Stability and optimised H∞ control of tripped and untripped vehicle rollover

Vehicle rollover is a serious traffic accident. In order to accurately evaluate the possibility of untripped and some special tripped vehicle rollovers, and to prevent vehicle rollover under unpredictable variations of parameters and harsh driving conditions, a new rollover index and an anti-roll control strategy are proposed in this paper. Taking deflections of steering and suspension induced by the roll at the axles into consideration, a six degrees of freedom dynamic model is established, including lateral, yaw, roll, and vertical motions of sprung and unsprung masses. From the vehicle dynamics theory, a new rollover index is developed to predict vehicle rollover risk under both untripped and special tripped situations. This new rollover index is validated by Carsim simulations. In addition, an H-infinity controller with electro hydraulic brake system is optimised by genetic algorithm to improve the anti-rollover performance of the vehicle. The stability and robustness of the active rollover prevention control system are analysed by some numerical simulations. The results show that the control system can improve the critical speed of vehicle rollover obviously, and has a good robustness for variations in the number of passengers and longitude position of the centre of gravity.     

Integration of vehicle yaw stabilisation and rollover prevention through nonlinear hierarchical control allocation

This work presents an approach to rollover prevention that takes advantage of the modular structure and optimisation properties of the control allocation paradigm. It eliminates the need for a stabilising roll controller by introducing rollover prevention as a constraint on the control allocation problem. The major advantage of this approach is the control authority margin that remains with a high-level controller even during interventions for rollover prevention. In this work, the high-level control is assigned to a yaw stabilising controller. It could be replaced by any other controller. The constraint for rollover prevention could be replaced by or extended to different control objectives. This work uses differential braking for actuation. The use of additional or different actuators is possible. The developed control algorithm is computationally efficient and suitable for low-cost automotive electronic control units. The predictive design of the rollover prevention constraint does not require any sensor equipment in addition to the yaw controller. The method is validated using an industrial multi-body vehicle simulation environment.     

Path-following in model predictive rollover prevention using front steering and braking

In this paper vehicle path-following in the presence of rollover risk is investigated. Vehicles with high centre of mass are prone to roll instability. Untripped rollover risk is increased in high centre of gravity vehicles and high-friction road condition. Researches introduce strategies to handle the short-duration rollover condition. In these researches, however, trajectory tracking is affected and not thoroughly investigated. This paper puts stress on tracking error from rollover prevention. A lower level model predictive front steering controller is adopted to deal with rollover and tracking error as a priority sequence. A brake control is included in lower level controller which directly obeys an upper level controller (ULC) command. The ULC manages vehicle speed regarding primarily tracking error. Simulation results show that the proposed control framework maintains roll stability while tracking error is confined to predefined error limit.     

Rollover mitigation for a heavy commercial vehicle

A heavy commercial vehicle has a high probability of rollover because it is usually loaded heavily and thus has a high center of gravity. An anti-roll bar is efficient for rollover mitigation, but it can cause poor ride comfort when the roll stiffness is excessively high. Therefore, active roll control (ARC) systems have been developed to optimally control the roll state of a vehicle while maintaining ride comfort. Previously developed ARC systems have some disadvantages, such as cost, complexity, power consumption, and weight. In this study, an ARC-based rear air suspension for a heavy commercial vehicle, which does not require additional power for control, was designed and manufactured. The rollover index-based vehicle rollover mitigation control scheme was used for the ARC system. Multi-body dynamic models of the suspension subsystem and the full vehicle were used to design the rear air suspension and the ARC system. The reference rollover index was tuned through lab tests. Field tests, such as steady state cornering tests and step steer tests, demonstrated that the roll response characteristics in the steady state and transient state were improved.     

Optimal controller design for a constrained polynomial vehicle system with an input-state linearized model

This paper presents a new controller design method based on a data-mining polynomial algorithm. We show application of a polynomial data-mining algorithm, where an input-state linearized polynomial vehicle model is developed for very low speed operation and, without introducing any processes with fudge factors, control inputs of a nonlinear system are obtained in the original coordinates. We verify the developed modeling method and controller design method through numerical experiments.     

半挂汽车列车高速公路弯道下坡路段运行安全研究（双语出版）

为提升半挂汽车列车在高速公路弯道下坡路段的运行安全，采用TruckSim仿真软件，构建了车辆模型、道路模型和驾驶人动力学仿真模型；基于蒙特卡罗可靠性分析法，分别建立了半挂汽车列车发生侧滑失效、侧翻失效、折叠失效和系统失效的功能函数，并选取设计速度80 km·h^-1的高速公路为研究路段，通过进行大量车辆动力学仿真试验，对不同圆曲线半径、纵坡坡度、路面附着系数、车速和车辆总质量对半挂汽车列车的运行安全的影响进行了数值分析。研究结果表明：半挂汽车列车发生侧滑和侧翻的概率随着圆曲线半径的增加而显著降低，在一般最小半径400 m的情况下，半挂汽车列车发生侧滑失效和侧翻失效的概率趋近于0；随着下坡坡度的增加，半挂汽车列车发生侧滑失效和侧翻失效的概率基本呈线性增长趋势；车速对于半挂汽车列车运行安全的影响尤为显著，当车速均值由60 km·h^-1增加到90 km·h^-1时，发生侧滑失效和侧翻失效的概率分别增加了634倍和336倍；车辆总质量的增加对半挂汽车列车侧翻有显著影响；在路面附着系数较低的条件下，半挂汽车列车的主要事故形态为侧滑和折叠，在路面附着系数较高的情况下，半挂汽车列车的主要事故形态为侧翻。因此，在道路设计中，应避免极限最小半径与陡坡组合，严格限速和限载可确保半挂汽车列车的运行安全性能。     

Design of rollover prevention controller with linear matrix inequality-based trajectory sensitivity minimisation

This paper presents a method to design a rollover prevention controller for vehicle systems. The vehicle rollover can be prevented by a controller that minimises the lateral acceleration and the roll angle. Rollover prevention capability can be enhanced if the controlled vehicle system is robust to the variation of the height of the centre of gravity and the speed of the vehicle. For this purpose, a robust controller is designed with linear matrix inequality-based trajectory sensitivity minimisation. Differential braking and active suspension are adopted as actuators that generate yaw and roll moments, respectively. The newly proposed method is shown to be effective in preventing rollover by the simulation on a non-linear multibody dynamic simulation software, CarSim^®.     

Bus mathematical model of acceleration threshold limit estimation in lateral rollover test

Vehicle safety is a major concerns for researchers, governments and vehicle manufacturers, and therefore a special attention is paid to it. Particularly, rollover is one of the types of accidents where researchers have focused due to the gravity of injuries and the social impact it generates. One of the parameters that define bus lateral behaviour is the acceleration threshold limit, which is defined as the lateral acceleration from which the rollover process begins to take place. This parameter can be obtained by means of a lateral rollover platform test or estimated by means of mathematical models. In this paper, the differences between these methods are deeply analysed, and a new mathematical model is proposed to estimate the acceleration threshold limit in the lateral rollover test. The proposed model simulates the lateral rollover test, and, for the first time, it includes the effect of a variable position of the centre of gravity. Finally, the maximum speed at which the bus can travel in a bend without rolling over is computed.     

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.     

Rollover risk prediction of heavy vehicles by reliability index and empirical modelling

This paper focuses on a combination of a reliability-based approach and an empirical modelling approach for rollover risk assessment of heavy vehicles. A reliability-based warning system is developed to alert the driver to a potential rollover before entering into a bend. The idea behind the proposed methodology is to estimate the rollover risk by the probability that the vehicle load transfer ratio (LTR) exceeds a critical threshold. Accordingly, a so-called reliability index may be used as a measure to assess the vehicle safe functioning. In the reliability method, computing the maximum of LTR requires to predict the vehicle dynamics over the bend which can be in some cases an intractable problem or time-consuming. With the aim of improving the reliability computation time, an empirical model is developed to substitute the vehicle dynamics and rollover models. This is done by using the SVM (Support Vector Machines) algorithm. The preliminary obtained results demonstrate the effectiveness of the proposed approach.     

Design of a rollover index-based vehicle stability control scheme

This paper presents a rollover index (RI)-based vehicle stability control (VSC) scheme. A rollover index, which indicates an impending rollover, is developed by a roll dynamics phase plane analysis. A model-based roll estimator is designed to estimate the roll angle and roll rate of the vehicle body with lateral acceleration, yaw rate, steering angle and vehicle velocity measurements. The rollover index is computed using an estimated roll angle, estimated roll rate, measured lateral acceleration and time-to-wheel lift. A differential braking control law is designed using a direct yaw control method. The VSC threshold is determined from the rollover index. The effectiveness of the RI, the performance of the estimator and the control scheme are investigated via simulations using a validated vehicle simulator. It is shown that the proposed RI can be a good measure of the danger of rollover and the proposed RI-based VSC scheme can reduce the risk of a rollover.     

Active roll control for rollover prevention of heavy articulated vehicles with multiple-rollover-index minimisation

This paper presents the application of a nominal control design algorithm for rollover prevention of heavy articulated vehicles with active anti-roll-bar control. This proposed methodology is based on an extension of linear quadratic regulator control for ‘state derivative-induced (control coupled) output regulation’ problems. For heavy articulated vehicles with multiple axles, a performance index with multiple rollover indices is proposed. The proposed methodology allows us to compare the usefulness of various control configurations (i.e. actuators at different axles of the vehicle) based on the interaction of this control configuration with vehicle dynamics. Application of this methodology to a specific heavy articulated vehicle with a tractor semi-trailer shows that a single active anti-roll-bar system at the trailer unit gives better performance than multiple-axle actuators at tractor and trailer together with the single lane change manoeuvre as the external disturbance. Thus, the proposed methodology of this paper not only highlights the importance of the interactions between control and vehicle dynamics in rollover prevention problems but, in fact, proposes a novel technique to exploit the benefits of these interactions judiciously.     

Integrated chassis control for a three-axle electric bus with distributed driving motors and active rear steering system

This paper describes an integrated chassis control framework for a novel three-axle electric bus with active rear steering (ARS) axle and four motors at the middle and rear wheels. The proposed integrated framework consists of four parts: (1) an active speed limiting controller is designed for anti-body slip control and rollover prevention; (2) an ARS controller is designed for coordinating the tyre wear between the driving wheels; (3) an inter-axle torque distribution controller is designed for optimal torque distribution between the axles, considering anti-wheel slip and battery power limitations and (4) a data acquisition and estimation module for collecting the measured and estimated vehicle states. To verify the performances, a simulation platform is established in Trucksim software combined with Simulink. Three test cases are particularly designed to show the performances. The proposed algorithm is compared with a simple even control algorithm. The test results show satisfactory lateral stability and rollover prevention performances under severe steering conditions. The desired tyre wear coordinating performance is also realised, and the wheel slip ratios are restricted within stable region during intensive driving and emergency braking with complicated road conditions.     

Contour line of load transfer ratio for vehicle rollover prediction

For vehicle rollover control systems, an accurate and predictive rollover index is necessary for a precise rollover threat detection and rollover prevention. In this paper, the contour line of load transfer ratio (CL-LTR) and the CL-LTR-based vehicle rollover index (CLRI) are proposed, describing LTR threshold and LTR change rate precisely, providing an accurate prediction of vehicle rollover threat. In detail, the CL-LTR is proposed via the roll dynamics phase plane analysis, and its analytical solution of one-degree-of-freedom vehicle roll model and extension for full vehicle are derived. Moreover, the predictive CLRI is proposed and evaluated via vehicle dynamics study. The results demonstrate that vehicle rollover threat is predicted accurately based on the CLRI, which shows benefits for the vehicle rollover prediction and stability control.     

New Model of Tire Overturning Moment Characteristics and Analysis of Their Influence on Vehicle Rollover Behavior

A newly developed tire model for the Overturning Moment (OTM) characteristics and the analysis of the influence of OTM on vehicle rollover behavior are presented. The new OTM model was developed based on the so-called Magic Formula tire model. The concept of the new model involves identifying the difference between the simple model and the measurements to the newly defined functions. It was seen that the new model agrees very well with the measured data over a wide range of tire vertical loads, slip angles and camber angles. The influence of tire OTM on the vehicle rollover behavior was also investigated by using a full vehicle simulation in which a rather large steering angle was input. The results obtained from the vehicle simulation with three different tire models (model without OTM, simple model and new model) were compared with the experimental results. It was found that the calculated result obtained with the new OTM model agreed best with the experiment.     

New Model of Tire Overturning Moment Characteristics and Analysis of Their Influence on Vehicle Rollover Behavior

A newly developed tire model for the Overturning Moment (OTM) characteristics and the analysis of the influence of OTM on vehicle rollover behavior are presented. The new OTM model was developed based on the so-called Magic Formula tire model. The concept of the new model involves identifying the difference between the simple model and the measurements to the newly defined functions. It was seen that the new model agrees very well with the measured data over a wide range of tire vertical loads, slip angles and camber angles. The influence of tire OTM on the vehicle rollover behavior was also investigated by using a full vehicle simulation in which a rather large steering angle was input. The results obtained from the vehicle simulation with three different tire models (model without OTM, simple model and new model) were compared with the experimental results. It was found that the calculated result obtained with the new OTM model agreed best with the experiment.     

汽车侧翻试验台非接触式防翻装置的设计开发

为保证汽车侧倾稳定角试验过程中的车辆安全,设计开发了一种用于防止试验车辆发生侧翻安全事故的非接触式防翻装置。该装置通过液压缸驱动防护支撑板,实现支撑板与侧翻试验台上的被试车辆保持一定安全距离的跟随运动,避免车辆达到侧倾稳定临界角时发生侧翻。经现场试验表明,该装置能够实现设计功能,在不影响试验结果的情况下保证车辆安全。     

基于制动与悬架系统的车辆主动侧翻控制的研究

为提高车辆抗侧翻能力,建立了10自由度整车侧翻动力学模型,应用车辆动力学和轮胎力耦合特性,提出了一种基于差动制动和半主动悬架协同工作的车辆主动抗侧翻控制策略。通过对制动力矩的差动调节和半主动悬架阻尼力的适时匹配,实现对车辆侧翻的有效控制。根据子系统运动特性,设计了制动系统基于滑移率的积分滑模控制器和悬架系统灰模糊控制器。分别对制动、悬架控制及综合控制进行的鱼钩试验仿真结果表明,综合控制策略可有效降低危险时域车辆的侧倾角,相对于单一系统控制进一步提高了车辆抗侧翻能力。     

Rollover detection and control on the non-driven axles of trucks based on pulsed braking excitation

The major challenges for rollover detection are the accurate modelling of vehicle dynamics and the real-time estimation of the varied parameters. To circumvent the dependence on vehicle parameters, a novel rollover detection method based on the pulsed braking excitation is proposed. With the lateral load transfer ratio (LTR), the relationship between rollover risks and non-driven wheel rotational dynamics is deduced, which is the basis to apply braking excitation on wheels. The lateral acceleration is adopted as the first criterion to activate the rollover detection. Once the pulsed braking is applied to the non-driven wheels, the braking pressure and wheel angular speeds are measured to estimate the LTR on the non-driven axle. In case of emergency, the differential braking-based anti-rollover is implemented. Experiments were conducted on a Hardware-in-Loop bench. The results show that, the pulsed braking can be activated timely, and the LTR on the non-driven axle is estimated accurately. With the anti-rollover control, the roll stability is improved considerably.     

Investigation into untripped rollover of light vehicles in the modified fishhook and the sine maneuvers. Part I: Vehicle modelling, roll and yaw instability

Vehicle rollovers may occur under steering-only maneuvers because of roll or yaw instability. In this paper, the modified fishhook and the sine maneuvers are used to investigate a vehicle's rollover resistance capability through simulation. A 9-degrees of freedom (DOF) vehicle model is first developed for the investigation. The vehicle model includes the roll, yaw, pitch, and bounce modes and passive independent suspensions. It is verified with the existing 3-DOF roll-yaw model. A rollover critical factor (RCF) quantifying a vehicle's rollover resistance capability is then constructed based on the static stability factor (SSF) and taking into account the influence of other key dynamic factors.

Simulation results show that the vehicle with certain parameters will rollover during the fishhook maneuver because of roll instability; however, the vehicle with increased suspension stiffness, which does not rollover during the fishhook maneuver, may exceed its rollover resistance limit because of yaw instability during the sine maneuver. Typically, rollover in the sine maneuver happens after several cycles.

It has been found that the proposed RCF well quantifies the rollover resistance capability of a vehicle for the two specified maneuvers. In general, the larger the RCF, the more kinetically stable is a vehicle. A vehicle becomes unstable when its RCF is less than zero. Detailed discussion on the effects of key vehicle system parameters and drive conditions on the RCF in the fishhook and the sine maneuver is presented in Part II of this study.