# Dynamics of Torque-Speed Profiles for Electric Vehicles and Nonlinear Models Based on Differential-Algebraic Equations

Melnik, R.V.N., Song, N. and Song and Sandholdt, P.

Discrete and Continuous Dynamical Systems, A Supplement Volume  ISSN 1078-0947, pp. 610--617, 2003  (based on the Proceedings of the Forth Int. Conf. on Dynamical Systems and Differential Equations, Eds: Feng, W., Hu, S. and Lu, X.)

### Abstract:

The so-called $\mu-\lambda$ curves, where $\lambda$ is the slip ratio and $\mu$ is the normalised traction force or the friction index, are nonlinear functions of the velocity of the vehicle and the wheel rotational velocity. Despite their predominant use in the literature, linear approximations of such curves may fail to predict correctly key characteristics of vehicle performance efficiency such as torque-speed profiles. Although attempts to model these characteristics in the context of slip phenomena have been made before, to our best knowledge a general model with respect to the vehicle velocity, the wheel rotating velocity, the slip ratio, the traction force, and the torque, has never been formulated and solved as a coupled nonlinear problem based on a system of differential-algebraic equations arising naturally in this context. In this paper, such a model is formulated, solved numerically, and some results of numerical simulation of driving an electric vehicle on different surface conditions are presented.