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（学号）： 0623208长春理工大学光电信息学院毕 业 设 计（论 文）译文姓 名卢雪学 院机电工程分院专 业机械设计制造及其自动化班 级06232指导教师张广杰2010年6月15日概要在过去十年中，德国涉及交通事故的汽车在汽车总量的比例没有明显减少，但致命伤害的事故发生数量却在持续的降低。大多数严重的事故是由于汽车失控导致的。驾驶员对汽车失去操纵稳定性的是一个有待解决的问题。构建车辆动力学控制系统ESP（电子稳定装置，也称为：VDC）的目的便是用来解决这一问题的。通过怎样的方法来实现这一目的将在下文提及。下文将谈到车辆的偏移角，这个在汽车操纵性能中至关重要的指标。由于完整的汽车状态不容易获得，估计运算法就为控制运算法的提供了足够的信息补充。通过对偏移角的自动调节，各自轮胎的滑动控制就可以产生所需的瞬时偏移了。通过接下来的两个例子可以看出，ESP可以通过自动控制发动机和制动器来显著提高车辆在突然转向下的操纵稳定性。控制理论ESP利用了防抱死系统ABS和牵引力控制系统ASR组件（图1、图2）。这些组件是：用来获得汽车车轮的转动速度的传感器，改变车轮制动器压力的液压单元以及实行控制运算、处理传感器信号、和控制液压单元的电子单元。一个联到发动机的管理控制器的接口也用来测量和改变发动机转矩的输出。为了获得驾驶员所需的操纵性和实际汽车的操纵特性，还添加了四个ESP传感器。这些传感器是转向角传感器，侧偏速度传感器，侧偏加速度传感器和压力传感器（图2）图1：安装在汽车上的ESP组件图2：ESP组件此外，这个系统还需要TCS-OFF（牵引力控制系统）开关，来阻止在牵引力控制中驱动轮的制动器抱死控制；制动报警灯开关，手刹开关，制动器液力水平开关，诊断串行接口和连接数据总线（CAN）。如果用一个灵敏的调压器实现辅助制动，那么需要附加的继电器来防止制动指示灯在给ESP液压单元加压时点亮。ESP的车辆动力学控制部分由上至下分级控制。在底部轮胎的滑动受控制的。车辆动力学控制部分由都各处理单元组成，第一单元处理传感器信号（如滤波器）。虽然观察者是基于单一因素的，但是整个汽车模型习惯是用来用来评估汽车侧偏角以及每个轮胎的侧偏角也在下文提到。还要加上每个轮胎的纵向力与侧向力作用。滑动控制器为观测者提供所需的信息，如车辆的速度和加速度以及轮胎纵向力。图3:ESP控制系统结构简图下面的微分方程可以初步估计汽车侧偏角：仅当汽车的侧倾角和滚动角为零时，该微分方程才是有效的。此外汽车在要在水平平面上，即该路面的纵向和横向的坡度为零。这个等式中是侧向加速度，是纵向加速度，是是前进速度，是侧向速度。当紧急制动和加速时，等式是有效的。如果侧偏角很小并且车速仍然恒定，等式可以化简得到简单的估计值加上测定变量，和估计变量，以及他们的误差，和分别综合起来。在传感信号中的偏移量和其他误差会很快导致侧偏角的较大的估算误差。而且完全制动时，汽车减速度和旋转角不能忽略，当急转向时汽车的偏转角也不能忽略。为了获得更加准确的汽车偏移角，就使用了观测仪。观测仪是基于汽车四轮简化模型和两个动力学等式，其中一个是计算汽车侧偏速度，另一个是用来计算汽车横向速度。横向运动的微分方程是：侧向运动的微分方程是：在这些等式中侧向力,和纵向力,是未知的；车辆的质量为，关于垂直轴的转动惯量为和长度a,b,c假设已知。任意车轮上的纵向力可以通过以下的普通等式估算：这里的是已知恒量，表示制动器轮缸内的液压，表示发动机传递到在车轴上的扭矩的一半，表示车轮的转动惯量，表示车轮的转速，它是车轮角速度与轮胎半径的乘积。发动机转矩值可以通过发动机管理系统得到，而车轮旋转速度可以由车轮速度传感器测量到。通过液压单元建模，可以计算出制动器主缸压力以及知道液压单元阀门开启次数，用这个液压模型可以估算每一个车轮上的制动器的压力。因此任何时候作用在车轮上的纵向力可用这种方法估算出来。侧向力的值不容易得到，因此就要运用车轮模型，8中描述的的轮胎模型HSRI就专门用来估算一些情况下的侧向力和纵向力。运用这些等式可以得到侧向力与纵向力之间的简单关系：在这些等式中和分别是轮胎滑动和转向时的刚度，l和a 分别表示轮胎侧滑和其侧偏角，时轮胎上的法向力，m是轮胎与路面最大摩擦系数.以上的侧向力与纵向力关系不仅适用于m-slip曲线开始的线性区域，也同样适用于非线性区域。由于轮胎的滑动和转向刚度主要取决与轮胎的材料，两者的比值虽轮胎由夏季到冬季的变化，以及轮胎的磨损而变化。接下来要说的是，侧偏角的正切值近似等于其本身：tan a = a整车模型的微分方程可以重新整理，并运用一个卡尔曼滤波模型的离散法解出。以下给出了重新整理后的等式结果离散化近似表示为欧拉公式：试中T是采样时间，k是时间指标。由于侧偏速度是已知的，汽车的横向速度的计算公式就可以通过侧偏速度的线性推断法和取代最后一个等式结果而得到：代入后，得到横向速度计算式：可是运用测量仪的先决条件是轮胎要有一定的纵向滑动，否则就不能运用侧向力与纵向力之间的关系。根据经验，在完全制动时估算的侧偏角可以非常精确。可是在轮胎自由滚动的时候测量仪无法运用，侧偏角的估计值就不得不通过本章开始所说的汽车横向加速度以及侧偏角速度来得到了。因此依据驾驶条件不同，车辆的侧偏角估计值的精确度是不同的。车辆动力学控制系统还有一个内部循环系统，紧接着来控制汽车的侧向速度。根据汽车二自由度模型，得到理论侧偏速度：轴距l与特征车速是取决于汽车设计的参数。可是特征车速同样也取决于轮胎的特性，如轮胎横向刚度。因此理论侧偏速度取决轮胎类型、制造、状态（新旧）。引入以下的控制模型从而引入了一种得到理论侧偏速度的方法。为了正确起效，ESP必须通过各种汽车轮胎的检验。转向角不是直接测量得到的，而是通过车轮转向角得到的。通常转向角是根据车轮转向角和转向器传动比算出。可是，作用在轮胎半径上的纵向力会影响这个值，于是就需要一个修正系统来解决这个问题。此外转向柱管有两个虎克铰型。如果其输入输出轴不平行，那么就会引入一个成正弦形状变化的误差。车辆前进速度是可以由滑动控制器测得。由于汽车横向加速度不能够超过轮胎与路面的最大摩擦系数，侧偏角速度必须又有一个限定值。汽车稳态角加速度由公式表示如下：其中是转向半径，它随侧偏频率变化，侧偏频率被限制在一定范围内。已知的横向加速度取代未知的。汽车侧偏角的一个限制条件运用法讨论，它来自轮胎与路面的附着系数。为了增加驾驶员保持其汽车在高速下的稳定能力的支持，这个值的要减少到另一值，而这个过程取决于汽车的速度。如果通过汽车侧偏速度和侧向角描述的状态与汽车的理论和不同，那么车辆动力学控制系统就会检测这种差异是否在可允许范围内。这个系统同样考虑到了人的行为。举个例子，在湿滑路面上，汽车对转向角变化的反应很小，结果驾驶员就会下意识的加大转向，从而导致了更危险的情况。为了使驾驶员的做出正常的反应，ESP瞬时侧偏速度的响应时间，直到汽车达到理论侧偏角。试验驾驶员同样也运用这样的瞬时过度转向的技术来达到这一目的。如上所示在侧偏运动中，各个轮胎可以通过改变它的侧偏参数来发生改变。可是由于各个轮胎上的增量不同，可以运用各轮胎上的偏移角变化来减小如汽车减速度之类的不良影响。如上所示，不幸的是，这种增量通常不能精确的测量到。为了获得各自轮胎的滑动力分配选择设计规则，运用了整车仿真模型。例如，在完全制动时，（ABS）外侧转向的前轮和内侧转向的侧偏改变都用来产生所需的侧偏运动。另外两轮的轮胎侧偏不变化。在摩擦系数m路面上行驶时，牵引力会通过使驱动轮在低一侧的制动器起作用来增加其大小。结果，汽车就产生驾驶员所不希望的侧偏运动，而且使汽车向低一侧偏驶。驾驶员为了阻止这一情况发生就不得不反打方向盘。如果反转方向盘角度过大或是驾驶员反应过慢，ESP就会减少制动器压力来减少侧偏运动。但是为了阻止低一侧车轮自转，发动机的转矩也应该减少。滑动控制器控制轮胎的侧滑。在制动和牵引力控制过程中，侧滑通过除驱动轮以外的制动滑动控制器来控制，牵引力滑动控制器控制驱动轮的侧滑值。当制动器压力调节器作用时，液压单元磁力阀受激打开，当发动机管理系统通过驱动力防滑系统调节转矩需求来进行驱动力的调节。如果运用了电力液压系统（EHB），可以直接得到额定制动液压值。结论图4冰面完全制动时，行驶方向改变的结果，而且比较了ESP和ABS的结果。在完全制动时，用测量仪可以获得足够的信息来估算车辆侧偏角。因而可以得到满意的侧偏角。 图4a是控制ABS（没有ESP）工作得到的结果。开始操纵不久，侧偏速度和侧偏角就变得很大使得驾驶员反向转向困难。结果侧偏角在其他方向快速增长，驾驶员不得不又一次快速反应。他几乎不能使汽车在一个方向稳定行驶。图4b所示的操纵ESP时车辆在其指定轨道内稳定行驶。可是应对行驶路线的改变所需的转向操纵比ABS要简便得多。ESP用来阻止驾驶员转向过度。侧偏速度和侧偏角都很小，后者比特征值小2。结果展示了测量仪在完全制动时的侧偏角已经相当精确了。对于普通驾驶者侧偏角和他日常很少低于2。使用ESP系统的制动距离比ABS制动距离少一些。原因是因为，采用ABS操纵会产生较大的侧偏角，从而降低了轮胎与路面的摩擦系数。ESP相对于ABS对车辆的稳定性能的提升是没有必要增加制动距离的。相反ESP的制动距离总体上要比ABS短。图4，在以相同的初速度50km/h行驶于冰面上（0.15），完全制动采用ABS(a)和ESP(b)时汽车轨迹的改变图5是后轮驱动汽车稳定行驶状态的仿真分析结果，在固定半径的圆形轨道内其汽车速稳定增加。在这种操纵环境下测试仪不能测量出汽车侧偏角，ESP不得不依赖于下面的控制模型。普通车辆没有安装ESP（图5a）和安装了ESP（图5b）的情况比较如下。它们的行驶轨迹是相同的，路面摩擦力系数也比较高。这是一个驾驶员必须保持汽车在一定轨道行驶的闭环控制系统，图表给出了所需的车轮转向角、车辆侧偏角值以及在轨迹上行驶的左右偏差。在两个图表内的曲线是从固定点采集的，在这些点上的计算是通过在各个车速下，变化转向角和发动机输出力矩仿真程序来完成的。图中虚线表示缓慢增加车速时的极限曲线。图5，安装ESP和没有安装ESP时汽车沿相同轨迹缓慢加速时状态的比较当汽车横向加速度接近7m/s时，普通车辆和装有ESP的车辆所表现出的行为相同，几乎可以说是一种固定行为。超过该横向加速度值时，两者就变得不一样了。车辆侧偏角和转向角快速增加。当横向加速度达到7.5m/s时，普通车辆就处于不稳定状态。超过汽车横向加速度接近7m/s，ESP系统对所需转向角和侧偏角的干扰就会减到很小。尽管驾驶员仍会逐渐的加大油门踏板力，但是在ESP的影响下发动机转矩值会受到限制，并且由于达到车辆运动极限，车速也不会再增加了。通过驾驶员的转向操纵，小的车辆偏驶会被减少。由结果可以看出，汽车横向加速度为7.5m/s，驾驶员的动作不会导致车辆的不稳定状态.车辆侧偏角和偏驶都控制在较小范围内。尽管ESP将车辆侧偏角控制在大约5左右而且低于最大稳定值（大概8），但是平均横向加速度值7.5m/s就几乎达到其允许最大值7.75m/s。参考书目1. Langwieder, K.: Mit ESP schwere Unflle vermeidenoder mildern. ESP-Workshop, November 10, 1999,Boxberg, Germany.2. Mller, A,; Achenbach, W,; Schindler, E.; Wohland,T.; Mohn, F.-W.:Das Neue FahrsicherheitssystemElectronic Stability Program von Mercedes Benz,ATZAutomobiltechnische Zeitschrift 96 (1994) 11, pp.656 - 670.3. van Zanten, A.; Erhardt, R.; Pfaff, G.:VDC, The Vehicle Dynamics Control System of Bosch,SAE95,Nr. 9507594. Fennel, H.; Gutwein, R.; Kohl, A.; Latarnik, M.; Roll,G.:Das modulare Regler- und Regelkonzept beim ESP von ITT Automotive,7. Aachener Kolloquium Fahrzeug- und Motortechnik, 5. - 7. Oktober, 1998,Aachen, S. 409 4315. Frster, H. -J.:Der Fahrzeugfhrer als Bindeglied zwischen Reifen, Fahrwerk und Fahrbahn,VDI Berichte, Nr. 916, 19916. Shibahata, Y.; Shimada, K.; Tomari, T.:Improvement of Vehicle Maneuverability by Direct Yaw Moment Control,In: Vehicle Systems Dynamics, 22 (1993),pp. 465 - 4817. Inagaki, S.; Kshiro, I.; Yamamoto, M.:Analysis on Vehicle Stability in Critical Cornering Using Phase-Plane Method,AVEC94, International Symposium onAdvanced Vehicle Control, Tsukuba Research Center,October 24 28, 1994, pp. 287 - 2928. van Zanten, A.T.; Erhardt, R.; Pfaff, G.; Kost, F.;Hartmann, U.; Ehret, T.:Control Aspects of the Bosch-VDC,AVEC96, International Symposium on Advanced Vehicle Control, Aachen, June 24 - 28,1996, pp. 576 - 60714ABSTRACTAlthough the total number of car occupants involved in accidents in Germany has not significantly reduced during the past 10 years, the number of fatalities has steadily decreased. Most of the severe accidents result from a loss of control of the car. The problem of the driver losing control of his car will be explained. This problem is then used to formulate the goal for the vehicle dynamics control system ESP (Electronic Stability Program, also known as VDC). The approach chosen to reach this goal will then be shown. It will be shown that the vehicle slip angle is a crucial indicator for the maneuverability of the automobile. Since the complete vehicle state is not readily available, estimation algorithms are used to supply the control algorithms with sufficient information. With the automatic control of the slip angle the required yaw moment can be generated by individual wheel slip control. By using two examples it will be shown, that ESP can significantly improve vehicle handling in extreme maneuvers by automatically controlling the brakes and the engine.CONTROL CONCEPTESP uses the components of the antilock brake system (ABS) and of the traction control system (ASR), Fig. 1, Fig. 2. These components are: sensors to derive the rotational velocity of the wheels, a hydraulic unit to modify the pressure in the wheel brakes and an electronic control unit to realize the control algorithm, to process the sensor signals and stimulate the hydraulic unit. An interface to the engine management controller is also used to measure and modify the engine torque output. Additionally four ESP sensors are required to derive the handling desire of the driver and to derive the actual handling behavior of the car. These sensors are a steering wheel angle sensor, a yaw velocity sensor, a lateral acceleration sensor and a pressure sensor (Fig.2).Figure 1. ESP components mounted in the carFigure 2. ESP componentsFurthermore, the system entails a TCS-OFF (Traction Control System) switch, to prohibit brake slip control of the driven wheels during traction control, a (redundant) brake light switch, a hand brake switch, a brake fluid level switch, a serial interface for diagnosis and a data bus connection (CAN). If a smart booster is used to realize a brake assistant, then an additional relay is required to prevent the brake lights from being lit during the precharging of the ESP hydraulic unit.The vehicle dynamics controller part of ESP (Fig. 3) constitutes the upper part of a hierarchical control. In the lower part the slips of the tires are controlled. The vehicledynamics controller part consists of several processing blocks. In the first block the sensor signals are processed (e.g. filtered). An observer based on a simple but full car model is used to estimate the slip angle of the car and of each tire as will be shown below. Also the normal and lateral forces on each tire are estimated. The slip controller supplies the required information for the observer like the vehicle velocity and acceleration, and the longitudinal tire forces.Figure 3. Simplified block diagram of the ESP controlAs a first approach in estimating the slip angle of the car, the following differential equation may be solved:This differential equation is valid only if the pitch and roll angles of the car are zero and furthermore, if the car moves on a horizontal plane, i.e. the slope of the road inlongitudinal and lateral direction is zero. In this equationis its lateral acceleration and is its longitudinal acceleration, is its lineal velocity andis its yaw velocity. The equation is valid during panic braking and also during acceleration. If the slip angle is small and if the car velocity is constant however, the equation can be reduced and integrated to result in the simple estimate:Together with the measured variables，and the estimated variable，their errors，and，respectively, are integrated also.Offset and other errors in the sensor signals may thus quickly lead to large errors in the estimate of the slipangle . Furthermore, during full braking the car deceleration and the pitch angle cannot be neglected and during heavy cornering, the car roll angle cannot be neglected. In order to obtain a more reliable estimate of the slip angle of the car an observer is used. Theobserver is based on a full four-wheel model of the car and uses two dynamic equations, one for the yaw velocity and the other for the lateral velocity of the car.The differential equation for the lateral motion is:The differential equation for the yaw motion is:In these equations the side forces,and the longitudinal forces,on the tires are unknown. The vehicle mass，the moment of inertia of the vehicleabout the vertical axis and the distances a,b,c are supposed to be approximately known.The longitudinal forceat any wheel can be estimated by the following generic equation:Heredenotes a known constant, denotes the brake fluid pressure in the brake wheel cylinder, Pwhl denotes the brake fluid pressure in the brake wheel cylinder, R denotes the known tire radius, MCaHalf denotes half of the engine torque at the axle, Jwhl denotes the knownmoment of inertia of the wheel and denotes the wheel speed which is the product of the wheel angular velocity and the tire radius. The engine torque value can be obtained from the engine management system, while the rotational wheel velocity is measured by the wheel velocity sensor. By modeling the hydraulic unit, measuring the brake master cylinder pressure and knowing the valve stimulation times of the hydraulic unit the wheel brake pressure can be estimated at each wheel using a hydraulic model. Thus the longitudinal forces can be estimated at any time for each wheel.The side forces are not readily available. Therefore a tire model is used. Specifically, the HSRI tire model as described in 8 is used which allows the computation of the side and longitudinal forces in a closed form.Using these equations, a simple relation between the lateral and the longitudinal force can be found:In these equations, andare the slip and cornering stiffness of the tire respectively, l and a are the tire slip and tire slip angle respectively, FN is the normal force on the tire and m is the maximum coefficient of friction between the tire and the road surface. The above relation between the lateral and longitudinal tire force is not only valid for the initial linear region of the m-slip curve, but also for the nonlinear region. Since the tire slip and cornering stiffness are mainly determined by the tire material, the ratio of the two is robust with respect to changes from summer to winter tires and changes due to tire wear. In the following, the tangent of the slip angle is approximated by the slip angle itself: tan a = aThe differential equations of the full car model can be rearranged and the solution discretized to be used as the model for a Kalman filter. It can be shown that rearranging the equations results in The discretization is approximated by an Euler integration:in which T is the sampling time and k is the time index. Since the yaw velocity is measured, it is possible to obtain the measurement equation for the lateral velocity of the car by linear extrapolation of the yaw velocity and substituting the result in the last equation:After substitution, the measurement equation for the lateral velocity is obtained:However, a prerequisite for using the observer is that the longitudinal tire slip is not too small. Otherwise the relation between the lateral and longitudinal force cannot be used. Experience has shown, that the slip angle estimation during full braking results in quite accurate slip angle estimates. However during the free rolling of the tires the observer cannot be used and slip angle estimates have to be derived from the lateral acceleration of the car as shown at the beginning of this chapter by integration of the slip angular velocity.Thus depending on the driving situation, the accuracy of the vehicle slip angle estimation is different. For this reason, the vehicle dynamics controller has as an inner loop a model following control of the yaw velocity of the car. Using the bicycle model of the car a first value for the nominal yaw velocityis obtained:The wheelbase I and the characteristic speed vch are parameters which depend on the car design. However the characteristic speed depends also on the tire characteristics like the lateral tire stiffness.Therefore, the nominal yaw velocity depends on the tire type, make and state (new or worn). Introducing the model following control thus introduces a complication in obtaining the nominal yaw velocity. To correctly function, ESP must therefore be checked with all released tires. The steering angle is not directly measured but is instead derived from the steering wheel angle. Usually the steering angle is obtained by division of the steering wheel angle by the steering gear ratio. However, in combination with the scrub radius longitudinal tire forces may corrupt this value so that a correction is required to account for this property. Furthermore, the steering column has two Hookes joints. If the ingoing and outgoing shafts are not parallel, then a superimposed error of sinusoidal shape is introduced. The vehicle forward velocity, is estimated by the slip controller.Since the lateral acceleration of the car cannot exceed the maximum coefficient of friction between the tire and the road m，the nominal yaw velocity must be limited to a second value. The steady state lateral acceleration of the car can be expressed as follows:in which Rt is the radius of the turn. It follows that the yaw rate must be limited by the following value:Sinceis unknown the measured lateral acceleration ay is taken instead. A first limit value for the slip angle of the car is derived as discussed using the b-method from the coefficient of friction between the tires and the road. This value is reduced depending on of the velocity of the car to a second valuebM, in order to increase the support of the driver in keeping his car stable at high speeds.If the state of the car described by its yaw velocityand its slip angle b differs from its nominal stateandrespectively, then the vehicle dynamics controller checks if this difference is within some tolerable dead zone. If not, a yaw moment has to be generated toreduce this difference to within this tolerable dead zone. Human behavior is included in the algorithm. As an example, on slippery roads the car reacts only slowly to steering angle changes. As a result the driver tends to steer too much and thus worsens the situation. In order to keep him from his natural but undesirable reaction, ESP reduces the response time of the yaw velocity for a short moment until the nominal slip angle of the car is reached. Test drivers also use this technique by steering too much for a short moment.As shown above each tire can contribute to a change in the yaw moment by changing its slip value. However, since the gains at the individual tires are different the slip changes at the individual tires can be chosen to minimize undesirable effects like deceleration of the car. Unfortunately as shown above, the gains cannot always be estimated with sufficient accuracy. Simulation studies with full vehicle models have been used in order to obtain design rules for the choice of the distribution of the slip among the individual tires. For instance, during full braking, (ABS) slip changes at the front wheel on the outside of the turn and at the rear wheel on the inside of the turn are used to generate the required yaw moment. The tire slips of the other two wheels are not modified.During driving on roads with a split-m coefficient of friction traction can be improved by active braking of the driven wheels on the low-m side. As a result, a yaw moment on the car is generated which is not desired by the driver and which pushes the car to the low-m side of the road. In order to prevent this, the driver has to countersteer. If the countersteering angle is too large or if the driver reacts too slow, then ESP reduces the yaw moment by reducing the brake pressure. But in order to prevent the low-m side wheel from spinning, the engine torque has to be reduced as well.The slip controller controls tire slip. During braking and also during traction control the slip is controlled by the brake slip controller except for the driven wheels where the traction slip controller controls the slip values. For the brake pressure modulation the magnetic valves of the hydraulic unit are stimulated while for the modulation of the drive torque the engine management system is used to realize the torque request from the traction slip controller. If an Electro Hydraulic Brake system (EHB) is available, then the nominal brake pressures can be requested directly.RESULTSFigure 4 shows the result of a lane change maneuver during full braking on ice and compares the results of production ABS and ESP. During full braking, sufficient information is available to use the observer for the estimation of the vehicle slip angle. A satisfactory control of the slip angle can therefore be expected. In Figure 4a the results of the maneuver with production ABS (i.e. without ESP) are shown. Shortly after the maneuver is initiated both the yaw velocity and the slip angle become so large that the driver has to heavily countersteer. As a result, the slip angle grows again rapidly in the other direction and the driver has to react fast by countersteering again. He is barely able to stabilize the car before it comes to a stop in the other lane. The ESP maneuver in Figure 4b also shows a stable vehicle trajectory. However the steering effort required to perform the stable lane change is much lower than with the production ABS maneuver. ESP helps to prevent the driver from steering too much. Both the yaw velocity and the slip angle remain small while the latter hardly exceeds the characteristic value of 2. This result shows that the precision with which the observer can estimate the slip angle at full braking is quite adequate. For the average driver this slip angle value fits to his daily experience where 2 is seldom exceeded. Even the stopping distance of the ESP maneuver is shorter than that of the production ABS maneuver. This can be explained because of the fact, that with the production ABS maneuver large slip angles occur which reduce the coefficients of friction between the tires and the road. Improvement of vehicle stability by using ESP does not necessarily increase the stopping distance as compared with production ABS control. On the contrary, stopping distances of ESP are in general shorter than those of production ABS.Figure4. Lane change at full braking with ABS (a) and with ESP (b) from an initial velocity of approx. 50 km/h on polished iceFigure 5 shows the simulation result of a steady state maneuver of a rear wheel driven car in which its speed is gradually increased while driving on a circular track of constant radius. In this maneuver, the observer cannot be used to estimate the slip angle of the car and ESP has to rely on the model following control. Comparison is made between a conventional vehicle without ESP (Fig. 5a) and the same vehicle with ESP (Fig. 5b). The track is homogeneous and the coefficient of friction is high (m = 1.0). This is a closed loop maneuver in which the driver has to keep the vehicle on the track. The diagrams show the required steering wheel angle, the resulting vehicle slip angle and the resulting lateral deviation from the track. The dashed curves in both graphs are the collections of stationary points which are iteratively computed for each vehicle speed by the simulation program through variations of the steering wheel angle and the engine output torque value. These dashed curves represent limit curves for the maneuver with the slowly increasing speed.Figure 5. Comparison of vehicle behavior without ESP (a) and with ESP (b) during slowly increasing speed along a homogeneous circular track Up to a lateral acceleration of approximately 7 m/s the behavior of the conventional vehicle and the ESP vehicle is identical and almost equal to the stationary behavior. Beyond this lateral acceleration value the behavior of the conventional vehicle becomes different from that of the ESP vehicle and from the stationary behavior. The vehicle slip angle and the steering angle increase rapidly and progressively. At the lateral acceleration of
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