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.
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Abbreviations
- 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
6. References
D'Azzo, J. J., Houpis, C. H., Linear Control System Analysis and Design, 5th Edition, McGraw Hill, New York, 1988.
Gera, A., Horowitz, I. M., Optimization of the Loop Transfer Function, International J. Control 31, 389–398, 1980.
Robinson, E. A., Random Wavelets and Cybernetic Systems, Hafner Publishers, New York 1962.
Thompson, D. F., Optimal and Sub-optimal Loop Shaping in Quantitative Feedback Theory, Ph. D. Thesis, Purdue University, August 1990.
Nwokah, O.D.I., Thompson, D. F., Perez, R. A., On the Existence of QFT Controllers, ASME-WAM, Dallas, TX, 1990.
Hoffman, K., Banach Spaces of Analytic Functions, Prentice-Hall, New Jersey, 1962.
Lurie, B.J., Feedback Maximization, Artech House Inc., Dedham, Massachusetts, 1986.
Freudenberg, J.S., Looze, D.P., Frequency Domain Properties of Scalar and Multivariable Feedback Systems, Springer-Verlag, New York, 1988.
Dorato, P., Yedavali, R. (Eds.), Recent Advances in Robust Control, IEEE Press, New York, 1990.
Zames, G., Feedback and Optimal Sensitivity: Model Reference Transformation, Multiplicative Semi Norms, and Approximate inverses, IEEE Trans. Autom Control, AC-26, April 1981.
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.
Maciejowski, J., Multivariable Feedback Design, Addison-Wesley, Reading, MA, 1989.
Horowitz, I.M., Synthesis of Feedback Systems, Academic Press, Orlando, FL, 1963.
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.
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.
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.
Thompson, D.F., Analytical Loop Shaping Methods in Quantitative Feedback Theory, ASME-Winter Annual Meeting, Dallas, Texas, November 1990.
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.
Morari, M., Zafiriou, E., Robust Process Control, Prentice-Hall, NJ, 1989.
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.
Nwokah, O.D.I., Strong Robustness In Uncertain Multivariable Systems, IEEE CDC, Austin, TX, December 1988.
Kwakernaak, H., Minimax Frequency Domain Performance and Robustness Optimization of Linear Feedback Systems IEEE Trans. Autom. Control AC-30, 994–1004, 1985.
Verma, M. Jonckheere, E. L∞ Compensation with Mixed Sensitivity as a Broadband Matching Problem, Systems and Control Letters, 4, 125–129, 1984.
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Nwokah, O., Jayasuriya, S., Chait, Y. (1992). Parametric robust control by quantitative feedback theory. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004310
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DOI: https://doi.org/10.1007/BFb0004310
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