Modeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfaces

The brake and steering systems in vehicles are the most effective actuators that directly affect the vehicle dynamics. In general, the brake system affects the longitudinal dynamics and the steering system affects the lateral dynamics; however, their effects are coupled when the vehicle is braking on a non-homogenous surface, such as a split-mu road. The yaw moment compensation of the steering control on a split-mu road is one of the basic functions of integrated or coordinated chassis control systems and has been demonstrated by several chassis suppliers. However, the disturbance yaw moment is generally compensated for using the yaw rate feedback or using wheel brake pressure measurement. Access to the wheel brake pressure through physical sensors is not cost effective; therefore, we modeled the hydraulic brake system to avoid using physical sensors and to estimate the brake pressure. The steering angle controller was designed to mitigate the non-symmetric braking force effect and to stabilize the yaw rate dynamics of the vehicle. An H-infinity design synthesis was used to take the system model and the estimation errors into account, and the designed controller was evaluated using vehicle tests.     

Modeling and Analysis of Automotive Antilock Brake Systems Subject to Vehicle Payload Shifting

The steerability and stability of vehicles must be maintained during emergency stopping and evasive driving maneuvers on degraded road surfaces. The introduction of antilock brake and traction control systems (ABS/TCS) has expanded the envelope of safe vehicle operation for the majority of drivers. These mechatronic systems combine an electronic controller with wheel speed sensors, an electro-mechanical hydraulic brake actuator, and in some instances, engine intervention through the engine control unit, to regulate wheel slip. The development of ABS systems has traditionally depended on extensive in-vehicle testing, at cold weather proving grounds, which contribute to lengthy product development cycles. However, recent attention has been focused on the use of simulation and hardware-in-the-loop strategies to emulate test conditions in a controlled setting to shorten product design time and methodically address critical safety issues. In this paper, the effect of transient load shifting due to cargo movement on ABS performance in light-duty vehicles will be investigated. Analytical and empirical mathematical models are presented to describe the chassis, tire/road interface, wheel, brake modulator, and cargo dynamics. Two strategies, a model-free table lookup and model-based discrete nonlinear controller, are presented to regulate the ABS modulator's operation. These vehicle and controller dynamics have been integrated into a simulation tool to investigate the effect of transient weight transfers on the vehicle's overall stopping distance and time. Representative numerical results are presented and discussed to quantify the ABS systems' performance for various loading and operating conditions.     

The Development and Implementation of Adaptive Semi-Active Suspension Control*

SUMMARY

Using adjustable shock absorbers within vehicle suspension systems, it is possible to improve ride comfort significantly when a control strategy is applied based on the so-called skyhook principle. However, the drawback is a poorly damped wheel-hop mode which makes the road holding ability worse. Using adaptive semi-active suspension control based on the tire load variations as introduced in this paper, the trade-off between road holding and ride comfort can be relaxed. Implementation of adaptive skyhook control requires the determination of a number of important and difficult to measure states of the vehicle. This can either be accomplished by several sensors and filters or by a state estimator in combination with less sensors and an internal model of the vehicle. Both methods are discussed. Finally some preliminary test results are discussed.     

The Use of GPS Based Velocity Measurements for Measurement of Sideslip and Wheel Slip

Summary This paper details a novel method for measuring three key vehicle states – wheel slip, body sideslip angle, and tire sideslip angle – using GPS velocity information in conjunction with other sensors. Based on initial noise data obtained from the system components, a prediction of the accuracy of the angle measurements is obtained. These results demonstrate that the errors due to stochastic noise in the GPS signal are below one degree for meaningful vehicle speeds and approach a tenth of a degree at highway speeds. Hence the limiting factor for measuring these states is not the GPS receiver, but the manner in which other implementation issues – such as bias elimination, off-axis dynamics and dead-reckoning during loss of satellite visibility – are handled. Subsequent experiments validate both the error analysis and the methodology for obtaining the measurements. The experimental results for this preliminary implementation of GPS-based state estimation compare favorably to theoretical predictions, suggesting that this technique has potential for future implementation in vehicle diagnostic and, ultimately, safety systems.     

Model-Based Road Friction Estimation

The tire/road friction coefficient, μ, has a significant role in vehicle longitudinal and lateral control, and there has been associated efforts to measure or estimate the road surface condition to provide additional information for stability augmentation systems of automobiles. In this paper, a model based road friction estimation algorithm is proposed from easily measured signals such as yaw rate and wheel speed. For the development of the estimator, a low order vehicle model incorporated with simple but effective tire model. Field tests of the estimator using actual vehicle measurements show promising results.     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

Full-slip kinematics based estimation of vehicle yaw rate from differential wheel speeds

Vehicle yaw rate is a key parameter required for various active stability control systems. Accurate yaw rate information may be obtained from the fusion of some on-vehicle sensors and GPS data. In this study, the closed-form expression of the yaw rate–written as a function of front wheel rolling speeds and steering angle–was derived via kinematic analysis of a planar four-wheel vehicle on the assumption of no longitudinal slip at the both front tires. The obtained analytical solution was primarily verified by computational simulation. In terms of implementation, the 1:10th scaled rear-wheel-drive vehicle was modified so that the front wheel rolling speeds and the steering angle could be measured. An inertial measurement unit was also installed to provide the directly measured yaw rate used for validation. Preliminary experiment was done on some extremely random sideslip maneuvers beneath the global positioning using four recording cameras. Comparing with the vision-based and the gyro-based references, the vehicle yaw rate could be well approximated at any slip condition without requiring integration or vehicle and tire models. The proposed cost-effective estimation strategy using only on-vehicle sensors could be used as an alternative way to enhance performance of the GPS-based yaw rate estimation system while the GPS signal is unavailable.     

Vehicle sideslip estimation and compensation for banked road

The sideslip driving status is of fundamental importance to the stability of a vehicle. This paper presents a practical vehicle sideslip driving status estimation method that uses ESP (electronic stability program) sensors. ESP sensors such as wheel speed, lateral acceleration, yaw rate and steering wheel angle sensors are used to determine the sideslip driving status and distinguish a banked road. This estimation algorithm contains front-rear sideslip and banked road detection methods. The proposed sideslip estimation algorithm was designed to use the analytical redundancy of these sensors and Lagrange interpolation methods. The performance and effectiveness of the proposed estimation and compensation algorithm were investigated using vehicle tests. This paper presents the results of two cases that were used for the experimental verification: a curved flat road and banked road.     

Effect of vehicle model on the estimation of lateral vehicle dynamics

A methodology is presented for estimating vehicle handling dynamics, which are important to control system design and safety measures. The methodology, which is based on an extended Kalman filter (EKF), makes it possible to estimate lateral vehicle states and tire forces on the basis of the results obtained from sinusoidal steering stroke tests that are widely used in the evaluation of vehicle and tire handling performances. This paper investigates the effect of vehicle-road system models on the estimation of lateral vehicle dynamics in the EKF. Various vehicle-road system models are considered in this study: vehicle models (2-DOF, 3-DOF, 4-DOF), tire models (linear, non-linear) and relaxation lengths. Handling tests are performed with a vehicle equipped with sensors that are widely used by vehicle and tire manufacturers for handling maneuvers. The test data are then used in the estimation of the EKF and identification of lateral tire model coefficients. The accuracy of the identified values is validated by comparing the RMS error between experimentally measured states and regenerated states simulated using the identified coefficients. The results show that the relaxation length of the tire model has a notable impact on the estimation of lateral vehicle dynamics.     

A Comparison between Four Computing Models of Different Complexity Describing the Steering Behavior of Two-axled Automobiles

SUMMARY

In this paper chassis controls for vehicle handling and active safety have been reviewed. In particular, we have observed the effectiveness and limit of 4WS and DYC. It is pointed out that DYC is more effective in vehicle motion with larger side-slip and/or higher lateral acceleration and taking the nonlinearity of tire and vehicle dynamics into consideration is essential for introducing the control law for the chassis controls and their integration/coordination. We wish to emphasize that there is a need to further propose control laws based on deeper observation and understanding on the tire and vehicle dynamics.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

轮胎尺寸对汽车结构疲劳累积损伤影响研究

基于结构耐久试验工况,通过六分力设备与底盘杆系所采集的整车道路载荷谱,应用动力学载荷分解方法获得虚拟随机载荷谱,对车身结构进行应力分析和疲劳累积损伤计算。在底盘关键位置布置传感器,同时在车身结构中CAE疲劳分析所对应的5个高应力区粘贴应变片,先后采用3套不同尺寸参数(包括胎高和胎面宽度)的轮胎以相同的耐久工况(同一个试验场,试验路面及对应的速度相同)来进行实车载荷对比测试。针对车身结构载荷幅值、频域进行分析,并基于雨流循环计数对车身和底盘件进行疲劳累积损伤计算与分析。整车实际测试的结果表明,CAE所预测到的损伤(裂纹)位置及其里程数与路试结果相吻合;在同样使用条件下,轮胎内径越大,车身结构和汽车底盘的寿命越低,已经可进行量化对比。     

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.     

Coordinated control of ESC and AFS with adaptive algorithms

This paper presents a coordinated control of electronic stability control (ESC) and active front steering (AFS) with adaptive algorithms for yaw moment distribution in integrated chassis control (ICC). In order to distribute a control yaw moment into control tire forcres of ESC and AFS, and to coordinate the relative usage of ESC to AFS, a LMS/Newton algorithm (LMSN) is adopted. To make the control tire forces zero in applying LMS and LMSN, the zero-attracting mechanism is adopted. Simulations on vehicle simulation software, CarSim®, show that the proposed algorithm is effective for yaw moment distribution in integrated chassis control.     

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.     

面向全矢量线控车辆极限运动的分层式协同控制

装配四轮分布式驱动-转向（4WID-4WIS）底盘的全矢量线控车辆具备多可控自由度、高速稳定性强的特点,是极限工况稳定裕度和安全性较高的理想车型。为了解决全矢量线控车辆在极限工况下纵横向控制冲突危害行车安全的问题,提出一种基于模型预测控制 （MPC） 的分层式车辆纵向和横向运动协同控制方法。建立基于单轨模型的期望运动状态识别方法,设计模型预测控制器转换动力学目标,采用泰勒展开和前向欧拉方法对预测模型进行线性离散化处理;设计基于负荷率的轮胎力优化分配方法,利用反正切轮胎逆模型求解控制执行量。仿真结果表明,协同控制方法能显著提高车辆在不同路面下的极限运动稳定性,更精准地跟踪期望运动状态,扩大稳定裕度,保障行车安全。     

Estimation of Tire-Road Friction Using Observer Based Identifiers

This paper presents methods for identifying the tire-road friction coefficient. The proposed methods are: an observer-based least square method and an observer/filtered-regressor-based method. These methods were designed assuming that some of the states are not available since physical parameter identification methods developed assuming that the system states are available are not attractive from a practical point of view. The observer is used to estimate signals which are difficult or expensive to measure. Using the estimated states of the system and the filtered-regressor, the parameter estimates are obtained. The proposed methods are evaluated on an eight state nonlinear vehicle/transmission simulation model with a Bakker-Pacejka's formula tire model. Vehicle tests have been performed on dry and wet roads to verify the performance of the methods. It has been shown through simulations and vehicle tests how the RPM sensors can be used with observer based identification methods to estimate the tire-road friction from measurements of engine rpm, transmission output speed and wheel speed. The proposed methods will be useful in the implementation and adaptation of vehicle collision warning/avoidance algorithm since the tire-road friction can be estimated only using the RPM sensors which are currently being used in production vehicles.     

Observer Design for Electronic Suspension Applications*

SUMMARY

This paper proposes a new methodology for designing observers for automotive suspensions. Automotive suspensions are disturbance-affected dynamic systems. Semi-active suspensions are bilinear while active suspensions with hydraulic actuators are nonlinear. The proposed methodology guarantees exponentially convergent state estimation for both these systems. It uses easily accessible and inexpensive measurements. The fact that sprung mass absolute velocity of the suspension cannot be estimated in an exponentially stable manner with such measurements is also demonstrated.

Controllers using estimated states are implemented experimentally on the Berkeley Active Suspension Test Rig. Experimental results for two cases are presented : use of observer states to improve ride quality in an active suspension and use of observer states to reduce dynamic tire loading in a semi-active heavy vehicle suspension.