Page - 72 - 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 1−i 1−ix 1−iv 1−ia 1−i,vehl i ix iv ia i,vehl 1+ix 1+iv 1+ia +1i 1+i,vehl · ··· ·· 1x 1v 1a 1 1,vehl Figure 6.1.: Platoon of vehicles time-derivative. The difference between eq. (6.1) and eq. (6.2) reads τlong ( ... xi−1− ...xi)︸ ︷︷ ︸... r i +(x¨i−1− x¨i)︸ ︷︷ ︸ r¨i = P3 [ (r˙i−1− r˙i)+P4 [ (vi−vi−1)︸ ︷︷ ︸ −r˙i τset+ri−1−ri ]] . (6.4) If all the initial conditions of ri and its derivatives are set to zero, the transfer function for the complex variable s∈C reads Ri(s) Ri−1(s) = sP3 +P3P4 s3 τlong+s2 +s(P3 +P3P4 τset)+P3P4 , (6.5) where the Laplace transform of the inter-vehicle distance L{ri(t)} = R(s) is used. According to [WDS09], [LP99], [dWB99] and [Raj06], the platoon is string stable if∣∣∣∣ Ri(jω)Ri−1(jω) ∣∣∣∣≤1,∀ω. (6.6) In other words, the spacing errors should decrease moving back in the platoon, meaning ei−1≥ei ,[dWB99]. This leads to the two constraints for choosingP3 andP4 reading P3 +P3P4 τset≤ 1 2τlong and P3P4 τ 2 set+2P3 τset≥2 or (6.7) P3 +P3P4 τset> 1 2τlong and ( P3− 1 2τlong )2 < ( τset τlong −2 ) P3P4. (6.8) Simulations were carried out in which the parameters were set to τset= 1.5s and τlong= 0.5s. In this case, the leading vehicle has an input for a desired acceleration of ades= −2m/s2 during the time t = 1 to 4s. With an initial vehicle speed of 30m/s the manoeuvre ends at a vehicle speed of about 24m/s. Most often, these manoeuvres are carried out to adjust the vehicle speed to a certain speed limit. Thus, it is a very slight deceleration. Figure 6.2(a) shows the output of a simulation with the parameters P4 = 1 τset and P3 = 2.5. These parameters satisfy the condition of eq. (6.7), and the simulations show that the platoon of vehicles is stable. In [WDS09], Winner proposed 72