Modeling and Numerical Analysis on Communication Delay Boundary for CACC String Stability

Co-operative Adaptive Cruise Control (CACC) uses wireless communication between vehicles to form a vehicle platoon. It has been proven that CACC aids in the stability and efficiency of traffic flow, and also reduces the energy consumption of the vehicles by lowering air resistance of the following vehicles. However, communication delay is a natural uncertainty for a platoon under CACC mode. When the delay gets worse to a particular level, the string stability of the platoon will be destroyed, meaning spacing or speed errors will be amplified upstream from vehicle to vehicle in the platoon. Therefore, in this study, a numerical method is proposed to identify the communication delay boundary according to the vehicle dynamics and the parameter settings of the CACC controller. First, in the Laplace domain, a series of string stable bodies under different disturbance frequencies are created based on the string stability criteria. Considering the frequency characteristics of traffic flows, the string stable bodies are then combined into a uniform one. Lastly, with the increase of communication delay, its upper bound will be obtained until the area of string stability totally disappears. Two simulations were conducted to verify the correctness and accuracy of the proposed method. The results indicate that the string stability cannot be guaranteed once the communication delay just exceeds the upper bound. This study can provide an objective boundary for practitioners or engineers, thereby allowing them to determine whether wireless inter-vehicle communication is capable of maintaining a string-stable platoon.