A method for optimizing energy efficiency of a vehicle based on a PnG mode

Abstract

The application discloses a kind of PnG mode-based automobile energy efficiency optimization method, it is related to automobile intelligent control technical field, in view of the problem that existing automobile energy efficiency optimization method energy-saving effect is poor, the vehicle instantaneous fuel consumption model under PnG mode is established in the application, and the constraint condition of optimization problem is analyzed in detail.Proposed optimal energy efficiency operating speed optimization model carries out in-depth study to the optimization control algorithm under PnG strategy, and finally proposes the optimization control model based on PnG strategy.Under PnG mode, the control method of the application can effectively optimize speed control in urban road scene, and can significantly improve the energy-saving effect of vehicle.The highest energy-saving rate of the technical scheme of the application can reach 39.4% compared with traditional control method.

Description

Technical Field

[0001] This invention relates to the field of automotive intelligent control technology, specifically to a method for optimizing automotive energy efficiency based on the PnG mode. Background Technology

[0002] Eco-driving, also known as energy-saving driving, refers to improving the energy efficiency of vehicles by optimizing driving strategies to reduce unnecessary fuel consumption and emissions.

[0003] Traditional eco-driving relies primarily on driver experience and awareness, achieving energy conservation and emission reduction through changes in driving style, selection of appropriate routes, and reasonable control of speed and acceleration. In recent years, with the rapid development of intelligent connected vehicles, the concept and technology of eco-driving have also been updated and developed.

[0004] PnG cooperative control strategies have been widely explored in recent years, especially in connected and automated vehicle (CAV) systems, where they have shown significant potential for energy savings. Research by Cao et al. indicates that in convoy following scenarios, PnG strategies achieve better fuel economy compared to constant-speed driving.

[0005] Due to the complexity of vehicle driving conditions on roads, existing research on PnG energy-saving mechanisms mostly uses simplified road conditions and vehicle dynamics models. These idealized assumptions differ significantly from actual road and traffic environments. For example, many theoretical studies are limited to straight roads and rarely consider road conditions with varying terrain, such as slopes. This leads to poor energy-saving performance of vehicles. Summary of the Invention

[0006] The purpose of this invention is to provide a vehicle energy efficiency optimization method based on the PnG model, addressing the problem of poor energy-saving performance of existing vehicle energy efficiency optimization methods.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] A vehicle energy efficiency optimization method based on PnG mode includes the following steps:

[0009] Step 1: Obtain the net wheel force F of the vehicle. w (t), wheel radius r w Transmission ratio i e,g and transmission system efficiency η t And based on the net force F of the wheel w (t), wheel radius r w Transmission ratio i e,g and transmission system efficiency η t The engine torque T is obtained.e (t);

[0010] Step 2: Obtain the vehicle speed v(t) and combine it with the wheel radius r. w and transmission ratio i e,g The rotational speed ω is obtained. e (t);

[0011] Step 3: Obtain the engine's minimum power P e,min and engine efficiency η e and will increase engine torque T e (t), rotational speed ω e (t), engine minimum power P e,min and engine efficiency η e Inputting the Willans model yields the power P generated by fuel consumption. f (t);

[0012] Step 4: Power P generated based on fuel consumption f (t), and combined with the operating mechanism of PnG mode, the energy consumption E of the vehicle's journey under PnG mode is obtained. PnG Model;

[0013] Step 5: Obtain the vehicle's net driving force F a (t), and the vehicle's net driving force F a (t), Engine torque T e (t), wheel radius r w Transmission system efficiency η t and transmission ratio i e,g Input the data into the Willans model to obtain the amount of fuel consumed per mileage traveled.

[0014] Step 6: Obtain the total fuel consumption J and trip end time t for the entire trip. f Initial velocity v of the journey i The speed v at the end of the journey f And travel distance s f And the amount of fuel consumed based on the mileage traveled. This serves as the objective function, thus constructing the optimal energy consumption control problem.

[0015] Step 7: Utilize the total fuel consumption J and the distance s of the entire trip f This yields the fuel consumption per unit distance.

[0016] Step 8: Based on fuel consumption per unit distance, and combined with the optimal energy consumption control problem, construct the unit energy consumption control problem, i.e., the PnG mode energy-saving optimal control problem;

[0017] Step 9: Solve the optimal energy-saving control problem of PnG mode to obtain the optimal speed and gear.

[0018] Furthermore, the net force F of the wheel w (t) is represented as:

[0019]

[0020] C0 = C rr mgcosθ+mgsinθ

[0021] C1 = 0

[0022]

[0023] Where C0, C1, and C2 are road load factors, C rr ρ is the rolling resistance coefficient, θ is the road slope angle, and ρ is the rolling resistance coefficient. a For air density, A c For the vehicle's frontal area, C D denoted as the air resistance coefficient, m as the sum of the vehicle's curb weight and the weight of passengers and cargo, and g as the acceleration due to gravity.

[0024] Furthermore, the engine torque T e (t) is represented as:

[0025]

[0026] Furthermore, the rotational speed ω e (t) is represented as:

[0027]

[0028] Furthermore, the power P f (t) is represented as:

[0029]

[0030] Where, k e,0 k e,1 k e,2 k e,3 k e,4 The correlation coefficient.

[0031] Furthermore, in the PnG mode, the energy consumption E during vehicle travel... PnG The model is represented as:

[0032]

[0033] Where n is the nth PnG segment, N is the total number of PnG segments, and t n,0 and t n,pngThe running time of the nth PnG segment starts from t n,0 to t n,png .

[0034] Furthermore, the amount of fuel consumed during the aforementioned driving mileage. Represented as:

[0035]

[0036] Among them, H f Because of the low calorific value of fuel oil, a p (t) represents the vehicle's driving acceleration.

[0037] Furthermore, the optimal energy consumption control problem is expressed as:

[0038]

[0039] Among them, a b (t) represents the braking acceleration, s(t) represents the distance traveled at time t, and s min (t) represents the minimum travel distance, s max (t) represents the maximum travel distance, a p,min (v(t), t) represents the minimum driving acceleration, a p,max (v(t),t) represents the maximum driving acceleration, a b,max For the maximum braking deceleration, v min (t,s(t)) represents the minimum instantaneous vehicle speed, v max (t,s(t)) represents the maximum instantaneous vehicle speed.

[0040] Furthermore, the optimal energy-saving control problem of the PnG mode is expressed as:

[0041]

[0042] Furthermore, the optimal speed and gear are expressed as follows:

[0043]

[0044] Among them, v c,opt To obtain the optimal instantaneous velocity, i e,c,opt To obtain the optimal transmission ratio, v is the instantaneous vehicle speed.

[0045] The beneficial effects of this invention are:

[0046] This application establishes a vehicle instantaneous fuel consumption model under PnG mode and analyzes the constraints of the optimization problem in detail. It proposes an optimal energy-efficient operating speed optimization model and conducts in-depth research on the optimization control algorithm under the PnG strategy, ultimately proposing an optimization control model based on the PnG strategy. Under PnG mode, the control method of this application can effectively optimize speed control in urban road scenarios, significantly improving the vehicle's energy-saving effect. Compared with traditional control methods, the technical solution of this application achieves a maximum energy saving rate of 39.4%. Attached Figure Description

[0047] Figure 1 This is a force diagram of a moving vehicle. Figure 2 This is a schematic diagram of the PnG mode; Figure 3 This is the engine speed versus output torque curve; Figure 4 The curve shows the engine speed versus fuel consumption. Figure 5 Fuel consumption per 100 kilometers includes idling fuel consumption; Figure 6 This refers to fuel consumption per 100 kilometers excluding idling fuel consumption; Figure 7 Fuel consumption per 100 kilometers includes idling fuel consumption; Figure 8 This refers to fuel consumption per 100 kilometers excluding idling fuel consumption; Figure 9 Fuel consumption per 100 kilometers includes idling fuel consumption; Figure 10 This refers to fuel consumption per 100 kilometers excluding idling fuel consumption; Figure 11 The fuel saving rate includes idling fuel consumption; Figure 12 This refers to the fuel saving rate excluding idling fuel consumption; Figure 13 The fuel saving rate includes idling fuel consumption; Figure 14 This refers to the fuel saving rate excluding idling fuel consumption; Figure 15 The fuel saving rate includes idling fuel consumption; Figure 16 This refers to the fuel saving rate excluding idling fuel consumption; Figure 17 Energy efficiency conversion (including idling fuel consumption); Figure 18 Energy efficiency conversion (excluding idling fuel consumption); Figure 19 PnG average speed and fuel consumption; Figure 20 The average speed and fuel saving rate of PnG; Figure 21 Engine efficiency under different average PnG speeds and different speed fluctuation amplitudes; Figure 22 Heatmap of Pearson correlation coefficient analysis for PnG model simulation test data; Figure 23 A heatmap of Spearman rank correlation coefficient analysis for PnG model simulation test data; Figure 24 This refers to the road slope curve; Figure 25 This is the optimal energy consumption operating speed curve. Detailed Implementation

[0048] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0049] Specific Implementation Method 1: This implementation method describes a vehicle energy efficiency optimization method based on the PnG mode. This application mainly studies the energy consumption during the longitudinal movement of the vehicle; therefore, it only considers the longitudinal dynamics of the vehicle. The force situation of the vehicle during longitudinal movement is as follows: Figure 1 As shown.

[0050] According to Newton's second law of motion:

[0051]

[0052] F a (t)=F p (t)-F res (t)-F b (t)

[0053] In equation (1), m t m is the total effective mass of the vehicle. t =m+m r Where m is the sum of the vehicle's curb weight and the weight of passengers and cargo, m r This refers to the effect of the inertia of rotating components (internal rotating components such as engines and transmissions) transmitted to the wheels. It usually changes with the transmission ratio, but this change is generally small and usually negligible.

[0054] F a (t) represents the net driving force of the vehicle, F p (t) represents the vehicle driving force (the sum of forces transmitted from the vehicle's power system to the wheel ends); F b (t) represents the braking force applied by the friction brake, F res (t) represents the vehicle's resistance. Because it affects F... res The factors affecting energy consumption (t) are numerous, but this paper focuses on the part that has the greatest impact on vehicle energy consumption during longitudinal movement. Therefore, the vehicle's driving resistance F res (t) can be expressed by equation (2):

[0055] F res (t)=F rol (t)+F gra (t)+F air (t) (2)

[0056] In equation (2), F rol (t) represents the rolling resistance, F gra (t) represents the slope resistance, F air (t) represents air resistance. It is also known that:

[0057] Rolling resistance:

[0058] F rol (t)=Crr mg cosθ (3)

[0059] Gradient resistance:

[0060] F gra (t)=mg sinθ (4)

[0061] Air resistance:

[0062]

[0063] In formulas (3) to (5), C rr ρ is the rolling resistance coefficient, θ is the road slope angle, R is the vehicle turning radius, and ρ a For air density, A c For the vehicle's frontal area, C D v is the air drag coefficient. w Let be the longitudinal wind speed. Substituting equations (3) to (5) into equation (2) yields equation (6):

[0064]

[0065] As can be seen from equation (6), the main factors affecting vehicle driving resistance include vehicle characteristics, road conditions, and weather conditions. For a given vehicle and distance, parameters such as vehicle mass, air resistance coefficient, and rolling resistance coefficient are usually considered fixed. However, under high-speed close-range following conditions, as the distance between vehicles decreases, C... D This will also change; this application assumes C D The value remains unchanged.

[0066] If we ignore the longitudinal wind speed v w (Wind speed when the vehicle is stationary), then equation (6) can be simplified to:

[0067]

[0068] To express it concisely and simplify calculations, F can usually be expressed as... res The constant term on the right side of (t) is processed as a whole, and assuming that the vehicle is traveling on a flat and windless road, it is expressed as a polynomial of the velocity function v(t). Then equation (7) can be expressed as:

[0069] F res (t)=C0+C1v(t)+C2v 2 (t) (8)

[0070] In the formula, C0, C1, and C2 are defined as road load coefficients, and it can be known that...

[0071] C0 = C rr mgcosθ+mgsinθ (9)

[0072] C1 = 0 (10)

[0073]

[0074] The core of the Willans model lies in defining two key parameters: efficiency η. e and minimum fuel power P e,min These two parameters are related to the engine speed ω. e It is relevant and can be used to describe the performance of an engine at different speeds.

[0075] (1) Efficiency η e The efficiency with which an engine converts fuel energy into mechanical work.

[0076] (2) Minimum fuel power P e,min The minimum fuel power consumed by an engine at idle or low load is used to overcome friction and other internal losses.

[0077] The Willans model considers the power P generated by fuel consumption as... f Expressed as engine torque T e and rotational speed ω e Functions:

[0078]

[0079] In equation (12), η e The efficiency of heat energy conversion due to the pressure generated by fuel combustion in the cylinder is related to engine speed ω. e (t) related functions, P e,min It is the minimum power required to maintain normal engine operation, and it is also related to ω. e (t) is related. 1 / η e and P e,min / η e Further parameterization as a function of engine speed yields...

[0080]

[0081] Substituting equations (13) and (14) into equation (12) yields the power output P from the fuel. f Closed expression:

[0082]

[0083] In the formula, k e,i (i = 0...4) are coefficients related to the design. For idling conditions, T can be set. e =0 and ω e (t)=ω e,idle ωe,idle Given the engine idle speed, equation (12) or equation (15) can also be used to calculate idle fuel consumption.

[0084] When the vehicle is idling or coasting, if the engine is shut off and fuel injection stops, let P... f When (t) = 0, the engine braking torque curve T can be obtained from equation (15). e,min (ω e (t)). Referring to the reasonable parameterization process of a naturally aspirated engine, the maximum torque curve T e,max (ω e (t) is a quadratic equation:

[0085]

[0086] In summary, the Willan's model is an effective tool for describing the relationship between internal combustion engine efficiency and engine operating point. It can help understand the variation patterns of engine efficiency, guide the optimization of engine operating point, and design fuel-efficient driving strategies.

[0087] Using the Willan's model to calculate the power output P of the fuel f The definition of vehicle energy consumption for vehicles with discrete gears is as follows:

[0088]

[0089] Assuming the engine consumes no fuel during coasting and braking, the engine braking power during coasting in gear is P. e,min The definition of vehicle braking force is P. e,min =F w (t)v(t) / η t Substituting into equation (16), we can obtain the engine braking energy as:

[0090]

[0091] By P e (t)=T e (t)ω e (t)=F w (t)v(t) / η t Converting engine torque and speed into wheel-end forces and vehicle speed, we can then calculate E. T Parameterized form:

[0092]

[0093] According to equations (1) and (8):

[0094]

[0095] We can also know the engine speed ω e (t) is related to the vehicle speed v(t):

[0096]

[0097] In the formula γ e,g Corresponding gear ratio, r w This is the rolling radius of the wheel.

[0098] Substituting equations (20) and (21) into equation (19) yields the actual energy consumption at different speeds:

[0099]

[0100] A typical PnG cycle consists of an acceleration phase P and a coasting phase G. Therefore, the vehicle energy consumption E in PnG mode can be determined. PnG It consists of two parts:

[0101] E PnG =E Pul +E Gli (twenty three)

[0102] In the formula E Pul and E Gli These are the energy consumption during the acceleration phase and the energy consumption during the coasting phase of PnG, respectively.

[0103] 1) Acceleration phase energy consumption E Pul

[0104] In PnG mode, the engine consumes fuel to generate traction during acceleration (P) and outputs it to the wheels. Therefore:

[0105]

[0106] 2) Energy consumption during taxiing phase E Gli

[0107] In the coasting phase G, if the vehicle enters engine braking mode, the energy consumption during the coasting phase can be determined as follows:

[0108]

[0109] In the formula η t For the efficiency of the transmission system, assuming no fuel is consumed during engine braking, let the power absorbed by the engine be P. e,min (In engine braking state), then:

[0110]

[0111] Substituting equation (24) into equation (23), we get:

[0112]

[0113] The preceding discussion focused on engine braking in segment G. Fuel consumption during coasting in other scenarios is as follows:

[0114] (1) If the transmission system is disconnected and the engine is idling, idling fuel consumption, E, will occur. Gli =E Idl ;

[0115] (2) If the transmission system is disconnected, for engines with coasting fuel cut-off function, then E Gli =0;

[0116] 3) Vehicle energy consumption E in PnG mode PnG

[0117] Substituting equations (24) and (27) into equation (21) yields the E value during the PnG coasting phase engine braking state. PnG for:

[0118]

[0119] For a vehicle operating in PnG mode, its speed curve consists of a series of PnG sawtooth waves, each sawtooth wave being a PnG segment (containing an acceleration segment P and a coasting segment G), such as... Figure 2 As shown.

[0120] set up Figure 2 The PnG mode process has N PnG sawtooth waves, where the running time of the nth PnG segment starts from t. n,0 to t n,png Its acceleration phase P starts from the lowest vehicle speed v min Start by rapidly accelerating to maximum speed v max The acceleration period is t p Then the gliding segment starts from the maximum speed v max Start gliding to v min The gliding time is t g Then a complete PnG segment is completed, let t png =t p +t g Define the velocity fluctuation amplitude of PnG as Δv (Δv = v max -v min ), Let be the average vehicle speed in PnG mode. Then, the fuel consumption for this PnG mode trip is:

[0121]

[0122] Combining equations (22) and (25), and introducing the Willanns model, we obtain the calculated E. PnG Preliminary parameterization form:

[0123]

[0124] The engine speed ω in equation (30) e (t) is converted to vehicle speed v(t) and substituted into equation (20) to replace F. w (t), and the final parameterized equation can be obtained:

[0125]

[0126] By organizing and analyzing the joint simulation results, it can be obtained that the vehicle's fuel consumption per 100 kilometers under different average PnG speeds and different speed fluctuation amplitudes is as follows: Figure 5 and Figure 6 As shown. For ease of explanation, three speed ranges are defined: low speed (30–60 km / h), medium speed (60–90 km / h), and high speed (90–120 km / h). A detailed analysis follows:

[0127] like Figure 5 As shown, for vehicles with the engine idling during coasting, in PnG mode, it was observed that when the vehicle speed varies from 30km / h to 120km / h, regardless of the speed fluctuation range, the fuel consumption curve per 100km exhibits a concave characteristic. Specifically, fuel consumption is relatively high at low and high speeds, while it is relatively low in the medium speed range. The trend of fuel consumption per 100km is consistent across different speed fluctuation ranges.

[0128] Furthermore, the trend shows that as the speed fluctuation amplitude increases in PnG mode, the fuel consumption per 100 kilometers decreases at the same average PnG speed. However, this trend of reduced fuel consumption gradually slows down as the speed fluctuation amplitude further increases. It can be observed that when the speed fluctuation amplitude reaches approximately 10 km / h, the fuel consumption curves begin to converge.

[0129] In the low-speed range, changes in speed fluctuations have a relatively small impact on fuel consumption per 100 kilometers, and the fuel consumption data under different fluctuation ranges are relatively similar and concentrated. Conversely, in the medium-to-high-speed range, under smaller speed fluctuation ranges (such as 4 km / h and 8 km / h), fuel consumption per 100 kilometers increases significantly with the increase of the average speed of PnG.

[0130] If we exclude the fuel consumption during the idling phase of PnG mode, we can obtain the vehicle's fuel consumption curves per 100 kilometers under different average PnG speeds and different speed fluctuation ranges, such as... Figure 6 As shown.

[0131] The curve trend in the graph clearly shows that, across low, medium, and high speeds, the vehicle's fuel consumption per 100 kilometers continuously increases with the average speed of PnG. Unlike the case including idling fuel consumption, no dip in the middle of the fuel consumption curve was observed, indicating that idling fuel consumption has a significant impact on overall fuel consumption in the low-to-medium speed range. Furthermore, the overall impact of speed fluctuation on fuel consumption per 100 kilometers is not significant; the difference is only noticeable at high speeds, especially when speed fluctuations are small (e.g., 2 km / h and 4 km / h). This finding further reveals the different impacts of idling fuel consumption on vehicle fuel economy across different speed ranges.

[0132] Figure 7 and Figure 8 This paper presents the vehicle's fuel consumption per 100 kilometers under different PnG speed fluctuation ranges and different average speed conditions, including and excluding idling fuel consumption. Through analysis... Figure 7 The data reveals the following trends:

[0133] (1) As the speed fluctuation amplitude of PnG increases, the fuel consumption per 100 kilometers of vehicles at each average speed generally shows a pattern of first decreasing and then stabilizing. Specifically, when idling fuel consumption is included, the impact on fuel consumption at low and medium speeds tends to be weak when the speed fluctuation amplitude exceeds 12 km / h. Conversely, when idling fuel consumption is not included, the impact of speed fluctuation amplitude on fuel consumption is further weakened. When the fluctuation amplitude reaches or exceeds 10 km / h, the impact on fuel consumption at all three speed ranges is not significant.

[0134] (2) Further comparative analysis of the curves in the two figures revealed that the curves including idling fuel consumption are denser than those without. This indicates that idling fuel consumption contributes significantly to fuel consumption per 100 kilometers at low and medium speeds, while its impact is relatively smaller at high speeds. The main reason for this phenomenon is that idling fuel consumption is relatively stable and less affected by fluctuations in vehicle speed. As vehicle speed increases, overall fuel consumption increases, thus relatively reducing the proportion of idling fuel consumption in total fuel consumption. Therefore, it can be concluded that the impact of idling fuel consumption on vehicle fuel economy varies significantly across different speed ranges.

[0135] Figure 9 and Figure 10 The surface analysis shown provides an intuitive perspective for understanding the overall impact of the average PnG speed and its fluctuation range on fuel consumption per 100 kilometers. In this figure, the upper part of each graph displays the surface representing fuel consumption per 100 kilometers, while the bottom plane is the projection of that surface, clearly showing how fuel consumption per 100 kilometers changes with variations in the average PnG speed and its fluctuation range. Figure 9 and Figure 10 The following overall trends can be observed:

[0136] (1) As the average vehicle speed increases, the fuel consumption per 100 kilometers also increases, a trend similar to that of the vehicle in non-PnG mode. Increased air resistance and engine load at high speeds are the main reasons for increased fuel consumption. This indicates that regardless of the driving mode used, high-speed driving results in higher fuel consumption.

[0137] (2) At low and medium speeds, the impact of speed fluctuations on fuel consumption per 100 kilometers is minimal, especially after eliminating idling fuel consumption. However, when speed fluctuations are small, fuel consumption per 100 kilometers increases significantly at high speeds. This phenomenon may be due to the vehicle frequently accelerating and decelerating under small speed fluctuations, which reduces fuel efficiency.

[0138] Therefore, the analysis results indicate that, in order to optimize fuel economy under PnG control mode, an appropriate speed range and suitable speed fluctuation range should be selected. An appropriate speed range ensures the vehicle operates within its efficient operating range, while a suitable speed fluctuation range helps reduce unnecessary acceleration and deceleration, thereby lowering overall fuel consumption.

[0139] In practical applications, PnG control strategies should take into account specific vehicle conditions, including engine efficiency, vehicle load, and road conditions, to determine the most economical speed range and speed fluctuation range. This approach can effectively improve vehicle fuel efficiency and reduce fuel consumption.

[0140] The fuel-saving curve is derived by comparing the fuel consumption per 100 kilometers under PnG mode with that under corresponding constant speed driving conditions. Figures 11 to 14 The fuel-saving rates under different average PnG speeds and different speed fluctuation ranges are shown. The following trends can be observed from the graphs:

[0141] As the average speed of PnG increases, regardless of whether the coasting segment includes idling fuel consumption, the overall fuel saving rate shows a significant downward trend (see...). Figure 11 and Figure 12 The fuel-saving rates in PnG mode dropped to -47.7% and -30.0% under both idling and non-idling conditions, respectively. This indicates that at higher speeds, the fuel-saving effect of PnG mode is not as significant as at lower speeds, and beyond a certain range, it may even further increase energy consumption.

[0142] At speeds below 60 km / h, fuel economy fluctuations are primarily influenced by gear selection. Some PnG average speed values ​​fall within the shift speed range, indicating that fuel economy is highly sensitive to gear selection at low to medium speeds, especially low speeds. At speeds above 60 km / h, the two sets of curves (including and excluding idle speed) exhibit essentially the same shape (see...). Figure 11 and Figure 12 This indicates that within this speed range, the impact of gear configuration on fuel efficiency is reduced.

[0143] When the average speed reaches 100 km / h, the fuel-saving curve shows a peak (see...). Figure 11 and Figure 12 The gear position has reached the highest gear in the high-speed range and has not changed. This should be related to the fact that the engine reaches its highest efficiency range at this speed.

[0144] As the amplitude of speed fluctuations increases, the fuel-saving rate shows an upward trend (see 13 and...). Figure 14 However, at high speeds, even small speed fluctuations can lead to additional fuel consumption, resulting in higher energy consumption than driving at a constant speed. This is likely due to the greater driving resistance at high speeds, making it difficult for the engine to reach its high-efficiency operating range with small speed fluctuations. Of course, this may also be related to the fact that discrete gear vehicles are not designed with more suitable gears at high speeds.

[0145] When the average speed and speed fluctuation range exceed a certain limit, the fuel saving rate becomes negative (see...). Figures 11 to 14 This means that the energy consumption of the vehicle in PnG mode is higher than that in the corresponding constant speed condition, and therefore it is no longer energy-saving.

[0146] Figure 15 and Figure 16 This demonstrates the combined impact of average vehicle speed and speed fluctuation on fuel consumption rate. The overall trend of the fuel-saving rate curve shows that:

[0147] At low to medium speeds, under different speed fluctuation ranges, there exists a relatively large operating range (the area above the zero reference plane) that allows vehicles to exhibit good fuel economy. This means that by appropriately controlling speed fluctuations when driving at low to medium speeds, good fuel economy can be achieved. Simultaneously, the fuel-saving rate decreases as the speed fluctuation range decreases, but the decrease is more significant at higher speeds. This indicates that, overall, the speed fluctuation range does not have a significant impact on the fuel-saving rate; simply exceeding a certain range (6-8 km / h at low to medium speeds) is sufficient to achieve a relatively ideal fuel-saving effect. This is mainly because at low to medium speeds, the engine has more fuel-saving potential to be tapped. By matching gear selection with the speed fluctuation range, it is easier for the engine to operate within its efficient operating range, and moderate speed fluctuations help to fully utilize this advantage.

[0148] At high speeds, the fuel-saving zone during coasting, including idling fuel consumption, is relatively small. This means that the presence of idling fuel consumption limits the ability of PnG mode to improve fuel efficiency during high-speed coasting. Compared to the case without idling fuel consumption, the increase in energy consumption in the non-fuel-saving zone (i.e., the area where fuel consumption is higher than under constant speed conditions) is greater when idling fuel consumption is included. This indicates that idling fuel consumption has a significant negative impact on fuel efficiency at high speeds. At high speeds, if idling fuel consumption is not considered, the area of ​​increased fuel consumption in PnG mode is relatively small, mainly occurring in the area of ​​higher vehicle speeds and lower speed fluctuations. This suggests that even without idling fuel consumption, PnG mode still has the potential to reduce fuel consumption at high speeds.

[0149] Figure 17 and Figure 18 The graph shows the combined impact of average vehicle speed and speed fluctuation on energy efficiency conversion (EPC). EPC is an important indicator that reflects the distance a vehicle can travel per unit of energy consumption, i.e., energy utilization efficiency. As can be seen from the graph, the overall trend of EPC is similar to the overall trend of fuel saving rate. This means that EPC can serve as an effective indicator for evaluating vehicle fuel economy under different driving modes.

[0150] Including idling fuel consumption, the energy efficiency conversion rate is relatively high in the low-to-medium speed range (e.g., Figure 17 As shown in the figure, the amplitude of speed fluctuation has a relatively small impact on the energy conversion efficiency, while its value decreases significantly in the high-speed and low-speed fluctuation ranges. Figure 18 As can be seen, for the case without idling fuel consumption, the change in energy efficiency with average speed is quite significant. This indicates that, without idling fuel consumption, the vehicle's average speed is a key factor affecting energy utilization efficiency. With increasing speed, the engine may need to consume more energy to overcome increased air resistance and other driving resistance. The energy efficiency is less affected by speed fluctuations.

[0151] The above analysis shows that when the speed fluctuation exceeds 6-8 km / h in the low-to-medium speed range, or exceeds 10-12 km / h in the high-speed range, increasing the speed fluctuation amplitude contributes very little to energy saving. Excessive speed fluctuation amplitude not only affects ride comfort but may also lead to traffic safety issues. Referring to relevant literature, an analysis of a typical operating condition with a speed fluctuation amplitude of 10% of the average speed of PnG yields the following results: Figure 19 and Figure 20 Two sets of curves.

[0152] Figure 19Data shows that when speed fluctuations remain within 10% of the average speed, fuel consumption per 100 kilometers gradually increases with the increase of the average speed under PnG conditions. Specifically, when the average speed exceeds the threshold of 100 km / h, fuel consumption under PnG conditions begins to be higher than that under constant speed conditions. This phenomenon is observed in... Figure 20 The text is presented visually.

[0153] The core mechanism by which PnG mode achieves energy savings lies in its ability to enable the engine to operate within its most efficient range. Figure 21 The engine efficiency distribution charts shown, displaying different average PnG speeds and speed fluctuation ranges, reveal that engine efficiency reaches its peak when the average PnG speed is around 100 km / h. Figure 21 The fundamental reason for the peak at the corresponding position in the fuel-saving rate curve is that although engine efficiency decreases slightly in the low-to-medium speed range, it remains at a relatively high level overall, which forms the basis for the significant fuel-saving effect of PnG mode. However, in a certain area of ​​the low-speed range (around 40 km / h) and in areas with small speed fluctuations, the engine's efficiency is relatively low. This phenomenon not only reveals that PnG mode still has untapped potential in terms of fuel saving, but also indicates that the experimental vehicle's design is more suitable for high-speed conditions. By optimizing the matching design of the engine and powertrain, the vehicle can be made more adaptable to the low-to-medium speed operating environment.

[0154] In summary, if the vehicle achieves zero fuel consumption during coasting, the overall fuel efficiency of PnG mode will be significantly improved at low and medium speeds. However, as vehicle speed increases, its fuel-saving effect gradually diminishes compared to constant-speed operation. Therefore, to maximize the fuel-saving potential of PnG mode, a strategy of disconnecting the drivetrain from the wheels should be adopted during coasting, ensuring that the engine stops consuming fuel during this period. Furthermore, regarding the magnitude of speed fluctuations, whether considering actual fuel efficiency, ride comfort, or safety, a larger fluctuation is not necessarily better; rather, an optimal balance must be sought under comprehensive constraints.

[0155] Energy consumption variations under PnG mode are influenced by a variety of factors, making it crucial to analyze which factors have a significant impact on fuel consumption. By analyzing a series of PnG operating state data from co-simulation, a correlation coefficient matrix is ​​used to evaluate the correlation between performance indicators and vehicle energy consumption under different driving conditions.

[0156] The Shapiro-Wilk normality test revealed that the experimental data did not conform to a normal distribution. Therefore, in addition to using the Pearson correlation coefficient matrix to assess the correlation, Spearman rank correlation coefficient matrix analysis was added.

[0157] After performing a logarithmic transformation on the experimental data that did not conform to a normal distribution, the processed data that conformed to a normal distribution were obtained. The Pearson correlation coefficient matrix was then plotted, as shown below. Figure 22 As shown in the diagram, the Pearson correlation coefficient matrix reveals that there are many factors affecting vehicle energy consumption in the PnG model.

[0158] The correlation coefficients between P-segment acceleration and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are -0.95, 0.9, and 0.95, respectively. A higher P-segment acceleration results in lower fuel consumption per 100 kilometers, a higher fuel saving rate, and a higher energy efficiency conversion rate. Higher P-segment acceleration means the engine has more opportunities to operate in its high-efficiency range. Furthermore, within a certain average speed range, compared to constant-speed operation, it achieves better fuel economy and a longer driving range with the same energy consumption.

[0159] The correlation coefficients between engine speed and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.89, -0.88, and -0.89, respectively. This means that the higher the engine speed, the higher the fuel consumption per 100 kilometers, and the lower the fuel saving rate and energy efficiency conversion rate. Higher engine speeds are usually accompanied by high loads, and the engine's higher efficiency range usually corresponds to a certain engine speed range. Excessively high engine speeds often mean that the engine is out of its high-efficiency operating range, resulting in increased fuel consumption.

[0160] The correlation coefficients between transmission gear and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.88, -0.80, and -0.88, respectively. Higher transmission gears result in higher fuel consumption per 100 kilometers, and lower fuel saving rate and energy efficiency conversion rate. The impact of increasing transmission gear on energy consumption is mainly reflected in the fact that as the gear increases, the average vehicle speed also increases, requiring the engine to output more power, thus leading to increased energy consumption. For a fixed average speed, increasing gear does have a certain energy-saving effect. Therefore, the increase in energy consumption due to increasing gear is more of a macroscopic observation of vehicle operation, corresponding to increased speed.

[0161] The correlation coefficients between the acceleration phase duration and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.99, -0.95, and -0.99, respectively. A higher acceleration phase duration corresponds to higher fuel consumption per 100 kilometers and lower fuel saving rate and energy efficiency conversion rate. The acceleration phase duration is related to P-segment acceleration; a larger acceleration phase duration means a smaller P-segment acceleration. A smaller P-segment acceleration means the vehicle spends more time in the low-speed and medium-speed range, and the engine is more likely to operate in a lower efficiency range, thus increasing energy consumption.

[0162] The correlation coefficients between transmission system efficiency and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.80, -0.71, and -0.80, respectively. Higher transmission system efficiency generally results in higher fuel consumption per 100 kilometers and lower fuel saving rate and energy efficiency conversion rate. Transmission system efficiency typically changes with the gear selection in the transmission, and its impact on energy consumption is consistent with gear selection, which usually implies higher vehicle speeds.

[0163] The correlation coefficients between average PnG speed and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.98, -0.92, and -0.98, respectively. A higher average PnG speed corresponds to higher fuel consumption per 100 kilometers and lower fuel saving rate and energy efficiency conversion rate. Consistent with the aforementioned points, increased average speed implies higher engine power output and higher driving resistance, thus leading to increased fuel consumption and lower fuel saving rate and energy efficiency conversion rate.

[0164] Analysis of the Pearson correlation coefficient matrix reveals that to reduce vehicle energy consumption, it is necessary to increase the P-segment acceleration, reduce the proportion of the vehicle's acceleration phase, select appropriate gears, and control engine speed to ensure it operates within its highest efficiency range. The above analysis also shows that there are cross-influences and interrelationships among the main influencing factors.

[0165] Spearman correlation coefficient focuses on ordinal relationships and is suitable for non-normally distributed or ordinal data. The generated rank correlation coefficient matrix is ​​as follows: Figure 23 As shown in the figure, the Spearman rank correlation coefficient matrix reveals that the following parameters have a significant impact on engine energy consumption.

[0166] The correlation coefficients between P-segment acceleration and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion are -0.95, 0.93, and 0.95, respectively. The greater the P-segment acceleration, the lower the fuel consumption per 100 kilometers, the higher the fuel saving rate, and the higher the energy efficiency conversion.

[0167] The correlation coefficients between engine speed and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.92, -0.91, and -0.92, respectively. This means that the higher the engine speed, the higher the fuel consumption per 100 kilometers, and the lower the fuel saving rate and energy efficiency conversion rate.

[0168] The correlation coefficients between transmission gear and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.89, -0.88, and -0.89, respectively. Higher transmission gears result in higher fuel consumption per 100 kilometers, but lower fuel saving rate and energy efficiency conversion rate.

[0169] The correlation coefficients between the proportion of acceleration time and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate were 1.00, -0.99, and -1.00, respectively. The higher the proportion of acceleration time, the higher the fuel consumption per 100 kilometers, and the lower the fuel saving rate and energy efficiency conversion rate.

[0170] The correlation coefficients between transmission system efficiency and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.80, -0.76, and -0.80, respectively. Higher transmission system efficiency leads to higher fuel consumption per 100 kilometers, and lower fuel saving rate and energy efficiency conversion rate.

[0171] The correlation coefficients between the average speed of PnG and fuel consumption per 100 kilometers, fuel saving rate, and energy efficiency conversion rate are 0.99, -0.98, and -0.99, respectively. The higher the average speed of PnG, the higher the fuel consumption per 100 kilometers, and the lower the fuel saving rate and energy efficiency conversion rate.

[0172] Comparing the results of the two correlation coefficient matrices, both revealed significant correlations between P-segment acceleration, engine speed, transmission gear, acceleration duration, transmission efficiency, average PnG speed, and fuel consumption. The difference lies in the slightly different correlation strengths between some variables in the Spearman correlation coefficient matrix and the Pearson correlation coefficient matrix. For example, the correlation between acceleration duration and fuel consumption is more pronounced in the Spearman correlation coefficient matrix.

[0173] The correlation analysis above revealed that the impact of speed fluctuation amplitude on engine energy consumption is relatively weak, with the highest correlation coefficient between it and fuel saving rate and energy efficiency conversion rate being only 0.15. This is consistent with the aforementioned joint simulation results, indicating that increasing the speed fluctuation amplitude is not ideal for reducing energy consumption.

[0174] This application first systematically analyzes the concept, classification, and energy-saving mechanism of the PnG strategy. Based on this, a vehicle dynamics model, a vehicle driving energy demand model, and a vehicle energy consumption model are established, and a vehicle fuel consumption model under the PnG mode is further constructed. To numerically solve for vehicle energy consumption, the Willanns model is introduced and elaborated in detail. Based on the Willanns model, a complete vehicle fuel consumption model and a vehicle energy consumption model under the PnG mode are established.

[0175] This application establishes a joint simulation platform using CarSim and MATLAB / Simulink. Based on this platform, the energy consumption of vehicles under different PnG average speeds and different speed fluctuation ranges was simulated, analyzed, and studied. Through analysis of the experimental data, the energy-saving effect of vehicles under different PnG average speeds and different speed fluctuation ranges was obtained. The impact of whether the vehicle consumes fuel in the G segment of PnG mode on the vehicle's energy consumption was analyzed. Furthermore, the correlation between various variables in the experimental data was analyzed, and the relevant factors affecting the energy-saving effect of PnG mode were identified.

[0176] Simulation results show that, compared with constant speed operation, PnG mode achieves significant fuel savings in the low-to-medium speed range. However, the fuel-saving effect gradually weakens as the average speed of PnG increases. Including idling fuel consumption, the energy consumption of PnG mode is higher than that of constant speed operation when the vehicle speed exceeds a certain level in the high-speed range. Except for small speed fluctuations, other speed fluctuations have little overall impact on the energy-saving effect of PnG mode.

[0177] For fuel consumption of gasoline-powered vehicles, the objective is to minimize the amount of fuel consumed by the vehicle over a certain distance under certain constraints. Therefore, J is defined as the total fuel consumption for the entire journey, which can be obtained from the fuel mass flow rate of the engine over a given time period.

[0178]

[0179] Where H f The fuel has a low calorific value. Substituting equation (15) into equation (33), and using the engine speed function ω... e (t) can be converted into the velocity function v(t), that is, by further substituting equation (21) into it, we can obtain:

[0180]

[0181] In the formula a p (t) represents the vehicle's traction acceleration, and a p (t)=F a (t) / m, to maximize energy saving, a fuel cutoff strategy is adopted, and the energy loss caused by restoring fuel supply is ignored, then:

[0182]

[0183] Equation (34) establishes the relationship between fuel consumption rate and speed and acceleration, that is, it establishes the relationship between fuel consumption rate and engine torque.

[0184] As can be seen from the formula, engine gear selection also has a significant impact on vehicle energy consumption. Therefore, the preset shift pattern of the selected transmission in CarSim is used for subsequent numerical calculations. The optimal energy consumption control problem is then:

[0185]

[0186] In the formula t f v is the trip end time. i v is the initial velocity of the journey. f The speed at the end of the journey, s f Let be the travel distance. By numerically solving for the minimum value of this integral, the vehicle speed curve corresponding to the lowest energy consumption during the vehicle's travel distance can be obtained.

[0187] Equation (35) contains many constraints on system state variables and control variables. The solution of the dynamic programming algorithm needs to be performed under these constraints. These constraints mainly include velocity constraints, acceleration constraints, torque constraints and distance constraints.

[0188] (1) Velocity constraint

[0189] Vehicles traveling on the road are subject to speed constraints in two aspects: one is the limitation of the vehicle's own performance, and the other is the speed limit of the road section in which the vehicle operates. For example, highways have minimum and maximum speed limits.

[0190] This application sets v i v is the vehicle speed at the start of the journey. f This refers to the vehicle speed at the end of the journey; typically, these two speeds are 0, with the minimum speed being v. min Maximum speed v max Let v(t) be the speed of the vehicle at any time during its journey. Then, for...

[0191] v min (t,s(t))≤v(t)≤v max (t,s(t)) (36)

[0192] (2) Acceleration constraints

[0193] Similar to speed constraints, acceleration constraints are also limited by the vehicle's own performance or the vehicle control mode. It is well known that vehicles accelerate well in power mode, but excessive acceleration leads to higher energy consumption and reduces passenger comfort; conversely, insufficient acceleration increases travel time. Therefore, it is necessary to comprehensively consider vehicle acceleration performance, comfort, and fuel economy. Define a p,min and a p,max Let be the minimum and maximum traction accelerations of the vehicle, respectively. Then, the acceleration 'a' at any given time is... p(t) needs to satisfy the following constraints:

[0194] a p,min (v(t),t)≤a p (t)≤a p,max (v(t),t) (37)

[0195] (3) Torque constraint

[0196] On the one hand, the characteristics of the engine dictate a limitation on its maximum output torque. On the other hand, during the solution process, the dynamic programming algorithm calculates the engine torque when transitioning from one state to the next. If this torque exceeds the maximum torque the engine can provide, the state transition cannot be completed. Let T... e,max For maximum engine torque, T e,min The minimum torque of the engine is the minimum torque required for the engine to maintain stable operation at the lowest possible speed.

[0197] (4) Distance constraints

[0198] The distance constraint is the mileage of one vehicle trip, where s(t) represents the trip distance. The maximum and minimum mileage can be set according to the needs of the study. Then s(t) needs to satisfy...

[0199] s min (t)≤s(t)≤s max (t) (38)

[0200] (5) Braking acceleration constraint

[0201] Braking acceleration constraints take into account both the vehicle's inherent characteristics and braking performance requirements, as well as considerations for ride comfort. However, in emergency braking situations, the vehicle's a b It should be less than or equal to the maximum braking deceleration a b,max For situations where braking is not required, or when the vehicle is coasting and there is no engine braking or energy recovery, the minimum braking deceleration can be 0. This will vary depending on the specific operating conditions of the vehicle. b (t) needs to satisfy

[0202] 0≤a b (t)≤a b,max (39)

[0203] Within a PnG segment, the vehicle's initial and final speeds are the same. For PnG control strategies employing different speed fluctuation amplitudes and different P-segment accelerations, their energy-saving effects can be measured by "fuel consumption per unit distance." Based on maximizing the energy-saving effect of the PnG strategy, the vehicle uses fuel cut-off during the coasting segment. Therefore, the optimal energy-saving control problem for the PnG strategy is:

[0204]

[0205]

[0206] The optimal energy consumption speed and the corresponding optimal gear are:

[0207]

[0208] To verify the previously constructed optimal energy consumption operating speed optimization algorithm, this application designed a comprehensive test condition including an incline, in which the vehicle traveled for a total of 1200m. The road conditions are described as follows:

[0209] (1) 0~200m: horizontal and straight road section; (2) 200~300m: downhill road section with a road gradient of 0.05; (3) 300~700m: horizontal and straight road section; (4) 700~900m: uphill road section with a road gradient of 0.05; (5) 900~1200m: horizontal and straight road section;

[0210] The vehicle's initial speed is 0 km / h, its final speed is 0, and its acceleration range is -3 to 3 m / s². The speed range is 0 to 100 km / h. The road gradient curve is shown in the figure, and the optimized energy-efficient operating speed curve is shown in the figure. Figure 24 and Figure 25 As shown.

[0211] from Figure 25 As can be seen, vehicle speed adjusts with changes in road gradient, indicating that variations in road load significantly impact the vehicle's optimal fuel-efficient operating speed. Based on a navigation map with road gradient information, a corresponding optimal fuel-efficient operating speed curve can be planned, and the optimized speed can serve as the target speed for ACC cruise control. The average speed in the example was 35.2 km / h. Compared to the corresponding constant-speed driving condition, fuel efficiency improved by 11.6%.

[0212] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A method for optimizing vehicle energy efficiency based on PnG mode, characterized in that... Includes the following steps: Step 1: Obtain the net wheel force F of the vehicle. w (t), wheel radius r w Transmission ratio i e,g and transmission system efficiency η t And based on the net force F of the wheel w (t), wheel radius r w Transmission ratio i e,g and transmission system efficiency η t The engine torque T is obtained. e (t); Step 2: Obtain the vehicle speed v(t) and combine it with the wheel radius r. w and transmission ratio i e,g The rotational speed ω is obtained. e (t); Step 3: Obtain the engine's minimum power P e,min and engine efficiency η e and will increase engine torque T e (t), rotational speed ω e (t), engine minimum power P e,min and engine efficiency η e Inputting the Willans model yields the power P generated by fuel consumption. f (t); Step 4: Power P generated based on fuel consumption f (t), and combined with the operating mechanism of PnG mode, the energy consumption E of the vehicle's journey under PnG mode is obtained. PnG Model; Step 5: Obtain the vehicle's net driving force F a (t), and the vehicle's net driving force F a (t), Engine torque T e (t), wheel radius r w Transmission system efficiency η t and transmission ratio i e,g Input the data into the Willans model to obtain the amount of fuel consumed per mileage traveled. Step 6: Obtain the total fuel consumption J and trip end time t for the entire trip. f Initial velocity v of the journey i The speed v at the end of the journey f And travel distance s f And the amount of fuel consumed based on the mileage traveled. This serves as the objective function, thus constructing the optimal energy consumption control problem. Step 7: Utilize the total fuel consumption J and the distance s of the entire trip f This yields the fuel consumption per unit distance. Step 8: Based on fuel consumption per unit distance and combined with the optimal energy consumption control problem, construct the unit energy consumption control problem, namely the PnG mode energy-saving optimal control problem; Step 9: Solve the optimal energy-saving control problem of PnG mode to obtain the optimal speed and gear.

2. The vehicle energy efficiency optimization method based on PnG mode according to claim 1, characterized in that... The wheel net force F w (t) is represented as: C0=C rr mgcosθ+mgsinθ C1＝0 Where C0, C1, and C2 are road load factors, C rr ρ is the rolling resistance coefficient, θ is the road slope angle, and ρ is the rolling resistance coefficient. a For air density, A c For the vehicle's frontal area, C D denoted as the air resistance coefficient, m as the sum of the vehicle's curb weight and the weight of passengers and cargo, and g as the acceleration due to gravity.

3. The vehicle energy efficiency optimization method based on PnG mode according to claim 2, characterized in that... The engine torque T e (t) is represented as:

4. The vehicle energy efficiency optimization method based on PnG mode according to claim 3, characterized in that... The rotational speed ω e (t) is represented as:

5. The vehicle energy efficiency optimization method based on PnG mode according to claim 4, characterized in that... The power P f (t) is represented as: Where, k e,0 k e,1 k e,2 k e,3 k e,4 The correlation coefficient.

6. The vehicle energy efficiency optimization method based on PnG mode according to claim 5, characterized in that... In the PnG mode, the energy consumption E during the vehicle's journey PnG The model is represented as: Where n is the nth PnG segment, N is the total number of PnG segments, and t n,0 and t n,png The running time of the nth PnG segment starts from t n,0 to t n,png .

7. The vehicle energy efficiency optimization method based on PnG mode according to claim 6, characterized in that... The amount of fuel consumed for the stated driving distance Represented as: Among them, H f Because of the low calorific value of fuel oil, a p (t) represents the vehicle's driving acceleration.

8. The vehicle energy efficiency optimization method based on PnG mode according to claim 7, characterized in that... The optimal energy consumption control problem is expressed as: Among them, a b (t) represents the braking acceleration, s(t) represents the distance traveled at time t, and s min (t) represents the minimum travel distance, s max (t) represents the maximum travel distance, a p,min (v(t), t) represents the minimum driving acceleration, a p,max (v(t),t) represents the maximum driving acceleration, a b,max For the maximum braking deceleration, v min (t,s(t)) represents the minimum instantaneous vehicle speed, v max (t,s(t)) represents the maximum instantaneous vehicle speed.

9. A vehicle energy efficiency optimization method based on PnG mode according to claim 8, characterized in that... The optimal energy-saving control problem of the PnG mode is expressed as:

10. A vehicle energy efficiency optimization method based on PnG mode according to claim 9, characterized in that... The optimal speed and gear are expressed as follows: Among them, v c,opt To obtain the optimal instantaneous velocity, i e,c,opt To obtain the optimal transmission ratio, v is the instantaneous vehicle speed.

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