A methodology for vehicle sideslip angle identification: comparison with experimental data

Sideslip angle could provide important information concerning vehicle's stability. Unfortunately direct measurement of sideslip angle requires a complex and expensive experimental set-up, which is not suitable for implementation on ordinary passenger cars; thus, this quantity has to be estimated starting from the measurements of vehicle lateral/longitudinal acceleration, speed, yaw rate and steer angle. According to the proposed methodology, sideslip angle is estimated as a weighted mean of the results provided by a kinematic formulation and those obtained through a state observer based on vehicle single-track model. Kinematical formula is considered reliable for a transient manoeuvre, while the state observer is used in nearly quasi-state condition. The basic idea of the work is to make use of the information provided by the kinematic formulation during a transient manoeuvre to update the single-track model parameters (tires cornering stiffnesses). A fuzzy-logic procedure was implemented to identify steady state or transient conditions.     

Sideslip angle estimation based on input–output linearisation with tire–road friction adaptation

An adaptive sideslip angle observer considering tire–road friction adaptation is proposed in this paper. The single-track vehicle model with nonlinear tire characteristics is adopted. The tire parameters can be easily obtained through road test data without using special test rigs. Afterwards, this model is reconstructed and a high-gain observer (HGO) based on input–output linearisation is derived. The observer stability is analysed. Experimental results have confirmed that the HGO has a better computational efficiency with the same accuracy when compared with the extended Kalman filter and the Luenberger observer. Finally, a road friction adaptive algorithm based on vehicle lateral dynamics is proposed and validated through driving simulator data. As long as the tires work in the nonlinear region, the maximal friction coefficient could be estimated. This algorithm has excellent portability and is also suitable for other observers.     

Sideslip estimation for articulated heavy vehicles at the limits of adhesion*

Various active safety systems proposed for articulated heavy goods vehicles (HGVs) require an accurate estimate of vehicle sideslip angle. However in contrast to passenger cars, there has been minimal published research on sideslip estimation for articulated HGVs. State-of-the-art observers, which rely on linear vehicle models, perform poorly when manoeuvring near the limits of tyre adhesion. This paper investigates three nonlinear Kalman filters (KFs) for estimating the tractor sideslip angle of a tractor–semitrailer. These are compared to the current state-of-the-art, through computer simulations and vehicle test data. An unscented KF using a 5 degrees-of-freedom single-track vehicle model with linear adaptive tyres is found to substantially outperform the state-of-the-art linear KF across a range of test manoeuvres on different surfaces, both at constant speed and during emergency braking. Robustness of the observer to parameter uncertainty is also demonstrated.     

Sideslip angle estimation considering short-duration longitudinal velocity variation

The accurate estimation of sideslip angle is necessary for many vehicle control systems. The detection of sliding and skidding is especially critical in emergency situations. In this paper, a sideslip angle estimation method is proposed that considers severe longitudinal velocity variation over the short period of time during which a vehicle may lose stability due to sliding or spinning. An extended Kalman filter (EKF) based on a kinematic model of a vehicle is used without initialization of the inertial measurement unit to estimate vehicle longitudinal velocity. A dynamic compensation method that compensates for the difference in the locations of the vehicle velocity sensor and the IMU in on-road vehicle tests is proposed. Evaluations with a CarSim™ 27-degree-of-freedom (DOF) model for various vehicle test scenarios and with on-road tests using a real vehicle show that the proposed sideslip angle estimation method can accurately predict sideslip angle, even when vehicle longitudinal velocity changes significantly.     

Disturbance Observer-Based Sideslip Angle Control for Improving Cornering Characteristics of In-Wheel Motor Electric Vehicles

In this paper, a robust sideslip angle controller based on the direct yaw moment control (DYC) is proposed for in-wheel motor electric vehicles. Many studies have demonstrated that the DYC is one of the effective methods to improve vehicle maneuverability and stability. Previous approaches to achieve the DYC used differential braking and active steering system. Not only that, the conventional control systems were commonly dependent on the feedback of the yaw rate. In contrast to the traditional control schemes, however, this paper proposes a novel approach based on sideslip angle feedback without controlling the yaw rate. This is mainly because if the vehicle sideslip angle is controlled properly, the intended sideslip angle helps the vehicle to pass through the corner even at high speed. On the other hand, the vehicle may become unstable because of the too large sideslip caused by unexpected yaw disturbances and model uncertainties of time-varying parameters. From this aspect, disturbance observer (DOB) is employed to assure robust performance of the controller. The proposed controller was realized in CarSim model described actual electric vehicle and verified through computer simulations.     

基于扩展卡尔曼滤波的汽车质心侧偏角估计

基于二自由度汽车动力学模型和轮胎模型,运用扩展卡尔曼滤波方法建立了汽车质心侧偏角估计器.利用汽车动力学仿真平台,通过仿真对比了线性轮胎模型和非线性轮胎模型的质心侧偏角估计结果.仿真结果表明,轮胎模型对于质心侧偏角估计精度至关重要,而采用非线性轮胎模型能显著提高质心侧偏角估计精度,估计结果能满足ESC控制的要求.     

Effect of handling characteristics on minimum time cornering with torque vectoring

In this paper, the effect of both passive and actively-modified vehicle handling characteristics on minimum time manoeuvring for vehicles with 4-wheel torque vectoring (TV) capability is studied. First, a baseline optimal TV strategy is sought, independent of any causal control law. An optimal control problem (OCP) is initially formulated considering 4 independent wheel torque inputs, together with the steering angle rate, as the control variables. Using this formulation, the performance benefit using TV against an electric drive train with a fixed torque distribution, is demonstrated. The sensitivity of TV-controlled manoeuvre time to the passive understeer gradient of the vehicle is then studied. A second formulation of the OCP is introduced where a closed-loop TV controller is incorporated into the system dynamics of the OCP. This formulation allows the effect of actively modifying a vehicle's handling characteristic via TV on its minimum time cornering performance of the vehicle to be assessed. In particular, the effect of the target understeer gradient as the key tuning parameter of the literature-standard steady-state linear single-track model yaw rate reference is analysed.     

Design and evaluation of sideslip angle observer for vehicle stability control

This paper presents a method for estimating the vehicle side slip angle, which is considered as a significant signal in determining the vehicle stability region in vehicle stability control systems. The proposed method combines the model-based method and kinematics-based method. Side forces of the front and rear axles are provided as a weighted sum of directly calculated values from a lateral acceleration sensor and a yaw rate sensor and from a tire model according to the nonlinear factor, which is defined to identify the degree of nonlinearity of the vehicle state. Then, the side forces are fed to the extended Kalman filter, which is designed based on the single-track vehicle model associated with a tire model. The cornering stiffness identifier is introduced to compensate for tire force nonlinearities. A fuzzy-logic procedure is implemented to determine the nonlinear factor from the input variables: yaw rate deviation from the reference value and lateral acceleration. The proposed observer is compared with a model-based method and kinematics-based method. An 8 DOF vehicle model and Dugoff tire model are employed to simulate the vehicle state in MATLAB/SIMULINK. The simulation results shows that the proposed method is more accurate than the model-based method and kinematics-based method when the vehicle is subjected to severe maneuvers under different road conditions.     

汽车侧偏角与横摆角的仿真与估计

为了提高汽车操纵稳定性和安全性,设计汽车状态观测器模型对难以测量的质心侧偏角与横摆角速度的数据进行估计是很有必要的。本文利用扩展卡尔曼滤波算法并基于二自由度汽车模型上对质心侧偏角进行估计及仿真分析,仿真的结果与估计的结果吻合,估计结果具有较高的应用价值。     

Optimal Control of Four Wheel Steering Vehicle

SUMMARY

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

Additional 4WS and Driver Interaction

SUMMARY

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Slip-Angle Estimation for Vehicle Stability Control

Recently, some direct yaw-moment control systems have been in development. Obviously, such systems need accurate slip-angle information. This paper describes a strategy of vehicle slip angle estimation. The difficulty in slip angle estimation is due to nonlinear characteristics of tyres and influence of relative slant of the road surface. To solve this difficulty, a combined method of model observer and direct integration method is proposed. In this method, two kinds of values of the side forces of the wheels are provided, i.e., direct detected values by the G-sensor and values from a tyre model. Then those values are combined appropriately which results in the combination of model observer and direct integration. A feedback algorithm, redesigned to suppress the influence of tyre model error, is applied in the observer. Considering interference of road surface and its avoidance, road slant angle is estimated and consequently vehicle model is corrected. The estimated value of the road friction coefficient is given by the acceleration, and an adequate bias, depending on yaw-deviation, is added. The calculation method of reference yaw-velocity is improved, in order to avoid interference of road slant and variation of dynamic characteristic of vehicle.     

Slip-Angle Estimation for Vehicle Stability Control

Recently, some direct yaw-moment control systems have been in development. Obviously, such systems need accurate slip-angle information. This paper describes a strategy of vehicle slip angle estimation. The difficulty in slip angle estimation is due to nonlinear characteristics of tyres and influence of relative slant of the road surface. To solve this difficulty, a combined method of model observer and direct integration method is proposed. In this method, two kinds of values of the side forces of the wheels are provided, i.e., direct detected values by the G-sensor and values from a tyre model. Then those values are combined appropriately which results in the combination of model observer and direct integration. A feedback algorithm, redesigned to suppress the influence of tyre model error, is applied in the observer. Considering interference of road surface and its avoidance, road slant angle is estimated and consequently vehicle model is corrected. The estimated value of the road friction coefficient is given by the acceleration, and an adequate bias, depending on yaw-deviation, is added. The calculation method of reference yaw-velocity is improved, in order to avoid interference of road slant and variation of dynamic characteristic of vehicle.     

Additional 4WS and Driver Interaction

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Optimal Control of Four Wheel Steering Vehicle

This paper derives a method of controlling four wheel steering using optimal control theory. The purpose of control is to minimize the sideslip angle at the center of gravity. The control method feeds forward the steering wheel angle and feeds back the yaw velocity and the sideslip angle to the front and rear wheel angles. Theoretical studies show that the sideslip angle is reduced to zero even in the transient state, and that the understeer characteristic and frequency response can be changed regardless of the vehicle static margin. This Paper also examines various characteristics of the influence of the side force nonlinearities of tires and crosswinds.     

车辆系统垂向与横向耦合的侧倾状态估计

为有效解决复杂行驶工况下车辆耦合侧倾运动状态无法精确获取,进而对车辆系统操纵稳定性与乘坐舒适性兼顾优化无法提供准确输入的难题,本文中设计了基于车辆垂向与横向耦合动力学的双非线性状态观测器算法,以实现复杂行驶工况下车辆耦合侧倾运动状态的实时准确估计。首先,建立了路面激励模型与整车系统垂向与横向耦合动力学模型;接着,利用无迹卡尔曼滤波方法(UKF)与非线性模糊观测(T-S)理论,设计了非线性状态观测算法,以在不同路面激励工况下对车辆系统簧载质量与侧倾状态进行联合估计;最后,运用CarSim■动力学软件,对比分析了在标准A级与C级路面上进行J-turn试验工况下,采用联合状态观测器(UKF&T-S)实时估计车辆侧倾角与侧倾率的观测精度。结果表明,本文所设计的UKF&T-S观测器可有效估计车辆侧倾状态,且与CarSim■仿真数据相比识别状态标准偏差不超过10%。     

汽车行驶状态参数的估计

介绍Sage-Husa自适应卡尔曼滤波算法和滤波估计流程,建立二自由度汽车模型,在模型中加入系统噪声和测量噪声,建立系统状态方程和观测方程。利用自适应卡尔曼滤波算法,对汽车质心侧偏角和横摆角速度进行估计,并进行转向盘转角正弦输入仿真分析,仿真结果表明两者的真实值和估计值吻合良好。利用自适应卡尔曼滤波算法对汽车行驶状态参数进行估计可以降低汽车的成本,是一种行之有效且具有工程应用价值的方法。     

基于MPC的独立驱动电动汽车稳定性集成控制

针对独立驱动电动汽车在高附着系数路面高速急转时易发生侧翻事故,在低附着系数路面急转易发生侧滑失稳事故,且单一控制器在不同附着系数路面适应性较差等问题,根据独立驱动电动汽车特点设计了基于分层式结构的稳定性集成控制器。建立了整车动力学模型,并进行了车辆状态参数估计;设计了稳定性集成控制器的控制策略,对车辆的侧倾、横向稳定性状态判定条件和协调策略的制定进行了研究,分别设计了侧倾稳定性控制器和横向稳定性控制器;设置了路面附着系数0.9到0.2的对接路面仿真工况,并在此工况下对所设计的控制器的控制性能进行了仿真测试。结果表明,所设计的稳定性集成控制器相比于单一控制器具有更好的适应性,可有效降低车辆高速行驶过程中的横向载荷转移系数、质心侧偏角等状态量,提高车辆行驶的稳定性和安全性。     

Predictive control of a vehicle trajectory using a coupled vector with vehicle velocity and sideslip angle

In this paper, a predictive algorithm for vehicle trajectory control using the vehicle velocity and sideslip angle is proposed. Since the driving state of a vehicle generates nonholonomic constraint equations, it is difficult to control the trajectory with a conventional control algorithm. Furthermore, control vectors such as vehicle velocity and sideslip angle are coupled together; hence, a separate control for each variable is not suitable. In this study, a coupled control vector that combines the velocity and sideslip angle is proposed for the predictive control of vehicle trajectory. Since the coupled control vector is derived from the status of the vehicle’s motion, it is easy to generate a feedback control vector for the predictive controller. The coupled vector cannot be directly used as input to the vehicle systems; therefore, the vehicle input vector should be calculated from the control vector using a nonlinear function. Since nonlinear functions are not inserted in the control loop, they are calculated by the controller. Therefore, this method does not require a linearization process in the control logic, which enhances the stability and accuracy of the predictive controller.