Numerical Simulation of Vehicle Behavior during Straight Line Keeping on Undulating Road Surfaces

SUMMARY

Numerical design of vehicles having optimal straight line stability on undulating road surfaces requires an accurate vehicle model based on knowledge of the relevant phenomena. Therefore, vehicle behavior on undulating straight roads has been analyzed and modeled. Measurements on a flat road surface have shown that the dedicated vehicle model yields accurate simulation results of the steering response to medium steering wheel angle inputs. In addition, the model has been validated by measuring two vehicle responses during normal driving on an undulating straight road: viz. the responses to the small steering wheel angle input and to the input by the global inclination of the road surface.     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

大型客车横向稳定性仿真分析

为了给营运客车横向稳定状态监测提供理论依据,针对极限工况下状态参数的临界值仿真结果,进行了营运客车稳定区域边界条件的研究。基于非线性三自由度车辆模型建立了基于扩展卡尔曼滤波（EKF）的状态参数估计器,对营运客车的质心侧偏角和横摆角速度进行实时估计,并利用Trucksim验证估计值具有较好的一致性和状态跟随能力。基于MATLAB/Simulink建立非线性七自由度车辆模型,分析不同行驶状态参数对质心侧偏角-质心侧偏角速度（β-β）相平面稳定区域边界的影响,基于仿真数据确定了以车速、前轮转角和路面附着系数为变量的稳定区域边界条件,结合状态估计模型获得以β-β决定的控制变量。在Trucksim中进行连续正弦方向盘转角输入标准稳定性试验,通过分析营运客车行驶过程中控制变量的曲线变化趋势是否超出稳定区域边界确定车辆的运行状态。结果表明：营运客车以60 km·h^-1车速、小方向盘转角行驶在低附着系数（μ=0.3）路面和高附着系数（μ=0.85）路面时,横摆角速度对驾驶人的意图（方形盘转角曲线趋势）有很好的跟随能力,具有较小的延迟响应,车辆处于稳定状态,此时控制变量曲线一直处于稳定区域内;当相同工况下以大方向盘转角输入时,横摆角速度已经不能很好地跟随驾驶人意图,且低附着系数路面下,在3.5 s左右时方向盘转角已经回正,但横摆角速度仍位于最大值,具有较大的延迟,营运客车发生急转侧滑;高附着系数路面下第2.5 s和第6.2 s左右车辆发生严重偏移,车辆处于失稳状态,而对应时刻的控制变量曲线部分超出稳定边界,验证了营运客车横向稳定状态判据的准确性。     

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.     

Vehicle steering returnability with maximum steering wheel angle at low speeds

In this paper, an analytical model with suitable vehicle parameters, together with a multi-body model is proposed to predict steering returnability in low-speed cornering with what is expected to be adequate precision as the steering wheel moves from lock to lock. This model shows how the steering response can be interpreted in terms of vertical force, lateral force with aligning moment, and longitudinal force. The simulation results show that vertical steering rack forces increase in the restoring direction according to steering rack displacement for both the inner and outer wheels. As lateral forces due to side-slip angle are directed toward the medial plane of the vehicle in both wheels, the outer wheel pushes the steering wheel in the returning direction while the inner wheel does not. In order to improve steering returnability, it is possible to increase the total steering rack force in both road wheels through adjustments to the kingpin axis and steering angle. This approach is useful for setting up a proper suspension geometry during conceptual chassis design.     

A lateral driver model for vehicle–driver closed-loop simulation at the limits of handling

This paper presents a lateral driver model for vehicle–driver closed-loop simulation at the limits of handling. An appropriate driver model can be used to evaluate the performance of vehicle chassis control systems via computer simulations before vehicle tests which incurs expenses especially at the limits of handling. The driver model consists of two parts. The first part is an upper-level controller employing force-based approach to reduce the number of unknown vehicle parameters. The feedforward part of the upper controller has been designed by using the centre of percussion. The feedback part aims to minimise ‘tangential error’, defined as the sum of body slip angle and yaw error, to match vehicle direction and road heading angle. The part is designed to regenerate an appropriate skid motion similar to that of a professional driver at the limits. The second part is a lower-level controller which converts the desired front lateral force to steering wheel angle. The lower-level controller also consists of feedforward and feedback parts. A two-degree-of-freedom bicycle model-based feedforward part provides nominal steering wheel angle, and the feedback part aims to eliminate unmodelled error. The performance of the lateral driver model has been investigated via computer simulations. It has been shown that the steering behaviours of the proposed driver model are quite close to those of a professional driver at the limits. Compared with the previously developed lateral driver models, the proposed lateral driver model shows good tracking performance at the limits of handling.     

自动驾驶汽车的仿真

随着汽车自动化程度的提高，自动驾驶汽车已成为国内外的研究热点之一。本文设计了一种自动驾驶汽车的模型，它能根据道路的弯曲程度变化实时地计算出车辆的转向角度输入，控制车辆按照预设想道路行吮。     

Resistance torque control for steer-by-wire system to improve human–machine interface

A steer-by-wire system, which has no mechanical constraints between steering wheel and front wheel, is expected to improve steering performance. The mechanical resistance torque is not transmitted from the front wheel to the steering wheel, and it is essential to simulate the torque around the steering wheel for better human-machine interface. Previous studies investigated resistance torque control originating from vehicle behaviour variables such as yaw rate and lateral acceleration. However, other variables such as steering wheel angle and front wheel actuation force are also good candidate sources to generate resistance torque. In this paper, first, four general guidelines are introduced to evaluate three types of resistance torques, i.e., the steering wheel angle origin, the steering force origin and the vehicle behaviour origin. First two guidelines are for ‘driver-made’ phase to make a turn, while the third guideline is for ‘vehicle-made’ phase to return to straight driving and the fourth one is the applicability guideline. Satisfaction of these guidelines by each of the three resistance torques is examined by the actual vehicle experiment. A necessity of combining these three types of resistance torques is indicated as a future subject.     

道路几何参数对车辆操纵稳定性影响

为研究道路几何参数对车辆操纵稳定性的影响,本文采用MATLAB/Simulink建立了3自由度整车动力学模型,通过数值仿真模拟,研究了车辆在不同超高、纵坡坡度以及合成纵坡下动力响应,在此基础上进一步分析了在不同车速以及前轮转角输入下,道路几何参数对车辆操纵稳定性的影响.结果表明:与水平路面相比,道路超高和纵坡坡度对车辆...     

前轮转角和车轮制动状态对汽车轨迹模拟的影响

对于碰撞后失去动力的汽车，建立其运动轨迹的计算机模型需要碰撞后汽车的初始速度和前轮转角，制动情况等初始值作为轨迹模型的输入参数，以便观察碰撞发生后的汽车运动情况。分析了碰撞后汽车车轮的受力情况，给出不同初始值情况下的轨迹模拟模型。分析结果得出，车轮在自由状态下，前轮的转角对汽车的运动距离有较大影响；当前轮转角为零时，汽车的质心运动几乎为一条直线；当车轮未完全抱死且前轮转角不为零时，汽车的质心运动为一条曲线。     

Implementation and validation of a three degrees of freedom steering-system model in a full vehicle model

This paper describes the coupling between a three degrees of freedom steering-system model and a multi-body truck model. The steering-system model includes the king-pin geometry to provide the correct feedback torque from the road to the steering-system. The steering-system model is combined with a validated tractor semi-trailer model. An instrumented tractor semi-trailer has been tested on a proving ground and the steering-wheel torque, pitman-arm angle, king-pin angles and drag-link force have been measured during steady-state cornering, a step steer input and a sinusoidal steering input. It is shown that the steering-system model is able to accurately predict the steering-wheel torque for all tests and the vehicle model is accurate for vehicle motions up to a frequency where the lateral acceleration gain is minimum. Even though the vehicle response is not accurate above this frequency, the steering-wheel torque is still represented accurately.     

汽车操纵稳定性的中间位置转向试验

操纵稳定性中间位置转向试验最初是由美国德尔福公司制定的，是汽车在高速行驶条件下操纵性和稳定性的重要评价方法。通过试验的原始数据可以绘制出转向盘转角与侧向加速度、转向盘力矩与侧向加速度、转向盘力矩与转向盘转角等多条特性曲线，以作为不同的评价指标。以CAll41载货汽车作为实例分析，发现该车转向干摩擦偏大，转向刚度偏低，高速行驶时的非线性路感不够理想。     

主动前轮转向客车的操纵稳定性仿真分析

建立某大型客车的含侧向、横摆及侧倾三自由度动力学模型,通过方向盘角阶跃转向仿真结果和试验数据的比较,验证了仿真分析的准确性。采用横摆角速度跟踪主动前轮转向控制策略,结合比例积分控制方法,在考虑作动器动态特性和前轮转角饱和特性的基础上,对主动前轮转向控制前后的车辆进行直线行驶下的侧向风扰动和湿滑路面急转弯情况下的仿真对比分析。结果表明,主动前轮转向控制后的车辆其操纵稳定性和行车安全性都有较大的提高。     

转向盘转角阶跃输入下半挂汽车列车操纵稳定性仿真分析

基于包括任意载荷分布的非线性轮胎模型在内的半挂汽车列车整车模型,应用汽车列车动力学仿真软件Arc Sim,分析了半挂汽车列车在转向盘转角阶跃输入时的转向特性。通过在不同车速、不同结构参数等条件下的仿真计算,揭示了半挂汽车列车的转向特性与车速、结构参数之间的内在联系,给出了半挂汽车列车转向特性在这些条件下的表现特征,为半挂汽车列车操纵稳定性分析提供了参考和借鉴。     

分段式转向梯形断开点的优化设计

文章建立了某轮式车辆的前独立悬架和转向系统的参数化模型,阐述了分段式梯形断开点设计需要遵循的两点原则,分析了断开点三个方向坐标对阿克曼转向特性以及车轮跳动过程中前束角变化的影响,以实际外轮转角与理论外轮转角差值最小以及前束角变化最小为优化目标,对断开点位置进行了优化分析。研究结果表明,断开点坐标的优化可以改善车辆转向特性,同时提高转向系统与悬架系统的运动协调性,为轮式车辆转向梯形的设计提出了较为合理的优化方案。     

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.     

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。     

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.     

Nähere Untersuchungen zur stationären Kurvenfahrt von Einspurfahrzeugen

Detailed Investigations of the Steady State Turning of Single Track Vehicles

In the paper the steady state turning of single track vehicles on a horizontal, even road is investigated, supposing the air to be at rest. The vehicle model used has six degrees of freedom: rolling, yawing, pitching and bouncing of the vehicle, rotation of the front wheel system (steering) relatively to the main frame and distortion of the rear wheel system due to limited stiffness of its linkage, and also takes into account wind drag and gyroscopic effects generated by wheels and other vehicle components. A special importance is given to the geometry of the vehicle

The results show a comparison of two types of motorcycles with different geometries and tires. To characterize the vehicle behaviour the roll, side slip and steering angle as functions of the normal acceleration are used. A more detailed study in respect to the steering torque is added.     

转向加速工况下汽车驱动防滑控制系统滑转率算法研究

汽车低速转弯加速时,用后轮轮速作为参考车速计算驱动轮滑转率会造成计算偏差,引起驱动防滑控制系统误干预,为此提出了驱动轮滑转率计算的修正算法.该修正算法不需要增加前轮转角传感器,而是采用两非驱动轮轮速估计车身横摆角速度和汽车前轮转角,进而计算出前轮参考轮速,并将前轮参考轮速代替车速对转弯工况的驱动轮滑转率计算进行修正.试验结果表明,该修正算法消除了滑转率计算误差,可防止汽车在高附着路面上转弯加速时驱动防滑控制系统的误干预.