Journal of the Korean Institute of Illuminating and Electrical Installation Engineers (조명전기설비학회논문지)

The Korean Institute of IIIuminating and Electrical Installation Engineers (한국조명전기설비학회)
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A Transfer Function Synthesis for Model Approximation with Resonance Peak Value

첨두공진점을 갖는 모델 근사화를 위한 전달함수 합성법

  • 김종근 (충주대학교 전기공학과) ;
  • 김주식 (충주대학교 전기공학과) ;
  • 김흥규 (충주대학교 전기공학과)
  • Published : 2008.01.31
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Abstract

This paper proposes a frequency transfer function synthesis for approximating a high-order model with resonance to a low-order model in the frequency domain. The presented model approximation method is based on minimizing the error function weighted by the numerator polynomial of approximated models, which is used of the RLS(Recursive Least Square) technique to estimate the coefficient vector of approximated models. The proposed method provides better fitting in a low frequency and peak resonance. And an example is given to illustrate feasibilities of the suggested schemes.

본 논문은 주파수영역에서 첨두공진점을 갖는 고차모델을 저차모델로 근사화하기 위한 주파수 전달함수 합성법을 제안한다. 제안된 근사화 방법은 근사화된 모델의 분모 다항식에 가중된 오차함수의 최소화에 근거하며, 근사화된 모델의 주파수 전달함수에 대한 계수벡터를 추정하기 위해 RLS 기법을 이용한다. 제안된 방법은 저주파수와 첨두공진점에서 우수한 정합특성을 나타내며, 예제에 의해 제안된 방식의 유용성을 검증한다.

Keywords

References

  1. T. C. Hsia, 'On the Simplification of Linear Systems', IEEE Trans. Auto. Cont., vol. AC-17, pp. 372-374, 1972
  2. Y. Shamash, 'Stable Reduced-Order Models Using Padé-Type Approximation', IEEE Trans. Auto. Cont., vol. AC-19, pp. 615-616, 1974
  3. H. Xiheng, 'FF-Pade Method of Model Reduction in Frequency Domain', IEEE Trans. Auto. Cont., vol. AC-32, no. 3, pp. 243-246, 1987
  4. C. F. Chen and L. S. Shieh, 'Continued Fraction Inversion by Routh's Algorithm', IEEE Trans. on Circuit Theory, vol. 16, no. 2, pp. 197-202, 1969 https://doi.org/10.1109/TCT.1969.1082925
  5. W. Krajewski, A. Lepschy, and U. Viaro, 'Model Reduction by Matching Markov Parameters, Time Moments, and Impulse-Response Energies', IEEE Trans. Auto. Cont., vol. AC-40, no. 5, pp. 949-953, 1995
  6. M. F. Hutton and B. Friedland, 'Routh Approximations for Reducing Order of Linear, Time-Invariant Systems', IEEE Trans. Auto. Cont., vol. AC-20, no. 3, pp. 329-337, 1975
  7. V. Krishnamurthy and V. Seshadri, 'Model Reduction Using the Routh Stability Criterion', IEEE Trans. Auto. Cont., vol. AC-23, no. 4, pp. 729-731, 1978
  8. C. S. Hsieh and C. Hwang, 'Model Reduction of Continuous-Time Systems Using a Modified Routh Approximation Method', IEE Proc. Control Theory Appl., vol. 136, no. 4, pp. 151-156, 1989
  9. Y. Choo, 'Direct Method for obtaining Modified Routh Approximants', IEE Electron. Lett., vol. 35, no. 19, pp. 1627-1628, 1999 https://doi.org/10.1049/el:19991135
  10. A. S. S. R. Reddy, 'A Method for Frequency Domain Simplification of Transfer Functions', Int. J. Control, vol. 23, no. 3, pp. 403-408, 1976 https://doi.org/10.1080/00207177608922167
  11. R. Luus, 'Optimization in Model Reduction', Int. J. Control, vol. 32, no. 5, pp. 741-747, 1980 https://doi.org/10.1080/00207178008922887
  12. C. K. Sanathanan and J. Koerner, 'Transfer Function synthesis as a Ratio of two Complex Polynomials', IEEE Trans. on Auto. Cont, pp.56-58, 1963
  13. M. T. Jong and K. S. Shanmugam, 'Determination of a Transfer Function from Amplitude Frequency Data', Int. J. Cont., vol. 25, no. 6, pp. 941-948, 1977 https://doi.org/10.1080/00207177708922280
  14. J. S. Kim, J. G. Kim and J. W. Ryu, 'A Model Reduction with Time Delay in Frequency Domain', KIIEE, vol. 18, no. 6, pp.176-182, 2004
  15. 김종근, '주파수 전달함수 합성법에 의한 모델축소 및 PID 제어기 설계', 공학박사학위논문, 2005
  16. B. C. Moore, 'Principal Component Analysis in Linear Systems : Controllability, Observability and Model Reduction', IEEE Trans. on Auto. Cont, vol. 26, no. 1, pp. 17-32, 1981 https://doi.org/10.1109/TAC.1981.1102568
  17. M. G. Safonov and R. Y. Chiang, 'A Schur Method for Balanced-Truncation Model Reduction', IEEE Trans. on Auto. Cont, vol. 34, no. 7, pp. 729-733, 1989 https://doi.org/10.1109/9.29399
  18. R. Pintelon, P. Guillaume, Y. Rolain, J. Schoukens and H. Van hamme, 'Parametric Identification of transfer functions in the frequency Domain - A Survey', IEEE Trans. on Auto. Cont, vol. 39, no. 11, pp. 2245-2260, 1994 https://doi.org/10.1109/9.333769
  19. T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice Hall, 2000
  20. Matlab Robust Control Toolbox, Ver.6.0