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.     

影响车辆转向瞬态响应特性的因素研究

利用ADAMS/CAR二次开发模块,建立了国产某小客车的整车多体系统动力学仿真模型。分析了车辆转向盘角阶跃输入和脉冲输入时的瞬态响应特性,并对相关的影响因素进行了预测分析,通过调整后轮侧倾刚度等参数,优化转向瞬态特性响应结果,经过样车的试验验证了优化结果。     

基于MATLAB/SIMULINK的车轮外倾角对车辆高速转向稳定性的影响研究

基于Matlab/Simulink建立了考虑汽车车身侧倾转向的3自由度仿真模型,研究了车轮外倾角对汽车高速转向稳定性的影响。结果表明前轮正外倾角、后轮负外倾角有利于提高转向稳定性,特别是在大转角的危险工况可以避免发生侧滑和侧翻。     

五连杆后悬架的后轴变形效应与转向随动性关系研究

针对某SUV转向随动性不足问题,利用后轴变形转向效应对该车五连杆后悬架上摆臂重新布置,并在ADAMS中建立了后悬架运动学模型及整车动力学模型。通过对转向盘转角阶跃输入、脉冲输入的仿真结果分析和对原车按新方案改进后进行的操纵稳定性主观试验验证表明,新方案较好地解决了转向随动性问题,减少了特殊工况时后轮侧滑及甩尾的危险性。     

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。     

线控转向系统转向盘力回馈控制模型的研究

根据轮胎和传统转向系的力学特性提出了利用车轮转角和车速计算得到转向盘回馈力的思路,并以此建立了线控转向系统转向盘回馈力控制模型,仿真和试验表明该模型能够满足路感要求。     

A Comparative Study of Four Wheel Steering Models Using the Inverse Solution

An inverse solution study of various four wheel steering models is carried out for the purpose of comparison of steering/braking input needed to track a lane change maneuver. Optimal control is used to solve the non-linear inverse problem. Comparisons are made when the vehicle is coasting, when the time required to track the trajectory is minimized with appropriate utilization of brake/traction forces, and in a front wheel lock situation. A rear steering model which produces neutral steering characteristics displayed the best steering behavior with respect to ease of steering.     

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.     

Crosswind Feedforward Control - A Measure to Improve Vehicle Crosswind Behaviour

The theory of crosswind feedforward control was explained using the example of a vehicle with active front-wheel steering. Beforehand, the calculation formulas and frequency responses of the transient crosswind force and of the wind yaw moment acting on the vehicle were derived using the example of a simple vehicle fluid model. The influence of the transiency of crosswind disturbance on the dynamic crosswind behaviour of a vehicle was then presented. The results of simulation confirmed the analyses carried out in the frequency domain for feedforward control with front, rear and all-wheel steering. With front-wheel steering, the influence of crosswind on one of the vehicle movement variables (lateral acceleration or yaw rate) could be almost completely compensated by dynamic feedforward control. With rear-wheel steering, it is only possible to compensate directly for the influence on the yawing rate. Due to the setting of the side force in the same direction as the lateral wind force at the start, active rear-wheel steering is not so successful as active front-wheel steering. Nevertheless, the crosswind behaviour of a vehicle can be considerably enhanced by feedforward control with rear-wheel steering. The best crosswind behaviour was obtained with active all-wheel steering: the vehicle hardly responds at all to crosswinds and remains on course despite heavy gusts of wind.     

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.     

轮式铣刨机电辅助驱动系统速度匹配分析

以轮式铣刨机为研究对象，针对前桥驱动牵引力不足的情况进行后轮电辅助驱动，在对铣刨机辅助驱动运动学研究的基础上，设计了电辅助驱动速度匹配策略，建立了该铣刨机电辅助驱动的数学模型，并运用Simulink模块对其进行了仿真分析。结果表明：前、后轮速度匹配策略确实可行。     

电动助力转向系统建模与控制策略研究

概述了电动助力转向系统的优点，建立了电动助力转向的数学模型。在此基础上对比分析了比例控制策略和比例微分控制策略的不同控制效果。仿真结果表明，在助力增益较大时，比例控制会引起转向盘振动，同时来自路面的高频干扰也容易传递到转向盘，使手感变差。比例微分控制引入微分环节，增加了系统的阻尼，通过调节微分系数，可以调节系统带宽，因而较好解决了转向轻便性、转向盘振动和抑制路面高频干扰之间的矛盾。     

On the feasibility of the optical steering wheel sensor: Modeling and control

This paper discusses the development of a system model for the wireless steering wheel angle sensor and steering wheel system for the evaluation of the steer by wire system in a vehicle dynamic system. The steering wheel sensor is a wireless, contact-less sensor utilizing an optical medium for angle detection. The optical medium is operated based on a photodiode and photo-detector head. A reflecting disc or code-wheel, working similar to a compact disc, is used to reflect the light from the photodiode back to the photo-detector. The beam is reflected based on the content in the reflective disc to measure the relative angle through a micro-controller. The proposed wireless steering sensor and steer by wire system is modeled using the Matlab/Simulink and their performance is investigated to evaluate the steering response, vehicle dynamics, and steering feel of the system. Finally, the feasibility of the proposed system is discussed based on the developed model and simulation results.     

基于统一模型的转向-悬架系统最优综合控制方法

通过对车辆底盘系统中的转向和悬架系统建立统一的数学模型,利用M atlab/S imu link仿真,结合最优控制理论,分别对被动悬架兼前轮转向系统与主动悬架兼四轮转向综合控制系统进行了对比研究。理论分析与仿真试验表明,综合控制系统下车辆的操纵稳定性和平顺性都得到了很大的提高。     

紧凑型扭杆弹簧悬架设计中车轮定位参数的计算

紧凑型扭杆弹簧悬架是普及型轿车中采用的一种主要的悬架结构形式。它属于纵臂式悬架,只能用于后轮,且不能用于转向轮,因此其定位参数只有车轮前束和外倾角两种。决定后轮定位参数的主要是与纵摆臂中制动鼓定位销轴空间有关的轴和孔的加工精度。对其几何模型和力学模型进行了分析,给出了该悬架车轮定位参数的计算方法,并以某车型为例进行了对比计算。     

ve-DYNA在电动助力转向助力特性仿真分析中的应用

介绍了ve—DYNA软件及在控制和实时仿真方面具有的优势。针对某一轿车,利用ve—DYNA软件建立了分析电动助力转向系统的整车动力学仿真模型,对不同车速下的转向盘转矩进行了仿真分析,获得了适宜的车速感应型助力特性曲线,为后续的电机控制和ECU的设计开发奠定了基础。     

Vergleich einiger Rechen- und Messergebnisse zum Fahrverhalten von Sattelzügen

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.     

Dynamic analysis and control of an anti-lock brake system for a motorcycle with a camber angle

This paper analyses the dynamic response of a motorcycle with an anti-lock brake system (ABS) and camber or steering angle. Most studies have assumed that motorcycles brake in a straight line – that is, without a steering or camber angle. In this work, the performance of an ABS modulator is designed and analysed at first. Then, a controller is designed for motorcycle turning. The controller uses angular acceleration and the pressure value in brake calipers on the front and rear wheels, camber angle and lateral acceleration as commands to control brake pressure on each wheel to prevent wheel locking. The equation of motion for a motorcycle is based on Weir's equations. This motorcycle model combines a mathematical equation of the ABS modulator, tyre model and controller in simulations.     

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.     

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。