Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.     

Wheel slip control with torque blending using linear and nonlinear model predictive control

Modern hybrid electric vehicles employ electric braking to recuperate energy during deceleration. However, currently anti-lock braking system (ABS) functionality is delivered solely by friction brakes. Hence regenerative braking is typically deactivated at a low deceleration threshold in case high slip develops at the wheels and ABS activation is required. If blending of friction and electric braking can be achieved during ABS events, there would be no need to impose conservative thresholds for deactivation of regenerative braking and the recuperation capacity of the vehicle would increase significantly. In addition, electric actuators are typically significantly faster responding and would deliver better control of wheel slip than friction brakes. In this work we present a control strategy for ABS on a fully electric vehicle with each wheel independently driven by an electric machine and friction brake independently applied at each wheel. In particular we develop linear and nonlinear model predictive control strategies for optimal performance and enforcement of critical control and state constraints. The capability for real-time implementation of these controllers is assessed and their performance is validated in high fidelity simulation.     

Robust estimation of maximum tire-road friction coefficient considering road surface irregularity

An accurate estimation of the maximum tire-road friction coefficient may provide higher performance in a vehicle active safety control system. Unfortunately, real-time tire-road friction coefficient estimation is costly and necessitates additional sensors that must be installed and maintained at all times. This paper proposes an advanced longitudinal tire-road friction coefficient estimation method that is capable of considering irregular road surfaces. The proposed algorithm uses a stiffness based estimation method, however, unlike previous studies, improvements were made by suggesting a third order model to solve problems related to nonlinear mu-slip curve. To attain the tire-road friction coefficient, real-time normalized force is obtained from the force estimator as exerted from the tire in the low slip region using the recursive least squares method. The decisive aspect of using the suggested algorithm lies in its low cost and versatility. It can be used under irregular road conditions due to its capability of easily obtaining wheel speed and acceleration values from production cars. The newly improved algorithm has been verified to computer simulations as well as compact size cars on dry asphalt conditions.     

ABS轮速信号测量误差分析及等周期采样方法研究

从理论分析的角度对ABS轮速信号测量的误差进行了研究,指出触发误差是影响轮速测量门槛值高低的主要因素,并通过试验测量了该误差随轮速的变化关系。等角度采样的轮速信号在ABS中需要变换成等控制周期采样的轮速信号。在低速测量场合,当ABS控制周期内没有轮速信号出现时,本文利用了一种基于二阶多项式拟合的预测算法来估计轮速信号,仿真试验结果表明该估计方法是可行且可靠的。     

Improvement of drivability and fuel economy with a hybrid antiskid braking system in hybrid electric vehicles

When braking on wet roads, Antilock Braking System (ABS) control can be triggered because the available brake torque is not sufficient. When the ABS system is active, for a hybrid electric vehicle, the regenerative brake is switched off to safeguard the normal ABS function. When the ABS control is terminated, it would be favorable to reactivate the regenerative brake. However, recurring cycles from ABS to motor regenerative braking could occur. This condition is felt to be unpleasant by the driver and has adverse effects on driving stability. In this paper, a novel hybrid antiskid braking system using fuzzy logic is proposed for a hybrid electric vehicle that has a regenerative braking system operatively connected to an electric traction motor and a separate hydraulic braking system. This control strategy and the method for coordination between regenerative and hydraulic braking are developed. The motor regenerative braking controller is designed. Control of regenerative and hydraulic braking force distribution is investigated. The simulation and experimental results show that vehicle braking performance and fuel economy can be improved and the proposed control strategy and method are effective and robust.     

Synthesis of a Model-Based Tire Slip Controller

The Anti-lock Braking System is an important component of the steering system in a modern car. In the latest generation of brake-by-wire systems, the performance requirements on the ABS are much higher. The controllers have to be able to maintain a specified tire slip for each wheel during braking. The authors propose a design model and based on that a gain-scheduled controller that regulates the tire-slip. Simulation and test results are presented.     

Synthesis of a Model-Based Tire Slip Controller

The Anti-lock Braking System is an important component of the steering system in a modern car. In the latest generation of brake-by-wire systems, the performance requirements on the ABS are much higher. The controllers have to be able to maintain a specified tire slip for each wheel during braking. The authors propose a design model and based on that a gain-scheduled controller that regulates the tire-slip. Simulation and test results are presented.     

Experimental investigations on continuous regenerative anti-lock braking system of full electric vehicle

Functions of anti-lock braking for full electric vehicles (EV) with individually controlled wheel drive can be realized through conventional brake system actuating friction brakes and regenerative brake system actuating electric motors. To analyze advantages and limitations of both variants of anti-lock braking systems (ABS), the presented study introduces results of experimental investigations obtained from proving ground tests of all-wheel drive EV. The brake performance is assessed for three different configurations: hydraulic ABS; regenerative ABS only on the front axle; blended hydraulic and regenerative ABS on the front axle and hydraulic ABS on the rear axle. The hydraulic ABS is based on a rule-based controller, and the continuous regenerative ABS uses the gain-scheduled proportional-integral direct slip control with feedforward and feedback control parts. The results of tests on low-friction road surface demonstrated that all the ABS configurations guarantee considerable reduction of the brake distance compared to the vehicle without ABS. In addition, braking manoeuvres with the regenerative ABS are characterized by accurate tracking of the reference wheel slip that results in less oscillatory time profile of the vehicle deceleration and, as consequence, in better driving comfort. The results of the presented experimental investigations can be used in the process of selection of ABS architecture for upcoming generations of full electric vehicles with individual wheel drive.     

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.     

A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis

Pacejka's Magic Formula Tyre Model is widely used to represent force and moment characteristics in vehicle simulation studies meant to improve handling behaviour during steady-state cornering. The experimental technique required to determine this tyre model parameters is fairly involved and highly sophisticated. Also, total test facilities are not available in most countries. As force and moment characteristics are affected by tyre design attributes and tread patterns, manufacturing of separate tyres for each design alternative affects tyre development cycle time and economics significantly. The objective of this work is to identify the interactions among various tyre design attributes-cum-operating conditions and the Magic Formula coefficients. This objective is achieved by eliminating actual prototyping of tyres for various design alternatives as well as total experimentation on each tyre through simulation using finite element analysis. Mixed Lagrangian–Eulerian finite element technique, a specialized technique in ABAQUS, is used to simulate the steady-state cornering behaviour; it is also efficient and cost-effective. Predicted force and moment characteristics are represented as Magic Formula Tyre Model parameters through non-linear least-squares fit using MATLAB. Issues involved in the Magic Formula Tyre Model representation are also discussed. A detailed analysis is made to understand the influence of various design attributes and operating conditions on the Magic Formula parameters. Tread pattern, tread material properties, belt angle, inflation pressure, frictional behaviour at the tyre–road contact interface and their interactions are found to significantly influence vehicle-handling characteristics.     

Improved Vehicle Performance Using Combined Suspension and Braking Forces

This work presents a preliminary investigation into the integration of particular subsystems of an automobile's chassis. The specific focus of this research is the integration of Active Suspension components with Anti-Lock braking (ABS) mechanisms. The performance objective for the integrated approach is defined as a reduction in braking distance over just anti-lock brakes. Several models, of varying degrees of complexity, are presented to determine the effect of modeling accuracy on the potential performance improvement. In the most detailed model, a four degree of freedom Half Car vehicle model is developed along with models for a hydraulic Active Suspension and an ABS system. For both subsystems, actuator dynamics are included. The tire-road interface is modeled using the Magic Formula tire model. Individual controllers are developed for the subsystems and a governing algorithm is constructed to coordinate the two controllers. Simulations of the integrated controller and an ABS system, for each system model, demonstrate a significant increase in performance.     

基于四轮轮边驱动电动车的路面附着系数估算方法

路面附着系数是影响车辆行驶安全性的重要因素,利用轮边驱动电动汽车驱动力矩可以对路面利用附着系数进行观测。当观测到μ-λ曲线接近于峰值点时,将该时刻的轮胎利用附着系数作为路面峰值附着系数,并根据识别的路面峰值附着系数进行驱动防滑控制。该方法能够有效防止轮胎滑转,提高车辆行驶稳定性。     

New Control Technique for Maximizing Braking Force on Antilock Braking System

In this paper, we propose a new control strategy for an antilock braking system (ABS) to maintain the braking force at maximum. The popularization of the ABS that prevents the wheels from locking has resulted in an improvement of the vehicle stability and shortening of the braking distance. Further improvement is anticipated if the maximization of the braking force is realized. We found an interesting phenomenon in which the characteristics of the resonance system composed of the vehicle body and the wheel and road surface reflects the slip condition of the road surface. Using this phenomenon, we realized a control method for maintaining the maximum value of the braking force.     

New Control Technique for Maximizing Braking Force on Antilock Braking System

In this paper, we propose a new control strategy for an antilock braking system (ABS) to maintain the braking force at maximum. The popularization of the ABS that prevents the wheels from locking has resulted in an improvement of the vehicle stability and shortening of the braking distance. Further improvement is anticipated if the maximization of the braking force is realized. We found an interesting phenomenon in which the characteristics of the resonance system composed of the vehicle body and the wheel and road surface reflects the slip condition of the road surface. Using this phenomenon, we realized a control method for maintaining the maximum value of the braking force.     

Study on flange climb derailment criteria of a railway wheelset

The wheel flange climb derailment, which can be usually considered as a quasi-static process, is one of the main types of derailment, and often occurs on curved tracks due to large wheel lateral force and reduced vertical force. The general formula for the wheel critical derailment coefficient Q/P, the ratio of wheel lateral force to vertical force, is derived through analysing the forces exerted on the flange climb wheel. Based on the Coulomb's friction law and the creep force laws, the Friction Formula and Creep Formula for the evaluation of derailment are derived, respectively. The analysis shows that the derailment coefficients of Friction Formula and Creep Formula required for derailment are increased considerably for smaller and negative yaw angles, and tend to the value of Nadal's Formula at larger wheelset yaw angles. The Creep Formula is more reasonable for the assessment of derailment. The effect of some parameters on flange climb derailment, such as wheel/rail friction coefficient, yaw angle, flange contact angle, wheel vertical load and curve radius, are investigated. Finally, a simplified formula for wheel climb derailment based on the Creep Formula is proposed.     

对开路面弯道制动ABS控制策略研究

在对开路面弯道制动工况下分析了轮胎受力情况,提出一种基于转角预测前馈、路径偏移量反馈的车辆最佳滑移率动态调节方法,在SIMPACK中建立汽车多体模型,在MATLAB/Simulink中搭建控制系统,并进行了虚拟在环试验。试验结果显示,与传统ABS相比,所提出的控制方法可以显著改善车辆的侧偏位移、横摆角速度以及制动时方向的稳定性,保证了制动效能,使车辆侧向稳定性得到显著提高。     

基于Matlab的ABS不同控制方式的仿真

汽车防抱制动系统（ABS）能实时控制车辆产生最佳的制动力矩,避免产生过大的车轮滑移,从而保持汽车的操纵性和稳定性。文中分别采用PID控制、逻辑开关控制两种方法对单轮汽车模型进行了模拟仿真。然后与没有ABS的情况进行对比,通过对仿真图形曲线的分析,得出ABS的防抱死效果明显。     

Study on flange climb derailment criteria of a railway wheelset

The wheel flange climb derailment, which can be usually considered as a quasi-static process, is one of the main types of derailment, and often occurs on curved tracks due to large wheel lateral force and reduced vertical force. The general formula for the wheel critical derailment coefficient Q/P, the ratio of wheel lateral force to vertical force, is derived through analysing the forces exerted on the flange climb wheel. Based on the Coulomb's friction law and the creep force laws, the Friction Formula and Creep Formula for the evaluation of derailment are derived, respectively. The analysis shows that the derailment coefficients of Friction Formula and Creep Formula required for derailment are increased considerably for smaller and negative yaw angles, and tend to the value of Nadal's Formula at larger wheelset yaw angles. The Creep Formula is more reasonable for the assessment of derailment. The effect of some parameters on flange climb derailment, such as wheel/rail friction coefficient, yaw angle, flange contact angle, wheel vertical load and curve radius, are investigated. Finally, a simplified formula for wheel climb derailment based on the Creep Formula is proposed.     

ABS功能,原理及控制逻辑分析

车辆制动过程是一能量转换过程。它受众多动力学参数的影响。ABS是以车轮的滑移率与附着系数的关系为理论依据的，在ABS的控制逻辑中选取正确的控制元，可规避众多动力学参数，保证ABS控制模式的正确性。     

电—液混合式制动系统试验台的开发

以电动汽车开发为例,设计了电—液混合式制动系统试验台。介绍了试验台设计、总体结构方案设计、硬件设计及控制系统设计。实际测试表明,该试验台可用于测试防抱制动控制算法的控制性能和电机再生制动性能、研究电—液制动力分配控制策略,并能够模拟在较小横摆角条件下直接横摆扭矩对制动状态的影响。