^{1, 2}

^{3}

^{1}

^{1}

^{1}

^{2}

^{3}

This paper proposes the integrated controller of the yaw and rollover stability controls based on the prediction model. A nonlinear 3-DoF vehicle model with a piecewise linearization tire model is built up as the rollover predictive model, and its accuracy is verified by vehicle tests. A yaw stability controller and a rollover stability controller are proposed, respectively. Then coordinated control strategy is investigated for the integration of vehicle yaw and roll stability controls. The additional yaw torque and braking torque of each wheel are calculated. The unified command of valves is sent combined with ABS control algorithm. Virtual tests in CarSim are carried out, including slalom condition and double-lane change condition. Results indicate that the coordinated control algorithm improves vehicle yaw and roll stability effectively.

Yaw and roll motions are two key lateral dynamic characteristics of the ground vehicles. The safety of driving vehicle is mainly dependent on yaw and rollover stability especially in emergency conditions. Yaw stability is the ability to keep vehicle turning and avoid the motion of skidding, and roll stability is to avoid vehicle turnover under certain lateral acceleration. In USA, the percentage of rollover occurrence in all crashes was about 2.7% in 2007. However, the percentage of rollover occurrence in fatal crashes was about 21.5% and was significantly higher than that in injury and property-damage-only crashes. Untripped rollovers account for less than 5% of rolled passenger vehicles in single-vehicle crashes, which often occur during high-speed collision avoidance manoeuvres [

Approaches proposed by researchers to prevent untripped rollover can be classified into three types. Using roller warning system, the first type controls the vehicle roll motions by the driver using roller warning systems indirectly. Rollover warning is one common method to prevent from rollover [

Among these three types, the third one would have the better performance than the other two. However, multiple actuators are needed and complexity would be increased. Among those ICC, the YSC contributes to maintain vehicle yaw stability by reducing the lateral acceleration through controlling the longitudinal speed [

Taking an SUV as the research object, whose parameters were given in Table

Parameter list of vehicle model.

Element | Value |
---|---|

Vehicle mass/kg | 1910 |

Sprung mass of vehicle/kg | 1664 |

Distance between the center of sprung mass and the vehicle roll axis/m | 0.316 |

CG height/m | 0.55 |

CG to rear axis/m | 1.165 |

Inertia around the ^{2} |
3089.2 |

Inertia around the ^{2} |
33.2 |

Inertia around the ^{2} |
2549.7 |

Inertia around the ^{2} |
32.1 |

CG to front axis/m | 1.411 |

This section describes a three-degree-of-freedom roll prediction model, which is shown in Figure

Small perturbations from straight running at constant forward speed on the flat and level road are neglected.

The front wheel steering angle is taken as model input.

The vertical motion and pitching motion are neglected when the vehicle is on the flat and level road.

Aerodynamic effects are neglected.

Change of tire characteristic and the aligning torque are neglected.

Axle lateral stiffness considers steering system stiffness, suspension stiffness, and tire lateral elasticity.

The location of the center of gravity is fixed.

3-DoF vehicle nonlinear prediction model schematic diagram.

Based on the above assumptions, the balance equations of the force along the

External forces can be expressed as

As a roll prediction model, vehicle model with three degrees-of-freedom should represent the real vehicle. When rollover occurs, the lateral acceleration of vehicle will generally reach a larger value, and then the lateral forces of tires are in a nonlinear area. In this case, the limit of tire’s lateral force due to road adhesion limit should be considered. In order to provide vehicle yaw stability and avoid oversteer caused by lateral force saturation of rear wheel, the saturation restriction is used for front wheel only. The cornering property of front wheel is nonlinear and that of the rear wheel is linear, respectively. The cornering characteristic of front tire is piecewise, and the lateral force is obtained as follows:

Diagram of simplified front wheel sideslip characteristics.

A 3-DOF vehicle model is derived from (

The 3-DoF vehicle dynamics model is verified by vehicle handling and stability experiment data. The main contents of the experimental verification include vehicle steady-state roll characteristics and steady-state cornering performance, vehicle transient steering characteristics, and steer on-center characteristics and returnability. The constant-speed variable-steer tests are carried out on a uniform, dry, level and hard road surface. A step input of steering wheel angle is applied when the vehicle runs at a constant-speed, and the slalom test was carried out at a speed of 30 km/h. Vehicle data are recorded at sampling rate of 200 Hz. The results show that the responses of the vehicle model coincide with the actual vehicle measurements (see Figures

Steering wheel angle step input test.

Slalom test (30 km/h).

The objectives of YSC and RSC are to follow the driver intention and limit the maximum of the vehicle lateral acceleration, respectively. In order to maximize the vehicle yaw and roll stability, YSC and RSC will be integrated in this section. Figure

Overall structure of coordinated control algorithm of vehicle yaw and rollover stability.

YSC is designed to enhance vehicle maneuverability by tracking a reference yaw rate generated by a driver’s steering input. The yaw moment control is adopted to generate a desired yaw moment in order to reduce the yaw rate error between the reference and actual yaw rate. A linear bicycle model is used to compute the reference yaw rate, and Figure

In order to obtain the reference yaw rate and vehicle sideslip angle, a single-track model is proposed. As is shown in Figure

Bicycle model.

The strategy of yaw rate control method takes the deviation

And the desired yaw moment can be obtained from the yaw error and vehicle sideslip angle error:

A weight is used to obtain the desired moment of the YSC as follows:

RSC is designed to generate a target braking force to reduce the lateral acceleration based on the LTR, while the brake intervention is decided on the TTR threshold. Both TTR and LTR are calculated based on the 3-DoF vehicle nonlinear prediction model described in the second section, and with denoting

Consider

LTR can be defined as

The roll dynamic can be described by

Hence, the LTR can be obtained from the previous equation:

So LTR can be obtained from the sate space model as follows:

The error between the nominal TTR and the estimated TTR is used to calculate the braking yaw moment of the RSC with a proportional controller, where

The safety of driving vehicle is mainly dependent on yaw and rollover stability. Unstability of yaw takes place on all roads, while rollover mainly happens on the high adhesion road. So YSC mainly works on the low adhesion road alone, while YSC and RSC may be simultaneously or separately triggered on the high adhesion road. There are two conditions when YSC and RSC simultaneously trigger. One, when vehicle exists the danger of oversteer and rollover at the same time, YSC and RSC make vehicle tend to understeer. The other, when the rollover takes place, RSC gradually intervenes the control system which leads to larger understeer of the vehicle. Then the understeer of vehicle triggers the YSC which makes the vehicle tend to oversteer.

Overall, there are three primary relationships between YSC and RSC.

When separately triggered, YSC and RSC are independent and maximize achievement of the control target separately.

When simultaneously triggered in line with control trend, YSC and RSC control the system at the same time with coupling interaction.

When simultaneously triggered in contrast to control trend, there is contradiction between YSC and RSC.

Hence, the control targets are to keep yaw and rollover stability and reduce contradiction between YSC and RSC, and coordinate those two controllers working as an integration to ensure vehicle stability according to the danger level of yaw and roll.

Coordinated control of yaw and rollover stability controllers is designed to coordinate the YSC and RSC, shown in Figure

Diagram of the additional yaw moment and brake torque.

The additional yaw moment

In order to prevent the wheel from being locked in braking and provide greater lateral force, ABS control is added to the coordinated control of yaw and roll stability. ABS control algorithm, mainly using the wheel acceleration and deceleration threshold method, is supplemented by reference slip rate threshold control. The comparisons between wheel acceleration and slip rate are carried out between vehicle data and corresponding threshold values. According to decision logic, the control command is sent to ABS hydraulic modulator to keep slip rate at the optimal value. As a result, the longitudinal or lateral force can obtain fully utilization, which will cause small braking distance and good yaw stability [

Figures

Braking in low adhesion road.

Braking in high adhesion road.

The results show that the ABS control algorithm designed in this paper can realize good control effect in the general condition, and it is helpful for supplying a good foundation for the coordinated control of yaw and roll stability.

The proposed CCYR stability controller is implemented under the Simulink platform and simulated with the CarSim software package. To evaluate the control strategy, the algorithms of YSC and RSC are also established, respectively. And all the algorithms are evaluated through the vehicle simulation.

For each system, three simulations including slalom test under high adhesion, double-lane change test under high adhesion, and sine dwell test under high adhesion are conducted to test the rollover prevention capabilities. The same driver model is used for each rollover controller and each simulation. In these simulations, the antilock braking system (ABS) is used to prevent the lock of wheels.

The adhesion coefficient of slalom test is 1, and the initial speed is 80 km/h.

As is shown in Figure

Driving track, steering wheel angle, and vehicle speed.

In Figures

Yaw rate, roll angle, lateral acceleration, and sideslip angle.

Wheel vertical force.

The adhesion coefficient of double-lane change test is 1, and the initial speed is 130 km/h.

In Figure

Driving track, steering wheel angle, and vehicle speed.

In Figures

Yaw rate, roll angle, lateral acceleration, and sideslip angle.

Wheel vertical force.

The adhesion coefficient of sine dwell test is 1. The initial speed is 80 km/h. The input of steering wheel angle is a 0.7 Hz sine with a dwell maneuver. The maximum amplitude of steering wheel angle is 280 degrees, shown in Figure

Steering angle.

In Figure

Yaw rate, roll angle, lateral acceleration and sideslip angle.

In this paper the coordinated control strategy of yaw and rollover stability is developed. A nonlinear 3-DoF vehicle prediction model is built and tested. The YSC traces the yaw motion and the sideslip error with a 3-DoF vehicle model via differential braking. The RSC applies a braking force according to the TTR threshold and TTR estimation with a 3-DoF nonlinear prediction vehicle model of the vehicle. Simulation is implemented on CarSim electronic stability control platform by the comparison among CCYR, YSC, and RSC. The results can be summarized as follows.

The nonlinear 3-DoF vehicle model is built up and tested, and the results show that the model has very high simulation accuracy.

The coordinated control algorithm has better stability of yaw and roll than YSC and RSC.

As the rollover predictive model, the proposed nonlinear 3-DoF vehicle model is effective for the coordinated control algorithm.

Distance from center of gravity (CG) to front axle

Distance from CG to rear axle

Track width

Front tire cornering stiffness

Rear tire cornering stiffness

Total mass of vehicle

Sprung mass of vehicle

Inertia around the

Inertia around the

Inertia around the

Inertia around the

Gravity acceleration

Distance between the center of sprung mass and the vehicle roll axis

Roll damping

Front tire lateral force

Rear tire lateral force

Left side tire vertical force

Right side tire vertical force

Roll stiffness

Roll moment

Yaw moment

Longitudinal vehicle speed

Lateral vehicle speed

Lateral vehicle acceleration

Front tire steer angle

Front tire slip angle

Rear tire slip angle

Vehicle sideslip angle

Yaw angle

Yaw rate

Yaw angular acceleration

Roll angle of vehicle body

Roll angular acceleration of vehicle body

Tire-road friction coefficient.

The authors thank the “research team of test technology on the active safety of automobile.” The work is sponsored by Shanghai Automobile Incorporation Company Industrial Technology Development Fund (SAIC Grant 1007).