Page - 40 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model Thus, as both the sensitivity analysis and the observer design share the same require- ments on the tire/road contact, the some model considerations apply for reduction of model complexity. To investigate the sensitivity of vehicle dynamic variables to the friction potential, the vehicle model needs to accurately represent the horizontal tire forces, the slip quantities and the wheel speeds for each wheel. The model is supposed to cover a wide variety of driving states, including situations near the physical limits. To keep computational effort manageable, model complexity must be kept low, while keeping model accuracy in mind. To validate whether a simplification of the vehicle model maintains an acceptable accuracy, an analysis based on a simulation with a model with higher model complexity was performed with different parameter settings and sub-model complexities. This as- sessment of required model accuracy is not to be confused with the main assessment of model sensitivity in Section 4. Inorder toquantify the influenceofdifferentmodelparameters, a reference simulation with a model containing all modelled physical phenomena is compared to simulations where these phenomena are successively deactivated. For this investigation, a vehicle model consisting of sprung and unsprung bodies with a total of 14 degrees of freedom (DOF) was used, see Figure 3.1. The model was validated with measured data obtained with an Opel Combo 1.6 CNG, [Roj12, p.13-15]. 3.1.1. Evaluation criteria The main evaluation criterion is the mean relative deviation of the vehicle state vari- ables between a reference simulation and a parameter or sub-model variation. Based on Weber, the mean relative deviation ∆w for an exemplary variablew can be calculated by comparing the time signal of the state variablewref from the reference simulation and wvar from the variation simulation by ∆w= ∫ |wref−wvar| ·dt∫ |wref| ·dt , (3.1) seealsoFigure3.2 foragraphicdepiction, [Web04,p.70-79]. It is importanttomention that the time integrals used in Equation 3.1 do not consider kinematic couplings of the state variables. For example, the relation ∫ bωz dt=ψ is only valid without considering roll and pitch motion of the chassis on an even road. The considerations shown in Equation 3.1 are only used to evaluate the relative change of a variable w between 40