Abstract
Given measured frequency response data from a linear system (amplitude ratio and phase shift) at a significant number of frequencies, one can use a recently developed rational approximation algorithm to find a reasonable model of the system (in the transfer function form) with H∞-norm error estimates. The H∞-norm error can be made arbitrarily small by increasing the order of the approximant and therefore leads to models which are sufficient for robust controller designs. The algorithm uses FFT type calculations which make it convenient to use and computationally well behaved. The use of the algorithm for system identification along with some aids developed to make it easier to use will be described.
The research reported on here was supported by NSF grant DMS 9002919.
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References
H. Beke, Transfer Function Fitting to Gain-Phase Constraints, Ph.D. Thesis, University of Minnesota, 1992.
R. F. Curtain and K. Glover, Robust Stabilization of infinite-dimensional systems by finite-dimensional controllers, Syst. Contr. Lett. 7 (1986), pp. 41–47.
J. C. Doyle, B. A. Francis, and A. R. Tannenbaum, Feedback Control Theory, Macmillan Publishing Co., New York, 1992.
P. A. Fuhrmann, Linear Systems and Operators in Hilbert Spaces, McGraw Hill Inc., New York, 1981.
G. Gu, P. Khargonekar, and E. B. Lee, Approximation of infinite-dimensional systems, IEEE Trans. on Automat. Contr. 34 (1989) 610–618.
G. Gu, P. Khargonekar, E. B. Lee, and P. Misra, Rational approximations of unstable infinite dimensional systems, SIAM J. Contr. and Opt., 1992.
A. J. Laub, "Computation of System Balancing Transformations," Proceedings of 25th Conference on Decision and Control, Dec. 1986, pp. 548–553.
P. Mäkilä, "Approximation of stable systems by Laguerre filters", Automatica, 26, 1990, 333–345.
B. C. Moore, "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," in IEEE trans. on automat contr., AC-26 (1981), pp.17–31.
K. Ogata, Modern Control Engineering, Prentice Hall Inc., New Jersey, 1970.
H. Özbay, "H∞ optimal controller design for a class of distributed parameter systems", EE Dept. preprint, Ohio State Univ., 1991.
H. Özbay, "Controller reduction in the two block H·-optimal design for distributed plants", Int. J. Control, 54 (1991) 1291–1308.
J. Partington, "Approximation of delay systems by Fourier-Laquerre Series", Automatica, 27, (1991), 569–572.
B. Wahlberg, System Identification Using Laguerre Models, IEEE Trans. on Automat. Contr. 36 (1991), 551–562.
Eva Wu and G. Gu, "Discrete fourier transform and H2 approximation", IEEE Trans. Automat. Contr. 35 (1990) 1044–1046.
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© 1992 Springer-Verlag
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Cai, Mp., Lee, E.B. (1992). Identification of linear systems using rational approximation techniques. In: Duncan, T.E., Pasik-Duncan, B. (eds) Stochastic Theory and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113232
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DOI: https://doi.org/10.1007/BFb0113232
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