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

Abstract

We present a switched adaptive observer for the estimation of the tyre 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 tyre-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 tyre relaxation length.

On Observer-based Asymptotic Stabilization of Non-uniformly Observable Systems via Hybrid and Smooth Control: a Case Study

“…Under Assumption 2, we may fix ẑ(0) such that |z(0)| ≤ R, where R > 0 is known. Therefore, from (17) we have V obs (z(0)) ≤ λ max (P ) R2 , which implies that…”

“…Thus, the controller is hybrid in nature and successfully stabilizes the origin semiglobally and asymptotically. Our contribution is a natural follow up on long-standing work led by the second author [5,13,15,17], but there no intellectual intersection with these references, devoted entirely to the observer-design problem. In addition, relatively to them, we provide here explicit exponential bounds on the observer's estimation errors.…”

“…In line with the keen assertion of [1], the estimation and stabilization tasks are competing processes for (1). On one hand, as explained in [17], the state estimator relies on the plant's output to provide certain persistency of excitation in order for the estimation errors to converge. This is a well-documented estimation mechanism employed for bilinear systems [4,18].…”

A Hybrid Observer-based Controller for a Non-uniformly Observable System

“…In this paper, we propose a novel hybrid controller that relies on the exponentially convergent observer previously proposed in [13], [15]. As explained in [17] and documented in the bilinear-systems literature [4], [18], such a state estimator relies on the output y = z 1 being persistently exciting, which is in clear conflict with the stabilization task. To circumvent this inadequacy, we propose a control strategy inspired from [15], [19] that consists in steering y to a vanishing piecewise-constant output reference z * .…”

“…This paper is a natural follow up on long-standing work led by the second author [5], [13], [15], [17], which are exclusively devoted to the observer-design problem.…”