Synthesis and Application of Nonlinear Observers for the Estimation of Tire Effective Radius and Rolling Resistance of an Automotive Vehicle

The rolling resistance and the effective radius of a vehicle's tires are two important characteristics that affect its dynamics, performance, and comfort. Because of their dependence on tire inflation pressure, online estimation of such parameters could be used to monitor tire pressures using an indirect approach. By considering rotational and longitudinal dynamics, the aim of this paper proposes to apply observers for this online estimation using measurements of the wheels' angular velocities and the engine torque. Because these signals are available on major vehicle controller area networks, the proposed solutions do not require additional sensors. These nonlinear observers are based, first, on a high-gain approach, and then on a high-order sliding-mode approach, allowing robustness and finite time convergence. The originality of the presented results consists in providing a joint estimation of both variables, i.e., wheel effective radius and rolling resistance force. The observers offer the very first solution for dynamical estimation of rolling resistance in standard driving conditions, but the rolling resistance is very difficult to estimate by an online procedure. Simulations and experimental results allow the discussion of the effect of tire pressure on these parameters and illustrate the applicability of the proposed approach.