Page - 78 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis 0.5 1 0 0.1 0.2 0.3 0.4 0.5 µmax 0.5 1 0 1 2 3 µmax 0.5 1 -15 -10 -5 0 µmax 0.5 1 -20 -15 -10 -5 0 µmax 0.5 1 -6 -5 -4 -3 -2 -1 0 µmax 0.5 1 0 0.5 1 1.5 µmax 0.5 1 0 0.5 1 1.5 µmax b a x =2.3, b a y =2 b a x =2, b a y =3 x10-3 Figure 4.8.: Relation between non-normalised sensitivity of state variables and the fric- tion potentialµmax for two combined longitudinal and lateral accelerations. Theunits of the shownsensitivities are the sameas for their respective state variable. vary. The sensitivity of the lateral velocity ∂vy/∂µ shows a comparable tendency to that of the longitudinal velocity vx, but one order of magnitude higher, despite the fact that the absolute value of vy during cornering is generally far lower than that for vx. Even without normalisation, this already indicates that considering vy to estimate µmax will contribute much more than considering vx during a manoeuvre that includes cornering. In comparison, the sensitivity∂bωz/∂µ is several orders of magnitude smaller and has a different sign. The yaw rate changes little with changingµmax due to the high vehicle’s yaw moment of inertia, see Figure 4.9. In comparison, vy changes significantly withµmax , as can also be seen in Figure 4.9. 4.5.1. Resulting normalised sensitivities at different driving states Figure4.10 showsall simulatedaccelerations (black lines) andthedifferent regions (gray areas) that have been analysed. The investigated area corresponds approximately to the area that is typically traversed by a non-professional driver within the maximum physicallypossible area, [Weg09, p.70-71]. Theblackdots showall analyseddatapoints, and the dark gray asterisks show all selected data points that are further shown and discussed in this section. It has to be mentioned that the resulting absolute values of the sensitivities depend on the initial longitudinal speed, see Section 4.3.2. Within one region, the initial longitudinal speed vx,0 is the same. The absolute values of the sensitivities can be directly compared within one region, but not across regions. 78