Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents

Abstract

For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.

Keywords:

• stability analysis
• 2-DOF vehicle model
• nonlinear tyre model
• concept of Lyapunov exponents
• stability region\vskip-1pc

Acknowledgements

We acknowledge the funding from Natural Sciences and Engineering Research Council of Canada.