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.     

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.     

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 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.     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

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.     

Model-Based Road Friction Estimation

The tire/road friction coefficient, μ, has a significant role in vehicle longitudinal and lateral control, and there has been associated efforts to measure or estimate the road surface condition to provide additional information for stability augmentation systems of automobiles. In this paper, a model based road friction estimation algorithm is proposed from easily measured signals such as yaw rate and wheel speed. For the development of the estimator, a low order vehicle model incorporated with simple but effective tire model. Field tests of the estimator using actual vehicle measurements show promising results.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

轮胎附着极限下差动制动对汽车横摆力矩的影响

本文以纵滑－侧偏联合工况的稳态轮胎模型为基础，分析了汽车极限转向条件下制动作用于不同车轮时对汽车横摆力矩的影响，并通过整车动力学仿真进行了验证，研究结果为利用差动制动控制提高汽车的高速操纵稳定性提供了动力学依据。     

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。     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

A novel direct yaw moment controller for in-wheel motor electric vehicles

A novel direct yaw moment controller is developed in this paper. A hierarchical control architecture is adopted in the controller design. In the upper controller, a driver model and a vehicle model are used to obtain the driver's intention and the vehicle states, respectively. The upper controller determines the desired yaw moment by means of sliding mode control. The lower controller distributes differential longitudinal forces according to the desired yaw moment. A nonlinear tyre model, ‘UniTire’, is utilised to develop the novel distribution strategy and the control boundary.     

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.     

Multi-axle vehicle dynamics stability control algorithm with all independent drive wheel

The stability driving characteristic and the tire wear of 8-axle vehicle with 16-independent driving wheels are discussed in this paper. The lateral stability of 8-axle vehicle can be improved by the direct yaw moment which is generated by the 16 independent driving wheels. The hierarchical controller is designed to determine the required yaw torque and driving force of each wheel. The upper level controller uses feed-forward and feed-backward control theory to obtain the required yaw torque. The fuzzification weight ratio of two control objective is built in the upper level controller to regulate the vehicle yaw and lateral motions. The rule-based yaw moment distribution strategy and the driving force adjustment based on the safety of vehicle are proposed in the lower level controller. The influence of rear steering angle is considered in the distribution of driving force of the wheel. Simulation results of a vehicle double lane change show the stability of 8-axle vehicle under the proposed control algorithm. The wear rate of tire is calculated by the interaction force between the tire and ground. The wear of tire is different from each other for the vehicle with the stability controller or not.     

基于NMPC的智能汽车纵横向综合轨迹跟踪控制

本文中针对大曲率转弯工况下,智能汽车纵横向动力学特性的耦合和动力学约束导致轨迹跟踪精度和稳定性下降的问题,提出一种基于非线性模型预测控制(NMPC)的纵横向综合轨迹跟踪控制方法,通过NMPC和障碍函数法(BM)的有效结合,提高了跟踪精度,改善了行驶稳定性.首先建立四轮驱动-前轮转向智能汽车动力学模型和轨迹跟踪模型,采用...     

Electronic stability control for electric vehicle with four in-wheel motors

The electric vehicle with four direct-driven in-wheel motors is an over actuated system. A three-level control strategy of electronic stability control (ESC) is proposed to achieve optimal torque distribution for four in-wheel motors. The first level is a gain-scheduled linear quadratic regulator which is designed to generate the desired yaw moment command for ESC. Control allocation is the second level which is used to distribute the desired longitudinal tire forces according to the yaw moment command while satisfying the driver’s intent for acceleration and deceleration. The associated weighting matrix is designed using the work load ratio at each wheel to prevent saturating the tire. The third level is slip ratio control (SRC) which is employed at each wheel to generate the desired longitudinal tire force based on a combined-slip tire model. Simulation results show that the proposed method can enhance the ESC performance for the test maneuvers. Since the tire model is often unknown for practical implementation, the effectiveness of the SRC is studied using the sine with dwell test. It is found that the SRC is not crucial for achieving performance similar to the proposed method with SRC, if the slip ratio can be maintained in the stable region using traction control system/anti-lock braking system.     

Coordinated control of ESC and AFS with adaptive algorithms

This paper presents a coordinated control of electronic stability control (ESC) and active front steering (AFS) with adaptive algorithms for yaw moment distribution in integrated chassis control (ICC). In order to distribute a control yaw moment into control tire forcres of ESC and AFS, and to coordinate the relative usage of ESC to AFS, a LMS/Newton algorithm (LMSN) is adopted. To make the control tire forces zero in applying LMS and LMSN, the zero-attracting mechanism is adopted. Simulations on vehicle simulation software, CarSim®, show that the proposed algorithm is effective for yaw moment distribution in integrated chassis control.     

Selection of Actuator Combination in Integrated Chassis Control Using Taguchi Method

This paper presents a method to select the actuator combination in integrated chassis control using Taguchi method. Electronic stability control (ESC), active front and rear steering (AFS/ARS) are used as an actuator, which is needed to generate a control tire force. After computing the control yaw moment in the upper-level controller, it is distributed into the control tire forces, generated by ESC, AFS and ARS in the lower-level controller. In this paper, the weighted pseudo-inverse control allocation (WPCA) with variable weights is used to determine the control tire forces of each actuator. Taguchi method is adopted for sensitivity analysis on variable weights of WPCA in terms of the control performances such as the maneuverability and the lateral stability. For sensitivity analysis, simulation is performed on a vehicle simulation package, CarSim. From sensitivity analysis, the most effective actuator combination is selected.