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.     

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.     

Lateral dynamics emulation via a four-wheel steering vehicle

In this paper, we examine the lateral dynamics emulation capabilities of an automotive vehicle equipped with four-wheel steering. We first demonstrate that the lateral dynamics of a wide range of vehicles can be emulated, either with little or with no modification on the test vehicle. Then we discuss a sliding mode controller for active front and rear wheel steering, in order to track some given yaw rate and side-slip angle. Analytically, it is shown that the proposed controller is robust to plant parameter variations by±10%, and is invariant to unmeasurable wind disturbance. The performance of the sliding mode controller is evaluated via computer simulations to verify its robustness to vehicle parameter variations and delay in the loop, and its insensitivity to wind disturbance. Finally, the emulation of a bus, a van, and two commercially available passenger vehicles is demonstrated in an advanced nonlinear simulator.     

Influencing driver chosen cornering speed by means of modified steering feel

This paper presents an investigation about influencing the driver's behaviour intuitively by means of modified steering feel. For a rollover indication through haptic feedback a model was developed and tested that returned a warning to the driver about too high vehicle speed. This was realised by modifying the experienced steering wheel torque as a function of the lateral acceleration. The hypothesis for this work was that drivers of heavy vehicles will perform with more margin of safety to the rollover threshold if the steering feel is altered by means of decreased or additionally increased steering wheel torque at high lateral acceleration. Therefore, the model was implemented in a test truck with active steering with torque overlay and used for a track test. Thirty-three drivers took part in the investigation that showed, depending on the parameter setting, a significant decrease of lateral acceleration while cornering.     

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。     

电子差速系统轮胎附着特性模拟仿真研究

电子差速系统相对于传统的机械式差速器可以实现转矩的精准分配,根据轮胎的纵向运动特性以及侧向运动特性,结合轮胎滑移率让内外侧车轮在过弯时拥有足够的附着力,减小整车的横摆角速度,提高过弯稳定性。采用后轮双电机的驱动方案,驱动电机采用直接转矩控制的方法,由整车控制器将指定的计算转矩信号发送给电机控制器完成动力分配,所需转矩根据驾驶员的加速踏板及方向盘转角,运用阿克曼转向模型计算得到。     

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.     

Improving vehicle dynamics by active rear wheel steering systems

This article presents two design strategies for an active rear wheel steering control system. The first method is a standard design procedure based on the well-known single track model. The aim of the feedback loop is to track a reference yaw rate in order to improve the handling behaviour. Unfortunately, a reasonable specification of the reference yaw rate proves to be a nontrivial task. A second approach avoids this drawback. The structure of the controller is regarded as a virtual mass-spring-damper system with adjustable parameters. Due to the high abstraction level of this method, the controller parameters can be tuned intuitively. Experiments with a prototype vehicle illustrate the effectiveness of the two proposed methodologies.     

An adaptive integrated algorithm for active front steering and direct yaw moment control based on direct Lyapunov method

In this article, an adaptive integrated control algorithm based on active front steering and direct yaw moment control using direct Lyapunov method is proposed. Variation of cornering stiffness is considered through adaptation laws in the algorithm to ensure robustness of the integrated controller. A simple two degrees of freedom (DOF) vehicle model is used to develop the control algorithm. To evaluate the control algorithm developed here, a nonlinear eight-DOF vehicle model along with a combined-slip tyre model and a single-point preview driver model are used. Control commands are executed through correction steering angle on front wheels and braking torque applied on one of the four wheels. Simulation of a double lane change manoeuvre using Matlab^®/Simulink is used for evaluation of the control algorithm. Simulation results show that the integrated control algorithm can significantly enhance vehicle stability during emergency evasive manoeuvres on various road conditions ranging from dry asphalt to very slippery packed snow road surfaces.     

Automatic path-tracking controller of a four-wheel steering vehicle

The present paper proposes an automatic path-tracking controller of a four-wheel steering (4WS) vehicle based on the sliding mode control theory. The controller has an advantage in that the front- and rear-wheel steering can be decoupled at the front and rear control points, which are defined as centres of percussion with respect to the rear and front wheels, respectively. Numerical simulations using a 27-degree-of-freedom vehicle model demonstrated the following characteristics: (1) the automatic 4WS controller has a more stable and more precise path-tracking capability than the 2WS controller, and (2) the automatic 4WS controller has robust stability against system uncertainties such as cornering power perturbation, path radius fluctuation, and cross-wind disturbance.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

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.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

SUMMARY

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

Steady-state steering of a tilting three-wheeled vehicle

The design of a narrow-track enclosed vehicle for urban transport was the subject of the CLEVER project. Due to its narrow track and requirement for car-like controls, an actively controlled tilting system was integrated into the chassis to allow for high lateral accelerations without rolling over. The cornering behaviour of this unique vehicle concept is investigated and compared with the ideal Ackermann response. The steer kinematics of this 1F1T (one front wheel, one wheel tilting) configuration are assessed through the use of a steady-state steering model, with attention focused on how steer parameters such as tilt axis height and inclination can be tuned to provide the required response. A prototype vehicle was designed and built and the results of experimental testing are presented to illustrate the real balancing performance of the combined steering and tilting approach used for the CLEVER vehicle. The experimental results follow the trends demonstrated in the model.     

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。     

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。     

Emergency steering control of autonomous vehicle for collision avoidance and stabilisation

ABSTRACT

Collision avoidance and stabilisation are two of the most crucial concerns when an autonomous vehicle finds itself in emergency situations, which usually occur in a short time horizon and require large actuator inputs, together with highly nonlinear tyre cornering response. In order to avoid collision while stabilising autonomous vehicle under dynamic driving situations at handling limits, this paper proposes a novel emergency steering control strategy based on hierarchical control architecture consisting of decision-making layer and motion control layer. In decision-making layer, a dynamic threat assessment model continuously evaluates the risk associated with collision and destabilisation, and a path planner based on kinematics and dynamics of vehicle system determines a collision-free path when it suddenly encounters emergency scenarios. In motion control layer, a lateral motion controller considering nonlinearity of tyre cornering response and unknown external disturbance is designed using tyre lateral force estimation-based backstepping sliding-mode control to track a collision-free path, and to ensure the robustness and stability of the closed-loop system. Both simulation and experiment results show that the proposed control scheme can effectively perform an emergency collision avoidance manoeuvre while maintaining the stability of autonomous vehicle in different running conditions.     

Pivot point-based control for active rear-wheel steering in passenger vehicles

This paper presents a new application of active rear-wheel steering control to improve the lateral vehicle behaviour. In the state of the art, yaw or lateral velocity is used as control variable that means one degree of freedom being not directly controlled. A worse subjective impressions due to movements in the rear end of the vehicle during strong counter-steering are a consequence. To avoid this effect in urban surroundings, an innovative structure to control the pivot point distance of the vehicle is proposed. In this case the coupled elementary states yaw and lateral velocity can be influenced based on a higher level criteria. Analysis show that pivot point fixing provides a comprehensible reference behaviour. Solving the issue of singularity during disappearing yaw movement is the basis to design a performant modified feedforward input–output linearisation. An analytic stability analysis of the internal dynamics shows system immanent limitations which do not influence the target of improving the lateral vehicle dynamics in urban manoeuvres. Finally, the advantages of pivot-based control are highlighted by a comparison with state of the art rear axle control.     

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.