Page - 129 - in Maximum Tire-Road Friction Coefficient Estimation

7 Summary of identifying state variables that contribute to the estimation of the friction potential is presented. Unlikemostof thepublished frictionestimationapproaches thatuseheuristic strategies, a sensitivity analysis was performed on a vehicle model described by ordinary differential equations (ODE) in order to identify the state variables that show a high sensitivity with respect to a change of the friction potential. To this end, different ma- noeuvres were simulated to cover longitudinal and lateral accelerations that are within physically possible limits and in a range in which vehicles are frequently driven. The resultsof theseanalyses showedthat, independentof the longitudinaland lateralacceler- ation, thewheel’s rotational speedhave thehighest sensitivity toachange in the friction potential. As the dynamic response of the body to a driver input is slow compared to the wheel’s reaction, the state variables describing the vehicle body’s state are omitted for estimation of the friction potential within the present thesis. Thefifthchapter (Tire/road friction estimator) includes themainpartof this thesis, which is the presentation of the observer used to estimate the friction potential during driving. First, ageneral introductiontotheparticlefilter,which isanobserverwithinthe Bayesian framework, was given. It enables the observation of non-linear internal states that are difficult or impossible to measure and is also able to deal with measurements that are subject to noise and inaccuracies. Second, the system model to be observed was presented, which was chosen based on the results of the sensitivity analysis. Using the wheel’s angular momentum, the longitudinal tire forces of all four wheels are calcu- lated. Within the particle filter, these are then compared to hypothetical longitudinal tire forces that are calculated for different values of the friction potential. In a third part of this chapter, information on signal processing of the measurement inputs was offered, as well as a discussion of the challenges to achieving the necessary signal quality. It was demonstrated that the accuracy with which the wheel’s longitudinal slip can be calculated is the main limiting factor for the proposed estimation procedure. Among other values, the vehicle’s longitudinal velocity is required to calculate the longitudinal slip. Toachieve the requiredaccuracyof thevelocitymeasurement, velocity signals from global navigation satellite system (GNSS) combined with inertial measurements had to be used, in addition to ESC standard sensors. The velocity estimator was not part of this thesis. The sixth chapter (Results and conclusion) applied the estimation results obtained using the proposed observer to real vehicle measurements. Different driving states were investigated, including accelerating and braking, as well as changing road conditions (µ 129