With the rapid development of the highway network construction and heavy-duty vehicle market, the rollover accidents of heavy-duty vehicle continue to increase. In order to improve rollover stability of vehicle, a four degree of freedom (DOF) heavy-duty vehicle model is established. An anti-rollover control strategy is designed by using differential braking system to control the lateral load transfer rate (LTR). The dynamic simulation of vehicle with and without control is fulfilled in Matlab/Simulink. Then, the vehicle responses under typical angle step input are compared and analyzed with different road surface adhesion coefficient, vehicle speed, steering wheel angle and vehicle load. The results show that the proposed control strategy is able to improve vehicle rollover stability greatly and is also beneficial to vehicle yaw stability. The increase of road surface adhesion coefficient, vehicle speed, steering wheel angle or vehicle load has positive correlation with the rollover control effect

Jianying Ren

Junwei Zhou

Shaohua Li

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. AUG 2016, VOL. 7. ISSN 2345-0533 129 
Anti-rollover control of a heavy-duty vehicle based on 
lateral load transfer rate 
Shaohua Li1, Junwei Zhou2, Jianying Ren3 
School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang Hebei 050043, China 
1Corresponding author 
E-mail: 1lshsjz@163.com, 2601920850@qq.com, 3aren1977@sina.com 
(Received 21 July 2016; accepted 26 July 2016) 
Abstract. With the rapid development of the highway network construction and heavy-duty 
vehicle market, the rollover accidents of heavy-duty vehicle continue to increase. In order to 
improve rollover stability of vehicle, a four degree of freedom (DOF) heavy-duty vehicle model 
is established. An anti-rollover control strategy is designed by using differential braking system 
to control the lateral load transfer rate (LTR). The dynamic simulation of vehicle with and without 
control is fulfilled in Matlab/Simulink. Then, the vehicle responses under typical angle step input 
are compared and analyzed with different road surface adhesion coefficient, vehicle speed, 
steering wheel angle and vehicle load. The results show that the proposed control strategy is able 
to improve vehicle rollover stability greatly and is also beneficial to vehicle yaw stability. The 
increase of road surface adhesion coefficient, vehicle speed, steering wheel angle or vehicle load 
has positive correlation with the rollover control effect. 
Keywords: heavy-duty vehicle, anti-rollover control, LTR, differential-braking, Matlab/Simulink. 
1. Introduction 
Heavy-duty vehicle has poor stability in the fast steering or turning radius too small or too 
large. The vehicle rollover process shows fast changing, significant nonlinear relationship, the 
complex coupling of tire and pavement and so on. The rollover accident is difficult to avoid if the 
driver correct operation is improper. Therefore, study of the vehicle anti-rollover control 
technology is very necessary.  
Because of the ABS mature, the differential braking applications are becoming more 
convenient and less costly. Scholars have studied the different models of differential braking about 
the rollover control. Gaspar [1] used the lateral load transfer rate LTR as the rollover indicator, 
and used roll bar and differential braking integrated approach to enhance the rollover stability. 
Suetake [2] established vehicle dynamics model and proposed self-adaptive system of rollover 
control. Imine [3] developed an active steering assist system to avoid rollover of heavy vehicles. 
Yim [4] proposed linear quadratic static output feedback system and study the control of 
sensitivity of parameter in rollover process by CarSim. Researchers in China have done a lot of 
valuable research about the control of vehicle rollover [5-8]. However, the current study focused 
on two axes sedan or sport utility vehicles and anti-rollover control research for the three-axis 
heavy-duty vehicles are still rare. 
In this paper, a four degree of freedom vehicle dynamics model is established for three axle 
heavy duty vehicles in Matlab/Simulink. In order to improve the rollover stability of vehicle, a 
differential braking control strategy taking the dynamic load transfer rate of LTR as control target 
is designed and simulation analysis is carried on different conditions. 
2. Vehicle dynamic model 
Considering the vehicle longitudinal, lateral, yaw and roll motion, this paper establishes the 
four degree of freedom heavy vehicle rollover model. According to D’Alembert principle, 
differential equations can be deduced about vehicle longitudinal, lateral, yaw and roll motion: 
ANTI-ROLLOVER CONTROL OF A HEAVY-DUTY VEHICLE BASED ON LATERAL LOAD TRANSFER RATE.  
SHAOHUA LI, JUNWEI ZHOU, JIANYING REN 
130 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. AUG 2016, VOL. 7. ISSN 2345-0533  
ە
ۖۖ
ۖۖ
۔
ۖۖ
ۖۖ
ۓ݉൫ ሶܸ௫ − ௬ܸ߱௥൯ = ෍[ܨ௦௜ cos(ߜ௜) − ܨఈ௜ sin(ߜ௜)]
଺
௜ୀଵ
,
݉൫ ሶܸ௬ + ௫ܸ߱௥൯ = ෍[ܨఈ௜ cos(ߜ௜) + ܨ௦௜ sin(ߜ௜)]
଺
௜ୀଵ
,
ܫ௭ ሶ߱ ௥ = ෍[(ܨఈ௜cos(ߜ௜) + ܨ௦௜sin(ߜ௜))݈௫௜
଺
௜ୀଵ
− (−ܨఈ௜sin(ߜ௜) + ܨ௦௜cos(ߜ௜))݈௬௜],
ܫ௫߶ሷ = ݉݃ℎsin߶ + ݉( ሶܸ௬ + ௫ܸ߱௥)ℎcos߶ − ݇థ߶ − ܿథ߶ሶ ,
 (1)
where ܯ, ܫ௫, ܫ௭ are gross vehicle mass and moment of inertia. ௫ܸ, ௬ܸ, ߱௥, are longitudinal, lateral 
speed and yaw rate. ߜ௜ is tire steering angle (݅ = 3-6, the rear wheel steering angle ߜ௜ = 0). ݈௫௜, ݈௬௜  
are the distance vehicle’s center of mass to the wheel center longitudinal and lateral. ℎ is the height 
of the center of mass of the vehicle, ݇థ is equivalent suspension roll stiffness. ܥథ is equivalent 
roll damping.  
Cornering force of each tire is: 
ܨఈ୧ = ݇୧ߙ௜,    (݅ = 1~6), (2)
where, ݇௜ is the cornering stiffness of each tire, and slip angle of each tire can be calculated: 
ߙ୧ =
ۖە
۔
ۖۓarctan ቆݒ௬ + ݈ଵ߱௥ݒ௫ ቇ − ߜ௜, ݅ = 1, 2,
arctan ቆݒ௬ − ݈ଶ߱௥ݒ௫ ቇ , ݅ = 3~6.
(3)
Longitudinal force of tires can be calculated by the brake force distribution formula, according 
to differential braking control. 
3. Control strategy based on LTR 
Lateral load transfer ratio LTR of tire is the ratio of the difference of the vertical load forces 
of the left wheels and the right wheels of the vehicle and the vehicle vertical load force. According 
to vehicle dynamics equation and LTR definitions, we can deduce the following equation: 
ܮܴܶ = − 2൫ܿ߶
ሶ + ݇߶൯
݉݃ܶ . (4)
During the process vehicle roll from the normal driving, LTR has a positive correlation with 
lateral acceleration of the vehicle, and LTR can be used as indicators of rollover. When the vehicle 
did not roll, ܮܴܶ = 0; When the wheel on the right side of the vehicle off the ground, ܮܴܶ = 1; 
when the left wheel off the ground, ܮܴܶ = –1. When the wheels of the vehicle off the ground, 
rollover occurs, then the value of rollover threshold of LTR is reached. 
In this paper, for three-axis heavy-duty vehicles, we use differential braking control to get 
compensation torque to achieve the purpose of controlling vehicle stability. If the tire is not locked, 
the relationship between braking force of the tire and its load is approximately proportional to the 
vertical. If the left or right wheel is braked, dynamic allocation of the braking force goes by the 
following formula [8]: 
ANTI-ROLLOVER CONTROL OF A HEAVY-DUTY VEHICLE BASED ON LATERAL LOAD TRANSFER RATE.  
SHAOHUA LI, JUNWEI ZHOU, JIANYING REN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. AUG 2016, VOL. 7. ISSN 2345-0533 131 
ܨ௦ଵ =
(1 + ܮܴܶ)݈ଶ߶௕
2(݈ଵ + ݈ଶ) , ܨ௦ଶ =
(1 − ܮܴܶ)݈ଶ߶௕
2(݈ଵ + ݈ଶ) ,    ܨ௦ଷ =
(1 + ܮܴܶ)݈ଵ߶௕
4(݈ଵ + ݈ଶ) ,
ܨ௦ସ =
(1 − ܮܴܶ)݈ଵ߶௕
4(݈ଵ + ݈ଶ) , ܨ௦ହ =
(1 + ܮܴܶ)݈ଵ߶௕
4(݈ଵ + ݈ଶ) ,    ܨ௦଺ =
(1 − ܮܴܶ)݈ଵ߶௕
4(݈ଵ + ݈ଶ) ,
(5)
where ߮௕ is braking force coefficient the ratio of the ground brake force to the vertical load. The 
numerical value is different when the slip ratio is different. 
Anti-rollover controller based on Matlab/Simulink is shown in Fig. 1. 
 
Fig. 1. LTR control 
 
 
Fig. 2. Angle step response in basic condition  
(dry asphalt, steering angle is 150 deg, the speed is 80 km/h, no-load) 
4. Simulation of typical conditions 
By using the robust control method presented for heavy duty vehicle differential braking, it 
takes angle step response of typical operating mode as an example, based on the three-axis 
heavy-duty vehicle [9], the different adhesion coefficient, different vehicle speed, different angle, 
and different load are simulated in Matlab, which is used to analysis and testify control effect. 
Choosing dry bituminous pavement. Setting the adhesion coefficient is 0.85, the initial speed of 
heavy-duty vehicle is 80 km/h, the vehicle’s mass is 10840 kg, and the steering angle is 150 deg 
as the basic working condition. The angle step response of vehicle is shown in Fig. 2. It can be 
seen from Fig. 2 that when no-load vehicle is exerted control on dry bituminous pavement, the 
roll angle decreased by 53 %, the lateral acceleration decreased by 60 %, the lateral load transfer 
2
Fb2
1
Fb1
Switch2
Switch1
Switch
Fzuo
Fyou0
Constant1
0
Constant
|u|
Abs
3
Fxright
2
Fxleft
1
LTR
ANTI-ROLLOVER CONTROL OF A HEAVY-DUTY VEHICLE BASED ON LATERAL LOAD TRANSFER RATE.  
SHAOHUA LI, JUNWEI ZHOU, JIANYING REN 
132 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. AUG 2016, VOL. 7. ISSN 2345-0533  
ratio decreased by 57 %, the yaw angle rate decreased 30 %, the speed from 80 km/h to 45 km/h 
evenly in 2 s, the rollover stability is improved, and the control effect is remarkable.  
4.1. Different road friction coefficient  
Choosing pavement is ice, the adhesion coefficient is set equal to 0.1, other parameters would 
be same with the basic operating condition, the response of vehicle which has a step input is shown 
in Fig. 3. It can be seen from Fig. 3 that when the vehicle is exerted control on the ice, the roll 
angle decreased by 30 %, the lateral acceleration decreased by 18 %, the lateral load transfer ratio 
decreased by 42 %, the yaw angle rate decreased 20 %, the speed from 80 km/h to 50 km/h evenly 
in 8 s. By comparing Fig. 3 and Fig. 2, when the vehicle is exerted control, the value of roll angle, 
lateral acceleration, LTR and yaw angle rate are bigger in low attachment surface, than in high 
attachment surface. The response can’t be controlled into a steady value, there is a degradation in 
control performance, but the control effect is still remarkable. Therefore, the anti-rollover control 
effect is positively correlated with the adhesion coefficient. 
 
 
Fig. 3. Angle step response in low attachment surface 
 
 
Fig. 4. Angle step response in low speed 
4.2. Different initial speed 
Setting the initial speed of vehicle to 50 km/h, other parameters would be same with the basic 
operating condition, the angle step response of vehicle is shown in Fig. 4. It can be seen from 
ANTI-ROLLOVER CONTROL OF A HEAVY-DUTY VEHICLE BASED ON LATERAL LOAD TRANSFER RATE.  
SHAOHUA LI, JUNWEI ZHOU, JIANYING REN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. AUG 2016, VOL. 7. ISSN 2345-0533 133 
Fig. 4 that when setting the initial speed of vehicle is 50 km/h, then the vehicle is exerted control, 
the roll angle decreased by 18 %, the lateral acceleration decreased by 15 %, the lateral load 
transfer ratio decreased by 14 %, the yaw angle rate decreased 8 %, the speed from 80 km/h to 
44 km/h evenly in 2 s. By comparing Fig. 4 and Fig. 2, roll angle, lateral acceleration, load transfer 
ratio and yaw angle rate decrease when the steering angle increases at very low vehicle speed. The 
anti-rollover control can enhance rollover stability whether vehicle speed is high or low. High 
speed is better than low speed for the anti-rollover control effect. The anti-rollover control effect 
is positively correlated with the vehicle speed. Hence, roll angle, lateral acceleration, load transfer 
ratio and yaw angle rate increase when the steering angle increases and has been very effective 
for anti-rollover control. 
In addition, the effects of steering angle and vehicle load are also researched. Due to article 
length limit, only some conclusions are listed here. It has been found that the anti-rollover effect 
is positively correlated with the steering angle’s value and the roll stability becomes poor when 
vehicle load increases.  
5. Conclusions 
In this paper a four degree of freedom (DOF) heavy-duty vehicle model is established for the 
three-axis heavy-duty vehicle. The anti-rollover control strategy is designed by using differential 
braking system of the lateral load transfer rate (LTR). The anti-rollover control system is 
constructed in Matlab/Simulink, and simulates the angle step response under different road surface 
adhesion coefficient, initial speed of vehicle, steering angle, and vehicle load. The study found 
that when increase of road surface adhesion coefficient, vehicle speed, steering angle and vehicle’s 
load, the anti-rollover control strategy has a significantly effect. In all kind of driving conditions, 
the anti-rollover control can be effective prevent vehicle rollover, and significantly improved 
vehicle yaw stability. Thus, the differential braking anti-rollover control has a wide scope, and a 
promising prospect. 
Acknowledgement 
This work was financially supported by the National Natural Science Foundation of China 
(11472180), the New Century Talent Foundation of Ministry of Education (NCET-13-0913) and 
Hebei Natural Science Foundation (A2014210103). 
References 
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vehicles. European Journal of Control, Vol. 10, 2004, p. 148-162. 
[2] Suetake Y., Oya M., Shu P. Adaptive rollover prevention controller for driver-vehicle systems. 
Artificial Life and Robotics, Vol. 19, Issue 1, 2014, p. 9-15. 
[3] Imine H., Fridman L. M., Madani T. Steering control for rollover avoidance of heavy vehicles. IEEE 
Transactions on Vehicular Technology, Vol. 61, Issue 8, 2012, p. 3499-3509. 
[4] Yim S. Design of a robust controller for rollover prevention with active suspension and differential 
braking. Journal of Mechanical Science and Technology, Vol. 26, Issue 1, 2012, p. 213-222. 
[5] Jin Z. L., Weng J. S., Hu H. Y. Anti-rollover control based on fuzzy differential braking for SUV. 
Automobile Technology, Vol. 1, 2008, p. 13-17. 
[6] Jin Z. L., Ma C. Z., Zhang J. L. Robust control strategy of SUV rollover prevention with electro 
hydraulic brake system. Journal of Chongqing University of Technology (Natural Science Edition), 
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[7] Pan S. H., Zhang X. D., Wang N. Research on simulation of vehicle anti-rollover control based on 
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Braking. Zhejiang University, Zhejiang, 2011. 
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Anti-rollover control of a heavy-duty vehicle based on lateral load transfer rate

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Anti-rollover control of a heavy-duty vehicle based on lateral load transfer rate

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