Page - 70 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis t1 b a t2 t f s =1 f s =0.5 1 Figure 4.2.: Instantsof time t1 and t2 atwhichthedrivingstateof ba=1m/s 2 (pure lon- gitudinal acceleration, no lateral acceleration) is reached for twosimulations with different scaling factors fs for the desired acceleration profile 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 1 2 3 4 5 6 x 10 -4 b a x = 0.45 in m/s2 b a x = 0.45 in m/s2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 −0.08 −0.07 −0.06 −0.05 −0.04 −0.03 −0.02 −0.01 0 Friction Potential µmax Friction Potential µmax f s =0.1 f s =0.2 f s =0.3 f s =0.4 f s =0.5 f s =0.6 f s =0.7 f s =0.8 f s =0.9 f s =1.0 Figure 4.3.: A comparison of the selected sensitivities ∂vx/∂µ (left) and ∂ωfl/∂µ (right) versus µmax shows similar behaviour for different scaling factors fs used to calculate the desired acceleration profile during the simulation manoeuvre. Since the curves are congruent for its simulatedµmax, the sen- sitivities displayed show no time-dependence, i.e. a dependence on the time it takes to reach the acceleration of 0.45 m/s2, for example. Influence of initial longitudinal velocity There are two methods with which the influence of the longitudinal velocity on the out- come of the sensitivities can be investigated. Although only one of the methods was performed, both will be described in this section. The influence of the initial longi- tudinal speed vx,0 on the outcome of the analysis can be treated as the investigation of the sensitivity of the model’s state variables with regard to the initial value of the longitudinal speed. Then, the same procedure of direct sensitivity analysis can be used 70