CN102842222B - Based on the FPGA on-line prediction control method of Phillips macroscopic traffic flow - Google Patents

Abstract

The invention discloses a kind of FPGA on-line prediction control method based on Phillips macroscopic traffic flow, for solving the technical matters of existing FPGA prediction control method poor real.Technical scheme is by the process of model approximate discretization, sets up parallel processing flow process, design dynamic data storage scheme, achieves the PREDICTIVE CONTROL of blocked road circle mouth based on Phillips macroscopic traffic flow and changeable message signs with FPGA.Make the traffic flow density of highway, road speed achieves and control in real time effectively.

Description

Based on the FPGA on-line prediction control method of Phillips macroscopic traffic flow

Technical field

The present invention relates to a kind of FPGA prediction control method, particularly a kind of FPGA on-line prediction control method based on Phillips macroscopic traffic flow.

Background technology

Along with the fast development of economy, the continuous increase of automobile pollution, the congested in traffic major issue having become focus and the urgent need solution jointly paid close attention to countries in the world, traffic congestion also result in serious environmental pollution simultaneously, in 9 kinds of main air pollutants, 6 kinds relevant with motor vehicle exhaust emission directly or indirectly, and the concentration of narmful substance that under traffic congestion state, automobile is discharged exceeds 5 ~ 6 times than during normal traveling; In addition, congested in traffic and traffic hazard is the two large problems of urban transportation symbiosis.On the one hand, the traffic flow that urban transportation peak time is intensive, makes traffic hazard take place frequently, very easily causes serious traffic congestion; On the other hand, when occurring when blocking up, vehicle driver, because excessively wait for, easily loses patience, traffic hazard odds is increased greatly; Visible traffic congestion has become the matter of the whole affecting global urban sustainable development.

In order to the service efficiency of the highway that effectively relieves traffic congestion, improves, usually use information displaying board as the means of Traffic information demonstration and control; Usually, information displaying board and variable speed-limit sign are issued as the important information of intelligent transportation system, Long-distance Control, transmission show various graph text information, the different surface conditions issuing different sections of highway to driver in time and all kinds of transport information, carry out traffic law is carried out by communication network by Surveillance center's computing machine, the publicity of traffic knowledge, reach the impact reducing highway reappearance and block, reduce the non-reappearance accident of highway, improve traffic safety; As described in document " Hai Yilatibala carries; Expressway Information display board arranges Discussion on Technology; the land bridge visual field; in October, 2010; 139-140 ", the mechanism that arranges of information displaying board system is: (1) sensor information is collected and disposal system, (2) information displaying board information provide, (3) communication system, (4) central control system; The setting of information displaying board should from the angle of whole traffic navigation system Construction, takes into full account associating of leading and control, takes the comprehensive benefit of surface road and overpass into consideration, formulate the leading scheme of globality, rationality, high efficiency; Information displaying board adopts different forms according to the place of setting and the difference of object; One is mounted on main line, carries out main line induction and outlet induction, with the traffic in character style display section, front as unimpeded, crowded, delay etc., thus makes driver can turn to surface road, avoids crowded district; Another kind is arranged near ring road entrance, and the queue length of ring road porch and crowded prediction case are reported to driver, also the traffic conditions on contiguous main line can be shown to the driver on ring road entrance, thus reasonably induce for they provide; But, these schemes, super expressway entrance is induced, road main line is induced, road way outlet is induced and only demarcated according to information requirement, organic phase is not had to combine, particularly the display information of information displaying board does not export setting automatically according to macro traffic model prediction, is difficult to the traffic flow density to highway, road speed control effectively.

In order to analyse in depth traffic system, a large amount of scholar's research traffic flow model both at home and abroad, the both macro and micro model analysis traffic characteristics person wherein adopting hydromechanical viewpoint to set up is in the majority; In macroscopic traffic flow, traffic flow is regarded as the compressible continuous fluid medium be made up of a large amount of vehicle, and the research average behavior of vehicle collective, the individual character of single unit vehicle do not highlight; Macroscopic traffic flow portrays traffic flow with the average density ρ of vehicle, average velocity v and flow q, study they the equation that meets; Macromodel can portray the collective behavior of traffic flow better, thus for designing effective traffic control strategy, simulation and estimating that the traffic engineering problem such as effect of road geometry modification provides foundation; In numerical evaluation, simulation Macro-traffic Flow required time is studied number of vehicles in traffic system with institute and is had nothing to do, with studied road, numerical method choose and middle space x, time t discrete steps Δ x relevant with Δ t.So macroscopic traffic flow is comparatively suitable for the traffic flow problem of the traffic system processing a large amount of vehicle composition; This class model is used for discussing the traffic behavior of blocked road by Most scholars in the world.

But, macroscopic traffic flow great majority adopt partial differential equation to describe, even if the macroscopic traffic flow of discrete form is also very complicated, the system process of process usually more than desktop computer of these models, is difficult to use macromodel to carry out on-line prediction control to blocked road circle mouth and changeable message signs.

Summary of the invention

In order to overcome the deficiency of existing FPGA prediction control method poor real, the invention provides a kind of FPGA on-line prediction control method based on Phillips macroscopic traffic flow.The method by the process of model approximate discretization, establishes parallel processing flow process, devises dynamic data storage scheme, achieves the PREDICTIVE CONTROL of blocked road circle mouth based on Phillips macroscopic traffic flow and changeable message signs with FPGA.The traffic flow density of highway, road speed can be made to realize effectively controlling in real time.

The technical solution adopted for the present invention to solve the technical problems: a kind of FPGA on-line prediction control method based on Phillips macroscopic traffic flow, is characterized in comprising the following steps:

Step one, according to Phillips model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\mathrm{\λ}\left(\mathrm{\ρ}\right)[V_e\left(\mathrm{\ρ}\right)-v]-\frac{1}{\mathrm{\ρ}}\frac{\∂P}{\∂\mathrm{\ρ}}\·\frac{\∂\mathrm{\ρ}}{\∂x}\\ \mathrm{\λ}\left(\mathrm{\ρ}\right)=3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-\mathrm{\ρ})/2\mathrm{n\ρ}\\ P=\mathrm{\ρ}\underset{0}{\overset{\∞}{\∫}}{(u-v)}^{2}f\left(u\right)\mathrm{du}\end{array}\right.$

In formula, ρ is the average density of vehicle, u is car speed, v is vehicle average velocity, t is the time, x is current location and the distance emulating road starting point, π [r (x, t), s (x, t) be] the rate of change of the density function that the vehicle flowrate entering due to circle mouth or roll away from causes, r (x, t) is the vehicle flowrate entered by circle mouth, s (x, t)=s ₀(x, t)+s _q(x, t) vehicle flowrate for being rolled away from by circle mouth, s ₀(x, t) normal vehicle flowrate, s for being rolled away from by circle mouth _qthe flow increment that (x, t) forces outgoing vehicles to cause for information displaying board, V _e(ρ) be equivalent speed, P=P (ρ, v), be that the variance of ρ, v distribution is long-pending, be similar to the pressure in gas dynamics, be referred to as traffic pressure, ρ ₀the jamming density of vehicle, υ ₁be the proportionality constant determined by experiment, n represents number of track-lines, and f (u, x, t) represents that x place is the probability of u at t car speed;

Represent differential term by difference scheme and omit higher order term, obtaining:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{k+1}-{\mathrm{\ρ}}_i^k}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{k+1}-v_i^k}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^k-v_i^k}{h}$

In formula, ξ is the step-length to t differential, i.e. sampling period; H is the differential step size to x, i.e. each road section length; The higher-order shear deformation that o (ξ) is ξ, the higher-order shear deformation that o (h) is h, ρ (x, t) be the average density of t x place vehicle, v (x, t) is the average velocity of t x place vehicle, road is divided into multiple section be the average density of i-th section at [k ξ, (k+1) ξ] interior vehicle, be the average velocity of i-th section at [k ξ, (k+1) ξ] interior vehicle;

The difference form obtaining Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}\\ -\frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}\underset{0}{\overset{\∞}{\∫}}{(u-v_i^k)}^{2}f\left(u\right)\mathrm{du}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula, r (i, k) represents that i-th section is at [k ξ, (k+1) ξ] the interior vehicle flowrate entered by circle mouth, s (i, k) represents the vehicle flowrate that i-th section is rolled away from by circle mouth in [k ξ, (k+1) ξ];

Consider that car speed can not be infinitely great, the difference form therefore improving Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}-\\ -\frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}{\underset{u=u_{\min }}{\overset{u_{\max }}{\mathrm{\Σ}}}(u-v_i^k)}^{2}f\left(u\right)\mathrm{\Δu}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula, u _minfor the minimum value of u, u _maxfor the maximal value of u, Δ u=(u _max-u _min)/(N+1), N is the big integer of setting;

Step 2, set up equivalent speed model and be:

In formula, v ₀, E, be constant, v _eafor variable information display board command speed;

I-th section:

In formula, v ₀, E, be constant, v _eai () is i-th section variable information display board command speed;

Step 3, in conjunction with difference form and the equivalent speed model of Phillips model, in FPGA, design comprises the computing module of vehicle average density k and average velocity v, according to the length of real road and circle message breath, highway is divided into multiple section, the corresponding computing module in each section, according to initial information and regulation and controlling of information, these computing modules of parallel running simultaneously in FPGA, dope vehicle average density and the average velocity of each section subsequent time period, then vehicle average density and average velocity stored in register, after all computing modules complete calculating, export vehicle average density and average velocity, these data back are carried out next step calculating to computing module simultaneously,

Step 4, enter blocked road flow as mode input using circle mouth, changeable message signs force Drazin inverse amount as pressure speed and circle mouth, given control inputs is predicted to average traffic current density and the vehicle average velocity in each section, if each section meets minimum speed, maximal density requirement, then select the program to control blocked road circle mouth and changeable message signs, otherwise adjustment control program.

Described computing module adopts floating point arithmetic, and self-defined floating number structure is as shown in the table:

1 symbol S

6 exponent e

17 mantissa M

Totally 24, wherein symbol 1, exponent 6, mantissa 17, the size of data of representative is F=(-1) ^s× 1.M × 2 ^e-31.

The invention has the beneficial effects as follows: owing to passing through the process of model approximate discretization, establish parallel processing flow process, devise dynamic data storage scheme, achieve the PREDICTIVE CONTROL of blocked road circle mouth based on Phillips macroscopic traffic flow and changeable message signs with FPGA.Make the traffic flow density of highway, road speed achieves and control in real time effectively.

Below in conjunction with drawings and Examples, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the computation structure figure of the FPGA on-line prediction control method that the present invention is based on Phillips macroscopic traffic flow.

Fig. 2 is that the FPGA of the FPGA on-line prediction control method that the present invention is based on Phillips macroscopic traffic flow realizes block diagram.

Embodiment

The present invention is described in detail with reference to Fig. 1,2.

1, according to Phillips model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\mathrm{\λ}\left(\mathrm{\ρ}\right)[V_e\left(\mathrm{\ρ}\right)-v]-\frac{1}{\mathrm{\ρ}}\frac{\∂P}{\∂\mathrm{\ρ}}\·\frac{\∂\mathrm{\ρ}}{\∂x}\\ \mathrm{\λ}\left(\mathrm{\ρ}\right)=3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-\mathrm{\ρ})/2\mathrm{n\ρ}\\ P=\mathrm{\ρ}\underset{0}{\overset{\∞}{\∫}}{(u-v)}^{2}f\left(u\right)\mathrm{du}\end{array}\right.$

In formula: ρ is the average density of vehicle, u is car speed, v is vehicle average velocity, t is the time, x is the distance with emulation road starting point, π [r (x, t), s (x, t)] be the rate of change of the density function that the vehicle flowrate entering due to circle mouth or roll away from causes, r (x, t) vehicle flowrate for being entered by circle mouth, s (x, t)=s ₀(x, t)+s _q(x, t) vehicle flowrate for being rolled away from by circle mouth, s ₀(x, t) normal vehicle flowrate, s for being rolled away from by circle mouth _qthe flow increment that (x, t) forces outgoing vehicles to cause for information displaying board, V _e(ρ) be equivalent speed, P=P (ρ, v), be that the variance of ρ, v distribution is long-pending, be similar to the pressure in gas dynamics, be referred to as traffic pressure, ρ ₀the jamming density of vehicle, υ ₁be the proportionality constant determined by experiment, n represents number of track-lines, and f (u, x, t) represents that x place is the probability of u at t car speed, and full application form symbol definition is identical;

Represent differential term by difference scheme and omit higher order term, obtaining:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{k+1}-{\mathrm{\ρ}}_i^k}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{k+1}-v_i^k}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^k-v_i^k}{h}$

In formula: ξ is the differential of t, h is the differential of x, the higher-order shear deformation that o (ξ) is ξ, the higher-order shear deformation that o (h) is h, ρ (x, t) be the average density of t x place vehicle, v (x, t) is the average velocity of t x place vehicle, road is divided into multiple section, each road section length is h, and the sampling period is ξ be the average density of i-th section at [k ξ, (k+1) ξ] interior vehicle, be the average velocity of i-th section at [k ξ, (k+1) ξ] interior vehicle;

The difference form obtaining Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}\\ -\frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}\underset{0}{\overset{\∞}{\∫}}{(u-v_i^k)}^{2}f\left(u\right)\mathrm{du}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula: r (i, k) vehicle flowrate that i-th section is entered by circle mouth in [k ξ, (k+1) ξ] is represented, s (i, k) vehicle flowrate that i-th section is rolled away from by circle mouth in [k ξ, (k+1) ξ] is represented;

Consider that car speed can not be infinitely great, the difference form therefore improving Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}-\\ -\frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}{\underset{u=u_{\min }}{\overset{u_{\max }}{\mathrm{\Σ}}}(u-v_i^k)}^{2}f\left(u\right)\mathrm{\Δu}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula: u _minfor the minimum value of u, u _maxfor the maximal value of u, Δ u=(u _max-u _min)/(N+1), N is the big integer of setting;

2, setting up equivalent speed model is:

I-th section:

In formula, v ₀, E, be constant, v _eai () is i-th section variable information display board command speed;

3, in the present embodiment, fpga chip selects the EP3C120F484C6 chip of altera corp, and communicating with host computer adopts RS-232 agreement, and level transferring chip selects MAX3232 chip; Then in FPGA, by computation structure shown in accompanying drawing 1, simulation calculation is carried out to each section.In the present embodiment, road is divided into 10 sections, in accompanying drawing 2, computing module 1-computing module 10 is the link traffic simulation computing module using floating point arithmetic device to combine according to the Difference Method of aforementioned partial differential equations, concrete data flow is: data reception module receives the traffic flow density in each section that host computer transmits, primary data and the regulation and control data of average velocity (comprise each section circle mouth and enter vehicle flowrate, roll vehicle flowrate and equivalent speed away from), then data allocation module is passed to, enable signal and these primary datas are passed to each computing module by data allocation module, each computing module carries out simulation calculation to vehicle average density and average velocity after receiving enable signal and result stored in register simultaneously, modules calculates and terminates rear respective calculating end signal to be passed to synchronization module, synchronization module completes at all computing modules and calculates the rear simulation result sending signal notification data distribution module and data outputting module reception vehicle average density and average velocity, data allocation module is distributed to computing module the simulation result in each section and regulation and controlling of information again and is carried out next step calculating, data outputting module Output simulation result simultaneously,

4, described floating point arithmetic device adopts self-defined floating number format, and floating number structure is as shown in the table:

1 symbol S

6 exponent e

17 mantissa M

Totally 24, wherein symbol 1, exponent 6, mantissa 17, the size of data of representative is F=(-1) ^s× 1.M × 2 ^e-31;

Described data reception module receives the data of 8 that host computer transmits, and is that 24 bit data pass to data allocation module the data transformations of continuous three 8;

Described data outputting module receives 24 result of calculations that computing module transmits, the data they being split into 8 export, before output result of calculation, first export valid data start identification code 0XFF, 0XF1,0XF1, result of calculation exports the complete valid data that export afterwards and terminates identification code 0XFF, 0XF2,0XF2;

5, blocked road flow is entered as mode input using circle mouth, changeable message signs force Drazin inverse amount as pressure speed and circle mouth, given control inputs is predicted to traffic density and the vehicle average velocity in each section, if each section meets minimum speed, maximal density requirement, then select the program to control blocked road circle mouth and changeable message signs, otherwise adjustment control program.

Claims (1)

1., based on a FPGA on-line prediction control method for Phillips macroscopic traffic flow, it is characterized in that comprising the following steps:

Step one, according to Phillips model:

$\left\{\begin{array}{c}\frac{\∂\mathrm{\ρ}}{\∂t}+\frac{\∂\left(\mathrm{\ρv}\right)}{\∂x}=\mathrm{\π}[r(x,t),s(x,t)]\\ \frac{\∂v}{\∂t}+v\frac{\∂v}{\∂x}=\mathrm{\λ}\left(\mathrm{\ρ}\right)[V_e\left(\mathrm{\ρ}\right)-v]-\frac{1}{\mathrm{\ρ}}\frac{\∂P}{\∂\mathrm{\ρ}}\·\frac{\∂\mathrm{\ρ}}{\∂x}\\ \mathrm{\λ}\left(\mathrm{\ρ}\right)=3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-\mathrm{\ρ})/2\mathrm{n\ρ}\\ P=\mathrm{\ρ}\underset{0}{\overset{\∞}{\∫}}{(u-v)}^{2}f\left(u\right)\mathrm{du}\end{array}\right.$

In formula, ρ is the average density of vehicle, u is car speed, v is vehicle average velocity, t is the time, x is current location and the distance emulating road starting point, π [r (x, t), s (x, t) be] the rate of change of the density function that the vehicle flowrate entering due to circle mouth or roll away from causes, r (x, t) is the vehicle flowrate entered by circle mouth, s (x, t)=s ₀(x, t)+s _q(x, t) vehicle flowrate for being rolled away from by circle mouth, s ₀(x, t) normal vehicle flowrate, s for being rolled away from by circle mouth _qthe flow increment that (x, t) forces outgoing vehicles to cause for information displaying board, V _e(ρ) be equivalent speed, P=P (ρ, v), be that the variance of ρ, v distribution is long-pending, be similar to the pressure in gas dynamics, be referred to as traffic pressure, ρ ₀the jamming density of vehicle, υ ₁be the proportionality constant determined by experiment, n represents number of track-lines, and f (u, x, t) represents that x place is the probability of u at t car speed;

Represent differential term by difference scheme and omit higher order term, obtaining:

$\frac{\∂\mathrm{\ρ}}{\∂t}=\frac{\mathrm{\ρ}(x,t+\mathrm{\ξ})-\mathrm{\ρ}(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{{\mathrm{\ρ}}_i^{k+1}-{\mathrm{\ρ}}_i^k}{\mathrm{\ξ}}$

$\frac{\∂\mathrm{\ρ}}{\∂x}=\frac{\mathrm{\ρ}(x+h,t)-\mathrm{\ρ}(x,t)}{h}+o\left(h\right)=\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}$

$\frac{\∂v}{\∂t}=\frac{v(x,t+\mathrm{\ξ})-v(x,t)}{\mathrm{\ξ}}+o\left(\mathrm{\ξ}\right)=\frac{v_i^{k+1}-v_i^k}{\mathrm{\ξ}}$

$\frac{\∂v}{\∂x}=\frac{v(x+h,t)-v(x,t)}{h}+o\left(h\right)=\frac{v_{i+1}^k-v_i^k}{h}$

In formula, ξ is the step-length to t differential, i.e. sampling period; H is the differential step size to x, i.e. each road section length; The higher-order shear deformation that o (ξ) is ξ, the higher-order shear deformation that o (h) is h, ρ (x, t) be the average density of t x place vehicle, v (x, t) is the average velocity of t x place vehicle, road is divided into multiple section be the average density of i-th section at [k ξ, (k+1) ξ] interior vehicle, be the average velocity of i-th section at [k ξ, (k+1) ξ] interior vehicle;

The difference form obtaining Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ =v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}\\ -\frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}\underset{0}{\overset{\∞}{\∫}}{(u-v_i^k)}^{2}f\left(u\right)\mathrm{du}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula, r (i, k) represents that i-th section is at [k ξ, (k+1) ξ] the interior vehicle flowrate entered by circle mouth, s (i, k) represents the vehicle flowrate that i-th section is rolled away from by circle mouth in [k ξ, (k+1) ξ];

Consider that car speed can not be infinitely great, the difference form therefore improving Phillips model is:

$\left\{\begin{array}{c}{\mathrm{\ρ}}_i^{k+1}=\mathrm{\ξ\π}[r(i,k),s(i,k)]-\frac{\mathrm{\ξ}}{h}[v_i^k({\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k)+{\mathrm{\ρ}}_i^k(v_{i+1}^k-v_i^k)]+{\mathrm{\ρ}}_i^k\\ =v_i^{k+1}=v_i^k+\mathrm{\ξ}\{\frac{\left[3{\mathrm{\ρ}}_0{\mathrm{\υ}}_1({\mathrm{\ρ}}_0-{\mathrm{\ρ}}_i^k)\right][V_e\left({\mathrm{\ρ}}_i^k\right)-v_i^k]}{2n{\mathrm{\ρ}}_i^k}\\ \frac{1}{{\mathrm{\ρ}}_i^k}\frac{{\mathrm{\ρ}}_{i+1}^k-{\mathrm{\ρ}}_i^k}{h}{\underset{u=u_{\min }}{\overset{u_{\max }}{\mathrm{\Σ}}}(u-v_i^k)}^{2}f\left(u\right)\mathrm{\Δu}-\frac{v_i^k(v_{i+1}^k-v_i^k)}{h}\}\end{array}\right.$

In formula, u _minfor the minimum value of u, u _maxfor the maximal value of u, Δ u=(u _max-u _min)/(N+1), N is the big integer of setting;

Step 2, set up equivalent speed model and be:

In formula, v ₀, E, be constant, v _eafor variable information display board command speed;

I-th section:

In formula, v ₀, E, be constant, v _eai () is i-th section variable information display board command speed;

Step 3, in conjunction with difference form and the equivalent speed model of Phillips model, in FPGA, design comprises the computing module of vehicle average density k and average velocity v, according to the length of real road and circle message breath, highway is divided into multiple section, the corresponding computing module in each section, according to initial information and regulation and controlling of information, these computing modules of parallel running simultaneously in FPGA, dope vehicle average density and the average velocity of each section subsequent time period, then vehicle average density and average velocity stored in register, after all computing modules complete calculating, export vehicle average density and average velocity, these data back are carried out next step calculating to computing module simultaneously,

Step 4, enter blocked road flow as mode input using circle mouth, changeable message signs force Drazin inverse amount as pressure speed and circle mouth, given control inputs is predicted to average traffic current density and the vehicle average velocity in each section, if each section meets minimum speed, maximal density requirement, then select the program to control blocked road circle mouth and changeable message signs, otherwise adjustment control program.