Identification of Nonlinear Systems in Frequency Domain

A frequency domain technique for identifying a class of nonlinear systems is presented. The class of nonlinear systems we consider in this paper consists of a power series nonlinearity sandwiched between two linear systems and the problem we address is one of identifying the transfer functions of the linear systems and the coefficients of the power series nonlinearity from the terminal behavior of the system. The identification procedure is based on a frequency domain model of the nonlinear system. The system is modeled by a set of nonlinear transfer functions in the frequency domain and the relationships between the transfer functions of the linear system, the power series coefficients of the nonlinearity, and the nonlinear transfer functions of the system are developed. The identification procedure is based on a simple algorithm for factoring the non-linear transfer functions of the system. The experimental data required for applying our identification procedure consists of the amplitude response of the system to multitone sinusoidal input. A minimum phase transfer function in a single variable is used to approximate the experimental data and the repeated application of the factoring algorithm leads to the identification of the system. Examples illustrating the use of the proposed procedure are also presented.