A method for modelling transfer functions using dominant frequency-response data and its applications

This paper presents a fundamental method for modelling transfer functions using the basic performance specifications and frequency-response data at the dominant frequencies. A set of non-linear equations is constructed from the definitions of the basic performance specifications, the dominant frequency-response data and the unknown coefficients of a transfer function. A Newton-Raphson multidimensional method is applied to solve the non-linear equations. Four methods are given to construct approximate representations of the desired transfer functions for the estimation of good starting values to ensure rapid convergence of the numerical method. The applications of the proposed method are : (1) developing a standard model and/or a transfer function of a filter or a compensator using the specified dominant frequency-response data ; (2) identifying the transfer function of a system from available experimental frequency-response data ; and (3) reducing high-order transfer functions to low-order models using dominant frequency-response data.