Determination of Simplified Models by means of Chebyshev Polynomials

  • Janusz Halawa
  • Anna Trzmielak-Stanisławska
Conference paper
Part of the Advances in Simulation book series (ADVS.SIMULATION, volume 1)


A method of simplifying the mathematical models described by high-order transfer functions is presented. The simplified transfer function is found by expanding the initial transfer function into a Chebyshev series and composing a rational approximation of this series. The time and frequency responses of the simplified model should ensure a good, in a sense of the norm assumed, approximation of these for the higher order models. The method presented provides better results than these in continued fraction method.


Transfer Function Frequency Response Rational Approximation Chebyshev Polynomial Initial System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bistritz, V., Langholz, G.: Model reduction by best Chebyshev rational approximations in the complex plane. Int. J. Control. 30 (1979) 2MathSciNetCrossRefGoogle Scholar
  2. [2]
    Chen, C. F. Shieh, L. S.: A novel, approach to liner model simplification Int. J., Control. 8 (1985). 399–402Google Scholar
  3. [3]
    Halawa, J., Halawa T.: Simulation investigations of interconnected power systems. Reduction of mathematical model. System Analysis and Simulation. t. II. Academie-Verlag, Berlin (1985), 399–402Google Scholar
  4. [4]
    Halawa, J., Trzmielak-Stanisławska, A.: Properties of Simplified Transfer Functions as Acquired with a Method of Continued Fractions Archiwum Automatyki i Telemechaniki, Tom XXXI, Zeszyt 1–2 (1986)Google Scholar
  5. [5]
    Paszkowski S: Zastosowania numeryczne wielomianów Czebyszewa, PWN, Warszawa (1975)MATHGoogle Scholar

Copyright information

© Akademie-Verlag Berlin 1988

Authors and Affiliations

  • Janusz Halawa
    • 1
  • Anna Trzmielak-Stanisławska
    • 2
  1. 1.Institute of Technical Cybernetic of Technical University of WrocławWrocławPoland
  2. 2.Institute of Computer Science of University of WrocławWrocławPoland

Personalised recommendations