Comparison of Frequency Response and Perturbation Methods to Extract Linear Models from a Nonlinear Simulation

Abstract

Abstract : The purpose of this paper is to compare two distinct methods to extract a linear state-space model about a reference flight condition from a nonlinear simulation. The frequency response method uses a time history input which contains the frequencies of interest to drive the simulation. The frequency response method uses a time history input which contains the frequencies of interest to drive the simulation frequency input and the output of the simulation are transformed to the frequency domain, and the desired frequency responses of the simulation are calculated. A linear model is then fit to the frequency responses using system identification techniques. The perturbation method extracts a linear model by perturbing the model states and inputs from the reference flight condition and calculating the resulting model coefficients. Both method were used to extract a fourth order longitudinal state-space model from the V-22 full nonlinear simulation. The time history responses and system matrices of the extracted model were compared. The comparison showed that both methods are effective means to reduce a nonlinear simulation to a linear state-space model.