Page - 82 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis 5 10 15 20 25 30 35 b a x = -1 -3 -5 -7 -9 µmax v x w fl , w fr w rl , w rr 0.6 1.00.2 µmax 0.6 1.00.2 µmax 0.6 1.00.2 µmax 0.6 1.00.2 µmax 0.6 1.00.2 Figure 4.12.: Normalised sensitivities for all state variables except vy and bωz, which are zero within this region, for selected acceleration data points in Region 2 (negative longitudinal excitation). The value for vx is close to zero for all simulations. transmitted tire forces, which differ at the inner (index fl) and outer wheel (index fr) during cornering. With higher dynamic excitation, the sensitivities of the front wheels increase by several orders of magnitude, from about 10−1 at 1 m/s2 to 102 at 7 m/s2. Again, the sensitivities of the chassis are small compared to those of the wheel speeds. Especially the sensitivities of the longitudinal speed vx and the yaw rate bωz can be omitted. Though smaller than the sensitivities of the wheel speeds, the lateral velocity vy shows a dependence on µ max. Starting at bay ≈−1 m/s2, the wheel speeds show significant sensitivities for µmax lower than≈ 0.5 for the simulated initial value of vx. At bay ≈−2 m/s2, the sensitivity of the front inner wheel speed ωfl indicates that a distinction ofµmax until≈1 might be possible. Region 4 (combined cornering and acceleration) The results for Region 4 (positive longitudinal and lateral excitation) in Figure 4.14 show the sensitivities for all state variables for selected data points of bax and bay. The bottomrowofdiagrams inFigure4.14 showsdatapointsof bay=1m/s 2 with increasing bax fromleft to right. Again, the frontwheel speeds showthehighest sensitivity toµ max. Thehigher the bax, the lowerthesensitivityof therearwheel speeds incomparisontothe front wheel speeds. The sensitivities pvx and pbωz are again negligible. The sensitivity pvy is small but noticeable. In the middle row of diagrams in Figure 4.14, bay between 82