Application And Research Of Control Theory In Macroscopic Lattice Hydrodynamic Model

Although the acceleration of urbanization has led to economic development,the traffic congestion caused by the increase of private vehicles has become increasingly serious.In recent years,traffic congestion has become a hot topic at home and abroad.For this reason,scholars have analyzed the traffic situation from different angles and established many traffic flux models.Based on Nagatani’s lattice hydrodynamic model,an improved lattice hydrodynamic model considering different traffic factors was proposed,and theoretical analysis and numerical simulation of the improved model are carried out.The main work is as follows:1.Lattice hydrodynamic model based on driver’s memory and delayed feedback controlOn the basis of Nagatani’s lattice model,considering the memory effect of driver and the influence of feedback control signal(the density difference of the first two lattice points),an improved lattice hydrodynamic model is proposed.The control method is used to deduce the model,and the linear stability condition of the model is obtained.In addition,the influence of the new model on vehicle energy consumption is also studied.Finally,MATLAB is used to simulate the model,which further verifies the accuracy of the theoretical analysis results.2.Lattice hydrodynamic model based on historical relative flux and feedback controlIn order to reduce the traffic pressure,a lattice hydrodynamic model considering the historical relative flux and feedback control is proposed.In the model,the rate of flux change is selected as the control item.The linear analysis of the model is carried out by using the control method,and the condition of linear stability is obtained.In order to verify the results of theoretical analysis,the model was simulated by MATLAB.The simulation results show that the historical relative flux speed up the traffic congestion,and the control signal can alleviate the traffic congestion.3.Lattice hydrodynamic model based on velocity deviation and expected flux differenceBased on the classical lattice model,a lattice hydrodynamic model considering velocity deviation and expected flux difference is proposed.In the linear analysis,the linear stability condition of the model is obtained by the control theory.In the nonlinear analysis,the m Kd V equation at the critical point is obtained by using the perturbation method.Finally,the linear and nonlinear parts are simulated by MATLAB.The simulation results show that the high estimated speed and the expected flux difference play a positive role in easing traffic congestion,and the low estimated speed aggravates traffic congestion,which is not conducive to the development of traffic flow system.4.Lattice hydrodynamic model based on expected effect of average flux differenceIn actual traffic,it is impossible for vehicles to drive on a single straight road all the time.Therefore,a lattice hydrodynamic model considering the expected effect of average flux difference is proposed in this paper.In linear analysis and nonlinear analysis,the condition of linear stability and m Kd V equation near the critical point are obtained by using control method and perturbation method respectively.Finally,the theoretical analysis is simulated and verified by computer,and the influence of the model on the stability of traffic flux can be seen more intuitively and clearly.