On a Transfer Function that Approximates Complex Dynamics

Abstract

This paper proposes a parallel combination model of the well-known transfer function G(s)-Kexp(-Ls)/(1+Ts) and shows its ability to approximate complex dynamic behaviour such as that of distributed parameter systems. First, the gain and phase of the transfer function were calculated and were shown to have resonance in its frequency response with appropriate parameters, which means that their slopes can be varied in a wide range. As a result, the function can approximate various dynamic behaviours well. Next, their asymptotic behaviours, which can represent the relation between the parameters of the function and help to estimate approximate values of the parameters, were shown. Fitting to frequency and indicial response data of heat exchangers which are common in chemical industries and the dynamic behaviours of which have been studied from theoretical and experimental points of view were done. Results of the fitting showed a good approximation, not only in frequency response but also in indicial response. This indicates that the transfer function model presented here can fit to various complex dynamic models. © 1992, The Society of Chemical Engineers, Japan. All rights reserved.