Synthesis and comparative analysis of three model-based observers for normal load and friction estimation in intelligent tyre concepts

Abstract

Recently, the growing trends towards autonomous driving and full automation of terrestrial vehicles have intensified the need for intelligent and interconnected systems to collect and communicate reliable data in real-time. Since the tyres represent the primary sensing system between the vehicle and the ground, it comes natural to designate them to acquire information about their interaction with the road. Intelligent or smart tyre technologies can, indeed, be used to estimate both vehicle’s performance and environmental conditions, leading to handling, NVH and comfort improvements. Inspired by some encouraging results found in previous works, in this investigation we present three model-based estimators to detect the forces acting in the contact patch for an intelligent tyre. The underlying mathematical foundation is the Flexible Ring Tyre Model (FRM), which is able to describe the in-plane dynamics of intelligent tyre systems. More specifically, it represents the tyre treadband by means of a flexible ring restrained at its mean radius by a viscoelastic foundation. Due to its relatively simplicity, the FRTM allows to obtain a closed-form solution for the treadband displacements, accelerations and circumferential strain, whilst being accurate enough to capture all the relevant phenomena concerning the tyre dynamics. The governing Partial Differential Equations (PDEs) of the system are reduced to a set of coupled Ordinary Differential Equations (ODEs) by performing the Fourier series expansion. An optimal observer is then designed based on the Unscented Kalman Filter to account for the nonlinearities which arise when the vertical load acting on the tyre and the friction coefficient are included in the augmented state space representation. The three different technologies considered in this study are: strain, displacement, and acceleration-based intelligent tyres. All of them are shown to be capable of estimating the quantities of interest – the actual state of the system, the normal force and the adhesion coefficient – with high accuracy in very short times. Furthermore, the robustness of the proposed approach is validated by considering a step variation in both the vertical load and the available friction. The performances of the observers are finally compared by using the RSS and MSE indices.

Keywords

Tyre road forces estimation Flexible Ring Tyre model Unscented Kalman Filter tyre sensors nonlinear dynamics longitudinal dynamics

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