Frequency-domain modeling of nonlinear multivariable systems

TL;DR: In this article, a frequency-domain technique for input/output (I/O) characterization of stable, multivariable, and highly nonlinear systems (e.g., industrial robots, aerospace vehicles, chemical processes) is presented.

Abstract: A frequency-domain technique for input/output (I/O) characterization of stable, multivariable, and highly nonlinear systems (e.g., industrial robots, aerospace vehicles, chemical processes) is presented. We require only that the nonlinear system is representable in state-variable differential equation form, and that it is possible to integrate the system of equations numerically when input signals are sinusoidal. Otherwise, the technique is not restricted with respect to system order, number of nonlinearities, configuration, or nonlinearity type. The I/O characterization technique involves determining the gain and phase of the nonlinear system response to sinusoidal inputs of various excitation amplitudes at a set of user-defined discrete frequencies. These sinusoidal-input describing function (S1DF) models are obtained by exciting all input channels at one time with sinusoids of different but nearly equal frequencies, integrating the dynamic equations of motion over time, and simultaneously performing a Fourier analysis (evaluating Fourier integrals) on the output signals after they are at steady-state. Repeating this procedure for various amplitude-levels of the excitation signal will result in a number of matrix sinusoidal-input describing function I/O models.