Simulation Study on Hydraulic Braking Control of Engine Motor of Hybrid Electric Vehicle

With the development of society, oil resources are gradually decreasing, and it is urgent to protect the ecological environment. Studying new energy vehicles is an effective way to reduce oil consumption. New energy vehicles are mainly divided into two categories: electric vehicles and hybrid vehicles [1]: electric vehicles are limited in their development because of their shortcomings such as short cruising range, long charging time, and insufficient power; However, in the braking process or deceleration process [2], the mechanical energy is converted into electrical energy and stored. In the starting or low-speed driving process, the electrical energy can be used to drive the car, and in the climbing or high-speed driving, the engine starts to work, thus driving the car. Therefore, compared with electric vehicles, hybrid vehicles can make up for the shortcomings of electric vehicles [3], which is of great significance for the development of new energy vehicle technology. The braking performance of hybrid electric vehicle directly affects the safety and energy recovery rate in the braking process [4], and the change of braking intensity will lead to a change in the distribution of electric braking force and hydraulic braking force [5], and their dynamic response characteristics are inconsistent. Therefore, the correct establishment of a braking control model is the key to realize the control method and dynamic performance optimization.

Aiming at the braking control method of hybrid electric vehicle, many scholars and related experts have studied this problem. For example, the hybrid braking control allocation method considering the dynamic behavior of the battery proposed by Lupberger et al. [6], under the given actuator constraints, the hybrid vehicle can optimize the braking performance and maximize the energy recovery. The complementary filter with an additional daisy chain is used to distribute the control between the hydraulic brake and the motor, and a model inversion method is described, which decouples the wheel speed control loop from the protection loop of modern battery management system and deduces the necessary battery limit at the same time. However, this method requires the hybrid electric vehicle system to have the boost function, which is not easy to realize. Vignati et al. [7] put forward the logic method of braking control for independently driven electric wheels. The purpose of the anti-lock braking control method is to avoid the situation of wheel locking, so as to reduce the parking distance and maintain the handling of the vehicle during braking. In the hybrid electric vehicle with independently driven wheels, each wheel has a motor, the wheels are braked by the motor, and the wheel dynamics are handled to avoid locking during braking. By estimating the longitudinal force exchange between tire and road, it is possible to estimate the motor torque. However, this method does not give enough consideration to the economy of hybrid electric vehicles and cannot make the economy of vehicles in the best state on the premise of ensuring safety. Eckert et al. [8] put forward a power distribution control method for electro-hydraulic hybrid electric vehicle, which optimizes the design variables of the whole hydraulic transmission system and electrical system. In the formulation of the optimization problem, a fuzzy logic controller is also setup, which outputs the start-stop state of the motor and the torque applied to the pump that pressurizes the accumulator, so as to adjust its membership function, rules and weights, realize the power braking distribution control of hybrid electric vehicle, optimize and maximize the mileage and battery life, and minimize it. However, this method is not stable enough to control the braking of hybrid electric vehicle, and it relies too much on the regulation of motor. Gaurkar et al. [9] put forward a braking method based on real-time wheel reference slip estimation and control. This method determines the road surface of hybrid electric vehicle when braking by implicitly tracking the traction limit, and takes wheel slip variance adjustment as a potential method of reference wheel slip estimation in wheel slip adjustment. The variance adjustment method uses the past wheel slip estimation to calculate the reference wheel slip. The change of wheel slip is adjusted at a set point, and the least square estimation method is used to solve the variance adjustment problem, and the reference slip dynamics is obtained. Based on the reference slip dynamics, a three-stage nested control system is proposed, and an anti-lock braking method composed of a brake controller, Wiki Structure Relation (WSR) algorithm, and reference slip estimation is generated. However, the response speed of engine torque control is slow.

Based on the shortcomings of the above methods, this article proposes a simulation study on hydraulic braking control of engine motor of hybrid electric vehicle. Hydraulic braking has the advantage of providing enough braking torque [10], but it has the disadvantages of long starting delay and inaccurate control; although motor braking has fast response speed and accurate control, its maximum braking torque is limited, and there are many factors affecting the maximum braking torque. The advantages of motor braking and hydraulic braking can just complement each other [11]. The motor and hydraulic brake are combined by combined control, the mechanical energy of the engine is converted into hydraulic energy through the generator, then the hydraulic energy is converted into braking force through the hydraulic system, and the current and voltage of the motor are controlled to control the braking strength and speed, so as to achieve the requirements of braking control intensity and accuracy, and to achieve faster deceleration and shorter braking distance, thus realizing the braking control of hybrid vehicles and making the braking of hybrid vehicles more stable.

Among them, M indicate the mass of the hybrid vehicle; g represents the acceleration of gravity; $Wf$ indicates the ground normal reaction force on the front axle; $Wr$ indicates the ground normal reaction force on the rear axle; $hg$ represents the height of the center of mass; L represents the wheelbase of a car; a represents the distance from the center of mass to the front axle; b represents the distance from the center of mass to the rear axle; z indicates the braking strength; and $zg=du/dt$⁠, indicating the speed of the hybrid vehicle.

Among them, $FXb$ represents the ground braking force; $Fbf$ indicates the front wheel braking force; $Fbr$ represents the braking force of the rear wheel; $Fφ$ indicates ground adhesion; G represents the vehicle power of the hybrid electric vehicle; and $ϕ$ represents the ground adhesion coefficient.

For hybrid electric vehicles, when the braking force is sufficient, the following three situations may occur during the braking process, namely:

1. The front wheel is locked and dragged first, and then, the rear wheel is locked and dragged.

2. The rear wheel is locked and dragged first, and then, the front wheel is locked and dragged.

3. The front and rear wheels are locked and dragged at the same time.

The result obtained is the distribution curve I of the braking force of the front and rear wheels when situation (3) is satisfied. This curve is the ideal distribution line of braking force for front and rear wheels, as shown in Fig. 1.

When the distribution point of the braking force of the front and rear axles is above the I curve, there will be a dangerous working condition that the rear wheels lock up first and drag and slip, so the distribution point of braking force should be controlled below the I curve.

Hybrid electric vehicles need to meet certain braking efficiency when braking [13] to ensure the stability of hybrid electric vehicles. Therefore, the United Nations Economic Commission for Europe has formulated the ECE R13 braking regulations, as shown in the ECE line in Fig. 1. The regulations clearly stipulate the braking force of the front and rear wheels of hybrid electric vehicles as follows.

To ensure the braking stability of hybrid electric vehicle [14], the distribution of braking force of front and rear axles of hybrid electric vehicle should be in the area formed by horizontal axis, ECE regulation line, f line and I line, as shown in the grid area in Fig. 1. Anti-lock braking system (ABS) is a necessary equipment in the braking process of hybrid electric vehicles. When the wheels are locked, ABS can control the wheel slip rate in a better area to avoid wheel locking.

The primary goal of the motor hydraulic braking control method of the hybrid electric vehicle engine is to improve the response characteristics of the braking system by taking advantage of the response speed and accuracy of the motor hydraulic braking, so that the sum of the braking torques provided by the motor and the hydraulic auxiliary brake can meet the required braking torque [15], so as to ensure the economy and safety of braking. According to the dynamics and ideal braking force distribution curve of hybrid electric vehicle in Sec. 2.1, combined with the common idea of motor hydraulic braking force distribution, the control method of motor hydraulic braking of hybrid electric vehicle engine is proposed. The overall structure is shown in Fig. 2, which is divided into three layers:

1. The management determines the braking intention through the pedal action of the driver of the hybrid electric vehicle and calculates the expected braking torque.

2. The control layer takes the economy and safety of the hybrid electric vehicle as the goal and obtains the target braking force distribution relationship through the real-time optimization braking force distribution method based on the logic gate limit. In the braking process of hybrid electric vehicle, with the change of braking torque and braking energy recovery capacity, the system enters different braking control modes, namely, economic braking control mode and safety braking control mode; because of the different dynamic response characteristics of motor hydraulic braking, there will be some fluctuations during compound braking, and there is a certain error between the actual braking intensity and the target braking intensity. Therefore, the braking intensity signal is corrected by the coordinated control method based on braking intensity correction, and finally, the control strategy instruction is transmitted to the executive layer through the vehicle controller.

3. The executive layer completes the motor hydraulic braking of the hybrid electric vehicle engine through the motor hydraulic composite braking system according to the instruction, and that actual brake force is returned to the control lay to realize the hydraulic braking cycle control of the motor of the hybrid electric vehicle engine.

Based on the idea of hierarchical control, the management determines the braking intention through the driver's pedal action, calculates the expected torque, and further obtains the target braking force distribution relationship according to the strategy formulated by the control layer. According to the actual motor torque signal fed back by the executive layer and the wheel cylinder pressure signal of the hydraulic braking system, the braking strength correction result is obtained through the coordinated control method based on braking strength correction, which acts on the motor hydraulic braking system of the executive layer to dynamically coordinate and control the braking force and regenerative braking force of the motor hydraulic braking system, so as to ensure the rapid, smooth, and timely transition of the state switching of each component.

Generally, there are two control methods [16] for the motor hydraulic braking system of the hybrid electric vehicle engine. For the serial control method, it coordinates regenerative braking and friction braking in real time, but it needs to install additional sensors and modify the structure of the braking system to accurately adjust the hydraulic braking force, which increases the complexity and cost of the system. The characteristic of parallel regenerative braking control strategy is that it is easy to realize, and it does not need to add any other hardware, but it increases the trend of front wheel locking.

The regenerative braking provided by the rear axle motor of the hybrid electric vehicle used in this article can just make up for the deficiency of the parallel control method, so the fixed distribution relationship between the hydraulic braking system and the braking force of the front and rear axles of the original traditional automobile hydraulic brake is maintained, and the requirements for hardware are reduced without fine adjustment of the braking force of the front and rear axles, and the braking safety is ensured on the basis of maximum braking energy recovery [17].

In the braking process of hybrid electric vehicle, according to the change of vehicle speed and braking demand at every moment, the speed ratio of continuously variable transmission (CVT) will adapt to the change of vehicle speed. In fact, the maximum regenerative braking force provided by front and rear axle motors changes in real time, ignoring the change of maximum braking intensity that the motors can meet. To make the best use of regenerative braking force, the control layer has formulated a braking force distribution control method based on real-time optimization of logic gate limits.

When point B is on the right side of the ideal I curve, the electric machine power can be fully utilized, and it can be fully recovered by motor braking when the braking intensity is small. The specific distribution method of braking force for hybrid electric vehicles is as follows

A variety of working modes are the unique characteristics of hybrid electric vehicles. Switching the corresponding working modes under different working conditions is conducive to improving fuel economy and reducing emissions. The disadvantage is that the switching of different braking modes in the braking process will cause dynamic problems between the motor and the hydraulic braking system, and the dynamic process control will be more complicated. The response characteristics of braking pressure are different, and sudden braking conditions may occur during the actual movement of hybrid electric vehicles, which will inevitably impact the whole vehicle. Therefore, by analyzing the characteristics of the coupling workspace, the coordinated control method of working parameters such as motor torque and brake system pressure is studied to minimize the impact.

Because the dynamic response characteristics of motor hydraulic braking are different [18], there will be some fluctuations during compound braking, and there is a certain error between the actual braking intensity and the target braking intensity, so the control layer corrects its braking intensity signal through hysteresis feedback control. When the actual braking strength range is $[z_reg−δ,z_reg+δ]$⁠, brake coordination does not work; when this range is exceeded, the correction value of $Δz$ is calculated according to the difference between the actual braking strength and the target braking strength. At the next moment, compensate the braking torque to meet the driver's demand.

The motor hydraulic braking system of the executive layer should follow the following principles in the process of braking control of hybrid electric vehicles:

1. Maximizing the use of the motor braking system.

2. Reducing the starting delay of the hydraulic braking system.

3. The motor braking system is used to compensate the deficiency of the control accuracy of the hydraulic braking system, so as to ensure the control accuracy of the whole vehicle.

In the braking process of hybrid electric vehicle [19], when the speed increases to a certain threshold, the controller will start the control model, actively keep the speed from increasing, and distribute and coordinate the total braking torque among the three braking systems according to the respective characteristics of the motor, engine and hydraulic braking system. Because the braking torque of the engine is only related to the vehicle speed and gear position, it is impossible to realize active control. When the three are braked at the same time, the torque distribution and dynamic coordination of the vehicle braking system mainly control the motor and hydraulic braking system.

Because hydraulic braking can provide enough stable braking torque, hydraulic braking system is widely adopted by various vehicles at present [20] and becomes the most effective braking mechanism. The shortcomings of hydraulic braking system are as follows: the energy of hydraulic braking is lost to the environment in the form of heat energy and cannot be recovered and long-term use under high power may cause braking safety problems due to thermal decay. To prevent thermal recession, the traditional vehicle braking assistance is limited to the low-speed of the vehicle, which has not been further studied and popularized in a wider range. Therefore, regardless of safety or economy, the hydraulic braking system can only be used as a backup braking system when the braking torque of other braking systems is insufficient or other braking systems fail.

Among them, $Tsum$ represents the total braking torque of the hybrid electric vehicle; $ΔV$ indicates the difference between the current vehicle speed and the target vehicle speed; $f(ΔV)$ represents the parameters of the controller; i represents the parameters of the controller; $Tm$ indicates the feedback value of motor braking torque; $Teng$ represents the engine braking torque; and $Thyd$ represents the feedback value of hydraulic braking torque.

Among them, $Tsum′$ represents the total torque of motor hydraulic braking.

Among them, $Thyd_on$ is a flag indicating that the hybrid electric vehicle enters the motor hydraulic braking (1 indicates entry, 0 indicates exit); h indicates the control coefficient for starting hydraulic braking; I indicates the control coefficient for exiting hydraulic braking; and $Teng_on$ indicates the braking state of the hybrid vehicle engine (1 indicates entry, 0 indicates exit).

Logic gate limit control, also known as two-position control, is a method to adjust the control variables by setting the threshold of sensitive variables closely related to the control target, and then according to the relationship between the actual measured values or indirectly calculated values and the threshold.

To verify the performance of the braking control method of hybrid electric vehicle, according to the basic parameters of a certain type of hybrid electric vehicle and the data of a section of highway in a city, several typical braking conditions are selected to build the control method model, and the simulation experiment is carried out to verify the effectiveness of the control strategy of hybrid electric vehicle. The basic parameters of hybrid electric vehicle and components are shown in Table 1.

AMESim simulation platform has a rich component library and can also build sub-models according to its own needs, which greatly reduces the difficulty and frequency of establishing mathematical models. Based on the actual physical structure, the components are established, and the complex mathematical models are visually represented by visual graphics, which is suitable for the modeling of this method. Simulink is a software package integrated in matlab, which has powerful calculation function and great advantages in control. To verify the braking characteristics of hybrid electric vehicle, the simulation will be carried out with Simulink-AMESim. Create a joint simulation interface on AMESim platform, call the S-function function in the corresponding matlab/Simulink, and set the step size and precision in the simulation process, so as to realize the motor hydraulic braking control joint system of hybrid electric vehicle.

To verify the effectiveness of the braking control method of hybrid electric vehicle proposed in this article, the hybrid electric vehicle is tested under three working conditions, and the test process and results are as follows.

When the initial speed of the hybrid electric vehicle is set at 60 km/h, when the braking intensity is less than 0.1, the regenerative braking can be completely realized by the motor for energy recovery, and the hydraulic braking system does not work. According to the brake allocation strategy formulated by this method, the obtained brake allocation is shown in Fig. 3.

It can be seen from Fig. 3 that the regenerative braking force was initially provided by the front and rear axle motors. With the decrease in vehicle speed during braking, the maximum regenerative braking force transmitted by the front axle motor increased continuously, and the rear axle motor gradually withdrew.

When the initial speed of the hybrid electric vehicle is 60 km/h and the braking strength is 0.3, the distribution of braking force is shown in Fig. 4(a), and the error of braking strength with or without control is shown in Fig. 4(b).

Due to the high initial vehicle speed, the maximum braking torque of the front and rear axle motors is small, which is not enough to provide the required braking force, so hydraulic braking intervention is needed. When the vehicle speed gradually decreases, the maximum regenerative braking force of the front and rear motors increases enough to provide the required braking force, and the hydraulic braking force gradually withdraws. As shown in Fig. 4(b), when there is no coordinated control strategy, the error between the actual braking strength and the target braking strength is large and will gradually increase with time, and the error will be significantly reduced and close to the target braking strength when the coordinated control strategy of this method is adopted.

When the initial speed of the hybrid electric vehicle is 60 km/h and the braking intensity is 0.6, the control result of this method is shown in Fig. 5.

As can be seen in Fig. 5, the target braking force distribution and actual braking force response of the braking system of the hybrid electric vehicle are quite different at the initial stage of braking. After the coordinated control of the method in this article, the motor and hydraulic braking system change smoothly when braking together, and the braking force fluctuation is not obvious, and the response speed of the process of increasing the electric braking force and decreasing the hydraulic braking force is faster.

To further verify the braking control effect of hybrid electric vehicle, the braking control results of this method are set when the initial regenerative accumulator pressure of hybrid electric vehicle is 14 MPa, the initial electro-hydraulic accumulator pressure is 10 MPa, and the initial braking speed of hybrid electric vehicle is 15 km/h, 25 km/h and 35 km/h, respectively. At the same time, when the initial braking speed of the hybrid vehicle is 15 km/h, the initial regenerative accumulator pressure is 14 MPa, and the initial electro-hydraulic accumulator pressure is 10 MPa, the braking control results of this method are 10%, 50%, and 100%, respectively. Collect the pressure curve of regenerative accumulator under various working conditions, as shown in Fig. 6.

It can be seen from Fig. 6 that the faster the initial braking speed of the hybrid vehicle is, the higher the pressure of the regenerative accumulator will be, and both will reach a stable value before 4 s; The greater the pedal dip range of hybrid electric vehicle, the lower the pressure of regenerative accumulator, and all of them reach a stable value before 3 s. It shows that the braking control of hybrid electric vehicle by this method makes the response speed of hybrid electric vehicle fast and the braking control performance is high.

To verify the application performance of the braking control method of hybrid electric vehicle, the energy recovery capacity of hybrid electric vehicle is set when the initial total braking energy is 600 kJ and the braking intensity is 0.09, 0.26, and 0.72, respectively. The hybrid braking control method considering the dynamic behavior of battery in literature [6], the braking control method of independently driven electric wheels in literature [7], the power system design of electro-hydraulic hybrid vehicle in literature [8], and the power distribution control method based on optimization and the control method based on real-time wheel reference slip in literature [9] are used as the comparison methods of this method to verify the braking energy recovery of the five methods under different braking intensities, as shown in Table 2.

From the analysis of Table 2, it can be seen that when the braking intensity is 0.09, all five methods consume a certain amount of energy. However, after the braking control of the hybrid electric vehicle is carried out by the method in Refs. [8,9], the regenerative braking energy of the hybrid electric vehicle is 390 kJ and 402 kJ, respectively, and the energy recovery rate is 65% and 67%, respectively, resulting in poor economic performance. The regenerative braking energy and energy recovery rate of hybrid electric vehicle are improved after the braking control by the methods in Refs. [6,7], but the energy recovery rate is still lower than 80%. However, the regenerative braking energy is 512 k and the energy recovery rate is 85%, which is 7% higher than that of the method in Ref. [7] and 20% higher than that of the method in Ref. [8]. Similarly, when the braking intensity is 0.26, the regenerative braking energy and energy recovery rate of this method are better than the other four methods. However, with the increase in braking intensity, the braking force of hybrid electric vehicle is provided by regenerative braking system and mechanical braking, so the advantage of recovering braking energy is not obvious. The maximum braking intensity is 0.35, so the energy recovery rate of the five methods is 0 when the braking intensity is 0.72. To sum up, after the braking control of hybrid electric vehicle is carried out by this method, the safety of hybrid electric vehicle is ensured and the economic performance is improved.

On the basis of analyzing the principles that should be followed in braking force distribution of hybrid electric vehicles, the overall configuration of hybrid electric vehicles is analyzed, and the reasonable distribution relationship between front and rear axle braking force and motor hydraulic braking force of hybrid electric vehicles is analyzed on the premise of meeting braking regulations. Through the control method of braking force distribution based on real-time optimization of threshold value, combined with the response change of motor hydraulic braking system when working together, the dynamic coordinated control of hybrid electric vehicle is carried out. The braking control of hybrid electric vehicle based on this method is simulated under various braking conditions. The results show that when the initial speed of hybrid electric vehicle is constant, the braking force can be distributed reasonably under different braking intensities, which makes the hybrid electric vehicle have faster reaction speed during braking and makes the braking switch more stable and safe, and the error between the braking control method based on this method and the actual braking force approaches zero. The faster the initial braking speed and the smaller the dip range of different pedals, the higher the regenerative accumulator pressure of hybrid electric vehicle during braking, which can reach the stable value of hybrid electric vehicle before 4 s and 3 s, respectively, so that the braking response speed of hybrid electric vehicle is rapid and the braking control performance is high; through the braking energy recovery of hybrid electric vehicles under different braking intensities, it can be seen that the braking control of hybrid electric vehicles based on this method can effectively improve the energy utilization rate of vehicles, achieve the best braking effect, and improve the control performance and economic performance of hybrid electric vehicles under the premise of ensuring braking stability.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.