Small scale stand for testing different control algorithms on assisted brake systems

Small scale stand for testing different control algorithms on assisted brake systems “Politehnica” University “Politehnica” University Abstract — The paper presents a scaled testing sta

Small scale stand for testing different control algorithms on assisted brake systems

“Politehnica” University “Politehnica” University

Abstract — The paper presents a scaled testing stand for

applying different algorithms onto an assisted brake system in

order to determine the best way to control the braking process

Keywords: test stand, braking, ABS, control, tire-slip

I Introduction

The Antilock Braking System (ABS) is an important

component of a complex braking-steering system for the

modern car It is now available on most of the vehicles,

enhancing their braking capabilities The early systems

were mechanical systems and performed with varying

degrees of efficiency, but they significantly improved

vehicle steerability during braking This ability of the

early systems encouraged further development

Today, ABS systems can be found on most of the

vehicles, tending to be standard equipment The main

objective of most of these control system is prevention of

wheel lock while braking This is important for two main

reasons First to maintain steering ability of the car while

hard emergency braking and in order to enable obstacle

avoidance in such situations Second, for decreasing the

braking distance in case of an emergency braking The

later is due to the fact that the maximum friction between

the road and the tires is, in most of the cases, achieved

when the wheel is still rotating and not when is locked

It turns out that this task is not trivial, one of the main

reasons being the high amount of uncertainty involved

Most uncertainty arises from the friction between the

tires and the road surface In addition, the tire-road

characteristic is highly nonlinear, which burdens even

further the control task

In order to design an efficient ABS one needs to know

the dependencies between the applied brake torque and

friction between tires and road surface

II The tire-road model

The model that describes forces involved during braking

is derived from the well known quarter car model This

consists of a single wheel attached to a mass, as shown in

figure 1

*E-mail: valentin.ciupe@mec.upt.ro

† E-mail: maniu.inocentiu@mec.upt.ro

Fig 1 Quarter car model

Fig 2 Longitudinal tire slip for different road surfaces

A simplified model of wheel dynamics subject to brake torque and ground forces is described by the following relations:

0 ))

( ( ) ( ))

( ( )

(

≥

⋅

−

⋅

−

⋅

dt

t d

ω µ τ β

λ µ α

)) ( ( )

(

t dt

t dv

λ µ

γ ⋅

−

) (

) ( ) ( ) (

t v

r t t v

where:

ω - angular velocity of the wheel;

v - velocity over ground of the car;

λ - longitudinal tire slip;

Tb - brake torque It is the input signal of the model;

µ  - road-tire friction coefficient;

µb - friction coefficient in the brakes;

τ - time delay;

r - wheel radius

α, β, γ - positive constants, resulting from physical

parameters of the vehicle

The constants given in the model have the following

physical interpretation:

,

1 ,

m

F J

J

F

=

=

⋅

where:

m – mass of the quarter car;

Fz – vertical (normal) force;

r – wheel radius;

J – wheel inertia

The longitudinal tire slip (λ) definition will imply that a

locked wheel (ω=0) is described by λ=1, while the free

motion of the wheel (ωr= v) is described by λ=0

The tire friction force, is determined by

Fz.µ(λ, µH, α, Fz, v) where µ(λ, µH, α, Fz) is the road-tire

friction coefficient This is a nonlinear function with a

typical dependence on the slip shown in (figure 1), based

on Pacejka’s “magic formula” This model uses static

maps to describe dependence between slip and friction

and it can depend on the vehicle’s velocity (v) This

function depends also on the normal force (Fz), steering

angle (α) and road surface (having different maximum

values µH for different road conditions) For ease of

writing, the model equations highlight only the

dependence on the longitudinal tire slip (λ)

In figure 2 there are shown tire friction curves,

generated by the Pacejka model, for four different kinds of

surfaces

Notice that this model contains a quite simple

description of the slip dynamics for a wheel It does not

capture pitching motion of the car body while braking,

suspension dynamics, actuator dynamics, tire dynamics

nor camber angle (in the above given model, the tire is

consider perpendicular on the road surface) However, it

captures the major control challenges of the problem

III Existent ABS operation algorithm

By looking at the curves, it is obvious that an efficient

anti lock system must maintain a slip percentage of the

tire at about 10-20% And that is what today’s ABS’ are

trying to do

The preferred method is the use of decoupling solenoid

valves and a piston electro-pump The functional principle

is as follows: the ABS controller (ECU) monitors wheel

speeds via reluctance speed sensors If (while braking)

one wheel spins slower (decelerates faster) then a software interrupt is triggered, raising a “lock tendency” event, which launches a special routine This routine looks-up in

a data table and figures out that the pressure in the caliper must be reduced A tri-state solenoid valve is actuated on its first stage, in order to release the excess pressure The routine looks up in the table again and after the requested time elapsed it knows that must enter maintaining phase The solenoid valve is now commuted to its second stage, the caliper is isolated from the rest of the brake circuit and, having a low pressure allows for the wheel to spin

up The routine looks one more time in the data table and after maintaining time elapsed commutes the valve in the third state and with help from the electro-pump builds up pressure to that caliper The pressure rises again until the lock tendency reappears and the whole process repeats until full stop (actually car speed less than 10 km/h) or foot off the brake pedal

The method described above ensures a good steerability and a very small percent of slip during braking But those ABS’ (which are the only ones used in today’s series passenger cars) have their disadvantages: the sudden changes in pressure give undesired vibrations in the brake pedal and chassis, big offset from the desired slip and in many cases it has been demonstrated to significantly increase stopping distance (panic brake cases)

IV The scaled test stand The test stand for the antilock brake systems must simulate real running conditions of a car over a certain surface (asphalt, concrete, muddy, icy or wet roads) by taking into account the dynamics of the that system and particularly the down force of the wheel (car’s mass), kinetic energy during braking (inertia) and adherence coefficient (nature and aspect of the road)

In order for the measurements to be precise every parameter must be modified according to test’s needs It must be stated that is sufficient to test only one wheel (out

of the four) in order to determine the functional parameters of the equipment

Also it is preferred to have a scaled test stand for space reasons and the ease of modifying

Due to the fact that in laboratory conditions cannot be realized a suitable longitudinal test track, it must be shaped as a cylindrical tambour having its width at least equal to that of the tested wheel This tambour should have its surface grade close to that of asphalt or concrete and its peripheral velocity should be similar (scaled) to a vehicle traveling at a safe speed (50-100 km/h) Also the inertia of the tambour should be scale-equivalent to that of

a quarter of the simulated vehicle

Considering solved the problem of the track (tambour) the following must be taken into account: the down force exerted by the wheel must be a quarter of the scaled-weight of the vehicle and the link between wheel and

tambour (track) must emulate the elastic component of the

suspension Such a solution is represented in figure 3

Fig 3 The scaled testing stand principle

The actual testing stand (figure 4) comprises a support

table (1), having the role to sustain the other components,

the track tambour (2) having the required inertial mass

and being driven by the electric motor (3), the test wheel

(4) having texture and form similar to a real-sized car

wheel The wheel is mounted with the fixtures (5) which

are fixed on the support plate (7) The caliper (6) is

mounted on its support in such a way that allows for

movement along the axis of the wheel (floating caliper)

Fig 4 3D model of the stand (general view)

Fig 5 3D model of the stand (test wheel assembly).

From a functional point of view (figure 5) the stand works as follows: the electric motor drives the tambour which is in contact with the rolling surface of the test wheel (9) On the wheel hub is mounted the brake disc (2) locked to the wheel with 6 bolts (1) This assembly is supported by two ball bearings at each end (4) Two brake pads press against the brake disc with the help of an electromagnetic caliper This comprises the floating frame supporting the coil and guiding the ferromagnetic core which in turn presses against the brake pads The beam (10) is there for reinforcing the assembly and at the same time supports different masses used to produce the normal down force onto the test wheel The optoelectronic transducer (11) feeds back to the computer pulses that translate into angular velocity of the test wheel There is another identical transducer mounted onto the motor’s shaft used to reference the tambour’s angular velocity

Fig 6 Electronic schematics of the test stand

N

G

M

ω

ω

Tω

Tω

track

test

F

From the control point of view, the stand is linked to the

parallel port of a regular PC By following the schematics

in figure 6, one can observe that bit D0 of port 378 opens

a bipolar transistor which in turn allows current through

the motor’s relay Bit D1 opens a MOS-FET transistor

which commands the caliper’s electromagnet Bits D2 and

D3 are used to feed current to the transducers’ IR emitting

diodes Values given by the IR transistors are read in the

status port 379, respectively pins S4 and S5

V The software component

In order to control de scale test stand a program has

been conceived in Visual Basic and the access to the

parallel port was achieved using a special driver, “io.dll”

Data processed by the program are saved in a file for later

analysis In figure 7 is presented a screen capture of the

program It can be noticed that it has the possibility to

change different parameters for the abs operation and also

to apply different control algorithms like panic brake with

no abs, normal abs and adaptive abs Adaptive ABS is a

newly proposed method that should keep the relative slip

of the wheel around 20% by controlling continuously the

braking torque

Fig 7 GUI for the ABS test stand

In the above image the blue line represents the trend of

the peripheral speed of the track (tambour) and the red

line is the trend of the test wheel’s peripheral velocity

Determination of the two peripheral velocities is done by

taking into account that: the run radius of the tambour at

contact point is 66mm; the run radius of the test wheel at

contact point is 65mm; there are 90 pulses per revolution

at both encoders The peripheral speeds resulting from

above parameters are given by relation (5):

] / [ 2

] / [ 2

s mm t

N

N

R

v

s mm t

N

N

R

v

p

IC C

C

p

IR R

R

⋅

⋅

⋅

⋅

=

⋅

⋅

⋅

⋅

=

π

π

(5)

where: vR – test wheel speed; vC – run track speed; RR – test speed radius; RC – run track (tambour) radius; NIR – number of pulses given by the wheel in the time tp; NIC – number of pulses given by the tambour in the time tp; N – number of pulses per revolution

VI Test results Using the above-presented test stand, different algorithms were tested in order to determine the most efficient one

In figure 8 the results of a braking with wheel lock-up is represented The blue line is the trend-line of the tambour’s velocity and the red line is the trend-line of the tested wheel It can be noticed that the wheel locks almost instantaneously (0.2s) and the whole system comes to a stop (from approximately 5.4 m/s) in 2.02 seconds

-1 0 1 2 3 4 5 6

0 0.5 1 1.5 2 2.5 3 3.5

Timp [s]

Fig 8 Braking with wheel lock-up

In figure 9 braking with normal ABS is executed The braking time (distance) increases close to 2.24 seconds when using ABS on a dry surface (obvious if one looks at the graph and notices lock-unlock cycles), but the gain is

in steering control due to the fact that the mediated wheel speed (red line) approaches a more desirable slip value

-1 0 1 2 3 4 5 6

0 0.5 1 1.5 2 2.5 3 3.5

Timp [s]

Fig 9 Braking with normal ABS

And in figure 10 a test result on braking with adaptive

ABS is shown It can be easily noticed that the mediated

wheel velocity stays closer to the desired 20% of relative

slippage, compared to normal ABS braking Also the

braking time was seriously reduced to 2.06 seconds

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5

Timp [s]

Fig 10 Braking with adaptive ABS

It must be stated that all three test were conducted with

the same stand setup in order to have as less parameter

variation as possible

VII Future work

The stand described in this paper offers a high flexibility

in implementing different control algorithms and

parameter modification This is first due to its reduced

size but mostly to the electromagnetic actuated caliper

The future for an assisted brake test stand is to build a

more versatile and closer to today’s automotive braking

systems scaled test stand This will be achieved by

constructing a remotely controlled, scaled vehicle (1:4.6

overall scale) having rear wheel drive, full independent

suspension and front Ackerman steering wheels It is

designed to have discs and hydraulic calipers all around

Master cylinder will be split in four, independently

controllable linear electro-hydraulic actuators

This approach will give far better results under different

braking conditions and will allow for numerous

algorithms and variations to be tested

VIII Conclusion

Making vehicles and roads safer is a top priority for

every design engineer in automotive industry or research

group

Different methods have been proposed over the years for

shortening stopping distances and maintaining a good

steerability while braking Of all, the current ABS

approach seems to be the design of choice due to

demonstrated reliability, developing-related, production

and integration costs

The use of a scaled test stand allows for numerous experimental tests with less costs and time It also permits the easy modification of every desired parameter, the results being ready for interpretation in a very short amount of time The results are fairly accurate when scaled back to real size system and the testing on a real size vehicle are more predictable; fine tuning the real system being effortless and time efficient

References [1] Ciupe V., Gligor O A different approach in the control methods for automotive antilock brake systems In The 2nd International conference on robotics, Timisoara & Resita, October 2004 [2] Solyom S Synthesis of a Model-based Tire Slip Controller Licentiate thesis, Department of Automatic Control Lund Institute

of Technology, 2002

[3] Ulsoy A G and Peng H Vehicle Control Systems, Lecture notes,

1997

[4] Solyom S., Rantzer A and Kalkkuhl J A Benchmark for Control of Antilock Braking Systems, Department of Automatic control Lund Institute of Technology, 2001

[5] Canuda-de-Wit C and others Dynamic Friction Models for Road/Tire Interaction Vehicle System Dinamics, Draft Article Laboratoire d'Automatique de Grenoble, 2002