The macroscopic LWR model of the transport equation viewed as a distributed parameter system

Abstract

The main aim of this paper is the obtaining of transfer function of the macroscopic traffic flow model using an exact analytical method of solution of the non-linear partial differential equations, presenting the transportation problem model as distributed parameter system. The different analytical methods of solution are shown, some of them giving an exact solution. Using this exact method we obtain directly the plant transfer function for the traffic flow model viewed as a distributed parameter system. The entire physical phenomenon is presenting through the partial differential equations whose show the distribution in vehicles on the high ways. All the research is devoted on the transfer function result because of the control system modeling. In the presenting paper we shown the verification of the analytical result of the model simulation thought the time and frequency characteristics analysis.