Page - 67 - in Maximum Tire-Road Friction Coefficient Estimation

4 Sensitivity Analysis Table 4.1.: Maximum longitudinal and lateral accelerations based on measurements Acceleration Measured value (approx.) ba max x (acceleration) 5 m/s 2 ba min x (braking) 10 m/s 2 ba max y 10 m/s 2 Finally, in a third step, the linear sensitivity model p˙ is solved for p. 4.3. Sensitivity analysis using vehicle model The sensitivity analysis is performed on the vehicle model described in Section 3.2. The differential equation system consists of the three equations of motion that describe the movement of the chassis, the four equations that describe the rotational movement of the wheels, and four equations for the lateral tire dynamics. The structure of the vehicle model adapted for the sensitivity analysis is shown in detail in Appendix C. This structure describes the inter-dependencies between the state variables, the inputs to the equations and the investigated parameterµmax. These inter-dependencies influence not only z˙, but also the Jacobian J and fc and thus the differential equation p˙ of the sensitivities. A simplification is necessary to calculate the tire load variation, as given by Equation 3.22, and the effective tire radius that depends on the tire load variation, as given in Equation 3.23. They depend on the horizontal accelerations and thus on z˙, which is not known before the differential equation system is solved for z. Since it is assumed that the horizontal accelerations change sufficiently slowly with time, both tire load variation and effective tire radius are calculated with the accelerations of the last time step k−1. 4.3.1. Driving manoeuvres to cover parameter space Different driving states have to be defined in order to investigate the sensitivity of the state variables with respect to µmax. The parameter space of driving states is defined by different areas of bax and bay in the Krempel diagram, as shown in Figure 2.5 and described in Section 2.1.2. It is assumed that for different horizontal accelerations at the vehicle’s COG, different state variables are sensitive to a change ofµmax. Thus, the parameter space of possible and realistic horizontal accelerations at the vehicle’s COG is to be investigated. The outer boundaries are defined by the maximum accelerations, as shown in Table 4.1. Time-dependent acceleration profiles are used to control the inputs 67