On the handling performance of a vehicle with different front-to-rear wheel torque distributions

ABSTRACT

The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.     

转矩式限滑差速器对后轮驱动汽车操纵稳定性影响的研究

采用7自由度车辆动力学模型,对装用JA1020LSD型转矩式限滑差速器的后轮驱动汽车进行了操纵稳定性研究。通过仿真分析和道路试验研究表明:装用限滑差速器后增加了后轮驱动车辆的不足转向趋势,即改善了操纵稳定性,但转向力矩略有增加。     

Lateral handling improvement with dynamic curvature control for an independent rear wheel drive EV

The integrated longitudinal and lateral dynamic motion control is important for four wheel independent drive (4WID) electric vehicles. Under critical driving conditions, direct yaw moment control (DYC) has been proved as effective for vehicle handling stability and maneuverability by implementing optimized torque distribution of each wheel, especially with independent wheel drive electric vehicles. The intended vehicle path upon driver steering input is heavily depending on the instantaneous vehicle speed, body side slip and yaw rate of a vehicle, which can directly affect the steering effort of driver. In this paper, we propose a dynamic curvature controller (DCC) by applying a the dynamic curvature of the path, derived from vehicle dynamic state variables; yaw rate, side slip angle, and speed of a vehicle. The proposed controller, combined with DYC and wheel longitudinal slip control, is to utilize the dynamic curvature as a target control parameter for a feedback, avoiding estimating the vehicle side-slip angle. The effectiveness of the proposed controller, in view of stability and improved handling, has been validated with numerical simulations and a series of experiments during cornering engaging a disturbance torque driven by two rear independent in-wheel motors of a 4WD micro electric vehicle.     

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.     

Haptic steering support for driving near the vehicle’s handling limits; skid-pad case

Current vehicle dynamic control systems from simple yaw control to high-end active steering support systems are designed to primarily actuate on the vehicle itself, rather than stimulate the driver to adapt his/her inputs for better vehicle control. The driver though dictates the vehicle’s motion, and centralizing him/her in the control loop is hypothesized to promote safety and driving pleasure. Exploring the above statement, the goal of this study is to develop and evaluate a haptic steering support when driving near the vehicle’s handling limits (Haptic Support Near the Limits; HSNL). The support aims to promote the driver’s perception of the vehicle’s behaviour and handling capacity (the vehicle’s internal model) by providing haptic (torque) cues on the steering wheel. The HSNL has been evaluated in (a) driving simulator tests and (b) tests with a vehicle (Opel Astra G/B) equipped with a variable steering feedback torque system. Drivers attempted to achieve maximum velocity while trying to retain control in a circular skid-pad. In the simulator (a) 25 subjects drove a vehicle model parameterised as the Astra on a dry skid-pad while in (b) 17 subjects drove the real Astra on a wet skid-pad. Both the driving simulator and the real vehicle tests led to the conclusion that the HSNL assisted subjects to drive closer to the designated path while achieving effectively the same speed. With the HSNL the drivers operated the tires in smaller slip angles and hence avoided saturation of the front wheels’ lateral forces and excessive understeer. Finally, the HSNL reduced their mental and physical demand.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Automotive Stability and Handling Dynamics in Cornering and Braking Maneuvers

SUMMARY

Automotive steering behaviour is classified for steady-state cornering and the definitions of over-/understeer and stability/instability are well known. In this paper it is intended to apply these definitions to combined cornering and braking maneuvers i.e. to extend the criteria to quasi-steady-state conditions. This way of investigation was chosen because it gives a clear idea of the typical handling behaviour. Furthermore, the vehicle behaviour is analyzed using the cornering stiffness of the axles and front/rear cornering stiffness ratio because this is always of primary significance. The following contribution is based on a theoretical analysis considering the most important non-linear vehicle properties.

The paper deals with two groups of vehicles: single vehicles (passenger cars) and combinations (passenger car/caravan and tractor/semitrailer). In the case of combinations the effect of trailers on the towing vehicles is examined. So, careful attention is paid to the coupling forces, which alter the wheel loads and influence steerability and stability.     

A Fuzzy Logic Direct Yaw-Moment Control System for All-Wheel-Drive Electric Vehicles

Summary In-wheel-motors are revolutionary new electric drive systems that can be housed in vehicle wheel assemblies. Such E-wheels permit packaging flexibility by eliminating the central drive motor and the associated transmission and driveline components, including the transmission, the differential, the universal joints and the drive shaft. Apart from many advantages of such a system, unequalled independent wheel control allows vehicle dynamic improvement to assist the driver in enhancing cornering and straight-line stability on slippery roads and in adverse ground conditions. In this paper a Fuzzy logic driver-assist stability system for all-wheel-drive electric vehicles based on a yaw reference DYC is introduced. The system assists the driver with path correction, thus enhancing cornering and straight-line stability and providing enhanced safety. A feed-forward neural network is employed to generate the required yaw rate reference. The neural net maps the vehicle speed and the steering angle to give the yaw rate reference. The vehicle true speed is estimated using a multi-sensor data fusion method. Data from wheel sensors and an embedded accelerometer are fed into an estimator, where a Fuzzy logic system decides which input is more reliable. The efficiency of the proposed system is approved by conducting a computer simulation. The proposed control system is an effective and easy to implement method to enhance the stability of all-wheel-drive electric vehicles.     

Integrated fuzzy/optimal vehicle dynamic control

There are basically two methods to control yaw moment which is the most efficient way to improve vehicle stability and handling. The first method is indirect yaw moment control, which works based on control of the lateral tire force through steering angle control. It is mainly known as active steering control (ASC). Nowadays, the most practical approach to steering control is active front steering (AFS). The other method is direct yaw moment control (DYC), in which an unequal distribution of longitudinal tire forces (mainly braking forces) produces a compensating external yaw moment. It is well known that the AFS performance is limited in the non-linear vehicle handling region. On the other hand, in spite of a good performance of DYC in both the linear and non-linear vehicle handling regions, continued DYC activation could lead to uncomfortable driving conditions and an increase in the stopping distance in the case of emergency braking. It is recommended that DYC be used only in high-g critical maneuvers. In this paper, an integrated fuzzy/optimal AFS/DYC controller has been designed. The control system includes five individual optimal LQR control strategies; each one, has been designed for a specific driving condition. The strategies can cover low, medium, and high lateral acceleration maneuvers on high-μ or low-μ roads. A fuzzy blending logic also has been utilized to mange each LQR control strategy contribution level in the final control action. The simulation results show the advantages of the proposed control system over the individual AFS or DYC controllers.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

A Fuzzy Logic Direct Yaw-Moment Control System for All-Wheel-Drive Electric Vehicles

Summary In-wheel-motors are revolutionary new electric drive systems that can be housed in vehicle wheel assemblies. Such E-wheels permit packaging flexibility by eliminating the central drive motor and the associated transmission and driveline components, including the transmission, the differential, the universal joints and the drive shaft. Apart from many advantages of such a system, unequalled independent wheel control allows vehicle dynamic improvement to assist the driver in enhancing cornering and straight-line stability on slippery roads and in adverse ground conditions. In this paper a Fuzzy logic driver-assist stability system for all-wheel-drive electric vehicles based on a yaw reference DYC is introduced. The system assists the driver with path correction, thus enhancing cornering and straight-line stability and providing enhanced safety. A feed-forward neural network is employed to generate the required yaw rate reference. The neural net maps the vehicle speed and the steering angle to give the yaw rate reference. The vehicle true speed is estimated using a multi-sensor data fusion method. Data from wheel sensors and an embedded accelerometer are fed into an estimator, where a Fuzzy logic system decides which input is more reliable. The efficiency of the proposed system is approved by conducting a computer simulation. The proposed control system is an effective and easy to implement method to enhance the stability of all-wheel-drive electric vehicles.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

SUMMARY

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

The handling surface: a new perspective in vehicle dynamics

The problem of describing the understeer–oversteer behaviour of a general vehicle, such as one with locked differential or tandem rear axle, is addressed taking a new perspective. The well-known handling diagram and the associated classical understeer gradient may be inadequate, mainly because they are no longer unique. The new concept of handling surface and a new definition of understeer gradient, which is indeed the gradient of the handling surface and hence a vector, are presented. It is also shown how the new concepts relate to and generalize the classical ones. Finally, a procedure for the experimental measure of the new understeer gradient is outlined.     

Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.     

Hierarchical Direct Yaw-Moment Control System Design for In-Wheel Motor Driven Electric Vehicle

In this study, a hierarchical structured direct yaw-moment control (DYC) system, which consists of a main-loop controller and a servo-loop controller, is designed to enhance the handling and stability of an in-wheel motor driven driven electric vehicle (IEV). In the main loop, a Fractional Order PID (FO-PID) controller is proposed to generate desired external yaw moment. A modified Differential Evolution (M-DE) algorithm is adopted to optimize the controller parameters. In the servo-loop controller, the desired external yaw moment is optimally distributed to individual wheel torques by using sequential quadratic programming (SQP) approach, with the tire force boundaries estimated by Unscented Kalman Filter (UKF) based on a fitted empirical tire model. The IEV prototype is virtually modelled by using Adams/Car collaborating with SolidWorks, validated by track tests, and serves as the control plant for simulation. The feasibility and effectiveness of the designed control system are examined by simulations in typical handling maneuver scenarios.     

Drive control system design for stability and maneuverability of a 6WD/6WS vehicle

This paper describes a drive controller designed to improve the lateral vehicle stability and maneuverability of a 6-wheel drive / 6-wheel steering (6WD/6WS) vehicle. The drive controller consists of upper and lower level controllers. The upper level controller is based on sliding control theory and determines both front and middle steering angle, additional net yaw moment, and longitudinal net force according to the reference velocity and steering angle of a manual drive, remotely controlled, autonomous controller. The lower level controller takes the desired longitudinal net force, yaw moment, and tire force information as inputs and determines the additional front steering angle and distributed longitudinal tire force on each wheel. This controller is based on optimal distribution control and takes into consideration the friction circle related to the vertical tire force and friction coefficient acting on the road and tire. Distributed longitudinal/lateral tire forces are determined as proportion to the size of the friction circle according to changes in driving conditions. The response of the 6WD/6WS vehicle implemented with this drive controller has been evaluated via computer simulations conducted using the Matlab/Simulink dynamic model. Computer simulations of an open loop under turning conditions and a closed-loop driver model subjected to double lane change have been conducted to demonstrate the improved performance of the proposed drive controller over that of a conventional DYC.     

Integrated control of ground vehicles dynamics via advanced terminal sliding mode control

An integrated vehicle dynamics control (IVDC) algorithm, developed for improving vehicle handling and stability under critical lateral motions, is discussed in this paper. The IVDC system utilises integral and nonsingular fast terminal sliding mode (NFTSM) control strategies and coordinates active front steering (AFS) and direct yaw moment control (DYC) systems. When the vehicle is in the normal driving situation, the AFS system provides handling enhancement. If the vehicle reaches its handling limit, both AFS and DYC are then integrated to ensure the vehicle stability. The major contribution of this paper is in improving the transient response of the vehicle yaw rate and sideslip angle tracking controllers by implementing advanced types of sliding mode strategies, namely integral terminal sliding mode and NFTSM, in the IVDC system. Simulation results demonstrate that the developed control algorithm for the IVDC system not only has strong robustness against uncertainties but also improves the transient response of the control system.     

Independent control of all-wheel-drive torque distribution

The sophistication of all-wheel-drive (AWD) technology is approaching the point where the drive torque to each wheel can be independently controlled. This potentially offers vehicle handling enhancements similar to those provided by dynamic stability control, but without the inevitable reduction in vehicle acceleration. Independent control of AWD torque distribution would therefore be especially beneficial under acceleration close to the limit of stability. A vehicle model of a typical sports sedan was developed in Simulink, with fully independent control of torque distribution. Box–Behnken experimental design was employed to determine which torque distribution parameters have the greatest impact on the vehicle course and acceleration. A proportional-integral control strategy was implemented, applying yaw rate feedback to vary the front–rear torque distribution and lateral acceleration feedback to adjust the left–right distribution. The resulting system shows a significant improvement over conventional driveline configurations under aggressive cornering acceleration on a high-μ surface. The performance approaches the theoretical limit for these conditions. In the medium term, such a system is only likely to be economically viable for premium vehicles. However, a future revolution of powertrain technology towards, for example, wheel-mounted motors, could realize these handling benefits far more widely.     

Independent control of all-wheel-drive torque distribution

The sophistication of all-wheel-drive (AWD) technology is approaching the point where the drive torque to each wheel can be independently controlled. This potentially offers vehicle handling enhancements similar to those provided by dynamic stability control, but without the inevitable reduction in vehicle acceleration. Independent control of AWD torque distribution would therefore be especially beneficial under acceleration close to the limit of stability. A vehicle model of a typical sports sedan was developed in Simulink, with fully independent control of torque distribution. Box-Behnken experimental design was employed to determine which torque distribution parameters have the greatest impact on the vehicle course and acceleration. A proportional-integral control strategy was implemented, applying yaw rate feedback to vary the front-rear torque distribution and lateral acceleration feedback to adjust the left-right distribution. The resulting system shows a significant improvement over conventional driveline configurations under aggressive cornering acceleration on a high-μ surface. The performance approaches the theoretical limit for these conditions. In the medium term, such a system is only likely to be economically viable for premium vehicles. However, a future revolution of powertrain technology towards, for example, wheel-mounted motors, could realize these handling benefits far more widely.