Page - 73 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis As an example, Figure 4.5 shows the comparison of two simulations at the data point where each reaches the driving state with a longitudinal acceleration of 1.2 m/s2 and a lateral acceleration of 1.9 m/s2. The absolute value of the sensitivities is higher for LQ manoeuvres. This is true for all simulations. This difference between the absolute values of the sensitivities for LQ and QL manoeuvres increases with higher acceleration conditions. This indicates that the influence of the longitudinal velocity is mainly re- sponsible for this effect. Nevertheless, the tendencies are similar, and it leads to the same conclusion that was drawn for the influence of the longitudinal speed, cf. Section 4.3.2. Thus, this does not limit the comparability of the tendencies, as the absolute value of the sensitivities is not of interest. 0 0.5 1 1.5 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Friction Potential µmax LQ QL 0 0.5 1 1.5 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 b a x = 1.2 in m/s2, b a y = 1.9 in m/s2 Friction Potential µmax Figure 4.5.: Comparison of the selected sensitivities∂vx/∂µ (left)and∂ωfl/∂µ (right) versusµmax shows similar behaviour for LQ and QL manoeuvres at a longi- tudinal acceleration of 1.2 m/s2 and a lateral acceleration of 1.9 m/s2. 4.4. Normalisation of sensitivities The state variables and their sensitivities with respect toµmax do not all have the same units and also vary in their orders of magnitude. To be able to choose the variables that 73