Stability Analysis For Intelligent Connected Vehicle Platoon With Input Delay And Communication Delay

Intelligent connected vehicles,whose state information can be shared by wireless communication,are moving under the desired spacing policy,providing an effective way of improving traffic capacity,enhancing road safety and reducing fuel consumption.Due to the limited bandwidth,transmission congestion and the computation time of the onboard computing unit,input delay and communication delay exist in vehicle platoon inevitably.The input delay and communication delay collectively affect the performance of the vehicle platoon,and sometimes induce instability.The existing studies,which concentrate on the internal stability analysis of vehicle platoon system under time delays,are difficult to obtain the exhaustive and exact time delay bounds of the system quickly;For the string stability analysis,the relationship between the time delays and the parameters and controller gains is rarely involved;For the vehicle platoon system with the distributed PID controller,which is neutral time delay system,the unique problem of the possible non-existence of time delays stable region must be taken into account.Therefore,for an intelligently connected vehicle platoon with input delay and communication delay,a method for quickly solving the exhaustive and exact time delay bounds is proposed in this paper.The strong stability condition of the vehicle platoon system with the distributed PID controller is derived.Based on the string stability condition,the influence of the time delay on parameters and controller gains is analyzed.The main research work and contributions are summarized as follows:(1)An efficient way to solve the exhaustive and exact time delay bounds is proposed for the vehicle platoon system with input delay and communication delay.Firstly,the closed-loop vehicle platoon systems are established based on the second-order and third-order vehicle dynamics models,respectively,and the whole systems are decoupled into several low-order subsystems.Secondly,by solving the input delay bound of a special subsystem with zero eigenvalue,an analytical expression of the upper bound of input delays for internal stability is given.Finally,with the upper bound of input delay,the exhaustive and exact time delay bounds are quickly solved by using the cluster treatment of characteristic roots paradigm.(2)For the vehicle platoon system with the constant distance policy and constant time headway policy,the string stability conditions are derived and the upper bounds of input delay for the string stability are given with the parameters and controller gains.Firstly,the distributed controllers with different spacing policies are designed under the communication delay and input delay,and error transfer functions between the successive vehicles are derived.Secondly,the string stability conditions under different spacing policies are obtained according to the definition of the string stability.On this basis,the upper bound of input delay and the maximum time headway are derived to ensure the string stability,and the relationship between the time delays and the parameters and controller gain is revealed.(3)For the vehicle platoon adopting the distributed PID controller with the input delay and communication delay,strong stability conditions are derived to ensure the existence of the stable region.Firstly,the vehicle platoon,which is constructed by the third-order vehicle dynamic model and the designed distributed PID controller,is decoupled into low-order subsystems.Secondly,by considering that the vehicle platoon system with the design PID controller is a neutral time delay system,the sufficient and necessary conditions for strong stability are proposed by combining Rekasius substitution and Routh table,which ensures the existence of the stable region of the vehicle platoon system.Under the strong stability condition,the upper bound of input delay is solved,and the cluster treatment of characteristic roots paradigm is used to solve the time delay bounds quickly.Finally,the string stability conditions and the upper bound of the input delay for the string stability are obtained by analyzing the error transfer function between the successive vehicles.