Estimating Nonlinearity Using Volterra Kernels in Feedback with Linear Models

Aeroelastic dynamics must be accurately known to ensure safe and efficient flight testing. Unfortunately, most models of aircraft systems typically describe only the linear dynamics. These models are inadequate for predicting behaviors, such as limit cycle oscillations, resulting from nonlinearities. This paper presents an approach to augment a linear model by identifying associated nonlinear operators. Essentially, the difference between a flight data measurement and a simulated measurement indicates the unmodeled dynamics. Volterra kernels are computed to represent the difference in measurement and, consequently, represent the unmodeled dynamics. The approach is applied to a nonlinear pitch–plunge system for which only a linear model is assumed available. The method is able to characterize errors due to incorrect parameters in the linear model and errors due to unmodeled nonlinearities of the dynamics.