokah, O.D.I., Thompson, D. F., Perez, R. A., On the Existence of QFT Controllers, ASME-WAM, Dallas, TX, 1990.Google Scholar
  6. 6.
    Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall, New Jersey, 1962.Google Scholar
  7. 7.
    Lurie, B.J., Feedback Maximization, Artech House Inc., Dedham, Massachusetts, 1986.Google Scholar
  8. 8.
    Freudenberg, J.S., Looze, D.P., Frequency Domain Properties of Scalar and Multivariable Feedback Systems, Springer-Verlag, New York, 1988.Google Scholar
  9. 9.
    Dorato, P., Yedavali, R. (Eds.), Recent Advances in Robust Control, IEEE Press, New York, 1990.Google Scholar
  10. 10.
    Zames, G., Feedback and Optimal Sensitivity: Model Reference Transformation, Multiplicative Semi Norms, and Approximate inverses, IEEE Trans. Autom Control, AC-26, April 1981.Google Scholar
  11. 11.
    Francis, B.A., A Course in An element of RH whose inverse ∈ H Control Theory, Lecture Notes in Control and Information Sciences, No., Springer-Verlag, New York, 1987.Google Scholar
  12. 12.
    Maciejowski, J., Multivariable Feedback Design, Addison-Wesley, Reading, MA, 1989.Google Scholar
  13. 13.
    Horowitz, I.M., Synthesis of Feedback Systems, Academic Press, Orlando, FL, 1963.Google Scholar
  14. 14.
    Jayasuriya, S., Nwokah, O.D.I., Yaniv, O., The Benchmark Problem Solution by Quantitative Feedback Theory, Proc. ACC, Boston, MA, 1991. Also submitted to AIAA Journal of Guidance and Control.Google Scholar
  15. 15.
    Chait, Y., Hollot, C.V., A Comparison Between An element of RH whose inverse ∈ H Methods and QFT for a SISO Plant with Both Plant Uncertainty and Performance Specifications, ASME Winter Annual Meeting, Dallas, TX, November 1990.Google Scholar
  16. 16.
    Betzold, R.W., MIMO Flight Control Design with Highly Uncertain Parameters: Application to the C-135 Aircraft, M.S. Thesis, Dept. of Electrical Engineering, Air Force Institute of Technology, AFIT/GE/EE/83D-11, WPAFB, OH 1983.Google Scholar
  17. 17.
    Thompson, D.F., Analytical Loop Shaping Methods in Quantitative Feedback Theory, ASME-Winter Annual Meeting, Dallas, Texas, November 1990.Google Scholar
  18. 18.
    Perez, R.A., Nwokah, O.D.I., Thompson, D.F., Almost Decoupling by Quantitative Feedback Theory, submitted to the American Control Conference, Boston, MA, 1991. Also submitted to the ASME Journal of Dynamic Systems and Control.Google Scholar
  19. 19.
    Morari, M., Zafiriou, E., Robust Process Control, Prentice-Hall, NJ, 1989.Google Scholar
  20. 20.
    Thompson, D.F., Nwokah, O.D.I., Frequency Response Specifications and Sensitivity Functions in Quantitative Feedback Theory, ACC, Boston, 1991, Also submitted to ASME J. Dynamic Systems Measurement and Control.Google Scholar
  21. 21.
    Nwokah, O.D.I., Strong Robustness In Uncertain Multivariable Systems, IEEE CDC, Austin, TX, December 1988.Google Scholar
  22. 22.
    Kwakernaak, H., Minimax Frequency Domain Performance and Robustness Optimization of Linear Feedback Systems IEEE Trans. Autom. Control AC-30, 994–1004, 1985.Google Scholar
  23. 23.
    Verma, M. Jonckheere, E. L Compensation with Mixed Sensitivity as a Broadband Matching Problem, Systems and Control Letters, 4, 125–129, 1984.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Osita Nwokah
    • 1
  • Suhada Jayasuriya
    • 2
  • Yossi Chait
    • 3
  1. 1.School of Mechanical EngineeringPurdue UniversityWest Lafayette
  2. 2.Department of Mechanical EngineeringTexas A&M UniversityCollege Station
  3. 3.Department of Mechanical EngineeringUniversity of MassachusettsAmherst

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