An electronic stability control (ESC) based on torque distribution is proposed for an eight inwheel motorindependent drive electric vehicle (8WIDEV). The proposed ESC is extremely suitable for the independent driving vehicle to enhance its handling stability performance. The vehicle model is established based on a prototype 8WIDEV. A hierarchical control strategy, which includes a reference state generation controller, an upperlevel vehicle controller, and a lowerlevel optimal control allocation controller, is utilized in the ESC. The reference state generation controller is used to obtain the ideal reference vehicle state. The upperlevel vehicle controller is structured based on sliding mode control, which obtains the generalized objective force during 8WIDEV movement, therein considering the side slip angle and yaw rate. The lowerlevel optimal control allocation controller attempts to allocate the vehicle’s objective force in each motor optimally and reasonably. The model is validated by field measurement results under the step input condition and snake input condition. Simulation results from a hardwareintheloop (HIL) simulation platform indicate that the ESC based on the optimized allocation proposed for 8WIDEV achieves better stability performance compared with direct yaw moment control (DYC).
The structure of an electric vehicle driven by inwheel motors is different from that of traditional vehicles driven by internal combustion engines in that it does not use an engine or transmission, places the motor inside the hub appropriately, and uses a battery as the power supply. The eight inwheel motorindependent drive electric vehicle (8WIDEV) has eight independent controllable motors, which has the potential to improve the vehicle handling stability [
Currently, there are three commonly used control structures for the dynamic control of a vehicle driven by inwheel motors: decentralized, centralized, and hierarchical control structures. Because of its flexibility, the hierarchical control strategy is more suitable for solving complex nonlinear and redundant systems with executive constraints, compared with decentralized and centralized control structures [
However, fewer studies have focused on the 8WIDEV with high weights. As the number of driving wheels increases, the 8WIDEV becomes applicable to more complicated driving conditions, given its greater flexibility and maneuverability. To improve the 8WIDEV handling stability, the longitudinal dynamic control and lateral dynamic control are constructed. The target lateral force and target yaw moment are obtained by controlling the two corresponding vehicle variables in lateral control [
The yaw rate is mathematically related to yaw moment; thus, it can be directly controlled. However, the relationship between the side slip angle and yaw moment represents an “unmatching system,” which can be expressed as that the side slip angle being tracked to an ideal stare quantity by controlling the yaw rate as an intermediate variable; however, the actual yaw rate is not sufficient to track its reference value [
Most control allocation rules now adopt traditional allocation methods such as average allocation and direct control allocation. These methods are faster in calculating the torque distribution; however, their torque allocation method is simple. The vehicle dynamics constraints and the optimization of the torque distribution need to be fully considered [
In this paper, ESC based on a hierarchical control strategy is established to enhance the performance of the handling stability and trajectory capability of 8WIDEV. The hierarchical control structure includes the reference state generation controller, the upperlevel vehicle controller, and the lowerlevel optimal control allocation controller. By utilizing the classic reference model of the vehicle, a monorail of fouraxle vehicles based on a two DoF model is established to obtain the required reference state of the vehicle. The reference state generation controller is designed using the reference state of the vehicle. In contrast to the linear control method, attempting to consider vehicle nonlinearity and uncertainty, the upperlevel vehicle controller is built using the nonlinear control method, therein achieving strong robustness to vehicle parameter uncertainties and external disturbances. The upperlevel vehicle controller includes a yaw moment synthesis controller, therein considering the two control variables related to lateral motion tracking while adjusting the weight coefficient. Actuator torque allocation for redundant systems is modeled as a constrained optimization problem. The main contribution of this paper lies in the following points. First, based on prototype vehicle parameters, a dynamic model of an 8WIDEV is established. This model can fully reflect the dynamic characteristics of the vehicle and provide a favorable basis and conditions for verifying the control method. The effectiveness of the vehicle model is verified through comparison simulations in MATLAB/Simulink with the experimental results for the prototype vehicle. Second, the vehicle slip angle and the yaw rate tracking are realized via sliding mode control, and the corresponding yaw moment is obtained. This provides the advantage of avoiding the saturation of the motor torque caused by satisfying the lateral force requirement. The stability control strategy proposed in this paper improves the stability of vehicles according to the simulation and contrasts with DYC control. Third, because most previous stability control studies on the 8WIDEV lack validation, in this paper, a hardwareintheloop (HIL) experiment verifies that the ESC proposed improves vehicle handling and stability [
The structure of this paper is divided into the following main parts: first, the 22DoF vehicle dynamic model is introduced, including the vehicle body model, suspension model, wheel model, tire model, and electric motor model. Second, a vehicle control strategy for the 8WIDEV based on a hierarchical structure is proposed, whereby the ESC system in the vehicle improves the vehicle handling stability. Finally, analysis of a simulation experiment and a hardwareintheloop (HIL) experiment to verify the vehicle dynamic model established in MATLAB/Simulink demonstrates the dynamic characteristics of the 8 × 8 prototype vehicle and verifies the effectiveness of the control strategy proposed in this paper to improve the vehicle handling stability and good trajectory tracking ability. Finally, we conclude the paper, therein describing valuable observations obtained in this study.
The research in this paper focuses on a 8WIDEV handling stability project. The 8 × 8 prototype vehicle is shown in Figure
8 × 8 prototype vehicle.
This section mainly describes the 22DoF vehicle dynamic mode, including a model of the vehicle body, suspension, tires, wheels, and electric motor. The vehicle body model usually only considers motion in three directions. Considering the static and unsteady problem of the suspension system and the body in the vertical dynamics, a suspension model based on the static equilibrium is constructed, and the vehicle body model considers the 6DoF of the body. Considering the effects of the slip rate, side slip angle, road adhesion coefficient concerning the tire forces, nonlinear saturation, and coupling of the total tire force, a tire model based on the nonlinear saturation and coupling characteristics of the tire is established. Table
The basic structure parameters of the 8WIDEV.
Parameter  Symbol  Unit  Value 

Vehicle weight 

kg  21000 
Spring weight 

kg  17000 
Track width 

m  2.6 
Distance from axles to centroid 

m  2.23/0.81/1.19/2.61 
Vehicle moment inertia 

kg·m^{2}  33625 
Centroid height 

m  1.1 
Tire radius 

m  0.6 
Electric wheel mass 

kg  400 
Wheel rotational inertia 

kg·m^{2}  120 
Suspension stiffness 

kN·m^{−1}  200 
Suspension damping 

kN·s·m^{−1}  400 
Fixed reducer ratio 

—  11 
Figure
The tire coordinate system is shown in Figure
Tire coordinate system.
The suspension and vehicle body in the vehicle vertical dynamics represent a statically indeterminate problem. Based on the traditional displacement method, the suspension force and vertical force of the tire are solved. In addition, the suspension model is built based on suspension parameters and suspension system theory of 8WIDEV and mainly refers to the dynamic method of multiaxle vehicle suspension modeling [
Under static balance of the vehicle, the balance of the vehicle vertical force and the balance equation of the body moment are given as follows:
It is assumed that the stiffness of each axle suspension is the same, and the static suspension force of each axle is obtained:
The static forces of each suspension are described as follows:
Then, the static vertical load of each wheel is described as follows:
The dynamic force of suspension caused by a change in the body posture is mainly reflected in the vehicle load transfer caused by the movement of the vehicle and the pitch motion. The dynamic suspension force expression is as follows:
The vertical movement, tilting movement, and pitching movement of the body lead to the vertical deformation of the suspension expressed as follows:
The dynamic vertical force of the wheel caused by the unevenness of the pavement is as follows:
The suspension system and the vertical load of the tire can be expressed as follows:
Based on the dynamic analysis of wheels in automobile theory [
Tires have strong nonlinear characteristics, which are mainly manifested in the relationship between the lateral force and the cornering angle of the tire and the relationship between the lateral force and the longitudinal force of the tire. It is important to establish a tire model that can reflect the nonlinear characteristics of vehicle tires. Currently, the “magic” tire model, power exponential unified tire model, and swift tire model are commonly used in tire modeling. In vehicle dynamics research, the widely used “magic” tire model established by Professor Pacejka [
Another way to express the longitudinal/lateral tire force and the tire slip rate/side slip angle is shown in Figure
Tire force under different conditions.
The parameter matching and selection requirements of inwheel motors are decided by the power and torque of the vehicle dynamics performance. It is important to describe the process of choosing motor specification based on the vehicle dynamics. The full load of the vehicle is tens of tons, and considering the relatively large available space for the hub, a planetary gear reducer for the drive system was selected, with a transmission ratio preset as 10. Next, the choice of motor specification was divided into two parts: the motor power demands and the motor torque and speed requirements. First, we introduce the power demands of the motor. The motor power depends on the vehicle power demand. Equation (
Based on the vehicle dynamics performance, the vehicle power demand mainly concerns three aspects: (1) the requirements for achieving maximum speed, (2) achieving the maximum gradability performance, and (3) satisfying the acceleration performance requirements of the vehicle. The vehicle maximum speed is the top speed on a straight and good road with full load or half load. In this case, the slope resistance and acceleration resistance are zero. The vehicle power demand can be obtained as follows:
Second, we calculate the motor torque and speed requirements. The maximum speed and rated speed of the wheel motor are decided by the maximum speed and commonly used speed, respectively. The maximum speed and rated speed of the motor can be calculated as follows:
The maximum speed
The rated torque of the motor is not less than 315 Nm after calculation. Permanent magnet synchronous motors (PMSMs) are used as inwheel motors to meet the vehicle performance requirements. By analyzing the requirements of vehicle dynamic performance, the rated power of the motor is finally chosen as 90 kW, and the rated torque is 340 Nm. The final selection of the motor specifications is shown in Table
Basic specifications of motor.
Parameter  Value 

Rated power  90 kW 
Maximum power  110 kW 
Rated torque  340 Nm 
Maximum torque  1100 Nm 
Rated speed  2600 rpm 
Maximum speed  50000 rpm 
After choosing the motor model, the PMSM was manufactured. A bench test of the PMSM was conducted in the laboratory, and the calibration was performed, as shown in Figure
PMSM calibration and debugging diagram.
External characteristic curve of the PWSM.
The vehicle controller, which contains the electric stability control system, sends the target torque command to the motor controller. The main research topic here is the vehicle control strategy toward improving the vehicle handling stability. The response speed of the PMSMs is high compared with the wheel dynamics; thus, the input and output of this motor torque is described as a firstorder system:
A planetary reducer is adopted between the inwheel motor and the hub. Thus, the output torque of the electric wheel is
An electronic stability control (ESC) is proposed in this paper for the object under study in this paper, 8WIDEV, to improve the vehicle stability performance, therein adopting a hierarchical control structure. A hierarchical control structure is suitable for overdriven electric vehicles, as shown in Figure
Traditional typical control structure for the 8WIDEV.
The hierarchical control structure is superior to the centralized control structure in terms of control flexibility and fault tolerance. Therefore, the commonly used hierarchical control structure is designed to control the handling stability of the 8WIDEV. The upper controller mostly controls the vehicle speed and yaw angular speed. Vehicle handling stability can be improved at low speed and good working conditions. The lower controller realizes the distribution of each motor’s torque by using different distribution methods. By reasonably and effectively allocating the torque control vehicles for each inwheel motor, the vehicle can track the reference path preferable. The ESC proposed in this paper fully utilizes the hierarchical structure and improves it on this basis. The ESC includes a reference state generation controller, an upperlevel vehicle controller, and a lowerlevel optimal control allocation controller, as illustrated in Figure
Control structure for 8WIDEV.
The most commonly used reference model in vehicle dynamic control, as shown in Figure
2DOF linear bicycle model.
The research object in this paper adopts a mechanical double front axle steering mechanism based on Ackerman steering theory. The state equation of the double front axle steering vehicle can be described as follows:
The ground adhesion vehicle limits the maximum lateral acceleration; thus, the maximum yaw rate is limited by the maximum lateral acceleration and the longitudinal speed. Similarly, satisfying the vehicle lateral safety, the side slip angle is subject to the longitudinal speed [
Based on the above analysis, the vehicle’s two ideal variables are described by the following equation:
In a sense, to simplify the algorithm, it is assumed that the vehicle acceleration and the displacement of the accelerator/brake pedal are linear. Thus, the expected speed of the vehicle is obtained:
The upperlevel vehicle controller contains the vehicle longitudinal motion controller and the vehicle yaw motion synthesis controller, whose purpose is to generate the objective longitudinal force and the objective yaw moment of the vehicle as needed. By tracking the longitudinal speed, the vehicle longitudinal motion controller obtains the desired longitudinal force. The side slip angle, as another variable, is controlled to obtain the objective yaw moment, instead of obtaining the lateral force required by the vehicle, which reduces the saturation of the tire longitudinal force distribution due to the lateral force required by the vehicle. The vehicle yaw moment synthesis controller obtains the synthetic moment by controlling the side slip angle and the yaw rate.
Vehicle handling stability is mainly determined by the longitudinal speed and yaw rate. According to the deviation from the reference state and actual state, the desired longitudinal force
The tire force control is realized by the actuator. Because of the nonlinear coupling between the longitudinal and lateral forces, the actuator faces difficulties in controlling the lateral force accurately. Moreover, the output torque of the motor and brake directly affects the longitudinal force of the tire. The vehicle studied in this paper does not utilize active steering; thus, it is difficult to control the lateral force accurately by compensating with the steering angle.
In this paper, the resultant force and yaw moment produced by the tire longitudinal force are taken as the target control force:
Because of its strong robustness and antiinterference ability, sliding model control (SMC) is adopted in this paper to address the vehicle nonlinearity, unmodeled dynamics, and parameter uncertainty [
Thus, the sliding mode function and the approach law are further expressed as follows:
In the sliding mode control law, we use the Lyapunov stability theory to design an appropriate sliding mode control to satisfy the reachability condition. The Lyapunov function is constructed as follows:
This represents the distance from the system curve to the switching function, and the Lyapunov inequality is described as follows:
As long as the Lyapunov arrival condition is satisfied, the moving points outside the sliding mode will reach the surface in a finite time approaching to the sliding surface. Thus, the inequality
Through equations (
The yaw moment synthesis controller obtains the objective yaw moment though a joint action calculation result though two variables by adjusting the corresponding weight coefficient [
As the most important part of the ESC system, the lowerlevel controller plays a crucial role in the motor torque distribution and manages the distribution of the longitudinal force/yaw moment acquired by the upperlevel vehicle controller. The force of each tire, including the tire longitudinal force and the tire lateral force, can be controlled theoretically. However, the wheel steering angle is directly related to the input of the steering wheel driver, and the 8WIDEV, as the research object in this paper, does not utilize active steering. The lateral force of the tire is difficult to control accurately. Therefore, the resultant force of the tire longitudinal force in the vehicle coordinate system is taken as the target force, defined as
According to the description of the vehicle steering in vehicle theory, the effect of each wheel generating a braking force on the yaw moment of the vehicle is different. The main contribution to the internal yaw moment of the vehicle comes from the rear inner wheel, whereas the lateral yaw moment produced by the front inner wheel is the most effective [
During vehicle steering, there are two cases of note: insufficient steering and excessive steering. Figure
Rulebased braking torque distribution.
By comprehensively analyzing and compensating the lack of vehicle steering in this case, the required yaw moment is found to be toward the inside, the inner rear wheel is the main brake wheel, and the other wheel on the left is the secondary brake wheel. The left wheel force produces the required yaw moment as follows:
Actuator torque allocation for redundant systems can be described as a constraint optimization problem. Considering the nonlinear saturation and coupling relationship of the tire force and torque saturation amplitude of the drive motor, the lowerlevel optimal control allocation controller is constructed. The nonlinear tire is regarded as a more extensive “constrained nonlinear actuator” in the control allocation. The optimizationbased control allocation methodweighted least square method (WLS) is introduced in this paper and can achieve the required vehicle stability performance [
According to equations (
The maximum tire longitudinal output force cannot exceed the tire friction ellipse constraint and external characteristic curve of the motor torque. First, the tire force is limited by the ground adhesion and the dynamic vertical force of each tire. According to the concept of the tire friction circle, the tire longitudinal force and lateral force need to satisfy the following conditions:
Overall, considering the friction circle constraint and the maximum torque constraint of the inwheel motor, the constraint of the longitudinal force of the tire can be merged into the following equation:
The constraint condition
To improve the vehicle stability by guaranteeing the output reserve of the tire longitudinal force, the vehicle’s stability margin is also considered when the vehicle torque is allocated. Therefore, considering further improvement in the stability under the limit condition and maneuverability under good conditions, an additional objective function is used based on the principle of the small tire load rate by reserving the load of the longitudinal force. Its norm expression is expressed by the following condition:
The distribution of the objective force/moment obtained by the upperlevel vehicle controller into the longitudinal force of each tire is an optimizationbased control allocation problem with a boundary constraint. This leads to a linear constrained quadratic programming problem. Such problem can be expressed as follows:
This problem is typical of the twostep optimization of sequential least squares (SLS). By setting the weight coefficient
The active set method algorithm is used to calculate the target torque of the inwheel motor, as shown in Figure
The active set method algorithm.
The 8WIDEV developed by our lab is a modified 8 × 8 prototype vehicle, whose basic structural parameters are shown in Table
First, we verify the effectiveness of the vehicle dynamic model builtin MATLAB/Simulink. The validity of the vehicle dynamic model can be approximately verified by comparing the prototype vehicle results with the simulation results of the dynamics model of the 8WIDEV under different and the same conditions. The experimental vehicle is equipped with gyroscopes, accelerator/brake pedal signal sensors, and a steering wheel angle sensor and is driven by eight inwheel motors with equal torque.
Through comparison of the experimental vehicle test data and simulation of the vehicle model, the accuracy of the model is verified. Under this scheme, deviations between the torque values obtained by each wheel and those of the wheels in the prototype vehicle are unavoidable. However, under the premise of sufficient power and satisfying the given vehicle working conditions, the influence of the deviations on the handling stability is not significant.
The vehicle angle step input and snake condition test are typical conditions for testing vehicle dynamics and are also important conditions in testing vehicle handling stability. Therefore, the two conditions are utilized based on controllability and stability test procedures for automobiles—the Pylon course slalom test of GB/T 6323.11994—to compare the results of the experimental vehicle and the simulation results of the vehicle model. The vehicle model established in MATLAB/Simulink uses the builtin MATLAB/Simulink Dormand–Prince algorithm to solve the problem.
Figure
Step input condition results: (a) steering wheel angle; (b) yaw rate; (c) lateral acceleration; (d) roll angle.
The simulation results reach their maximum in a very short period of time and remain unchanged for a typical angular step change of 2 seconds. In contrast, the experimental vehicle was slightly delayed; however, it also completed a step change in 0.4 seconds and remained unchanged. Both vehicles ended up at 57 degrees. Figure
The vehicle during the snake experiment passes through four piles at a constant speed of 50 km/h. Figure
8WIDEV experiment at the test site.
Snake condition results: (a) trajectory; (b) longitudinal velocity; (c) steering wheel angle; (d) yaw rate; (e) roll angle; (f) lateral velocity.
The solid line in Figure
Through the simulation test and real vehicle test of the 8 × 8 prototype vehicle, the response speed of the vehicle model is found to be related to the real vehicle test. The main reason for this is that the simulation model does not consider the characteristics of free travel, inertia, and stiffness of the steering system, and there are differences between the actual driver’s operation and an ideal driver’s operation in the simulation model. In terms of response amplitude, the deviation between the simulation results and the real vehicle tests is large at the peak, mainly because the simulation model neglects the inertia of certain rotating parts in the real vehicle and simplifies the suspension system to be a massfree, fixed stiffness, and fixed damping object. In addition, the accuracy of the tire model also produces deviations from the test results. However, these deviations are essentially unavoidable. Generally, the test results are consistent in terms of their trend, and the deviations between the results are within a reasonable range. Therefore, from a practical point of view, the simulation model can accurately reflect the response characteristics of the real vehicle. From a theoretical point of view, the accuracy of the simulation model can satisfy the requirements of vehicle dynamics research and can be used as a simulation model for vehicle handling and stability control.
It is demonstrated that the vehicle model based on MATLAB/Simulink can reflect the dynamic characteristics of the 8 × 8 prototype vehicle. The errors between the vehicle model and experimental vehicle remain as less than 8%. This is sufficient to show that the vehicle model can replace the experimental 8WIDEV for simulation experiments, thereby providing a favorable basis and conditions for the validation of the control strategy of handling stability.
This section mainly verifies the ESC proposed in this paper. Because the test prototype vehicle is still in the debugging stage, it is not possible to verify the ESC proposed in this paper on the experimental vehicle driven by 8 inwheel motors developed by our lab. To verify the ESC strategy proposed in this paper, a hardwareintheloop (HIL) test platform based on dSPACE/AutoBox is built by the authors. The HIL platform includes a AC/DC inverter, dSPACE/AutoBox, VCU, brake/accelerator pedal, steer wheel, CAN bus, and related accessories.
Figure
Schematic process of the HIL system.
The above introduced the construction of the HIL simulation platform. The construction of the test bed mainly concerns the process and theory of building the HIL simulation platform. The completed HIL simulation platform is shown in Figure
Hardwareintheloop test platform.
During the test, the driver inputs the driving intent instructions to the VCU through the A/D interface. The vehicle controller filters and calibrates these signals linearly for the acceleration/brake pedal and steering wheel sensor signals, which are converted into digital signals. Based on these signals and the realtime vehicle status feedback, such as the inwheel motor working status and the wheel angle of dSPACE/AutoBox, the realtime operation control algorithm is implemented, and control instructions are sent to dSPACE/AutoBox for realtime control.
Simultaneously, the AutoBox DS1005 processing board receives the inwheel motor torque command sent by the VCU and runs the vehicle dynamic simulation model in real time through the realtime control module. The realtime change of the vehicle state value and the inwheel motor state value are fed back to the monitoring interface of the ControlDesk and PC. The measurement, control, parameter adjustment, and monitoring interface based on the ControlDesk integrated testing software can interact with the vehicle motion parameter signals and driving environment information.
The doubleline simulation with a driverinloop setup is a classic test condition for vehicle stability testing; this testing type is selected in this paper and sets a constant longitudinal vehicle speed of 100 km/h. The purpose of the highspeed setting is to conduct investigations and evaluate the stability performance of the vehicle. The DYC method based on the hierarchical control structure utilizes the same reference model and upper controller as the ESC. The difference between them is that the DYC method uses the proposed method in Section
Figure
HIL simulation results: (a) trajectory; (b) longitudinal speed; (c) yaw rate; (d) side slip angle; (e) side slip angle change rate; (f) side slip angle and its rate.
Figures
HIL simulation results: (a) ESC torque distribution of front four wheels; (b) ESC torque distribution of rear four wheels; (c) DYC torque distribution of front four wheels; (d) DYC torque distribution of rear four wheels.
Each inwheel motor is independently and precisely controlled, making the system more likely to achieve vehicle dynamic stability control. The ESC proposed for an 8WIDEV improves the vehicle handling and control stability. A hierarchical topdown control structure includes a reference state generation controller, an upperlevel vehicle controller, and a lowerlevel optimal control allocation controller. The upperlevel vehicle controller, including the yaw moment synthesis controller, comprehensively considers the objective yaw moment calculated from the error of the side slip angle and the error of the yaw rate by adjusting the weight coefficient. The lowerlevel optimal allocation controller based on an accurate control allocation method takes not only the friction circle constraint of the mutual coupling of the tire longitudinal force/lateral force and external characteristic constraint of the inwheel motor into account but also utilizes an advanced fast calculation method, WLS, for the torque distribution in each inwheel motor. The effectiveness of the vehicle dynamic model based on prototype parameters is verified by comparison under two different conditions. The validity of the vehicle dynamic model established in this paper is verified by comparing simulation and experiment results. In addition, the HIL experimental results confirmed that the ESC proposed in this paper, compared with the DYC, can improve the handling and control stability of the vehicle. Each motor has two different working modes, which can coordinate generating the desired yaw moment. Both simulation results and experimental results have shown that the transient response speed of the vehicle is high.
Our next task is to apply the ESC proposed in this paper to the experimental vehicle after completing debugging and verifying the ESC control strategy. More importantly, the inwheel motor more effectively enables the regeneration of energy to the battery during braking and thus increases the vehicle’s range, which is another hot topic and direction worth studying.
The data used to support the finding of this study are available from the corresponding author.
The authors declare that there are no conflicts of interest.
The research funding for this paper comes from a grant from the Chinese PLA General Armament of Department (no. 40402050101). This project funding support is gratefully acknowledged and laid the foundation for this paper to proceed smoothly.