This paper takes the electric offroad vehicle with separated driven axles as the research object. To solve the longitudinal dynamics driving control problems, vehicle dynamics model, and control strategies were studied and the corresponding simulation was carried out. An 8DOF vehicle dynamics model with separated driven axles was built. The driving control strategies on the typical roads were put forward. The recognition algorithm of the typical road surfaces based on the wheels’ slip rates was proposed. And the two control systems were designed including the pedal opening degree adjustment control system based on PI algorithm and the interaxle torque distribution control system based on sliding mode control algorithm. The driving control flow of the proposed vehicle combining the pedal adjustment control system with the interaxle torque distribution control system was developed. And the driven control strategies for the typical roads were simulated. Simulation results show that the proposed drive control strategies can adapt to different typical road surfaces, limit the slip rates of the driving wheels within the stable zone, and ensure the vehicle driving safely and stably in accordance with the driver's intention.
The deterioration problem of energy and environment makes the ecovehicles with motor driving develop rapidly. Several types of drive systems have been proposed for ecovehicles such as front or rearwheeldrive system with two inwheel motors and fourwheeldrive system with independently driven front and rear motors or four inwheel motors [
Control strategy is the key of traction control [
Focusing on electric vehicles with independently driven front and rear wheels, taking an electric offroad vehicle as the research platform, combined with the antislip control for the fourwheeldrive vehicle, we studied the driving control strategies and algorithms for longitudinal dynamics to improve the dynamic performance and safety on different road surfaces. Based on the pedal adjustment control system and the interaxle torque distribution control system, the driving control flow, through which the driving control strategies can switch adaptively according to road surfaces, was proposed. And the driving control strategies for different road surfaces were verified through the simulation.
The powertrain of an electric offroad vehicle with independently front and rear drive wheels is shown in Figure
Powertrain system structure of an electric offroad vehicle.
The basic parameters of the vehicle are shown in Table
Basic parameters of the vehicle.
Parameters  Symbols  Units  Values 

Gross mass 

kg  7000 
Wheelbase (front, rear) 

m  (2.262, 1.638) 
Track width (front, rear) 

m  (2.1, 2.1) 
Centroid height 

m  0.9 
Windward area 

m^{2}  3.9 
Air drag coefficient 

—  0.65 
Wheel rolling radius 

m  0.450 
Rolling resistance coefficient 

—  0.015 
Wheel rotational inertia 

kg·m^{2}  1.25 
Rotary mass coefficient 

—  1.1794 
Fixed reducer ratio 

—  3.36 
Main reducer ratio 

—  4.9152 
Efficiency of transmission 

—  0.9 
Motor peak/rated power 

kW  90/45 
Motor maximum/rated speed 

rpm  6000/2000 
Motor peak/rated torque 

N·m  430/215 
Using modular method, each part of the dynamic models of the vehicle is established as follows.
Figure
The static and dynamic characteristics of the motor: (a) static drive torque and regenerative torque characteristic; (b) torque step response of the motor.
Take
Tire parameters based on “Magic Formula.”
0  1  2  3  4  5  6  7  8  


1.374  −0.2501  −980.0  −1845  10.80  −0.0110  −0.0295  0.4052  0.0207 

1.5  −2.4  1050  20  226  0.069  −0.006  0.056  0.486 

2.34  −0.9250  −6.417  2.004  0.0577  0.0984  0.0028  −0.0100  0.0100 
 
9  10  11  12  13  14  15  16  17  
 

0  0  −14.24  0  0  —  —  —  — 

0  0  —  —  —  —  —  —  — 

−3.000  0.0255  0.0036  0.0103  −0.0647  −0.0111  −0.3947  −0.0994  −3.337 
The 8DOF vehicle dynamics model established in this paper included the longitudinal, lateral, and yaw displacements of the body, the rotational displacements of the four independent wheels, and the steering angle displacement of the front wheels, with the assumption that the two front wheels had the same steering angle and there was no rubbing effect in the differential mechanism. Using the dynamic models established above, the dynamics model of the vehicle with independently driven front and rear wheels was built as shown in Figure
Overall structure of the vehicle system dynamics model.
In Figure
This paper mainly studied the control strategies on driving condition, involving the two decision variables, namely,
The fixed pedal adjustment coefficient and fixed torque distribution coefficient are the initial values of the two decision variables at the same time, namely:
In summary, the driving strategies on different typical road surfaces were designed as shown in Table
Driving strategies on different typical surfaces.
Typical surfaces  Driving control strategies 

High 

Low and uniform  Pedal adjustment control, 
Bisectional  Pedal adjustment control, 
Joint  Pedal adjustment control, torque distribution control 
The driving control system needs to judge the vehicle driving conditions realtimely according to the four wheels’ slip rates, namely
In order to facilitate the recognition, the mean of the slip rates was calculated as follows:
Based on the slip rates and the mean variables given above, the recognition algorithms of the typical road surfaces were proposed as follows.
In summary, the recognition algorithms of typical road surfaces based on slip rates were proposed as shown in Table
Recognition algorithms of typical surfaces based on slip rates.
Typical surfaces  Recognition algorithms 

High 

Low and uniform 

Bisectional 

Joint 

Back to high 

The pedal adjustment control system was designed to control the slip rates of the seriously slipping wheels within the stable zone and close to
The deviation variable was designed as
In this paper, the PI control algorithm was adopted to the pedal adjustment control system, which would lead the deviation variable, that is,
Pedal adjustment control system based on PI algorithm.
When the vehicle is driving on the joint road or the axle load is heavily transferred, the interaxle torque distribution control system was designed to optimize the torque distribution between the axles, which would keep the slip rate difference between front and rear axle in the allowable range. According to the definition of slip rate, the algorithm could just minimize the speed difference of the axles.
The deviation variable was designed as
The sliding control mode has been applied to many vehicle control systems, such as the ABS control system [
According to the motion equation on driving condition, considering a bicycle model, the equations were deduced as
Substituting (
According to the driver’s driving intention
Substituting (
Considering the validity conditions of sliding control algorithm as follows:
In accordance with the designed driving control strategies and the proposed recognition algorithms of typical surfaces, using the established pedal adjustment control system and the torque distribution control system above, the driving control flow for the longitudinal dynamics of the vehicle with independently driven front and rear wheels was designed as shown in Figure
Control flow of the driving control system.
The driving control flow shown in Figure
The road adhesion conditions are represented by the peak adhesion coefficients at each wheel. Use to represent the peak adhesion coefficients at front and left wheel, front and right wheel, rear and left wheel and rear and right wheel, respectively. This paper set the surface parameters at each wheel of different typical surfaces as shown in Table
Adhesion coefficients of typical surfaces.
Typical surfaces  Adhesion coefficients 

High adhesion  (0.8, 0.8, 0.8, 0.8) 
Low and uniform  (0.2, 0.2, 0.2, 0.2) 
Bisectional  (0.2, 0.8, 0.2, 0.8) 
Joint  (0.2, 0.2, 0.8, 0.8) 
In Table
Figures
Simulation results with average torque distribution on high adhesion road: (a) slip rates of the front and rear axles; (b) acceleration of the vehicle.
Simulation results with fixed proportion torque distribution on high adhesion road: (a) slip rates of the front and rear axles; (b) acceleration of the vehicle.
The simulation results show that the fixed proportion torque distribution mode according to the static axles load can significantly reduce the slip rate difference of front and rear wheels with no reduction of the vehicle acceleration, which is beneficial to the equal life design of the tires as the wear rates of the front and rear wheels are similar. As the acceleration of the vehicle and the ramp resistance transfer the axles load, and the longitudinal force and the vertical force of the tire have nonlinear relationship, there is inevitable difference between the front and rear slip rates, which, however, would not influence the dynamics performance of the vehicle on high adhesion road.
Figures
Simulation results without pedal control on low adhesion and homogenous surface: (a) slip rates of the front and rear axles; (b) acceleration of the vehicle.
Simulation results with pedal adjustment control on low adhesion and homogenous surface: (a) slip rates of the front and rear wheels on the left side; (b) acceleration of the vehicle; (c) average slip rate of the wheels; (d) the pedal adjustment coefficient.
The simulation results show that, without pedal adjustment control, the slip rates of the front and rear wheels were in unstable zone when the motor works in the high torque zone, as shown in Figure
Figures
Simulation results without pedal control on bisectional road: (a) average slip rates of the left and right side wheels; (b) acceleration of the vehicle.
Simulation results with pedal adjustment control on bisectional road: (a) average slip rates of the left and right side wheels; (b) acceleration of the vehicle; (c) slip rates of the front and rear wheels on the left side; (d) the pedal adjustment coefficient.
The simulation results show that, without pedal adjustment control, the slip rates of the wheels at the low adhesion side were in unstable zone and the slip rates of the wheels at the high adhesion side were in stable zone when the motor worked in the high torque zone, as shown in Figure
Figures
Simulation results without torque distribution control on joint road: (a) average slip rates of the front and rear wheels; (b) slip rate difference between front and rear wheels; (c) output torques of the front and rear wheels; (d) acceleration of the vehicle.
Simulation results with torque distribution control on joint road: (a) average slip rates of the front and rear wheels; (b) slip rate difference between front and rear wheels; (c) output torques of the front and rear wheels; (d) acceleration of the vehicle; (e) the torque distribution coefficient.
The simulation results in Figure
The simulation results in Figure
For a front and rear axle independently driven system, an 8DOF dynamics model of the vehicle system was established, which serves as the testing platform of the driving control strategies.
The driving control strategies for different typical surfaces were studied, and the recognition algorithms for the typical surfaces based on the slip rates were proposed. Two control systems including the pedal adjustment control system based on PI algorithm and the torque distribution control system based on SMC algorithm were designed. The driving control flow of the electric vehicle with independently driven front and rear wheels was developed.
Several simulation experiments were carried out, we compared the simulation results of the slip rates, the accelerations and so forth, under different driving control strategies, which confirmed the rationality of the strategies on different typical surfaces. The pedal adjustment control system could effectively prevent the slipping of the driving wheel, and the interaxle torque distribution system could reduce the slip difference between the front and rear wheels. As a result, the dynamic performance and safety of the vehicle were ensured.
The authors declare that there is no conflict of interests regarding the publication of this paper.