Modelling and stability analysis of a longitudinal wheel dynamics control loop with feedback delay

Abstract

Vehicle safety is an important field of today's engineering practice and the scientific research as well. One of the basics of the modern vehicle system dynamics control systems is braking or driving torque control. Ensuring proper connection between the tyre and the road surface is essential for safety and good handling behaviour. Fundamental questions may arise about the details of the model, such as feedback delay, sampling effect, numerical differentiation in the control algorithm or the dynamical characteristics of the tyre model. In this article, a connected dynamical system is presented which contains a wheel model and a PID type traction controller. Steady state and dynamical brush type tyre models are presented and compared. Two different ways are described to model the feedback delay. The fully continuous time model contains constant time delay, while there is another case, where the sampling effect and the numerical differentiation methods of the control algorithm are presented. Finally, stability analysis of the delayed system is performed. The stability and performance characteristics and different bifurcations are presented using stability charts. The type of the tyre model has significant effect on the stability characteristics.