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Modelling and testing of in‐wheel motor drive intelligent electric vehicles based on co‐simulation with Carsim/Simulink

2018; Institution of Engineering and Technology; Volume: 13; Issue: 1 Linguagem: Inglês

10.1049/iet-its.2018.5047

1751-9578

Yong Li, Huifan Deng, Xing Xu, Wujie Wang,

Real-time simulation and control systems

IET Intelligent Transport SystemsVolume 13, Issue 1 p. 115-123 Special Issue: Recent Advancements on Electrified, Low Emission and Intelligent Vehicle-SystemFree Access Modelling and testing of in-wheel motor drive intelligent electric vehicles based on co-simulation with Carsim/Simulink Yong Li, Corresponding Author Yong Li liyongthinkpad@outlook.com Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorHuifan Deng, Huifan Deng School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorXing Xu, Xing Xu Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorWujie Wang, Wujie Wang School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this author Yong Li, Corresponding Author Yong Li liyongthinkpad@outlook.com Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorHuifan Deng, Huifan Deng School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorXing Xu, Xing Xu Automotive Engineering Research Institute, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this authorWujie Wang, Wujie Wang School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang, 212013 People's Republic of ChinaSearch for more papers by this author First published: 04 October 2018 https://doi.org/10.1049/iet-its.2018.5047Citations: 10AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract To study the overall performance of the distributed drive intelligent electric vehicle (EV), a in-wheel motor drive (IWMD) vehicle is developed in this study. The configuration and 11-degrees of freedom model of IWMD EV is introduced firstly. Then, the co-simulation model of IWMD EV based on Carsim and Matlab/Simulink is established. The block design is employed for the co-simulation modelling, including the in-wheel motor model, driver model, tyre model, steering model, braking model, suspension model, aerodynamic model, and road surface model. The effectiveness and the reasonableness of the co-simulation model of IWMD EV are verified by the snake testing with on the campus road. The co-simulation model provides accuracy and reliable simulation method for the path-tracking and self-driving study of IWMD intelligent vehicle in the future. 1 Introduction With the escalating problem of the oil crisis and environmental pollution, electric vehicle (EV) has become an effective way to solve the above-mentioned problem due to its energy-saving, environmental-friendly, and safety properties. In recent years, the United States, Japan, Europe, China, and other countries and regions have proposed their own electric car development strategies. EVs generally considered as the transport tools in the 21st century are facing the rapid development of strategic opportunities [1, 2]. Compared with traditional internal combustion engine vehicles, in-wheel motor drive (IWMD) EV directly driven by the in-wheel motor not only has higher energy efficiency but also achieves regenerative braking. In addition, the IWMD EV also has the advantages of compact structure, high transmission efficiency, short transmission chain etc., which can utilise the coordinated control of redundant degrees of freedom (DOF) to optimise the distribution of driving and braking force [3, 4]. That greatly improves the active safety and energy consumption of the whole vehicle. It is of great significance to establish the accurate simulation model for the handling stability study of IWMD EV. Early studies on vehicle systems generally linearised the vehicle model to make the parameters as simple as possible, such as the linear 2-DOF monorail model. In the 2-DOF model, the slip angle of the tyre is proportional to the lateral force by limiting the lateral acceleration [5, 6]. With the development of computer technology, it is possible to get the solution of the vehicle model with strong non-linear and multi-DOF. For the two-axis vehicle, Guo proposed 12-DOF non-linear model, in which 6-DOF of vehicle motion, 4-DOF of the wheel rotating, and 2-DOF of the steering wheel are considered. This model fully reflects vehicle dynamic characteristics [7]. Considering the vertical movement of the vehicle, Jin established the 18-DOF dynamic model of four-wheel independent drive EV with Simulink [8]. Liu proposed the simulation model of 4IWMD EV and studied the slip rate control scheme [9]. Wang established the dynamics model of EV and the mathematical model of permanent magnet DC motor, which reflects the particularity that vehicle movement is influenced by the wind resistance [10]. Yang built the dynamic model of quarter EV for slip and studied the control method of anti-slip and yaw stability [11]. Zong established the vehicle model used for special conditions simulation of a four-wheel drive and steering EV [12]. However, most of the current models of IWMD EV are established based on Matlab/Simulink, remaining greatly simplified vehicle motion model, the complex setting of simulation condition and inadequate driver model. To adequately and accurately reflect the operating condition of IWMD EV, it is necessary to carry out the co-simulation study using Simulink and Carsim. In this paper, a IWMD EV developed by our research group is taken as the research object. Firstly, a co-simulation model of IWMD EV is established with Simulink and Carsim. The simulation model is designed by blocks, including in-wheel motor model, battery model, driver model, tyre model, suspension model, steering model, braking model, aerodynamic model, and road surface model. Considering the longitudinal, lateral, and vertical properties, the 11-DOF non-linear model of the vehicle is established in Carsim. The co-simulation study is supposed to take advantages of Simulink and Carsim software and reflect the real motion status of IWMD EV. The rationality and accuracy of the vehicle simulation model is verified by snake testing on the campus road. The paper is organised as follows. First, the configuration and 11-DOF model of IWMD EV are analysed in Section 2. The blocks of the co-simulation model of IWMD EV, in Section 3, are established. After that, in Section 4, the co-simulation model with Simulink and Carsim is presented. In Section 5, the co-simulation model is verified by road testing. Section 6 is devoted to the conclusions and future work of the work. 2 Configuration and 11-DOF model of IWMD EV The configuration of IWMD EV studied in this paper is shown in Fig. 1. The IWMD EV has four in-wheel motors that can be independently controlled by motor controller [13, 14]. The EV is powered by lithium-ion battery, consisting of six modules connected in series. The module voltage is 12 V. The nominal voltage and current of the battery are 72 V and 100 A, respectively. Fig. 1Open in figure viewerPowerPoint Configuration of the 4IWMD EV Each of the four in-wheel motors can be controlled to produce traction torque and make the corresponding wheel works an active wheel. The wheel will work as a passive if the motor is not controlled. In this paper, two front in-wheel motor are used to drive the vehicle. The 11-DOF model of IWMD EV shown in Fig. 2 consists of 6-DOF of the vehicle body, 4-DOF of wheel steering, and 1-DOF of front wheel steering angle [15-19]. The 11-DOF vehicle model is built with Carsim software. Fig. 2Open in figure viewerPowerPoint 11-DOF model of IWMD EV (a) Top view, (b) Left view The longitudinal equation of motion is expressed as (1) where FR is the sum of rolling resistance, ramp resistance, and wind resistance. Lateral longitudinal motion equation is written as (2) Yaw equation of motion is expressed as (3) . Vertical motion equation is written as (4) Rolling equation of motion is written as (5) Pitch motion equation is written as (6) Wheel balance equation is described as (7) where m is the vehicle kerb weight. ms is the sprung mass, g is the acceleration of gravity. Bf is the wheelbase of the front wheel. Br is the wheelbase of the rear wheel. lf is the distance from the front axle to the centre of the mass. lr is the distance from the rear axle to the centre of mass. ax and ay are the longitudinal acceleration and the lateral acceleration of the vehicle, respectively. Fx_fl, Fx_fr, Fx_rl, and Fx_rr are the tyre longitudinal force of the left of the front axle, the right of the front axle, the left of the rear axle, and the right of the rear axle, respectively. Fy_fl, Fy_fr, Fy_rl, and Fy_rr are the tyre lateral force of the left of the front axle, the right of the front axle, the left of the rear axle, and the right of the rear axle, respectively. These are the components of the tyre force in the vehicle's coordinate system. Fs_ij is the suspension force. Tx_ij is the wheel drive torque. Tb_ij is the wheel brake torque. Mf_ij is the tyre rolling resistance. ωij is the wheel speed. Iij is the moment inertia of the wheel. ij = fl, fr, rl, and rr. fl, fr, rl, and rr represent the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectively. vx, vy and vz are the vehicle speed on x -axis, y -axis and z -axis, respectively. , and are the angular velocity of the vehicle on x -axis, y -axis and z -axis, respectively. δ is the front wheel angle. Ix, Iy and Iz are the moment inertia of the vehicle on x -axis, y -axis and z -axis, respectively. 3 Simulation block of IWMD EV Fig. 3 shows the block diagram of the simulation model of IWMD EV. The vehicle model consists of several subsystem models, including, steering model, in-wheel motor model, battery model, driver model, tyre model, steering model, braking model, suspension model, aerodynamic model, and road surface model. Fig. 3Open in figure viewerPowerPoint Block diagram of 4IWMD EV In this paper, the steering model, the braking model, the suspension model, the aerodynamics model, and the road surface model are built with CarSim, and the in-wheel motor model, the battery model, the driver model, and the tyre model are built with Simulink. 3.1 In-wheel motor model The in-wheel motor is the most important actuator of the IWMD EV. In this paper, the inner rotor permanent magnet synchronous motor (IPMSM) is employed as the in-wheel motor. The stator is connected to the vehicle body, and the rotor is coupled to the wheel rim. The in-wheel motor is a strong coupled, multivariable, and non-linear system. The following assumptions are adopted to simplify the system model: (i) The inside permeability of the permanent magnet is the same as the air. (ii) The magnetic field generated by the permanent magnet and the armature reaction generated by the three-phase stator windings are sine distribution in the air gap. (iii) Under the steady-state condition, the electromotive force (EMF) is sine wave. (iv) The higher harmonic components are ignored. The mathematical model of the in-wheel motor in the synchronously rotating d -q reference frame is expressed as follows [2, 20]: (8) where id and iq are the d -axis and q -axis current of the stator, respectively. ud and uq represent the voltage component on the d -axis and q -axis, respectively. ω denotes the electrical angular velocity of the PMIWM rotor. Ld and Lq indicate the inductance of the d -axis and q -axis, respectively. Rs shows the stator resistance. ψf means the permanent magnet flux linkage of the rotor. The electromagnetic torque equation of the PMIWM in the d-q coordinate is described as follows: (9) where Te is the electromagnet torque of the PMIWM. pn is the number of pole pairs. The control diagram of the in-wheel motor is shown in Fig. 4. Fig. 4Open in figure viewerPowerPoint Control diagram of the in-wheel motor The four independent in-wheel motors are employed to drive or brake [21-23]. The mathematical model of the in-wheel motor is described by its motion equation, torque equation, and voltage equation shown as following: (10) (11) (12) where Te and TL are the electromagnetic torque and load torque, respectively. ωi, J, fm, Re, I, La are the rotating angular velocity, the moment of inertia, the friction coefficient, the armature resistance, the armature current, and inductance of the in-wheel motor, respectively. Km and Ke are the torque coefficient and the back EMF coefficient, respectively. E is the input voltage of the in-wheel motor. i = fl, fr, rl, and rr. Each in-wheel motor has a separate motor controller. The closed-loop characteristics of the motor can be simplified to a delay shown as follows: (13) where τ is the closed-loop response time. Tc is the motor drive command. The power loss characteristic is described by the motor efficiency MAP. First, the motor efficiency MAP under different speeds and torques is measured through experiments. Then, the motor efficiency η at the current operating point can be obtained according to the current speed and torque. The multiplication of speed and torque is used as the output power [24-27]. The input power can be calculated by the ratio of output power and η, which is shown as (14) The powertrain system is matched and tested on the test bench. The efficiency MAP of the in-wheel motor is shown in Fig. 5. The motor efficiency can be obtained from the efficiency map. The motor current can be calculated by the following equations: (15) Fig. 5Open in figure viewerPowerPoint Efficiency Map of the IPMSM where im is the motor current. n is the motor speed. ubat is the battery voltage. 3.2 Battery model The Rint model, RC model, Thevenin model, PNGV model, and DP model are widely used in the equivalent circuit model study of Lithium-ion battery. Simulation and experiments were carried out to investigate the effectiveness of the model and model-based SOC estimation methods. Compared to other battery models, the Rint model is reliable due to its simple topology structure [28-31]. The Rint model is adopted in this paper. The equivalent circuit is shown in Fig. 6. Fig. 6Open in figure viewerPowerPoint Equivalent circuit of the Lithium battery The relationship between the open circuit voltage Eb, the equivalent internal resistance Rb, the battery current Ib, and the DC bus terminal voltage Ubbus is expressed as follows: (16) SOC represents the battery state of charge and can be calculated by the following equations: (17) where is the remaining battery capacity (Ah). is the used battery capacity (Ah). When SOC = 0, the battery is exhausted. When SOC = 1, the battery is fully charged. For the safety of lithium-ion battery, the SOC range is set as . The LiFePO4 battery is used in this study, and the curve of battery capacity varies with temperature is shown in Fig. 7. As is seen from Fig. 7, the battery capacity changes with the temperature [32]. Fig. 7Open in figure viewerPowerPoint Curve of LiFePO4 battery capacity vs. temperature 3.3 Driver model The driver model is an indispensable part of the closed-loop simulation of vehicle dynamics. The model accuracy is very important for the closed-loop simulation results. Many studies about the drive model have been carried out by scholars, in which speed and direction control are mainly considered [33, 34]. The steering-follow driver model with the arbitrary path is established based on the preview-follow driver model proposed by Guo. The centroid longitudinal vehicle speed is employed as the model input. The steering wheel angle, brake pedal opening, and accelerator pedal opening are used as the output signals. PID control scheme is implemented for vehicle speed control shown in Fig. 8. The corresponding offset of acceleration and deceleration pedal can be calculated by the PID controller, in which the error between the actual vehicle speed and the ideal vehicle speed is used as the input. The offset of the braking pedal is utilised as the input of the braking system model. The offset of the acceleration pedal is used as the input of the motor drive system model. The steering angle is employed as the input of the steering system model. The desired traction/brake torque can be obtained for the target vehicle speed, and the torque will be distributed to the four in-wheel motors to achieve constant speed operation. Fig. 8Open in figure viewerPowerPoint Driver model 3.4 Tyre model The tyre model is responsible for the adhesion with the ground and plays an essential role in vehicle dynamics model. The non-linear characteristics and high accuracy of the tyre should be considered for the tyre model [35-37]. The Uni Tire model proposed by Guo is employed as the tyre model in this study. The following assumption should be considered. (i) The carcase only undergoes lateral deformation. (ii) The offset along z -axis is ignored. (iii) The rotating angle and the tyre camber around x -axis are ignored. The force and torque of the tyre are shown as Sx and Sy are introduced into the unified semi-empirical model (18) (19) where Vω = ωRtyre is the wheel rolling speed. ω is the wheel speed. is the rolling radius. The unsteady rolling resistance is described as (20) where h is the rolling resistance coefficient. θr is the relaxation angle. 3.5 Steering model The high-precision and the fast-respond servo motor is selected as the actuator of the steering system in this study, and supposed to execute the steering commands. The input signal is generated by the steering angle. Considering the impact of the tyre back torque, the front wheel angle can be obtained according to the angle transfer transmission characteristics of the steering system [38-40]. The relationship between the front wheel angle δ and the steering wheel angle input δsw can be described as (21) where δ is the front wheel angle. δsw is the steering angle. isteer is the angle transmission ratio of the steering system. Ksteer is the positive stiffness of the steering system. Mz is the torque used to feedback to neutral of the wheel. 3.6 Braking model Regenerative braking system (RBS) that converters part of the vehicle kinetic energy into electrical energy storage is of great significance to improve the economy of the vehicle. However, the RBS cannot provide enough braking force when emergency braking or the vehicle speed is low. Considering the operating safety of the vehicle, the coordination of hydraulic brake system (HBS) and RBS is adopted in this study. The HBS and RBS are coupled in parallel and worked separately. The brake force produced by RBS is controlled by the system, and the braking force generated by the HBS is controlled by the braking pedal [41]. To improve the economy, a large brake pedal travel is employed in this study. RBS just works in the condition of small braking force. The braking force of the front and rear shaft of the vehicle is expressed as (22) where Fxbf and Fxbr are the ground braking force of the front axle and rear axle, respectively. β is the distribution coefficient of brake braking force. 3.7 Suspension model The suspension force between each wheel and the vehicle body can be calculated from wheel jump, vertical movement of the sprung mass, roll and pitch movements [42, 43]. Suspension force of sprung mass can be expressed as (23) where ks_ij is the suspension stiffness. zij is the height of the connection point between the body and suspension. bs_ij is suspension damping. 3.8 Aerodynamic model The force while EV is operating includes rolling resistance, wind resistance, climbing resistance, and accelerate resistance. EV in the driving process by and driving force and the resistance equal, the formula is (24) where Ft is the driving force for the vehicle. Ff is the rolling resistance. Fw is the wind resistance. Fi is the climbing resistance. Fj is the acceleration resistance. f is the rolling resistance coefficient. m is the vehicle mass. α is the road slope angle. CD is the wind resistance coefficient. A is the upwind area of the vehicle. v is the vehicle speed. δ is the coefficient of the rotating mass. The demand torque of the in-wheel motor can be obtained by the following equations: (25) where T is the output torque for the motor. r is the wheel radius. i is the corresponding gear ratio. ηt is the transmission efficiency. 3.9 Road surface model The adhesion coefficient of the front and rear shaft can be defined as (26) where φi is the coefficient of i -axis. Fxbi is the ground braking force. Fzi is the ground reaction force. 4 Co-simulation model The Carsim user interface shown in Fig. 9 mainly includes definition of the vehicles parameters and simulation conditions, simulation solution configurations and simulation results processing. Fig. 9Open in figure viewerPowerPoint Carsim software To realise the co-simulation of IWMD EV, the interface between Simulink and Carsim must be set firstly. The vehicle speed and motor speed of four wheels in Carsim need to be given to driver model and in-wheel motor model in Simulink. The traction torque distribution is used to generate the input command for the in-wheel motor. The torque is distributed to the two front in-wheel motors in Carsim. The data is transferred through CarSim/S-Function block in the co-simulation model. The input and output variables are set in Carsim. When the simulation starts, the variables in Simulink are passed to Carsim while the variables in Carsim are also fed back to Simulink. In the Simulink environment, the electronic differential (ED) control system, and differential assist steering (DAS) control system are coordinated as the upper-level controller to receive the feedback dynamic parameters from Carsim model, in which the control signal for each in-wheel motor can be computed. Meanwhile, the driver model also receives the vehicle speed signal from Carsim and calculates the control signal for the in-wheel motor. The in-wheel motor model receives the control signal of the ED-DAS coordination system and the driver model and generates the traction torque signal. The torque signal is passed to the vehicle model in Carsim through S-Function block. The co-simulation model is shown in Fig. 10. Fig. 10Open in figure viewerPowerPoint Co-simulation model 5 Experimental verification 5.1 Testing vehicle setup A novel IWMD EV is developed in this study. The parameters of the IWMD EV are illustrated in Table 1. Table 1. Parameters of the IWMD EV Parameter Value Unit vehicle parameters vehicle length 2.55 m vehicle width 1.35 m vehicle height 1.5 m tread 1.085 m wheelbase 1.635 m gross vehicle weight 710 kg centroid height 0.7 m wheel radius 0.245 m frontal area 1.87 m2 max. speed 60 km/h kerb weight 520 kg full load quality 800 kg steering angle −540∼540 deg front wheel corner −27 deg drive system mass 18.6 kg nominal Power 4 kW nominal frequency 50 Hz nominal Voltage 72 V nominal Speed 1200 r/min nominal Torque 80 Nm moment of Inertia 0.06 kg·m2 pole pair number 2 pair battery pack system nominal voltage 72 V nominal capacity 40 Ah battery name Chunlan / battery brand IFPE40 / To analyse the status of each in-wheel motor, a voltage sensor and four current sensors are used to monitor the input voltage and input current of each motor controller. The torque sensor and the steering angle sensor mounted on the steering column are employed to measure the steering torque and steering angle. The hall speed sensor is utilised to obtain the wheel speed. The steering angle sensor and torque sensor are shown in Fig. 11. Fig. 11Open in figure viewerPowerPoint Steering angle sensor and Torque sensor (a) Steering angle sensor, (b) Steering torque sensor The D2P-Moto Hawk is used for designing the upper vehicle controller and coordinating four in-wheel motor controllers. Also, the signals from the controllers and sensors are measured, recorded, and passed by CAN bus. The vehicle controller based on D2P-Moto is shown in Fig. 12. All the data from vehicle sensors is measured and processed in the analogue and frequency channels. The control signals are solved and passed to the in-wheel motor controller through PWM output channel. The PWM analogue convert module is designed to convert the control quantity, and match the input and output of the in-wheel motor controller due to the analogue signal of the in-wheel motor controller. All the control and status signals of the vehicle can be monitored and recorded by a laptop through CAN bus of the D2P-based rapid prototype [13]. Fig. 12Open in figure viewerPowerPoint Vehicle controller based on D2P-Moto 5.2 Co-simulation model verification To verify the established co-simulation model, simulation and vehicle testing under the same condition are carried out on the IWMD EV. 5.2.1 Steering torque and yaw rate testing The snake testing is implemented the straight campus road shown in Fig. 13. The road surface adhesion coefficient is 0.85. The sine wave is used as the input signal of the steering angle, which is in the range of 0–60 degrees. The vehicle speed is shown in Fig. 14. The test vehicle accelerates from standstill and keeps 15 km/h after 20 s. The steering angle and steering torque are shown in Figs. 15 and 16. The sine wave is used as the input signal of the steering angle when the vehicle speed is stable, and it lasts for ∼7 s with 50-deg amplitude. The data recorded in the test including steering angle, electronic throttle, in-wheel motor speed, longitudinal speed, lateral acceleration, and yaw rate. Fig. 13Open in figure viewerPowerPoint Test vehicle of UJS Fig. 14Open in figure viewerPowerPoint Vehicle speed of road testing Fig. 15Open in figure viewerPowerPoint Steering wheel angle Fig. 16Open in figure viewerPowerPoint Comparison of steering torque The steering angle signal obtained from the vehicle testing is used as the input of the model simulation. The simulation speed is set to 15 km/h, which makes the co-simulation condition close to the road testing condition. Fig. 16 shows the comparison results of steering torque. It can be seen that the steering torque increases with the steering angle. The peak value of the steering torque is appropriate 5 Nm. The steering torque with road testing tracks well with that with co-simulation results. The yaw rate response of the vehicle is shown in Fig. 17. It can be seen that the yaw rate increases with the steering angle when the vehicle speed keeps stable under the co-simulation and the vehicle testing results. The peak value is ∼0.1 rad/s. Fig. 17Open in figure viewerPowerPoint Vehicle yaw rate From the comparison results in Figs. 16 and 17, we can see that the actual status of the road testing vehicle agrees with co-simulation results with the same input. The reliability of the co-simulation model is verified. 5.2.2 ED and DAS testing To further verify the co-simulation model, ED and DAS testing are carried out under snake testing. i. Without torque distribution When the road testing is implemented without torque distribution, the same control signal is generated to each in-wheel motor controller by the vehicle controller according to the pedal signal, which means the in-wheel motor has the same power. The speed of the road testing vehicle is shown in Fig. 18. It can be seen that the test vehicle takes 20 s to accelerate to 15 km/h. A trough appears at ∼50 s due to the bulge on the road, which causes a decrease in the vehicle speed. Fig. 18Open in figure viewerPowerPoint Vehicle speed of road testing without torque distribution The steering torque of co-simulation and road testing results is shown in Fig. 19. It can be seen that the actual value is greatly larger than the ideal value. That is also caused by the same control without torque distribution, and verified by the co-simulation results in Fig. 16. Fig. 19Open in figure viewerPowerPoint Steering torque without torque distribution Fig. 20 shows the yaw rate curve of the road testing. It can be seen that the amplitude of the yaw rate is ∼0.1 rad/s with the sine wave input of steering angle when the vehicle operates at 15 km/h. This value is smaller than the ideal condition. That is caused by the same control without torque distribution of the in-wheel motor, which agrees with the co-simulation results in Fig. 17. ii. ED model verification Fig. 20Open in figure viewerPowerPoint Vehicle yaw rate without torque distribution The vehicle yaw rate is used as the target by the vehicle controller for the torque distribution. The road testing speed shown in Fig. 21 illustrates the speed keeps 15 km/h after 20 s. The speed trough at ∼45