Page - 28 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2. Adaptive Cruise Control Thus, the error signal for the inter-vehicle distance reads er= srOTF−sset (2.23) and the error for the inter-vehicle range rate reads er˙= sr˙OTF, (2.24) where sr˙OTF is the relative velocity between ego vehicle and OTF. Both should be controlled to zero. Notice that eq. (2.24) is not the derivative with respect to time of eq. (2.23). The derivative e˙r is given in eq. (2.29) below. For the design of the lower level controller, a simplified vehicle model is used, which reads τlong ... x (t)+ x¨(t) =u(t) , (2.25) where x¨ is the longitudinal vehicle acceleration, and ... x is the longitudinal vehicle jerk. According to [Ise02], the time constant τlong = 0.5s and the control variable describe the desired acceleration generated by the lower level controller u(t) = ades. For the controller design, eq. (2.25) can be rewritten as x˙=   0 1 00 0 1 0 0 − 1τlong   ︸ ︷︷ ︸ A x+   00 1 τlong   ︸ ︷︷ ︸ b u, (2.26) where x = [ vxx vvx vax ]T . If the target vehicle is driving at a constant speed, eq. (2.26) can be transformed to e˙=   0 1 00 0 −1 0 0 − 1τlong   ︸ ︷︷ ︸ Ae e+bu (2.27) with the state vector e= [ er er˙ vax ]T . The switch between the speed and distance controller is controlled by selecting the minimum of the outputs of the CC and ACC controllers. 2.4.3.1. Constant Time Gap Controller In [Raj06], Rajamani describes the so-called Continuous Time Gap (CTG) controller. Its control law reads ades= 1 τset (er˙+k er). (2.28) 28