A switched adaptive observer for extended braking stiffness estimation

Abstract

We present a switched adaptive observer for the estimation of the tyre extended braking stiffness (XBS) during 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. Asymptotic stability of the estimation error is established on the basis of dwell-time and persistency of excitation conditions. The approach is validated via numerical simulations considering realistic perturbations on the system's measured output.

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

“…(27) Note that the system formed by (26) and (27) has a cascade structure. Moreover, note that the dynamics of η given by (27) has exactly the same form as that of the system (12). Thus, it follows from Proposition 1 that the origin of (27) is globally asymptotically stable.…”

“…The proposed observer has an overall better performance than that of [10] and provides a good estimation of the XBS even after large changes in road conditions. This paper builds upon the preliminary results presented in [12], which are extended here in three directions. First, the stability properties of the observer are established with a more rigorous theoretical analysis and clearer hypotheses.…”

“…In what follows, we show how to define the observer gain K(t, y) and establish global asymptotic stability of the origin for the system (12).…”

“…The reader is referred to[10], as well as[12], for the complete derivation of this simplified model.…”

A Switching Observer for a Class of Nonuniformly Observable Systems via Singular Time-Rescaling

“…Most observer-based schemes in the literature rely on the assumption that the system is uniformly observable. Yet, this is frequently untrue in many concrete control engineering problems [15], [16]. Indeed, in many cases γ(y(t)) may be equal (or tend) to zero, which leads to loss of observability.…”