Extended-Braking-Stiffness Estimation Under Varying Road-Adherence Conditions

We present a switched adaptive observer for the estimation of the tire extended braking stiffness (XBS) during ABS braking scenarios. The design of the observer is based on Burckhardt's friction model and on a model of the wheel dynamics in which the XBS appears as one of the state variables. Global asymptotic stability of the estimation error is established, provided that certain dwell time and persistency of excitation conditions hold. The approach is validated under constant road conditions with experimental data from a tire-in-the-loop test rig and under varying road conditions via numerical simulations on a two-axle vehicle model that includes dynamic load transfer and tire relaxation length.