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The performance of the classical car-following system is easily affected by external disturbances. To enhance the performance of the classical car-following model under sudden external disturbances, a novel car-following model is established to smooth traffic flow.

This paper proposed a Proportion Integration Differentiation (PID) control strategy based on classical control theory and developed a novel car-following model. The linear system theory and Laplace transform are used to derive a closed-loop transfer function. Then, the stability condition is obtained by using the Routh stability criterion and the small gain theorem. Finally, the validity and feasibility of the PID control strategy is proved by numerical simulations.

The analytic results and the numerical simulation results show that both the integration part and the differential part have the positive effect to suppress traffic oscillation efficiently; the collaboration of these two parts has more power to improve the stability of traffic flow. It means that the proposed model integrated with the PID control strategy has the ability of anti-interference and smooth traffic compared with the classical car-following model.

This paper introduces the PID control strategy into the classical car-following system, which enhances the stability of the system and also provides an efficient method for optimizing the traffic flow system.