Page - 82 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

6. Upper Level Controller Parameter Identification acceleration ades < 0. This is guaranteed by eq. (6.26). If the inter-vehicle distance equals zero er= 0 and the relative velocity error is negative, er˙<0, meaning the vehicle is approachingg the OTF, the output should be a negative desired acceleration,ades<0. This can only be guaranteed if the conditions of eq. (6.26) and the parameterP4>0 are satisfied. To sum up, the boundary conditions and the initial conditions were set to 0<P1<0.5, 0<P2, 0<P3<0.5, 0<P4 and (6.28) P1,0 = 0.3, P2,0 = 0.5, P3,0 = 0.1, P4,0 = 0.1. (6.29) The upper boundaries of P1 andP3 were set for comfort reasons. These limits should lead to small values forP1 andP3 in order tohave small accelerations for small synthetic errors esyn, defined in eq. (6.24). The parameterP2 affects the desired acceleration for small errors as well, but it is not limited to an upper boundary to ensure string stability. These boundaries led to the results P ′1 = 0.9685, P ′ 2 =−0.0983, P ′3 = 0.3850 and P ′4 =−1.5967 (6.30) after 205 iterations, which could be transformed back to P1 = 0.3624, P2 = 0.9063, P3 = 0.2975 and P4 = 0.2026 (6.31) with the resulting cost function of JDF = 3769829. Figure 6.10 shows the parameter histories forP1 toP4 andP ′ 1 toP ′ 4 with the corresponding cost functionJDF. 6.3. Validation of the Identified Parameters The validation of the identified parameters is carried out in three steps. First, the string stability is checked. Next, simulations with the simplified longitudinal vehicle model are performed, and the output is compared with the measured data. For the third step, the performance of the controller is compared to measurements obtained with a production vehicle equipped with an ACC system. Chapters 6.3.1 to 6.3.3 provide a detailed description of the three steps. 6.3.1. String Stability Figure6.11 showsthe timehistories foraplatoonof100vehicles, eachequippedwith the ACC controller of eq. (6.9) using the parameters of eq. (6.31). The first vehicle copies the movement of the leading vehicle in fig. 6.2, with a desired acceleration of−2m/s2 in the timespan between 1 to 4s. Figure 6.11 illustrates that the platoon is string stable due to the decreasing inter-vehicle error er going backwards in the platoon. String stability cannot be proven analytically because the Laplace-Transform of the control law of eq. (6.9) cannot be rearranged in the form of eq. (6.6), due to the trigonometric function in the control algorithm. 82