Stability of PID control system for vehicle platoon with input delay and communication delay

The internal stability and string stability of the PID control system were analyzed for vehicle platoon with input delay and communication delay, the sufficient and necessary conditions of the internal stability were emphatically studied, and the exhaustive and exact time delay margins were derived. In the internal stability analysis, considering that the PID control system for vehicle platoon is a neutral time delay system with input delay and communication delay, the sufficient and necessary strong stability conditions were proposed by analyzing the stability of the neutral operator via Rckasius substitution and Routh table. In order to facilitate selecting the PID parameters, a sufficient condition with a more concise form was derived. Then, the clustering method of characteristic roots was applied to obtain the exhaustive and exact time delay margins. Considering the vehicle platoon with an odd number of following vehicles, the upper bound of the input delay, which was independent of the scale of the vehicle platoon, was derived. In order to ensure that the interference and error propagated backward along the vehicle platoon without divergence, the error transfer function among the vehicles was analyzed, and the sufficient condition of string stability under the influence of two delays was given. Simulation results show that the internal stability and string stability of vehicle platoon can be guaranteed simultaneously by the distributed PID controllers under communication delay and input delay. The state errors quickly converge to zero within 15 s. When the velocities of the vehicles are constant, an desired safe distance maintains 50 m between the successive vehicles. When the leader vehicle accelerates at 0. 5 m · s-2and decelerates at 0. 8 m · s-2, the velocities and accelerations of the following vehicles asymptotically change with those of the leader and arc consistent with the leader when the leader's velocity is constant. Under the different driving conditions, the spacing errors caused by the acceleration and deceleration of the leader are less than 0. 2 m, and propagate backward along vehicle platoon without divergence. 1 tab, 11 figs, 36 refs. © 2022 Chang'an University. All rights reserved.