bosch-esp-2000

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SAE TECHNICALPAPER SERIES 2000-01-1633

Bosch ESP Systems: 5 Years of Experience

A. T. van ZantenRobert Bosch G.m.b.H.

Reprinted From: Proceedings of the Automotive Dynamics & Stability Conference(P-354)

SAE Automotive Dynamics &Stability Conference

Troy, MichiganMay 15-17, 2000

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1

2000-01-1633

Bosch ESP Systems: 5 Years of Experience

A. T. van ZantenRobert Bosch G.m.b.H.

Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

Although the total number of car occupants involved inaccidents in Germany has not significantly reducedduring the past 10 years, the number of fatalities hassteadily decreased. Most of the severe accidents resultfrom a loss of control of the car. The problem of the driverlosing control of his car will be explained. This problem isthen used to formulate the goal for the vehicle dynamicscontrol system ESP (Electronic Stability Program, alsoknown as VDC). The approach chosen to reach this goalwill then be shown. It will be shown that the vehicle slipangle is a crucial indicator for the maneuverability of theautomobile. Since the complete vehicle state is notreadily available, estimation algorithms are used tosupply the control algorithms with sufficient information.With the automatic control of the slip angle the requiredyaw moment can be generated by individual wheel slipcontrol. By using two examples it will be shown, that ESPcan significantly improve vehicle handling in extrememaneuvers by automatically controlling the brakes andthe engine.

INTRODUCTION

Since 1991 the number of injuries or fatalities in caraccidents in Germany has remained at an almostconstant level between 300,000 and 350,000 [1]. Thenumber of occupant fatalities as a result of an accidenthas steadily been reduced from 7,000 in 1991 to 4,700 in1998. Based on a study of approx. 17,000 car accidents,Langwieder showed that 20% - 25% of all car accidentswith injuries or fatalities were the result of spinning cars.In approximately 60% of the accidents with spinning carsonly a single car was involved. While inexperienceddrivers tend to correct the spinning motion with a singlesteering wheel correction, experienced drivers perform asequence of corrections to gain control of their car. Oftenthe vehicle motion reaches the physical limit of adhesionbetween the tires and the road because of the panicreactions of the driver in dangerous traffic situations.

It is rare for drivers with average driving experience toknow when they are driving a car at the physical limit, i.e.

at the limit of adhesion between the tires and the road.At this limit the tire behavior is extremely nonlinear andthe linearized tire-wheel-brake system is unstable. As aresult, the vehicle may suddenly spin and the driver iscaught by surprise. Usually in these situations the drivertends to automatically steer too much and thus worsenthe situation. In both cases the vehicle dynamics controlsystem ESP helps the driver keep his car under control([2], [3], [4]).

Förster ([5]) demands putting the average driver and thehuman behavior at the center of all considerationsregarding the concept of vehicle handling. ESP, whichinfluences handling at the physical limit is also designedto follow that principle. Since the average driver has noidea of the frictional stability margin between the tire andthe road he may panic if the physical limit is reached andif the car starts to spin. He cannot be expected to react ina thoughtful manner. On the contrary, his reaction is oftenwrong and he will usually steer too much. ESP musttherefore also be designed from the point of view ofpreventing panic situations.

Shibahata [6] has explained why the handling of cars atthe physical limit is so difficult. He developed a simplemethod, the β-method (Fig. 1) with which this difficultycan easily be explained. If the steering wheel is turned,then a yaw moment on the car is generated by the lateralforces on the tires. The yaw moment leads to a change inthe yaw velocity of the car. However, the yaw momentalso depends on the slip angle of the car. With increasingslip angles, the yaw moment gain decreases. At large slipangles the yaw moment can hardly be influenced bychanging the steering angle. Typically, at the physicallimit the steerability of the car is almost lost. On dryasphalt roads the physical limit is reached at a slip angleof approx. ±12°, while on ice this value is approx. ±2°. Ifthe car slip angle nears this characteristic value control isvirtually lost and the chances of the average driver inavoiding an accident are slim. Figure 1 shows thesituation for dry asphalt. During normal driving averagedrivers will not exceed slip angles of ±2°. Beyond thisvalue the driver has no experience.



2

Figure 1. (a-b) The β-method

Inagaki [7] uses the phase plane method to showthat if the steering angle is zero, the origin of the phaseplane constitutes a stable convergence point. Within acertain area around the origin (the stability area) phaseplane points converge to the origin. Outside the stabilityarea phase plane points diverge from the origin and thevehicle behavior is unstable. During cornering, if thesteering angle is not zero, the slip angle stability marginbecomes asymmetric and reduced in the direction ofsteering. For the driver it becomes more difficult to keephis car under control. For large steering angles, thestability margin disappears, there is no stablecombination of and there is no stable solution ofthe vehicle motion. This situation then results in aspinning car.

The main task of ESP is to limit the slip angle in order toprevent vehicle spin. Another task of ESP is to keep theslip angle below the characteristic value to preservesome yaw moment gain. If the slip angle reaches thecharacteristic value the gain will be low and the drivermay notice that he starts to lose control of his vehicle andhe may start to panic. Therefore ESP has to start controlbefore this characteristic slip angle value is reached. Thisstarting time is not too late since, (at the characteristicslip angle value), ESP can also still generate large yawmoments by (active) control of brake and traction slip atselected wheels. This can be shown by the influence ofsome brake slip value λ0 at the left front tire of a freerolling car in a right turn (Fig. 2). FR(λ=0) is the lateralforce on the free rolling tire. Because of the brake slip λ0

the lateral force will be reduced to FS(λ0) where it isassumed, that neither the normal force FN nor the tire slipangle α0 are changed. As a result of the brake slip thebrake force FB(λ0) is generated. FR(λ0) is the resultantforce on the tire, which is the vectorial sum of FS(λ0) andFB(λ0). If the tire friction is saturated, i.e. at the limit ofadhesion between the tire and the road, the magnitudesof FR(λ=0) and FR(λ0) are approximately equal. Theinfluence of brake slip λ is now obvious: a change in thebrake slip value results in a rotation of the resultant forceon the tire. As a result of the rotation the yaw moment onthe car is changed. However, also the lateral force andthe longitudinal force on the car are influenced. Thecontrol concept determines by what amount the slip ateach tire shall be changed to generate the requiredchange in the yaw moment. Boundary conditions likekeeping the velocity or the acceleration of the carconstant as well as the accuracy with which the operatingpoint (α0,λ0) of the tire is known must be considered.

Figure 2. Yaw moment change by slip control

ββ �−

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3

Unfortunately, no sensor is available to measure the slipangle of the car. Furthermore, no sensor is available tomeasure the limit of adhesion between the tire and theroad. ESP uses estimation algorithms to generate suchmissing values. In particular it is not possible to alwaysobtain a reliable value of the slip angle. For this reason acascade control with a yaw velocity control, for which asensor is available, at the inner loop is introduced. Aprecise inner loop yaw velocity control creates a goodbasis for the outer loop slip angle control. However, withthe introduction of yaw velocity control new controlproblems like the determination of the nominal yawvelocity are introduced. ESP uses nominal yaw velocityvalues which are derived from measurements of the carhandling. These measurements are plotted andapproximated using the bicycle model of the car. Theinner loop yaw velocity control is thus a model followingcontrol. During the lifetime of the car its characteristichandling behavior may change for example because oftire wear or even because of a change of tires. Then thefixed model does not exactly represent the real handlingbehavior of the car and these changes have to becarefully considered in the inner loop yaw velocity control.

CONTROL CONCEPT

ESP uses the components of the antilock brake system(ABS) and of the traction control system (ASR), Fig. 3,Fig. 4. These components are: sensors to derive therotational velocity of the wheels, a hydraulic unit to modifythe pressure in the wheel brakes and an electroniccontrol unit to realize the control algorithm, to process thesensor signals and stimulate the hydraulic unit. Aninterface to the engine management controller is alsoused to measure and modify the engine torque output.Additionally four ESP sensors are required to derive thehandling desire of the driver and to derive the actualhandling behavior of the car. These sensors are asteering wheel angle sensor, a yaw velocity sensor, alateral acceleration sensor and a pressure sensor (Fig.4).

Figure 3. ESP components mounted in the car

Figure 4. ESP components

Furthermore, the system entails a TCS-OFF (TractionControl System) switch, to prohibit brake slip control ofthe driven wheels during traction control, a (redundant)brake light switch, a hand brake switch, a brake fluid levelswitch, a serial interface for diagnosis and a data busconnection (CAN). If a smart booster is used to realize abrake assistant, then an additional relay is required toprevent the brake lights from being lit during theprecharging of the ESP hydraulic unit.

The vehicle dynamics controller part of ESP (Fig. 5)constitutes the upper part of a hierarchical control. In thelower part the slips of the tires are controlled. The vehicle



4

dynamics controller part consists of several processingblocks. In the first block the sensor signals are processed(e.g. filtered). An observer based on a simple but full carmodel is used to estimate the slip angle of the car and ofeach tire as will be shown below. Also the normal andlateral forces on each tire are estimated. The slipcontroller supplies the required information for theobserver like the vehicle velocity and acceleration, andthe longitudinal tire forces.

Figure 5. Simplified block diagram of the ESP control

As 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 rollangles of the car are zero and furthermore, if the carmoves on a horizontal plane, i.e. the slope of the road inlongitudinal and lateral direction is zero. In this equation

is it’s lateral acceleration and is its longitudinal

acceleration, is its lineal velocity and is its yawvelocity. The equation is valid during panic braking andalso during acceleration. If the slip angle is small and if

the car velocity is constant however, the equation can bereduced 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 thusquickly lead to large errors in the estimate of the slip

angle . Furthermore, during full braking the cardeceleration and the pitch angle cannot be neglected andduring heavy cornering, the car roll angle cannot beneglected. In order to obtain a more reliable estimate ofthe slip angle of the car an observer is used. Theobserver is based on a full four-wheel model of the carand uses two dynamic equations, one for the yaw velocityand 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

vehicle about the vertical axis and the distances a,b,c(see Fig. 2) are supposed to be approximately known.

The longitudinal force at any wheel can be estimatedby the following generic equation:

Here cp denotes a known constant, Pwhl denotes thebrake fluid pressure in the brake wheel cylinder, Rdenotes the known tire radius, MCaHalf denotes half of theengine torque at the axle, Jwhl denotes the known

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moment of inertia of the wheel and denotes thewheel speed which is the product of the wheel angularvelocity and the tire radius. The engine torque value canbe obtained from the engine management system, whilethe rotational wheel velocity is measured by the wheelvelocity sensor. By modeling the hydraulic unit,measuring the brake master cylinder pressure andknowing the valve stimulation times of the hydraulic unitthe wheel brake pressure can be estimated at eachwheel using a hydraulic model. Thus the longitudinalforces can be estimated at any time for each wheel.

The side forces are not readily available. Therefore a tiremodel is used. Specifically, the HSRI tire model asdescribed in [8] is used which allows the computation ofthe side and longitudinal forces in a closed form.

Using these equations, a simple relation between thelateral and the longitudinal force can be found:

In these equations, and are the slip andcornering stiffness of the tire respectively, and arethe tire slip and tire slip angle respectively, FN is thenormal force on the tire and is the maximumcoefficient of friction between the tire and the roadsurface.

The above relation between the lateral and longitudinaltire force is not only valid for the initial linear region of theµ-slip curve, but also for the nonlinear region. Since thetire slip and cornering stiffness are mainly determined bythe tire material, the ratio of the two is robust with respectto changes from summer to winter tires and changes dueto tire wear. In the following, the tangent of the slip angleis approximated by the slip angle itself: .

The differential equations of the full car model can berearranged and the solution discretized to be used as themodel for a Kalman filter. It can be shown thatrearranging the equations results in

The discretization is approximated by an Eulerintegration:

in which T is the sampling time and k is the time index.

Since the yaw velocity is measured, it is possible toobtain the measurement equation for the lateral velocityof the car by linear extrapolation of the yaw velocity andsubstituting the result in the last equation:

After substitution, the measurement equation for thelateral velocity is obtained:

However, a prerequisite for using the observer is that thelongitudinal tire slip is not too small. Otherwise therelation between the lateral and longitudinal force cannotbe used. Experience has shown, that the slip angleestimation during full braking results in quite accurate slipangle estimates. However during the free rolling of thetires the observer cannot be used and slip angleestimates have to be derived from the lateral accelerationof the car as shown at the beginning of this chapter byintegration of the slip angular velocity.

Thus depending on the driving situation, the accuracy ofthe vehicle slip angle estimation is different. For thisreason, the vehicle dynamics controller has as an innerloop a model following control of the yaw velocity of thecar. Using the bicycle model of the car a first value for thenominal yaw velocity is obtained:

The wheelbase and the characteristic speed vch areparameters which depend on the car design. Howeverthe characteristic speed depends also on the tirecharacteristics like the lateral tire stiffness .Therefore, the nominal yaw velocity depends on the tiretype, make and state (new or worn). Introducing themodel following control thus introduces a complication inobtaining the nominal yaw velocity. To correctly function,ESP must therefore be checked with all released tires.

The steering angle is not directly measured but isinstead derived from the steering wheel angle . Usuallythe steering angle is obtained by division of the steeringwheel angle by the steering gear ratio. However, incombination with the scrub radius longitudinal tire forces

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may corrupt this value so that a correction is required toaccount for this property. Furthermore, the steeringcolumn has two Hooke’s joints. If the ingoing andoutgoing shafts are not parallel, then a superimposederror of sinusoidal shape is introduced. The vehicleforward velocity, is estimated by the slip controller.

Since the lateral acceleration of the car cannot exceedthe maximum coefficient of friction between the tire andthe road , the nominal yaw velocity must be limited to asecond value. The steady state lateral acceleration of thecar can be expressed as follows:

in which Rt is the radius of the turn. It follows that the yawrate must be limited by the following value:

(1)

Since is unknown the measured lateral acceleration ayis taken instead. A first limit value for the slip angle of thecar is derived as discussed using the β-method from thecoefficient of friction between the tires and the road. Thisvalue is reduced depending on of the velocity of the car toa second value , in order to increase the support ofthe driver in keeping his car stable at high speeds.

If the state of the car described by its yaw velocity andits slip angle differs from its nominal state and

respectively, then the vehicle dynamics controllerchecks if this difference is within some tolerable deadzone. 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 anexample, on slippery roads the car reacts only slowly tosteering angle changes. As a result the driver tends tosteer too much and thus worsens the situation. In order tokeep him from his natural but undesirable reaction, ESPreduces the response time of the yaw velocity for a shortmoment until the nominal slip angle of the car is reached.Test drivers also use this technique by steering too muchfor a short moment.

As shown above each tire can contribute to a change inthe yaw moment by changing its slip value. However,since the gains at the individual tires are different the slipchanges at the individual tires can be chosen to minimizeundesirable effects like deceleration of the car.Unfortunately as shown above, the gains cannot alwaysbe estimated with sufficient accuracy. Simulation studieswith full vehicle models have been used in order to obtaindesign rules for the choice of the distribution of the slipamong the individual tires. For instance, during fullbraking, (ABS) slip changes at the front wheel on theoutside of the turn and at the rear wheel on the inside ofthe 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-µ coefficient of frictiontraction can be improved by active braking of the drivenwheels on the low-µ side. As a result, a yaw moment onthe car is generated which is not desired by the driverand which pushes the car to the low-µ side of the road. Inorder to prevent this, the driver has to countersteer. If thecountersteering angle is too large or if the driver reactstoo slow, then ESP reduces the yaw moment by reducingthe brake pressure. But in order to prevent the low-µ sidewheel from spinning, the engine torque has to bereduced as well.

The slip controller controls tire slip. During braking andalso during traction control the slip is controlled by thebrake slip controller except for the driven wheels wherethe traction slip controller controls the slip values. For thebrake pressure modulation the magnetic valves of thehydraulic unit are stimulated while for the modulation ofthe drive torque the engine management system is usedto realize the torque request from the traction slipcontroller. If an Electro Hydraulic Brake system (EHB) isavailable, then the nominal brake pressures can berequested directly.

PERFORMANCE REQUIREMENTS

Performance requirements relate primarily to the supportwhich the average driver can observe. The driver mustfeel secure in the directional control of his car in alldriving situations like panic braking combined with panicsteering or panic acceleration combined with panicsteering etc. In order to achieve this security a preciseyaw moment must be quickly generated during panicbraking as well as during panic acceleration etc.Furthermore the yaw velocity must immediately respondto the steering input of the driver (see above). Usually, fullcontrol performance is required in the ambienttemperature range of –20°C to 120°C and in the ambientpressure range above 0.75 bar which corresponds to analtitude of approx. 2500 m above sea level.

ESP must support the driver in all situations, duringbraking and coasting, on all road surfaces, on split µsurfaces and on surfaces with jumps in the coefficient offriction. The support must be such, that the steering effortrequired from the driver is substantially reduced.However the driver must not have the impression that heis slower with ESP during sporty driving on handlingcourses than without the system. The system must betolerant of environmental changes like rough roads, deepor wet snow, hydroplaning, gravel etc. and must notintervene if the physical limit is not reached.

While it is possible to estimate the slip angle of the carand of the tires during full braking as shown above thereare driving situations where the slip angles cannot beestimated with sufficient accuracy. In those cases theabsolute value of the slip angular velocity is oftenrequired to remain smaller than a prescribed value. Oralternatively, the absolute value of the slip angle isrequired to remain smaller than some maximum value

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7

during the first couple of seconds after the incipientinstability is detected. These values are further reduceddepending on the car speed, lateral acceleration,steering wheel angle, steering wheel angular velocity etc.Particularly on very slippery roads (µ<0.25) it is difficult todifferentiate unstable car behavior using the bicyclemodel for the nominal yaw velocity from driving through abanked turn. Therefore, in general, on very slipperyroads the sensitivity of the control is reduced in order notto have unnecessary interventions during banked turndriving. In order to limit the reduction in the ESPsensitivity, the ESP is tuned so as not to intervene onpublic roads. On special roads like racing tracks, thelarger lateral slope of the road is recognized by ESP andthe system is shut off. However, during full braking wherethe slip angle can be determined using the observerwithout the use of the lateral acceleration signal thisreduction is not required. Thus also on very slipperyroads during panic braking, the full performance of ESPis available. During driving in reverse gear the sign of theyaw velocity is opposite to that in forward gear. Thissituation is detected by ESP and interventions areprohibited.

If the absolute values of the slip angles at the tires arelarger than those at the maximum of the µ-slip anglecurves, then the radius of the turn is not minimal. In panicsituations drivers usually steer too much. Therefore ESPgives the driver immediate response of to his steeringmaneuver in order to reduce his tendency to steer toomuch. Corresponding to the smaller steering angles therequirement to reduce the steering angle drastically if theroad friction suddenly turns from low to high is thenreduced as well. It turned out that this concept is notsufficient for all driving situations, in particular for J-turnsin which the turning radius is continuously reduced alongthe trajectory (this is typical for exits from the highway). Inthose cases the requirement of the ESP- intervention tohave a minimal influence on the car speed is reduced inits priority. And by reducing the speed of the car, theradius of the turn may be reduced correspondingly.

Since in principle ESP cannot increase the magnitude ofthe tire forces if the physical limit is reached only the yawmoment on the car may be controlled. If the slip isreduced then the absolute value of the lateral force onthe tire and on the car is increased and the radius of theturn may be reduced. Conversely, if the tire slip isincreased the lateral force on the tire and on the car isreduced. In general this will increase the radius of theturn. In case of brake slip, the car will slow down and thishas a compensating effect. During the transient however,the radius will be increased. This increase must be keptsmall for the car not to leave the nominal track by morethan say 0.5 m.

ESP interventions disturb smooth driving particularlyduring cruising and accelerating since the brake forceson the tires may rock the car. The advantage ordisadvantage of the rocking behavior can be seen fromthe safety or the comfort point of view. Often the drivers

cannot relate the unusual motion of the car to the drivingsafety. Therefore, car manufacturers require differentESP performance at different driving situations. Duringbraking at high speeds, the deceleration is of utmostimportance on straight line braking and stability is ofutmost importance during handling. In both casescomfort has the least importance. The driver must not getthe impression, that because of the steering maneuverthe car deceleration is reduced. It has been shownhowever, that also during braking while handling, thestopping distance can also be reduced as compared toproduction ABS (e.g. by more than 15% during brakingwhile cornering). During partial braking in combinationwith ESP interventions the car deceleration must relate tothe increase or decrease of the brake pedal force.Comfort can in some way be improved by handlingdependent brake force distribution to increase the lateralstability margin of the car. ESP interventions can thus bereduced in their frequency of occurrence during sportydriving.

Split-µ braking presents a special situation for ESP sincethe steering angle cannot be interpreted as a corneringdesire. Production ABS uses open loop control of theasymmetric brake force gradient on the front tires andselect low control on the rear tires to keep the car undercontrol with good deceleration performance. ESP has aclosed loop control of the asymmetric brake forces on thefront and the rear axle. This control depends on thedriver’s countersteering input by which the yaw momentfrom the asymmetry of the brake forces is balanced bythe yaw moment from the lateral forces on the tires. If thedriver reacts slowly, then the yaw moment from theasymmetric brake forces must not be increased fast andconversely, if the driver reacts fast the brake forceasymmetry may be increased fast. By this closed loopcontrol the braking distance can be reduced ascompared to production ABS by more than 15% atcomparable steering effort.

During driving while handling and at high speeds stabilityof the car is of prime importance. Control must be suchthat the magnitude of the slip angle of the car does notexceed 6°. At high speeds traction is the least importantwhile at low speeds and during handling comfort is of thelowest importance. Only at low speed straight line drivingtraction is of the highest importance. Traction on split-µroads is improved by braking the wheel on the low-µ sideof the driven axle. The resulting asymmetric longitudinalforces exert an involuntary yaw moment on the car whichmust be compensated by countersteering. Similarly asduring split-µ braking, the yaw moment must not increasetoo fast in order to allow the driver sufficient time toperform this task. This is in conflict with driving off on asteep road with split-µ since it is also not allowed to havethe car roll back too much.

The model following control using the bicycle model tocompute the nominal yaw velocity is sensitive to changesin the tire characteristics. If winter tires are used, thenominal yaw velocity is different from that if summer tires

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8

are used. If the tires on the front axle are different fromthe tires on the rear axle, i.e. because of different wear atthe axles, then the yaw velocity is also different from thatif equal tires are used on both axles. Since the changesin tires cannot be identified by the control program, thecontrol sensitivity must be reduced. This is realized byintroducing a dead zone for the nominal yaw velocity.Since the dead zone also reduces the performance ofESP, the type and make of the tires which can bereleased for the car must be carefully checked. A highlevel of performance of ESP in cases where the slipangle cannot be adequately estimated, such as duringcruising, can be maintained. Fortunately the observeruses the ratio between the lateral and longitudinal tirestiffness only. Therefore, the estimation of the slip angleis much less sensitive to changes in the tires than thenominal yaw velocity. This means that ESP control forexample during panic braking is robust with respect to tirechanges. ESP also maintains excellent performanceduring panic braking for different tires. A further difficultyis the determination of the stopping conditions of thecontrol during acceleration. Often the control continues tokeep the engine torque at a low value after a stabilizingESP intervention even if the driver steers again straightahead. Careful tuning of the control is required to haveESP quickly recognize that the car motion is stable againand that the engine torque can be quickly increasedagain to its desired value.

Changes in the tire and car data such as resulting fromusual wear and tear or even from small accidents mustnot reduce the ESP performance or at least must notresult in adverse behavior. Before the system is released,a catalog of special test maneuvers must be checked.Flat tires and trailers should be included in the catalog.Also the “Moose Test” has become a part of the catalog.Particularly at low ambient temperatures where fastactive braking is hampered by the increasing viscosity ofthe brake fluid the interventions must be checked to befast enough to achieve the required yaw moment on thecar in time.

Since ESP must function for both manual and automatictransmissions the gear ratio is always estimated, thusresulting in a backup solution for automatic transmissionif the communication between the two systems fails. Theestimation routine works so well that it can also be usedfor CVT (Continuously Variable Transmission) and forsemi automatic transmissions.

RESULTS

Figure 6 shows the result of a lane change maneuverduring full braking on ice and compares the results ofproduction ABS and ESP. During full braking, sufficientinformation is available to use the observer for theestimation of the vehicle slip angle. A satisfactory controlof the slip angle can therefore be expected. In Figure 6athe 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 becomeso large that the driver has to heavily countersteer. As aresult, the slip angle grows again rapidly in the otherdirection and the driver has to react fast bycountersteering again. He is barely able to stabilize thecar before it comes to a stop in the other lane. The ESPmaneuver in Figure 6b also shows a stable vehicletrajectory. However the steering effort required to performthe stable lane change is much lower than with theproduction ABS maneuver. ESP helps to prevent thedriver from steering too much. Both the yaw velocity andthe slip angle remain small while the latter hardlyexceeds the characteristic value of 2°. This result showsthat the precision with which the observer can estimatethe slip angle at full braking is quite adequate. For theaverage driver this slip angle value fits to his dailyexperience where 2° is seldom exceeded. Even thestopping distance of the ESP maneuver is shorter thanthat of the production ABS maneuver. This can beexplained because of the fact, that with the productionABS maneuver large slip angles occur which reduce thecoefficients of friction between the tires and the road.Improvement of vehicle stability by using ESP does notnecessarily increase the stopping distance as comparedwith production ABS control. On the contrary, stoppingdistances of ESP are in general shorter than those ofproduction ABS.

Figure 6. Lane change at full braking with ABS (a) and with ESP (b) from an initial velocity of approx. 50 km/h on polished ice (µ ≈ 0,15)

Figure 7 shows the simulation result of a steady statemaneuver of a rear wheel driven car in which its speed isgradually increased while driving on a circular track ofconstant radius. In this maneuver, the observer cannot beused to estimate the slip angle of the car and ESP has torely on the model following control. Comparison is madebetween a conventional vehicle without ESP (Fig. 7a)and the same vehicle with ESP (Fig. 7b). The track ishomogeneous and the coefficient of friction is high (µ =1.0). This is a closed loop maneuver in which the driverhas to keep the vehicle on the track. The diagrams showthe required steering wheel angle, the resulting vehicleslip angle and the resulting lateral deviation from thetrack. The dashed curves in both graphs are thecollections of stationary points which are iteratively



9

computed for each vehicle speed by the simulationprogram through variations of the steering wheel angleand the engine output torque value. These dashedcurves represent limit curves for the maneuver with theslowly increasing speed.

Figure 7. Comparison of vehicle behavior without ESP (a) and with ESP (b) during slowly increasing speed along a homogeneous circular track (µ = 1.0)

Up to a lateral acceleration of approximately 7 m/s² thebehavior of the conventional vehicle and the ESP vehicleis identical and almost equal to the stationary behavior.Beyond this lateral acceleration value the behavior of theconventional vehicle becomes different from that of theESP vehicle and from the stationary behavior. Thevehicle slip angle and the steering angle increase rapidlyand progressively. At the lateral acceleration of 7.5 m/s²the conventional vehicle becomes unstable. Beyond thelateral acceleration value of 7 m/s² the ESP systemintervenes such that the required steering angle valuesare reduced and such that the vehicle slip angle value islimited. Although the driver still gradually increases theaccelerator pedal stroke the value of the engine outputtorque is kept limited under the influence of ESP and thevehicle speed is no longer increased since the physicallimit of the vehicle motion is reached. The small lateral

deviations of the vehicle from the track are reduced bythe steering actions of the driver. As can be seen fromthe results, the driver’s actions at the lateral accelerationvalue of 7.5 m/s² do not result in an unstable vehiclebehavior. The resulting changes in the vehicle slip angleand the lateral deviations of the vehicle from the trackstay both within a small range. Although ESP keeps thevehicle slip angle at approx. 5° and well below itsmaximum stationary value (approximately 8°), themaximum average lateral acceleration of 7.5 m/s² almostreaches its maximum value of 7.75 m/s².

ACKNOWLEDGMENTS

The author would like to express his deep gratitude toJosef Mack, SAE organizer, for his in depth review of thepaper and for his great help to put the paper from theinitial rough draft into its final form.

REFERENCES

1. Langwieder, K.: Mit ESP schwere Unfälle vermeidenoder mildern. ESP-Workshop, November 10, 1999,Boxberg, Germany.

2. Müller, 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, TheVehicle Dynamics Control System of Bosch,SAE95,Nr. 950759

4. Fennel, H.; Gutwein, R.; Kohl, A.; Latarnik, M.; Roll,G.:Das modulare Regler- und Regelkonzept beimESP von ITT Automotive,7. Aachener KolloquiumFahrzeug- und Motortechnik, 5. - 7. Oktober, 1998,Aachen, S. 409 – 431

5. Förster, H. -J.:Der Fahrzeugführer als Bindegliedzwischen Reifen, Fahrwerk und Fahrbahn,VDIBerichte, Nr. 916, 1991

6. Shibahata, Y.; Shimada, K.; Tomari, T.:Improvementof Vehicle Maneuverability by Direct Yaw MomentControl,In: Vehicle Systems Dynamics, 22 (1993),pp. 465 - 481

7. Inagaki, S.; Kshiro, I.; Yamamoto, M.:Analysis onVehicle Stability in Critical Cornering Using Phase-Plane Method,AVEC’94, International Symposium onAdvanced Vehicle Control, Tsukuba ResearchCenter,October 24 – 28, 1994, pp. 287 - 292

8. van Zanten, A.T.; Erhardt, R.; Pfaff, G.; Kost, F.;Hartmann, U.; Ehret, T.:Control Aspects of theBosch-VDC,AVEC’96, International Symposium onAdvanced Vehicle Control, Aachen, June 24 - 28,1996, pp. 576 - 607



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