Assignment of Rightmost Pole in Vehicle Platoon Based on Proportional-Retarded Controller

Vehicle platoon holds great potential in enhancing traffic capacity, reducing fuel consumption, and decreasing pollution emissions. Due to the communication blockages and bandwidth limitations, it is inevitable to induce delay. However, most of the current research on the vehicle platoon with delay only focuses on analyzing and mitigating the negative impacts of the delay but overlooks its positive effects. To exert the positive effect of delay on the vehicle platoon control effectively, a proportional-retarded (PR) controller is designed in this paper. Then, by analyzing the closed-loop characteristic equation via the Cauchy-Riemann equation, a novel method of assigning the rightmost pole is proposed. Meanwhile, according to the Routh-Hurwitz criterion and rigorous derivative analysis, it is confirmed that the rightmost pole cannot be arbitrarily assigned, thereby the assignment range of the rightmost pole is derived. Additionally, a strategy of the rightmost pole assignment that maximizes the response speed of the vehicle platoon is proposed. Finally, simulations are conducted to demonstrate the correctness of the theoretical claims.