Powiadomienia systemowe
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The continued fraction expansions (CFE) approach coupled with several powerful stable reduction methods is proposed for the reduction of high order z-transfer functions. These methods include the advantages of stability preservation methods (SPM), such as Routh approximation, Routh Hurwitz array and stability equation method etc., with those of the method based on continued fraction expansions. The high order z-transfer functions are transformed in w-domain using bilinear transformation and the denominator of the reduced models are found in w-domain. The numerators of reduced order models are determined by matching the quotients of continued fraction expansions in w-domain. Finally, the reduced z-transfer functions are determined using reverse bilinear transformation. In this paper, combined features of SPM and CFE have been utilised to reduce the linear discrete time systems. To match the initial value of the original step response the bilinear transformation is applied in the high order z transfer function in such a way that the numerator and denominator polynomials of original system are separately expressed in w domain. And, to remove any steady error between the system and model responses, steady state values of original, and reduced systems are matched. The method proposed preserves the time domain and frequency domain characteristics and gives stable models for stable systems. An example illustrates the method.
Czasopismo
Rocznik
Tom
Strony
65--76
Opis fizyczny
Bibliogr. 23 poz., wykr.
Bibliografia
- [1] Genesio R., Milanese M., A note on derivation and use of reduced order models, IEEE Trans. Automat. Contr., Vol. AC-21, 1976, 118-122.
- [2] Jamshidi M., Large scale systems modelling and control series. Vol. 9, North Holland, New York, Amsterdam, Oxford, 1983.
- [3] Mahmoud M. S., Singh M. G., Large scale systems modelling. Vol. 3, Pergamon Press, England, First Edition, 1981.
- [4] Sinha N. K., Kuszta B., Modelling and identification of dynamic systems. Van Nostrand Reinhold Company Inc. Electrical/Computer Science and Engineering Series, New York 1983.
- [5] Fortuna G., Nunnari G., Gallo A., Model order reduction techniques with applications in Electrical Engineering, Springer-Vedag, London Limited, 1992.
- [6] Farsi M. K., Warwick G., Doust M., Stable reduced order models for discrete time systems, lEE Proc. PtD, Vol. 133, 1986, 137-141.
- [7] Puri N. N., Lim. M. T., Stable optimal model reduction of linear discrete time systems, ASME J. of Dynamic Syst. Meas. and Contr., Vol. 119, 1997, 300-304.
- [8] Hwang C., Shieh Y. P., A combined time and frequency domain method for model reduction of discrete systems, J. Franklin Institute, Vol. 311, No. 6, June 1981, 391-402.
- [9] Shieh Y. P., WU W. T., Simplifications of z-transfer functions by continued fractions. Int. J. Control., Vol. 17, No. 5, 1973, 1089-1094.
- [10] Pal J., Prasad R., Biased reduced order models for discrete time systems. Systems Science, Vol. 18, No. 3, 1992, 41-50.
- [11] Hution M. F., Friedland B., Routh approximants for reducing order of linear time invariant systems, IEEE Trans. Automat. Contr., Vol. AC-20, 1975, 329-337.
- [12] Krishnamurthi V., Seshadri V., Model reduction using Routh stability criterion, IEEE Trans. Automat. Contr., Vol. AC-23, No. 4, Aug. 1978, 729-731.
- [13] Chen T. C, Chang C. Y., Reduction of transfer functions by the stability equation method, J. of Franklin Institute, Vol. 308, No. 4, Oct. 1979, 389-404.
- [14] Wall H. S., Analytic theory of continued fractions. Van Nostrand, N.Y. 1948.
- [15] Chen C. F., Shieh L. S., A novel approach to linear model simplification. Int. J. Control., Vol. 8, 1968, 561-570.
- [16] Shieh L. S., Goldman M. J., Continued fraction expansion and inversion of the Cauer third form, IEEE Trans. Circuits and Systems, Vol. CAS-21, 1974, 341-345.
- [17] Chen C. F., Shieh L. S., Continued fraction inversion by Routh's algorithm, IEEE Trans. Circuit Theory, Vol. C.T16, 1969, 197-202.
- [18] Rao S. V., Lamba S. S., A note on continued fraction inversion by Routh's algorithm, IEEE Trans. Automat. Contr., Vol. AC-19, No. 3, June 1974, 727-737.
- [19] Prasad R., Linear system reduction using mixed methods in frequency domain. Int. Conf. on Mathematical Modelling, Tata McGraw-Hill Publishing Company Limited, New Delhi, Jan. 29-31, 2001, 161-167.
- [20] Parthasarathy R., Jayasimha K. N., Modelling of Linear Discrete Time Systems using Modified Cauer Continued Fraction, Journal of the Franklin Institute, Pergamon Press Ltd, Vol. 316, No. 1, July 1983, 79-86.
- [21] Bistritz Y., a discrete Routh stability method for discrete system modelling. System and Control Letters, Vol. 2, 1982, 83-87.
- [22] Pal J., System reduction by a mixed method, IEEE Trans. Automat. Contr., Vol. AC-25, No. 5, 1980, 973-976.
- [23] Prasad R., Pal J., Stable reduction of linear systems by continued fractions, J. of Institution of Engineers of India, Vol. 72, Oct. 1991, 113-117.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0008-0060