CN104608771B

CN104608771B - Vehicle energy conservation acceleration way optimization method based on pseudo-spectral method

Info

Publication number: CN104608771B
Application number: CN201410809301.9A
Authority: CN
Inventors: 李升波; 成波; 徐少兵; 郭强强; 王文军; 李国法; 李仁杰; 忻隆
Original assignee: Tsinghua University; Suzhou Automotive Research Institute of Tsinghua University
Current assignee: Tsinghua University; Suzhou Automotive Research Institute of Tsinghua University
Priority date: 2014-12-23
Filing date: 2014-12-23
Publication date: 2017-02-01
Anticipated expiration: 2034-12-23
Also published as: CN104608771A

Abstract

The invention provides an optimization method of a vehicle energy-saving acceleration mode based on a pseudo-spectrum method, and belongs to the technical field of automobile driving assistance systems. The method includes constructing an integer optimal control model composed of an objective function and multiple constraints, and transforming the integer optimal control model into a multi-segment smooth model: the multi-segment smooth model is solved by using the Legendre pseudo-spectral splicing method, and the optimized Energy-saving acceleration mode. The method of the invention can be used as a driving assistance algorithm to provide an acceleration mode for improving energy saving for a vehicle with discrete gear positions. Through simulation calculation, under certain conditions, compared with the constant acceleration mode, the optimized acceleration mode of the present invention can save fuel by 24.76%. Has a strong fuel-saving ability.

Description

An optimization method for vehicle energy-saving acceleration based on pseudospectral method

技术领域technical field

本发明属于汽车驾驶辅助系统技术领域，特别涉及一种挡位离散型车辆节能加速方式的优化计算方法。The invention belongs to the technical field of automobile driving assistance systems, and in particular relates to an optimization calculation method for an energy-saving acceleration mode of a gear-discrete vehicle.

背景技术Background technique

作为能源消耗大户，在石油资源紧缺的现状下，汽车面临着巨大的节油压力。国务院颁布的《节能与新能源汽车产业发展规划》指出，乘用车平均百公里油耗至2020年须从2010年的7.71L降至5L。严格的法规将极大地促进各类汽车节能技术的发展。目前，主要的提高汽车节油能力的技术领域有四个：更高效的汽车、智能化交通、新能源利用和经济性驾驶。其中，经济性驾驶是一种较为高效的节能驾驶方式。研究表明，节能驾驶方式具有10～15％的节油潜力，这几乎接近混合动力等技术的节油能力，将成为汽车节能减排的重要技术方向。加速过程是一种高能耗且频繁出现的驾驶状态，有研究表明：加速过程和怠/低速过程是导致驾驶员油耗差异的两个最重要原因，因此探索加速过程的节能操作方式对降低行车油耗具有积极意义。As a large energy consumer, automobiles are facing enormous pressure to save fuel under the current situation of shortage of oil resources. The "Energy Conservation and New Energy Automobile Industry Development Plan" promulgated by the State Council pointed out that the average fuel consumption per 100 kilometers of passenger cars must be reduced from 7.71L in 2010 to 5L by 2020. Strict regulations will greatly promote the development of various energy-saving technologies for vehicles. At present, there are four main technical fields to improve the fuel-saving ability of automobiles: more efficient automobiles, intelligent transportation, new energy utilization and economical driving. Among them, economical driving is a more efficient way of energy-saving driving. Studies have shown that energy-saving driving has a fuel-saving potential of 10-15%, which is almost close to the fuel-saving ability of technologies such as hybrid power, and will become an important technical direction for energy-saving and emission-reduction of vehicles. The acceleration process is a high energy consumption and frequent driving state. Studies have shown that: the acceleration process and the idling/low speed process are the two most important reasons for the driver's fuel consumption difference. have a positive meaning.

车辆节能加速方式即指确定换挡时刻以及某一具体挡位下最合适的油门开度，然后通过驾驶员操纵换挡杆以及油门踏板来实现。The energy-saving acceleration mode of the vehicle refers to determining the shifting time and the most suitable accelerator opening under a specific gear, and then realizing it through the driver's manipulation of the shift lever and the accelerator pedal.

目前，车辆节能加速方式多基于实验统计分析得到。国内外学者对此作了很多实验方法的研究，得出了包括“激进加速(加速度＞1.5m/s2)影响油耗的显著性指标是正常加速的2.5倍，激进的加速和制动会导致油耗提高30-40％”等结论。但这也反映了该实验方法的弊端，At present, vehicle energy-saving acceleration methods are mostly obtained based on experimental statistical analysis. Scholars at home and abroad have done a lot of experimental research on this, and have concluded that the significant indicators including "radical acceleration (acceleration > 1.5m/s2) affecting fuel consumption are 2.5 times that of normal acceleration, and radical acceleration and braking will lead to fuel consumption." Increased by 30-40%" and other conclusions. But this also reflects the drawbacks of the experimental method,

即无法定量化地表达节油方式，且难以解释内在的节油机理。此外，该实验方法需要投入大量实验成本，且实验结论在不同车型之间无迁移性。That is, it is impossible to express the fuel-saving method quantitatively, and it is difficult to explain the internal fuel-saving mechanism. In addition, this experimental method needs to invest a lot of experimental costs, and the experimental conclusions are not transferable between different models.

国内外学者典型研究如针对巡航工况和跟车工况方式的优化。一篇最早的研究源于Johns Hopkins大学的Gilbert(1976)。他证明了巡航工况下，周期控制行车节能优于匀速行车节能方式，而后者通常被误认为具有“油耗最优性”。Li等人针对装备CVT(速比连续)型变速器的车辆，提出的最优控制行车的方法为：在跟随匀速行驶的前车时，油耗最优驾驶是一种等周期的“加速-滑行”(PnG，Pulse and Glide)方式，并利用图解法定量地分析了PnG方式的形成原因以及关键参数。也有人利用轮毂试验台验证了该类方式的省油能力，基于该方式的周期切换型的自适应巡航控制器与传统准稳态控制器相比，省油能力达到13％以上。实际上，典型的节能驾驶方式辨识均可构建为一个最优控制模型，包括加速过程，类似研究如：Kuriyama等建立了电动汽车坡道工况下的能耗最优控制模型，采用动态规划法优化出车辆速度和加速曲线；Thomas等建立了交通灯约束下的油耗最优控制模型，通过Dijkstra算法优化得到车辆速度曲线。Typical research by scholars at home and abroad, such as optimization for cruising conditions and car-following conditions. One of the earliest studies comes from Gilbert (1976) at Johns Hopkins University. He proved that under cruising conditions, the cycle control driving energy saving method is better than the constant speed driving energy saving method, and the latter is usually mistaken for "optimal fuel consumption". For vehicles equipped with CVT (Continuous Ratio Ratio) transmission, Li et al. proposed an optimal driving control method: when following a vehicle ahead at a constant speed, driving with optimal fuel consumption is an equal-period "acceleration-coasting" (PnG, Pulse and Glide) method, and quantitatively analyzed the formation reasons and key parameters of the PnG method by using the graphic method. Some people have also verified the fuel-saving ability of this type of method by using the hub test bench. Compared with the traditional quasi-steady-state controller, the cycle-switching adaptive cruise controller based on this method can save more than 13% of fuel. In fact, the identification of typical energy-saving driving methods can be constructed as an optimal control model, including the acceleration process. Similar studies such as: Kuriyama et al. established an optimal control model of energy consumption under the ramp condition of electric vehicles, using the dynamic programming method Optimize the vehicle speed and acceleration curve; Thomas et al. established the optimal control model of fuel consumption under the constraints of traffic lights, and obtained the vehicle speed curve through Dijkstra algorithm optimization.

目前，对于装备了传统机械式变速器的车辆加速过程中的节能加速方式的理论研究基本空白，一个重要原因是因变速器速比离散，理论或者数值求解困难。也就不能据此开发该类型车辆的节能辅助技术。At present, there is basically no theoretical research on energy-saving acceleration methods during the acceleration process of vehicles equipped with traditional mechanical transmissions. One important reason is that due to the discrete speed ratio of the transmission, it is difficult to solve them theoretically or numerically. Just can not develop the energy-saving auxiliary technology of this type of vehicle accordingly.

发明内容Contents of the invention

本发明的目的是为解决装备了传统机械式变速器的车辆加速过程中的节能加速方式的优化问题，提供一种基于伪谱法的车辆节能加速方式的优化方法。本发明通过构建挡位离散型车辆的节能最优加速模型，结合伪谱法提出通用的数值求解方法，并对加速工况进行优化和分析，形成定量化的节能加速方式，具有很强的节油能力。The purpose of the present invention is to solve the problem of optimizing the energy-saving acceleration mode in the acceleration process of a vehicle equipped with a traditional mechanical transmission, and provide a method for optimizing the energy-saving acceleration mode of the vehicle based on the pseudo-spectral method. The present invention constructs an energy-saving optimal acceleration model of a vehicle with discrete gears, combines the pseudo-spectrum method to propose a general numerical solution method, and optimizes and analyzes the acceleration conditions to form a quantitative energy-saving acceleration mode, which has strong energy saving oil capacity.

本发明提出的一种基于伪谱法的车辆节能加速方式的优化方法，针对MT型车辆加速过程的优化，其特征在于，该方法包括以下步骤：A kind of optimization method of the vehicle energy-saving acceleration method based on the pseudo-spectrum method proposed by the present invention is aimed at the optimization of the acceleration process of the MT type vehicle, and it is characterized in that the method comprises the following steps:

1)构建整型最优控制模型的目标函数如式(1)所示：1) The objective function of constructing the integer optimal control model is shown in formula (1):

式中：J为当量油耗，k_s为距离修正系数，s_f为加速距离，t_f为加速终止时间，T_e为发动机转矩，w_e为发动机转速，为发动机瞬时喷油率；In the formula: J is the equivalent fuel consumption, k _s is the distance correction coefficient, s _f is the acceleration distance, t _f is the acceleration termination time, T _e is the engine torque, w _e is the engine speed, is the instantaneous fuel injection rate of the engine;

2)构建该最优控制模型的多个约束条件：2) Construct multiple constraints of the optimal control model:

车辆行驶距离与速度关系约束如式(2)所示：The constraints on the relationship between vehicle travel distance and speed are shown in formula (2):

$\overset{\cdot \cdot}{s the s} = = v v,, - - - - - - ((22))$

式(2)中：s为车辆行驶距离，s上方的小点为求导符号，v为车辆行In formula (2): s is the driving distance of the vehicle, the dot above s is the derivation symbol, and v is the driving distance of the vehicle

驶速度；driving speed;

车辆行驶速度约束如式(3)所示：The vehicle speed constraint is shown in formula (3):

$\overset{\cdot \cdot}{v v} = = \frac{{i i}_{00} {η η}_{T T}}{{δ δ}_{{i i}_{g g}} {Mr Mr.}_{w w}} {i i}_{g g} {T T}_{ed ed} - - \frac{{k k}_{a a} {v v}^{22} + + {k k}_{f f}}{{δ δ}_{{i i}_{g g}} M m},, - - - - - - ((33))$

式(3)中：i₀为主减速比，i_g为变速器速比，r_w为车轮半径，η_T为传动系传动总效率，δ_ig为速比为i_g时的旋转质量系数，M为整车质量，T_ed为发动机动态有效输出力矩，k_f为滚动阻力，k_a为风阻系数；In formula (3): i ₀ is the main deceleration ratio, i _g is the speed ratio of the transmission, r _w is the wheel radius, η _T is the total transmission efficiency of the drive train, δ _ig is the rotating mass coefficient when the speed ratio is i _g , M is the mass of the vehicle, T _ed is the dynamic effective output torque of the engine, k _f is the rolling resistance, and k _a is the drag coefficient;

发动机动态有效输出力矩约束，如式(4)所示：The dynamic effective output torque constraint of the engine is shown in formula (4):

${T T}_{ed ed} = = {T T}_{e e} ((11 - - {γ γ}_{d d} \frac{{dw dw}_{e e}}{dt dt})),, - - - - - - ((44))$

式中：γ_d为动态修正系数，取为γ_d＝0.003s²/rad；In the formula: γ _d is the dynamic correction coefficient, which is taken as γ _d =0.003s ² /rad;

发动机转速约束如式(5)-(7)所示：The engine speed constraints are shown in equations (5)-(7):

w_e＝k_wvi_g (5)w _e =k _w vi _g (5)

${k k}_{w w} = = 6060 \times \times \frac{v v}{22 {πr πr}_{w w}} {i i}_{g g} {i i}_{00} - - - - - - ((66))$

式中：为v_eco下发动机的喷油率，v_eco为车辆匀速行驶百公里In the formula: is the fuel injection rate of the engine under v _eco , and v _eco is the constant speed of the vehicle for 100 kilometers

油耗最低对应的速度；且满足式(8)-(10)：The speed corresponding to the lowest fuel consumption; and satisfy the formula (8)-(10):

w_emin≤w_e≤w_emax， (8)w e _min ≤ w _e ≤ w e _max , (8)

0＜T≤T_max(w_e)， (9)0<T≤T _max (w _e ), (9)

i_g∈{i_g1，i_g2，i_g3，i_g4，i_g5}. (10)i _g ∈ {i _g1 ，i _g2 ，i _g3 ，i _g4 ，i _g5 }. (10)

约束条件的状态变量为距离s、速度v，记为x＝[s，v]^T，控制变量为发动机力矩T_e、变速器速比i_g，记为u＝[T_e，i_g]^T；The state variables of the constraint conditions are distance s and speed v, denoted as x=[s, v] ^T , and the control variables are engine torque _Te and transmission speed ratio i _g , denoted as u=[T _e , i _g ] ^T ;

4)基于伪谱法精确求解式(1)-(10)组成的最优控制模型，求解出的挡位的切换时刻T₁，T₂，…，T_Q以及发动机力矩具体包括：4) Based on the pseudo-spectral method, the optimal control model composed of formulas (1)-(10) is accurately solved, and the obtained gear switching times T ₁ , T ₂ ,..., T _Q and engine torque Specifically include:

31)将整型最优控制模型转化为多段光滑模型：31) Transform the integer optimal control model into a multi-segment smooth model:

定义i_gv，min和i_gv，max表示速度v可以对应的最低和最高挡位，首先确定加速起始挡位：设加速起始挡位为i_gs，加速终止挡位为i_ge，其中加速起始挡位i_gs如式(11)Define i _{gv, min} and i _{gv, max} to represent the lowest and highest gears that speed v can correspond to, first determine the starting gear for acceleration: set the starting gear for acceleration as i _gs , and the end gear for acceleration as i _ge , where the acceleration The starting gear i _{gs is} as formula (11)

式(11)表示：不可退挡时，起始挡位i_gs为起始时刻的原挡位i_g(t₀)；可退挡时，起始挡位为该速度对应的最低挡位；Equation (11) indicates: when the gear cannot be reversed, the initial gear i _gs is the original gear i _g (t ₀ ) at the initial moment; when the gear can be reversed, the initial gear is the lowest gear corresponding to the speed;

加速终止挡位i_ge取为加速终止时速度对应的最大挡位i_gvf，max；The acceleration termination gear i _ge is taken as the maximum gear i _{gvf, max} corresponding to the speed at the acceleration termination;

确定多段光滑模型的分段数和分段点：分段数为i_ge-i_gs+1段，记为Q段，存在Q-1个时间分段点，记为T₁，T₂，…，T_Q-1；将加速的初始时间t₀和加速的终止时间t_f记录为T₀和T_Q，其中时间分段点满足约束T₀＜T₁＜…＜T_Q，设置任意两时间分段点的间距大于设定的参数δ_t，即Determine the number of segments and segment points of the multi-segment smooth model: the number of segments is i _ge -i _gs +1 segment, which is recorded as Q segment, and there are Q-1 time segment points, which are recorded as T ₁ , T ₂ ,… , T _Q-1 ; record the initial time t ₀ of acceleration and the end time t _f of acceleration as T ₀ and T _Q , where the time segmentation point satisfies the constraint T ₀ <T ₁ <...<T _Q , set any two times The distance between segment points is greater than the set parameter δ _t , that is

T_q-T_q-1≥δ_t，q∈[1，Q]∩Z⁺ (12)：T _q -T _q-1 ≥ δ _t , q∈[1,Q]∩Z ⁺ (12):

32)采用Legendre伪谱拼接法对多段光滑模型求解：32) Using the Legendre pseudospectral splicing method to solve the multi-segment smooth model:

首先对多段光滑模型进行时域转化：将各段的时间域[T_q-1，T_q]统一转化为标准区间[-1，1]如式(13)所示，用以与Legendre正交多项式的定义区间一致：First, the time domain transformation is performed on the multi-segment smooth model: the time domain [T _q-1 , T _q ] of each segment is uniformly transformed into the standard interval [-1, 1] as shown in formula (13), which is used to be orthogonal to Legendre Polynomials are defined interval-unanimously:

$τ τ = = \frac{22 t t - - (({T T}_{q q} + + {T T}_{q q - - 11}))}{{T T}_{q q} - - {T T}_{q q - - 11}},, τ τ &Element; &Element; [[- - 1,1 1,1]] . . - - - - - - ((1313))$

再对式(13)进行配点与离散化：对各段设置不同的配点个数，记为N_q+1，每段内配点记为τ_q，i，其中i＝0，1，…，N_q；q＝1，2，…，Q；将各段内的状态变量距离s、车速v在LGL点离散化为式(14)：Then carry out collocation and discretization of formula (13): set different numbers of collocation points for each segment, denoted as N _q +1, collocation points in each segment are denoted as τ _{q, i} , where i=0, 1, ..., N _q ; q=1, 2,..., Q; discretize the state variable distance s and vehicle speed v in each segment into formula (14):

${x x}_{q q} = = [\begin{matrix} {S S}_{q q,, 00} & {S S}_{q q,, 11} & . . . . . . & {S S}_{q q,, {N N}_{q q}} \\ {V V}_{q q,, 00} & {V V}_{q q,, 11} & . . . . . . & {V V}_{q q,, {N N}_{q q}} \end{matrix}] - - - - - - ((1414))$

将控制变量发动机转矩T_e离散化为式(15)：The control variable engine torque T _e is discretized into formula (15):

式(14)和(15)所示的状态和控制变量，其动态曲线x_q(τ)和u_q(τ)通过Lagrange插值多项式逼近如式(16)和(17)所示：For the state and control variables shown in equations (14) and (15), their dynamic curves x _q (τ) and u _q (τ) are approximated by Lagrange interpolation polynomials as shown in equations (16) and (17):

${x x}_{q q} ((τ τ)) \approx \approx {Σ Σ}_{i i = = 00}^{{N N}_{q q}} {L L}_{q q,, i i} ((τ τ)) {X x}_{q q,, i i};; - - - - - - ((1616))$

${u u}_{q q} ((τ τ)) \approx \approx {Σ Σ}_{i i = = 00}^{N N} {L L}_{q q,, i i} ((τ τ)) {U u}_{q q,, i i} . . - - - - - - ((1717))$

其中，L_q，i(τ)为Lagrange插值基函数：Among them, L _{q, i} (τ) is the Lagrange interpolation basis function:

${L L}_{q q,, i i} ((τ τ)) = = {Π Π}_{j j = = 00,, j j &NotEqual; &NotEqual; i i}^{{N N}_{q q}} \frac{τ τ - - {τ τ}_{q q,, j j}}{{τ τ}_{q q,, i i} - - {τ τ}_{q q,, j j}} . . - - - - - - ((1818))$

对状态的微分运算转化为对插值基函数的微分运算如式(19)：The differential operation on the state is transformed into the differential operation on the interpolation basis function as formula (19):

${\overset{\cdot \cdot}{x x}}_{q q} (({τ τ}_{q q,, k k})) = = {Σ Σ}_{i i = = 00}^{{N N}_{q q}} {\overset{\cdot &Center Dot;}{L L}}_{q q,, i i} (({τ τ}_{q q,, k k})) {X x}_{q q,, i i} = = {Σ Σ}_{i i = = 00}^{{N N}_{q q}} {D D.}_{ki the ki}^{q q} {X x}_{q q,, i i} . . - - - - - - ((1919))$

其中，k＝0，1，2，…，N，D^q为微分矩阵，表示各Lagrange基函数在各LGL配点处的微分值，如式(20)所示：Among them, k=0, 1, 2, ..., N, D ^q is a differential matrix, which represents the differential value of each Lagrange basis function at each LGL collocation point, as shown in formula (20):

针对式(2)-(7)所述的约束方程，每段内的速比i_g为常数，对发动机转速的微分转化为对速度的微分，即：For the constraint equations described in formulas (2)-(7), the speed ratio i _g in each section is a constant, and the differential of the engine speed is transformed into the differential of the speed, namely:

${T T}_{ed ed} = = {T T}_{e e} ((11 - - {γ γ}_{d d} \frac{{dw dw}_{e e}}{dt dt})) = = {T T}_{e e} ((11 - - {γ γ}_{d d} {k k}_{w w} {i i}_{g g} \overset{\cdot \cdot}{v v})) . . - - - - - - ((21 twenty one))$

对式(2)-(7)及(21)进一步化简整理得After further simplification of formulas (2)-(7) and (21), we get

$\overset{\cdot \cdot}{s the s} = = v v,, - - - - - - ((22 twenty two))$

$\overset{\cdot &Center Dot;}{v v} = = \frac{{i i}_{g g} {i i}_{00} {η η}_{T T} {T T}_{e e} / / {r r}_{w w} - - {k k}_{a a} {v v}^{22} - - {k k}_{f f}}{{δ δ}_{{i i}_{g g}} M m + + {i i}_{00} {η η}_{T T} {γ γ}_{d d} {k k}_{w w} {i i}_{g g}^{22} {T T}_{e e} / / {r r}_{w w}} . . - - - - - - ((23 twenty three))$

式(22)、(23)转化为在配点处的等式约束：Equations (22), (23) are transformed into equality constraints at collocation points:

${Σ Σ}_{i i = = 00}^{{N N}_{q q}} {D D.}_{ki the ki}^{q q} {S S}_{q q,, i i} = = \frac{{T T}_{q q} - - {T T}_{q q - - 11}}{22} {V V}_{q q,, k k},, - - - - - - ((24 twenty four))$

最后，对式(1)所示的目标函数进行转化为式(26)：Finally, the objective function shown in formula (1) is transformed into formula (26):

其中，为发动机转速的离散值，w为积分权重，定义为：in, is the discrete value of the engine speed, w is the integral weight, defined as:

${w w}_{q q,, i i} = = {&Integral; &Integral;}_{- - 11}^{11} {L L}_{q q,, i i} ((τ τ)) dτ dτ = = \frac{22}{{N N}_{q q} (({N N}_{q q} + + 11)) {P P}_{{N N}_{q q}}^{22} (({τ τ}_{q q,, i i}))};;$

即经过以上拼接法，最优控制模型式(1)-(10)转化为以下形式：That is, through the above splicing method, the optimal control model formula (1)-(10) is transformed into the following form:

目标函数：Objective function:

服从以下约束：subject to the following constraints:

且满足式(27)-(29)：And satisfy formula (27)-(29):

T_q-T_q-1≥δ_t. (29)T _q -T _q-1 ≥δ _t . (29)

其中，k＝0，1，2，…，N；待优化变量为配点处的距离S_q，k、速度V_q，k、发动机输出力矩以及挡位的切换时刻T₁，T₂，…，T_Q。Among them, k=0, 1, 2, ..., N; the variables to be optimized are the distance S _{q, k} at the collocation point, the speed V _{q, k} , and the output torque of the engine And the shifting time T ₁ , T ₂ , . . . , T _Q of the gears.

通过优化求解出的挡位的切换时刻T₁，T₂，…，T_Q以及发动机力矩确定换挡时刻和相应的油门开度(与发动机力矩正相关)，即确定了加速过程中何时换挡，以及某一特定挡位下所需的油门开度。由此构成优化的节能加速操作方式。The switching time T ₁ , T ₂ ,..., T _Q and the engine torque of the gear obtained by optimization Determine the shifting moment and the corresponding throttle opening (positively correlated with the engine torque), that is, determine when to shift gears during acceleration, and the required throttle opening for a specific gear. This constitutes an optimized energy-saving acceleration operation mode.

本发明的特点与效果：Features and effects of the present invention:

本发明的挡位离散型车辆节能加速方式的伪谱法优化方法可以定量计算出一种挡位离散型车辆的节能加速方式，与传统求解方法相比，本发明方法具有明显较高的收敛速度和精确度。The pseudo-spectral optimization method of the energy-saving acceleration mode of the discrete-gear vehicle of the present invention can quantitatively calculate the energy-saving acceleration mode of a discrete-gear vehicle. Compared with the traditional solution method, the method of the present invention has a significantly higher convergence speed and precision.

本发明的挡位离散型车辆节能加速方式的伪谱法优化方法不仅可求解能耗最优问题，亦可求解时间最优问题，实际上，当问题的性能函数发生变化或者增加新的约束时，本方法仍然适用，是这类问题的一种通用的数值解法。The pseudo-spectral optimization method of the gear-discrete vehicle energy-saving acceleration mode of the present invention can not only solve the problem of optimal energy consumption, but also solve the problem of optimal time. In fact, when the performance function of the problem changes or new constraints are added , this method is still applicable, and it is a general numerical solution to this kind of problem.

应用到实际中，本发明方法可以作为一种驾驶辅助算法为挡位离散型车辆提供一种提高节能的加速方式。通过仿真计算，在一定条件下，与采用恒定加速度方式相比，本发明优化出的加速方式可以节油24.76％。具有很强的节油能力。When applied in practice, the method of the present invention can be used as a driving assistance algorithm to provide an acceleration method for improving energy saving for vehicles with discrete gear positions. Through simulation calculation, under certain conditions, compared with the constant acceleration mode, the optimized acceleration mode of the present invention can save fuel by 24.76%. Has a strong fuel-saving ability.

附图说明Description of drawings

图1为本发明方法的总体流程框图。Fig. 1 is the overall flowchart of the method of the present invention.

具体实施方式detailed description

本发明提出的基于伪谱法的车辆节能加速方式的优化方法结合附图及实施例详细说明如下：The optimization method of the vehicle energy-saving acceleration method based on the pseudo-spectral method proposed by the present invention is described in detail as follows in conjunction with the accompanying drawings and embodiments:

本发明的方法针对MT型车辆，加速过程的优化，该方法具体实施方式总体流程如图1所示，包括以下步骤：The method of the present invention is aimed at the optimization of the acceleration process for the MT type vehicle, and the overall process of the specific implementation of the method is as shown in Figure 1, comprising the following steps:

$\overset{\cdot &Center Dot;}{s the s} = = v v,, - - - - - - ((22))$

驶速度；driving speed;

$\overset{\cdot &Center Dot;}{v v} = = \frac{{i i}_{00} {η η}_{T T}}{{δ δ}_{{i i}_{g g}} {Mr Mr.}_{w w}} {i i}_{g g} {T T}_{ed ed} - - \frac{{k k}_{a a} {v v}^{22} + + {k k}_{f f}}{{δ δ}_{{i i}_{g g}} M m},, - - - - - - ((33))$

式中：γ_d为动态修正系数，取为 In the formula: γ _d is the dynamic correction coefficient, which is taken as

为发动机转速约束如式(5)-(7)所示：The engine speed constraints are shown in equations (5)-(7):

w_e＝k_wvi_g， (5)w _e =k _w vi _g , (5)

式中：为v_eco下发动机的喷油率，v_eco为车辆匀速行驶百In the formula: is the fuel injection rate of the engine under v _eco , and v _eco is the percentage of the vehicle running at a constant speed

公里油耗最低对应的速度；且满足式(8)-(10)：The speed corresponding to the lowest fuel consumption per kilometer; and satisfy the formula (8)-(10):

w_emin≤w_e≤w_emax， (8)w e _min ≤ w _e ≤ w e _max , (8)

0＜T≤T_max(w_e)， (9)0<T≤T _max (w _e ), (9)

约束条件的状态变量为距离s、速度v，记为x＝[s，v]^T，控制变量为发动机力矩T_e、变速器速比i_g，记为u＝[T_e，i_g]^T。；The state variables of constraints are distance s and speed v, denoted as x=[s, v] ^T , and the control variables are engine torque _Te and transmission speed ratio i _g , denoted as u=[T _e , i _g ] ^T . ;

5)基于伪谱法精确求解式(1)-(10)组成的最优控制模型，具体包括：5) Accurately solve the optimal control model composed of formulas (1)-(10) based on the pseudospectral method, specifically including:

定义i_gv，min和i_gv，max表示速度v可以对应的最低和最高挡位，首先确定加速起始挡位，包括两种情况：Define i _{gv, min} and i _{gv, max} to indicate the lowest and highest gears that the speed v can correspond to, first determine the starting gear for acceleration, including two situations:

1)不允许退挡(即加速过程只能从当前挡位i_g(t₀)继续升挡)；1) Reverse gear is not allowed (that is, the acceleration process can only continue to upshift from the current gear i _g (t ₀ ));

2)允许退挡(由于不能确定退至何挡最优，因此设定均先退到最低挡位)；2) Reverse gear is allowed (Because it is impossible to determine which gear is the best to retreat to, it is set to retreat to the lowest gear first );

因此，设加速起始挡位为i_gs，加速终止挡位为i_ge，其中加速起始挡位i_gs如式(11)Therefore, let the acceleration start gear be i _gs and the acceleration end gear be i _ge , where the acceleration start gear i _{gs is} as in formula (11)

式(11)表示：不可退挡时，起始挡位i_gs为起始时刻的原挡位i_g(t₀)，；可退挡时，起始挡位为该速度对应的最低挡位；Equation (11) indicates: when the gear cannot be reversed, the initial gear i _gs is the original gear i _g (t ₀ ) at the initial moment; when the gear can be reversed, the initial gear is the lowest gear corresponding to the speed ;

再确定加速终止挡位i_ge，加速终止挡位i_ge取为加速终止时速度对应的最大挡位 Then determine the acceleration end gear i _ge , the acceleration end gear i _ge is taken as the maximum gear corresponding to the speed at the end of acceleration

确定多段光滑模型的分段数和分段点：分段数为i_ge-i_gs+1段，记为Q段，存在Q-1个时间分段点，记为T₁，T₂，…，T_Q-1；将加速的初始时间t₀和加速的终止时间t_f记录为T₀和T_Q，其中时间分段点满足约束T₀＜T₁＜…＜T_Q，为保证数值稳定，设置任意两时间分段点的间距大于设定的参数δ_t，即Determine the number of segments and segment points of the multi-segment smooth model: the number of segments is i _ge -i _gs +1 segment, which is recorded as Q segment, and there are Q-1 time segment points, which are recorded as T ₁ , T ₂ ,… , T _Q-1 ; record the initial time of acceleration t ₀ and the end time of acceleration t _f as T ₀ and T _Q , where the time segmentation points satisfy the constraint T ₀ <T ₁ <...<T _Q , in order to ensure numerical stability , set the distance between any two time-segment points to be greater than the set parameter δ _t , namely

T_q-T_q-1≥δ_t，q∈[1，Q]∩Z⁺ (12)T _q −T _q-1 ≥δ _t , q∈[1,Q]∩Z ⁺ (12)

式(12)中，δ_t可以取值δ_t＝0.25。In formula (12), δ _t may take a value of δ _t =0.25.

再对式(13)进行配点与离散化：(Legendre伪谱法采用LGL配点，为Legendre正交多项式一阶导数的根加上-1和1两点，等价于多项式的根，共N+1个配点。)对各段设置不同的配点个数，记为N_q+1，每段内配点记为τ_q，i，其中i＝0，1，…，N_q；q＝1，2，…，Q。；将各段内的状态变量距离s、车速v在LGL点离散化为式(14)：Then collocate and discretize equation (13): (Legendre pseudospectral method adopts LGL to collocate points, adding -1 and 1 to the root of the first-order derivative of the Legendre orthogonal polynomial, which is equivalent to the polynomial The root of , a total of N+1 collocation points. ) set different number of collocation points for each segment, denoted as N _q +1, collocation points within each segment are denoted as τ _{q, i} , where i=0, 1,..., N _q ; q=1, 2,..., Q . ; Discretize the state variable distance s and vehicle speed v in each segment at the LGL point into formula (14):

${\overset{\cdot &Center Dot;}{x x}}_{q q} (({τ τ}_{q q,, k k})) = = {Σ Σ}_{i i = = 00}^{{N N}_{q q}} {\overset{\cdot &Center Dot;}{L L}}_{q q,, i i} (({τ τ}_{q q,, k k})) {X x}_{q q,, i i} = = {Σ Σ}_{i i = = 00}^{{N N}_{q q}} {D D.}_{ki the ki}^{q q} {X x}_{q q,, i i} . . - - - - - - ((1919))$

${T T}_{ed ed} = = {T T}_{e e} ((11 - - {γ γ}_{d d} \frac{d d {w w}_{e e}}{dt dt})) = = {T T}_{e e} ((11 - - {γ γ}_{d d} {k k}_{w w} {i i}_{g g} \overset{\cdot \cdot}{v v})) - - - - - - ((21 twenty one))$

$\overset{\cdot \cdot}{s the s} = = v v,, - - - - - - ((22 twenty two))$

最后，对式(1)所示的目标函数进行转化(目标函数的积分项则可以通过数值积分进行逼近。加速过程总油耗为各段油耗的总和，积分项可通过Gauss-Lobatto积分方法计算)为式(26)：Finally, transform the objective function shown in formula (1) (the integral term of the objective function can be approximated by numerical integration. The total fuel consumption during the acceleration process is the sum of the fuel consumption of each section, and the integral term can be calculated by the Gauss-Lobatto integral method) For formula (26):

即经过以上拼接法分析，最优控制模型式(1)-(10)转化为以下形式：目标函数：That is, after the above splicing method analysis, the optimal control model formula (1)-(10) is transformed into the following form: Objective function:

服从以下约束：subject to the following constraints:

且满足式(27)-(29)：And satisfy formula (27)-(29):

T_q-T_q-1≥δ_t. (29)T _q -T _q-1 ≥δ _t . (29)

其中，k＝0，1，2，…，N。待优化变量为配点处的距离S_q，k、速度V_q，k、发动机输出力矩以及挡位的切换时刻T₁，T₂，…，T_Q；Wherein, k=0, 1, 2, . . . , N. The variables to be optimized are the distance S _{q, k} at the distribution point, the speed V _{q, k} , and the engine output torque And the switching time T ₁ , T ₂ ,..., T _Q of gears;

求解式(24)-(29)得到优化的车辆节能加速方式(本发明求解方法本质上是一个高维稀疏非线性规划问题，待优化变量个数为Q+3∑_q(N_q+1)。该类问题的求解已较成熟，可以进行精确求解。)。Solve equations (24)-(29) to obtain the optimized vehicle energy-saving acceleration mode (the solution method of the present invention is a high-dimensional sparse nonlinear programming problem in essence, and the number of variables to be optimized is Q+3∑ _q (N _q +1) The solution to this type of problem is relatively mature and can be solved accurately.).

Claims

1. A method for optimizing a vehicle energy-saving acceleration mode based on a pseudo-spectral method is used for optimizing an MT type vehicle acceleration process, and is characterized by comprising the following steps:

1) the objective function for constructing the integer optimal control model is shown as formula (1):

in the formula: j is equivalent oil consumption, k_sIs a distance correction factor, s_fFor the acceleration distance, t_fTo accelerate the end time, T_eIs the engine torque, w_eIs the rotational speed of the engine and,the instantaneous fuel injection rate of the engine;

2) constructing a plurality of constraint conditions of the optimal control model:

the constraint of the relation between the vehicle running distance and the speed is shown as the following formula (2):

\overset{\cdot}{s} = v - - - (2)

in formula (2): s is the vehicle running distance, the small point above s is a derivation symbol, and v is the vehicle running speed;

the vehicle travel speed constraint is as shown in equation (3):

\overset{\cdot}{v} = \frac{i_{0} η_{T}}{δ_{i_{g}} {Mr}_{w}} i_{g} T_{e d} - \frac{k_{a} v^{2} + k_{f}}{δ_{i_{g}} M} - - - (3)

in formula (3): i.e. i₀Is a main reduction ratio i_gTo the transmission ratio, r_wIs the wheel radius, η_TIn order to provide the overall efficiency of the drive train,_igat a speed ratio of i_gThe coefficient of rotational mass of the time, M being the mass of the entire vehicle, T_edFor dynamic effective output torque, k, of the engine_fAs rolling resistance, k_aIs the wind resistance coefficient;

and (3) restricting the dynamic effective output torque of the engine as shown in the formula (4):

T_{e d} = T_{e} (1 - γ_{d} \frac{{dw}_{e}}{d t}) - - - (4)

in the formula: gamma ray_dFor dynamic correction factor, take gamma_d＝0.003s²/rad；

The engine speed constraint is as shown in equations (5) - (7):

w_e＝k_wvi_g(5)

k_{w} = 60 \times \frac{v}{2 {πr}_{w}} i_{g} i_{0} - - - (6)

in the formula:is v is_ecoFuel injection rate of lower engine, v_ecoThe speed corresponding to the lowest oil consumption of the vehicle running for hundreds of kilometers at constant speed; and satisfy formulae (8) to (10):

w_emin≤w_e≤w_emax(8)

0<T≤T_max(w_e) (9)

i_g∈{i_g1,i_g2,i_g3,i_g4,i_g5} (10)

the state variables of the constraint are distance s and speed v, and are marked as x ═ s, v]^TThe controlled variable being the engine torque T_eSpeed ratio i of the transmission_gAnd is recorded as [ T ═ u ═ T_e,i_g]^T；

3) Based on an optimal control model formed by accurately solving the formulas (1) - (10) by a pseudo-spectrum method, the switching time T of the gears is solved₁,T₂,…,T_QAnd engine torqueThe method specifically comprises the following steps:

31) converting the integer optimal control model into a multi-section smooth model:

definition of i_gv,minAnd i_gv,maxRepresenting the lowest and highest gears to which the speed v can correspond, the acceleration start gear is first determined:

setting the acceleration starting gear as i_gsThe acceleration stop gear is i_geIn which the acceleration starting gear i_gsSuch as (11)

Formula (11) represents: when the gear can not be shifted, the initial gear i_gsOriginal gear i as starting time_g(t₀) (ii) a When the gear can be shifted, the initial gear is the lowest gear corresponding to the speed;

acceleration end gear i_geTaking the maximum gear i corresponding to the speed at the end of acceleration_gvf,max；

Determining the number of segments and segmentation points of the multi-segment smooth model: number of segments i_ge-i_gs+1 segment, denoted Q segment, there are Q-1 time segmentation points, denoted T₁,T₂,…,T_Q-1(ii) a Initial time t to be accelerated₀And accelerated end time t_fIs recorded as T₀And T_QWherein the time segmentation points satisfy the constraint T₀<T₁<…<T_QSetting the distance between any two time segmentation points to be larger than a set parameter_tI.e. by

T_q-T_q-1≥_t,q∈[1,Q]∩Z⁺(12)；

32) Solving the multi-section smooth model by adopting a Legendre pseudo-spectrum splicing method:

firstly, performing time domain conversion on a multi-segment smooth model: time domain [ T ] of each segment_q-1,T_q]Unified transformation into the Standard Interval [ -1,1 [ -1]As shown in equation (13), the interval used to define the Legendre orthogonal polynomial is consistent:

τ = \frac{2 t - (T_{q} + T_{q - 1})}{T_{q} - T_{q - 1}}, τ &Element; [- 1, 1] . - - - (13)

then, matching and discretizing the formula (13): setting different distribution point numbers for each section, and recording the number as N_q+1, the coordinate in each segment is denoted as τ_q,iWhere i is 0,1, …, N_q(ii) a Q ═ 1,2, …, Q; discretizing the state variable distance s and the vehicle speed v in each segment into a formula (14) at an LGL point:

X_{q} = [\begin{matrix} S_{q, 0} & S_{q, 1} & ... & S_{q, N_{q}} \\ V_{q, 0} & V_{q, 1} & ... & V_{q, N_{q}} \end{matrix}] - - - (14)

will control the variable engine torque T_eDiscretization into equation (15):

the state and control variables shown in equations (14) and (15), their dynamic curves x_q(τ) and u_q(τ) is approximated by a Lagrange interpolation polynomial as shown in equations (16) and (17):

x_{q} (τ) \approx Σ_{i = 0}^{N_{q}} L_{q, i} (τ) X_{q, i}; - - - (16)

u_{q} (τ) \approx Σ_{i = 0}^{N} L_{q, i} (τ) U_{q, i} . - - - (17)

wherein L is_q,i(τ) is the Lagrange interpolation basis function:

L_{q, i} (τ) = Π_{j = 0, j &NotEqual; i}^{N_{q}} \frac{τ - τ_{q, j}}{τ_{q, i} - τ_{q, j}} . - - - (18)

the differential operation on the state is converted into the differential operation on the interpolation basis function as shown in formula (19):

\overset{\cdot}{x_{q}} (τ_{q, k}) = Σ_{i = 0}^{N_{q}} {\overset{\cdot}{L}}_{q, i} (τ_{q, k}) X_{q, i} = Σ_{i = 0}^{N_{q}} D_{k i}^{q} X_{q, i} . - - - (19)

wherein k is 0,1,2, …, N, D^qThe differential matrix represents the differential value of each Lagrange basis function at each LGL node, as shown in equation (20):

for the constraint equations described in equations (2) - (7), the speed ratio i in each segment_gAs a constant, the differential to the engine speed translates to a differential to speed, i.e.:

T_{e d} = T_{e} (1 - γ_{d} \frac{{dw}_{e}}{d t}) = T_{e} (1 - γ_{d} k_{w} i_{g} \overset{\cdot}{v}) . - - - (21)

further simplifying and finishing the formulas (2) - (7) and (21) to obtain

\overset{\cdot}{s} = v, - - - (22)

\overset{\cdot}{v} = \frac{i_{g} i_{0} η_{T} T_{e} / r_{w} - k_{a} v^{2} - k_{f}}{δ_{i_{g}} M + i_{0} η_{T} γ_{d} k_{w} {i_{g}}^{2} T_{e} / r_{w}} . - - - (23)

Equations (22), (23) translate to the equality constraints at the collocation points:

Σ_{i = 0}^{N_{q}} D_{k i}^{q} S_{q, i} = \frac{T_{q} - T_{q - 1}}{2} V_{q, k}, - - - (24)

finally, the objective function shown in formula (1) is converted into formula (26):

wherein,is a discrete value of engine speed, and w is an integral weight defined as:

w_{q, i} = {&Integral;}_{- 1}^{1} L_{q, i} (τ) d τ = \frac{2}{N_{q} (N_{q} + 1) P_{N_{q}}^{2} (τ_{q, i})} .

that is, through the above splicing method, the optimal control model equations (1) to (10) are converted into the following forms:

an objective function:

subject to the following constraints:

Σ_{i = 0}^{N_{q}} D_{k i}^{q} S_{q, i} = \frac{T_{q} - T_{q - 1}}{2} V_{q, k}, - - - (24)

and satisfy formulae (27) to (29):

T_q-T_q-1≥_t. (29)

where k is 0,1,2, …, N. (ii) a The variable to be optimized is the distance S at the assembly point_q,kVelocity V_q,kEngine output torqueAnd the switching time T of the gear₁,T₂,…,T_Q；。