Closed-Loop Directional Stability of Car-Trailer Combinations in Straight-Line Motion

SUMMARY

This work focuses on the interaction between a driver and a car-trailer combination. A model characterizing human operator behavior in regulation task is employed to study directional stability of the overall system. The vehicle-trailer model retains nonlinear cornering force and other kinematic nonlinearities. Linear stability of the straight line motion is analyzed by the application of Routh-Hurwitz criteria and stability boundaries in parameter space are constructed by setting appropriate Hurwitz determinant to zero. It is shown that two types of transition in stability are possible in the driver/car-trailer system. They correspond to one pair or two pairs of complex conjugate eigenvalues crossing the imaginary axis simultaneously. The implications in terms of resulting motions for the nonlinear system are also discussed. It is shown that stabilization of the combination can be achieved by adding a passive controller at the articulation point. Articulation damper turns out to be a more useful device for controlling trailer oscillations instability although a combination of damper and torsional spring would be a more ideal solution.     

Finite Disturbance Directional Stability of Vehicles with Human Pilot Considering Nonlinear Cornering Behavior

The driver of a vehicle has a significant influence on handling and stability of the vehicle. Due to the complex behavior of a human pilot, a driver model is usually neglected when dealing with the problem of vehicle stability. This work focuses on the interaction between the vehicle and the human pilot. A model characterizing human operator behavior in a regulation task is employed to study directional stability. Linear stability is analyzed by the application of the Routh-Hurwitz criterion and stability boundaries separating the stable domain of operation of the driver from the unstable one are constructed.

The linear analysis predicts that the only possible instability in a driver/vehicle system is an oscillatory instability with increasing amplitude. It is shown that the addition of kinematic as well as slip angle nonlinearities in the vehicle model can have a stabilizing effect on these oscillations of the combined driver/vehicle system. They may also be responsible for the opposite, namely a linearly stable motion may become unstable to finite size disturbances. These nonlinear motions are predicted by a bifurcation analysis and are verified by direct numerical simulation.     

Handling Characteristics of Car-Trailer Systems; A State-of-the-Art Survey

Work relevant to the state of the art as regards passenger cars towing trailers is referenced and reviewed. Not only included is the very limited amount of work specifically dealing with passenger cars towing trailers, but also reviewed is the much larger body of work having a bearing on car-trailer systems. Topics included are aerodynamic forces, tire forces, the compliance concept, relevant work on vehicles without trailers, vehicles with trailers, and the role of the driver. The types of stability problems exhibited by car-trailer systems are discussed.

The state of the art as regards ability to predict vehicle response to specific steering inputs is shown to be fairly advanced. Recent significant advances include the appearance of experimental data useful for validating theoretical models. However, the state of the art as regards definition of what constitute desirable handling characteristics is still at a primitive stage, largely because of a lack of understanding of the roles played by drivers as part of the vehicle -driver - environment systems.

Throughout the review an effort was made to point out topic areas where it is likely that significant future contributions to the state of the art can be made. These areas are reviewed in the conclusions.     

基于ADAMS与Matlab的ABS模糊控制仿真研究

将多体系统动力学与智能控制理论相结合对汽车制动防抱死控制系统进行了研究，利用ADAMS／CAR建立了汽车整车的多体力学模型，模型包含了前后悬架、动力总成、转向系统、稳定杆、制动系、轮胎力学模型以及车身，同时也考虑了轮胎、衬套、弹簧、减震器等部件的非线性，准确地表达了车辆的动态特性；利用Matlab／Simulink模糊控制工具箱建立了制动防抱死控制系统的模糊控制策略，利用ADAMS／Control接口进行模型的集成、协同仿真，并将仿真结果与另一种控制策略一逻辑门限值控制的仿真结果进行了比较和分析，仿真反映出模糊控制在整车制动防抱死控制系统上的应用效果，结果表明该控制算法稳定好并具有较强的鲁棒性。     

Automatic Cruise Control of a Mechatronically Steered Vehicle Convoy

In this paper a convoy of two vehicles is considered where the second one is mechatronically operated. The convoy model used for simulation and controller design is derived by the method of multibody systems. A nonlinear cruise controller based on the concept of flat outputs in connection with exact state linearization is derived. A nonlinear local observer is also implemented. It is shown that such a system responds properly to arbitrary maneuvers performed by the driver of the leading vehicle.     

Stabilization of Passenger Car-Caravan Combination Using Four Wheel Steering Control

This study aims to stabilize the trailer at high speed. The behavior of passenger cars with four wheel steering system, vehicles with rear wheel steering and of trailer and passenger car are similar. This is regarded as an optimal regulator problem with linear equation of motion, and a state variables feedback control system is adopted. The problem of stability at high speed on a straight course can be solved. Therefore, the passenger car-trailer system can be stabilized. Furthermore, this study indicates the way forward to stabilize a passenger car-trailer system.     

Automatic Cruise Control of a Mechatronically Steered Vehicle Convoy

In this paper a convoy of two vehicles is considered where the second one is mechatronically operated. The convoy model used for simulation and controller design is derived by the method of multibody systems. A nonlinear cruise controller based on the concept of flat outputs in connection with exact state linearization is derived. A nonlinear local observer is also implemented. It is shown that such a system responds properly to arbitrary maneuvers performed by the driver of the leading vehicle.     

Two degrees of freedom PID multi-controllers to design a mathematical driver model: experimental validation and robustness tests

This paper proposes a mathematical driver model based on PID multi-controllers having two degrees of freedom. Each PID controller making up this model is synthesised by the Ziegler–Nichols oscillation method, using the linear time invariant models which are obtained around their nominal operating points. Different PID controllers are combined using nonlinear optimisation and the H _∞ constraint. To demonstrate its robustness, it was tested on two models: a linear parameter variant model and a nonlinear four-wheel model. It was also tested in situations of high dynamic demand. The driver model showed good performance, stability and trajectory tracking. The performance tests were carried out using experimental data acquired by a Laboratory Peugeot 307 developed by INRETS-MA. This driver model was developed for an application known as ‘Itinerary Rupture DIagnosis’ (DIARI), which aims to evaluate the physical limits of a vehicle negotiating a bend. DIARI requires a tool to determine the steering commands to be applied to a vehicle model, making extrapolations with respect to speed.     

整车多体动力学模型的建立、验证及仿真分析

利用多体动力学方法建立了某轿车的整车非线性多体动力学模型,模型中考虑了前后悬架、转向系统的详细几何结构参数,以及连接处的橡胶衬套、阻尼器的非线性特性,轮胎采用M agic Formu la模型。对所建模型进行了多种试验验证,并分析了该样车的操纵稳定性等相关特性,仿真结果表明所建整车多体模型有较高的精度。     

Analysis of a Passive Sequential Hydraulic Damper for Vehicle Suspension

Vibration isolation characteristics of a sequential hydraulic damper, employing external pressure relief valves, are investigated via analytical means. The sequential hydraulic damper is modelled as a nonlinear dynamical system incorporating nonlinearities due to orifice flows, gas spring and pressure relief mechanisms. The damping characteristics of the sequential hydraulic damper, are compared to those of a constant orifice and a semi-active sequential damper, and discussed in view of their vibration isolation performance. It is established that the performance characteristics of the sequential hydraulic damper are similar to that of a semi-active sequential damper. A tuning methodology to achieve appropriate control of the resonant peak and effective vibration isolation is proposed. The shock and vibration isolation performance of the vehicle model employing a sequential damper are evaluated and compared to those of the vehicle model employing a constant orifice hydraulic damper. It is concluded that the vehicle ride performance can be improved considerably using an adequately tuned sequential damper.     

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.     

非线性粘滞阻尼器对悬索桥地震反应的影响

通过对粘滞阻尼器的力学特性进行分析,提出了在塔、梁连接处设置非线性粘滞阻尼器来控制塔、梁相对位移的减震措施。在对大跨度悬索桥动力特性分析的基础上,结合单自由度系统的震反应,提出了一种分析塔、梁相对位移的简化方法,并给出了非线性粘滞阻尼器参数设计的简便流程。利用非线性时程地震反应分析方法对一座带有非线性粘滞阻尼器的大跨度悬索桥进行了分析和研究,研究结果表明在塔、梁连接处设置非线性粘滞阻尼器可以在不增加塔底内力情况下,显著地减小塔、梁相对位移。     

半挂汽车列车闭环非线性系统行驶稳定性分析

对半挂汽车列车行驶稳定性的闭环非线性系统进行了研究,建立了半挂汽车列车三自由度非线性模型。以单点预瞄驾驶员模型与半挂汽车列车三自由度非线性模型的耦合系统为研究对象,应用李雅普诺夫一次近似定理,在线性范围内分析了系统参数的特征根轨迹,并在线性范围内分析了驾驶员预瞄时间和轮胎侧偏刚度对临界车速的影响。     

车辆转弯制动横向轨迹控制驾驶员模型研究

为了较为真实地反映车辆转弯制动工况,建立了含Pacejka"魔术公式"非线性联合工况轮胎模型的4轮8自由度车辆系统模型,并基于预瞄跟随理论、加速度反馈控制和模糊PID控制技术建立了车辆转弯制动横向轨迹控制驾驶员模型。针对不同初始速度和制动强度,利用MATLAB/Simulink进行了横向轨迹控制仿真分析。分析结果表明,驾驶员控制模型能很好地跟踪横向轨迹,模型的可行性和有效性得到验证,同时不同仿真条件下结果的一致性也说明该控制方法具有较强的自适应能力和鲁棒性,为进一步研究复杂工况下的驾驶员模型及横向轨迹控制提供了一条可行的途径。     

Optimal preview game theory approach to vehicle stability controller design

Dynamic game theory brings together different features that are keys to many situations in control design: optimisation behaviour, the presence of multiple agents/players, enduring consequences of decisions and robustness with respect to variability in the environment, etc. In the presented methodology, vehicle stability is represented by a cooperative dynamic/difference game such that its two agents (players), namely the driver and the direct yaw controller (DYC), are working together to provide more stability to the vehicle system. While the driver provides the steering wheel control, the DYC control algorithm is obtained by the Nash game theory to ensure optimal performance as well as robustness to disturbances. The common two-degrees-of-freedom vehicle-handling performance model is put into discrete form to develop the game equations of motion. To evaluate the developed control algorithm, CarSim with its built-in nonlinear vehicle model along with the Pacejka tire model is used. The control algorithm is evaluated for a lane change manoeuvre, and the optimal set of steering angle and corrective yaw moment is calculated and fed to the test vehicle. Simulation results show that the optimal preview control algorithm can significantly reduce lateral velocity, yaw rate, and roll angle, which all contribute to enhancing vehicle stability.     

汽车磁流变半主动悬架的控制研究

为了改善汽车的乘坐舒适性和行驶安全性,提出了一种汽车磁流变半主动悬架的控制策略。首先,设计了磁流变减振器的工作模式,通过试验获得了其速度特性和力学特性,建立了磁流变减振器的数学模型;其次,建立了带磁流变减振器的二自由度车辆简化模型及其参数表;最后,基于双环控制理论,设计了一种控制系统,其外环产生理想的结构阻尼力,内环调节电流驱动器的电流,以使磁流变减振器实时地产生控制阻尼力。仿真结果表明:以磁流变减振器为基础,通过半主动控制技术,悬架系统的振动动态性能得到了有效的控制。     

Stability control of 4WS vehicles using robust IMC techniques

A robust nonparametric approach to vehicle stability control by means of a four-wheel steer by wire system is introduced. Both yaw rate and sideslip angle feedbacks are used in order to effectively take into account safety as well as handling performances. Reference courses for yaw rate and sideslip angle are computed on the basis of the vehicle speed and the handwheel angle imposed by the driver. An output multiplicative model set is used to describe the uncertainty arising from a wide range of vehicle operating situations. The effects of saturation of the control variables (i.e. front and rear steering angles) are taken into account by adopting enhanced internal model control methodologies in the design of the feedback controller. Actuator dynamics are considered in the controller design. Improvements on understeer characteristics, stability in demanding conditions such as turning on low friction surfaces, damping properties in impulsive manoeuvres, and improved handling in closed loop (i.e. with driver feedback) manoeuvres are shown through extensive simulation results performed on an accurate 14 degrees of freedom nonlinear model, which proved to give good modelling results as compared with collected experimental data.     

Using µ Feedforward for Vehicle Stability Enhancement

A differential braking control strategy using yaw rate feedback, coupled with µ feedforward is introduced for a vehicle cornering on different µ roads. A nonlinear 4-wheel car model is developed. A desired yaw rate is calculated from the reference model based on the driver steering input. It is shown that knowledge of µ offers significant improvement of the vehicle desired trajectory over that of a yaw rate controller alone. Uncertainties and time delay in estimating µ are shown to still yield a system that is superior to using no µ information at all.