Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Simplification of Linear Time-Invariant Systems by Least Squares Method

최소자승법을 이용한 선형시불변시스템의 간소화

  • 추연석 (홍익대학교 전자ㆍ전기ㆍ컨퓨터공학부) ;
  • 문환영 (㈜선양테크 자동제어부)
  • Published : 2000.05.01
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Abstract

This paper is concerned with the simplification of complex linear time-invariant systems. A simple technique is suggested using the well-known least squares method in the frequency domain. Given a high-order transfer function in the s- or z-domain, the squared-gain function corresponding to a low-order model is computed by the least squares method. Then, the low-order transfer function is obtained through the factorization. Three examples are given to illustrate the efficiency of the proposed method.

Keywords

References

  1. L. Fortuna, G. Nunnari, and A. Gallo, Model order reduction techniques with applications in electrical engineering, Springer-Verlag, N.Y., 1992
  2. R. Genesio and M. Milanese, 'A note on the derivation and use of reduced order models,' IEEE Trans. Automat. Contr., AC-21, pp. 118-122, 1976 https://doi.org/10.1109/TAC.1976.1101127
  3. L. S. Shieh, M. Datta-Baura, and R. E. Yates, 'A method of modelling transfer function using dominant frequency-response data and its application,' Int. J. Sys. Sci., vol. 10, pp. 1097-1114, 1979
  4. A. Lepschy, G. Mian, and U. Viaro, 'Frequency-domain approach to model reduction problem,' Electron. Lett., vol. 18, pp. 829-830, 1982 https://doi.org/10.1049/el:19820563
  5. H. Xiheng, 'FF-Pade method of model reduction in frequency domain,' IEEE Trans. Automat. Contr., vol. AC-32, pp. 243-246, 1987
  6. M. H. Cheng and J. Y. Chang, 'Model reduction for continuousand discrete-time systems via squared-magnitude responses matching by linear programming,' Int J. Sys. Sci., vol. 22, pp. 723-734, 1991
  7. L. A. Aguirre, 'The least squares Pade method for model reduction,' Int. J. Sys. Sci., vol. 23, pp. 1559-1570, 1992
  8. O. A. Sebakhy and M. N. Aly, 'Discrete-time model reduction with optimal zero locations by norm minimization,' IEE Proc. Part D, Contr. Contr. Th Appl., vol. 145, pp. 499-506, 1998 https://doi.org/10.1049/ip-cta:19982400
  9. K. J. Astrom, Introduction to stochastic control theory, N. Y., Academic Press, 1970