Evolution of Electronic Control Systems for

Improving the Vehicle Dynamic Behavior

Anton T. van ZantenRobert Bosch GmbH

CS-AS/ESFP.O. Box 30 02 40

70442 StuttgartGERMANY

Phone: (+49) 711 811 1860Fax: (+49) 711 811 1862

E-mail: antonvan.zanten@de.bosch.com

Starting with ABS (Antilock Brake System) the steps towards integrated active safetysystems dealing with vehicle dynamics is shown. While ABS and TCS were initially de-signed as open loop controllers for the lateral vehicle motion a first approach towardsclosed loop control of the lateral vehicle motion for active safety systems was realized byESP (Electronic Stability Program. Estimation algorithms and model following control areused with ESP to compensate for the lack of sensors. Since 2001 ESP is available forcars with an electro hydraulic brake system. The extension of ESP in combination withactive front steering is expected to enter the market in 2003.

Keywords: Safety, Handling, Observers, Yaw moment, Brakes, Steering, Suspension

1. INTRODUCTION

The loss of yaw response of the vehicle tosteering inputs during full braking while the wheelsare locked has lead to very early investigations (inthe beginning of the 20th century) to prevent wheellock. ABS, which can prevent this can preserve ahigh level of handling performance during fullbraking [1]. Similarly, if the driven wheels spin dueto excess engine torque handling becomes difficult,particularly if the driven and steered wheels areidentical. This has lead then to the introduction oftraction control systems which preserve also a highlevel of handling performance during driving withexcess engine torque. Since neither the steeringangle nor the yaw moment on the car were avail-able, even a feed forward handling control by con-trol of the brake and engine was not possible. Withthe introduction of ESP these important quantitiesbecame available. Together with the measurementof the yaw velocity, a feed back control of the vehi-cle handling could be introduced [2], [3], [4].

The difficulty of handling of a car at the physicallimit can be explained by the research contributionof Shibahata [5]. In this paper the β-method wasdeveloped to analyze the influence of the slip angleof the vehicle on its maneuverability. One importantresult is, that the sensitivity of the yaw moment onthe vehicle w.r.t. changes in the steering angledecreases rapidly as the slip angle of the vehicleincreases (Fig. 1). Large slip angles mean herevalues at which the µ-slip angle curve of the tirehas its maximum. Therefore, on dry surfaces vehi-cle maneuverability is lost at vehicle slip angle val-ues larger than approximately 15°, whereas onpacked snow this value is approximately 4°. Ina-gaki [6] has shown the inherent instability of thevehicle motion for certain combinations of the slipangle and its velocity (Fig. 2, dark areas). For othercombinations, the slip angle velocity will return tozero and lead to a stable value of the slip angle(white area). However, for increasing steering an-gles the stability area shrinks to become eventuallyzero: the vehicle motion is unstable for all combi-nations of slip angle and slip angle velocity.

Another reason for the problems normal drivershave in these situations is, that their driving experi-ence is limited largely to driving well within thephysical limit of adhesion. Förster [7] has analyzedthis situation and set up some important rules.First, the driver can never recognize the coefficientof friction between the tires and the road and hehas no idea of the vehicle's lateral stability margin.Second, if the limit of adhesion is reached thedriver is caught by surprise and very often reacts ina wrong way and usually steers too much. This, henotes, is the real weak point in the system vehicle-driver-environment. Third, in traffic situations theneed for the driver to act thoughtfully has to beminimized. Förster therefore comes to the conclu-sion that the concept of the vehicle including thetires and the suspension should very strongly ac-count for the normal human behavior. Deviationsfrom normal vehicle behavior that are inherent tothe vehicle design must be controlled and reducedto negligible differences. Unexpected vehicle mo-tions may lead to panic reactions of normal drivers.

The design of vehicles should therefore centeraround the normal driver. Professional testers, testengineers and endurance testers are not at alltypical for the real population of normal drivers, andtherefore it is not unrealistic that they judge vehiclebehavior according to criteria that are not relevantto the large number of average drivers.

Accidents are often said to be in 90% of allcases the result of driver errors. Käppler [8] how-ever, notes that these statements must be takenvery carefully since they originate from the policejargon. According to Brown [9] drivers are only in19% of all cases responsible for the accidents.Vehicles are in 31% and the environment in 50% ofall cases responsible for the accidents. Rompe etal [10] investigated the activities of drivers in criticaldriving situations just before the accidents hap-pened. He found that steering was most often(50%) involved. Similarly Edwards et al [11] foundthat evasive maneuvers took place just ahead of48% of all accidents, 50% just ahead of all colli-sions and 64% just ahead of all accidents in whichthe vehicle left the road.

Statistics from the German Association of In-surance Companies (GdV) [12] show that severeaccidents typically involve spinning cars (Fig. 3).Furthermore, while the number of people killeddecreases continuously, the total number of peopleinjured and killed remained approximately constantduring an 8-year period (Fig. 4).

Contrary to the common belief that spinning ofcars mainly occurs on slippery roads and at highspeeds the statistics show, that by far most severeaccidents occur on dry roads and at speeds be-tween 60 km/h and 100 km/h.

A first approach to solve the problem of han-dling at the physical limit is given by van Zanten in[13]. Here the brake slip distribution is investigatedduring full braking while cornering which results ina reduced deviation of the vehicle motion from adesired nominal motion and simultaneously in aminimum stopping distance. Optimal control theorywas used to get an idea of the best tuning of the

Fig. 1: Yaw moment in dependence of the slip angle fordifferent steering angles (source: [5])

Fig. 2: Phase plane of the vehicle slip angle and itsangular velocity at zero steering angle (source: [6])

Fig. 3: Typical severe accident resulting from car spin(source: [12])

Fig. 6: ABS control concept

brake control. It is shown, that given the momen-tary slip angle of a tire the brake slip of that tiremust not necessarily be optimized to get the largestpossible brake force.

An industrial approach is given by Heess [14].He describes ways in which available control sys-tems like Antilock Brake Systems (ABS) and trac-tion control systems (ASR), suspension controlsystems and steering control systems can be usedas subsystems for a superimposed vehicle dy-namics control system. His suggestion applied to afull four wheel ABS/ASR led to the development ofthe Vehicle Dynamics Control system ESP ofBosch which controls the motion of the vehicle notonly during full braking but in all situations like par-tial braking, coasting, acceleration and engine dragon the driven wheels. Its area of operation istherefore extended well beyond that of ABS (fullbraking control) and TCS (traction control).

2. ANTILOCK BRAKE SYSTEM

Locked wheels generate forces on the car whichare in a direction opposite to the lineal wheel mo-tion. Changing the steering angle has virtually noeffect on the force vectors on the wheels. If thebrake pressure induced by the driver is such thatthe wheels lock, then the brake pressure must bereduced to regain steerability.

For this task ABS uses a hydraulic unit whichhas electromagnetic valves to keep the pressure inthe wheel brakes below the level induced by thedriver

The main task of the control algorithm is to keepa high level of braking force while at the same timekeeping a sufficient level of lateral force generationby steering to preserve a high level of handlingperformance. This information is not readily avail-able and thus ABS relies on assumptions about theshape of the µ-slip curve and the wheel behaviorduring braking and cornering (Fig. 5).

The question how much the wheel brake pres-sures should be reduced is solved by the controlalgorithm which monitors the wheel speeds but notthe brake pressures (Fig. 6). If a wheel deceleratestoo fast (Phase 2), then its brake pressure is re-duced and if because of the pressure reduction thewheel accelerates again then the pressure is in-creased again. The increase will be done in astepwise manner in order to reduce the influence ofthe transients in the wheel behavior (phase 7) andthe pressure may be reduced immediately if thedeceleration becomes large (phase 8). Thus theaverage slip value is kept close to kλλλλ (Fig 5).

Fig. 4: Number of people injured and killed in Ger-many (source: [12])

Fig. 5: Typical µ-slip curve

3. TRACTION CONTROL SYSTEM

As a first approach to control the driving forceson the driven wheels one may try to control the tireslip to the value kλλλλ of the µ-slip curve (Fig. 5) bythe same concept chosen for ABS. This howeverfails, since not only the rotating inertia of the drivenwheels is too large for a significant change in thewheel acceleration (because of the engaged en-gine and transmission) but also the engine torqueis nonlinearly dependent on the engine speed, andthus also on the wheel speed. Therefore duringtraction control it is not possible to clearly differen-tiate between the stable and the unstable region ofthe µ-slip curve.

Fortunately, for single axle driven cars, thespeeds of the non driven wheels may be used tocompute the free rolling speed of the drivenwheels. Therefore slip control of the driven wheelsbecomes now possible. The only unknown variablethen is the value of kλλλλ which may vary with theroad surface and the tire type and state. Tractioncontrol uses a mean value of kλλλλ and increases itfor low car speeds. For four wheel driven cars, thedetermination of the free rolling speed is not easilypossible and only estimates can be made whichdepend on the distribution of the engine torquebetween the front and the rear axle.

Drive slip can be reduced by reducing the enginetorque or additionally by applying the brakes at thedriven wheels (Fig. 7). By closing the throttle valve,reducing the spark advance or inhibiting fuel injec-tion the engine torque may be reduced. Because ofengine and exhaust emission regulations, all threeinterventions are not always and at the same timeavailable. Furthermore, the time constants of thesethree different interventions are mutually differentand vary with the state of the engine (cold start, lowambient temperature, state of the catalyst etc.).Similarly the time constant of the brake pressurevaries, in particular with the temperature of thehydraulic unit.

4. ELECTRONIC STABILITY PROGRAM

Feedback control of the vehicle motion is possi-ble by extending the traction control system withfour additional sensors: steering wheel angle,brake pressure, yaw rate and lateral acceleration.

Since the nominal trajectory desired by the driveris unknown, the driver's inputs are taken to obtainnominal state variables that describe the intendedvehicle motion instead. These inputs are thesteering wheel angle, the engine drive torque asderived from the accelerator pedal position and thebrake pressure.

The handling performance of the car can be im-proved if in dependence of the steering wheel an-gle the yaw moment on the car can be controlled.The main task of ESP as an active safety systemis, however, to limit the slip angle of the vehicle ββββin order to prevent vehicle spin.

ESP can control the yaw moment on the car bycontrolling the value of the slip at each wheel. Thiscan be shown by the influence of some brake slipvalue λλλλ0 at the left front tire of a free rolling car in aright turn (Fig. 8). FR(λλλλ=0) is the lateral force on thefree rolling tire. Because of the brake slip λλλλ0 thelateral force will be reduced to FS(λλλλ0) where it isassumed, that neither the normal force FN nor thetire slip angle αααα0 are changed. As a result of thebrake slip the brake force FB(λλλλ0) is generated.FR(λλλλ0) is the resultant force on the tire, which is thevectorial sum of FS(λλλλ0) and FB(λλλλ0). If the tire frictionlimit is reached, the magnitudes of FR(λλλλ=0) andFR(λλλλ0) are approximately equal.

The influence of brake slip λλλλ is now obvious: achange in the brake slip value results in a rotationof the resultant force on the tire. As a result of therotation the yaw moment on the car is changed.However, simultaneously the lateral force and thelongitudinal force on the car are influenced. The

Fig. 8: Yaw moment change by slip control

Fig. 7: Fundamental blocks of the traction control sys-tem. 1: Wheel Speed Sensor, 2: Hydraulic Unit,3: TCS-ECU, 4: Throttle-ECU, 5 Engine-ECU

control concept determines by what amount the slipat each tire shall be changed to generate the re-quired change in the yaw moment. Usually it isrequired that the driver must not have the impres-sion that with ESP the car is slower than withoutESP.

The vehicle dynamics controller part of ESP(Fig. 9) constitutes the upper part of a hierarchicalcontrol. Output are the nominal tire slips Noiλλλλ . Inthe lower part the slip values of the tires are con-trolled. The vehicle dynamics controller part con-sists of several processing blocks. On the top leftthe motion desired by the driver is derived from hisinputs by a linear bicycle model (which uses a lin-ear relationship between the slip angle and thelateral force of the tire). On the top right the motionof the car is measured and missing state variablesare estimated.

As a first approach to estimate the slip angle ofthe car the derivative of the slip angle is used:

( )ββββββββψψψψββββ sincos1 ⋅−⋅+−= xyv

aav

&&

This estimate is valid if the pitch and roll anglesof the car are neglected and furthermore, if the carmoves on a horizontal plane. In this equation ya is

the lateral acceleration of the car and xa is its

longitudinal acceleration, vv is its velocity and ψψψψ&is its yaw velocity. If the car velocity is constant and

its slip angle is small then the estimate can bereadily obtained by a simple time integration

∫∫

−+=+=t

v

yt

dtva

dtt0

00

0)( ψψψψββββββββββββββββ &&

Offset and other errors in the sensor and esti-mated signals may quickly lead to large errors inthe estimate. Furthermore, during full braking thecar deceleration can not be neglected. Therefore,during full braking an alternative estimate of the slipangle based on an observer is used.

The observer is based on a full four wheel modelof the car and uses two dynamic equations, one forthe yaw velocity and the other for the lateral veloc-ity of the car ([15]). These equations are rear-ranged and discretized to be used as the model fora Kalman filter. Since the yaw velocity is meas-ured, the solution of the differential equation of theyaw velocity is used to derive the measurementequation.

For these equations the longitudinal force BF atany wheel is required and can be estimated by thefollowing generic equation

whlwhlCaHalfwhl

pB vdtd

RJ

RM

Rp

cF ⋅+−⋅= 2

Here pc denotes a known brake constant, whlpdenotes the brake fluid pressure in the brake wheelcylinder, R denotes the known tire radius,

CaHalfM denotes half of the engine torque at the

axle, whlJ denotes the known moment of inertia ofthe wheel about its axis of rotation and

whlv denotes the wheel speed which is the productof the wheel angular velocity and the tire radius.The engine torque value can be obtained from theengine management system, while the rotationalwheel velocity is measured by the wheel speedsensor. Finally by modeling the hydraulic unit thewheel brake pressure is estimated at each wheel.

The side forces are not readily available.Therefore a tire model is used. Specifically, theHSRI tire model as described in [15] is used whichallows for a simple relation between the lateral andthe longitudinal force.

BS FC

CF ⋅

⋅⋅

=λλλλ

αααα

λλλλ

αααα tan

In these equations, λλλλC and ααααC are the slip andcornering stiffness of the tire and λλλλ and αααα are thetire slip and slip angle respectively.

The estimate of the lateral velocity by the Kal-man filter is robust to tire changes as only the ratioof the lateral and longitudinal tire stiffness is used.For winter tires the ratio is nearly the same as forsummer tires. The same is true for new and worntires, conventional and wide tires etc. Thus bothevaluations of the slip angle are more or less in-sensitive to changes in the tire properties.

Fig. 9: Simplified block diagram of the ESP control

Unfortunately the vehicle slip angle estimation isnot always sufficiently accurate and the confidencelevel of its value is sometimes low. Therefore, thevehicle dynamics controller uses additionally amodel following control for the yaw velocity of thecar, for which the already mentioned linear bicyclemodel is taken. Output of the linear bicycle modelis the nominal value of the yaw rate Noψψψψ& . Thus a

first value for the nominal yaw velocity Noψψψψ& is ob-tained (Fig. 10).

+⋅

⋅=

2

1ch

x

wxNo

vv

l

v δδδδψψψψ&

The wheel base l is a simple geometric pa-rameter while the vehicle forward velocity xv isestimated by the brake slip controller.

The characteristic speed chv depends mainly

on the lateral tire stiffness ααααC of the tires. There-fore, the nominal yaw velocity changes with the tiretype, make and state (new or worn). This changemay occur suddenly if new tires are mounted. Themodel following control is thus sensitive to changesin the tire stiffness and ESP may suddenly changeits behavior. This will be shown below. ESP musttherefore be checked to correctly perform with allreleased tires.

Since the lateral acceleration of the car can notexceed the maximum coefficient of friction betweenthe tire and the road µµµµ , the nominal yaw velocitymust be limited to a second value by the followingrelation (see the hyperbola in Fig. 10)

vNo vg⋅≤ µµµµψψψψ&For summer tires the nominal yaw velocity is

different from that of winter tires (Fig. 11). Similarly,for worn tires the yaw velocity is different from thatof new tires. The vehicle becomes oversteer if on

the front axle worn and on the rear axle new tiresare mounted (Fig. 12). In such cases the vehicle

behavior deviates significantly from the behavior ofthe linear bicycle model (Fig. 10) and ESP inter-ventions can be expected for vehicle maneuverswhich are well within the physical limit.

A first nominal limit value for the slip angle of thecar (Fig. 9) is chosen as discussed using the Betamethod in dependence of the coefficient of frictionbetween the tires and the road. This value is re-duced in dependence of the velocity of the car to asecond value Noββββ , in order to improve the supportfor the driver at higher speeds.

If the state of the car as described by its yawvelocity and its slip angle differs from its nominalstate, then the vehicle dynamics controller checksif this difference is within some tolerable deadzone. If not, a yaw moment is generated to reducethis difference to within this tolerable dead zone.Slip is controlled by the brake slip and traction slipcontrollers as described in [15].

Fig. 10: Nominal yaw velocity from the linear bicyclemodel

Fig. 11: Nominal yaw velocity from the full four wheelmodel with nonlinear new and worn summer and wintertires (steering wheel angle 60°)

Fig. 12: Nominal yaw velocity from the full four wheelmodel with nonlinear summer and winter tires, withworn tires at the front axle and new tires at the rear axle(steering wheel angle 60°)

5. ELECTROHYDRAULIC BRAKE SYSTEM

The Electro Hydraulic Brake System (EHB, alsocalled SBC: Sensotronic Brake Control) is a brakeby wire system, where the brake pressure in thewheel brakes are controlled in accordance with thebrake master cylinder pressure using proportionalvalves.

Fig. 13 shows the concept of EHB. ESP (herecalled VDC) is housed in the block named �Brakefunctions�. Essential for the control of the vehicledynamics is, that the wheel brake cylinder pres-sures are measured. Furthermore, pressure can bevery rapidly increased resulting in very fast activebrake slip interventions.

Since the estimation of the brake pressure at thewheels is no longer required, the confidence levelof the brake force estimation is higher than before.This improves the estimation and control of thevehicle slip angle as can be seen from the resultsof a double lane change maneuver (Fig. 14). Earlyinterventions are possible so that they are lessvicious and more comfortable.

Not only during maneuvers at the physical limit,but also during all brake maneuvers EHB improvesthe handling performance of the car. EHB allowsfor complete flexibility in choosing the brake forcedistribution in any situation, so that the brake forcedistribution can be chosen in dependence of thebraking situation as a feed forward control. Thusalmost neutral handling performance can be ob-tained during any combined braking and steeringmaneuver. Thus ESP is extended to control thevehicle handling well within the physical limit (Fig.15).

Although the ESP control performance is im-proved, limits on the improvement are set by thesafety concept. It is not possible to immediatelyreact on rapid changes in the sensor signals sincethe possibility of signal failures can not be disre-garded. Internal tests like that of the yaw rate sen-sor triggered by the ECU introduce delays in thesignal analysis like the estimation of its time de-rivative (Fig. 16). Thus the limits in the reliability ofthe signals limit the performance of the EHB.

To partially compensate this drawback a newconcept �suspicion of failure� was introduced. Onlyif a signal is suspicious of a possible failure theintervention of EHB is delayed by increasing thedead zone in the yaw rate (Fig. 9) and by reducing

Fig. 14: Improvement of slip angle control of ESPduring a double lane change maneuver by SBC(Source: [16])

Fig. 15: Improvement of cornering stability by im-proved brake force distribution (Source: [16])

Fig. 13: Block diagram of the Electro HydraulicBrake System

Fig. 16: Yaw rate signal with superimposed testsignal

the pressure gradient. The general rule for thesafety concept is to better not intervene where itwould be beneficial for the driver then to surprisehim with an intervention resulting from a corruptedsensor signal.

6. FUTURE SYSTEMS

If an active steering system is available, ESPcan also use this system to control the handlingbehavior of the car, not only in limit situations butalso during normal driving. Fig. 17 shows the con-cept of a first realization of such a system withwhich ESP can modify the steering angle [17]. An-other system is shown in Fig. 18, in which ESP canmodify the normal force distribution on the tires bycontrol of special anti roll bars [17].

Each of these systems can influence the yawmoment on the car. The question is now, how toimplement the total yaw rate control. Early propos-als were based on the observation of the differentintervention bandwidths of the brake, engine, activesteering and active suspension actuators. Eachactuator had its own yaw rate controller (Fig. 19).The controller gains had to be tuned such that theinterference between the interventions did not leadto undesirable or even unstable vehicle behavior.The charm of this approach is, that to some extendthe development of the controllers can be doneindependent of each other. Obviously, if the con-troller gains must be drastically reduced to guar-antee the peaceful coexistence of the controllers,

important performance potential is lost. Identifica-tion, adaptation and learning control is not feasible.

Later proposals use a central yaw rate controllerwhich takes the different properties of the actuatorsin consideration (Fig. 20). This is particularly im-portant if the brake actuation is no more muchslower than the steering actuation as is the casewith EHB. The superimposed central yaw rate con-trol uses then the subsystems as intelligent actua-tors.

EHB and the future systems can influence thehandling behavior of the car also in situationswhere the physical limit is not reached. If the pas-sive car handling changes, e.g. because ofchanges in the tire properties, than these systemscan restore normal vehicle behavior by interven-tions which are not noticed by the driver. Thesesystems therefore have the potential of makinghandling robust against parameter changes. How-ever, in order to fully exploit the high speed of theinterventions, the test cycle of the yaw rate signal(Fig. 16) must be avoided which results in the re-quirement for redundant yaw rate signals.

Fig. 17: Active steering system with incrementalsteering angle

Fig. 19: Coexistence approach using the brakes,active steering and active suspension to controlvehicle handling

Fig. 20: Integration approach using the brakes activesteering and active suspension to control vehiclehandling

Fig. 18: Active suspension with split anti roll bar

7. CONCLUSION

ESP has extended active safety systems from awheel behavior control (ABS, TCS) to a vehiclebehavior control resulting in an increased activesafety of the car. A practical system solution re-quires a model following yaw rate control whichintroduces robustness problems with changingvehicle parameters like the tire properties. Futuresystems may compensate these changes to a ro-bust vehicle behavior but the safety concept mustbe changed to fully exploit the fast actuator inter-ventions.

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