Describing function-based identification of nonlinear transfer functions for nonlinear systems from experimental/simulation data

A new method for identification of nonlinear transfer functions to represent the pseudo frequency domain models of nonlinear systems (from experimental or simulation data) is presented. The method is based on obtaining the output of the nonlinear system to sinusoidal inputs of different amplitudes and frequencies followed by evaluation of the Fourier integrals. First, the pseudo amplitude dependent frequency domain models are computed followed by identification of the class of transfer functions that may represent the obtained pseudo frequency response data. Second, for various amplitudes of excitation, the coefficients of the corresponding transfer functions are determined. The coefficient values as a function of the amplitudes of excitation are treated as the describing function models of the as yet unknown nonlinearities representing the nonlinear coefficients of the final transfer function. The unknown nonlinear coefficients are determined by describing function inversion. The procedure is experimentally verified and demonstrated by solving a servo problem.