Page - 81 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

6.2. ACC Controller Parameter Identification i ′P min,iP max,iP upper and lower limit lower limit upper limit 0 Figure 6.9.: Transformation rule for either upper or lower bounds or both upper and lower bounds ofPi For further considerations, the term used in the trigonometric and the linear part of eq. (6.9) was replaced by a new variable defined as esyn= (er˙+P4er). (6.24) As mentioned above, the desired acceleration of the ACC controller should increase with an increasing error. This could be described by ∂ades ∂esyn =P1P2cosh(P2esyn)︸ ︷︷ ︸ ≥1, ∀esyn +P3>0. (6.25) The trigonometric function in eq. (6.25) is always equal to or larger than one for all P2esyn. Therefore, the conditions for the parametersP1 toP3 can be found reading P1P2>0 and P3>0 or (6.26) P1P2<0 and P3 = lim x→∞x. (6.27) Due to the fact that eq. (6.27) is impossible in reality, only the conditions of eq. (6.26) are used. The first conditionP1P2> 0 leads to (P1>0∩P2>0)∪ (P1<0∩P2<0). These two parameters do not influence any part of the optimization other than the ACC controller. Therefore, it does not matter which of the two cases is used. A negative inter-vehicle error er<0 and no relative velocity error er˙= 0 means that the ego vehicle is too close to the OTF. Therefore, the controller should output a negative 81