Time-optimal control of the race car: influence of a thermodynamic tyre model

The robustness of an existing numerical method for the time-optimal control of the race car is demonstrated through its application to a model of a Formula 1 car equipped with a simplified thermodynamic tyre model. The tyre model includes a temperature- and frequency-dependent model of road/tyre friction. A lumped parameter approach is used to model the thermodynamics of the various parts of the tyre such as the tread, carcass and inflation gas. The influence of tyre, track surface and ambient temperatures on time-optimal manoeuvring is presented.     

高速公路爆胎事故的影响因素及其预防

通过调查和实验分析,影响爆胎事故的有轮胎气压、车辆装载质量、行车速度和轮胎磨损4个主要因素,高速公路的道路特点和车辆的运行特点(如高速度、重装载、远距离)对这些因素有着直接的影响,控制这些因素所带来的影响,可以有效地预防高速公路爆胎事故的发生。     

胎面轮廓形状优化技术研究--提高轮胎耐磨耗性能

胎面轮廓形状对轮胎的耐磨耗性能影响很大，因此对其进行优化很有意义。针对胎面轮廓形状比较复杂的特点，文中采用多个变量来定义胎面轮廓。同时，在现有磨耗理论的基础上，通过对胎面轮廓形状的优化初步给出了评价轮胎耐磨耗性能的指标。在此基础上，采用自编的多目标优化程序对胎面轮廓进行优化，并将计算结果与原胎数据进行了比较，结果表明，不论是从胎面的磨耗速度还是从胎面磨耗的均匀性来说优化胎都要优于原始。     

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.     

A tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel independent brake from moderate driving to limit handling

This paper presents a tyre slip-based integrated chassis control of front/rear traction distribution and four-wheel braking for enhanced performance from moderate driving to limit handling. The proposed algorithm adopted hierarchical structure: supervisor – desired motion tracking controller – optimisation-based control allocation. In the supervisor, by considering transient cornering characteristics, desired vehicle motion is calculated. In the desired motion tracking controller, in order to track desired vehicle motion, virtual control input is determined in the manner of sliding mode control. In the control allocation, virtual control input is allocated to minimise cost function. The cost function consists of two major parts. First part is a slip-based tyre friction utilisation quantification, which does not need a tyre force estimation. Second part is an allocation guideline, which guides optimally allocated inputs to predefined solution. The proposed algorithm has been investigated via simulation from moderate driving to limit handling scenario. Compared to Base and direct yaw moment control system, the proposed algorithm can effectively reduce tyre dissipation energy in the moderate driving situation. Moreover, the proposed algorithm enhances limit handling performance compared to Base and direct yaw moment control system. In addition to comparison with Base and direct yaw moment control, comparison the proposed algorithm with the control algorithm based on the known tyre force information has been conducted. The results show that the performance of the proposed algorithm is similar with that of the control algorithm with the known tyre force information.     

Geometric-based tyre vertical force estimation and stiffness parameterisation for automotive and unmanned vehicle applications

Advanced empirical, and physical-based tyre models have proven to be accurate for simulating tyre dynamics; however, these tyre models typically require expensive and intensive tyre parameterisation. Recent research into wheeled unmanned ground vehicles requiring vertical force analysis has shown good results using a simple linear spring model for the tyre which demonstrate the continued use for simple tyre models; however, parameterisation of the tyre still remains a challenge when load test equipment is not available. This paper presents a cost-effective tyre vertical stiffness parameterisation procedure using only measured tyre geometry and air pressure for applications where high-fidelity tyre models are unnecessary. Vertical forces calculated through an air volume optimisation approach are used to estimate tyre vertical stiffness. Nine tyres from the literature are compared to evaluate the performance of the vertical force estimation and stiffness parameterisation algorithms. Experimental results on a pair of ATV tyres are also presented.     

Models and methodology for optimal trajectory generation in safety-critical road–vehicle manoeuvres

There is currently a strongly growing interest in obtaining optimal control solutions for vehicle manoeuvres, both in order to understand optimal vehicle behaviour and, perhaps more importantly, to devise improved safety systems, either by direct deployment of the solutions or by including mimicked driving techniques of professional drivers. However, it is non-trivial to find the right combination of models, optimisation criteria, and optimisation tools to get useful results for the above purposes. Here, a platform for investigation of these aspects is developed based on a state-of-the-art optimisation tool together with adoption of existing vehicle chassis and tyre models. A minimum-time optimisation criterion is chosen for the purpose of gaining an insight into at-the-limit manoeuvres, with the overall aim of finding improved fundamental principles for future active safety systems. The proposed method to trajectory generation is evaluated in time-manoeuvres using vehicle models established in the literature. We determine the optimal control solutions for three manoeuvres using tyre and chassis models of different complexities. The results are extensively analysed and discussed. Our main conclusion is that the tyre model has a fundamental influence on the resulting control inputs. Also, for some combinations of chassis and tyre models, inherently different behaviour is obtained. However, certain variables important in vehicle safety-systems, such as the yaw moment and the body-slip angle, are similar for several of the considered model configurations in aggressive manoeuvring situations.     

纯电动汽车轮胎磨损关键影响因素研究

木文在分析纯电动车汽车不同于传统燃油车对于轮胎磨损关键因素的基础上,对纯电动车汽车轮胎磨损影响因素进行了试验验证。试验针对栽荷及动力系统两个因素采用控制单一变量法进行轮胎道路磨损试验,并通过对试验路线优化及驾驶员驾驶习惯的约束,使得测试结果更加准确及客观。最后对测试完成之后的轮胎花纹形态、轮胎花纹深度及轮胎预计里程寿命进行了详细数据分析。     

Optimisation of driver actions in RWD race car including tyre thermodynamics

ABSTRACT

The paper presents an innovative method for a lap time minimisation by using genetic algorithms for a multi objective optimisation of a race driver–vehicle model. The decision variables consist of 16 parameters responsible for actions of a professional driver (e.g. time traces for brake, accelerator and steering wheel) on a race track part with RH corner. Purpose-built, high fidelity, multibody vehicle model (called ‘miMa’) is described by 30 generalised coordinates and 440 parameters, crucial in motorsport. Focus is put on modelling of the tyre tread thermodynamics and its influence on race vehicle dynamics. Numerical example considers a Rear Wheel Drive BMW E36 prepared for track day events. In order to improve the section lap time (by 5%) and corner exit velocity (by 4%) a few different driving strategies are found depending on thermal conditions of semi-slick tyres. The process of the race driver adaptation to initially cold or hot tyres is explained.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Contents Index Volume 35 and 36

Active safety systems would benefit from tyre force and friction potential information. Different sensor concepts, including, among others, the EU–funded Apollo–project developed tyre sensor based on optical position detection, are being studied. The sensor can measure tyre carcass deflections with respect to the rim. The carcass deflections can be used to calculate tyre forces and they may be exploited in the estimation of friction potential. The waveforms of the sensor signal are illustrated. The vertical and lateral force estimations are presented with unavoidable compensation parts. The tyre sensor measurements were compared to the measurement–vehicle results and good correlations achieved. Continuing activities are concerned with the estimation of friction potential and the detection of aquaplaning.     

A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces

Direct yaw moment control (DYC), which differentially brakes the wheels to produce a yaw moment for the vehicle stability in a steering process, is an important part of electric stability control system. In this field, most control methods utilise the active brake pressure with a feedback controller to adjust the braked wheel. However, the method might lead to a control delay or overshoot because of the lack of a quantitative project relationship between target values from the upper stability controller to the lower pressure controller. Meanwhile, the stability controller usually ignores the implementing ability of the tyre forces, which might be restrained by the combined-slip dynamics of the tyre. Therefore, a novel control algorithm of DYC based on the hierarchical control strategy is brought forward in this paper. As for the upper controller, a correctional linear quadratic regulator, which not only contains feedback control but also contains feed forward control, is introduced to deduce the object of the stability yaw moment in order to guarantee the yaw rate and side-slip angle stability. As for the medium and lower controller, the quantitative relationship between the vehicle stability object and the target tyre forces of controlled wheels is proposed to achieve smooth control performance based on a combined-slip tyre model. The simulations with the hardware-in-the-loop platform validate that the proposed algorithm can improve the stability of the vehicle effectively.     

The effect of the inflation pressure of tyres on motorcycle weave stability: experiments and simulation

Increasing the stability of a motorcycle requires an understanding of the optimal conditions of the tyre. The inflation pressure is one of the main parameters that directly affects the tyre properties, which in turn influences motorcycle stability and safety. This paper focuses on the effect of the inflation pressure of the tested tyres on motorcycle weave stability. Experimental data are collected from tests carried out in straight running at constant speed. The data analysis is based on stochastic subspace identification methods. Simulations are performed using an advanced motorcycle multi-body code with parameters measured from the tested vehicle. Finally, the comparison between simulations and experimental tests is discussed. The research results show an agreement between experimental tests and simulations where weave stability increases with inflation pressure for the specified range of tyre pressure.     

An optimal torque distribution control strategy for four-independent wheel drive electric vehicles

In this paper, an optimal torque distribution approach is proposed for electric vehicle equipped with four independent wheel motors to improve vehicle handling and stability performance. A novel objective function is formulated which works in a multifunctional way by considering the interference among different performance indices: forces and moment errors at the centre of gravity of the vehicle, actuator control efforts and tyre workload usage. To adapt different driving conditions, a weighting factors tuning scheme is designed to adjust the relative weight of each performance in the objective function. The effectiveness of the proposed optimal torque distribution is evaluated by simulations with CarSim and Matlab/Simulink. The simulation results under different driving scenarios indicate that the proposed control strategy can effectively improve the vehicle handling and stability even in slippery road conditions.     

Tyre friction behaviour under abrupt wheel torque transients on slippery road surfaces: experimental analysis and modelling

The paper shows that, during abrupt wheel torque transients for ice surface and low vehicle speeds, the tyre can develop significantly larger longitudinal force than the peak value of the tyre static curve. This so-called dynamic tyre friction potential (DTFP) effect has many influencing factors such as the rate of change of the wheel torque, the vehicle speed, and the tyre dwell time. The paper presents a detailed analysis of the DTFP behaviour based on the experimental data collected by using an in-wheel motor-based tyre test vehicle. The analysis results and an insight into the brush structure of a tyre model lead to the hypothesis that the different influencing factors may be predominantly explained by the bristle dwell time (BDT) effect. Following this hypothesis, the LuGre model of the tyre friction dynamics is extended with a physical BDT sub-model. The experimental validation results show that the proposed model can accurately capture the low-speed tyre–ice friction behaviour during abrupt wheel torque transients.     

Energy analysis of the Von Schlippe tyre model with application to shimmy

Shimmy is an engineering example of self-excited vibrations. Much research on shimmy has considered the tyre as a positive feedback or negative damping to introduce instability of the entire system. In this context, we focus on the behaviour of the tyre under periodic excitations. The Von Schlippe tyre model is selected and the energy flow method is applied to illustrate the energy transfer by the tyre during shimmy. The energy flow method evaluates the tyre performance with a prescribed sinusoidal motion and provides a novel evaluation method for tyre models. With the help of straight contact line assumption in the Von Schlippe tyre model, the relative motion between the contact line and the wheel centre is studied to understand the path dependency of the energy transfer. It turns out that the tyre is extracting energy from the forward motion to induce unstable lateral and yaw vibrations when the motion or orientation of the contact line has a phase lead with respect to the wheel centre.