CN110135632B - PHEV self-adaptive optimal energy management method based on path information - Google Patents

PHEV self-adaptive optimal energy management method based on path information Download PDF

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CN110135632B
CN110135632B CN201910352493.8A CN201910352493A CN110135632B CN 110135632 B CN110135632 B CN 110135632B CN 201910352493 A CN201910352493 A CN 201910352493A CN 110135632 B CN110135632 B CN 110135632B
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郭建华
王引航
刘康杰
刘翠
刘纬纶
聂荣真
王继新
初亮
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Abstract

The invention discloses a PHEV self-adaptive optimal energy management method based on path information, which comprises the steps of planning a traveling path through a vehicle-mounted navigation system and generating a predicted working condition of a front path; establishing a trip mileage prediction strategy to predict the trip mileage of the user every day; generating a reference SOC based on an SOC planning algorithm through the generated prediction data and the initial SOC; carrying out APMP optimization algorithm: taking the minimum oil consumption as a global optimization target, introducing a collaborative state value, and converting the global optimization problem into a plurality of instantaneous optimization problems with Hamilton operators; optimizing the initial value of the collaborative state by adopting a genetic algorithm; calculating a cooperative state initial value in the MAP graph by using an interpolation method, and correcting the cooperative state initial value in real time according to the working condition information and the reference SOC obtained by the vehicle navigation system; and power distribution is carried out by utilizing a PMP optimization algorithm, and the power is transmitted to each execution component controller through a CAN bus, so that the whole vehicle control of the PHEV is completed.

Description

基于路径信息的PHEV自适应最优能量管理方法Adaptive optimal energy management method for PHEV based on path information

技术领域technical field

本发明涉及一种插电式并联混合动力汽车的整车控制方法,尤其涉及一种基于路径信息的插电式并联混合动力汽车自适应最优能量管理方法,属于新能源汽车控制技术领域。The invention relates to a vehicle control method for a plug-in parallel hybrid electric vehicle, in particular to an adaptive optimal energy management method for a plug-in parallel hybrid electric vehicle based on path information, and belongs to the technical field of new energy vehicle control.

背景技术Background technique

随着能源危机、环境污染、全球变暖等问题的日益加重以及节能减排的迫切需求,新能源汽车的发展受到了越来越多的关注。插电式混合动力汽车(Plug-in HybridElectric Vehicle,PHEV)对比混合动力汽车(Hybrid Electric Vehicle,HEV)具有较大容量的蓄电池,并且可以从电网获取电能。PHEV兼具HEV和纯电动汽车(Battery ElectricVehicles,BEV)的优点,当电池电量充足时,PHEV处于电量消耗模式(Charge Depleting,CD),主要由电机驱动车辆,具有低油耗、低排放的优势;当电池电量较低时,PHEV处于电量维持模式(Charge Sustaining,CS),发动机作为主要动力源驱动车辆,与传统汽车和HEV具有相同的续驶里程。PHEV构型包括串联、并联及混联等多种形式。并联构型具有结构简单,加工制造容易,动力性和经济性好等优点,并且其构型不涉及专利保护,我国的PHEV多采用此类构型。但是,并联构型PHEV的发动机与车轮存在机械连接,其经济性受工况影响较大。With the increasing aggravation of energy crisis, environmental pollution, global warming and the urgent need for energy conservation and emission reduction, the development of new energy vehicles has received more and more attention. A plug-in hybrid electric vehicle (Plug-in Hybrid Electric Vehicle, PHEV) has a battery with a larger capacity than a hybrid electric vehicle (Hybrid Electric Vehicle, HEV), and can obtain electric energy from the grid. PHEV has the advantages of both HEV and battery electric vehicles (BEV). When the battery is fully charged, PHEV is in charge depleting (CD) mode and is mainly driven by a motor, which has the advantages of low fuel consumption and low emissions; When the battery power is low, the PHEV is in charge sustaining mode (Charge Sustaining, CS), and the engine is used as the main power source to drive the vehicle, which has the same driving range as conventional cars and HEVs. PHEV configurations include various forms such as series, parallel and hybrid. The parallel configuration has the advantages of simple structure, easy processing and manufacturing, good power and economy, and its configuration does not involve patent protection. Most PHEVs in my country adopt this configuration. However, there is a mechanical connection between the engine and the wheels of the parallel configuration PHEV, and its economy is greatly affected by the working conditions.

插电式混合动力汽车能量管理策略是PHEV设计的关键问题,目前,实际运行的PHEV多采用基于规则的门限值控制策略(Rule-based control strategy,RB),该种策略计算量小,实时性好,易于车辆控制器编程实现。但是,RB策略的控制门限往往是固定的一组门限,工况适应性较差。PHEV经济性受电池荷电状态(State of Charge,SOC)、车速、行驶里程、路面坡度、温度等多种因素影响,尤其受电池SOC、车速和行驶里程影响较大。当RB策略的控制门限值固定时,则无法自动适应工况变化的影响。这可能造成电池电量提前“耗光”(SOC处于最小允许值),或者电池电量在行程结束时没用完全使用的情况。研究表明,这两种情况都会使并联PHEV油耗升高,经济性变差。此外,由于控制门限值是常数,在大多数工况下,瞬时和全局的油耗往往不是最优的,甚至在某些低速拥堵工况,并联PHEV能耗会超过传统内燃机汽车。因此,传统的门限值控制策略不仅无法适应工况的变化,在全局和瞬时无法达到油耗最优,这是造成并联PHEV能耗高,节油潜力无法发挥的重要原因之一。The energy management strategy of plug-in hybrid electric vehicles is a key issue in the design of PHEVs. At present, most PHEVs in actual operation adopt a rule-based threshold control strategy (Rule-based control strategy, RB), which has a small amount of calculation and real-time Good performance, easy to program the vehicle controller. However, the control threshold of the RB strategy is often a fixed set of thresholds, which is poorly adaptable to working conditions. PHEV economy is affected by various factors such as battery state of charge (State of Charge, SOC), vehicle speed, mileage, road slope, temperature, etc., especially by battery SOC, vehicle speed and mileage. When the control threshold of the RB strategy is fixed, it cannot automatically adapt to the influence of changes in working conditions. This can result in premature battery "depletion" (SOC at the minimum allowable value), or a condition where the battery is not fully used at the end of the trip. Studies have shown that both of these situations will increase the fuel consumption of parallel PHEVs and worsen the economy. In addition, since the control threshold is constant, the instantaneous and global fuel consumption is often not optimal under most operating conditions, and even in some low-speed congested operating conditions, the energy consumption of parallel PHEVs will exceed that of traditional internal combustion engine vehicles. Therefore, the traditional threshold control strategy not only cannot adapt to changes in working conditions, but also fails to achieve optimal fuel consumption globally and instantaneously. This is one of the important reasons for the high energy consumption of parallel PHEVs and the inability to realize fuel-saving potential.

目前,许多学者提出了基于最优控制理论的PHEV能耗策略,如全局优化的动态规划算法(Dynamic Programming,DP),瞬时优化的等效油耗最小算法(EquivalentConsumption Minimum Strategy,ECMS)和庞特里亚金最小值算法(Pontryagin’s MinimumPrincipal,PMP)等。在工况已知的前提下,全局优化算法DP通过逆向求解,能够得到该工况下的理论最优解,此时,能耗是最优的。但是,由于是逆向求解,DP算法的前提是工况已知,并且计算量巨大,这显然无法直接应用到PHEV实际车辆的能量管理中。ECMS算法属于瞬时最优控制算法,能够实现瞬时最优,但是在工况变化时仍然不是全局最优的,并且,ECMS算法主要应用于混合动力汽车,其约束条件要求SOC要维持平衡。因此,很难直接应用到PHEV的控制中。PMP算法也属于瞬时最优控制,与ECMS一样,在工况变化时也不是全局最优的。但是,通过引入协同状态变量,PMP算法能够动态分配发动机和电机功率,实现对SOC消耗率的在线控制。因此,PMP可以不要求维持SOC的平衡,这非常适合PHEV的能量管理。At present, many scholars have proposed PHEV energy consumption strategies based on optimal control theory, such as the global optimization dynamic programming algorithm (Dynamic Programming, DP), the instantaneous optimization equivalent fuel consumption minimum algorithm (EquivalentConsumption Minimum Strategy, ECMS) and Pontry Pontryagin's MinimumPrincipal (PMP) etc. On the premise that the working conditions are known, the global optimization algorithm DP can obtain the theoretical optimal solution under the working conditions through inverse solution, at this time, the energy consumption is optimal. However, due to the reverse solution, the premise of the DP algorithm is that the working conditions are known, and the calculation amount is huge, which obviously cannot be directly applied to the energy management of the actual PHEV vehicle. The ECMS algorithm is an instantaneous optimal control algorithm, which can achieve instantaneous optimality, but it is still not globally optimal when the operating conditions change. Moreover, the ECMS algorithm is mainly used in hybrid electric vehicles, and its constraints require that the SOC should maintain balance. Therefore, it is difficult to directly apply to the control of PHEV. The PMP algorithm also belongs to the instantaneous optimal control. Like ECMS, it is not globally optimal when the working conditions change. However, by introducing cooperative state variables, the PMP algorithm can dynamically allocate engine and motor power, and realize online control of SOC consumption rate. Therefore, PMP may not be required to maintain the balance of SOC, which is very suitable for the energy management of PHEV.

从以上分析可以,PHEV能量管理中要解决的关键问题是:在任何工况下,在相同的电量消耗下,实现PHEV能耗的全局和瞬时最优控制,使能耗最小。目前,车载导航系统(包括智能交通系统、电子地图、GPS等),不仅可以提供导航、路况查询及预测等服务,还可以提供车辆的工况数据。PHEV控制系统能够从车载导航系统中获取行驶里程、拥堵状况(车速分布)以及历史出行里程等信息。From the above analysis, the key problem to be solved in PHEV energy management is to realize the global and instantaneous optimal control of PHEV energy consumption under any working conditions and under the same power consumption, so as to minimize energy consumption. At present, vehicle navigation systems (including intelligent transportation systems, electronic maps, GPS, etc.) can not only provide services such as navigation, road condition query and prediction, but also provide vehicle operating condition data. The PHEV control system can obtain information such as driving mileage, congestion status (vehicle speed distribution) and historical travel mileage from the car navigation system.

发明内容Contents of the invention

本发明提供一种基于路径信息的插电式并联混合动力汽车自适应最优能量管理方法,该方法基于瞬时最优的PMP算法,通过车载导航系统获取未来路径信息,使得PMP控制策略的协同矩阵状态值能够依据未来路径信息,行驶工况以及电池SOC进行在线调整,实现并联PHEV能量管理的瞬时和全局最优,全面提高并联PHEV在不同类型工况下的能耗,充分发挥并联PHEV的节能潜力。The present invention provides an adaptive optimal energy management method for plug-in parallel hybrid electric vehicles based on path information. The method is based on the instantaneous optimal PMP algorithm, and obtains future path information through the vehicle navigation system, so that the synergy matrix of the PMP control strategy The state value can be adjusted online based on future path information, driving conditions and battery SOC, to realize the instantaneous and global optimization of energy management of parallel PHEVs, comprehensively improve the energy consumption of parallel PHEVs under different types of working conditions, and give full play to the energy saving of parallel PHEVs potential.

本发明的目的是通过以下技术方案实现的:The purpose of the present invention is achieved through the following technical solutions:

一种基于路径信息的PHEV自适应最优能量管理方法,包括以下步骤:A PHEV adaptive optimal energy management method based on path information, comprising the following steps:

步骤一、行驶工况与里程预测:Step 1. Driving conditions and mileage prediction:

1.1)通过车载导航系统获取车辆位置信息并在电子地图中规划出行驶路径,同时获取该规划行驶路径的实时路况信息,生成前方路径的预测工况;1.1) Obtain the vehicle location information through the vehicle navigation system and plan the driving route in the electronic map, and at the same time obtain the real-time road condition information of the planned driving route, and generate the predicted working conditions of the ahead route;

1.2)车载导航系统获取车辆的历史行驶数据,建立出行里程预测策略对每日用户出行里程进行预测,并绘制车辆累积平均行驶里程曲线;1.2) The car navigation system obtains the historical driving data of the vehicle, establishes a travel mileage prediction strategy to predict the daily travel mileage of users, and draws the cumulative average mileage curve of the vehicle;

步骤二、基于SOC规划算法生成参考SOC:Step 2. Generate a reference SOC based on the SOC planning algorithm:

通过步骤一生成的预测数据,包括预测工况、全天行驶总里程、本次出行里程以及初始SOC,基于SOC规划算法生成参考SOC;Through the forecast data generated in step 1, including the forecast working conditions, the total mileage of the whole day, the mileage of this trip and the initial SOC, the reference SOC is generated based on the SOC planning algorithm;

步骤三、APMP优化算法:Step 3, APMP optimization algorithm:

3.1)以油耗最小为全局优化目标,引入协同状态值,将全局优化问题转化为若干个带有汉密尔顿算子的瞬时优化问题;3.1) With the minimum fuel consumption as the global optimization goal, the collaborative state value is introduced, and the global optimization problem is transformed into several instantaneous optimization problems with Hamiltonian operators;

3.2)协同状态初值优化:采用遗传算法优化协同状态初值,建立协同状态初值随SOC初值和出行里程变化的MAP图;3.2) Optimization of the initial value of the collaborative state: the initial value of the collaborative state is optimized using a genetic algorithm, and a MAP diagram of the initial value of the collaborative state changing with the initial value of the SOC and the travel mileage is established;

3.3)协同状态值在线修正:在实际工况下,利用插值法在MAP图中求出协同状态初值,根据车载导航系统获得的工况信息及参考SOC对协同状态初值进行实时的修正;3.3) On-line correction of the cooperative state value: Under actual working conditions, the initial value of the cooperative state is obtained in the MAP diagram by interpolation method, and the initial value of the cooperative state is corrected in real time according to the working condition information obtained by the vehicle navigation system and the reference SOC;

3.4)对汉密尔顿函数求解,利用PMP优化算法进行动力分配,通过CAN总线传递给各执行部件控制器,完成PHEV的整车控制。3.4) Solve the Hamilton function, use the PMP optimization algorithm to distribute the power, and transmit it to the controllers of each executive component through the CAN bus to complete the vehicle control of the PHEV.

所述的一种基于路径的插电式混合动力汽车自适应最优能量管理方法,步骤1.2)具体过程为:PHEV能量管理系统对用户每日的车速-时间里程数据进行记录,然后对车速进行积分得到行驶里程,按小时统计当天行驶里程,并写入出行里程特征数据库,工作日和节假日的行驶里程需分别统计;分别统计工作日和节假日每时段的平均行驶里程,绘制工作日和节假日各时段累积平均行驶里程曲线。Described a kind of path-based plug-in hybrid electric vehicle self-adaptive optimal energy management method, step 1.2) specific process is: PHEV energy management system records the user's daily vehicle speed-time mileage data, and then carries out vehicle speed The mileage is obtained by the points, and the mileage of the day is counted by hour, and written into the travel mileage characteristic database. The mileage of weekdays and holidays needs to be counted separately; Time period cumulative average mileage curve.

所述的一种基于路径信息的PHEV自适应最优能量管理方法,步骤二的具体过程为:The specific process of step 2 of the PHEV adaptive optimal energy management method based on path information is as follows:

首先生成参考SOC:以行驶里程为横坐标,SOC为纵坐标,连接(0,SOCini)和(St,SOCmin)两点,得到SOCrefFirst generate the reference SOC: take the mileage as the abscissa and the SOC as the ordinate, connect the two points (0,SOC ini ) and (S t ,SOC min ) to get the SOC ref ;

其中,SOCref为参考SOC;SOCini为行程初始SOC;SOCmin为CD模式最小SOC;St为全天总出行里程,St根据当前出行时间由所述步骤一得到的车辆累积平均行驶里程曲线中插值得到;Among them, SOC ref is the reference SOC; SOC ini is the initial SOC of the trip; SOC min is the minimum SOC of the CD mode; S t is the total travel mileage of the whole day, and S t is the cumulative average mileage of the vehicle obtained from the step 1 according to the current travel time The interpolation in the curve is obtained;

在每次出行前系统都会进行SOC规划,对于单次出行来讲,本次出行结束时的SOCend计算公式如下:The system will carry out SOC planning before each trip. For a single trip, the calculation formula of SOC end at the end of this trip is as follows:

Figure BDA0002044389170000031
Figure BDA0002044389170000031

其中,Si为本次出行里程。Among them, S i is the mileage of this trip.

所述的一种基于路径的插电式混合动力汽车自适应最优能量管理方法,步骤3.1)以油耗最小为全局优化目标,引入协同状态值,将全局优化问题转化为若干个带有汉密尔顿算子的瞬时优化问题的具体过程为:Described a kind of path-based method for self-adaptive optimal energy management of plug-in hybrid electric vehicles, step 3.1) takes the minimum fuel consumption as the global optimization goal, introduces the cooperative state value, and converts the global optimization problem into several The specific process of sub-instantaneous optimization problem is:

以油耗最小为全局优化问题,其目标函数为:Taking the minimum fuel consumption as the global optimization problem, the objective function is:

Figure BDA0002044389170000032
Figure BDA0002044389170000032

其中:x(t)是汽车在t时刻的SOC,即被控系统的状态变量;u(t)为t时刻的转矩分配比,即系统控制变量,它是电机转矩Tm与总需求转矩Tdmd之比;

Figure BDA0002044389170000033
代表汽车在t时刻的瞬时燃油消耗速率,单位:kg/s;Among them: x(t) is the SOC of the vehicle at time t, that is, the state variable of the controlled system; u(t) is the torque distribution ratio at time t, that is, the system control variable, which is the motor torque T m and the total demand ratio of torque T dmd ;
Figure BDA0002044389170000033
Represents the instantaneous fuel consumption rate of the car at time t, unit: kg/s;

该优化问题的约束包含:The constraints of this optimization problem include:

Figure BDA0002044389170000041
Figure BDA0002044389170000041

其中,f(x(t),u(t),t)是汽车在t时刻状态变量x(t)的变化率,单位:1/s;Among them, f(x(t), u(t), t) is the rate of change of the state variable x(t) of the car at time t, unit: 1/s;

其中,第一个式子表示该系统的状态转移方程,第二个式子表示该优化问题的终值约束条件,即当该过程结束时,车辆的SOC不能低于xminAmong them, the first formula represents the state transition equation of the system, and the second formula represents the final value constraint condition of the optimization problem, that is, when the process ends, the SOC of the vehicle cannot be lower than x min ;

利用庞特里亚金极值原理通过引入协同状态量将式(2)全局优化问题转换成若干个关于汉密尔顿函数瞬时优化问题:PMP优化算法定义汉密尔顿函数H(x(t),u(t),λ(t),t)作为瞬时优化问题的优化目标,如下式所示:Using Pontryagin's extreme value principle to convert the global optimization problem of formula (2) into several instantaneous optimization problems about the Hamiltonian function by introducing cooperative state quantities: PMP optimization algorithm defines the Hamiltonian function H(x(t),u(t) ,λ(t),t) as the optimization objective of the instantaneous optimization problem, as shown in the following formula:

Figure BDA0002044389170000045
Figure BDA0002044389170000045

其中,λ(t)为协同状态量;汉密尔顿函数中第一项为发动机的瞬时油耗,根据发动机转速和转矩在发动机万有特性MAP图中查得;第二项为协同状态值乘以SOC瞬时变化,协同状态量为PMP优化算法引入的新状态量,与行驶工况有相关性,在不同的驾驶事件中,协同状态量的初始值不同;求解每一时刻的汉密尔顿函数的最小值,得出的最优控制变量序列即为优化结果,如下式所示:Among them, λ(t) is the cooperative state quantity; the first item in the Hamiltonian function is the instantaneous fuel consumption of the engine, which is found in the engine universal characteristic MAP diagram according to the engine speed and torque; the second item is the multiplication of the cooperative state value by the SOC Instantaneous change, the cooperative state quantity is a new state quantity introduced by the PMP optimization algorithm, which is related to the driving conditions. In different driving events, the initial value of the cooperative state quantity is different; the minimum value of the Hamilton function at each moment is solved, The obtained optimal control variable sequence is the optimization result, as shown in the following formula:

Figure BDA0002044389170000042
Figure BDA0002044389170000042

其协同状态转移方程为:Its cooperative state transition equation is:

Figure BDA0002044389170000043
Figure BDA0002044389170000043

所述的一种基于路径信息的PHEV自适应最优能量管理方法,步骤3.2)协同状态初值优化包括以下过程:A kind of PHEV self-adaptive optimal energy management method based on path information, step 3.2) collaborative state initial value optimization comprises the following process:

采用遗传算法来求解协同状态初值λ0The genetic algorithm is used to solve the initial value of the cooperative state λ 0 ,

遗传算法以油耗最小为优化目标,以协同状态初值λ0为个体,个体的适应度函数为:The genetic algorithm takes the minimum fuel consumption as the optimization goal, and takes the initial value of the collaborative state λ 0 as the individual, and the fitness function of the individual is:

Figure BDA0002044389170000044
Figure BDA0002044389170000044

适应度函数最小值对应的协同状态值即为优化结果,并绘制协同状态值MAP图;在行程开始前,系统通过当前SOC初始值和未来行程的总里程,使用协同状态值MAP图插值确定系统状态初始值λ0The synergy state value corresponding to the minimum value of the fitness function is the optimization result, and a synergy state value MAP diagram is drawn; before the start of the trip, the system uses the synergy state value MAP diagram interpolation to determine the system State initial value λ 0 .

所述的一种基于路径信息的PHEV自适应最优能量管理方法,步骤3.3)协同状态值在线修正包括以下过程:Described a kind of PHEV self-adaptive optimal energy management method based on path information, step 3.3) cooperative state value online correction comprises the following process:

依据所述步骤二得到的参考SOC,并引入SOC惩罚因子和速度惩罚因子,使实际SOC能实时跟随参考SOC,修正后的协同状态值由下式计算:According to the reference SOC obtained in step 2, and introduce the SOC penalty factor and the speed penalty factor, so that the actual SOC can follow the reference SOC in real time, and the corrected cooperative state value is calculated by the following formula:

λ(t)=λ0+s(ΔSOC,t)+s(ΔV,t)λ(t)=λ 0 +s(ΔSOC,t)+s(ΔV,t)

λ(t)受SOC差值ΔSOC和车速差值ΔV两个因素影响,ΔSOC=SOC-SOCref,ΔV=V-Vmλ(t) is affected by two factors: SOC difference ΔSOC and vehicle speed difference ΔV, ΔSOC=SOC-SOC ref , ΔV=VV m ;

SOC差值的惩罚因子s(ΔSOC,t)在偏离参考SOC较小时取极小值,在偏离参考SOC过多时,取值应快速增大;The penalty factor s(ΔSOC,t) of the SOC difference takes a minimum value when the deviation from the reference SOC is small, and the value should increase rapidly when the deviation from the reference SOC is too large;

在ΔSOC>0时,惩罚因子s值取正;在ΔSOC<0时,惩罚因子s值取负;惩罚因子s(ΔSOC,t)表达式如下:When ΔSOC>0, the value of penalty factor s is positive; when ΔSOC<0, the value of penalty factor s is negative; the expression of penalty factor s(ΔSOC,t) is as follows:

Figure BDA0002044389170000051
Figure BDA0002044389170000051

车速差值的惩罚因子s(ΔV,t)在偏离平均车速较小时取极小值,在偏离平均车速过多时,取值应快速增大;The penalty factor s(ΔV,t) of the vehicle speed difference takes a minimum value when the deviation from the average vehicle speed is small, and the value should increase rapidly when the deviation from the average vehicle speed is too large;

当ΔV>0时,惩罚因子s值取负;当ΔV<0时,惩罚因子s值取正;惩罚因子s(ΔV,t)表达式如下:When ΔV>0, the value of penalty factor s is negative; when ΔV<0, the value of penalty factor s is positive; the expression of penalty factor s(ΔV,t) is as follows:

Figure BDA0002044389170000052
Figure BDA0002044389170000052

所述的一种基于路径信息的PHEV自适应最优能量管理方法,步骤3.4)对汉密尔顿函数求解包括以下过程:Described a kind of PHEV self-adaptive optimal energy management method based on path information, step 3.4) comprises the following process to Hamilton function solution:

使用数值解法求解汉密尔顿函数:先计算动力学方程求取总需求转矩,再根据本次出行的出行里程和初始SOC用插值法确定协同状态初值,通过车辆状态确定SOC差值和车速差值,修正当前的协同状态值;建立汉密尔顿函数,将转矩分配比u(t)的可行域分为若干份;若u(t)>0,代表电机和发动机共同驱动车辆或电机单独驱动车辆;若u(t)<0,代表电机处于发电机状态;计算数值网格划分后所有的汉密尔顿函数值,求出相应汉密尔顿函数最小的转矩分配比即为所求。Use the numerical solution to solve the Hamiltonian function: first calculate the dynamic equation to obtain the total demand torque, then determine the initial value of the cooperative state by interpolation method according to the travel mileage of this trip and the initial SOC, and determine the SOC difference and vehicle speed difference based on the vehicle state , modify the current cooperative state value; establish a Hamiltonian function to divide the feasible region of the torque distribution ratio u(t) into several parts; if u(t)>0, it means that the motor and the engine drive the vehicle together or the motor drives the vehicle alone; If u(t)<0, it means that the motor is in the generator state; calculate all the Hamiltonian function values after numerical grid division, and find the minimum torque distribution ratio of the corresponding Hamiltonian function.

本发明具有以下有益效果:The present invention has the following beneficial effects:

1)本发明将车载导航系统引入到PHEV能量管理中,通过车载导航系统对路况特征进行预测并对车辆的历史出行信息进行统计,提出的SOC规划方法(参考SOC),解决了传统PMP算法无法适应工况变化,油耗不是全局最优的问题。1) The present invention introduces the vehicle navigation system into PHEV energy management, predicts the road condition characteristics through the vehicle navigation system and makes statistics on the historical travel information of the vehicle, and proposes a SOC planning method (refer to SOC), which solves the problem that the traditional PMP algorithm cannot To adapt to changes in working conditions, fuel consumption is not a global optimal issue.

2)提出一种基于SOC反馈的工况自适应PMP控制策略。为实现实车在线控制,利用离线MAP图求解协同状态初值。根据工况信息和参考SOC修正协同状态值,利用PMP优化算法合理分配使用电量,使PHEV油耗在任何工况下都能接近理论最优水平。2) A working condition adaptive PMP control strategy based on SOC feedback is proposed. In order to realize the online control of the real vehicle, the initial value of the cooperative state is solved by using the offline MAP graph. According to the working condition information and reference SOC to correct the cooperative state value, the PMP optimization algorithm is used to reasonably allocate the power consumption, so that the fuel consumption of the PHEV can be close to the theoretical optimal level under any working condition.

附图说明Description of drawings

本发明的具体实施方式将在下文通过结合应用示例进行详细阐述。Specific implementations of the present invention will be described in detail below in conjunction with application examples.

图1是并联PHEV传动及控制系统硬件结构图;Figure 1 is a hardware structure diagram of the parallel PHEV transmission and control system;

图2是基于路径信息的PHEV自适应最优控制策略架构;Figure 2 is a PHEV adaptive optimal control strategy architecture based on path information;

图3是百度智能交通系统路径规划及交通信息实例;Figure 3 is an example of Baidu intelligent transportation system route planning and traffic information;

图4是根据百度地图实时交通系统信息转换的平均车速图;Fig. 4 is the average vehicle speed figure converted according to the real-time traffic system information of Baidu map;

图5(a)是工作日累积平均行驶里程曲线;Figure 5(a) is the cumulative average mileage curve of working days;

图5(b)是节假日累积平均行驶里程曲线;Figure 5(b) is the cumulative average mileage curve during holidays;

图6是参考SOC算法原理图;Figure 6 is a schematic diagram of the reference SOC algorithm;

图7是WLTC工况测试循环;Figure 7 is the WLTC working condition test cycle;

图8是协同状态初值MAP图;Figure 8 is a MAP diagram of the initial value of the collaborative state;

图9是实际SOC与参考SOC下降曲线Figure 9 is the actual SOC and reference SOC drop curve

图10是SOC惩罚因子曲线;Figure 10 is the SOC penalty factor curve;

图11是平均车速惩罚因子曲线;Fig. 11 is average vehicle speed penalty factor curve;

图12是汉密尔顿函数的求解流程图。Fig. 12 is a flow chart of solving the Hamiltonian function.

具体实施方式Detailed ways

下面结合附图对发明做进一步说明。以下实例将有助于本领域的技术人员进一步理解本发明,但不以任何形式限制本发明。The invention will be further described below in conjunction with the accompanying drawings. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form.

本发明的应用对象是并联构型PHEV,图1是其动力系统和能量管理系统的硬件结构。本例中的PHEV采用同轴并联结构。其中,电机同轴安装在自动变速器的输入轴上,电池可由外接充电器充电。PHEV整车控制系统包括:油门踏板(含踏板开度传感器)、制动踏板(含踏板开度传感器)、整车控制器(HCU)、GPS定位模块、远程通信模块、发动机控制器(ECU)、电机控制器(MCU)、自动变速器控制器(TCU)、电池管理单元(BMU),各部件之间通过CAN总线交互信息。整车控制器(HCU)通过GPS模块获取车辆当前位置,并通过远程通信模块与智能交通系统(ITS)进行远程通信以获取路径信息。ITS系统包括交通状况信息服务、地理信息服务及导航服务等多个子系统,当ITS获取车辆位置信息和导航目的地后,通过导航系统对行驶路径进行规划,将该路径的工况信息,如路径总里程、各路段车速特征、路面坡度等通过远程信息模块传递给整车控制器(HCU)。同时,该对象车辆HCU中的存储器还能够存储一段时间该车辆用户的出行数据,如车速,行驶时间,车辆位置等信息。The application object of the present invention is a parallel configuration PHEV, and Fig. 1 is the hardware structure of its power system and energy management system. The PHEV in this example adopts a coaxial parallel structure. Wherein, the motor is coaxially installed on the input shaft of the automatic transmission, and the battery can be charged by an external charger. PHEV vehicle control system includes: accelerator pedal (including pedal opening sensor), brake pedal (including pedal opening sensor), vehicle controller (HCU), GPS positioning module, remote communication module, engine controller (ECU) , Motor Controller (MCU), Automatic Transmission Controller (TCU), Battery Management Unit (BMU), all components exchange information through the CAN bus. The vehicle controller (HCU) obtains the current location of the vehicle through the GPS module, and communicates remotely with the Intelligent Transportation System (ITS) through the remote communication module to obtain route information. The ITS system includes multiple subsystems such as traffic condition information service, geographic information service, and navigation service. The total mileage, the speed characteristics of each road section, and the slope of the road surface are transmitted to the vehicle controller (HCU) through the telematics module. At the same time, the memory in the HCU of the target vehicle can also store travel data of the vehicle user for a period of time, such as vehicle speed, driving time, vehicle location and other information.

本发明主要包括“工况与里程预测算法”,“参考SOC生成算法”以及“自适应PMP(APM)控制算法”三部分。“工况与里程预测算法”通过车载导航系统获取前方路径行驶里程、道路坡度、红绿灯信号以及车速分布等工况信息,生成前方路径的预测工况;通过车载导航系统获取历史工况数据,生成历史出行里程预测曲线。参考SOC生成算法通过预测工况以及预测出行里程,基于全局最优原理生成参考SOC(SOCref)。“APMP优化算法”以油耗最小为全局优化目标,引入协同状态值,将全局问题转化为若干个带有汉密尔顿算子的瞬时优化问题。采用离线优化的方法,建立了协同状态初值随SOC初值和出行里程变化的MAP图。在实际工况下,利用插值法在MAP图中求出协同状态初值,根据车载导航系统所获得的工况信息及参考SOC对协同状态初值进行实时的修正。利用PMP优化算法进行动力分配,使整车油耗接近理论最优水平。The invention mainly includes three parts: "working condition and mileage prediction algorithm", "reference SOC generation algorithm" and "adaptive PMP (APM) control algorithm". "Working condition and mileage prediction algorithm" obtains working condition information such as the mileage of the forward path, road slope, traffic light signal and vehicle speed distribution through the vehicle navigation system, and generates the predicted working condition of the forward path; obtains the historical working condition data through the vehicle navigation system, and generates Historical travel mileage prediction curve. The reference SOC generation algorithm generates the reference SOC (SOC ref ) based on the global optimal principle by predicting the operating conditions and predicting the travel mileage. The "APMP optimization algorithm" takes the minimum fuel consumption as the global optimization goal, introduces the cooperative state value, and transforms the global problem into several instantaneous optimization problems with Hamiltonian operators. Using the offline optimization method, the MAP diagram of the initial value of the cooperative state changing with the initial value of SOC and the travel mileage is established. Under actual working conditions, the initial value of the cooperative state is obtained in the MAP diagram by using the interpolation method, and the initial value of the cooperative state is corrected in real time according to the working condition information obtained by the vehicle navigation system and the reference SOC. The PMP optimization algorithm is used for power distribution, so that the fuel consumption of the vehicle is close to the theoretical optimal level.

实施例Example

图2是基于路径信息的PHEV自适应最优控制策略架构,结合图1,对本发明提出的能量管理方法具体实现过程介绍如下:Fig. 2 is a PHEV self-adaptive optimal control strategy architecture based on path information. In combination with Fig. 1, the specific implementation process of the energy management method proposed by the present invention is introduced as follows:

步骤1:车辆启动后,系统进行自检并初始化。若驾驶员在车载导航系统中输入出行的目的地,则使用本发明提出控制策略(方法)对PHEV能量进行管理。Step 1: After the vehicle starts, the system performs self-check and initialization. If the driver inputs the travel destination in the vehicle navigation system, the control strategy (method) proposed by the present invention is used to manage the PHEV energy.

步骤2:驾驶员在车载导航系统中输入出行目的地后,车载导航系统中的GPS会获取车辆位置信息并在电子地图中规划出行驶路径。同时在ITS系统中获取该规划路径的实时交通路况,通过电子地图测距功能进行顺畅、缓行、拥堵距离的测量,以计算出路况的拥堵比例。由测距功能和拥堵比例可分别得到自适应策略所需的本次出行里程和平均车速信息。图3为百度智能交通系统路径规划及实时交通信息实例。采用4种颜色代表该路段的交通状况:深红代表严重拥堵(平均车速低于15km/h);红色代表拥挤(平均车速在15km/h~25km/h);黄色代表缓行(平均车速25km/h~40km/h);绿色代表顺畅(平均车速40km/h以上)。该系统中车速信息来自交通监控系统中的交通流速传感器或者出租车(流动车)上的GPS。假设驾驶员行驶的路径如图3所示,同时还显示了该路径上的实时路况信息。从系统中还可以获取该段路径总行程为8.2公里,预计行驶时间为20min。计算得到该段路径的平均行驶车速为24.6km/h,将颜色信息转换成预测平均车速信息,如图4所示。其中深红代表5km/h;红色代表20km/h;黄色代表30km/h;绿色代表45km/h。Step 2: After the driver enters the travel destination in the car navigation system, the GPS in the car navigation system will obtain the vehicle location information and plan the driving route on the electronic map. At the same time, the real-time traffic conditions of the planned route are obtained in the ITS system, and the smooth, slow, and congestion distances are measured through the electronic map distance measurement function to calculate the congestion ratio of the road conditions. From the distance measurement function and the congestion ratio, the current travel mileage and average vehicle speed information required by the adaptive strategy can be obtained respectively. Figure 3 is an example of Baidu intelligent transportation system route planning and real-time traffic information. Four colors are used to represent the traffic conditions of this road section: dark red represents severe congestion (average speed is less than 15km/h); red represents congestion (average speed is between 15km/h and 25km/h); h~40km/h); green means smooth (average vehicle speed above 40km/h). The vehicle speed information in this system comes from the traffic velocity sensor in the traffic monitoring system or the GPS on the taxi (mobile vehicle). Assuming that the driver's driving route is shown in Figure 3, the real-time road condition information on the route is also displayed. It can also be obtained from the system that the total travel distance of this section of the route is 8.2 kilometers, and the estimated travel time is 20 minutes. The calculated average vehicle speed of this section of the route is 24.6km/h, and the color information is converted into predicted average vehicle speed information, as shown in Figure 4. Among them, deep red represents 5km/h; red represents 20km/h; yellow represents 30km/h; green represents 45km/h.

步骤3:出行里程识别模块根据车辆历史行驶数据,建立出行里程预测策略对每日用户出行里程进行预测。由于出行规律的私家车用户的出行里程呈现出一定的收敛性,本发明统计和预测的出行里程特征为单个用户在不同日期和不同时段的出行里程。PHEV能量管理系统对用户每日的行驶工况(车速-时间里程)数据进行记录,然后对车速进行积分得到行驶里程,按小时统计当天行驶里程,并写入出行里程特征数据库。工作日和节假日的行驶里程需分别统计。当统计天数足够时,由收敛条件判断用户出行特征是否收敛。在本例中,统计90天的行驶里程,若行驶里程以90%的概率落在平均值[-5km,+5km]范围内,则该用户的出行里程有收敛特征。工作日和休息日的行驶特征收敛性需分别进行统计。如果不收敛则继续进行统计,直到收敛为止;如果收敛,则分别统计工作日和节假日每时段的平均行驶里程,绘制工作日和节假日各时段累积平均行驶里程曲线。图5(a)和图5(b)为某私家车用户的累计平均行驶里程曲线。Step 3: The travel mileage identification module establishes a travel mileage prediction strategy to predict the daily user travel mileage based on the vehicle's historical driving data. Since the travel mileage of private car users with travel rules shows a certain degree of convergence, the statistics and predictions of the travel mileage feature of the present invention are the travel mileage of a single user on different dates and different time periods. The PHEV energy management system records the user's daily driving conditions (vehicle speed-time mileage) data, then integrates the vehicle speed to obtain the mileage, calculates the mileage of the day by hour, and writes it into the travel mileage characteristic database. The mileage of working days and holidays shall be counted separately. When the number of statistical days is sufficient, the convergence condition is used to judge whether the user's travel characteristics are converged. In this example, the 90-day mileage is counted. If the mileage falls within the range of the average value [-5km, +5km] with a probability of 90%, then the travel mileage of the user has convergence characteristics. The convergence of driving characteristics on weekdays and rest days needs to be counted separately. If it does not converge, continue to make statistics until it converges; if it converges, calculate the average mileage of each period of weekdays and holidays, and draw the cumulative average mileage curve of each period of weekdays and holidays. Figure 5(a) and Figure 5(b) are the cumulative average mileage curves of a private car user.

步骤4:SOC规划模块根据预测得到的数据,包括全天行驶总里程、本次出行里程以及初始SOC,电动附件状态等信息,基于SOC规划算法生成参考SOC曲线,其具体生成过程如图6所示,过程如下:Step 4: The SOC planning module generates a reference SOC curve based on the SOC planning algorithm based on the predicted data, including the total mileage of the whole day, the mileage of this trip, the initial SOC, and the status of electric accessories. The specific generation process is shown in Figure 6 , the process is as follows:

首先生成参考SOC(SOCref),以行驶里程为横坐标,SOC为纵坐标,连接(0,SOCini)和(St,SOCmin)两点,得到直线型参考SOCref(图6细线)。其中,SOCini为行程初始SOC;SOCmin为CD模式最小SOC;St为全天总出行里程。St根据当前出行时间由步骤3得到的累积平均行驶里程曲线中插值得到。以某用户为例,在行程开始时,系统根据当前的出行时间以及是否是节假日通过累计平均行驶里程曲线预测该车当天剩余的总里程。如判断当天为工作日,则使用图5(a)的工作日累计平均行驶里程曲线,设当前的出行时间为6:30,则全天的总出行里程St为39.5km;下一次出行的时间为16:30,则St为19.8km。在每次出行前系统都会进行SOC规划,对于单次出行来讲,本次出行结束时的SOCend计算公式如下:First generate the reference SOC (SOC ref ), take the mileage as the abscissa and SOC as the ordinate, connect the two points (0, SOC ini ) and (S t , SOC min ) to obtain the linear reference SOC ref (thin line in Figure 6 ). Among them, SOC ini is the initial SOC of the trip; SOC min is the minimum SOC in CD mode; S t is the total travel mileage of the whole day. S t is obtained by interpolation from the cumulative average mileage curve obtained in step 3 according to the current travel time. Taking a user as an example, at the beginning of the trip, the system predicts the remaining total mileage of the car on the day based on the current travel time and whether it is a holiday or not through the cumulative average mileage curve. If it is judged that the day is a working day, use the cumulative average mileage curve of the working day in Figure 5(a), set the current travel time as 6:30, then the total travel mileage S t for the whole day is 39.5km; The time is 16:30, then S t is 19.8km. The system will carry out SOC planning before each trip. For a single trip, the calculation formula of SOC end at the end of this trip is as follows:

Figure BDA0002044389170000081
Figure BDA0002044389170000081

其中Si为本次出行里程。本次出行里程的参考SOC线实例如图6中圆圈内粗线所示。Where S i is the mileage of this trip. The example of the reference SOC line for the mileage of this trip is shown in the thick line inside the circle in Figure 6.

步骤5:APMP优化模块根据SOC初值SOCini,出行里程Si,协同状态初值λ0,SOC差值ΔSOC和车速差值ΔV确定协同状态值,利用APMP优化算法计算发动机及电机的控制转矩、启停状态、离合器状态等并,通过CAN总线传递给各执行部件控制器,完成PHEV的整车控制。APMP优化模块原理及优化过程如下:Step 5: The APMP optimization module determines the cooperative state value according to the SOC initial value SOC ini , the travel mileage S i , the cooperative state initial value λ 0 , the SOC difference ΔSOC and the vehicle speed difference ΔV, and uses the APMP optimization algorithm to calculate the control speed of the engine and motor. Torque, start-stop status, clutch status, etc. are transmitted to the controllers of each executive part through the CAN bus to complete the vehicle control of the PHEV. The principle and optimization process of the APMP optimization module are as follows:

5.1PMP能量管理策略5.1 PMP Energy Management Strategy

本发明的目的是提高插电式并联混合动力汽车的在不同工况下的燃油经济性,在特定工况下,使插电式并联混合动力汽车在一段时间内(t0~tf秒)燃油消耗量最小是一个典型的全局优化问题,由式(2)、(3)来表示:The purpose of the present invention is to improve the fuel economy of the plug-in parallel hybrid electric vehicle under different working conditions, and make the plug-in parallel hybrid electric vehicle in a period of time (t 0 ~ t f seconds) The minimum fuel consumption is a typical global optimization problem, expressed by equations (2) and (3):

Figure BDA0002044389170000082
Figure BDA0002044389170000082

Figure BDA0002044389170000091
Figure BDA0002044389170000091

其中:x(t)是汽车在t时刻的SOC,即被控系统的状态变量;u(t)为t时刻的转矩分配比,即系统控制变量,它是电机转矩Tm与总需求转矩Tdmd之比;

Figure BDA0002044389170000092
代表汽车在t时刻的瞬时燃油消耗速率(单位:kg/s);f(x(t),u(t),t)是汽车在t时刻状态变量x(t)的变化率(单位:1/s)。因此式(2)为该全局优化问题的目标函数,表示汽车在t0~tf秒在特定工况运行过程中的总油耗,该优化问题的目标函数是要使得该段总油耗最小;式(3)包含两个式子均为该优化问题的约束,其中第一个式子表示该系统的状态转移方程,第二个式子表示该优化问题的终值约束条件,即当该过程结束时,车辆的SOC不能低于xmin。Among them: x(t) is the SOC of the vehicle at time t, that is, the state variable of the controlled system; u(t) is the torque distribution ratio at time t, that is, the system control variable, which is the motor torque T m and the total demand ratio of torque T dmd ;
Figure BDA0002044389170000092
Represents the instantaneous fuel consumption rate of the car at time t (unit: kg/s); f(x(t), u(t), t) is the rate of change of the state variable x(t) of the car at time t (unit: 1 /s). Therefore, Equation (2) is the objective function of the global optimization problem, which represents the total fuel consumption of the car during the operation of a specific working condition from t 0 to t f seconds. The objective function of this optimization problem is to minimize the total fuel consumption of this section; Equation (3) Contains two formulas that are the constraints of the optimization problem, where the first formula represents the state transition equation of the system, and the second formula represents the final value constraint of the optimization problem, that is, when the process ends When , the SOC of the vehicle cannot be lower than x min .

本发明利用庞特里亚金极值原理(PMP)通过引入协同状态量将式(2)全局优化问题转换成若干个关于汉密尔顿函数瞬时优化问题。PMP优化算法定义汉密尔顿函数H(x(t),u(t),λ(t),t)作为瞬时优化问题的优化目标,如公式(4)所示:The invention converts the global optimization problem of the formula (2) into several instantaneous optimization problems about the Hamiltonian function by using the Pontryagin extremum principle (PMP) by introducing cooperative state quantities. The PMP optimization algorithm defines the Hamiltonian function H(x(t), u(t), λ(t), t) as the optimization objective of the instantaneous optimization problem, as shown in formula (4):

Figure BDA0002044389170000097
Figure BDA0002044389170000097

其中,λ(t)为协同状态量。汉密尔顿函数中第一项为发动机的瞬时油耗,可根据发动机转速和转矩在发动机万有特性MAP图中查得;第二项为协同状态值乘以SOC瞬时变化,协同状态量为PMP优化算法引入的新状态量,与行驶工况有相关性。在不同的驾驶事件中,协同状态量的初始值不同。求解每一时刻的汉密尔顿函数的最小值,得出的最优控制变量序列即为优化结果,如公式(5)所示:Among them, λ(t) is the cooperative state quantity. The first item in the Hamilton function is the instantaneous fuel consumption of the engine, which can be found in the engine universal characteristic MAP diagram according to the engine speed and torque; the second item is the multiplication of the synergistic state value by the instantaneous change of SOC, and the synergistic state quantity is the PMP optimization algorithm The new state quantity introduced is related to the driving conditions. In different driving events, the initial value of the cooperative state quantity is different. Solving the minimum value of the Hamiltonian function at each moment, the optimal control variable sequence obtained is the optimization result, as shown in formula (5):

Figure BDA0002044389170000093
Figure BDA0002044389170000093

其协同状态转移方程为:Its cooperative state transition equation is:

Figure BDA0002044389170000094
Figure BDA0002044389170000094

不考虑动力电池SOC对发动机瞬时油耗的影响,因此发动机瞬时油耗对SOC的偏导数为0。The influence of the power battery SOC on the instantaneous fuel consumption of the engine is not considered, so the partial derivative of the instantaneous fuel consumption of the engine to the SOC is 0.

Figure BDA0002044389170000095
Figure BDA0002044389170000095

系统状态转移方程为:The state transition equation of the system is:

Figure BDA0002044389170000096
Figure BDA0002044389170000096

假设电池SOC的变化率近似为0,求解式(7)正则方程可以发现协同状态值的变化幅度非常小,可认为是一个不随时间变化的常数,即Assuming that the rate of change of the battery SOC is approximately 0, solving the regular equation (7), it can be found that the change range of the cooperative state value is very small, which can be considered as a constant that does not change with time, that is,

Figure BDA0002044389170000101
Figure BDA0002044389170000101

综上,PMP优化算法将油耗最小的全局优化问题转化成求解汉密尔顿函数最小值的瞬时优化问题。在可行域中,求解所有时刻的汉密尔顿函数最小值对应的转矩分配比,即为最优控制变量序列。按照上述原理建立插电式混合动力汽车PMP能量管理仿真模型,本例中,PMP能量管理策略模型由Matalb/Simulink搭建,车辆模型采用AVL Cruise搭建,连接上述两个模型进行联合仿真,得到PHEV动力学联合仿真程序,即可得到某工况下的油耗值。In summary, the PMP optimization algorithm transforms the global optimization problem of minimizing fuel consumption into an instantaneous optimization problem of solving the minimum value of the Hamiltonian function. In the feasible region, solve the torque distribution ratio corresponding to the minimum value of the Hamiltonian function at all moments, which is the optimal control variable sequence. According to the above principle, the PMP energy management simulation model of plug-in hybrid electric vehicle is established. In this example, the PMP energy management strategy model is built by Matalb/Simulink, and the vehicle model is built by AVL Cruise. The above two models are connected for joint simulation to obtain the PHEV power By learning the joint simulation program, the fuel consumption value under a certain working condition can be obtained.

5.2协同状态初值优化5.2 Initial Value Optimization of Collaborative State

本发明采用遗传算法来求解式(9)的协同状态初值λ0。遗传算法以油耗最小为优化目标,以协同状态初值λ0为个体,个体的适应度函数为:The present invention uses a genetic algorithm to solve the initial value λ 0 of the collaborative state in formula (9). The genetic algorithm takes the minimum fuel consumption as the optimization goal, and takes the initial value of the collaborative state λ 0 as the individual, and the fitness function of the individual is:

Figure BDA0002044389170000102
Figure BDA0002044389170000102

协同状态值的大小决定着整个运行工况的油电分配比,受动力电池初始SOC和行驶里程两个因素影响。选择世界轻型汽车标准驾驶循环(Worldwide harmonized Light-duty driving Test Cycle,WLTC)作为仿真工况,如图7所示。WLTC工况分成四个阶段:低速段、中速段、高速段、超高速段。其平均速度从低至高,分别代表了支路(Low3)、干路(Medium3-1)、市郊(High3-1)和高速(ExtraHigh3)四种典型行驶工况。单个WLTC循环工况里程为23.2km,可将WLTC进行倍程以获得不同行驶里程。设置SOC值为0.35时进入电量维持模式。分别在初始SOC为0.9,0.8,07,0.6,0.5,0.4,仿真工况为1倍,2倍,3倍,4倍,5倍WLTC工况,求解共计30种条件下的协同状态值。The size of the synergy state value determines the oil-to-electricity distribution ratio of the entire operating condition, which is affected by two factors: the initial SOC of the power battery and the mileage. The Worldwide harmonized Light-duty driving Test Cycle (WLTC) is selected as the simulation condition, as shown in Figure 7. The WLTC working condition is divided into four stages: low-speed section, medium-speed section, high-speed section, and ultra-high-speed section. The average speeds range from low to high, respectively representing four typical driving conditions of branch road (Low3), main road (Medium3-1), suburban road (High3-1) and high speed (ExtraHigh3). The mileage of a single WLTC cycle is 23.2km, and the WLTC can be multiplied to obtain different mileage. When the SOC value is set to 0.35, it enters the battery maintenance mode. The initial SOC is 0.9, 0.8, 07, 0.6, 0.5, 0.4, and the simulation working conditions are 1 times, 2 times, 3 times, 4 times, 5 times the WLTC working conditions, and the synergy state values under a total of 30 conditions are solved.

下面以SOC初值为0.9,行驶工况为5倍WLTC为例,介绍遗传算法优化协同状态值的流程。先预设协同状态值的取值范围,可通过减小遗传算法中变量的取值范围来加快优化速度。本例用Matlab的GA工具箱求解,设置变量范围为[-1,-4],最大遗传代数是15,GA工具箱调用PHEV动力学联合仿真程序计算适应度函数,适应度函数最小值对应的协同状态值即为优化结果,本例为-1.94kg。30种工况条件下求解的协同状态值如表1所示,并绘制协同状态值MAP图,如图8所示。在行程开始前,系统通过当前SOC初始值和未来行程的总里程,使用协同状态值MAP图插值确定系统状态初始值λ0Taking the initial SOC value of 0.9 and the driving condition of 5 times WLTC as an example, the following describes the process of genetic algorithm optimization of the synergy state value. Presetting the value range of the cooperative state value firstly can speed up the optimization speed by reducing the value range of the variables in the genetic algorithm. In this example, the GA toolbox of Matlab is used to solve the problem, the variable range is set to [-1,-4], and the maximum genetic algebra is 15. The GA toolbox calls the PHEV dynamics co-simulation program to calculate the fitness function, and the minimum value of the fitness function corresponds to The synergy state value is the optimization result, which is -1.94kg in this example. The coordinated state values solved under 30 working conditions are shown in Table 1, and the coordinated state value MAP diagram is drawn, as shown in Figure 8. Before the start of the trip, the system determines the initial value of the system state λ 0 through the initial value of the current SOC and the total mileage of the future trip, using the cooperative state value MAP graph interpolation.

表1油电等效因子MAP数据(单位:-1×kg)Table 1 Oil-electric equivalent factor MAP data (unit: -1×kg)

Figure BDA0002044389170000103
Figure BDA0002044389170000103

Figure BDA0002044389170000111
Figure BDA0002044389170000111

5.3协同状态值在线修正策略5.3 Cooperative state value online correction strategy

上述通过遗传算法优化求解出的协同状态值,是工况WLTC下的最优值。而实际的出行工况是复杂多变的,因此要在实车上实现工况自适应控制策略,需要进一步实时修正协同状态值λ0。本发明依据步骤4得到的参考SOCref,并引入SOC惩罚因子和速度惩罚因子,使实际SOC能实时跟随参考SOCref,修正后的协同状态值由下式计算:The cooperative state value obtained through genetic algorithm optimization above is the optimal value under the working condition WLTC. However, the actual travel conditions are complex and changeable, so in order to realize the condition adaptive control strategy on the real vehicle, it is necessary to further correct the cooperative state value λ 0 in real time. The present invention is based on the reference SOC ref obtained in step 4, and introduces the SOC penalty factor and the speed penalty factor, so that the actual SOC can follow the reference SOC ref in real time, and the corrected cooperative state value is calculated by the following formula:

λ(t)=λ0+s(ΔSOC,t)+s(ΔV,t) (11)λ(t)=λ 0 +s(ΔSOC,t)+s(ΔV,t) (11)

APMP优化算法能够实现工况自适应,其中协同状态值λ(t)起到了关键作用,λ(t)值的大小决定了油电使用比例。当λ(t)值偏大时,控制策略会偏于多使用燃油(发动机),当λ(t)值偏小时,控制策略会偏于多使用电量(电机)。因此,λ(t)可以调整发动机与电机的转矩分配比。λ(t)受SOC差值(ΔSOC=SOC-SOCref)和车速差值(ΔV=V-Vm)两个因素影响。当车辆处于较拥堵路段行驶且前速度会低于整段行程的平均速度,即ΔV=V-Vm值为负,可以相应地减小λ(t)值,使系统偏于多使用电机,低速区采用电机驱动有利于提高燃油经济性,反之亦然。由于工况的变化,实际SOC下降曲线不会完全跟随参考SOC,如图9所示。λ(t)值也受SOC差值的影响,当行驶距离为S1时,其ΔSOC为负值,实际的SOC比参考SOC小,为了达到SOC跟随效果,要减少用电量,可以相应地提高λ(t)值,使系统偏于多使用发动机,反之亦然。The APMP optimization algorithm can realize the self-adaptation of working conditions, in which the cooperative state value λ(t) plays a key role, and the value of λ(t) determines the proportion of gasoline and electricity used. When the value of λ(t) is too large, the control strategy tends to use more fuel (engine), and when the value of λ(t) is too small, the control strategy tends to use more electricity (motor). Therefore, λ(t) can adjust the torque distribution ratio of the engine and the motor. λ(t) is affected by two factors: SOC difference (ΔSOC=SOC-SOC ref ) and vehicle speed difference (ΔV=VV m ). When the vehicle is driving on a relatively congested road section and the front speed will be lower than the average speed of the entire journey, that is, the value of ΔV=VV m is negative, the value of λ(t) can be reduced accordingly, so that the system tends to use more motors, and the low-speed area Driving with an electric motor is good for fuel economy and vice versa. Due to changes in working conditions, the actual SOC drop curve will not completely follow the reference SOC, as shown in Figure 9. The λ(t) value is also affected by the SOC difference. When the driving distance is S1, its ΔSOC is a negative value, and the actual SOC is smaller than the reference SOC. In order to achieve the SOC following effect and reduce power consumption, it can be increased accordingly The value of λ(t) makes the system bias towards using the engine more, and vice versa.

SOC差值的惩罚因子s(ΔSOC,t)在偏离参考SOC较小时取极小值,在偏离参考SOC过多时,取值应快速增大。在ΔSOC>0时,为了加快使用电量,惩罚因子s值取正。在ΔSOC<0时,为了减缓使用电量,惩罚因子s值取负。因此惩罚因子s(ΔSOC,t)表达式如下:The penalty factor s(ΔSOC,t) of the SOC difference takes a minimum value when the deviation from the reference SOC is small, and the value should increase rapidly when the deviation from the reference SOC is too large. When ΔSOC>0, in order to speed up the use of power, the value of the penalty factor s is positive. When ΔSOC<0, in order to slow down the power consumption, the value of the penalty factor s is negative. Therefore, the penalty factor s(ΔSOC,t) is expressed as follows:

Figure BDA0002044389170000112
Figure BDA0002044389170000112

设定ΔSOC取值范围是(-0.1,0.1),s(ΔSOC,t)惩罚因子曲线如图10所示。Set the value range of ΔSOC to be (-0.1, 0.1), and the penalty factor curve of s(ΔSOC,t) is shown in Figure 10.

车速差值的惩罚因子s(ΔV,t)应该在偏离平均车速较小时取极小值,在偏离平均车速过多时,取值应快速增大。当ΔV>0时,为了缓慢使用电量,惩罚因子s值取负。当ΔV<0时,为了加快使用电量,惩罚因子s值取正。因此惩罚因子s(ΔV,t)表达式如下:The penalty factor s(ΔV,t) of the vehicle speed difference should take a minimum value when the deviation from the average vehicle speed is small, and the value should increase rapidly when the deviation from the average vehicle speed is too large. When ΔV>0, in order to use electricity slowly, the value of penalty factor s is negative. When ΔV<0, in order to speed up the use of power, the value of the penalty factor s is positive. Therefore, the penalty factor s(ΔV,t) is expressed as follows:

Figure BDA0002044389170000121
Figure BDA0002044389170000121

设定ΔV取值范围是(-10,10),s(ΔV,t)惩罚因子如图11所示。Set the value range of ΔV to (-10, 10), and the penalty factor of s(ΔV,t) is shown in Figure 11.

5.4汉密尔顿函数的求解5.4 Solution of Hamilton function

由于汉密尔顿函数是一个求解非常复杂函数方程,所以本发明使用数值解法求解汉密尔顿函数。汉密尔顿函数求解流程如图12所示,先计算动力学方程求取总需求转矩,再根据本次出行的出行里程和初始SOC用插值法确定协同状态初值,通过车辆状态确定SOC差值和车速差值,修正当前的协同状态值。接着建立汉密尔顿函数,将转矩分配比u(t)的可行域分为100份。若u(t)>0,代表电机和发动机共同驱动车辆或电机单独驱动车辆。若u(t)<0,代表电机处于发电机状态。采用数值网格划分法可以保证在可行域中的求解精度。计算划分后所有的汉密尔顿函数值,求出相应汉密尔顿函数最小的转矩分配比即为所求。Since the Hamiltonian function is a very complicated functional equation to solve, the present invention uses a numerical solution to solve the Hamiltonian function. The solution process of the Hamiltonian function is shown in Figure 12. First, the dynamic equation is calculated to obtain the total demand torque, and then the initial value of the cooperative state is determined by interpolation method according to the travel mileage of this trip and the initial SOC, and the SOC difference and SOC are determined by the vehicle state. Vehicle speed difference, correct the current coordination state value. Then the Hamiltonian function is established, and the feasible region of the torque distribution ratio u(t) is divided into 100 parts. If u(t)>0, it means that the motor and the engine jointly drive the vehicle or the motor drives the vehicle alone. If u(t)<0, it means the motor is in generator state. The numerical grid division method can guarantee the solution accuracy in the feasible region. Calculate all the Hamilton function values after division, and find the minimum torque distribution ratio of the corresponding Hamilton function.

Claims (6)

1.一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,包括以下步骤:1. A PHEV adaptive optimal energy management method based on path information, is characterized in that, comprises the following steps: 步骤一、行驶工况与里程预测:Step 1. Driving conditions and mileage prediction: 1.1)通过车载导航系统获取车辆位置信息并在电子地图中规划出行驶路径,同时获取该规划行驶路径的实时路况信息,生成前方路径的预测工况;1.1) Obtain the vehicle location information through the vehicle navigation system and plan the driving route in the electronic map, and at the same time obtain the real-time road condition information of the planned driving route, and generate the predicted working conditions of the ahead route; 1.2)车载导航系统获取车辆的历史行驶数据,建立出行里程预测策略对每日用户出行里程进行预测,并绘制车辆累积平均行驶里程曲线;1.2) The car navigation system obtains the historical driving data of the vehicle, establishes a travel mileage prediction strategy to predict the daily travel mileage of users, and draws the cumulative average mileage curve of the vehicle; 步骤二、基于SOC规划算法生成参考SOC:Step 2. Generate a reference SOC based on the SOC planning algorithm: 通过步骤一生成的预测数据,包括预测工况、全天行驶总里程、本次出行里程以及初始SOC,基于SOC规划算法生成参考SOC;Through the forecast data generated in step 1, including the forecast working conditions, the total mileage of the whole day, the mileage of this trip and the initial SOC, the reference SOC is generated based on the SOC planning algorithm; 步骤三、APMP优化算法:Step 3, APMP optimization algorithm: 3.1)以油耗最小为全局优化目标,引入协同状态值,将全局优化问题转化为若干个带有汉密尔顿算子的瞬时优化问题;3.1) With the minimum fuel consumption as the global optimization goal, the collaborative state value is introduced, and the global optimization problem is transformed into several instantaneous optimization problems with Hamiltonian operators; 3.2)协同状态初值优化:采用遗传算法优化协同状态初值,建立协同状态初值随SOC初值和出行里程变化的MAP图;3.2) Optimization of the initial value of the collaborative state: the initial value of the collaborative state is optimized using a genetic algorithm, and a MAP diagram of the initial value of the collaborative state changing with the initial value of the SOC and the travel mileage is established; 3.3)协同状态值在线修正:在实际工况下,利用插值法在MAP图中求出协同状态初值,根据车载导航系统获得的工况信息及参考SOC对协同状态初值进行实时的修正;所述协同状态值在线修正包括以下过程:3.3) On-line correction of the cooperative state value: Under actual working conditions, the initial value of the cooperative state is obtained in the MAP diagram by interpolation method, and the initial value of the cooperative state is corrected in real time according to the working condition information obtained by the vehicle navigation system and the reference SOC; The online correction of the coordination state value includes the following process: 依据所述步骤二得到的参考SOC,并引入SOC惩罚因子和速度惩罚因子,使实际SOC能实时跟随参考SOC,修正后的协同状态值由下式计算:According to the reference SOC obtained in step 2, and introduce the SOC penalty factor and the speed penalty factor, so that the actual SOC can follow the reference SOC in real time, and the corrected cooperative state value is calculated by the following formula: λ(t)=λ0+s(ΔSOC,t)+s(ΔV,t)λ(t)=λ 0 +s(ΔSOC,t)+s(ΔV,t) λ(t)受SOC差值ΔSOC和车速差值ΔV两个因素影响,ΔSOC=SOC-SOCref,ΔV=V-Vmλ(t) is affected by two factors: SOC difference ΔSOC and vehicle speed difference ΔV, ΔSOC=SOC-SOC ref , ΔV=VV m ; SOC差值的惩罚因子s(ΔSOC,t)在偏离参考SOC较小时取极小值,在偏离参考SOC过多时,取值应快速增大;The penalty factor s(ΔSOC,t) of the SOC difference takes a minimum value when the deviation from the reference SOC is small, and the value should increase rapidly when the deviation from the reference SOC is too large; 在ΔSOC>0时,惩罚因子s值取正;在ΔSOC<0时,惩罚因子s值取负;惩罚因子s(ΔSOC,t)表达式如下:When ΔSOC>0, the value of penalty factor s is positive; when ΔSOC<0, the value of penalty factor s is negative; the expression of penalty factor s(ΔSOC,t) is as follows:
Figure FDA0003875144080000011
Figure FDA0003875144080000011
车速差值的惩罚因子s(ΔV,t)在偏离平均车速较小时取极小值,在偏离平均车速过多时,取值应快速增大;The penalty factor s(ΔV,t) of the vehicle speed difference takes a minimum value when the deviation from the average vehicle speed is small, and the value should increase rapidly when the deviation from the average vehicle speed is too large; 当ΔV>0时,惩罚因子s值取负;当ΔV<0时,惩罚因子s值取正;惩罚因子s(ΔV,t)表达式如下:When ΔV>0, the value of penalty factor s is negative; when ΔV<0, the value of penalty factor s is positive; the expression of penalty factor s(ΔV,t) is as follows:
Figure FDA0003875144080000021
Figure FDA0003875144080000021
3.4)对汉密尔顿函数求解,利用PMP优化算法进行动力分配,通过CAN总线传递给各执行部件控制器,完成PHEV的整车控制。3.4) Solve the Hamilton function, use the PMP optimization algorithm to distribute the power, and transmit it to the controllers of each executive component through the CAN bus to complete the vehicle control of the PHEV.
2.如权利要求1所述的一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,所述步骤1.2)具体过程为:PHEV能量管理系统对用户每日的车速-时间里程数据进行记录,然后对车速进行积分得到行驶里程,按小时统计当天行驶里程,并写入出行里程特征数据库,工作日和节假日的行驶里程需分别统计;分别统计工作日和节假日每时段的平均行驶里程,绘制工作日和节假日各时段累积平均行驶里程曲线。2. A PHEV adaptive optimal energy management method based on path information as claimed in claim 1, characterized in that, the specific process of said step 1.2) is: the PHEV energy management system calculates the user's daily vehicle speed-time mileage The data is recorded, and then the vehicle speed is integrated to obtain the driving mileage, and the driving mileage of the day is counted by hour, and written into the travel mileage characteristic database. The driving mileage on weekdays and holidays needs to be counted separately; Mileage, draw the cumulative average mileage curve of each time period on weekdays and holidays. 3.如权利要求1所述的一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,所述步骤二的具体过程为:3. A kind of PHEV adaptive optimal energy management method based on path information as claimed in claim 1, is characterized in that, the specific process of described step 2 is: 首先生成参考SOC:以行驶里程为横坐标,SOC为纵坐标,连接(0,SOCini)和(St,SOCmin)两点,得到SOCrefFirst generate the reference SOC: take the mileage as the abscissa and the SOC as the ordinate, connect the two points (0,SOC ini ) and (S t ,SOC min ) to get the SOC ref ; 其中,SOCref为参考SOC;SOCini为行程初始SOC;SOCmin为CD模式最小SOC;St为全天总出行里程,St根据当前出行时间由所述步骤一得到的车辆累积平均行驶里程曲线中插值得到;Among them, SOC ref is the reference SOC; SOC ini is the initial SOC of the trip; SOC min is the minimum SOC of the CD mode; S t is the total travel mileage of the whole day, and S t is the cumulative average mileage of the vehicle obtained from the step 1 according to the current travel time The interpolation in the curve is obtained; 在每次出行前系统都会进行SOC规划,对于单次出行来讲,本次出行结束时的SOCend计算公式如下:The system will carry out SOC planning before each trip. For a single trip, the calculation formula of SOC end at the end of this trip is as follows:
Figure FDA0003875144080000022
Figure FDA0003875144080000022
其中,Si为本次出行里程。Among them, S i is the mileage of this trip.
4.如权利要求1所述的一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,所述步骤3.1)以油耗最小为全局优化目标,引入协同状态值,将全局优化问题转化为若干个带有汉密尔顿算子的瞬时优化问题的具体过程为:4. A kind of PHEV self-adaptive optimal energy management method based on route information as claimed in claim 1, it is characterized in that, described step 3.1) take minimum fuel consumption as global optimization goal, introduce cooperative state value, global optimization problem The specific process of transforming into several instantaneous optimization problems with Hamiltonian operator is: 以油耗最小为全局优化问题,其目标函数为:Taking the minimum fuel consumption as the global optimization problem, the objective function is:
Figure FDA0003875144080000031
Figure FDA0003875144080000031
其中:x(t)是汽车在t时刻的SOC,即被控系统的状态变量;u(t)为t时刻的转矩分配比,即系统控制变量,它是电机转矩Tm与总需求转矩Tdmd之比;
Figure FDA0003875144080000032
代表汽车在t时刻的瞬时燃油消耗速率,单位:kg/s;
Among them: x(t) is the SOC of the vehicle at time t, that is, the state variable of the controlled system; u(t) is the torque distribution ratio at time t, that is, the system control variable, which is the motor torque T m and the total demand ratio of torque T dmd ;
Figure FDA0003875144080000032
Represents the instantaneous fuel consumption rate of the car at time t, unit: kg/s;
该优化问题的约束包含:The constraints of this optimization problem include:
Figure FDA0003875144080000033
Figure FDA0003875144080000033
其中,f(x(t),u(t),t)是汽车在t时刻状态变量x(t)的变化率,单位:1/s;Among them, f(x(t), u(t), t) is the rate of change of the state variable x(t) of the car at time t, unit: 1/s; 其中,第一个式子表示该系统的状态转移方程,第二个式子表示该优化问题的终值约束条件,即当该过程结束时,车辆的SOC不能低于xminAmong them, the first formula represents the state transition equation of the system, and the second formula represents the final value constraint condition of the optimization problem, that is, when the process ends, the SOC of the vehicle cannot be lower than x min ; 利用庞特里亚金极值原理通过引入协同状态量将式(2)全局优化问题转换成若干个关于汉密尔顿函数瞬时优化问题:PMP优化算法定义汉密尔顿函数H(x(t),u(t),λ(t),t)作为瞬时优化问题的优化目标,如下式所示:Using Pontryagin's extreme value principle to convert the global optimization problem of formula (2) into several instantaneous optimization problems about the Hamiltonian function by introducing cooperative state quantities: PMP optimization algorithm defines the Hamiltonian function H(x(t),u(t) ,λ(t),t) as the optimization objective of the instantaneous optimization problem, as shown in the following formula:
Figure FDA0003875144080000034
Figure FDA0003875144080000034
其中,λ(t)为协同状态量;汉密尔顿函数中第一项为发动机的瞬时油耗,根据发动机转速和转矩在发动机万有特性MAP图中查得;第二项为协同状态值乘以SOC瞬时变化,协同状态量为PMP优化算法引入的新状态量,与行驶工况有相关性,在不同的驾驶事件中,协同状态量的初始值不同;求解每一时刻的汉密尔顿函数的最小值,得出的最优控制变量序列即为优化结果,如下式所示:Among them, λ(t) is the cooperative state quantity; the first item in the Hamiltonian function is the instantaneous fuel consumption of the engine, which is found in the engine universal characteristic MAP diagram according to the engine speed and torque; the second item is the multiplication of the cooperative state value by the SOC Instantaneous change, the cooperative state quantity is a new state quantity introduced by the PMP optimization algorithm, which is related to the driving conditions. In different driving events, the initial value of the cooperative state quantity is different; the minimum value of the Hamilton function at each moment is solved, The obtained optimal control variable sequence is the optimization result, as shown in the following formula:
Figure FDA0003875144080000035
Figure FDA0003875144080000035
其协同状态转移方程为:Its cooperative state transition equation is:
Figure FDA0003875144080000036
Figure FDA0003875144080000036
5.如权利要求1所述的一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,所述步骤3.2)协同状态初值优化包括以下过程:5. A kind of PHEV self-adaptive optimal energy management method based on path information as claimed in claim 1, is characterized in that, described step 3.2) optimization of cooperative state initial value comprises the following process: 采用遗传算法来求解协同状态初值λ0The genetic algorithm is used to solve the initial value of the cooperative state λ 0 , 遗传算法以油耗最小为优化目标,以协同状态初值λ0为个体,个体的适应度函数为:The genetic algorithm takes the minimum fuel consumption as the optimization goal, and takes the initial value of the collaborative state λ 0 as the individual, and the fitness function of the individual is:
Figure FDA0003875144080000041
Figure FDA0003875144080000041
适应度函数最小值对应的协同状态值即为优化结果,并绘制协同状态值MAP图;在行程开始前,系统通过当前SOC初始值和未来行程的总里程,使用协同状态值MAP图插值确定系统状态初始值λ0The synergy state value corresponding to the minimum value of the fitness function is the optimization result, and a synergy state value MAP diagram is drawn; before the start of the trip, the system uses the synergy state value MAP diagram interpolation to determine the system State initial value λ 0 .
6.如权利要求1所述的一种基于路径信息的PHEV自适应最优能量管理方法,其特征在于,所述步骤3.4)对汉密尔顿函数求解包括以下过程:6. A kind of PHEV self-adaptive optimal energy management method based on path information as claimed in claim 1, is characterized in that, described step 3.4) comprises the following process to Hamilton function solution: 使用数值解法求解汉密尔顿函数:先计算动力学方程求取总需求转矩,再根据本次出行的出行里程和初始SOC用插值法确定协同状态初值,通过车辆状态确定SOC差值和车速差值,修正当前的协同状态值;建立汉密尔顿函数,将转矩分配比u(t)的可行域分为若干份;若u(t)>0,代表电机和发动机共同驱动车辆或电机单独驱动车辆;若u(t)<0,代表电机处于发电机状态;计算数值网格划分后所有的汉密尔顿函数值,求出相应汉密尔顿函数最小的转矩分配比即为所求。Use the numerical solution to solve the Hamiltonian function: first calculate the dynamic equation to obtain the total demand torque, then determine the initial value of the cooperative state by interpolation method according to the travel mileage of this trip and the initial SOC, and determine the SOC difference and vehicle speed difference based on the vehicle state , modify the current cooperative state value; establish a Hamiltonian function to divide the feasible region of the torque distribution ratio u(t) into several parts; if u(t)>0, it means that the motor and the engine drive the vehicle together or the motor drives the vehicle alone; If u(t)<0, it means that the motor is in the generator state; calculate all the Hamiltonian function values after numerical grid division, and find the minimum torque distribution ratio of the corresponding Hamiltonian function.
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