Design of an Electronic Stability Program for vehicle simulation software

B.J.S. van Putten

DCT 2008.138 Master Traineeship Supervisors Dipl. Ing. M. Baderschneider, TESIS DYNAware GmbH Dipl. Ing. Dipl. Phys. A. Pinnel, TESIS DYNAware GmbH Dr. Ir. I.J.M. Besselink, Technische Universiteit Eindhoven

Eindhoven University of Technology Department of mechanical engineering

Automotive Engineering Science

Eindhoven, November 2008

1

Abstract Whereas these days in most vehicles an Electronic Stability Program (ESP) is standard or available as an option, in highly realistic vehicle simulators and vehicle simulation packages ESP is not always included as such. The investigation is aimed at obtaining an efficient and effective ESP for this application, which is then built in a Matlab/Simulink environment to suit veDYNA vehicle simulation software. An analytical analysis, supported by experimental results, shows the abilities of an ESP, using sensitivities to determine at which wheel an intervention takes place and a combination of the direct influence of braking as well as its secondary effect, to control vehicle behavior under critical circumstances.

2

Table of Contents 1. Introduction .......................................................................................................................... 3 2. ESP General and Starting Point ........................................................................................... 4 

2.1 Critical behavior .......................................................................................................... 4 2.2 ESP Controller Essen Duisburg .................................................................................. 5 2.3 Desired values ............................................................................................................ 5 2.4 Controller .................................................................................................................... 6 2.5 Operation Algorithm .................................................................................................... 7

3. Design of the Electronic Stability Program ........................................................................... 8

3.1 Controller .................................................................................................................... 8 3.2 Desired values ............................................................................................................ 8 3.3 Brake Pressure Allocation ........................................................................................... 9

4. Experiments ....................................................................................................................... 14 

4.1 Test cases ................................................................................................................ 14 4.2 Test maneuver .......................................................................................................... 15 4.3 Test 1: Vehicle without ESP ...................................................................................... 15 4.4 Test 2: Vehicle with ESP control torque .................................................................... 17 4.5 Test 3: Vehicle with improved ESP algorithm vs. ESP Duisburg ............................... 18 4.6 Test 4: Redesigned ESP vs. ESP Duisburg .............................................................. 21

5. Conclusion and Recommendations .................................................................................... 23 

5.1 Conclusion ................................................................................................................ 23 5.2 Recommendations .................................................................................................... 23

List of Symbols ....................................................................................................................... 24 

3

1. Introduction Weather conditions as well as critical situations on the road can cause a driver to be unable to control behavior of his or her vehicle. In this case, the Electronic Stability Program (ESP) helps to stabilize vehicle movement. Driver assistance systems like ESP which improve a car’s active safety are on the market for about two decades and have almost become standard equipment. Thorough testing and development have made these systems into lifesavers that can assist the driver in most hazardous situations. Contrary to the actual car, in the digital testing and simulation environment, ESP is not always included as such. However, because ESP has become a very important and well recognized safety system, it is useful to include this system as a parameterizable stand-alone unit in vehicle simulation software. This feature improves opportunities to simulate the entire vehicle behavior in the development and testing phase. In this phase it is not possible to implement the actual ESP, because its algorithm is not freely available. The investigation presented in this report is aimed at obtaining a stand-alone ESP for the virtual-realistic car simulator Ftronik. This car simulator runs on veDYNA vehicle simulation software and a highly realistic BMW 5-series dataset. The goal for the investigation is formulated as follows. Design, build and test an effective and efficient Electronic Stability Program for the veDYNA vehicle simulation package veDYNA veDYNA vehicle simulation software is widely used in industry and is respected for its precision and the fact that it can be implemented with ease in Hardware-in-the-Loop (HiL) and Software-in-the-Loop (SiL) test benches. In contrast to other software, the veDYNA package is built in a Matlab/Simulink environment. The successor of veDYNA3 is DYNA4. This simulation framework covers the entire range of vehicle simulation. In addition to the vehicle dynamics simulation package, the framework includes engine and drive train simulation as well as a traffic simulator. The simulation results are shown in both a graphical animation and detailed figures that show plots of variables which are free to choose.

During the traineeship the scope of the investigation has changed from application just for the Ftronik car simulator to general application as an add-on in veDYNA software. Contact information TESIS DYNAware GmbH TESIS DYNAware GmbH Baierbrunnerstraße 15 81379 München, Germany

2. E The Esupplname

2.1 CCriticaand e UnderWhensteeri OversWhendecre

Not oconditaccelestableits frorear asituat

Figure This cvelociestimaveDY

ESP GenElectronic Stier Bosch and

e implies, is to

Critical beal dynamical

excessive ove

rsteer n, to maintainng wheel ang

steer n, to maintaineased, the veh

only this bastions. In ceeration or dee situation whont tyres. On taxle is lower aions are show

2.1 Excessive un

controller usuity. In a real ated. In this NA vehicle m

neral andtability Prograd car manufa

o increase veh

ehavior vehicle beha

ersteer. Under

n a certain cgle has to be

a constant rahicle is called

sic chassis lartain cases, celeration in

here grip on ththe contrary, and the car tuwn in figure 2.

ndersteer

ually controlsvehicle espestudy, vehic

model.

d Startinam (ESP) isacturer Mercehicle stability

avior can be rsteer and ov

curvature witincreased, th

adius at incre oversteered.

ayout of the vehicle beh

a corner or lhe front axle excessive ov

urns curve inw.1 and figure

2 motion vaecially the fircle side slip

ng Points originally dedes-Benz in under critical

divided into tersteer gener

h constant re vehicle is s

easing speed.

vehicle detehavior can boad transfer.is reduced an

versteer is an ward and tend2.2 below.

Figure 2.2

ariables, vehirst variable is

angle is a

t developed by

the early 198circumstance

two situationsrally are car s

radius during aid to be und

, the steering

ermines vehibe provoked Excessive und the car sliunstable situ

ds to spin aro

Excessive overs

cle side slip s hard to devariable dire

y the Germa80’s. Its purpes.

s, excessive specific prope

increasing sersteered.

g wheel angle

icle behaviord, i.e. by infundersteer hodes curve ou

uation where ound its axis.

steer

angle and vtermine and ctly available

n car part pose, as its

understeer erties.

speed, the

e has to be

r under all fluence of

owever is a tward over grip on the These two

ehicle yaw has to be

e from the

5

2.2 ESP Controller Essen Duisburg As starting point for the design of an ESP controller, at hand there is a design of University Essen Duisburg. This design can be divided into 3 parts;

• calculation of desired values • controller • operation algorithm

These three parts are subsequently shortly explained in the following sections.

2.3 Desired values The original controller includes 2 Single Track Models (STM), one to determine the desired values and one to provide a state space model of the vehicle. This means every parameter that has to be defined by the user in these models, occurs twice. The models are not exactly equal; the cornering stiffnesses of both models can be adjusted to achieve certain behavior.

The first STM is used to calculate the desired values for vehicle side slip angle and vehicle yaw velocity. Under steady state conditions this model, whose parameters are determined by experiments, delivers fairly acceptable values which can be used as an input variable for the controller. Following equations are used to determine desired values for yaw velocity and side slip angle. Desired yaw rate

2

2

1ch

L

Ldes

vv

vli

+=δ

ψ&

With

wheel toe angle due to steering wheel angle

Maximum desired yaw rate

vgs

desμ

ψ 8.0max =& (2.1)

Desired vehicle side slip angle

ρρβ

α

2

2

vlC

mll FRdes −=

With

Rl distance CoG to rear axle

Fl distance CoG to front axle l wheel base

ψρ

&

v= inverse corner radius

2αC cornering stiffness rear axle

L

L

iδ

6

Empirical relation to determine maximum vehicle side slip angle

)02.0(tan 1max gsdes μβ −= (2.2)

With

sμ friction coefficient tyres to road g gravitational acceleration These relations for desired values in side slip angle and yaw rate lead to the following formulation of the error vector, which serves as input for the controller.

desact

desacteψψββ&& −

−=

2.4 Controller A Linear Quadratic (LQ) Optimal Controller is based on the following state space description of vehicle behavior, which is deduced from the single track model with state variables β and ψ& .

vJlClC

JlClC

mvlClC

mvCC

z

RF

z

FR

FR

22

2112

21221 1

αααα

αααα

+−

−

−+

+− 0

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−

−

−+

+−

=

vJlClC

JlClC

mvlClC

mvCC

A

z

RF

z

FR

FR

22

2112

21221 1

αααα

αααα

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛=zJ

E 10

KeMEMAee

−=+=&

(2.3)

7

The LQ Controller has to be chosen such that it minimizes

( )∫∞

+=0

2 dtRMQeeJ T

With

2

2

2

lim1

lim10

0lim

1

⎟⎠⎞

⎜⎝⎛=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

=

MR

Q

ψ

β

&

Where the limits are weighting factors, free to choose to influence controller output. Essen Duisburg proposed to use user defined maximum values for respectively side slip angle, yaw rate and output control torque for these weighting factors. Limit factors βlim and ψ&lim in this case are chosen equal to the maximum vehicle side slip angle (2.2) and vehicle yaw velocity (2.1), respectively. The controller calculates the control torque M by solving the Riccati equation every time step, due to non linearity caused by changing vehicle speed and steering wheel angle. This linearizes the system every time step and thereby allows for the linear observer. The actual control torque which is required to stabilize the vehicle is determined by (2.3). This control torque is subsequently used in an operation algorithm to prescribe brake pressures to the ABS brake system.

2.5 Operation Algorithm The operation algorithm is based on basic theory stating oversteer requires an ESP intervention on the outer front wheel, whereas in case of understeer the inner rear wheel is braked. Inner and outer wheels of course are determined by the direction of the curve. At first two boundary conditions are checked, vehicle speed should be above 5 m/s and control torque has to be larger than some threshold. Then a distinction is made between several cases. The sign of the steering wheel angle is used to recognize left and right curves, whereas the error in yaw velocity distinguishes between understeer and oversteer. In each of these cases, brake pressures are calculated by incrementally increasing or decreasing brake pressure for the chosen wheel as long as a control torque exists.

8

3. Design of the Electronic Stability Program

State Space Description

LQR Controller

Desired Side Slip Angle

Desired Yaw Velocity

Operation Algorithm

Brake Pressure Allocation

K1

K2-

-Control

Torque

δ

V

actψ&

actβ

Wheel FR

Wheel FL

Wheel RR

Wheel RL

BrakePressures

Electronic Stability Program

Figure 3.1 Schematic representation of the ESP A schematic representation of the Electronic Stability Program is show in figure 3.1 above. It shows the two controlled variables, the controller which provides controller gains K1 and K2 and the operation algorithm and brake pressure allocation. In this study, the focus is on improving this last sub block.

3.1 Controller As the controller of the design at hand already is influenced by both yaw rate and side slip angle and optimizes the control torque to comply to both variables, this controller is used in the new ESP design. Correct operation of the controller is supported by simulation results, presented in chapter 5.4.

3.2 Desired values Instead of using the output of a Single Track Model, the desired values for yaw velocity and side slip angle are measured in a single measurement and stored in a 2D look-up-table. To be sure to take variables into account that influence these 2 reference values for the controller, measurements are carried out. Results of these measurements are that both yaw velocity and side slip angle are mainly influenced by vehicle velocity and steering wheel angle. Therefore, these 2 variables as well as the 2 output variables are measured in a semi-steady-state cornering experiment in which speed varies from 30 to 180 [kmh] and steering wheel angles vary from 0 to 720 [deg]. Afterwards, the results are mirrored to cover all possible situations.

The advantage of the direct use of measurements is not only that the actual data of the vehicle is used, but also parameterization of the controller becomes more clear. The use of actual vehicle data improves parameter correspondence to the actual vehicle behavior, especially at high lateral acceleration. One of the 2 Single Track Models that determine ESP behavior is now obsolete.

9

3.3 Brake Pressure Allocation Whereas the operation algorithm of the ESP Duisburg is based on the rule of thumb described in chapter 2.5, here a second look is taken at the way that this ESP distinguishes between cases and determines which intervention is done. The basic theory behind this analysis is the moment equilibrium around the z-axis. The longitudinal, braking and driving, and lateral forces each create a torque around the z-axis, leading to the equilibrium around the centre of gravity in (3.1).

ysyyryyqyypyxsxxrxxqxxpxz sFrFqFpFsFrFqFpFM −−+++−+−= (3.1) where the lever arms are defined as shown in figure 3.2.

Figure 3.2 Definition of lever arms Lever arms for the rear axle are constant, lever arms for the front axle however are variable and depend on the wheel toe angles. The constant lever arms are defined as

R

R

R

R

lsy

Tsx

lry

Trx

=

=

=

=

2

2

Where TR is the track width rear and Rl is the distance from the centre of gravity to the rear axle in x-direction.

10

Figure 3.3 shows the variable lever arms for the front axle.

Figure 3.3 Variable lever arms front axle due to toe angle Depending on the sign of the steering wheel angle, the lever arms are calculated as follows. Left corner

)sin(

)cos()sin(

)cos(

2tan

4

2

1

22

δς

δςδς

δ

ς

δδδ

−=−′=

−⋅=−⋅=

=′

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=

+=

+=

−

F

F

FF

F

F

FF

RL

lqypxTqx

aapyaapxTT

l

T

lTaa

Right corner Figure 3.4 Variables used in calculation of lever arms front axle

)cos()sin(

)sin(

δςδςδς

+⋅=+⋅=+=

−′=

aaqyaaqxlpy

qxTpx

F

F

where figure 3.4 shows the respective variables.

11

Brake forces are defined in negative x-direction and are always positive. As shown in (3.2), brake forces have a direct influence on the moment equilibrium around the z-axis and therefore can generate a control torque. The control torque created directly by the brake forces is called primary control torque.

xBSxBRxBQxBPPC sFrFqFpFM −+−= (3.2) with FBi with i=p,q,r,s the respective brake forces for each wheel. In addition to the primary control torque it is possible to create a second torque around the z-axis. This is called the secondary control torque and does occur when the side force of the current wheel is reduced by applying a brake force. This effect however can only be generated when the tyre currently close to the friction limit. This is shown in figure 3.5 as the red outline of the friction circle of a tyre.

Figure 3.5 Tyre friction circle When the tyre is on the edge of slip-slide during pure cornering, the side force consumes all transferrable force at that moment in time. This is shown in figure 3.6 below. If a brake force is applied, the available total force is divided between a longitudinal brake force and the side force. This causes the available side force to reduce, which is shown in figure 3.7.

Figure 3.6 Pure cornering Figure 3.7 Combined cornering and braking

The reduction in side force is a function of the brake force and maximum tyre force, which comes from the veDYNA vehicle model, and introduces an additional torque around the z-axis.

12

( )22maxmax by FFFF −−=Δ

ysyyryyqyypySC sFrFqFpFM Δ+Δ+Δ−Δ−= (3.3) Combining (3.2) and (3.3) gives the total available control torque which can be achieved by braking.

ysyyryyqyypyxBSxBRxBQxBPCT sFrFqFpFsFrFqFpFM Δ+Δ+Δ−Δ−−+−= (3.4) As yFΔ is only a function of the semi-constant maxF and the applied brake force BF , control

torque CTM is only a function of variable BF .

To make a correct decision in which wheel is braked, for each wheel a sensitivity is calculated. The sensitivity shows how much brake force is required for that wheel to produce the control torque calculated by the controller. As an example, the calculation of the sensitivity for wheel P is shown below.

( )( ) yBPxBPCT pFFFpFM 22maxmax −−−= (3.6)

(3.6) can be solved for BPF by solving quadratic equation (3.7)

0222

1 max

2

2max2

2

=+⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+−⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛

y

PCT

y

CTBP

y

xCT

y

PxBP

y

x

pFM

pM

Fp

pMpFp

Fpp

(3.7)

This required brake force BPF now shows how much brake force is required for only

wheel P to produce the entire control torque. As this is done for every wheel, the 4 required brake forces can be sorted and the wheel that requires least brake force is chosen to carry out the ESP intervention. This guarantees that the intervention is done on a wheel which is able to produce the control torque and additionally this is the wheel that requires the least brake force, so that comfort is optimized. In certain cases it is possible that not the entire control torque can be produced by a single wheel ESP intervention. This means there is a remaining control torque after applying maximum allowable brake force on the first selected wheel. Then the wheel requiring second least brake force is additionally braked.

The way a wheel is braked is not always the same. As shown before, there is a division between primary and secondary control torque. Not in every case the secondary control torque is useful in producing the required control torque. As shown in (3.4), the secondary effect has an opposite sign to the primary effect for wheel P and S. This is dependent on the direction of the curve and the sign of the control torque, so whether understeer or oversteer has to be corrected. In practice this means that a check is necessary to determine whether it is useful to exploit the entire potential of primary and secondary control torque for each wheel. If the secondary control torque produced is useful, the wheel is braked into the sliding region. If not, a safety threshold is used to make sure the wheel is kept entirely in the slipping region. This means ESP has to work together with the Antilock Braking System (ABS) to make sure these operations are possible.

13

In addition to the ESP intervention by applying a brake force, to effectively control vehicle behavior it is necessary to exclude any interference by the engine driving the front, rear or all wheels. This is done by cutting off engine torque during an ESP intervention in 3 phases.

Phase 1 Phase 1 starts at the moment an ESP intervention is initiated. At this moment the engine torque is reduced to 0 by either reducing or increasing the throttle angle. It has to be noted that engine torque is negative, engine braking, when the throttle valve is completely closed, so a small angle has to be kept in order to compensate for internal losses in the engine such as friction and changes in entropy/enthalpy. Phase 2 Phase 2 is used to make sure the engine torque is cut off for at least 200 ms or as long as the ESP system is active. Phase 3 During phase 3 the maximum engine torque is raised back to its original value over 500 ms. This is done linearly and combined with the 2 previously described phases ensures smooth operation of the ESP system in the complete vehicle model. The ESP system is implemented and tested in Matlab/Simulink.

14

4. Experiments

4.1 Test cases As testing is a crucial part of the assignment, this chapter includes tests with intermediate designs that are not explained in detail in this report. For convenience, a short description of the versions that are tested is presented below.

1. Vehicle without ESP A vehicle model that is not equipped with ESP serves as a reference to both assess the maneuver in its ability to show critical vehicle behavior and demonstrate the functionality of an ESP.

2. Vehicle with control torque In this case, the control torque calculated by the controller is applied directly to the vehicle. In the veDYNA vehicle model, this is possible by applying the control torque as an external input around the z-axis. This model shows whether the control torque in itself is able to stabilize vehicle behavior or not.

3. Vehicle with ESP with improved algorithm vs. ESP Duisburg Some errors are detected while thoroughly assessing the algorithm that determines ESP interventions in the starting point ESP. The changes made concern the way left curves are distinguished from right curves and the distinction between understeer and oversteer. In the starting point ESP, left and right curves are detected by evaluating the sign of the steering wheel angle. As during a critical maneuver the driver reacts by counteracting movement by steering in the opposite direction, the sign of the steering wheel angle can be opposite to the actual curve that is followed. In the improved algorithm, this distinction is made by evaluating the sign of the lateral acceleration. In the improved algorithm, understeer and oversteer are no longer detected by looking at the error in yaw velocity, but by evaluation of the sign of the control torque. As the control torque incorporates both yaw velocity and side slip angle, this variable is better suited.

4. Vehicle with new ESP design vs. ESP Duisburg This test shows the performance of the design presented in chapter 3 compared to the ESP designed by University Essen Duisburg.

15

4.2 Test maneuver To verify the operation of the ESP system a double lane change maneuver is commonly used and gives insight in vehicle behavior under circumstances that drives the car’s chassis to its limits. The principle of this test is shown in figure 4.1

Figure 4.1 ISO 3888-1 double lane change To show the differences between the several designs, a test is done at 100 km/h. The driver used during this maneuver is adjusted such that driver behavior does not interfere with the expected ESP results. If, for example, the driver is able to counteract oversteering by a steering wheel correction, it is impossible to identify ESP influence on vehicle behavior. Therefore the steering wheel rate is limited to 270 deg/s. In the assessment of results, focus is on vehicle stability, required control torque and applied brake pressure. Table 4.1 Boundary conditions maneuver

Variable Value Vehicle speed 100 [kmh] Max. steering wheel angle rate 270 [deg/s]

4.3 Test 1: Vehicle without ESP As a reference, the test is first performed with a vehicle that is not equipped with an ESP system. The vehicle, a BMW 530i E60, has a basic chassis design which under steady state conditions tends to understeer. However during this maneuver the vehicle is supposed to become unstable.

Figurelane cunsta

Figure

Figure

e 4.2 and 4.3change maneble as expect

4.2 Side slip ang

4.3 Vehicle traje

3 below showeuver. It is clted.

gle [deg] vs. simu

ectory

w both side slear that beha

ulation time

lip angle and avior is not a

vehicle trajeas desired an

ectory during nd the vehicle

the double e becomes

4.4 TIn ordcontroproveshowirequir

Figure

Figure

Test 2: Veder to test theol torque is apen whether theing side slip red confirmati

4.4 Side slip ang

4.5 Steering whe

ehicle withe working prinpplied directlye control torq

angle, steerion that the ca

gle [deg] vs. simu

eel angle [deg] v

h ESP connciple of the y into the chasue actually isring wheel aalculated con

ulation time for E

vs. simulation tim

ntrol torquESP system,ssis in order t

s able to stabiangle and ventrol torque is

ESP control torqu

me for ESP contro

ue a test is donto control the lize the vehic

ehicle trajectoable to stabil

ue

ol torque

ne where the vehicle. In th

cle or not. Figory, clearly pize vehicle be

calculated his way it is ures below,

provide the ehavior.

Figure

4.5 TAs devehiclUnive

Figure

4.6 Vehicle traje

Test 3: Veescribed in chle stabilizatio

ersity Duisburg

4.7 Side slip ang

ectory for ESP co

ehicle withhapter 4.1, Eon. Figures bg and the imp

gle [deg] vs. simu

ontrol torque

h improveESP operationbelow show proved algorit

ulation time for E

ed ESP algn algorithm isdifferences b

thm for key va

ESP Duisburg an

gorithm vss improved inbetween the ariables.

d improved algo

s. ESP Dun order to ob

starting poi

rithm

uisburg btain better nt ESP of

Figure

Figure

4.8 Steering whe

4.9 Vehicle traje

eel angle [deg] v

ectory for ESP Du

vs. simulation tim

uisburg and impr

me for ESP Duisb

roved algorithm

burg and improveed algorithm

Figure Figuretrack,shownstabili

4.10 Brake pres

es above sho while requirn clearly by tized about 2 s

sure front left [Pa

ow improveming less steethe combinatiseconds earli

a] for ESP Duisb

ments in all diering wheel inon of vehicleier with the im

burg and improve

isciplines, thenput and all ie trajectory anmproved algor

ed algorithm

e vehicle morin all also lesnd brake presrithm compare

re effectively ss brake presssure that theed to the star

follows its ssure. It is e vehicle is rting point.

4.6 TAfter doublUnivecomp

Figure Figurefrom oversslip an

Test 4: Reduring the ree lane chang

ersity Duisburared.

4.11 Vehicle traj

e 4.11 showsUniversity Duteer reaction ngle gives mo

edesignedference test ie maneuver,

rg and the ES

jectory compared

that ESP 2 isuisburg. Alsois expected

ore clarity abo

d ESP vs. it is shown ththis test is pe

SP system d

d between ESP D

s able to conto it is shown between x=3out this obser

ESP Duishat vehicle beerformed withescribed in th

Duisburg and ES

trol vehicle trathat althoug

00 and x=350rvation in figu

burg ehavior becomh both the EShis report. Fi

SP 2

ajectory moreh an ESP sy0 m. Assessmre 4.12

mes unstable P system prorst, vehicle tr

e precisely thaystem is activment of the v

during the ovided from rajectory is

an the ESP ve, still an ehicle side

Figure AbsolIn thismade Furthefor theexper

Figure MaximABS driving

4.12 Vehicle sid

ute values ofs case, the a

e to the ESP s

ermore, the ae left front whrience of com

4.13 Wheel brak

mum brake pintervention g comfort dur

e slip angle [deg

f vehicle side nimation indesystem provid

applied brakeheel, which is fort.

ke pressure front

ressures are is required. Cring ESP inter

g] vs. simulation t

slip angles laeed shows ande a more reli

pressures arrepresentativ

t left vs. simulatio

two times asCombined wrvention.

time

arger than 5 n oversteeredable vehicle s

re evaluated.ve for the ove

on time

s small as in ith the lower

degrees indicd vehicle. It isstabilization.

Figure 4.13erall required b

the initial cor brake force

cate potentials clear that th

shows brakebrake force a

oncept, also im, this largely

oversteer. he changes

e pressures and thereby

mplying no y increases

23

5. Conclusion and Recommendations 5.1 Conclusion In this report, an Electronic Stability Program is presented that is implemented as a stand-alone subsystem in the veDYNA vehicle simulation package. The ESP has following main attributes.

• Vehicle control using a Linear Quadratic Optimal controller which is calculated every time step

• Two variables are controlled, vehicle yaw velocity and vehicle side slip angle by

applying brake pressures to the individual wheels • Desired values for the two controlled variables are determined based on semi-steady

state measurements on the actual vehicle • Applied brake forces are calculated exactly, based on the control torque produced by

the controller, variable lever arms of brake forces and current slip-slide condition of the tyres

• By assessing the sensitivity of each wheel to create the required control torque, a

decision is made on where the ESP intervention takes place • In application of brake pressures both primary and secondary effects of brake forces

are taken into account The controller is implemented in a Matlab/Simulink environment In experiments and simulation it is shown that the ESP is effective and efficient in controlling vehicle behavior under critical circumstances. A comparison is made between the redesign and the starting point design delivered by University Essen Duisburg. This comparison shows that at a double lane change test maneuver at 100 [kmh], the redesign of the ESP is able to entirely keep vehicle behavior within stable boundaries, whereas the ESP of University Essen Duisburg still shows unstable vehicle movement. In addition to better stabilization, the required peak brake forces are only half as large.

5.2 Recommendations Below 30 [kmh] the ESP is not active. Under normal conditions, this is not considered a problem. At specific conditions such as a road with a low friction coefficient however, this can still cause undesired vehicle behavior. It is recommended to execute more experiments in order to better investigate vehicle yaw velocity and side slip angle below 30 [kmh]. Dynamic tyre behavior and vehicle chassis dynamics are not taken into account in the calculation of desired values. In certain cases, this causes the ESP to become active during swift alterations in direction. Possibly a more detailed vehicle model as observer or look-up-tables that take dynamics into account, are able to solve this issue. Controller parameterization is unclear because the parameters ruling controller behavior have no physical meaning. Iteratively an optimum for the division between yaw velocity and side slip angle influence can be found. Possibly these controller parameters have to be chosen variable to vehicle speed and/or steering wheel angle. Other tests can be performed to examine behavior of the ESP system under more circumstances. Although the double lane change maneuver identifies critical vehicle behavior in most cases, it does not cover every situation that can be encountered. This additional testing could include the J-turn maneuver, fishhook maneuver and step steer response, as well as testing on road surfaces with low friction coefficient.

24

List of Symbols β vehicle side slip angle δ steering wheel angle

sμ friction coefficient ρ inverse corner radius ψ& vehicle yaw velocity

αC effective cornering stiffness

BF brake force

maxF maximum tyre force g gravitational constant i steer ratio

zJ inertia around z-axis l wheel base

Fl distance front axle to centre of gravity

Rl distance rear axle to centre of gravity βlim weighting factor, maximum allowable vehicle side slip angle ψ&lim weighting factor, maximum allowable vehicle yaw velocity

zMlim weighting factor, maximum allowable control torque around z-axis

CTM overall control torque

PCM primary control torque

SCM secondary control torque

zM moment around z-axis p wheel index front left q wheel index front right r wheel index rear left s wheel index rear right

FT track width front

RT track width rear v vehicle velocity

chv vehicle characteristic velocity