Bosch-ESP-2000

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SAE TECHNICAL PAPER SERIES 

2000-01-1633

Bosch ESP Systems: 5 Years of Experience A. T. van Zanten Robert Bosch Bo sch G.m.b.H.

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

SAE Automotive Dynamics & Stability Conference Troy, Michigan May 15-17, 2000 400 Commonweal Commonwealth th Drive, Drive, Warren Warrendale, dale, PA 15096-0001 15096-0001 U.S.A.

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2000-01-1633

Bosch ESP Systems: 5 Years of Experience A. T. van Zanten Robert Bosch G.m.b.H. Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

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

Although 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 goa l 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.

Förster ([5]) demands putting the average driver and the human behavior at the center of all considerations regarding the concept of vehicle handling. ESP, which influences handling at the physical limit is also designed to follow that principle. Since the average driver has no idea of the frictional stability margin between the tire and the road he may panic if the physical limit is reached and if the car starts to spin. He cannot be expected to react in a thoughtful manner. On the contrary, his reaction i s often wrong and he will usually steer too much. ESP must therefore also be designed from the point of view of preventing panic situations. Shibahata [6] has explained why the handling of cars at the physical limit is so difficult. He developed a simple method, the β-method (Fig. 1) with which this difficulty can easily be explained. If the steering wheel is turned, then a yaw moment on the car is generated by the lateral forces on the tires. The yaw moment leads to a change in the yaw velocity of the car. However, the yaw moment also depends on t he slip angle of the car. With increasing slip angles, the yaw moment gain decreases. At large slip angles the yaw moment can hardly be influenced by changing the steering angle. Typically, at the physical limit the steerability of the car is almost lost. On dry asphalt roads the physical limit is reached at a slip angle of approx. ±12°, while on ice this value is approx. ±2°. If the car slip angle nears this characteristic value control is virtually lost and the chances of the average driver in avoiding an accident are slim. Figure 1 shows the situation for dry asphalt. During normal driving average drivers will not exceed slip angles of ±2°. Beyond this value the driver has no experience.

INTRODUCTION Since 1991 the number of injuries or fatalities in car accidents in Germany has remained at an almost constant level between 300,000 and 350,000 [1]. The number of occupant fatalities as a result of an accident has steadily been reduced from 7,000 in 1991 to 4,700 in 1998. Based on a study of approx. 17,000 car accidents, Langwieder showed that 20% - 25% of all car accidents with injuries or fatalities were the result of spinning cars. In approximately 60% of the a ccidents with spinning cars only a single car was involved. While inexperienced drivers tend to correct the spinning motion with a single steering wheel correction, experienced drivers perform a sequence of corrections to g ain control of their car. Often the vehicle motion reaches the physical limit of adhesion between the tires and the road because of the panic reactions of the dr iver in dangerous traffic situations. It is rare for drivers with average driving experience to know when they are driving a car at the physical limit, i.e.

1

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the lateral force will be reduced to FS(λ0) where it is assumed, that neither the normal force FN nor the tire slip angle α0 are changed. As a result of the brake slip the brake force FB(λ0) is generated. FR(λ0) is the resultant force on the tire, which is the vectorial sum of FS(λ0) and FB(λ0). If the tire friction is saturated, i.e. at the limit of adhesion between the tire and the road, the magnitudes of FR(λ=0) and FR(λ0) are approximately equal. The influence of brake slip λ is now obvious: a change in the brake slip value results in a rotation of t he resultant force on the tire. As a result of the rotation the yaw moment on the car is changed. However, also the lateral force and the longitudinal force on the car are influenced. The control concept determines by what amount the slip at each tire shall be changed to generate the required change in the yaw moment. Boundary conditions like keeping the velocity or the acceleration of the car constant as well as the accuracy with which the operating point (α0,λ0) of the tire is known must be considered.

Figure 1.

(a-b) The β-method

Inagaki [7] uses the β  − β  phase plane method to show that if the steering angle is zero, the origin of the phase plane constitutes a stable convergence point. Within a certain area around the origin (the stability area) phase plane points converge to the origin. Outside the stability area phase plane points diverge from the origin and the vehicle behavior is unstable. During cornering, if the steering angle is not zero, the slip angle stability margin becomes asymmetric and reduced in the direction of steering. For the driver it becomes more difficult to keep his car under control. For large steering angles, the stability margin disappears, there is no stable combination of β  − β  and there is no stable solution of the vehicle motion. This situation then results in a spinning car. The main task of ESP is to limit the slip angle in order to prevent vehicle spin. Another task of ESP is to keep the slip angle below the characteristic value to preserve some yaw moment gain. If the slip angle reaches the characteristic value the gain will be low and the driver may notice that he starts to lose control of his vehicle and he may start to panic. Therefore ESP has to start control before this characteristic slip angle value is reached. T his starting time is not too late since, (at the characteristic slip angle value), ESP can also still generate large yaw moments by (active) control of brake and traction slip at selected wheels. This can be shown by the influence of some brake slip value λ0 at the left front tire of a free rolling car in a right turn (Fig. 2). FR(λ=0) is the lateral force on the free rolling tire. Because of the brake slip λ0

Figure 2.

2

Yaw moment change by slip control

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Unfortunately, no sensor is available to measure the slip angle of the car. Furthermore, no sensor is available to measure the limit of adhesion between the tire and the road. ESP uses estimation algorithms to generate such missing values. In particular it is not possible to always obtain a reliable value of the slip angle. For this reason a cascade control with a yaw velocity control, for which a sensor is available, at the inner loop is introduced. A precise inner loop yaw velocity control creates a good basis for the outer loop slip angle control. However, with the introduction of yaw velocity control new control problems like the determination of the nominal yaw velocity are introduced. ESP uses nominal yaw velocity values which are derived from measurements of the car handling. These measurements are plotted and approximated using the bicycle model of the car. The inner loop yaw velocity control is thus a model following control. During the lifetime of the car its characteristic handling behavior may change for example because of tire wear or even because of a change of tires. Then the fixed model does not exactly represent the real handling behavior of the car and these changes have to be carefully considered in the i nner loop yaw velocity control.

Figure 3.

ESP components mounted in the car

Figure 4.

ESP components

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 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 p rocess 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. 4).

Furthermore, 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. 5) constitutes the upper part of a hierarchical control. In the lower part the slips of the tires are controlled. The vehicle

3

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dynamics 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. Vw

δSAS

.

ψ  PMC MMOT

Vw

Driver Desire βM

δ

.

ψ M

the car velocity is constant however, the equation can be reduced and integrated to result in the simple estimate:

v  β(t ) = β 0 + ∫ βdt = β 0 + ∫  y − ψ  ψ dt v  0 0 v t

the estimated variable v v (t ) , their

. δSAS PMC MMOT ψ  ay

λ1 λ4

Vv

Vv

. . .

∆ψ  ψ (t )

and ∆v v (t ) , respectively, are integrated also. Offset and other errors in the sensor signals may thus quickly lead to large errors in the estimate of the slip

Observer

angle β(t ) . Furthermore, during full braking the car deceleration and the pitch angle cannot be neglected a nd 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. The observer 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.

ay

Limiter .

ψ M

.

ψ M

ay

.

+

Vv

ψ  -

βM +

βM

-

β

Vv .

∆ψ 

∆β .

∆ψ No

∆βNo

∆ψ .

∆β .

∆βNo

∆ψ No

The differential equation for the lateral motion is:

Car Motion Controller

mv ⋅ v y − v x ⋅ ψ  =

MYawNo

λ Noi αi

λ No1

MYawNoi

. . .

(FS1 + FS 2 )⋅ cos(δ w ) − (FB1 + FB 2 ) ⋅ sin(δ w ) + FS3 + FS 4

λNo4

Brake Slip Controller Traction Slip Controller PWhlNo1

. . .

The differential equation for the yaw motion is:

PWhlNo4

Hydraulic Model/  EHB-Pressure Controller tEV1, tAV1 . . IEV1,I AV1

. . .

⋅ ψ  ψ  = − [(FS1 + FS 2 )⋅ cos(δ w ) ⋅ a − (FS1 − FS 2 ) ⋅ sin(δ w ) ⋅ b ] + (FS3 + FS 4 ) ⋅ c + (FB1 + FB 2 ) ⋅ sin(δ w ) ⋅ a + (FB1 − FB 2 )⋅ cos(δ w ) ⋅ b + (FB3 − FB 4 ) ⋅ b Jv

tEV4, tAV4 . . IEV4,IAV4

Hydraulic Unit with Valve Stimulation

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:

β=

ψ  ψ (t ) and errors ∆v y ( t ) ,

Together with the measured variables v y (t ) ,

Car Motion δ

t

In these equations the side forces FS1 ,

FS 4 and the

longitudinal forces FB1 , FB 4 on the tires are unknown. The vehicle mass m v , the moment of inertia of the vehicle J v about the vertical axis and the distancesa,b,c (see Fig. 2) are supposed to be approximately known.

 vy  vx 2 ⋅ − − ⋅ − ⋅ ψ  β β ψ  ψ   ψ    vv 1+ β2  vv  1

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 in longitudinal and lateral direction is zero. In this equation v y is it’s lateral acceleration and v x is its longitudinal

The longitudinal force FB at any wheel can be estimated by the following generic equation:

FB

ψ  is its yaw acceleration, v v is its lineal velocity and ψ  velocity. The equation is valid during panic braking and also during acceleration. If the slip angle is small and if

= cp ⋅

p whl R

−

M CaHalf  R

+

J whl R2

⋅

d dt

v whl

Here cp denotes a known constant, 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 known

4

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moment of inertia of the wheel and v whl 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 discretization integration:

v y ,k +1

 λ  1  C  C H =  ⋅ λ  + ⋅ α ⋅ tan α  1 − λ µ ⋅ FN  1 − λ µ ⋅ FN 

ψ  ψ k +1 = 2 ⋅ ψ  ψ k − ψ  ψ k −1 After substitution, the measurement equation for the lateral velocity is obtained:

=

C α ⋅ tan α Cλ

⋅λ

1

2  

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 velocity ψ  ψ No is obtained:

⋅ FB

In these equations, C λ and C α are the slip and cornering stiffness of the tire respectively, λ and α are the tire slip and tire slip angle respectively, FN is the normal force on the tire and µ is the maximum coefficient of friction between the tire and the road surface.

ψ  ψ No =

The above relation between the lateral and longitudinal tire force is not only valid for the initial linear region of the µ-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 α = α .

v v ⋅ tan δ w

   v v  2    l ⋅ 1 +   v    ch     

The wheelbase l 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 C α . 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 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

vy

= ψ  ψ k ⋅ (1 − A 22 ⋅ T ) − ψ  ψ k −1 − T ⋅ u 2,k

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.

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

FS

Euler

= (A 11 ⋅ T + 1) ⋅ v y ,k + A 12 ⋅ T ⋅ ψ  ψ k + u 1,k ⋅ T

A 21 ⋅ T ⋅ v y ,k

2

an

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:

1

2

by

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

1 1   ⋅ Cα ⋅    − 2  ⋅ tan α 1− λ  H 4H   λ 1 1   ⋅ C λ ⋅   FB =  − 2   1− λ  H 4H  

=

approximated

ψ  ψ k +1 = A 21 ⋅ T ⋅ v y ,k + (A 22 ⋅ T + 1)⋅ ψ  ψ k + u 2,k ⋅ T

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.

FS

is

The steering angle δ w is not directly measured but is instead derived from the steering wheel angle δ . 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

= A11 ⋅ v y + A12 ⋅ ψ  ψ + u1

ψ  ψ  = A 21 ⋅ v y + A 22 ⋅ ψ  ψ + u 2

5

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During driving on roads with a split-µ coefficient of friction traction can be improved by active braking of the driven wheels on the low-µ 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-µ 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-µ side wheel from spinning, the engine torque has to be reduced as well.

may corrupt this value so that a correction is required to account for this property. Furthermore, the steering column has two Hooke’s joints. If the ingoing and outgoing shafts are not parallel, then a superimposed error of sinusoidal shape is introduced. The vehicle forward velocity, v x 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 µ , the nominal yaw velocity must be limited to a second value. The steady state lateral acceleration of the car can be expressed as follows:

vy

≈v

2

v

Rt

=

vv Rt

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.

⋅ v v = ψ  ψ ⋅ v v

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

ψ  ψ No ≤ µ ⋅ g

vv

(1)

Since µ is 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 β-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 value β M , in order to increase the support of the driver in keeping his car stable at high speeds.

PERFORMANCE REQUIREMENTS Performance requirements relate primarily to the suppor t which the average driver can observe. The driver must feel secure in the directional control of his car in all driving situations like panic braking combined with panic steering or panic acceleration combined with panic steering etc. In order to achieve this security a precise yaw moment must be quickly generated during panic braking as well as during panic acceleration etc. Furthermore the yaw velocity must immediately respond to the steering input of the driver (see above). Usually, full control performance is required in the ambient temperature range of –20°C to 120°C and in the ambient pressure range above 0.75 bar which corresponds to an altitude of approx. 2500 m above sea level.

If the state of the car described by its yaw velocity ψ  ψ  and its slip angle β differs from its nominal state ψ  ψ M and β M respectively, then the vehicle dynamics controller checks if this difference is within some tolerable dead zone. If not, a yaw moment has to be generated to reduce 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 i s reached. Test drivers also use this technique by steering too much for a short moment.

ESP must support the driver in all situations, during braking and coasting, on all road surfaces, on split µ surfaces and on surfaces with jumps in the coefficient of friction. The support must be such, that the steering effort required from the driver is substantially reduced. However the driver must not have the impression that he is slower with ESP during sporty driving on handling courses than without the system. The system must be tolerant of environmental changes like rough roads, de ep or wet snow, hydroplaning, gravel etc. and must not intervene if the physical limit is not reached.

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.

While it is possible to estimate the slip angle of the car and of the tires during full braking as shown above there are driving situations where the slip angles cannot be estimated with sufficient accuracy. In those cases the absolute value of the slip angular velocity is often required to remain smaller than a prescribed value. Or alternatively, the absolute value of the slip angle is required to remain smaller than some maximum value 6

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during the first couple of seconds after the incipient instability is detected. These values are further reduced depending on the car speed, lateral acceleration, steering wheel angle, steering wheel angular velocity etc. Particularly on very slippery roads (µ