Research on Composite Braking Control Strategy of Four-Wheel-Drive Electric Vehicles With Multiple Motors Based on Braking Energy Recovery Optimization

Four-wheel-drive system with multiple motors has been one of the important development trends of electric vehicles, which has an important impact on the regenerative braking of electric vehicles. Aiming at the configuration characteristics of a composite braking system for the four-wheel-drive electric vehicle with multiple motors, this paper proposed a novelty composite braking control strategy based on braking energy recovery optimization. Firstly, the characteristics and constraints of braking dynamics of four-wheel-drive electric vehicles with multiple motors were analyzed. Secondly, the composite braking control strategy to optimize braking energy recovery was developed. The control strategy mainly optimized the motor braking of the front and rear axle according to the braking energy recovery efficiency within the range of motor braking to maximize the recovery of braking energy. And the motor and hydraulic braking forces were concertedly distributed to improve braking stability. Finally, the semi-physical simulation platform is used to verify the composite braking control strategy under single braking conditions and CLTC-P cycle condition. The test results demonstrate that the composite braking control strategy proposed in this paper can effectively improve braking energy recovery and braking stability.


I. INTRODUCTION
Traditional fuel vehicles consume a large number of fossil fuels and have brought environmental pollution problems, thereby aggravating the global environmental crisis and energy crisis [1].Therefore, electric vehicles with the advantage of energy saving and emission reduction have become the development direction for many countries in recent years.Electric vehicles can use motor regenerative The associate editor coordinating the review of this manuscript and approving it for publication was Amin Mahmoudi .
braking to recover the braking energy to the energy storage device, which is mostly dissipated by the traditional mechanical brake into the air, thereby effectively improving the vehicle's energy efficiency [2].Therefore, the composite braking system composed of regenerative braking and mechanical braking has become the common configuration of most electric vehicles [3].Furthermore, the control strategy of composite braking can not only principally decide the recovered braking energy of regenerative braking, but also effectively affect the braking safety and stability of electric vehicles [4].Hence, the control strategy of composite braking has been becoming an important research focus of electric vehicles.So far, much research on composite braking control has been achieved.In general, composite braking control strategies can be divided into two categories: one is a parallel braking control strategy, and the other is a series braking control strategy [5].Among them, the parallel composite braking control strategy has a simple structure and low cost because it does not need to change the structure of the traditional mechanical braking system, so it has been applied to many electric vehicles as a mainstream technical solution in the early stage [6].However, as the braking energy recovery rate of the parallel braking control strategy is not high [7], the series braking system has gradually replaced the parallel braking control strategy with the development of pressure precise control technology in a hydraulic braking system, thereby being adopted by most electric vehicles [8].More specifically, the main advantage of series composite braking is that the braking energy recovery rate is drastically improved through increasing the proportion of regenerative braking is increased with the decoupling of regenerative braking force and mechanical braking force.Zijian Zhang developed a fuzzy control algorithm for the composite braking system, which took demand braking force, SOC, and velocity as input, and took motor regenerative braking force as output, thereby improving braking safety and energy recovery rate [9].Chakraborty D optimized the braking distance and braking comfort of the series braking system by using a multi-objective genetic algorithm with the goal of optimal braking deceleration [10].
As we all know, since the braking energy recovery only occurs on the driving wheels which connect the drive motor, the vehicle's driving form has an important influence on the braking energy recovery rate.In addition, as the braking force distribution of the front and rear axles will vary with the wheel load transfer changing, the all-wheel-drive electric vehicle has more advantages in braking energy recovery rate compared with the two-wheel-drive electric vehicle [11].Shoeib Heydari has shown that all-wheel-drive electric vehicles can recover 23% and 317% more braking energy than front-wheel-drive and rear-wheel-drive electric vehicles respectively [12].Accordingly, with the rapid development of electric drive system integration, four-wheeldrive architecture is gradually becoming an important trend in the development of medium/high-class electric vehicles.Therefore, by optimizing the regenerative braking control strategy, the braking energy recovery rate of four-wheeldrive electric vehicles can be significantly improved, and the braking economy of four-wheel-drive electric vehicles can be improved.Hongyu Zheng optimized the regenerative power state of four hub motors by reducing the participation of mechanical braking and improved the braking energy recovery rate under the premise of ensuring braking performance [13].Xianxu Bai studied the critical velocity of regenerative braking based on 14 typical urban driving cycles to maximize the use of braking energy [14].Regarding the impact of braking comfort for in-wheel motor-driven electric vehicles, Jin Xianjian proposed a µ-Synthesis Methodology and a robust finite frequency H ∞ control strategy for the inwheel motor-active suspension system, effectively improving vibration performance and ride comfort [15], [16].In addition, braking energy recovery is also related to driving conditions.For common urban working conditions, slight braking deceleration which can be satisfied by motor braking accounts for most braking conditions [17].Therefore, optimization of the motor braking in slight braking conditions will effectively improve the braking energy recovery efficiency.
For four-wheel-drive electric vehicles, there are two key issues to improve the braking energy recovery rate: one is braking force distribution between the front and rear axle; the second is the distribution of the motor braking force and the mechanical braking force for the front or rear axle.Particularly, factors such as demand braking intensity, velocity, motor regenerative braking characteristics, mechanical braking characteristics, road adhesion conditions, braking regulations, and so on affect braking energy recovery.It is necessary to concertedly distribute the braking force according to vehicle braking dynamics and characteristics of composite braking system to improve braking performance [18].Therefore, for four-wheel-drive electric vehicles with multiple motors, how to maximize the proportion and efficiency of motor braking is the key step in improving braking energy recovery.At present, regenerative braking of two-wheel-drive electric vehicles has been studied extensively, but there are few types of research on braking distribution and braking energy recovery of four-wheel-drive electric vehicles.So the advantages of motor braking in braking energy recovery of four-wheel-drive electric vehicles are not fully utilized.Therefore, according to the composite braking system characteristics of four-wheel-drive electric vehicles with multiple motors, this work mainly optimizes the motor braking torque distribution of front motors and rear motor to improve the efficiency of motor regenerative braking, thereby improving the braking energy recovery rate.The contributions of this work are summarized below: • Braking dynamics of the four-wheel-drive electric vehicle is analyzed based on characteristics of vehicle structure and drivetrain configuration with multiple motors.The analysis can fully consider the impact of different braking conditions and different braking components on braking energy recovery, therefore, it can help to fully exploit the braking energy recovery rate of four-wheel-drive electric vehicles.
• According to the characteristics of the electric vehicle with multiple motors, we propose an optimal braking force distribution strategy for motor braking state.The high-efficiency working area of motor braking is maximized by distributing the front and rear wheel braking torque, thereby effectively improving the braking energy recovery rate.
• Coordinated control strategy of electric-hydraulic hybrid braking is proposed based on the optimal braking force distribution curve, which can improve braking stability and braking safety while ensuring braking energy recovery.
110152 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The structure of this paper is as follows: Section II analyzes the vehicle braking dynamics according to the structural characteristics of a four-wheel-drive electric vehicle with multiple motors.Section III establishes the composite braking control strategy of the four-wheel-drive electric vehicle with multiple motors according to the vehicle braking dynamics characteristics.Particularly, the optimal braking force distribution based on the maximum instantaneous braking energy recovery under slight braking conditions is emphatically elaborated.Section IV, the composite braking control strategy under single braking conditions and CLTC-P cycle condition are verified by the semi-physical simulation platform.Section V, Conclusion.

II. BRAKING DYNAMICS ANALYSIS BASED ON CHARACTERISTICS OF THE FOUR-WHEEL-DRIVE ELECTRIC VEHICLE WITH MULTIPLE MOTORS A. STRUCTURE AND CHARACTERISTIC ANALYSIS OF ELECTRO-HYDRAULIC COMPOSITE BRAKING SYSTEM FOR FOUR-WHEEL-DRIVE ELECTRIC VEHICLE WITH MULTIPLE MOTORS
As shown in Figure 1, the composite braking system of the four-wheel-drive electric vehicle with multiple motors studied in this paper is composed of a hydraulic braking system and motor braking system of the front and rear axle motors.The specific parameters of the vehicle studied in this paper are shown in Table 1.The drive system is composed of dual motors on the front axle and a single motor on the rear axle.The composite braking system adopts the eBooster series braking system, which can switch motor braking and hydraulic braking forces, and adjust the front and rear axle hydraulic braking force through the pressure regulator to meet the distribution and adjustment of electro-hydraulic braking forces under different braking conditions.

B. VEHICLE BRAKING DYNAMICS ANALYSIS
Under the condition of ignoring the rolling resistance couple moment, air resistance, and inertial resistance couple moment generated by rotating mass deceleration, the braking forces on the horizontal road surface with the adhesion coefficient ϕ are shown in Figure 2.And the moments of the front and rear wheels can be obtained respectively [19]: where, F z1 and F z2 are the normal reaction forces of the ground to the front and rear wheels in N, respectively; G is vehicle gravity in N; a and b are the distances from the vehicle's mass center to the front and rear axles in m; L is wheelbase in m; h g is the height of mass center in m; du/dt is vehicle braking deceleration in m/s 2 .The braking intensity z b = du/dt/g, then formula (1) can be changed into [19]: The braking forces generated by the front and rear wheels are [19]: where, F bf and F br are front and rear wheel braking forces in N. It can be seen from Formulas (2) and (3) that, the ground vertical reaction force of the front and rear wheels during vehicle braking will change with the change of vehicle braking strength z b , which will change the braking force of the front and rear wheels.Therefore, when the vehicle brakes, the braking forces distribution of the front and the rear wheel will significantly affect the braking direction stability and the utilization of the adhesion conditions.Therefore, one of the key issues of vehicle braking control is how to reasonably distribute the front and rear wheel braking forces.
With different braking force distributions of front and rear wheels, the vehicle may produce three working conditions: the front wheel locked first, the rear wheel locked first, and the front and rear wheels locked at the same time.Among them, the working condition that the front and rear wheels are locked at the same time can ensure the braking directional stability and improve the utilization rate of the ground adhesion coefficient, so it is an ideal working condition [20].The corresponding front and rear axle braking force distribution curve is called the ''I curve'', as shown in the following formulas [21]: For different braking intensity, the utilization adhesion coefficients of the front and rear wheels are as follow: where, ϕ f is the adhesion coefficient of the front wheels, and ϕ r is the adhesion coefficient of the rear wheels.When the adhesion utilization coefficient of the front wheel or the rear wheel is closer to the braking intensity, the ground adhesion condition of this wheel is more fully utilized, and the corresponding braking force distribution is more reasonable.

C. ECE BRAKING REGULATIONS REQUIREMENTS
As shown in Figure 3, according to the ECE regulations, for various vehicles with adhesion coefficient ϕ = 0.2 ∼ 0.8, the required braking intensity is: In general, when the vehicle is in various loading states, the front axle utilization adhesion coefficient curve should be above the rear axle utilization adhesion coefficient curve.However, for the passenger car, when the braking strength is 0.3∼0.4 and the rear axle utilization adhesion coefficient curve does not exceed the straight line ϕ = z + 0.05, the rear axle utilization adhesion coefficient curve is allowed to be above the front axle utilization adhesion coefficient curve.Therefore, the limit constraint range of the front and rear axle braking force distribution should be fully taken into account.

D. MOTOR BRAKING CHARACTERISTICS
The motor is in the generator state when the motor braking, and the motor braking torque cannot exceed the maximum torque limited by the power generation at the current speed [22].The external characteristics of the motor braking torque can maintain constant torque below the base speed, and can maintain constant power in the range from the base speed to the maximum speed, which satisfies the following formula: where, T reg0 is the motor braking torque in N•m; P max is the maximum motor braking torque in N•m; P max is motor power in kW; n b is the motor base speed in r/min; n is the motor speed in r/min.When the motor speed is too low, the back electromotive force of the motor will decrease sharply.In order to maintain the required braking torque, the motor needs to be in the state of energy consumption braking, which will not recover energy but consume electric energy.Therefore, exiting motor braking at low speed will effectively reduce the consumption of electric energy and improve the vehicle economy [23].Therefore, in order to improve the recovered energy of motor braking at low speed, a low-speed threshold is often set as the exiting speed threshold of motor braking.When the motor speed is lower than the threshold, the motor braking will be withdrawn, so the motor braking torque needs to be corrected as follows: 110154 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
where, T reg is the revised motor regenerative braking torque in N•m; λ(n) is the correction factor related to motor speed, λ(n) =0 represents the coefficient when exiting motor braking, 0< λ(n) <1 is the transition coefficient to prevent fluctuations before motor braking exiting, and λ(n) =1 represents the normal coefficient of motor braking.

E. BATTERY CONSTRAINTS
The electric energy generated by the motor's regenerative braking is finally stored in the battery, so the maximum charging current, maximum charging power, and battery state of charge (SOC) will affect the efficiency of regenerative braking energy.Hence, in order to ensure braking stability and improve the braking recovery energy, the charging current and charging power during regenerative braking should be limited by the maximum charging current and maximum charging power, and the battery SOC threshold for regenerative braking should be set to avoid the adverse effects of overcharging on battery life [24].Therefore, the battery's constraints for regenerative braking are as follows: where, P bat and P batmax are regenerative braking charging power and battery maximum charging power respectively in kW; U OC is the open circuit voltage in V, which is the function of battery SOC; R is the battery internal resistance in ; I 0 is the maximum initial charging current at t =0 in A; σ is the attenuation coefficient; I reg and I regmax are regenerative braking charging current and battery maximum charging current in A, respectively.

III. COMPOSITE BRAKING CONTROL STRATEGY BASED ON BRAKING DYNAMIC CHARACTERISTICS OF THE FOUR-WHEEL-DRIVE ELECTRIC VEHICLE MULTIPLE MOTORS A. COMPOSITE BRAKING STRATEGY CONSIDERING INDIVIDUAL MOTOR BRAKING CAPACITY CONSTRAINTS
The command of brake control comes from the driver's manipulation of the braking pedal, and the braking pedal opening is then converted to the demand braking intensity and the demand braking torque.Therefore, the demand braking intensity and total demand braking torque have the following relationship with the brake pedal opening: where, T breq is the total demand braking torque in N•m; z req is the required braking intensity; α bp is the brake pedal opening in %.The total demand braking torque is provided by the front and the rear axle braking torque together, so: (11) For the four-wheel-drive electric vehicle with multiple motors studied in this paper, the braking force of the front and rear axles are both constituted by motor braking and hydraulic braking.However, when individual motor braking working, the braking torque generated at the wheel is: where, T regtotal is the total motor braking torque in Nm; T regf and T regr are the motor braking torques of the front and rear axles in Nm, respectively; i f and i r are the speed ratios of the front and rear main reducers, respectively; T reg_em1 is the braking torque of a single motor on the front axle in Nm; T reg_em0 is the braking torque of the rear axle motor in Nm.
It can be known from Equation ( 7) that the motor braking force is closely related to motor speed, and motor speed is determined by vehicle velocity, namely: where, v is the vehicle velocity in km/h; r is the wheel radius in m; i is the transmission ratio.By combining formulas ( 10) and ( 11), the maximum motor braking intensity z b_reg_max achieved only by motor braking is: According to Formula ( 14), it is calculated that the maximum braking intensity achieved by individual motor braking at the maximum velocity of 140 km/h is 0.11.In other words, individual motor braking can meet the requirements of braking intensity at various velocities when braking strength is less than 0.11.Therefore, 0.11 is finally selected as the switching threshold of individual motor braking, and the composite braking control strategy is made as follows: (1) When the required braking intensity z req ≤ 0.11, the braking demand under all working conditions can be met by individual motor braking, so the vehicle is in the motor braking state.This braking state is mainly aimed at the driver's light braking conditions, that is, when the driver lightly steps on the brake pedal to reduce speed or slowly stop, corresponding to a smaller braking intensity [25], [26].In this state, the main mission is to achieve optimal braking energy recovery.Hence, according to the instantaneous braking energy recovery power of the motor braking, the motor braking force distribution of the front and rear axle motor is optimized, and recovery energy will be effectively improved.
(2) When the required braking intensity 0.11 < z req ≤ 0.7, the individual motor braking cannot meet the braking demand, so the motor braking and hydraulic braking will work together.The vehicle is in the electro-hydraulic combined braking state.This braking state is mainly aimed at the driver's moderate braking conditions, that is, when the driver normally steps on the brake pedal to stop [25], [26].In this state, the front and rear wheel braking force distribution is carried out according to the I curve.In addition, in order to improve the braking energy recovery rate, the braking force of each axle is preferentially allocated to the motor braking, and the insufficient part is supplemented by hydraulic braking.
(3) When the required braking intensity z req > 0.7, the vehicle is in the emergency braking state, and only the hydraulic brake is retained with the motor braking exiting as the ABS is triggered.Emergency braking conditions refer to situations where, in the face of sudden danger, the driver quickly and forcefully steps on the brake pedal to perform an emergency stop, with a high braking intensity [25], [26].
(4) When the motor speed is less than the speed threshold, to avoid change from regenerative braking to energy consumption braking, the motor braking should stop working and hydraulic braking provides full braking torque.

B. OPTIMAL BRAKING FORCE DISTRIBUTION STRATEGY FOR MOTOR BRAKING STATE BASED ON MAXIMUM INSTANTANEOUS BRAKING ENERGY RECOVERY
In the motor braking state, the required braking force is all provided by the front or rear axle motor.Since the motor efficiency is different at different speeds and torques, the different ratios of the front and rear motor braking torque will also affect the braking energy recovery rate [27].Therefore, in the motor braking state, this paper takes the braking torque ratio of the front motors as the optimization variable, and the regenerative power of the motor braking as the objective function.Then a real-time optimization algorithm of braking force distribution is applied to obtain a maximum braking energy recovery under the constraints of ECE regulations, load, ground adhesion capability, and battery SOC.

1) REGENERATIVE BRAKING OPTIMIZATION FUNCTION BASED ON INSTANTANEOUS BRAKING ENERGY RECOVERY
In the motor braking state, both the front axle braking force and rear axle braking force are provided by the motor braking, so the total braking power is as follows: P reg = P reg_f + P reg_r (15) where, P reg is the total braking power of the motors in kW.
And for the front and rear motor braking power: where, P em1 and P em2 are the regenerative braking power of the left front motor and right front motor in the front axle respectively in kW; P em0 is the regenerative braking power of the rear motor in kW.Among them, where, ω em1 , ω em2 , ω em0 is the rotational speed of the front left motor, the front right motor, the rear motor after conver-sion to international standards in rad/s, namely: Among them, In the process of regenerative braking, the motors work in the generator state, so P em0, P em1, and P em2 are equivalent to the input power of the generator.The input power is equal to the sum of various loss power such as copper loss, iron loss, and mechanical loss, and the power is finally recovered to the battery.As the recovery braking energy is the energy recovered to the battery, the final recovery braking power is: P mreg_1 = P mreg_2 = P em1 − P em1_loss P mreg_0 = P em0 − P em0_loss (20) where, P mreg_1 and P mreg_2 are the regenerative braking power of the left front motor and the right front motor recovered to the battery respectively in kW; P mreg_0 is the braking power of the rear motor recovered to the battery in kW.In order to facilitate the control, the efficiency Map of motor braking is adopted to calculate the motor recovery braking power.Therefore, the braking power of each motor finally recovered to the battery is: where, η(T em1 , ω em1 ) is the efficiency of the front left motor at the specific speed ω em1 and the specific torque T em1 , η(T em0 , ω em0 ) is the efficiency of the rear motor at the specific speed ω em0 and the specific torque T em0 , and which are generally obtained through the motor calibration test.As the braking torque is all provided by the front and rear axle motor in the motor braking state, this work assumes κ to be the distribution ratio of the braking torque which is the front axle motor braking torque to the total required braking torque: where, κ is the braking torque distribution coefficient of the front wheels, and in essence, it represents the ratio of the braking force of the front axle motor to the total braking force under the motor braking state.Its value range is 0 ≤ κ ≤1, κ =1 means the front axle motors' individual braking mode, κ = 0 means the rear motor's individual braking mode, and 0 < κ <1 indicates all motors simultaneously braking mode.The total braking power recovered to the battery is: 110156 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
The formula ( 21) ∼ ( 22) is brought into the formula (23) to be stated as: P reg_bat (κ) is the total braking power of motors under κ in kW.According to Formula (24), it can be known that the demand torque T breq can be obtained by analyzing the opening of the brake pedal, the velocity v can be measured, and other parameters are constant.The braking energy recovered to the battery can finally be expressed as a function of the braking force distribution ratio κ.Moreover, by optimizing κ, the motor working points will move towards the high-efficiency area as much as possible, as a result, the instantaneous braking energy recovery power will be improved, thereby improving the vehicle economy.Based on the ideas above, in this paper, the front motor braking torque distribution coefficient κ is used as the optimization variable, and the objective function equation is set as Formula (24).

2) OPTIMIZATION CONSTRAINT a: MOTOR TORQUE CONSTRAINT
When optimizing the braking torque distribution, it should be ensured that the braking torque distributed to each motor does not exceed its maximum external characteristic curve limit of braking torque, otherwise, the motor will heat seriously and even be damaged, so the following constraints must be met: where, T em1_max (ω em1 ) is the maximum external characteristic braking torque of the front motor at the speed ω em1 in N•m; T em0_max (ω em0 ) is the maximum external characteristic braking torque of the rear motor at the speed ω em0 in N•m;

b: ECE Regulation
In the motor braking state, the adhesion utilization coefficient of the front and rear wheels can be obtained by Equation ( 5) and stated as: The power distribution of the front and rear motor should also be constrained by the ECE regulation, that is, the following equation needs to be satisfied: Therefore, the optimization model of instantaneous braking energy recovery power can be expressed as follows: In this optimization model, κ is the optimization variable, the equation where P reg_bat (κ) is the optimization cost function, and the five inequalities after S.t. are the constraint conditions.
The goal of this optimization model is to maximize the power recovered to the battery by optimizing the front axle braking force distribution coefficient κ under constraints such as the maximum braking torque of the front and rear motors, vehicle braking dynamics, and ECE regulations.In this process, the motor working points will move towards the high-efficiency area as much as possible by optimizing κ, thereby maximizing the power recovered to the battery and achieving the maximization of braking energy recovery.
Since the above optimization model is a convex optimization problem with inequality constraints, the Lagrangian Slack Variable Method is used to solve the optimization problem in this paper.Through the optimization above, the braking torque distribution ratio of the front motor corresponding to the optimal instantaneous braking energy recovery power under different velocities and different demand braking torques can be quickly obtained, and it is used as the reference torque distribution ratio.The braking torque distribution ratio can maximize the braking energy recovery and achieve optimal vehicle economy.

C. COORDINATED CONTROL STRATEGY OF ELECTRO-HYDRAULIC BRAKING FORCE BASED ON OPTIMAL BRAKING FORCE DISTRIBUTION CURVE
With the increase of demanded braking intensity or velocity, the demanded braking intensity will reach 0.11 < z req ≤ 0.7, the vehicle is in the electro-hydraulic combined braking state, and the motor braking and hydraulic braking will work together.In this state, to ensure braking stability, the front and rear axle braking torque is distributed according to the optimal braking force distribution curve (i.e.I curve) and can be calculated as follows.
     Meanwhile, the braking torque is jointly undertaken by the motor braking and the hydraulic braking, so where, T bf and T hr are the front and rear axle hydraulic braking torque in Nm respectively; T reg_f and T reg_r are the braking torque in Nm generated by the front and rear axle motors, respectively.
where, T em1 and T em2 are the braking torque generated by the left front motor and the right front motor on the front axle in Nm, respectively.T em0 is the braking torque of the rear axle motor in Nm; i f and i r are the transmission ratio of the front and rear axle, respectively; η f and η r are the transmission efficiency of the front and rear axle, respectively.
In the electro-hydraulic combined braking state, the required braking torque of each axle is preferentially assigned to the motor braking.That is, the motor braking with the maximum braking torque at the corresponding velocity to ensure the braking energy recovery, and the insufficient braking torque is supplemented by the hydraulic braking.In addition, in the electro-hydraulic combined braking state, the braking torque distribution of the front and rear wheels should also comply with ECE regulations, load, ground adhesion capability, battery SOC and other constraints.If not, the braking torque distribution should be adjusted accordingly.

IV. SEMI-PHYSICAL SIMULATION AND RESULTS ANALYSIS
In order to verify the composite braking control strategy proposed in this paper, a semi-physical simulation system shown in Figure 4 is established.In the semi-physical simulation system, the real-time verification forward simulation model including the vehicle, power system, and braking system is developed in MATLAB/ Simulink, then it is compiled and written into Speedgoat through the host computer.The Speedgoat real-time simulator simulates the controlled object and receives the torque command through CAN communication.The driver's operating system is simulated by the Logitech G29 pedal combination.Among them, the throttle pedal and brake pedal signals are collected and calibrated by the Joystick Input module in the Simulink software and transmitted to the vehicle controller through Kvaser.The vehicle controller has control algorithms such as driving and braking.Among them, the control model of the composite braking control strategy together with the driving control strategy is also developed in MATLAB/ Simulink primarily, then compiled and downloaded into the RapidECU through the rapid code generation technology.The control signal and vehicle status signal are transmitted between the real-time simulator and RapidECU with the composite braking control strategy by the CAN bus.In order to fully verify the effect of the composite braking control strategy, the single braking condition modes and the cycle condition mode are selected respectively.

A. SIMULATION RESULTS ANALYSIS OF THE SINGLE BRAKING MODE
In order to effectively verify the performance of the composite control strategy proposed in this paper under different braking conditions, this paper first selected a series of test conditions for single braking mode for simulation tests.In the single braking mode, the road conditions were selected as dry asphalt or concrete roads conditions and the vehicle loading situation was chosen as fully loaded.In addition, according to the ''GB21670-2008 Technical Requirements and Test Methods for Passenger Car Braking Systems'', the initial brake velocity was set as 50km/h in the semi-physical simulation system, and three braking conditions, such as light brake, middle brake, and emergency brake, were selected to operate in the single braking conditions.And velocity, braking torque, SOC, and recovery energy in every braking condition were analyzed respectively.
As shown in Figure 5, the braking time of light braking, middle braking, and emergency braking conditions is 27s, 4.8s, and 2.3s respectively.Figures 6 to Figure 8 respectively show the changes in motor braking torque and mechanical braking torque in every braking condition.In Figure 6, the demand braking torques are provided by electric braking of the front motors and rear motor at the outset.In addition, due to the composite braking optimization control strategy under the motor braking mode corresponding to the reference formula (28) proposed in this paper, the braking force of the front and rear axle motors has been allocated 110158 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.accordingly, effectively utilizing the different motor braking efficiencies under different speeds and load conditions to improve the recovery of braking energy.Subsequently, at 55 s in Figure 6 (a) and at 58s in Figure 6 (b), hydraulic braking is gradually added in front and rear axle braking, mainly because the fixed slope drops after the motor speed are lower than the threshold until the motor braking finally exits.Figure 6 (c) shows the proportion of front axle braking torque obtained by the braking energy optimization strategy in this paper under slight braking conditions.As can be seen from Figure 7, under the electro-hydraulic combined braking mode, the required braking torque of the front and rear axles is first allocated to the motor braking, and the part that is insufficient for motor braking is supplemented by the corresponding hydraulic braking.In this process, the proportion of motor braking and hydraulic braking the front axle is quite similar, while in the rear axle, due to the large transmission ratio and large motor torque, most of the braking force is provided by the motor.By comparing 6 and Figure 7, it can be seen that motor braking plays the most role under light braking condition in Figure 6, while the hydraulic braking undertakes a great part of front axle braking in Figure 7.In the emergency braking condition shown in Figure 8, the motor braking of the front and rear axles does not work, and the mechanical braking provides all the required braking torque.In this condition, braking is mainly to ensure safety and stability, so it no longer involves the optimization of the braking force of the front and rear axles.
As can be seen from Figure 9, Figure 10, and Table 2, under slight and middle braking conditions, battery SOC is increased, and the energy recovery rate of slight braking reaches 29%, much higher than that of middle braking.The main reason is that the motor braking optimization strategy adopted in this paper can optimize the regenerative braking torque in slight braking, so as to effectively improve the braking energy recovery rate, which is conducive to the improvement of vehicle economy.In the emergency braking condition, the motor braking exits to ensure braking safety, thereby braking energy recovery no longer working.In summary, the motor braking optimization control strategy proposed in this paper can be braking, and emergency braking, and can improve the braking energy recovery efficiency by effectively optimizing the motor braking distribution ratio of the front and rear motors during slight braking, thus improving the vehicle economy.

B. SIMULATION RESULTS AND ANALYSIS OF THE CYCLE CONDITION MODE
Since the vehicle driving process includes various states such as driving, coasting, braking, and parking, the braking energy  recovery performance obtained from a single braking cannot fully reflect the energy recovery effect of the vehicle in the entire cycle condition.Therefore, it is necessary to conduct cycle condition tests to fully test the vehicle braking  performance under various states.In the cycle condition mode, the road conditions were also selected as dry asphalt or concrete roads conditions and the vehicle loading situation was chosen as fully loaded.In order to verify the effect of the composite braking control strategy in the cycling condition, the CLTC-P for Chinese passenger cars was selected as the cycle condition, which included three velocities intervals of low velocity, medium velocity, and high velocity, which could 110160 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.fully and accurately reflect the driving characteristics of Chinese passenger cars.Moreover, in order to demonstrate the performance of the braking control strategy proposed in this paper, a commonly used composite braking force distribution strategy based on the brake pedal load signal as the control on electric vehicles is used as a compared strategy.This compared strategy mainly transmits the brake load signal of the brake pedal directly to the motor braking and hydraulic braking of the front and rear axles without any optimization process for braking force distribution.By comparing the performance obtained by this compared strategy with that of the strategy proposed in this paper, the effectiveness of our control strategy can be effectively verified.The results of the HIL test for CLTC-P are depicted in Figures.11-15.In these figures, the results were compared from velocity, braking torque, motor braking working point, SOC, and recovery energy, respectively.As shown in Figure 11, it can be concluded that the actual velocity can follow the desired velocity well in the whole CLTC-P, so the braking control strategy in this paper can better ensure the vehicle deceleration requirements.
Based on Figure 12, the changes of motor braking torque and hydraulic braking torque on the front and rear axle by using the composite braking control strategy proposed in this paper are analyzed.The displayed motor braking torque is the value multiplied by the speed ratio of the respective reducer.Hydraulic braking only plays a role in supplementing the lack of motor braking, and due to the braking load transfer, the front axle braking torque is generally larger than the rear axle braking torque.The front and rear axle motor braking torque   are dynamically distributed according to the control strategy in this paper with different braking requirements.Figure 13 compares the efficiency intervals of the braking working points of the front and rear motors under the two control strategies.As shown in Figure 13 (a), compared with the comparison strategy, the working points of the front motors adopted the proposed braking control strategy decrease in the low-efficiency region K1 where are low speed and low torque, while the working points in large braking torque and higher motor efficiency interval increase.Correspondingly, as can be seen in Figure 13 (b), the working points of the rear motor in the low-efficiency region K2 with low speed and low torque are also reduced by using the proposed braking control strategy.The main reason for these results is that the braking strategy proposed in this paper optimizes the distribution of the dynamic braking torque between the front and rear motors, making the overall braking efficiency of the motor move towards the high-efficiency range, which is conducive to the improvement of the braking energy recovery rate.
Combined with Figure 14 and Table 3, it can be seen that at the end of the cycle, the battery SOC using the composite braking control strategy in this paper is 0.87% higher than that with the compared braking control strategy.It can be calculated from Figure 15 that the braking energy recovered is 336kJ more than that with the compared braking control strategy, and the recovery rate of braking energy is increased by 3.2%.Therefore, the composite braking control strategy proposed in this paper can improve the energy recovery rate more effectively, and reduce energy consumption, thereby improving the vehicle economy.

V. CONCLUSION
Four-wheel-drive electric vehicles not only have excellent dynamic performance but also can improve the motor efficiency in driving and braking state by optimizing each motor load, so as to improve the vehicle energy utilization efficiency.In this paper, a composite braking control strategy based on the optimization of braking energy recovery is proposed for multi-motor four-drive electric vehicles.This strategy mainly applies to improve the motor regenerative braking recovery efficiency under slight braking, which accounts for the majority of urban road conditions.Consequently, the motors' energy utilization efficiency is improved by optimizing the distribution of regenerative braking torque of the front and rear axle motor under the premise of ensuring braking safety, and the vehicle's instantaneous braking recovery energy is improved, thus improving the vehicle economy.In addition, braking stability and braking energy recovery are ensured through the reasonable distribution of hydraulic braking and motor braking torque in middle braking, while only hydraulic braking is applied to ensure braking safety and stability in emergency braking.Afterwards, the semi-physical simulation is established and the results show that the proposed composite braking control strategy can effectively improve the braking energy recovery rate and the vehicle economy under both single braking conditions and CLTC-P cycle condition.
However, due to the limitations of test conditions and research time, the control strategy proposed in this paper has not been verified by road tests, hence its application on real vehicles more accurate control rulers and detailed control criteria.The future research focus is to deploy this composite braking control strategy on real vehicles and conduct road tests under various braking conditions.

FIGURE 1 .
FIGURE 1. Composite braking system structure of the four-wheel-drive electric vehicle with multiple motors.

FIGURE 2 .
FIGURE 2. Diagram of force analysis during braking.

FIGURE 3 .
FIGURE 3. Braking force distribution of ECE car.

FIGURE 6 .
FIGURE 6. Torque distribution in light braking condition.

FIGURE 7 .
FIGURE 7. Torque distribution in middle braking condition.

FIGURE 8 .
FIGURE 8. Torque distribution in emergency braking condition.

FIGURE 9 .
FIGURE 9. SOC comparison in single braking conditions.

FIGURE 10 .
FIGURE 10.Recovery energy in single braking conditions.

FIGURE 11 .
FIGURE 11.Desired velocity and actual velocity in CLTC-P.

FIGURE 12 .
FIGURE 12.Braking force of front and rear axle in CLTC-P.

FIGURE 13 .
FIGURE 13.Work of two control strategies in CLTC-P.

FIGURE 15 .
FIGURE 15.Comparison of recovery braking energy in CLTC-P.
SHIWEI XU (Member, IEEE) received the M.S. and Ph.D. degrees in vehicle engineering from Chang'an University, in 2013 and 2017, respectively.He is currently a Postdoctoral Researcher with the Beijing Institute of Technology.He is also an Associate Professor with the Xi'an University of Architecture and Technology.He has undertaken several scientific research projects, such as the National Natural Science Foundation of China and the Natural Science Foundation of Shaanxi Province.His research interests include the chassis system of intelligent electric vehicles and the composite braking technology of new energy vehicles.JUNQIU LI received the Ph.D. degree in vehicle engineering from the Beijing Institute of Technology, Beijing, China, in 2005.He is currently a Professor with the National Engineering Laboratory for Electric Vehicles, School of Mechanical Engineering, Beijing Institute of Technology.He directs the National Fund Project, the Defense Advance Research Fund, and the Beijing Municipal Education Commission Fund.He has developed electrical transmission synthetical controllers, power battery management systems, and heavy-duty vehicle electric wheel systems in application.He has been engaged in the research of electric vehicle transmission, energy management, and vehicle energy storage technologies.XIAOPENG ZHANG received the bachelor's degree in fluid transmission and control engineering from the Taiyuan University of Science and Technology, in 2002, and the M.S. degree in mechanical engineering from Xiangtan University, in 2009.He is currently a Senior Engineer with Jianglu Machinery and Electronics Group Company Ltd.His research interest includes transmission control systems for electric drive vehicles.JIAN SONG is currently pursuing the M.S. degree with the School of Mechanical Engineering, Beijing Institute of Technology.His research interest includes distributed electric drive vehicle control.XINYU ZENG is currently pursuing the M.S. degree with the School of Mechanical and Electrical Engineering, Xi'an University of Architecture and Technology.His research interest includes the composite braking technology of new energy vehicles.

TABLE 1 .
Vehicle parameters and performance index.

TABLE 2 .
Simulation results in single braking conditions.

TABLE 3 .
Performance comparison of different braking control strategies in CLTC-P.