Distributed PID Controller Design and Stability Analysis for the Vehicle Platoon with Communication Delay and Input Delay

Communication delay and input delay degrade the performance and robustness of the vehicle platoon, even resulting in instability. In this paper, a distributed proportion-integral-derivative (PID) controller is designed to enhance the robustness of the vehicle platoon with these two delays, and the exact time delay margins (ETDMs) are obtained by employing the cluster treatment of characteristic roots (CTCR) paradigm. Firstly, the strong stability condition with respect to the PID controller gains is obtained to guarantee the existence of the ETDMs. Secondly, we propose a way of obtaining the upper bound of the communication delay and limiting the ETDMs to a small delay region, which enormously reduces the computational burden of calculating the ETDMs via the CTCR paradigm. Finally, simulation results illustrate the effectiveness and superiority of our proposed method.