Optimal Torque Distribution Strategy for Minimizing Energy Consumption of Four-wheel Independent Driven Electric Ground Vehicle

Journal of Applied Science and Engineering, Vol. 21, No. 3, pp. 375 384 (2018) DOI: 10.6180/jase.201809_21(3).0008 Optimal Torque Distribution Strategy for Minimizing Energy Consumption of Four-wheel Independent Driven Electric Ground Vehicle Zhao Tang, Xing Xu*, Xinwei Jiang, Haobin Jiang and Hongbing Zhao School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, P.R. China Abstract In order to improve the energy efficiency of a four-wheel independent driven ground vehicle, a vehicle model consisting of the vehicle dynamics model, in-wheel motor model and driver model is built in Matlab/Simulink and Carsim. The feasibility of the control allocation to distribute the total required torque to four in-wheel motors is analyzed and proved. Generally, motor rotation speed and torque have a great influence on the motor efficiency. Therefore, it is an effective method to improve the energy efficiency of vehicle by reasonably allocating the torque of the four in-wheel motors to make the motors work in high efficient regions. The total cost function of vehicle economy and motor torque mutation is constructed, then, the dynamic programming (DP) algorithm is adopted to obtain the optimized control instruction sequence of the motor torque. Simulation of the new control allocation algorithm is carried out on the federal test program (FTP) drive cycle and the urban new European driving cycle (NEDC). The results show that the energy consumption is significantly reduced with the proposed control allocation. Key Words: Electric Ground Vehicle, Four-wheel Independent Driven, Energy Efficiency Optimization, Dynamic Programming 1. Introduction Since the invention of vehicles, the internal combustion engine vehicles have always been the main choice for the manufacturers and consumers. However, in the last few years, with the increasing awareness of energy saving and environment protection, electric ground vehicle (EGV), as a clean, efficient and environmentally friendly mobility option, has drawn growing attention both from industrial and academic communities [1 5]. However, there are still some problems in electric ground vehicles, one is the short driving range caused by the low energy density of the power battery. Although electric ground vehicle is an emerging vehicle, it has many different types. Generally, according to *Corresponding author. E-mail: xuxing@ujs.edu.cn the vehicle driving patterns, pure electric ground vehicles could be classified into two categories: directly-driven electric vehicles and indirectly-driven electric vehicles. Compared with the indirectly-driven electric vehicles, the directly-driven vehicles have higher efficiency and control flexibility, because the directly-driven vehicles equipped with in-wheel motors can reduce energy losses and improve control flexibility by abandoning transmission and differential gears [6,7]. As a result, the directly-driven electric vehicles achieve more attention than the indirectly-driven electric vehicles. In contrasted to the indirectly-driven vehicles and the internal combustion engine vehicles, the directly-driven electric vehicles belong to the over-actuated system, whose number of actuators is greater than the degrees of freedom [8 11]. Due to the number of actuators is greater than the degrees of freedom, a variety of different alloca-

376 Zhao Tang et al. tion methods can be proposed to solve the actuator redundancy [12]. Therefore, the optimized torque distribution can be achieved on the directly-driven electric vehicles possibly with the same driving power requirement. At present, the research on torque control allocation is mainly focused on wheel slip control and lateral stability control. Kim proposed a fuzzy rule based control algorithm with a rear motor and electrohydraulic brake for the stability of four-wheel driven vehicle [13]. Zhao and Zhang adopted the sliding mode control and sequential quadratic programming control to achieve direct yaw moment and dynamic force distribution [14]. Chen and Kuo realized the optimal torque distribution of four in-wheel motors by using the control allocation strategy of electronic stability control [15]. However, there is a few literature studying torque control allocation for improving the energy efficiency of the four-wheel driven electric ground vehicles. Lu and Ouyang suggested that the average torque allocation to the four hub motors of the electric vehicle gave the best efficiency [16]. In this paper, a new optimal control torque allocation method considering torque mutation is introduced to save energy consumption of the four-wheel driven electric ground vehicles. In the section 2, the vehicle dynamics model, the motor model and the driver model are described. Then, the feasibility of the control allocation to distribute the total required torque to four in-wheel motors is analyzed and proved, the basic principles and methods of DP are reviewed, and the DP method is applied to torque control distribution in the section 3. In section 4, the application of new control allocation in co-simulation with Matlab/Simulink and Carsim is presented, and then the simulation results are shown. Finally, a conclusion is drawn in the section 5. 2. Vehicle Model The directly-driven electric ground vehicles with four in-wheel brushless motors can be seen as a control system with four agents: the vehicle controller works as a global coordinator; and the four in-wheel motors are controlled by four local inverters. Figure 1 shows the global-local structure of the vehicle. In addition, the global coordinator calculates total required torque of the vehicle, and then sends different torque commands to the inverters to control the four in-wheel motors. A four wheel motor driven electric vehicle model is built and the vehicle model contains vehicle dynamics model, in-wheel motor model and driver model. The vehicle dynamics model is built in Carsim, and the in-wheel motor model and driver model are built in Matlab/Simulink. The inwheel motor model gives the torque sign to the vehicle dynamics model. The vehicle dynamics model gives the vehicle speed sign to the driver model. The driver model sends motor sign to the in-wheel motor model. The main characteristics of the vehicle is given in Table 1. 2.1 Vehicle Dynamics Model In this paper, the vehicle dynamics model only concerns the longitudinal dynamics of the vehicle. The input of the model is motor driving torque, and the output is the vehicle speed. The driving force of the vehicle can be expressed as (1) where F t is the overall driving force, T i is the torque va- Figure 1. Global and local structure illustration of an EGV. Table 1. Main characteristics of the vehicle Parameters Value Curb weight m (kg) 710 Cross sectional area A (m 2 ) 0.87 Rolling friction coefficient C r 0.008 Aerodynamic drag coefficient C D 0.32 Rolling radium r (mm) 245 Rated power (kw) 3 Maximum torque (Nm) 150 Battery voltage (V) 72 Energy capacity (Ah) 140

Torque Distribution, Energy Consumption Optimization, Four-wheel Independent Driven Electric Vehicle lue of each drive motor, i = 1, 2, 3, 4, represents the front left wheel, the front right wheel, the rear left wheel and the rear right wheel respectively, r is the effective rolling radius. The overall resistance force of the vehicle is consisted of rolling resistance, air resistance, grade resistance and acceleration resistance. (2) where Fr is the overall resistance force, m is the vehicle mass, f is the rolling resistance coefficient, a is the angle of gradient, r is the air density, CD is the drag coefficient, A is the cross sectional area exposed to air flow, v is the velocity of the vehicle, d is the mass factor. When the vehicle is driving, the overall driving force should be equal to the overall resistance force. Ft = Fr is used to provide the electric energy to the motors. Figure 3 shows the efficiency map of the front in-wheel motors, while the efficiency map of the rear motors is depicted in Figure 4. As can be seen from Figure 3 and Figure 4, the motor efficiency is high in high speed and high torque regions. The maximum and minimum motor driving torque and rotational speeds can also be found. Furthermore, compared with the front motors, the rear motors have higher efficiency. According the motor efficiency built by experimental data, the input power of the motor can be easily calculated. (4) (3) Furthermore, the vehicle speed can be calculated from the formula above. 2.2 In-wheel Motor Model In this paper, the electric ground vehicle is equipped with two kinds of in-wheel motors, and both of them are permanent magnet brushless DC motors. The dynamics of the motors can be neglected, because the in-wheel motors have a fast and accurate response. The in-wheel motor models are built based on the efficiency map of the motors which is based on related experimental data. The data is derived from the motor characteristic test experimental which is carried on the motor characteristic test bench. The motor characteristic test bench is shown in Figure 2. Normally, the test bench mainly consists of motor, torque sensor, speed sensor and magnetic powder brake. Besides, a constant voltage power Figure 2. Motor characteristics test bench. 377 Figure 3. Efficiency map of the front motor. Figure 4. Efficiency map of the rear motor.

378 Zhao Tang et al. where P i is the motor input power. n i is the motor rotation speed, i is the efficiency of the motors, i =1,2,3, 4, represents the front left wheel, front right wheel, the rear left wheel and rear right wheel respectively. 2.3 Driver Model A driver model is built based on a PI controller to simulate the behavior of the driver when driving the vehicle. According to the input of the difference between target speed and actual speed, the PI controller makes the right control sign, then the driver manipulates the acceleration and brake pedal. The acceleration pedal sign is sent to the in-wheel motor model, and the brake pedal sign is sent to a simple breaking model. 3. Control Allocation Algorithm for Energy Efficiency Optimization When the drive cycle is provided, the total torque requirement can be achieved according to the vehicle dynamics model. Due to the efficiency of motors is determined by the motor output torque and rotation speed, a reasonable torque control allocation which changes the output torque of the motors could make the motors work in high efficient regions. For example, if the total torque requirement is small and can be met by two motors alone, the total torque should be offered by front motors or rear motors only, because in this condition the working motors are working at a higher overall efficiency. So, control allocation could improve the vehicle energy efficiency. With the advantages of obtaining a globally optimal solution as well as the strengths on handling nonlinear non-convex problem and constrains, dynamic programming is a powerful method to solve the general dynamic optimization problems [17,18]. The basis of the dynamic programming technique is the Bellman s principle of optimality. Generally, the main content of DP method is that the optimal control during an whole process can be achieved by dividing the whole process into N intervals first, and then solving the optimal problem in the last interval, and next solving the optimal problem in the last two intervals, last three intervals, and etc, until the whole optimization problem is solved [19]. Usually, the DP method is applied in the hybrid vehicle to improve the fuel economy of the vehicle, but seldom is used in the electric vehicle, especially the fourwheel independent driven electric ground vehicle. For the four-wheel independent driven electric ground vehicle, most of the torque control allocation strategies are determined by the optimized torque distribution matrix which is based on the motor efficiency. Considering the advantages of the dynamic programming, a new control allocation algorithm in virtue of DP method is used to optimize the energy consumption of the vehicle. When the DP method is applied to optimize the torque control allocation to reduce energy consumption and motor torque mutation, all the vehicle dynamic equations and objective cost formulation should be discretized in a discrete-time format. Then, the torque distribution coefficient is selected as the decision variable. Because of the rapid change of the motor output torque, the riding comfort of the vehicle and the service life of the motor will be reduced, the cost function should consist of the energy consumption and the cost of the motor torque mutation. So the energy optimization problem is reformulated as followed. T req = T f + T r (5) (6) (7) Because the vehicle dynamics model is concerned the longitudinal dynamics and the front motors are the same as well as the rear motors, only half of total required torque is considered in this research. Where, J e is energy consumption function, T req is the required torque, T f and T r are the front motor output torque and the rear motor output torque. Furthermore, time grid is fixed to 1s. u is the distribution coefficient. Where, equation (7) is the expression of the energy consumption within an interval. (8) where, Jp is the punish function to make sure that the output torque of the motors does not change rapidly. When the output torque of the motors changes rapidly, the riding comfort of the vehicle and the life of the mo-

Torque Distribution, Energy Consumption Optimization, Four-wheel Independent Driven Electric Vehicle 379 tors will be significantly reduced. Therefore, a punish function should be contained in the total cost function. is the weighting factor to balance the energy consumption and the torque mutation. The greater the value of the, the more the motor torque mutation is considered. Several different values have chosen to simulate. Finally, a suitable value is selected to run the later simulation. (9) The J is the total cost function consisting of energy consumption function J e and punish function J p. Subject to (10) n min and n max represent the minimum and maximum motor rotation speed. Where, T min and T max represent the minimum and maximum motor torque when the motor rotational speed is n. Generally, the backward induction method is taken to solve the problem of dynamic programming. The energy optimization problem is solved from the last interval to the first interval, and the main solutions are as followed. First, the distribution coefficient and its range should be identified. Then, by multiple iterations, the appropriate allocation coefficient is chosen to minimize the cost function of the last interval. Another distribution coefficient is chosen in the penultimate interval to make the cost function minimum for the last two intervals similarly. Select the coefficients of each interval until the first one. Finally, the coefficients from the first interval to the last interval can be obtained and form a torque control demand sequence. The calculation flow chart of the distribution coefficient is shown in Figure 5. In the flow chart, the total object function subject to the following recursive equations. where, x k and u k is the state and decision. v k (x k, u k )isthe value function when the state is x k and decision is u k. By applying the control allocation of the DP algorithm, the optimal decision sequence u* ={u 1 *, u 2 *,, u N *} can be obtained. The required torque of the vehicle is reasonably allocated, and the motors all work in high efficient regions, as a result, the energy consumption is obviously reduced, and the riding comfort of the vehicle and the service life of the motor are effectively improved. In the process of concrete calculation, the more is the number of state variables and the smaller is the value of t, the smaller is the error, as a result the optimized solution is closer to the optimal solution obtained by the continuous optimization equation, but it will also increase the computation cost of the optimization algorithm. 4. Simulation Result The proposed control allocation algorithm is simulated in Matlab/Simulink and Carsim. The simulation runs in the FTP drive cycle and NEDC in the form of speedtime as the input. Unlike the internal combustion engine, the motor does not have idle state, so the time of idle state could be omitted in the simulation. Besides, the maximum speed in FTP is in the limit of maximum vehi- (11) Figure 5. Distribution coefficient calculation flow chart.

380 Zhao Tang et al. cle speed which is 65 km/h. The maximum speed in NEDC is 70 km/h which exceeds the maximum vehicle speed. So just the urban drive cycle of NEDC is taken into simulation. 4.1 FTP Drive Cycle The new control allocation algorithm is compared with the conventional control allocation algorithm which distributes the total required torque evenly all the time. The total required torque can be obtained by inputting the drive cycle to the vehicle dynamics model. The drive cycle is depicted in Figure 6. According to the vehicle dynamics model, the total required torque of the vehicle could be obtained. Figure 7 shows the total required torque of the vehicle. Figure 8 is the torque allocation when the vehicle applies the DP method to allocate torque. Figure 9 and Figure 10 express the motor operating points when the motors output the same torque. The operating points show motor rotation speed and torque, and the figure s horizontal axis shows the rotation speed and the vertical axis shows the motor torque. Figure 11 and Figure 12 show Figure 9. Operating points of front motor. Figure 6. FTP drive cycle. Figure 10. Operating points of rear motor. Figure 7. Total required torque. Figure 11. Operating points of front motor. Figure 8. Torque allocation.

Torque Distribution, Energy Consumption Optimization, Four-wheel Independent Driven Electric Vehicle the motor operating points according the torque allocation. Figure 8, Figure 11 and Figure 12 show that, due to the efficiency of the front motor is lower than the rear motor, the rear motor works more frequently. As can be seen from Figure 9 and Figure 11, the probability of the front motor working in the high efficiency regions increases, while in the low efficiency regions decreases. The rear motor has the same physical change. According to the efficiency of the motors, the energy consumption can be calculated. Finally, the simulation results show that the energy consumption is 2.2176 106 J in the FTP drive cycle, and when all the motors output the same torque, the energy consumption is 2.8028 106 J, which means an improvement of 26.39%. 4.2 NEDC Drive Cycle Next, an urban NEDC simulation is carried out. The drive cycle and the total required torque of the vehicle are shown in Figure 13 and 14 respectively. Figure 15 is the torque allocation when the vehicle takes the DP method. Figure 16 and Figure 17 are the 381 motor operating points when the motors make the same output torque. Figure 18 and Figure 19 show the operating points of the motors when the motors output torque according allocation. Table 2 lists the energy consumption of the vehicle with different torque output in the different drive cycles. As the FTP drive cycle simulation results show, the motors work more frequently in the high efficiency region when the torque is distributed. The energy consumption of the vehicle with the proposed torque control allocation is 9.5530 105 J, and when the Figure 14. Total required torque. Figure 12. Operating points of rear motor. Figure 15. Torque allocation. Figure 13. NEDC drive cycle. Figure 16. Operating points of front motor.

382 Zhao Tang et al. Figure 17. Operating points of rear motor. Figure 19. Operating points of rear motor. Table 2. Energy consumption Cycle FTP drive cycle NEDC drive cycle Torque Energy consumption (J) Even torque 2.8028 10 6 Distribute torque 2.2176 10 6 Even torque 1.1519 10 6 Distribute torque 0.9553 10 6 Figure 18. Operating points of front motor. motors output the same torque, the energy consumption is 1.1519 10 6 J, which means an improvement of 17.44%. The improvement in FTP drive cycle is superior to NEDC drive cycle, because the vehicle in FTP drive cycle starts and accelerates more frequently. With the development of autonomous driving and intelligent transportation, the application of DP technology in real vehicle control becomes possible. However, Some research still needs to be implemented before the new control algorithm is applied in the real vehicle. The relationship between the accelerator pedal signal and the required torque of vehicle should be studied. Then, the vehicle state and speed commands of vehicle could be considered by the global coordinator to send instruction to four inverters. Besides, some more factors should be taken into account. For example, the adhesion coefficient between tire and road and the temperature of the in-wheel motor should be considered. Near the peak power, the motor efficiency is higher, but when the motor is always working in the peak power, the temperature of motor rises rapidly with the motor efficiency decreasing, even the operation safety. So, it is necessary to limit the operation time at peak power. 5. Conclusions For the goal of extending the driving range of fourwheel independent driven electric ground vehicle and reducing the vehicle energy consumption with the consider of motor torque mutation, a new control allocation algorithm to optimize the overall energy efficiency is developed. Firstly, a vehicle model is built, which consists of a vehicle dynamics model, a in-wheel motor model and a driver model. The efficiency maps of the in-wheel motors are achieved and analyzed. Then, the feasibility of the control allocation to distribute the total required torque to four in-wheel motors is analyzed. Considering the development of the road detection system and vehicle GPS navigation system, the DP method is studied to control the torque allocation. Finally, according the control allocation obtaining from the DP procedure, the simulations of the modified driving cycle are carried out in Matlab/Simulink and Carsim. The results show that, with the proposed control allocation method, the vehicle energy in FTP drive cycle and NEDC drive cycle improves 26.39%

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