Nonlinear single track model analysis using Volterra series approach

Abstract

In this paper, an original approach based on the Volterra series theory is applied in order to analyse a nonlinear single track model, which is considered to describe the vehicle dynamics behaviour in the nonlinear domain. This model is based on a polynomial approximation up to the third order of the Pacejka formula that describes the full tyre behaviour. The analysis of the model is carried out using a truncated form of the Volterra series; this allows the extraction of an analytical formulation of the nonlinear response characteristics. The analysis is focused on the extraction of the first order frequency response function expression and the understeer angle curve vs lateral acceleration, which characterises the vehicle typology and stability. The resulting equations and illustrations in both the cases are presented.

Keywords:

• Volterra series
• single track model
• vehicle dynamics
• multi-dimensional Laplace transform
• nonlinear systems