On the Local Stability of Braking Dynamics of a Slip-Controlled Two-Axle Vehicle with Multiple Time-Delays

Improving vehicle safety is one of the most challenging tasks of nowadays. During braking appropriate slip control of the wheel is essential to ensure proper performance regarding brake distance or lateral vehicle handling characteristics. Modern electronically controlled brake systems are equipped with several sensors, actuators and electronic control units (ECU), and there is a communication network that provides a connection between these nodes of the control system. As the speed of information is finite, and the communication protocol needs time to send and receive information packages, there is communication delay in the system that can be the root cause of performance and stability issues. The aim of the present research is to perform a local stability analysis on a two-axle vehicle model that is equipped with a slip controller in the presence of communication delay. Steady-state and dynamic brush models are used, and a PID controller is used for slip regulation. Communication delay is modelled as a constant time-delay, and as a time-varying time-delay that can model the effect of sampling as well. Boundaries of stability are determined in terms of the controller gains, stability maps are constructed, and finally the practical invariance of these stability maps for different other parameters are investigated.