Validation of the 6-dof vehicle dynamics model and its related VBA program under the constant radius turn manoeuvre

For a 6-dof (degrees of freedom) nonlinear vehicle dynamics model and its related VBA (Visual Basic for Applications) program, which were recently derived and coded by the authors, validations are carried out under the constant radius turn manoeuvre. This model has the uniqueness that the longitudinal translation, lateral translation and yaw rotation of a platform are described by an inertial ground coordinate system and the body-roll, body-pitch, and body-yaw rotations by a platform-fixed coordinate system. The simplified STI tire model is applied for the calculation of combined longitudinal and lateral tire forces. Vehicles used in the calculation are a NISSAN DATSUN 210 (manufactured in 1980) and a HONDA ACCORD (1984). The calculation results of the present 6-dof model are compared with the published test data and those of a simpler 3-dof lateral dynamic equation based on another coordinate system. As a result of the comparison, the present 6-dof results agree very well with those of the 3-dof model and give a partial consistency with the test data.     

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.     

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.     

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.     

Fuzzy-logic applied to yaw moment control for vehicle stability

In this paper, we propose a new yaw moment control based on fuzzy logic to improve vehicle handling and stability. The advantages of fuzzy methods are their simplicity and their good performance in controlling non-linear systems. The developed controller generates the suitable yaw moment which is obtained from the difference of the brake forces between the front wheels so that the vehicle follows the target values of the yaw rate and the sideslip angle. The simulation results show the effectiveness of the proposed control method when the vehicle is subjected to different cornering steering manoeuvres such as change line and J-turn under different driving conditions (dry road and snow-covered).     

Fuzzy-logic applied to yaw moment control for vehicle stability

In this paper, we propose a new yaw moment control based on fuzzy logic to improve vehicle handling and stability. The advantages of fuzzy methods are their simplicity and their good performance in controlling non-linear systems. The developed controller generates the suitable yaw moment which is obtained from the difference of the brake forces between the front wheels so that the vehicle follows the target values of the yaw rate and the sideslip angle. The simulation results show the effectiveness of the proposed control method when the vehicle is subjected to different cornering steering manoeuvres such as change line and J-turn under different driving conditions (dry road and snow-covered).     

Application of Aerodynamic Actuators to Improve Vehicle Handling

This exploratory study considers applications of active aerodynamic devices for suppressing parasitic motion and for improving the response of vehicles to steering, within the scope of the linear dynamic behaviour. A three DOF linear model is chosen to describe the side slip, yaw and roll motion of a baseline front-wheel steered vehicle. The improvements in performance of the base-line vehicle that are achievable by the application of direct yaw and roll moments are determined when either an open loop control pre-filter or a state feedback control law based on LQR design is applied. Unlike the former control, the state feedback control is unable to make the body side-slip angle vanish. The feedback control performance of each of the two moment actuators has been examined separately and then jointly. The advantages of combining the open loop and feedback dual actuator configurations are demonstrated using the two-degree of freedom control scheme. It is found that the scheme yields a spectacular performance but demands unreasonably large moments from the actuators in the context of available aerodynamic forces. On the other hand, the demand on direct yaw and roll moment of actuators is modest when the actuators are controlled using the LQR feedback only and if the control design is used to track a desired yaw rate trajectory and simultaneously to reduce the parasitic rolling motion. Significant improvements in handling and dynamic stability of a base-line vehicle can be achieved by aerodynamically generated direct yaw and roll actuator moments provided the target control performance is reasonable. The configurations of aerodynamic actuators considered are feasible for improving vehicle handling in cornering on motorways but more work remains to be done to explore alternative aerodynamic configurations that give rise to less side effects and higher lift coefficients.     

Application of Aerodynamic Actuators to Improve Vehicle Handling

This exploratory study considers applications of active aerodynamic devices for suppressing parasitic motion and for improving the response of vehicles to steering, within the scope of the linear dynamic behaviour. A three DOF linear model is chosen to describe the side slip, yaw and roll motion of a baseline front-wheel steered vehicle. The improvements in performance of the base-line vehicle that are achievable by the application of direct yaw and roll moments are determined when either an open loop control pre-filter or a state feedback control law based on LQR design is applied. Unlike the former control, the state feedback control is unable to make the body side-slip angle vanish. The feedback control performance of each of the two moment actuators has been examined separately and then jointly. The advantages of combining the open loop and feedback dual actuator configurations are demonstrated using the two-degree of freedom control scheme. It is found that the scheme yields a spectacular performance but demands unreasonably large moments from the actuators in the context of available aerodynamic forces. On the other hand, the demand on direct yaw and roll moment of actuators is modest when the actuators are controlled using the LQR feedback only and if the control design is used to track a desired yaw rate trajectory and simultaneously to reduce the parasitic rolling motion. Significant improvements in handling and dynamic stability of a base-line vehicle can be achieved by aerodynamically generated direct yaw and roll actuator moments provided the target control performance is reasonable. The configurations of aerodynamic actuators considered are feasible for improving vehicle handling in cornering on motorways but more work remains to be done to explore alternative aerodynamic configurations that give rise to less side effects and higher lift coefficients.     

A new formulation of the understeer coefficient to relate yaw torque and vehicle handling

The handling behaviour of vehicles is an important property for its relation to performance and safety. In 1970s, Pacejka did the groundwork for an objective analysis introducing the handling diagram and the understeer coefficient. In more recent years, the understeer concept is still mentioned but the handling is actively managed by direct yaw control (DYC). In this paper an accurate analysis of the vehicle handling is carried out, considering also the effect of drive forces. This analysis brings to a new formulation of the understeer coefficient, which is almost equivalent to the classical one, but it can be obtained by quasi-steady-state manoeuvres. In addition, it relates the vehicle yaw torque to the understeer coefficient, filling up the gap between the classical handling approach and DYC. A multibody model of a Formula SAE car is then used to perform quasi-steady-state simulations in order to verify the effectiveness of the new formulation. Some vehicle set-ups and wheel drive arrangements are simulated and the results are discussed. In particular, the handling behaviours of the rear wheel drive (RWD) and the front wheel drive (FWD) architectures are compared, finding an apparently surprising result: for the analysed vehicle the FWD is less understeering than for RWD. The relation between the yaw torque and the understeer coefficient allows to understand this behaviour and opens-up the possibility for different yaw control strategies.     

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.     

Vehicle Dynamic Control for In-Wheel Electric Vehicles Via Temperature Consideration of Braking Systems

?Vehicle dynamic control (VDC) systems play an important role with regard to vehicle stability and safety when turning. VDC systems prevent vehicles from spinning or slipping when cornering sharply by controlling vehicle yaw moment, which is generated by braking forces. Thus, it is important to control braking forces depending on the driving conditions of the vehicle. The required yaw moment to stabilize a vehicle is calculated through optimal control and a combination of braking forces used to generate the calculated yaw moment. However, braking forces can change due to frictional coefficients being affected by variations in temperature. This can cause vehicles to experience stability problems due an improper yaw moment being applied to the vehicle. In this paper, a brake temperature estimator based on the finite different method (FDM) was proposed with a friction coefficient estimator in order to solve this problem. The developed braking characteristic estimation model was used to develop a VDC cooperative control algorithm using hydraulic braking and the regenerative braking of an in-wheel motor. Performance simulations of the developed cooperative control algorithm were performed through cosimulation with MATLAB/Simulink and CarSim. From the simulation results, it was verified that vehicle stability was ensured despite any changes in the braking characteristics due to brake temperatures.     

Integrated control of brake pressure and rear-wheel steering to improve lateral stability with fuzzy logic

This study introduces an integrated dynamic control with steering (IDCS) system to improve vehicle handling and stability under severe driving conditions. It integrates an active rear-wheel steering control system and a direct yawmoment control system with fuzzy logic. Direct yaw-moment control is achieved by modifying the optimal slip of the front outer wheel. An 8-degree-of-freedom vehicle model was used to evaluate the proposed IDCS for various road conditions and driving inputs. The results show that the yaw rate tracked the reference yaw rate and that the body slip angle was reduced when the IDCS was employed, thereby increasing the controllability and stability of the vehicle on slippery roads. The IDCS system reduced the deviation from the center line for a vehicle running on a split m road.     

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.     

Stability control of 4WS vehicles using robust IMC techniques

A robust nonparametric approach to vehicle stability control by means of a four-wheel steer by wire system is introduced. Both yaw rate and sideslip angle feedbacks are used in order to effectively take into account safety as well as handling performances. Reference courses for yaw rate and sideslip angle are computed on the basis of the vehicle speed and the handwheel angle imposed by the driver. An output multiplicative model set is used to describe the uncertainty arising from a wide range of vehicle operating situations. The effects of saturation of the control variables (i.e. front and rear steering angles) are taken into account by adopting enhanced internal model control methodologies in the design of the feedback controller. Actuator dynamics are considered in the controller design. Improvements on understeer characteristics, stability in demanding conditions such as turning on low friction surfaces, damping properties in impulsive manoeuvres, and improved handling in closed loop (i.e. with driver feedback) manoeuvres are shown through extensive simulation results performed on an accurate 14 degrees of freedom nonlinear model, which proved to give good modelling results as compared with collected experimental data.     

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.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A'GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A’GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

电动汽车转矩定向分配差速器建模与动态仿真

本文中提出一种新型具备转矩定向分配功能差速器的集中式电驱动桥系统。该集中驱动系统可以在不改变总驱动转矩的条件下,类似分布式驱动方式实现驱动转矩在左右轮间的任意分配,从而产生改变车辆横摆动力学的直接横摆力偶矩。首先,分析了转矩定向分配差速器结构特点及其工作原理;其次,利用键合图理论建立了其动力学模型,并仿真分析了其动态响应特性;然后,设计了转矩响应控制系统以改善该差速器的动态性能;最后,嵌入整车模型进行了联合仿真。结果表明,装备该差速器的车辆可任意分配左右轮驱动转矩,并有效改善车辆操控特性。     

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.     

Full drive-by-wire dynamic control for four-wheel-steer all-wheel-drive vehicles

Most of the controllers introduced for four-wheel-steer (4WS) vehicles are derived with the assumption that the longitudinal speed of the vehicle is constant. However, in real applications, the longitudinal speed varies, and the longitudinal, lateral, and yaw dynamics are coupled. In this paper, the longitudinal dynamics of the vehicle as well as its lateral and yaw motions are controlled simultaneously. This way, the effect of driving/braking forces of the tires on the lateral and yaw motions of the vehicle are automatically included in the control laws. To address the dynamic parameter uncertainty of the vehicle, a chatter-free variable structure controller is introduced. Elimination of chatter is achieved by introducing a dynamically adaptive boundary layer thickness. It is shown via simulations that the proposed control approach performs more robustly than the controllers developed based on dynamic models, in which longitudinal speed is assumed to be constant, and only lateral speed and yaw rate are used as system states. Furthermore, this approach supports all-wheel-drive vehicles. Front-wheel-drive or rear-wheel-drive vehicles are also supported as special cases of an all-wheel-drive vehicle.