Page - 87 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis µmax b a x =0.4, b a y =0 b a x =1.4, b a y =0 b a x =2.4, b a y =0 b a x =3.4, b a y =0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.2 0.6 1.0 v x w fl , w fr w rl , w rr µmax 0.2 0.6 1.0 µmax 0.2 0.6 1.0 µmax 0.2 0.6 1.0 Figure 4.16.: Normalised sensitivities for all state variables except vy and bωz, which are zero within this region, for selected acceleration data points in Region 1 (positive longitudinal excitation) for an AWD (torque distribution front and rear 50 % each) front wheel speed’s sensitivities are higher. This indicates that estimating µmax based on the front wheels would work better for this case than for the conventional braking system. This also highlights the results of the influence of the wheel’s torque from the comparison of FWD and AWD for positive bax. The sensitivities of the rear wheels are very small and do not change much versus the simulated areas of µmax, as there is no braking torque present. 4.6. Choice of sensitive parameters for the estimation observer This investigationclearly showsthat thewheelsare themostqualifiedsensors for friction estimation among the investigated variables, and thus are assumed to be quite qualified for friction estimation in general. Across all investigated areas shown in Figure 4.10, the wheel speeds show the highest sensitivity to µmax. Although much smaller, the lateral velocity vy also shows a dependence on µ max in regions with lateral excitation. The sensitivity of β can be calculated using the already known sensitivities pvx = ∂vx/∂µ and pvy =∂vy/∂µ using Equation 4.11. As vy/v 2 x ·pvx<<1/vx ·pvx, the first term can be omitted. When vx is within the range of 0 to v max x =62.5 m/s, [AG08], the maximum value of pβ≈1/vx ·pvy is within the order of magnitude of pvy, and the minimum value is about two orders of magnitudes smaller. Thus, other than its maximum value, the order of magnitude of pβ is below that of pvy. Nevertheless, as β is more likely to be 87