A nonlinear sideslip observer design methodology for automotive vehicles based on a rational tire model

Abstract

In this paper we develop a nonlinear vehicle sideslip observer design that is based on a nonlinear lateral dynamics vehicle model. In doing so we utilize a novel simplified rational tire model to compute the lateral wheel forces. This tire model is significantly simpler than the well known Magic Formula (in terms of the number of model parameters), yet it provides sufficient detail over a wide range of operating conditions for the purpose of estimating the sideslip angle. The input to the nonlinear observer are typical signals that are available within lateral stability control systems, which include vehicle speed, steer angle, lateral acceleration and yaw rate measurements. In our analysis, we assume the road friction to be a known parameter. We utilize a recent theorem from the literature and show that the suggested nonlinear state estimator a) is asymptotically stable for the case where the observer makes use of the exact tire model, b) is stable (in the sense of Lyapunov) providing uniformly bounded error dynamics for the case where it makes use the proposed rational tire model to approximate the exact tire model. Finally, we provide numerical simulations to demonstrate the efficacy of our nonlinear observer based estimation technique under varying road friction conditions.

Simultaneous estimation of road friction and sideslip angle based on switched multiple non-linear observers

“…[1,12] for a detailed discussion). In the current paper, the proposed rational tire model is of the following form…”

“…It should also be emphasised that the underlying methodology for non-linear observer design in the current paper was initially developed in a recent paper by the authors [1], the fundamental difference here being in taking the road friction estimation into account through the use of a switched estimator structure. We provide the proof of convergence for the designed switched non-linear observer error dynamics.…”

“…An inherent problem with linearised vehicle models (and observers based on these) is that they lose validity under extreme driving manoeuvres, which is because of the nonlinear nature of the tire dynamics in such situations [7]. These extreme driving conditions are often characterised by large sideslip angles, and the knowledge of this variable is essential to accurately monitor and assess vehicle behaviour for the purpose of active safety control [1]. Furthermore, a number of researchers addressed the problem of online road friction estimation.…”

“…Such systems help to maintain vehicle directional stability proactively under adverse driving situations, where the vehicle is likely to loose control [1]. Such systems are available on many modern road vehicles, and in some countries they are required by law on all new vehicles as standard; for example, in the US, all light vehicles produced after 1 September 2011 need an ESC system as a standard fitment [2].…”

“…In the automotive engineering context, this parameter is defined as the angle between the vehicle's velocity vector and the vehicle centreline measured with respect to the vehicle's centre of gravity (CG) [1]. The vehicle sideslip angle is commonly denoted as β and is shown in Fig.…”