CA7160后輪制動器設計【領從蹄式制動器制動蹄采用浮式支撐附裝有駐車制動機構】

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級06232指導教師張廣杰2010年6月15日概要在過去十年中，德國涉及交通事故的汽車在汽車總量的比例沒有明顯減少，但致命傷害的事故發(fā)生數(shù)量卻在持續(xù)的降低。大多數(shù)嚴重的事故是由于汽車失控導致的。駕駛員對汽車失去操縱穩(wěn)定性的是一個有待解決的問題。構建車輛動力學控制系統(tǒng)ESP（電子穩(wěn)定裝置，也稱為：VDC）的目的便是用來解決這一問題的。通過怎樣的方法來實現(xiàn)這一目的將在下文提及。下文將談到車輛的偏移角，這個在汽車操縱性能中至關重要的指標。由于完整的汽車狀態(tài)不容易獲得，估計運算法就為控制運算法的提供了足夠的信息補充。通過對偏移角的自動調(diào)節(jié)，各自輪胎的滑動控制就可以產(chǎn)生所需的瞬時偏移了。通過接下來的兩個例子可以看出，ESP可以通過自動控制發(fā)動機和制動器來顯著提高車輛在突然轉(zhuǎn)向下的操縱穩(wěn)定性?？刂评碚揈SP利用了防抱死系統(tǒng)ABS和牽引力控制系統(tǒng)ASR組件（圖1、圖2）。這些組件是：用來獲得汽車車輪的轉(zhuǎn)動速度的傳感器，改變車輪制動器壓力的液壓單元以及實行控制運算、處理傳感器信號、和控制液壓單元的電子單元。一個聯(lián)到發(fā)動機的管理控制器的接口也用來測量和改變發(fā)動機轉(zhuǎn)矩的輸出。為了獲得駕駛員所需的操縱性和實際汽車的操縱特性，還添加了四個ESP傳感器。這些傳感器是轉(zhuǎn)向角傳感器，側(cè)偏速度傳感器，側(cè)偏加速度傳感器和壓力傳感器（圖2）圖1：安裝在汽車上的ESP組件圖2：ESP組件此外，這個系統(tǒng)還需要TCS-OFF（牽引力控制系統(tǒng)）開關，來阻止在牽引力控制中驅(qū)動輪的制動器抱死控制；制動報警燈開關，手剎開關，制動器液力水平開關，診斷串行接口和連接數(shù)據(jù)總線（CAN）。如果用一個靈敏的調(diào)壓器實現(xiàn)輔助制動，那么需要附加的繼電器來防止制動指示燈在給ESP液壓單元加壓時點亮。ESP的車輛動力學控制部分由上至下分級控制。在底部輪胎的滑動受控制的。車輛動力學控制部分由都各處理單元組成，第一單元處理傳感器信號（如濾波器）。雖然觀察者是基于單一因素的，但是整個汽車模型習慣是用來用來評估汽車側(cè)偏角以及每個輪胎的側(cè)偏角也在下文提到。還要加上每個輪胎的縱向力與側(cè)向力作用?；瑒涌刂破鳛橛^測者提供所需的信息，如車輛的速度和加速度以及輪胎縱向力。圖3:ESP控制系統(tǒng)結(jié)構簡圖下面的微分方程可以初步估計汽車側(cè)偏角：僅當汽車的側(cè)傾角和滾動角為零時，該微分方程才是有效的。此外汽車在要在水平平面上，即該路面的縱向和橫向的坡度為零。這個等式中是側(cè)向加速度，是縱向加速度，是是前進速度，是側(cè)向速度。當緊急制動和加速時，等式是有效的。如果側(cè)偏角很小并且車速仍然恒定，等式可以化簡得到簡單的估計值加上測定變量，和估計變量，以及他們的誤差，和分別綜合起來。在傳感信號中的偏移量和其他誤差會很快導致側(cè)偏角的較大的估算誤差。而且完全制動時，汽車減速度和旋轉(zhuǎn)角不能忽略，當急轉(zhuǎn)向時汽車的偏轉(zhuǎn)角也不能忽略。為了獲得更加準確的汽車偏移角，就使用了觀測儀。觀測儀是基于汽車四輪簡化模型和兩個動力學等式，其中一個是計算汽車側(cè)偏速度，另一個是用來計算汽車橫向速度。橫向運動的微分方程是：側(cè)向運動的微分方程是：在這些等式中側(cè)向力,和縱向力,是未知的；車輛的質(zhì)量為，關于垂直軸的轉(zhuǎn)動慣量為和長度a,b,c假設已知。任意車輪上的縱向力可以通過以下的普通等式估算：這里的是已知恒量，表示制動器輪缸內(nèi)的液壓，表示發(fā)動機傳遞到在車軸上的扭矩的一半，表示車輪的轉(zhuǎn)動慣量，表示車輪的轉(zhuǎn)速，它是車輪角速度與輪胎半徑的乘積。發(fā)動機轉(zhuǎn)矩值可以通過發(fā)動機管理系統(tǒng)得到，而車輪旋轉(zhuǎn)速度可以由車輪速度傳感器測量到。通過液壓單元建模，可以計算出制動器主缸壓力以及知道液壓單元閥門開啟次數(shù)，用這個液壓模型可以估算每一個車輪上的制動器的壓力。因此任何時候作用在車輪上的縱向力可用這種方法估算出來。側(cè)向力的值不容易得到，因此就要運用車輪模型，8中描述的的輪胎模型HSRI就專門用來估算一些情況下的側(cè)向力和縱向力。運用這些等式可以得到側(cè)向力與縱向力之間的簡單關系：在這些等式中和分別是輪胎滑動和轉(zhuǎn)向時的剛度，l和a 分別表示輪胎側(cè)滑和其側(cè)偏角，時輪胎上的法向力，m是輪胎與路面最大摩擦系數(shù).以上的側(cè)向力與縱向力關系不僅適用于m-slip曲線開始的線性區(qū)域，也同樣適用于非線性區(qū)域。由于輪胎的滑動和轉(zhuǎn)向剛度主要取決與輪胎的材料，兩者的比值雖輪胎由夏季到冬季的變化，以及輪胎的磨損而變化。接下來要說的是，側(cè)偏角的正切值近似等于其本身：tan a = a整車模型的微分方程可以重新整理，并運用一個卡爾曼濾波模型的離散法解出。以下給出了重新整理后的等式結(jié)果離散化近似表示為歐拉公式：試中T是采樣時間，k是時間指標。由于側(cè)偏速度是已知的，汽車的橫向速度的計算公式就可以通過側(cè)偏速度的線性推斷法和取代最后一個等式結(jié)果而得到：代入后，得到橫向速度計算式：可是運用測量儀的先決條件是輪胎要有一定的縱向滑動，否則就不能運用側(cè)向力與縱向力之間的關系。根據(jù)經(jīng)驗，在完全制動時估算的側(cè)偏角可以非常精確?？墒窃谳喬プ杂蓾L動的時候測量儀無法運用，側(cè)偏角的估計值就不得不通過本章開始所說的汽車橫向加速度以及側(cè)偏角速度來得到了。因此依據(jù)駕駛條件不同，車輛的側(cè)偏角估計值的精確度是不同的。車輛動力學控制系統(tǒng)還有一個內(nèi)部循環(huán)系統(tǒng)，緊接著來控制汽車的側(cè)向速度。根據(jù)汽車二自由度模型，得到理論側(cè)偏速度：軸距l(xiāng)與特征車速是取決于汽車設計的參數(shù)?？墒翘卣鬈囁偻瑯右踩Q于輪胎的特性，如輪胎橫向剛度。因此理論側(cè)偏速度取決輪胎類型、制造、狀態(tài)（新舊）。引入以下的控制模型從而引入了一種得到理論側(cè)偏速度的方法。為了正確起效，ESP必須通過各種汽車輪胎的檢驗。轉(zhuǎn)向角不是直接測量得到的，而是通過車輪轉(zhuǎn)向角得到的。通常轉(zhuǎn)向角是根據(jù)車輪轉(zhuǎn)向角和轉(zhuǎn)向器傳動比算出?？墒?，作用在輪胎半徑上的縱向力會影響這個值，于是就需要一個修正系統(tǒng)來解決這個問題。此外轉(zhuǎn)向柱管有兩個虎克鉸型。如果其輸入輸出軸不平行，那么就會引入一個成正弦形狀變化的誤差。車輛前進速度是可以由滑動控制器測得。由于汽車橫向加速度不能夠超過輪胎與路面的最大摩擦系數(shù)，側(cè)偏角速度必須又有一個限定值。汽車穩(wěn)態(tài)角加速度由公式表示如下：其中是轉(zhuǎn)向半徑，它隨側(cè)偏頻率變化，側(cè)偏頻率被限制在一定范圍內(nèi)。已知的橫向加速度取代未知的。汽車側(cè)偏角的一個限制條件運用法討論，它來自輪胎與路面的附著系數(shù)。為了增加駕駛員保持其汽車在高速下的穩(wěn)定能力的支持，這個值的要減少到另一值，而這個過程取決于汽車的速度。如果通過汽車側(cè)偏速度和側(cè)向角描述的狀態(tài)與汽車的理論和不同，那么車輛動力學控制系統(tǒng)就會檢測這種差異是否在可允許范圍內(nèi)。這個系統(tǒng)同樣考慮到了人的行為。舉個例子，在濕滑路面上，汽車對轉(zhuǎn)向角變化的反應很小，結(jié)果駕駛員就會下意識的加大轉(zhuǎn)向，從而導致了更危險的情況。為了使駕駛員的做出正常的反應，ESP瞬時側(cè)偏速度的響應時間，直到汽車達到理論側(cè)偏角。試驗駕駛員同樣也運用這樣的瞬時過度轉(zhuǎn)向的技術來達到這一目的。如上所示在側(cè)偏運動中，各個輪胎可以通過改變它的側(cè)偏參數(shù)來發(fā)生改變?？墒怯捎诟鱾€輪胎上的增量不同，可以運用各輪胎上的偏移角變化來減小如汽車減速度之類的不良影響。如上所示，不幸的是，這種增量通常不能精確的測量到。為了獲得各自輪胎的滑動力分配選擇設計規(guī)則，運用了整車仿真模型。例如，在完全制動時，（ABS）外側(cè)轉(zhuǎn)向的前輪和內(nèi)側(cè)轉(zhuǎn)向的側(cè)偏改變都用來產(chǎn)生所需的側(cè)偏運動。另外兩輪的輪胎側(cè)偏不變化。在摩擦系數(shù)m路面上行駛時，牽引力會通過使驅(qū)動輪在低一側(cè)的制動器起作用來增加其大小。結(jié)果，汽車就產(chǎn)生駕駛員所不希望的側(cè)偏運動，而且使汽車向低一側(cè)偏駛。駕駛員為了阻止這一情況發(fā)生就不得不反打方向盤。如果反轉(zhuǎn)方向盤角度過大或是駕駛員反應過慢，ESP就會減少制動器壓力來減少側(cè)偏運動。但是為了阻止低一側(cè)車輪自轉(zhuǎn)，發(fā)動機的轉(zhuǎn)矩也應該減少?；瑒涌刂破骺刂戚喬サ膫?cè)滑。在制動和牽引力控制過程中，側(cè)滑通過除驅(qū)動輪以外的制動滑動控制器來控制，牽引力滑動控制器控制驅(qū)動輪的側(cè)滑值。當制動器壓力調(diào)節(jié)器作用時，液壓單元磁力閥受激打開，當發(fā)動機管理系統(tǒng)通過驅(qū)動力防滑系統(tǒng)調(diào)節(jié)轉(zhuǎn)矩需求來進行驅(qū)動力的調(diào)節(jié)。如果運用了電力液壓系統(tǒng)（EHB），可以直接得到額定制動液壓值。結(jié)論圖4冰面完全制動時，行駛方向改變的結(jié)果，而且比較了ESP和ABS的結(jié)果。在完全制動時，用測量儀可以獲得足夠的信息來估算車輛側(cè)偏角。因而可以得到滿意的側(cè)偏角。 圖4a是控制ABS（沒有ESP）工作得到的結(jié)果。開始操縱不久，側(cè)偏速度和側(cè)偏角就變得很大使得駕駛員反向轉(zhuǎn)向困難。結(jié)果側(cè)偏角在其他方向快速增長，駕駛員不得不又一次快速反應。他幾乎不能使汽車在一個方向穩(wěn)定行駛。圖4b所示的操縱ESP時車輛在其指定軌道內(nèi)穩(wěn)定行駛?？墒菓獙π旭偮肪€的改變所需的轉(zhuǎn)向操縱比ABS要簡便得多。ESP用來阻止駕駛員轉(zhuǎn)向過度。側(cè)偏速度和側(cè)偏角都很小，后者比特征值小2。結(jié)果展示了測量儀在完全制動時的側(cè)偏角已經(jīng)相當精確了。對于普通駕駛者側(cè)偏角和他日常很少低于2。使用ESP系統(tǒng)的制動距離比ABS制動距離少一些。原因是因為，采用ABS操縱會產(chǎn)生較大的側(cè)偏角，從而降低了輪胎與路面的摩擦系數(shù)。ESP相對于ABS對車輛的穩(wěn)定性能的提升是沒有必要增加制動距離的。相反ESP的制動距離總體上要比ABS短。圖4，在以相同的初速度50km/h行駛于冰面上（0.15），完全制動采用ABS(a)和ESP(b)時汽車軌跡的改變圖5是后輪驅(qū)動汽車穩(wěn)定行駛狀態(tài)的仿真分析結(jié)果，在固定半徑的圓形軌道內(nèi)其汽車速穩(wěn)定增加。在這種操縱環(huán)境下測試儀不能測量出汽車側(cè)偏角，ESP不得不依賴于下面的控制模型。普通車輛沒有安裝ESP（圖5a）和安裝了ESP（圖5b）的情況比較如下。它們的行駛軌跡是相同的，路面摩擦力系數(shù)也比較高。這是一個駕駛員必須保持汽車在一定軌道行駛的閉環(huán)控制系統(tǒng)，圖表給出了所需的車輪轉(zhuǎn)向角、車輛側(cè)偏角值以及在軌跡上行駛的左右偏差。在兩個圖表內(nèi)的曲線是從固定點采集的，在這些點上的計算是通過在各個車速下，變化轉(zhuǎn)向角和發(fā)動機輸出力矩仿真程序來完成的。圖中虛線表示緩慢增加車速時的極限曲線。圖5，安裝ESP和沒有安裝ESP時汽車沿相同軌跡緩慢加速時狀態(tài)的比較當汽車橫向加速度接近7m/s時，普通車輛和裝有ESP的車輛所表現(xiàn)出的行為相同，幾乎可以說是一種固定行為。超過該橫向加速度值時，兩者就變得不一樣了。車輛側(cè)偏角和轉(zhuǎn)向角快速增加。當橫向加速度達到7.5m/s時，普通車輛就處于不穩(wěn)定狀態(tài)。超過汽車橫向加速度接近7m/s，ESP系統(tǒng)對所需轉(zhuǎn)向角和側(cè)偏角的干擾就會減到很小。盡管駕駛員仍會逐漸的加大油門踏板力，但是在ESP的影響下發(fā)動機轉(zhuǎn)矩值會受到限制，并且由于達到車輛運動極限，車速也不會再增加了。通過駕駛員的轉(zhuǎn)向操縱，小的車輛偏駛會被減少。由結(jié)果可以看出，汽車橫向加速度為7.5m/s，駕駛員的動作不會導致車輛的不穩(wěn)定狀態(tài).車輛側(cè)偏角和偏駛都控制在較小范圍內(nèi)。盡管ESP將車輛側(cè)偏角控制在大約5左右而且低于最大穩(wěn)定值（大概8），但是平均橫向加速度值7.5m/s就幾乎達到其允許最大值7.75m/s。參考書目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