CN105882658A - Method for saving energy between two intersections through three-phase driving mode involving acceleration phase, constant speed phase and deceleration phase - Google Patents

Abstract

The invention discloses a method for saving energy between two intersections through a three-phase driving mode involving an acceleration phase, a constant speed phase and a deceleration phase, and belongs to the technical field of vehicle driving assistance systems. The method aims to establish three energy saving optimization models for the acceleration phase, the phase constant speed and the deceleration phase respectively on the basis of three determined speeds; wherein, for the acceleration phase, a model of optically controlling the economic efficiency of a vehicle with continuous gear is established, and a universal numerical solution method is identified on the basis of the variational method; for the constant speed phase, the accelerated speed is 0 m/s, and the vehicle cruises at the final speed of the acceleration phase; for the deceleration phase, engine output power is 0 kw, the speed of the constant speed phase is the initial speed of the deceleration phase, and an optimal decelerated speed is determined on the basis of the vehicle longitudinal dynamic model; after integrated optimization and analysis of all the three phases, the quantitative three-phase energy-saving driving mode involving the acceleration phase, the constant speed phase and the deceleration phase is established. The method has the advantages of higher computing accuracy, faster computing speed and excellent oil saving capacity.

Description

The power-economizing method of acceleration-at the uniform velocity-deceleration syllogic driving model between two crossings

Technical field

The invention belongs to car steering aid system technical field, particularly to a kind of gear continuous vehicle between two crossings The power-economizing method of acceleration-at the uniform velocity-deceleration syllogic driving model.

Background technology

Instantly seriously, energy-conservation and green technology has become as the research emphasis of automobile industry in China's energy scarcity, atmospheric pollution, Also paid much attention to by country and government." energy-conservation with new-energy automobile industrial development planning " issued by the State Council is pointed out, The average fuel consumption per hundred kilometers of passenger car must be down to 5L from the 7.71L of 2010 to the year two thousand twenty." 2014-2015 energy-saving and emission-reduction Low carbon development action scheme " in point out, per GDP CO2 emissions decline 4%, more than 3.5% in 2 years respectively, this Automobile is proposed the strictest energy-saving and emission-reduction requirement.It practice, the traveling oil consumption of vehicle is not only relevant to vehicle itself, The most inseparable with the drive manner of driver.Research shows, economy driving behavior can averagely reduce fuel oil about 10%.Add Speed-at the uniform velocity-deceleration syllogic driving model is the typical driving model that vehicle travels, especially at economy Driving Scene multi signal Under conditions of crossing, this driving model be vehicle travel substantially drive unit, its stop the process of restarting be to cause oil consumption The major reason increased.Therefore the economized operation modes exploring syllogic driving model has positive effect to reducing driving oil consumption.

At present, Chinese scholar mainly have studied vehicle energy-saving driving strategy under general driving meaning, cut-offs mutually by building Model and optimal control problem based on this model, the driving strategy of solving-optimizing.Present inventor Tsing-Hua University Li Sheng Ripples etc. have studied the economy acceleration strategy of gear discrete type vehicle, it is indicated that the most radical or the mildest acceleration all can cause Economy is deteriorated.Xu Shaobing etc., for the vehicle of outfit CVT (gear continuous) type variator, use pseudo-spectrometry to study it Economy acceleration strategy, this research shows: (1) economy acceleration strategy is substantially to improve engine efficiency and reduce windage energy The total tune optimization of consumption；(2) optimum acceleration strategy is and engine characteristics and the closely-related dynamic strategy of target end speed； (3) the fiercest or mild acceleration all can make oil consumption increase.The pseudo-spectrometry that Xu Shaobing etc. use is a kind of method for optimally controlling, It uses overall situation point collocation, has more preferable solving precision and convergence compared to other tradition direct methods such as point collocation, shooting method Speed, but its solving speed is still difficult to meet the requirement of reality application.And the most domestic research is limited only to vehicle and accelerates Process, does not propose a kind of effective fuel-economizing driving strategy for specific Driving Scene.

Though foreign scholar travels the research carrying out oil consumption optimisation strategy between multi signal crossing for vehicle, but there is also oil consumption Model simply, do not consider the shortcomings such as vehicle dynamic model.2012, the scientific paper that Henry X.Liu etc. delivers carries Go out application multistage method in optimal control and solve vehicle optimal velocity control problem between multi signal crossing.For simplifying calculating process, This paper assumes that vehicle travels with economy speed the most as far as possible, and acceleration is constant in same boost phase (acceleration of different boost phases can be different), by general with application for the method pseudo-spectrometry optimum control software (General Pseudo-spectral Optimal Control Software, GPOPS) solve, three kinds of results not taking optimisation strategy to solve are entered Row contrast, find analytic method can fuel-economizing 70%, GPOPS solving result can fuel-economizing 64%, and the calculating time of analytic method is remote Less than GPOPS method.But this paper have employed the oil consumption model of simplification, i.e. calculates vehicle with car speed, acceleration etc. Transient demand power, and then table look-up and obtain the traveling oil consumption of automobile.Its advantage is model simple, it is simple to experiment obtains, and lacks Point is cannot to reflect electromotor injection characteristics accurately, and model accuracy is low.Galpin Thomas etc. use shortest path first (Dijkstra algorithm) gives the driving path of the vehicle oil consumption optimum by multi signal crossing.But this paper have ignored The Longitudinal Dynamic Model of vehicle, it is assumed that vehicle at the uniform velocity travels between two signalized intersections, and use simple empirical equation (false If the function that oil consumption is speed, acceleration) calculate engine consumption, it is impossible to accurately reflect electromotor reality when driving Oil consumption.SanjibanKundu etc. provide the vehicle three kinds of speed control algorithms by signalized intersections, by given three kinds Rule, carries out simulation study, finds when ensureing that vehicle passes through in green light interval, and makes the vehicle (can with economy speed as far as possible Obtaining according to engine MAP and vehicle parameter) oil-saving effect that travels is optimum, and can fuel-economizing 10% for single fleet. Weak point is still that oil consumption model is simple, it is impossible to reflection practical oil consumption, and does not considers longitudinal vehicle dynamic model.At present, It is the most blank for being equipped with the theoretical research of the vehicle acceleration-at the uniform velocity-deceleration syllogic fuel-economizing optimization method of CVT type variator, One important reason is the discontinuity of engine consumption so that the Optimal Control Model that boost phase is set up is discontinuous (is subordinate to Belong to mixing integer problem), theoretical the most difficult with numerical solution.Another reason is how to consider acceleration-at the uniform velocity- The deceleration these three stage need research.

Summary of the invention

It is an object of the invention to, for solving the problem that prior art exists, propose acceleration-at the uniform velocity-deceleration syllogic between two crossings The power-economizing method of driving model, for equipping the vehicle of CVT type variator.The acceleration of the vehicle of the present invention-at the uniform velocity-deceleration three Segmentation is driven power-economizing method and is referred to reasonably control engine power so that boost phase engine consumption is minimum.With traditional joint Can method compare, the inventive method has higher computational accuracy, calculates speed and stronger fuel-economizing ability faster.

Accelerate at the uniform velocity to slow down between two crossings that the present invention proposes the power-economizing method of syllogic driving model, it is characterised in that: The method includes determining the speed of constant velocity stage, the end speed of boost phase and the initial velocity in decelerating phase, according to three determined Plant speed and set up the energy saving optimizing model in boost phase, constant velocity stage, decelerating phase respectively；Wherein, boost phase passes through structure Build the economy Optimal Control Model of gear continuous vehicle, propose general method of value solving in conjunction with the calculus of variations；At the uniform velocity rank It is 0m/s that section controls acceleration, and cruises with the end speed of boost phase；Decelerating phase controls engine output 0kw, and using the speed of constant velocity stage as the initial velocity in this stage, in conjunction with subtracting that longitudinal vehicle dynamic model obtains optimizing Speed；In the comprehensive these three stage, this process it is optimized on the whole and analyzes, forming the acceleration-at the uniform velocity-deceleration of quantification Syllogic drives energy saver mode.

Specifically include following steps:

1) speed corresponding to three stages is determined:

Determine the speed v that vehicle at the uniform velocity travels_cAs shown in formula (1), the economy speed v of vehicle_ecoWith road speed limit v_maxThe most Know, if v_eco≤v_max, the speed v that the most at the uniform velocity travels_cFor v_ecoOtherwise, then it is v_max；

$v_c=\left\{\begin{array}{cc}{v}_{eco},& v_{eco}\≤v_{\max }\\ v_{max},& v_{eco}>v_{\max }\end{array}\right.---\left(1\right)$

Wherein, described v_ecoFor the speed that vehicle is corresponding under at the uniform velocity travelling fuel consumption per hundred kilometers lowest term；

Therefore, end speed v of vehicle boost phase is obtained_afAnd the initial velocity v in decelerating phase_d0As shown in formula (2):

v_c=v_af=v_d0 (2)

2) the energy saving optimizing model of boost phase is set up:

The object function of vehicle boost phase of the present invention is made up of with acceleration distance correction term the total oil consumption of electromotor, wherein, starts Machine total oil consumption J_LAs shown in formula (3):

$J_L={\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(3\right)$

Wherein, t_fFor acceleration time, P_eFor engine power, Q_s(P_e) represent electromotor total instantaneous fuel injection rate, the present invention adopts Instantaneous fuel injection rate is estimated with engine consumption MAP；

Due to CVT type variator can continuous transformation speed ratio, motor instant fuel injection rate q_sIt is reduced to the function of engine power, As shown in formula (4):

$q_s\left(P_e\right)=a_0+a_1{P}_e+a_2{P}_e^2,P_e\≥0---\left(4\right)$

Wherein, a_i(i=0,1,2) is fitting coefficient, a_iSpan be 10^-2To 10；

Introduce electromotor dynamic corrections item k_e(dP_e/dt)², obtain the dynamic oil consumption Q of electromotor_s:

$Q_s=q_s+k_e{\left(\frac{{\mathrm{dP}}_e}{dt}\right)}^2---\left(5\right)$

Wherein, k_eFor electromotor dynamic oil consumption correction factor, k_eThe order of magnitude be 10^-4；

Described acceleration distance correction term J_MFor:

J_M=-k_sS_f (6)

Wherein, k_sFor acceleration distance correction factor, it is set as k_s=-Q_s(v_eco)/v_eco, Q_s(v_eco) represent that vehicle is at warp Ji property speed v_ecoThe total instantaneous fuel injection rate of lower electromotor, S_fFor acceleration distance；

Therefore equivalent the criterion of the fuel consumption is:

$J=J_M+J_L=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(7\right)$

In accelerator, equality constraint includes formula (8) and (9):

Electromotor economy curve obedience formula (8):

T_eco(w_eco)=k_eco(w_eco-b)^γ (8)

Wherein, T_eco(w_eco) torque of electromotor that is expressed as on the economy curve of BSFC, w_ecoEconomy for BSFC Engine speed on curve, k_eco, γ and b be fitting coefficient；

Meanwhile, engine speed is coordinated to reach optimum by formula (9):

$i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}---\left(9\right)$

Wherein, i_gFor transmission gear ratio, i₀For speed ratio of main reducer, r_wFor vehicle tyre radius, c is coefficient；

Inequality constraints condition includes: engine power P_e, transmission gear ratio i_g, road maximum speed limit v_maxConstraint:

$\begin{array}{c}{P}_{e\min }\≤P_e\≤P_{emax}\\ i_{g\min }\≤i_g\≤i_{gmax}\\ 0\≤v\≤v_{\max }\end{array}---\left(10\right)$

Wherein, P_emin、P_emaxIt is respectively minima and maximum, the i of engine power_gmin、i_gmaxFor transmission gear ratio Minima and maximum；

Vehicle is carried out following simplification: a) ignore electromotor and the high-order dynamic characteristic of CVT type variator rotary part, and The gap of drive system and torsional deflection；B) assume in clutch dynamic process without sliding wear phenomenon；C) assume that drive system is not Same gear ratio, different transmission power underdrive efficiency are consistent；According to kinetics equation and above-mentioned reduced condition, obtain accelerate, At the uniform velocity and the state equation of energy saving optimizing model that is all suitable for of decelerating phase is:

$\begin{array}{c}\stackrel{\·}{s}=v\\ \stackrel{\·}{v}=(\frac{{\mathrm{\η}}_T{P}_e}{v}-C_A{v}^2-Mfg)\·\frac{1}{\mathrm{\δ}M}\end{array}---\left(11\right)$

Wherein, s is vehicle operating range, and v is speed, η_TFor power train transmission aggregate efficiency, C_A=0.5C_Dρ_aA_v, C_DFor Air resistance coefficient, ρ_aFor atmospheric density, A_vFor vehicle front face area, M is complete vehicle quality, and g is gravity coefficient, and f is friction system Number, δ is gyrating mass coefficient；

To sum up, the boost phase energy saving optimizing model that the present invention builds is as follows:

$\min J=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt$

Submit to

$\begin{array}{c}\left(\begin{array}{c}\stackrel{\·}{s}\\ \stackrel{\·}{v}\end{array}\right)=\left(\begin{array}{cc}0& 1\\ 0& -\frac{C_A{v}^2+Mfg}{\mathrm{\δ}Mv}\end{array}\right)\left(\begin{array}{c}s\\ v\end{array}\right)+\left(\begin{array}{c}0\\ \frac{{\mathrm{\η}}_T}{\mathrm{\δ}Mv}\end{array}\right)P_e\\ T_{eco}\left(w_{eco}\right)=k_{eco}{(w_{eco}-b)}^{\mathrm{\γ}}\\ i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}\\ P_{e\min }\≤P_e\≤P_{e\max }\\ i_{g\min }\≤i_g\≤i_{g\max }\\ 0\≤v\≤v_{\max }\\ x\left(0\right)={\left(\begin{array}{cc}0& 0\end{array}\right)}^T\\ x\left(t_f\right)={\left(\begin{array}{cc}{S}_f& 0\end{array}\right)}^T\end{array}---\left(12\right)$

Wherein, x (0)=(0 0)^TRepresent that initial distance and speed are 0, x (0)=(0 0)^TRepresent terminal distance and speed Degree is respectively S_fWith 0；

At boost phase, solve formula (12) and obtain, the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔFor:

$\begin{array}{c}{E}_{\mathrm{\Δ}}=\frac{-k_s\left(v_{eco}\right)v+q_s\left(P_e\right)}{g(P_e,v)}\\ =\frac{1}{3.6a}\[a_0+{10}^{-3}{a}_1(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d(v\left)\right)+{10}^{-6}{a}_2{(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d(v\left)\right)}^2\mathrm{...}\\ +P_d{\left(v\right)}^2\]-\frac{1}{a}{q}_s(v_f,0)\frac{v}{v_f}\end{array}---\left(13\right)$

Wherein, a is the acceleration of boost phase；P_d(v)=(C_Av²+Mgf)v/η_T, P_dV () represents when speed is v, Vehicle provide to overcome the power needed for air drag and frictional resistance；q_s(v_f, 0) and=a₀+10^-3a₁P_e(v_f,0)+ 10^-6a₂P_e ²(v_f, 0), represent that acceleration is motor instant fuel injection rate when 0； P_e(v_f, 0) and expression speed is v_fAnd acceleration is when being 0, vehicle provide to overcome the power needed for air drag and frictional resistance；

Therefore work as the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔWhen taking minima, obtain boost phase at various speeds excellent Change acceleration a_aFor:

The optimization total time t of boost phase_afFor

$t_{af}=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{ai}}{{\mathrm{\Δa}}_{ai}}---\left(15\right)$

Wherein, D is integration step；v_a0Initial velocity for boost phase；v_afEnd speed for boost phase；Δv_i、Δa_aiWith (v_af-v_a0)/D representation unit speed interval respectively, unit acceleration interval and unit interval；

Therefore total distance S of the optimization of boost phase_aFor:

$S_a={\∫}_{t_{a0}}^{t_{af}}vdt=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i{v}_{ai}---\left(16\right)$

Wherein, t_a0Initial time for boost phase；

Total oil consumption of boost phase is:

$J_a={\∫}_{v_{a0}}^{v_{af}}{E}_{\mathrm{\Δ}}dv---\left(17\right)$

2) the energy saving optimizing model in decelerating phase is set up:

In the decelerating phase, make vehicle sliding to terminal, control engine power P_ed≡ 0, vehicle is with at the uniform velocity travel speed v_cMake Initial velocity v for the decelerating phase_d0, according to equation of state (11), obtaining optimization of vehicle deceleration is:

$a_d=-(C_A{v}^2+Mgf)\frac{1}{\mathrm{\δ}M}---\left(18\right)$

The optimization total time t in decelerating phase_dfFor:

$t_{df}=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{dj}}{{\mathrm{\Δa}}_{dj}}---\left(19\right)$

Wherein, v_d0Initial velocity for the decelerating phase；v_dfEnd speed for the decelerating phase；

Therefore total distance S of the optimization in decelerating phase_dFor:

$S_d={\∫}_{t_{d0}}^{t_{df}}vdt=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j{v}_{dj}---\left(20\right)$

Wherein, t_d0Initial time for the decelerating phase；

Therefore, total oil consumption in decelerating phase is

$J_d={\∫}_{t_{d0}}^{t_{df}}{q}_s\left(P_e\right)dt=a_0(t_{df}-t_{d0})/3.6---\left(21\right)$

4) the energy saving optimizing model of constant velocity stage is set up:

At constant velocity stage, vehicle acceleration a_cFor 0m/s², vehicle is with end speed v of boost phase_afAs constant velocity stage's Travel speed v_c；According to equation of state (11), obtain vehicle optimal engine powerFor:

$P_{ec}^{*}=(C_A{v}_c^2+Mgf)\frac{v_c}{{\mathrm{\η}}_T}---\left(22\right)$

Therefore constant velocity stage, total distance S of the optimization at the uniform velocity travelled_cFor:

S_c=S_T-S_a-S_d (23)

Wherein, S_TFor accelerating, at the uniform velocity with triphasic total distance of slowing down, and be known quantity；

The optimization total time t of constant velocity stage_cFor:

$t_c=\frac{S_c}{v_c}---\left(24\right)$

Finally give and accelerate three stages corresponding optimization travel speed, acceleration and the power that at the uniform velocity slows down, thus constitute optimization Energy-conservation syllogic mode of operation.

The feature of the present invention and beneficial effect:

The present invention consider longitudinal vehicle dynamic model and based on engine MAP oil consumption model on the basis of, propose Between two crossings ,-at the uniform velocity-deceleration three sections is accelerated with " auto model+syllogic analytical model " CVT type vehicle as framework The power-economizing method of formula driving model.The method quantitative scoring can calculate the acceleration-at the uniform velocity-deceleration syllogic of a kind of CVT type vehicle and drive Sailing the power-economizing method of pattern, compared with traditional method for solving, the inventive method has degree of precision and calculates speed.And Thus method can analyze influence factor and the mechanism in each stage.

The energy conservation optimizing method of the CVT type vehicle acceleration-at the uniform velocity-deceleration syllogic of the present invention is applicable not only to generally to accelerate-and even Speed-deceleration mode, is also applied for acceleration-deceleration two-part pattern.Additionally, both can be applicable to the fuel-economizing of vehicle between two crossings Travel, also extend to the situation of multiple continuous green light crossing, when the number of this continuous green light changes, the method Stand good, therefore it is the general solution of acceleration-at the uniform velocity-deceleration syllogic driving model.

Being applied in reality, the inventive method can drive aided algorithm as one provides one to improve warp for CVT type vehicle The power-economizing method of the acceleration-at the uniform velocity-deceleration syllogic driving model of Ji property, has stronger fuel-economizing ability.

Accompanying drawing explanation

Fig. 1 is the overall procedure block diagram of the inventive method；

Fig. 2 is the optimization accelerating curve in the present invention under boost phase friction speed；

Fig. 3 is the optimization projectile deceleration history in the present invention under decelerating phase friction speed；

Fig. 4 is the speed/time graph of different total distance；

Fig. 5 is the optimal speed curve comparison figure of analytic method and pseudo-spectrometry.

Detailed description of the invention

The power-economizing method of syllogic driving model of accelerating at the uniform velocity to slow down between two crossings that the present invention proposes combines accompanying drawing and concrete Data describe in detail as follows:

The method that the present invention proposes, for equipping the vehicle of CVT type variator, it realizes flow process as it is shown in figure 1, include really Determining the speed of constant velocity stage, the end speed of boost phase and the initial velocity in decelerating phase, three kinds of speed according to determining are built respectively Vertical boost phase, constant velocity stage, the energy saving optimizing model in decelerating phase, specifically include following steps:

1) speed corresponding to three stages is determined:

Determine the speed v that vehicle at the uniform velocity travels_cAs shown in formula (1), the economy speed v of vehicle_ecoWith road speed limit v_maxThe most Know, if v_eco≤v_max, the speed v that the most at the uniform velocity travels_cFor v_ecoOtherwise, then it is v_max；

$v_c=\left\{\begin{array}{cc}{v}_{eco},& v_{eco}\≤v_{\max }\\ v_{max},& v_{eco}>v_{\max }\end{array}\right.---\left(1\right)$

Wherein, described v_ecoFor the speed that vehicle is corresponding under at the uniform velocity travelling fuel consumption per hundred kilometers lowest term；

Therefore, end speed v of vehicle boost phase can be obtained_afAnd the initial velocity v in decelerating phase_d0As shown in formula (2):

v_c=v_af=v_d0 (2)

2) the energy saving optimizing model of boost phase is set up:

This method selects suitable accelerator open degree and transmission gear ratio so that vehicle boost phase engine consumption is minimum as excellent Change model；Therefore, the object function of this energy saving optimizing model is that the total oil consumption of electromotor of vehicle boost phase is repaiied with acceleration distance Positve term, state equation obedience longitudinal vehicle dynamic model, state variable is distance and speed, and control variable is electromotor merit Rate, constraint set (including equality constraint and inequality constraints condition) is vehicle performance and road conditions constraint；

The object function of vehicle boost phase of the present invention is made up of with acceleration distance correction term the total oil consumption of electromotor, wherein, starts Machine total oil consumption J_LAs shown in formula (3):

$J_L={\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(3\right)$

In formula (3), t_fFor acceleration time, P_eFor engine power, Q_s(P_e) represent electromotor total instantaneous fuel injection rate, this Bright employing engine consumption MAP estimates instantaneous fuel injection rate；

Due to CVT type variator can continuous transformation speed ratio, motor instant fuel injection rate q_sThe function of engine power can be reduced to, As shown in formula (4):

$q_s\left(P_e\right)=a_0+a_1{P}_e+a_2{P}_e^2,P_e\≥0---\left(4\right)$

Wherein, a_i(i=0,1,2) is fitting coefficient, a_iSpan be 10^-2To 10)；

(it practice, electromotor is in dynamic process, due to factor impacts such as the reduction of cylinder charge coefficient, fuel-oil atmozation variation, Utilizing engine consumption MAP to estimate there is certain error in dynamic fuel injection rate) introduce electromotor dynamic corrections item k_e(dP_e/dt)², Obtain the dynamic oil consumption Q of electromotor_s:

$Q_s=q_s+k_e{\left(\frac{{\mathrm{dP}}_e}{dt}\right)}^2---\left(5\right)$

Wherein, Q_s(P_e) it is the total instantaneous fuel injection rate of electromotor, k_eFor electromotor dynamic oil consumption correction factor, k_eThe order of magnitude be 10^-4)；

Described acceleration distance correction term J_MFor:

J_M=-k_sS_f (6)

Wherein, k_sFor acceleration distance correction factor, it is set as k_s=-Q_s(v_eco)/v_eco, Q_s(v_eco) represent that vehicle is at warp Ji property speed v_ecoThe total instantaneous fuel injection rate of lower electromotor, S_fFor acceleration distance；J_MPhysical significance be: for arbitrarily strategy, Vehicle is deducted with economy speed v on the basis of total oil consumption in acceleration stage_ecoTravel acceleration distance S_fCorresponding oil consumption, Thus eliminate the impact that between Different Strategies, acceleration distance difference is brought；

Therefore equivalent the criterion of the fuel consumption is:

$J=J_M+J_L=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(7\right)$

In accelerator, equality constraint includes formula (8) and (9):

Calculate for simplifying, it is assumed that electromotor controls CVT type variator according to the economy curve on BSFC (whole performance map), Electromotor economy curve obedience formula (8):

T_eco(w_eco)=k_eco(w_eco-b)^γ (8)

Wherein T_eco(w_eco) torque of electromotor that is expressed as on the economy curve of BSFC, generally 0～200Nm, w_eco For the engine speed on the economy curve of BSFC, generally 0～6000rpm, k_eco, γ and b be fitting coefficient, typically Its span is respectively 0～20,0～1 and 900～1100；

Meanwhile, engine speed is coordinated to reach optimum by formula (9):

$i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}---\left(9\right)$

Wherein, i_gFor transmission gear ratio, i₀For speed ratio of main reducer, r_wFor vehicle tyre radius, c is coefficient, the value of c Scope is 10～100；

Inequality constraints condition includes: engine power P_e, transmission gear ratio i_g, road maximum speed limit v_maxConstraint:

$\begin{array}{c}{P}_{e\min }\≤P_e\≤P_{emax}\\ i_{g\min }\≤i_g\≤i_{gmax}\\ 0\≤v\≤v_{\max }\end{array}---\left(10\right)$

Wherein, P_emin、P_emaxIt is respectively minima and maximum, the i of engine power_gmin、i_gmaxFor transmission gear ratio Minima and maximum, determine all in accordance with vehicle and road conditions；

It is furnished with the vehicle meeting above-mentioned economy curve CVT type variator, the state side of its boost phase energy saving optimizing model Journey obeys vehicle dynamic model, and the present invention studies the drive system of vehicle and includes electromotor, CVT type variator etc., it is considered to To terseness and accuracy, vehicle is carried out following simplification: a) ignore electromotor and the high-order of CVT type variator rotary part Dynamic characteristic, and the gap of drive system and torsional deflection；B) assume in clutch dynamic process without sliding wear phenomenon；C) false If drive system is consistent in different drive ratios, different transmission power underdrive efficiency；According to kinetics equation and above-mentioned simplification bar Part, obtains accelerating, at the uniform velocity and the state equation of energy saving optimizing model that is all suitable for of decelerating phase, to determine the acceleration of vehicle Degree, described state equation is:

$\begin{array}{c}\stackrel{\·}{s}=v\\ \stackrel{\·}{v}=(\frac{{\mathrm{\η}}_T{P}_e}{v}-C_A{v}^2-Mfg)\·\frac{1}{\mathrm{\δ}M}\end{array}---\left(11\right)$

Wherein, for vehicle operating range, v is speed, η_TFor power train transmission aggregate efficiency, C_A=0.5C_Dρ_aA_v, C_DFor Air resistance coefficient, ρ_aFor atmospheric density, A_vFor vehicle front face area, M is complete vehicle quality, and g is gravity coefficient, and f is friction system Number, span is 0～0.1, and δ is gyrating mass coefficient, and general span is 1～2；

To sum up, the boost phase energy saving optimizing model that the present invention builds is as follows:

$\min J=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt$

Submit to

$\begin{array}{c}\left(\begin{array}{c}\stackrel{\·}{s}\\ \stackrel{\·}{v}\end{array}\right)=\left(\begin{array}{cc}0& 1\\ 0& -\frac{C_A{v}^2+Mfg}{\mathrm{\δ}Mv}\end{array}\right)\left(\begin{array}{c}s\\ v\end{array}\right)+\left(\begin{array}{c}0\\ \frac{{\mathrm{\η}}_T}{\mathrm{\δ}Mv}\end{array}\right)P_e\\ T_{eco}\left(w_{eco}\right)=k_{eco}{(w_{eco}-b)}^{\mathrm{\γ}}\\ i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}\\ P_{e\min }\≤P_e\≤P_{e\max }\\ i_{g\min }\≤i_g\≤i_{g\max }\\ 0\≤v\≤v_{\max }\\ x\left(0\right)={\left(\begin{array}{cc}0& 0\end{array}\right)}^T\\ x\left(t_f\right)={\left(\begin{array}{cc}{S}_f& 0\end{array}\right)}^T\end{array}---\left(12\right)$

Wherein, x (0)=(0 0)^TRepresent that initial distance and speed are 0, x (0)=(0 0)^TRepresent terminal distance and speed Degree is respectively S_fWith 0；

Using the theory of optimal control calculus of variations to solve formula (12), detailed process is described as follows:

Assume original state variable (distance, the speed)=(s of vehicle₀,v₀) it is fixed value；To acceleration time t_fAnd acceleration distance S_fIt is not provided with constraint, is free variable；Terminal velocity v_f(represent that vehicle travels speed to terminal, v_fFor fixed value；For It is easy to analyze further, is energy saving optimizing model based on speed by this time-based energy saving optimizing model conversation:

$\min J=-k_s\left(v_f\right)S_f+{\∫}_0^{v_f}\frac{Q_s\left(P_e\right)}{g(P_e,v)}dv---(12-1)$

Submit to

$\begin{array}{c}\frac{ds}{dv}=\frac{v}{g(P_e,v)}\\ g(P_e,v)=\stackrel{\·}{v}=(\frac{{\mathrm{\η}}_T{P}_e}{v}-C_A{v}^2-Mfg)\·\frac{1}{\mathrm{\δ}M}\end{array}---(12-2)$

The essential condition existed according to extreme value, the Hamiltonian function of formula (12 1) is:

$H=\frac{Q_s\left(P_e\right)}{g(P_e,v)}+\mathrm{\λ}\left(t\right)\frac{v}{g(P_e,v)}---(12-3)$

Wherein, λ (t) is association's state vector, and therefore, the governing equation of available formula (12 3) is:

$\frac{\∂H}{\∂P_e}=\frac{\∂}{\∂P_e}\left(\frac{q_s\left(P_e\right)}{g(P_e,v)}\right)+\mathrm{\λ}\frac{\∂}{\∂P_e}\left(\frac{v}{g(P_e,v)}\right)=0---(12-4)$

According to adjoint equation, it is known that:

$\stackrel{\·}{\mathrm{\λ}}=-\frac{\∂H}{\∂s}=0---(12-5)$

By transversality condition, can obtain:

$\begin{array}{c}\mathrm{\λ}\left(t_f\right)=-k_s\left(v_f\right)\\ v\left(t_f\right)=v_f\end{array}---(12-6)$

Therefore, association state vector λ (t) ≡-k_s(v_f), convolution (12 4), it is known that the optimal engine power of vehicle boost phase For speed v and terminal velocity v_fFunction:

$P_e^{*}\left(v\right)=h(v,k_s(v_f\left)\right)---(12-7)$

Wherein, h is a unJeiermined function, refers to speed and end speed and function；Illustrate for different acceleration tasks, Under a certain speed determined, optimal power depends on terminal velocity v_f；

For different acceleration tasks, by k_s(v_f) it is set to a fixed value, thus λ is a constant,It is only the letter of speed v Number:

$P_e^{*}\left(v\right)=\tilde{h}\left(v\right)---(12-8)$

Refer to the function of speed v, be a unJeiermined function.

Result shows that optimum accelerating power is only determined by present speed, arranges k_s(v_f) it is a constant k_s(v_eco), by solving formula (12 9), the suboptimal solution of available optimal power:

$\frac{\∂H}{\∂P_e}=\frac{1}{g^2}(\frac{\∂Q_s}{\∂P_e}g-q_s\frac{\∂g}{\∂P_e}-\mathrm{\λ}v\frac{\∂g}{\∂P_e})=0---(12-9)$

Meanwhile, the minimum equivalent oil consumption that vehicle accelerates to needed for speed v+Δ v from speed v is:

$\underset{P_e}{min}\mathrm{\Δ}J=\mathrm{\Δ}v\frac{-k_s\left(v_{eco}\right)v+Q_s\left(P_e\right)}{a}---(12-10)$

Therefore, the minimum equivalent oil consumption E that unit speed changes delta v is corresponding_ΔFor:

$\underset{P_e}{min}{E}_{\mathrm{\Δ}}=\underset{\mathrm{\Δ}v\→0}{\lim }\frac{\mathrm{\Δ}J}{\mathrm{\Δ}v}=\frac{-k_s\left(v_{eco}\right)v+q_s\left(P_e\right)}{g(P_e,v)}---(12-11)$

Due to

$\frac{\∂E_{\mathrm{\Δ}}}{\∂P_e}=\frac{\∂H}{\∂P_e}=\frac{\∂}{\∂P_e}\left(\frac{q_s\left(P_e\right)}{g(P_e,v)}\right)+\mathrm{\λ}\frac{\∂}{\∂P_e}\left(\frac{v}{g(P_e,v)}\right)---(12-12)$

Therefore can be converted into the formula of solving (12 11) by solving formula (12 1), thus can ask by solving one-dimensional optimization formula (12 11) Solution formula (12), and then obtain engine optimum power

At boost phase, from formula (12), the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔFor:

$\begin{array}{c}{E}_{\mathrm{\Δ}}=\frac{-k_s\left(v_{eco}\right)v+q_s\left(P_e\right)}{g(P_e,v)}\\ =\frac{1}{3.6a}\[a_0+{10}^{-3}{a}_1(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d(v\left)\right)+{10}^{-6}{a}_2{(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d(v\left)\right)}^2\mathrm{...}\\ +P_d{\left(v\right)}^2\]-\frac{1}{a}{q}_s(v_f,0)\frac{v}{v_f}\end{array}---\left(13\right)$

Wherein, a is the acceleration of boost phase；P_d(v)=(C_Av²+Mgf)v/η_T, P_dV () represents when speed is v, vehicle There is provided to overcome the power needed for air drag and frictional resistance；q_s(v_f, 0) and=a₀+10^-3a₁P_e(v_f,0)+ 10^-6a₂P_e ²(v_f, 0), represent that acceleration is motor instant fuel injection rate when 0； P_e(v_f, 0) and expression speed is v_fAnd acceleration is when being 0, vehicle provide to overcome the power needed for air drag and frictional resistance； Therefore work as the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔWhen taking minima, it is known that boost phase optimization at various speeds adds Speed a_aFor:

The optimization total time t of boost phase_afFor:

$t_{af}=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{ai}}{{\mathrm{\Δa}}_{ai}}---\left(15\right)$

Wherein, D is integration step；v_a0Initial velocity for boost phase；v_afEnd speed for boost phase；Δv_i、Δa_aiWith (v_af-v_a0)/D representation unit speed interval respectively, unit acceleration interval and unit interval；

Therefore total distance S of the optimization of boost phase_aFor:

$S_a={\∫}_{t_{a0}}^{t_{af}}vdt=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i{v}_{ai}---\left(16\right)$

Wherein, t_a0For the initial time of boost phase, typically from the beginning of 0s；

Total oil consumption of boost phase is:

$J_a={\∫}_{v_{a0}}^{v_{af}}{E}_{\mathrm{\Δ}}dv---\left(17\right)$

Fig. 2 gives the optimization accelerating curve under vehicle boost phase friction speed；

3) the energy saving optimizing model in decelerating phase is set up:

In the decelerating phase, make vehicle sliding to terminal, control engine power P_ed≡ 0, vehicle is with at the uniform velocity travel speed v_cMake Initial velocity v for the decelerating phase_d0, according to equation of state (11), it is known that optimization of vehicle deceleration is:

$a_d=-(C_A{v}^2+Mgf)\frac{1}{\mathrm{\δ}M}---\left(18\right)$

The optimization total time t in decelerating phase_dfFor:

$t_{df}=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{dj}}{{\mathrm{\Δa}}_{dj}}---\left(19\right)$

Wherein, v_d0Initial velocity for the decelerating phase；v_dfEnd speed for the decelerating phase；

Therefore total distance S of the optimization in decelerating phase_dFor:

$S_d={\∫}_{t_{d0}}^{t_{df}}vdt=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j{v}_{dj}---\left(20\right)$

Wherein, t_d0For the initial time in decelerating phase, equal to end speed and constant velocity stage's running time sum of boost phase；

Therefore, total oil consumption in decelerating phase is:

$J_d={\∫}_{t_{d0}}^{t_{df}}{q}_s\left(P_e\right)dt=a_0(t_{df}-t_{d0})/3.6---\left(21\right)$

Fig. 3 gives the optimization projectile deceleration history under vehicle deceleration stage friction speed；

4) the energy saving optimizing model of constant velocity stage is set up:

At constant velocity stage, vehicle acceleration a_cFor 0m/s², vehicle is with end speed v of boost phase_afAs constant velocity stage's Travel speed v_c.；According to equation of state (11), it is known that vehicle optimal engine powerFor:

$P_{ec}^{*}=(C_A{v}_c^2+Mgf)\frac{v_c}{{\mathrm{\η}}_T}---\left(22\right)$

Therefore constant velocity stage, total distance S of the optimization at the uniform velocity travelled_cFor:

S_c=S_T-S_a-S_d (23)

Wherein, S_TFor accelerating, at the uniform velocity with triphasic total distance of slowing down, and be known quantity；

The optimization total time t of constant velocity stage_cFor:

$t_c=\frac{S_c}{v_c}---\left(24\right)$

Finally give and accelerate three stages corresponding optimization travel speed, acceleration and the power that at the uniform velocity slows down, thus constitute optimization Energy-conservation syllogic mode of operation.

Said method is used to be described in conjunction with the embodiments as follows:

Use an actual vehicle model parameter that the triphasic energy saving optimizing model that accelerates described in this method at the uniform velocity to slow down is carried out Solving, vehicle major parameter is as shown in table 1:

Table 1 vehicle major parameter

1) speed corresponding to three stages is determined:

The economy speed v of vehicle in the present embodiment_ecoFor 25.6m/s, road speed limit v_maxFor 30m/s, therefore according to formula (1) With formula (2), it is known that v_c=v_af=v_d0=25.6m/s.；

2) the energy saving optimizing model of boost phase is set up:

According to formula (14), it is known that boost phase optimization acceleration a at various speeds_aFor

According to formula (15), it is known that the optimization total time t of boost phase_afFor

$t_{af}=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{ai}}{{\mathrm{\Δa}}_{ai}}$

Wherein, D is integration step, takes 0.1；v_a0For the initial velocity of boost phase, take 3m/s；v_afFor boost phase End speed, takes 25.6m/s；

Total distance S of optimization of vehicle boost phase is obtained according to formula (16)_aFor:

$S_a={\∫}_{t_{a0}}^{t_{af}}vdt=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i{v}_{ai}$

According to formula (17), obtain total oil consumption J of vehicle boost phase_aFor:

$J_a={\∫}_{v_{a0}}^{v_{af}}{E}_{\mathrm{\Δ}}dv$

3) the energy saving optimizing model in decelerating phase is set up:

In the decelerating phase, according to equation of state (11) and formula (18), it is known that optimization of vehicle deceleration a_dFor:

$a_d=-(0.43v^2+439.04)\frac{1}{1920}$

According to formula (19), it is known that the optimization total time t in vehicle deceleration stage_dfFor:

$t_{df}=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{dj}}{{\mathrm{\Δa}}_{dj}}$

Wherein, v_d0For the initial velocity in decelerating phase, take 25.6m/s；v_dfFor the end speed in decelerating phase, take 3m/s.

According to formula (20), it is known that total distance S of the optimization in vehicle deceleration stage_dFor

$S_d={\∫}_{t_{d0}}^{t_{df}}vdt=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j{v}_{dj}$

Wherein, D is integration step, takes 0.1；v_d0For the initial velocity in decelerating phase, take 25.6m/s；v_dfFor the decelerating phase End speed, take 3m/s；t_d0Initial time for the decelerating phase；

According to formula (21), obtain total oil consumption J in vehicle deceleration stage_dFor:

$J_d={\∫}_{t_{d0}}^{t_{df}}{q}_s\left(P_e\right)dt=a_0(t_{df}-t_{d0})/3.6$

4) the energy saving optimizing model of constant velocity stage is set up:

According to equation of state (11) and formula (22), it is known that constant velocity stage's vehicle optimal engine powerFor:

$P_{ec}^{*}=(C_A{v}_c^2+Mgf)\frac{v_c}{{\mathrm{\η}}_T}=0.4778v_c^3+487.8222v_c$

According to formula (23), it is known that total distance S of the optimization that vehicle at the uniform velocity travels_cFor:

S_c=S_T-S_a-S_d

According to formula (24), it is known that the optimization total time t that vehicle at the uniform velocity travels_cFor:

$t_c=\frac{S_c}{v_c}$

According to the method for the invention, obtain the different traveling total time in vehicle three stage travelling the present embodiment under total distance condition T and travel total oil consumption Q, as shown in table 2.

The result of the different operating range of table 2

As shown in Figure 4, the energy conservation optimizing method of the present invention can effectively be given vehicle acceleration of vehicle between two crossings-at the uniform velocity- Deceleration syllogic fuel-economizing driving model.Fig. 4 shows that under different total distance condition, the speed of acceleration-at the uniform velocity-moderating process is at any time Between change curve, as can be seen from Figure 4, for the different total distances of traveling, vehicle is the most identical at the acceleration of boost phase, Deceleration in the decelerating phase is the most identical, and total distance is the longest, then the operating range of constant velocity stage is the longest.Therefore, if vehicle Travel total distance to change, can travel according to following fixing rule: vehicle add fast mode and deceleration mode all takes Fig. 4 In fixed model, only need to regulate the distance that vehicle at the uniform velocity travels.This rule also can be as vehicle by continuous green light The economy driving model of crossing.

Fig. 5 illustrates the power-economizing method of the syllogic driving model using the present invention and the optimal speed curve pair using pseudo-spectrometry Ratio, it can be seen that under identical operating range, the curve of two methods essentially coincides, but the latter is from the mistake of constant velocity stage to decelerating phase Cross and more relax.

Table 3 analytic method and pseudo-spectrometry Comparative result

Table 3 gives the syllogic analytic method using the present invention and the oil consumption contrast using pseudo-spectrometry to obtain, it is known that both phases To error less than ± 0.15%.And compared to pseudo-spectrometry, acceleration-at the uniform velocity-deceleration syllogic energy saving optimizing side that the present invention proposes Method solving speed is fast, can meet the requirement of application in real time.

Claims (3)

1. accelerate between a crossing at the uniform velocity to slow down the power-economizing method of syllogic driving model, it is characterised in that: the method Including determining the speed of constant velocity stage, the end speed of boost phase and the initial velocity in decelerating phase, according to the three kinds of speed determined Set up the energy saving optimizing model in boost phase, constant velocity stage, decelerating phase respectively；Wherein, boost phase is by building gear The economy Optimal Control Model of continuous vehicle, proposes general method of value solving in conjunction with the calculus of variations；Constant velocity stage controls Acceleration is 0m/s, and cruises with the end speed of boost phase；It is 0kw that decelerating phase controls engine output, and Using the speed of constant velocity stage as the initial velocity in this stage, obtain the deceleration optimized in conjunction with longitudinal vehicle dynamic model；Combine Closing the these three stage, be optimized this process on the whole and analyze, the acceleration-at the uniform velocity-deceleration syllogic forming quantification is driven Sail energy saver mode.

Accelerate between two crossings the most as claimed in claim 1 at the uniform velocity to slow down the power-economizing method of syllogic driving model, its feature It is: the method specifically includes following steps:

1) speed corresponding to three stages is determined:

Determine the speed v that vehicle at the uniform velocity travels_cAs shown in formula (1), the economy speed v of vehicle_ecoWith road speed limit v_maxAll If it is known that v_eco≤v_max, the speed v that the most at the uniform velocity travels_cFor v_ecoOtherwise, then it is v_max；

$v_c=\left\{\begin{array}{cc}{v}_{eco},& v_{eco}\≤v_{\max }\\ v_{max},& v_{eco}>v_{\max }\end{array}\right.---\left(1\right)$

Wherein, described v_ecoFor the speed that vehicle is corresponding under at the uniform velocity travelling fuel consumption per hundred kilometers lowest term；

Therefore, end speed v of vehicle boost phase is obtained_afAnd the initial velocity v in decelerating phase_d0As shown in formula (2):

v_c=v_af=v_d0 (2)

2) the energy saving optimizing model of boost phase is set up:

The object function of vehicle boost phase of the present invention is made up of with acceleration distance correction term the total oil consumption of electromotor, wherein, starts Machine total oil consumption J_LAs shown in formula (3):

$J_L={\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(3\right)$

Wherein, t_fFor acceleration time, P_eFor engine power, Q_s(P_e) represent electromotor total instantaneous fuel injection rate, the present invention adopts Instantaneous fuel injection rate is estimated with engine consumption MAP；

Due to CVT type variator can continuous transformation speed ratio, motor instant fuel injection rate q_sIt is reduced to the function of engine power, As shown in formula (4):

$q_s\left(P_e\right)=a_0+a_1{P}_e+a_2{P}_e^2,P_e\≥0---\left(4\right)$

Wherein, a_i(i=0,1,2) is fitting coefficient, a_iSpan be 10^-2To 10；

Introduce electromotor dynamic corrections item k_e(dP_e/dt)², obtain the dynamic oil consumption Q of electromotor_s:

$Q_s=q_s+k_e{\left(\frac{{\mathrm{dP}}_e}{dt}\right)}^2---\left(5\right)$

Wherein, k_eFor electromotor dynamic oil consumption correction factor, k_eThe order of magnitude be 10^-4；

Described acceleration distance correction term J_MFor:

J_M=-k_sS_f (6)

Wherein, k_sFor acceleration distance correction factor, it is set as k_s=-Q_s(v_eco)/v_eco, Q_s(v_eco) represent that vehicle is at warp Ji property speed v_ecoThe total instantaneous fuel injection rate of lower electromotor, S_fFor acceleration distance；

Therefore equivalent the criterion of the fuel consumption is:

$J=J_M+J_L=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(7\right)$

In accelerator, equality constraint includes formula (8) and (9):

Electromotor economy curve obedience formula (8):

T_eco(w_eco)=k_eco(w_eco-b)^γ (8)

Wherein, T_eco(w_eco) torque of electromotor that is expressed as on the economy curve of BSFC, w_ecoEconomy for BSFC Engine speed on curve, k_eco, γ and b be fitting coefficient；

Meanwhile, engine speed is coordinated to reach optimum by formula (9):

$i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}---\left(9\right)$

Wherein, i_gFor transmission gear ratio, i₀For speed ratio of main reducer, r_wFor vehicle tyre radius, c is coefficient；

Inequality constraints condition includes: engine power P_e, transmission gear ratio i_g, road maximum speed limit v_maxConstraint:

$\begin{array}{c}{P}_{e\min }\≤P_e\≤P_{e\max }\\ i_{g\min }\≤i_g\≤i_{g\max }\\ 0\≤v\≤v_{\max }\end{array}---\left(10\right)$

Wherein, P_emin、P_emaxIt is respectively minima and maximum, the i of engine power_gmin、i_gmaxFor transmission gear ratio Minima and maximum；

Vehicle is carried out following simplification: a) ignore electromotor and the high-order dynamic characteristic of CVT type variator rotary part, and The gap of drive system and torsional deflection；B) assume in clutch dynamic process without sliding wear phenomenon；C) assume that drive system is not Same gear ratio, different transmission power underdrive efficiency are consistent；According to kinetics equation and above-mentioned reduced condition, obtain accelerate, At the uniform velocity and the state equation of energy saving optimizing model that is all suitable for of decelerating phase is:

$\begin{array}{c}\stackrel{\·}{s}=v\\ \stackrel{\·}{v}=(\frac{{\mathrm{\η}}_T{P}_e}{v}-C_A{v}^2-Mfg)\·\frac{1}{\mathrm{\δ}M}\end{array}---\left(11\right)$

Wherein, s is vehicle operating range, and v is speed, η_TFor power train transmission aggregate efficiency, C_A=0.5C_Dρ_aA_v, C_DFor Air resistance coefficient, ρ_aFor atmospheric density, A_vFor vehicle front face area, M is complete vehicle quality, and g is gravity coefficient, and f is friction system Number, δ is gyrating mass coefficient；

To sum up, the boost phase energy saving optimizing model that the present invention builds is as follows:

$\min J=-k_s{S}_f+{\∫}_0^{t_f}{Q}_s\left(P_e\right)dt---\left(12\right)$

Submit to

$\left(\begin{array}{c}\stackrel{\·}{s}\\ \stackrel{\·}{v}\end{array}\right)=\left(\begin{array}{cc}0& 1\\ 0& -\frac{C_A{v}^2+Mfg}{\mathrm{\δ}Mv}\end{array}\right)\left(\begin{array}{c}s\\ v\end{array}\right)+\left(\begin{array}{c}0\\ \frac{{\mathrm{\η}}_T}{\mathrm{\δ}Mv}\end{array}\right)P_e$

T_eco(w_eco)=k_eco(w_eco-b)^γ

$i_g=\frac{{\mathrm{\πr}}_w}{{\mathrm{cvi}}_0}\·w_{eco}$

P_emin≤P_e≤P_emax

i_gmin≤i_g≤i_gmax

0≤v≤v_max

X (0)=(0 0)^T

x(t_f)=(S_f 0)^T

Wherein, x (0)=(0 0)^TRepresent that initial distance and speed are 0, x (0)=(0 0)^TRepresent terminal distance and speed Degree is respectively S_fWith 0；

At boost phase, solve formula (12) and obtain, the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔFor:

$\begin{array}{c}{E}_{\mathrm{\Δ}}=\frac{-k_s\left(v_{eco}\right)v+q_s\left(P_e\right)}{g\left(P_e,v\right)}\\ =\frac{1}{3.6a}\[a_0+{10}^{-3}{a}_1\left(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d\left(v\right)\right)+{10}^{-6}{a}_2{\left(a\mathrm{\δ}M\frac{v}{{\mathrm{\η}}_T}+P_d\left(v\right)\right)}^2...\\ +P_d{\left(v\right)}^2\]-\frac{1}{a}{q}_s\left(v_f,0\right)\frac{v}{v_f}\end{array}---\left(13\right)$

Wherein, a is the acceleration of boost phase；P_d(v)=(C_Av²+Mgf)v/η_T, P_dV () represents when speed is v, Vehicle provide to overcome the power needed for air drag and frictional resistance；q_s(v_f, 0) and=a₀+10^-3a₁P_e(v_f,0)+ 10^-6a₂P_e ²(v_f, 0), represent that acceleration is motor instant fuel injection rate when 0； P_e(v_f, 0) and expression speed is v_fAnd acceleration is when being 0, vehicle provide to overcome the power needed for air drag and frictional resistance；

Therefore work as the equivalent oil consumption E that unit speed changes delta v is corresponding_ΔWhen taking minima, obtain boost phase at various speeds excellent Change acceleration a_aFor:

The optimization total time t of boost phase_afFor

$t_{af}=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{ai}}{{\mathrm{\Δa}}_{ai}}---\left(15\right)$

Wherein, D is integration step；v_a0Initial velocity for boost phase；v_afEnd speed for boost phase；Δv_i、Δa_aiWith (v_af-v_a0)/D representation unit speed interval respectively, unit acceleration interval and unit interval；

Therefore total distance S of the optimization of boost phase_aFor:

$S_a={\∫}_{t_{a0}}^{t_{af}}vdt=\underset{i=1}{\overset{i=(v_{af}-v_{a0})/D}{\Σ}}{t}_i{v}_{ai}---\left(16\right)$

Wherein, t_a0Initial time for boost phase；

Total oil consumption of boost phase is:

$J_a={\∫}_{v_{a0}}^{v_{af}}{E}_{\mathrm{\Δ}}dv---\left(17\right)$

3) the energy saving optimizing model in decelerating phase is set up:

In the decelerating phase, make vehicle sliding to terminal, control engine power P_ed≡ 0, vehicle is with at the uniform velocity travel speed v_cMake Initial velocity v for the decelerating phase_d0, according to equation of state (11), obtaining optimization of vehicle deceleration is:

$a_d=-(C_A{v}^2+Mgf)\frac{1}{\mathrm{\δ}M}---\left(18\right)$

The optimization total time t in decelerating phase_dfFor:

$t_{df}=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}\frac{{\mathrm{\Δv}}_{dj}}{{\mathrm{\Δa}}_{dj}}---\left(19\right)$

Wherein, v_d0Initial velocity for the decelerating phase；v_dfEnd speed for the decelerating phase；

Therefore total distance S of the optimization in decelerating phase_dFor:

$S_d={\∫}_{t_{d0}}^{t_{df}}vdt=\underset{j=1}{\overset{j=(v_{d0}-v_{df})/D}{\Σ}}{t}_j{v}_{dj}---\left(20\right)$

Wherein, t_d0Initial time for the decelerating phase；

Therefore, total oil consumption in decelerating phase is

$J_d={\∫}_{t_{d0}}^{t_{df}}{q}_s\left(P_e\right)dt=a_0(t_{df}-t_{d0})/3.6---\left(21\right)$

4) the energy saving optimizing model of constant velocity stage is set up:

At constant velocity stage, vehicle acceleration a_cFor 0m/s², vehicle is with end speed v of boost phase_afAs constant velocity stage's Travel speed v_c；According to equation of state (11), obtain vehicle optimal engine powerFor:

$P_{ec}^{*}=(C_A{v}_c^2+Mgf)\frac{v_c}{{\mathrm{\η}}_T}---\left(22\right)$

Therefore constant velocity stage, total distance S of the optimization at the uniform velocity travelled_cFor:

S_c=S_T-S_a-S_d (23)

Wherein, S_TFor accelerating, at the uniform velocity with triphasic total distance of slowing down, and be known quantity；

The optimization total time t of constant velocity stage_cFor:

$t_c=\frac{S_c}{v_c}---\left(24\right)$

Finally give and accelerate three stages corresponding optimization travel speed, acceleration and the power that at the uniform velocity slows down, thus constitute optimization Energy-conservation syllogic mode of operation.

Accelerate between two crossings the most as claimed in claim 2 at the uniform velocity to slow down the power-economizing method of syllogic driving model, and it is special Levying and be, the solution procedure of described formula (12) specifically includes following steps:

Assume the original state variable (s of vehicle₀,v₀) it is fixed value；To acceleration time t_fWith acceleration distance S_fIt is not provided with constraint, It is free variable；Terminal velocity v_fFor fixed value；It is joint based on speed by this time-based energy saving optimizing model conversation Energy Optimized model:

$\min J=-k_s\left(v_f\right)S_f+{\∫}_0^{v_f}\frac{Q_s\left(P_e\right)}{g(P_e,v)}dv---(12-1)$

Submit to

$\begin{array}{c}\frac{ds}{dv}=\frac{v}{g\left(P_e,v\right)}\\ g(P_e,v)=\stackrel{\·}{v}=(\frac{{\mathrm{\η}}_T{P}_e}{v}-C_A{v}^2-Mfg)\·\frac{1}{\mathrm{\δ}M}\end{array}---(12-2)$

The essential condition existed according to extreme value, the Hamiltonian function of formula (12 1) is:

$H=\frac{Q_s\left(P_e\right)}{g(P_e,v)}+\mathrm{\λ}\left(t\right)\frac{v}{g(P_e,v)}---(12-3)$

Wherein, λ (t) is association's state vector, and the governing equation obtaining formula (12 3) is:

$\frac{\∂H}{\∂P_e}=\frac{\∂}{\∂P_e}\left(\frac{q_s\left(P_e\right)}{g(P_e,v)}\right)+\mathrm{\λ}\frac{\∂}{\∂P_e}\left(\frac{v}{g(P_e,v)}\right)=0---(12-4)$

According to adjoint equation, learn:

$\stackrel{\·}{\mathrm{\λ}}=-\frac{\∂H}{\∂s}=0---(12-5)$

By transversality condition, must obtain:

$\begin{array}{c}\mathrm{\λ}\left(t_f\right)=-k_s\left(v_f\right)\\ v\left(t_f\right)=v_f\end{array}---(12-6)$

Therefore, association state vector λ (t) ≡-k_s(v_f), convolution (12 4), learn the optimal engine power of vehicle boost phaseFor speed v and terminal velocity v_fFunction:

$P_e^{*}\left(v\right)=h(v,k_s(v_f\left)\right)---(12-7)$

Wherein, h is a unJeiermined function, refers to speed and end speed and function；Illustrate for different acceleration tasks, Under a certain speed determined, optimal power depends on terminal velocity v_f；

For different acceleration tasks, by k_s(v_f) it is set to a fixed value, thus λ is a constant,It is only the letter of speed v Number:

$P_e^{*}\left(v\right)=\tilde{h}\left(v\right)---(12-8)$

Wherein,Refer to the function of speed v, be a unJeiermined function；

Result shows that optimum accelerating power is only determined by present speed, arranges k_s(v_f) it is a constant k_s(v_eco), by solving formula (12 9), obtain the suboptimal solution of optimal power:

$\frac{\∂H}{\∂P_e}=\frac{1}{g^2}(\frac{\∂Q_s}{\∂P_e}g-q_s\frac{\∂g}{\∂P_e}-\mathrm{\λ}v\frac{\∂g}{\∂P_e})=0---(12-9)$

Meanwhile, the minimum equivalent oil consumption that vehicle accelerates to needed for speed v+Δ v from speed v is:

$\underset{P_e}{min}\mathrm{\Δ}J=\mathrm{\Δ}v\frac{-k_s\left(v_{eco}\right)v+Q_s\left(P_e\right)}{a}---(12-10)$

Therefore, the minimum equivalent oil consumption E that unit speed changes delta v is corresponding_ΔFor:

$\underset{P_e}{min}{E}_{\mathrm{\Δ}}=\underset{\mathrm{\Δ}v\→0}{\lim }\frac{\mathrm{\Δ}J}{\mathrm{\Δ}v}=\frac{-k_s\left(v_{eco}\right)v+q_s\left(P_e\right)}{g(P_e,v)}---(12-11)$

By (12 11) to power P_eSeek local derviation, can obtain

$\frac{\∂E_{\mathrm{\Δ}}}{\∂P_e}=\frac{\∂H}{\∂P_e}=\frac{\∂}{\∂P_e}\left(\frac{q_s\left(P_e\right)}{g(P_e,v)}\right)+\mathrm{\λ}\frac{\∂}{\∂P_e}\left(\frac{v}{g(P_e,v)}\right)---(12-12)$

Therefore can be converted into the formula of solving (12 11) by solving formula (12 1), solve formula by solving one-dimensional optimization formula (12 11) (12)。