Accurate Modeling of Nonlinear Systems using Volterra Series Submodels

We investigate the problem of accurately modeling nonlinear systems (such as aircraft flight in high angle-of-attack/sideslip flight) using simple low-order Volterra submodels. First, we apply this technique to a simplified nonlinear stall/post-stall aircraft model for the case of a longitudinal limit cycle. Our simulation study demonstrates that the responses of the Volterra submodels accurately match the responses of the original nonlinear model, whereas the responses of a piecewise-linear model do not. Next, we apply the technique to a simplified high a nonlinear model of wing rock. Our simulation study demonstrates that the second-order Volterra approximation predicts the wing rock limit cycle, while a linear approximation does not. Third-, fourth- and fifth-order Volterra approximations are observed to give wing rock amplitudes that converge quadratically to the nonlinear value.