An Investigation of High-Speed Automobile Steering Response

SUMMARY

The significance of the effects of steering compliance and aerodynamic life on high speed automobile's steering response was investigated on two vehicles, a Ford Falcon XW (1969) station-wagon and a GM-Holden Kingswood HQ (1974) sedan. An aerofoil was mounted above the front bumper bar of the Ford Falcon to enable the simulation of vehicles with very degraded aerodynamic characteristics. Mathematical analysis showed the importance of the inclusion of steering compliance effects in determining stability factor, and hence the vehicle's high speed yaw rate sensitivity. Both experiments and theory showed that the actual high speed yaw rate response is not significantly less than that predicted from a low speed skid pad test, however, slight errors were found which are likely to be due to steering system nonlinearity and the effects of aerodynamic lift.     

Asymptotic sideslip angle and yaw rate decoupling control in four-wheel steering vehicles

This paper shows that, for a four-wheel steering vehicle, a proportional-integral (PI) active front steering control and a PI active rear steering control from the yaw rate error together with an additive feedforward reference signal for the vehicle sideslip angle can asymptotically decouple the lateral velocity and the yaw rate dynamics; that is the control can set arbitrary steady state values for lateral speed and yaw rate at any longitudinal speed. Moreover, the PI controls can suppress oscillatory behaviours by assigning real stable eigenvalues to a widely used linearised model of the vehicle steering dynamics for any value of longitudinal speed in understeering vehicles. In particular, the four PI control parameters are explicitly expressed in terms of the three real eigenvalues to be assigned. No lateral acceleration and no lateral speed measurements are required. The controlled system maintains the well-known advantages of both front and rear active steering controls: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres and improved manoeuvrability. In particular, zero lateral speed may be asymptotically achieved while controlling the yaw rate: in this case comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced. Also zero yaw rate can be asymptotically achieved: in this case additional stable manoeuvres are obtained in obstacle avoidance. Several simulations, including step references and moose tests, are carried out on a standard small SUV CarSim model to explore the robustness with respect to unmodelled effects such as combined lateral and longitudinal tyre forces, pitch, roll and driver dynamics. The simulations confirm the decoupling between the lateral velocity and the yaw rate and show the advantages obtained by the proposed control: reduced lateral speed or reduced yaw rate, suppressed oscillations and new stable manoeuvres.     

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.     

Lateral dynamics of single unit skid-steered tracked vehicle

In the design and development of high-speed tracked vehicles, it is necessary to have an understanding of the interrelationship between the terrain factors and the vehicle characteristics during steering. The handling behavior of skid-steered tracked vehicles is more complex than that of wheeled vehicles because of non-linear characteristics arising from the sliding interface between the track and the ground. In the present work, a five degree-of-freedom (DOF) steering model of a tracked vehicle is developed, and the handling behavior during non-stationary motion is studied when operating at high and low speeds. It is demonstrated that the inclusion of roll and pitch DOF changes the steering response when compared to the response from three DOF models proposed earlier by several researchers. This is due to the strong coupling between the pitch and yaw motions. The effect of the initial forward velocities on the trajectory of the vehicle during non-stationary motion is also studied. It is observed from the results that the stability is influenced by the type of steering input, steering ratio and vehicle forward speed.     

基于MPC的分布式驱动越野车辆原地转向控制研究

针对轮毂电机分布式驱动越野车辆在狭小空间快速机动的需求,设计了一种分层结构的原地转向控制策略。基于动力学原理分析了各轮载荷、附着条件对原地转向横摆速度的影响机理,并搭建原地转向运动学模型,上层采用模型预测控制算法设计原地转向理想轨迹以及期望的横摆角速度,开发基于PI滑模控制的横摆运动跟踪算法,通过补偿转向横摆力矩以提高方向角控制的鲁棒性和稳定性,下层以最优轮胎利用率为目标,设计二次规划算法优化分配各轮附加横摆力矩。dSPACE硬件在环测试结果表明,所提出的控制算法可在保证稳定性的前提下实现原地转向,大幅提高了车辆的转向机动性,在方向盘动态输入仿真中,车辆最大转弯半径为0.157 m,转向中心的最大偏移量为3.610 m;同时,驾驶员能对转向过程进行闭环控制,实现了原地转向过程中横摆速度的实时调节。     

Vehicle stability control based on driver’s emergency alignment intention recognition

In this work, the reference model modification strategy for vehicle stability control based on driver's intention recognition under emergent obstacle avoidance situation was proposed. First the conflicts between the driver's emergency alignment (EA) intention and vehicle response characteristics were analyzed in critical emergent obstacle avoidance situation. Second combining steering wheel angle and its speed, the driver's EA intention was recognized. The reference model modification strategy based on steering operation index (SOI) was presented. Then a LQR model following controller with tire cornering stiffness adaption was used to generate direct yaw moment for tracking modified reference yaw rate and reference sideslip angle. Finally based on the four-in-wheel-motor-drive (FIWMD) electric vehicles (EV), double lane change and slalom tests were conducted to compare the results using modified reference model with the results using normal reference model. The experimental tests have proved the effectiveness of the reference model modification strategy based on driver's intention recognition.     

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.     

分布式驱动电动汽车转向工况转矩分配控制研究

针对分布式驱动车辆转向工况在低速下期望提高转向机动性能,高速下期望保证行驶稳定性的需求,充分考虑转向行驶内外侧车轮的转向关系以及车辆动力学,制定了适应车速变化的四轮转矩分配策略,建立了四轮轮毂电机驱动模型以及二自由度参考模型。为了改善分布式驱动转向机动性能,建立自抗扰控制器调整内外侧车轮转矩,形成合理的转速差,减小转向半径,以提高转向机动性;对于高速转向行驶稳定性的需求,通过二次规划方法优化分配各车轮驱动力矩,分析轮胎纵横向附着裕度建立目标函数,并加入附加横摆力矩和路面附着力的限制,进行车轮驱动转矩的在线优化分配,提高车辆转向行驶的稳定性;另外为避免2种控制模式转换时驱动转矩突变,根据车速和稳定性参数制定模糊规则决策2种模式的协调系数,保证2种控制模式的平滑过渡。基于CarSim和MATLAB/Simulink进行联合仿真,并搭建硬件在环平台进行试验,对所提出的方法进行验证。结果表明：在低速转向工况下,提出的分配策略能够调节内外侧车轮产生差速效果,与转矩平均分配的策略相比,转向半径有所减小,提高车辆机动性;高速转向工况下,分配策略能够保证车辆稳定转向,与未考虑稳定性控制的分配策略相比,能更好地跟踪目标轨迹,且横摆角速度控制在参考横摆角速度附近,证明了所提控制策略的有效性。     

智能汽车自动紧急转向避撞的跟踪控制方法对比研究

为了提高智能汽车的主动安全性,提出3种不同的自动紧急转向避撞跟踪控制方法。首先建立汽车避撞简化模型,对制动、转向及两者相结合的3种不同避撞方式进行对比分析。其次,为深入研究汽车避撞过程中的实际响应,建立包含转向、制动及悬架3个子系统耦合特性的底盘18自由度统一动力学模型,并进行相关试验验证。随后构建智能汽车自动紧急转向避撞控制框架,对五次多项式参考路径和七次多项式参考路径的横摆角速度和横摆角加速度进行对比分析。接着以线性2自由度转向动力学模型为参考对象,对最优控制四轮转向、最优控制前轮转向、前馈与反馈控制相结合的前轮转向3种不同的跟踪控制系统分别进行设计。最后,以汽车底盘18自由度统一动力学模型为研究对象,对上述3种避撞控制系统进行仿真试验对比分析。研究结果表明：与制动避撞相比而言,转向避撞所需的纵向距离有较大降低,随着车速的增加和路面附着系数的越低,效果越明显;七次多项式参考路径比五次多项式参考路径的避撞过渡过程更为平缓,当实际车速与控制器所用车速不一致时,前者避撞性能表现更优;最优四轮转向控制系统在高、低2种不同附着路面都具有较好的避撞效果,最优前轮转向控制系统次之,而前馈与反馈相结合的前轮转向控制系统在低附着路面上则表现出严重的失稳。     

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.     

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.     

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.     

Modeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfaces

The brake and steering systems in vehicles are the most effective actuators that directly affect the vehicle dynamics. In general, the brake system affects the longitudinal dynamics and the steering system affects the lateral dynamics; however, their effects are coupled when the vehicle is braking on a non-homogenous surface, such as a split-mu road. The yaw moment compensation of the steering control on a split-mu road is one of the basic functions of integrated or coordinated chassis control systems and has been demonstrated by several chassis suppliers. However, the disturbance yaw moment is generally compensated for using the yaw rate feedback or using wheel brake pressure measurement. Access to the wheel brake pressure through physical sensors is not cost effective; therefore, we modeled the hydraulic brake system to avoid using physical sensors and to estimate the brake pressure. The steering angle controller was designed to mitigate the non-symmetric braking force effect and to stabilize the yaw rate dynamics of the vehicle. An H-infinity design synthesis was used to take the system model and the estimation errors into account, and the designed controller was evaluated using vehicle tests.     

Steady State Steering Response

The yaw rate response for a two-degree-of-freedom car model requires a family of curves for different degrees of oversteer or understeer. By use of non-dimensional co-ordinates this family is reduced to one single curve. The ordinate ρ is the ratio of yaw rate response to that of a neutral steering car at the same speed and is less than 1 for understeer and greater than 1 for oversteer. Since ρ is also the ratio of the side-slip angle response it is hence, a unique measure of the steady-state steering characteristics.     

Robust yaw stability control for electric vehicles based on active front steering control through a steer-by-wire system

A robust yaw stability control design based on active front steering control is proposed for in-wheel-motored electric vehicles with a Steer-by-Wire (SbW) system. The proposed control system consists of an inner-loop controller (referred to in this paper as the steering angle-disturbance observer (SA-DOB), which rejects an input steering disturbance by feeding a compensation steering angle) and an outer-loop tracking controller (i.e., a PI-type tracking controller) to achieve control performance and stability. Because the model uncertainties, which include unmodeled high frequency dynamics and parameter variations, occur in a wide range of driving situations, a robust control design method is applied to the control system to simultaneously guarantee robust stability and robust performance of the control system. The proposed control algorithm was implemented in a CaSim model, which was designed to describe actual in-wheel-motored electric vehicles. The control performances of the proposed yaw stability control system are verified through computer simulations and experimental results using an experimental electric vehicle.     

Directional Dynamics of a Tractor-Loader-Backhoe

This paper presents a study of the directional dynamics of large industrial tractors. These vehicles have special properties which make their dynamics interesting, including soft rear tires, large yaw moments of inertia and low or negative understeer gradients.

A linear yaw plane model was used for the analysis. The lateral compliance of the tires was included via a simplified version of the stretched-string model. Measurements were performed in support of the modeling effort, including inertial parameters, understeer gradient and transient response. A comparison between calculations and test results indicated that lateral compliance was an important influence on the transient response of these vehicles.     

Directional Dynamics of a Tractor-Loader-Backhoe

SUMMARY

This paper presents a study of the directional dynamics of large industrial tractors. These vehicles have special properties which make their dynamics interesting, including soft rear tires, large yaw moments of inertia and low or negative understeer gradients.

A linear yaw plane model was used for the analysis. The lateral compliance of the tires was included via a simplified version of the stretched-string model. Measurements were performed in support of the modeling effort, including inertial parameters, understeer gradient and transient response. A comparison between calculations and test results indicated that lateral compliance was an important influence on the transient response of these vehicles.     

基于变传动比的全轮线控转向车辆可拓H∞控制方法研究

为了解决传统固定转向传动比以及鲁棒H_∞控制方法无法很好地改善车辆稳定性的问题,提出全轮线控转向车辆的变传动比和可拓H_∞控制策略。首先,建立八自由度车辆动力学模型和轮胎模型。其次,以车辆方向盘转角和车速为输入信息,基于模糊控制方法设计全轮线控转向车辆的转向传动比,并计算出全轮线控转向车辆的前轮转角。然后,以横摆角速度偏差和偏差微分为特征值,基于可拓控制理论将车辆状态划分为3个区域：经典域、可拓域和非域;在经典域中,采用基于横摆角速度反馈的鲁棒H_∞控制方法,实时获取全轮线控转向车辆的后轮转角;在可拓域和非域中,结合可拓控制和H_∞控制策略,动态调整H_∞控制器的输出信号,在保证控制系统鲁棒性的前提下改善车辆的操纵稳定性。最后,基于MATLAB/Simulink仿真平台和自主研制的全轮线控转向特种消防救援车辆,通过正弦转向、单移线、阶跃转向、双移线等典型工况对所提控制方法进行验证,并以平均绝对误差和均方根误差为评价指标,与无控制和H_∞控制方法进行对比分析。仿真和试验测试结果表明：①变传动比控制方法不仅可以提高车辆低速时的转向灵敏度,也能改善车辆高速时的稳定性;②相比传统鲁棒H_∞控制,可拓H_∞控制策略提高了全轮线控转向车辆的操纵稳定性,改善了车辆全轮线控转向控制系统的鲁棒性。     

Robustness to Speed of 4WS Vehicles for Yaw and Lateral Dynamics

This paper addresses the issue of robustness and closed loop performance of four wheel steering (4WS) vehicles for yaw and lateral maneuvers for fixed and non-fixed speeds. A feedback structure derived from the plant inverse dynamic, such that the vehicle 2×2 matrix transfer function is robust to speed, is proposed. The efficiency of the proposed structure depends on the actuator's bandwidth and non-linearities, and on the sensor delay. A design example which shows how to implement the proposed algorithm in highly uncertain vehicles, subject to actuator bandwidth limitations and sensor delay, is provided.