A Novel Piecewise Affine Model for Vehicle Lateral Dynamics

The lateral tire force is of crucial importance for the vehicle lateral dynamics modeling. Linear and nonlinear models have been proposed to describe the characteristic of the force. Due to its simplicity, the linear model is widely used in a vehicle controller and an observer design at present. However, this model has a limited application area since it is accurate only when tires operate in the linear region and fails to reflect the nonlinear behavior of the tire force. Contrary to the linear model, nonlinear models can represent the behavior entirely with complex nonlinear functions, which are difficult to be used for the controller or the observer design. Aiming at these problems, a piecewise affine (PWA) model for the lateral tire force is proposed in this paper. According to the relationship between the tire lateral force and the tire slip angle, the lateral tire force is approximated by a five-segment PWA model with different slopes. Model parameters are calculated by the tire analysis tool of the high-precision real-time simulation software of vehicle dynamics called veDYNA. Combining the PWA model with the lateral dynamic model, a novel two-degree-of-freedom model is obtained to describe the vehicle lateral dynamics. Based on veDYNA, simulation results with different maneuvers show that the proposed model is valid and has a higher precision.