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

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.