Page - 102 - in Maximum Tire-Road Friction Coefficient Estimation

5 Tire/road friction estimator Table 5.1.: Necessary signals for the tire/road friction estimator, all measured with a sample rate of 200 Hz Necessary Signal Symbol Source Steering wheel angle δS measured Wheel speeds ωi measured Longitudinal chassis accelerations bax measured Lateral chassis acceleration bay measured Yaw rate bωz measured Wheel’s torque MD,i calculated, see Section 5.5.3 Compared toMD,i, the absolute values ofMR,i and Ir ·∆ωi are small and therefore play a minor role. The calculation of the wheel torqueMD,i is shown in Section 5.5.3. Within the calculation ofMD,i, the vehicle’s longitudinal acceleration bax is necessary. The acceleration bax is also required to calculate the dynamic tire load distribution, as well as bay during cornering. It has to be mentioned that for the results presented in Section 6, the acceleration signals have not been taken from the vehicle’s CAN bus, as they were not available for all measurements due to a procedural error. Instead, the acceleration signals of an advanced measurement system, [Gmb14], were used. Since the higher accuracy of bax is not necessary within the observer, it is assumed that estima- tion with ESC acceleration sensors would not perform worse. As the results presented in Section 6 are limited to longitudinal manoeuvres, the influence of the accuracy of bay is not further discussed. It also has to be noted that estimates of vx are typically available in the vehicle’s COG. By measuring both the yaw rate and the steering wheel angle, the longitudinal velocity vx in the vehicle’s COG can be transformed to the i-th wheel-fixed coordinate system when the the horizontal distances between wheel centreC and the vehicle’s COG are known, cf. Section 3.2. 5.4.2. Model parameters For the observer model, the knowledge of some vehicle and tire parameters is necessary. The vehicle parameters include the vehicle’s massmb, the wheels’ moment of inertia Ii and the rolling resistance coefficient fr,i. To transform vx and vy or β from the vehicle’s COG to the wheel’s coordinate systems and into the wheel’s contact points Wi, the horizontal distances from the four wheels’ centres to the vehicle’s COG have to be known. To calculateFz,i, the position of the vehicle’s COG, the vehicle’s mass and the spring stiffnesses of the front and rear suspension have to be known (cf. Equation 102