Closed-loop wheel-acceleration control based on an extended braking stiffness observer

In the context of hybrid anti-lock brake systems (ABS), we provide a closed-loop wheel-acceleration controller based on the observation of the extended braking stiffness (XBS). Its objective is to improve the system´s robustness with respect to changes in the environment (as changes in road conditions, brake properties, etc.). In our design, we take advantage of Burckhardt´s tyre model, in order to obtain a wheel acceleration dynamics that is linear up to time-scaling. The XBS is one of the state variables of this model. Our main result is an observer that estimates this unmeasured variable. The observer´s convergence analysis is established using tools for switched linear systems that allow us to ensure its uniform exponential stability (provided that a dwell-time condition is satisfied). Our simulation results confirm the convergence properties predicted by our main theorem.