Proportional–differential effects in traffic car-following model system

Traffic flow system’s stability analysis can be seen as a typical control system problem, which has three kinds of damping ratio properties from the viewpoint of control theory. To discover the damping ratio characteristics of traffic flow system under sudden outer impulse, firstly, we proposed a new method to build the traffic flow model based on state space theory. Secondly, we deduced one form of state transfer matrix from system closed-loop transfer function reversely. Lastly, we fully investigated the proportional–differential effects in the traffic car-following model system analytically and numerically. For unsteady traffic flow system with the proportional–differential (PD) term, in order to suppress the traffic jam, we derived a kind of decoupled delay-feedback control algorithm, which used H∞-norm and the numerical simulation method to find the feedback gain k and delay time τ. The traffic flow system’s transient performance formula was presented with and without PD term, and we found out the important impact of PD term on traffic flow system’ stability. The numerical simulation results substantiate our theoretical and analytical results.