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

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.     

Vergleich einiger Rechen- und Messergebnisse zum Fahrverhalten von Sattelzügen

SUMMARY

In this paper some results of theoretical and experimental investigations on the dynamic directional properties of heavy tractor-semitrailer vehicles are presented.

A nonlinear digital computer model was developed on which the theoretical system analysis is based. This model takes account of the nonUnear tire properties and the friction couple of the fifth wheel. A combination of numerical computation methods (Runge-Kutta and Newton-Raphson techniques) is used for the digital computer simulation.

Full scale road tests with articulated vehicles of 38 ton total weight were conducted for experimental validation of the used theoretical model. As input signals to the vehicle, predetermined steering wheel angle functions were used. The system output signals corresponding to these input functions were measured and stored.

A comparison of the obtained theoretical and experimental results shows a very good qualitative agreement and hence leads to the conclusion that the developed theoretical model can give consistent estimates of the basic dynamic vehicle properties.     

Additional 4WS and Driver Interaction

SUMMARY

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

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。     

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.     

Optimization of Vehicles Elasto-Damping Elements Characteristics from the Aspect of Ride Comfort

SUMMARY

Spatial random vibrations of a vehicle that arise during driving represent an important factor in functioning of a dynamic system: Driver - Vehicle - Environment. They carry certain information for driver and also cause fatigue of driver and passenger.

This is the reason why the tendency is towards the minimization of vibratory loads, what in practice can be achieved by optimization of characteristics of elasto - damping elements of a vehicle.

In this paper for optimization of elasto - damping elements of a vehicle we used a complex nonlinear model of a driver and a vehicle during the straight - line motion of the vehicle on a rough road. Optimization was performed by application of the Hooke - Jeeves method and by use of outside penalty functions as well as the objective function that enabled simultaneous optimization of vertical vibrations of the driver's seat, vibrations of the steering wheel, and normal reactions in the contact surface of the tyre and road. The optimization was performed with application of the computer HP 9000/800 SE on the example of a medium passenger car.     

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...     

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.     

Road roughness estimation based on discrete Kalman filter with unknown input

ABSTRACT

The road roughness acts as a disturbance input to the vehicle dynamics, and causes undesirable vibrations associated with the ride and handing characteristics. Furthermore, the accurate measurement of road roughness plays a key role in better understanding a vehicle dynamic behaviour and active suspension control systems. However, the direct measurement by laser profilometer or other distance sensors are not trivial due to technical and economic issues. This study proposes a new road roughness estimation method by using the discrete Kalman filter with unknown input (DKF-UI). This algorithm is built on a quarter-car model and uses the measurements of the wheel stroke (suspension deflection), and the acceleration of the sprung mass and unsprung mass. The estimation results are compared to the measurements by laser profilometer in-vehicle test.     

Research on control strategy for differential steering system based on H mixed sensitivity

The differential steering system (DSS) of electric wheel vehicle gets rid of the restrictions of traditional steering system completely. As an ideal steering technology, it not only realizes the perfect combination of the road feel and the steering portability, but also realizes the harmony and unification between the steering maneuverability and safety. The structure and basic theory of the DSS of electric wheel vehicle are discussed in this paper. Based on these, the dynamic model of the steering system is built. Considering of the uncertainties and disturbances existing in the model, the H_∞ mixed sensitivity control theory is applied to achieve better tracking performance and road feel in the process of steering. Then, a H_∞ mixed sensitivity controller is designed to restrain the effect of the road disturbance and model uncertainties. The simulation results indicate that the DSS with the designed controller can effectively restrain the effect of noises and disturbances caused by random motivation from road, torque sensor measurement and model parameter uncertainty, and enable the driver to obtain satisfactory road feel.     

Simulation of the Interaction between Vehicle Wheel and the Unevenness of Road Surface

SUMMARY

A model of the relationship between a vehicle wheel and the unevenness of the road surface is defined. The wheel is considered to be of circular shape. For a given form of unevenness, the excitation functions are evaluated for the individual subsystems of the dynamic vehicle model having 5 degrees of freedom. The vehicle model traverses the uneven surface at a variable velocity. The model provides for the study of the complex dynamic phenomena which occur between the wheel and the unevenness. The response of the model also includes the dynamic stress on the drive when the wheel passes over the unevenness of the road surface.     

Development and Evaluation of Vehicle Simulation Models for a 4WS Application

SUMMARY

In the scope of the European Prometheus project a passenger car with active rear wheel steering was developed by TNO in cooperation with PSA. During development and engineering of the rear wheel steering system simulation tools have been used to reduce development costs. This paper describes the evaluation of different simulation models, from simple to complex, with results of full vehicle driving tests. The optimal balance for model complexity and accuracy was achieved with a 2-dimensional model with an added roll degree of freedom. The results show that validation using time responses can give ambiguous and inaccurate results, and that frequency response functions are much more usable in validation.     

Effects of Free-Control Variables on Automobile Handling

SUMMARY

Compared with the fixed-control case, relatively few studies of the effects on handling quality of the nature of the free-control response of an automobile to steering torque inputs have been reported. Prior to reviewing these studies, an attempt is made in this paper to provide a conceptual framework for assessing the results, by drawing on analytical and experimental work concerned with manual control in closed-loop tracking systems. Application of these ideas to the automobile shows that a fixed-control driver strategy is required where precise path control is necessary. Less demanding situations would allow a free-control driving mode. Steering task performance is found to be relatively insensitive to free-control vehicle responses. However, drivers exhibit clear preferences for certain ranges of steering torque gradient, and for rapid responses of steering wheel angle to torque inputs. Vehicle handling variables interact strongly in their effect on driver opinion. For example, the optimum steering torque gradient (in N m/G) decreases, and the optimum steering “stiffness” (in N m/rad) increases, as the fixed-control response sensitivity increases. Within fairly wide ranges, the damping of the free-control oscillatory mode has little effect on handling quality.     

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.     

电动助力转向系对汽车角输入响应影响的仿真

详细地分析和推导出了具有不同控制方式的EPS系统的传递函数，在Matlab环境中进行了仿真计算并对结果进行了分析，定性地说明了EPS系统的控制方式和结构参数对汽车转向盘角阶跃输入下的稳态、瞬态和频率响应特性的影响。     

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。     

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.     

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。