Evaluation of Approximation And Reduction Method for Fractional Order Transfer Function

Abstract

Mathematical models used to represent physical processes are generally large and complex. Large models are difficult to implement in industry, so model simplification methods are needed. Model simplification is a process of reducing high system order to low system order. Complex models such as fraction-order transfer functions are very difficult to apply in industry. The simplification of the fraction-order transfer function can be approximated by filtering to an integer-order transfer function. This study discusses the method of simplifying the fraction-order transfer function to an integer-order transfer function using an refined oustaloop filter. Improved approximation of the oustaloop filter and the oustaloop filter resulted in a high-order transfer function that could not be implemented. The high-order transfer function is then reduced by the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm method to obtain a simple and easy-to-design model system such as FOPDT and SOPDT. The evaluation of the reduced model can be seen by comparing the time characteristics (response step) and frequency response (bode plot) of the real system with the reduced system model. The data simulation results show increasing 10% - 15% gain margin error in the refined oustaloop filter and oustaloop filter with the addition of zero to the transfer function of the real system. Refine oustaloop filters give better approximation results than oustaloop filters. The oustaloop filter method, refine oustaloop filter, and H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm reduction did not change the stability of the system in a stable system.