Extended Braking Stiffness Estimation Based on a Switched Observer, With an Application to Wheel-Acceleration Control

In the context of hybrid anti-lock brake systems, a closed-loop wheel-acceleration controller based on the observation of the extended braking stiffness (XBS) is provided. Its objective is to improve the system´s robustness with respect to changes in the environment (as changes in road conditions, brake properties, etc.). The observer design is based on Burckhardt´s tire model, which provides a wheel acceleration dynamics that is linear up to time-scaling. The XBS is one of the state variables of this model. This paper´s main result is an observer that estimates this unmeasured variable. When the road conditions are known, a 3-D observer solves the problem. However, for unknown road conditions, a more complex 4-D observer must be used instead. In both the cases, the observer´s convergence is analyzed using tools for switched linear systems that ensure uniform exponential stability (provided that a dwell-time condition is satisfied). Both experiments and simulations confirm the convergence properties predicted by the theoretical analysis.