A frequency-domain model-order-deduction algorithm for nonlinear systems

Several model-order deduction algorithms (MODAs) have been developed to coordinate the synthesis of lumped (finite-dimensional), linear system models, of acceptable order, that accurately characterize the behavior of a system over a frequency range of interest (FROI) [ω_min,ω_max]. The most recent of these techniques considers the frequency response of the model as the “performance metric” and systematically increases model complexity until the frequency response over a FROI has converged to within a user-specific tolerance. The linear MODA algorithm based on frequency response is being extended to support the synthesis of models of nonlinear systems. This technique follows a procedure similar to the linear frequency-domain algorithm, but uses a describing-function approach to develop an amplitude-dependent characterization of the nonlinear system frequency response. The extended algorithm synthesizes model that are also of low order; in addition, they include only those nonlinear effects that influence the frequency response significantly over the FROI and for an amplitude range of interest