ANTILOCK BRAKING SYSTEM

An anti-lock braking system (ABS) is a safety system that prevents the

wheels on a motor vehicle from locking up (or ceasing to rotate) while

braking.

•A rotating road wheel allows the driver to maintain steering control under heavy

braking by preventing a skid and allowing the wheel to continue interacting

tractively with the road surface as directed by driver steering inputs.

•ABS offers improved vehicle control and decreases stopping distances on dry

and especially slippery surfaces for many drivers, but on loose surfaces like

gravel and snow-on-pavement it can slightly increase braking distance, while still

improving vehicle control.

•Since initial widespread use in production cars, anti-lock braking systems have

evolved considerably.

•Recent versions not only prevent wheel lock under braking, but also

electronically control the front-to-rear brake bias.

How does an ABS work? •The anti-lock brake controller is also known as the CAB (Controller

Anti-lock Brake).

ABS Components

There are four main components to an ABS system:

Speed sensors

Valves

Pump

Controller

Speed Sensors

The anti-lock braking system needs some way of knowing when a wheel is

about to lock up. The speed sensors, which are located at each wheel, or in

some cases in the differential, provide this information.

Valves

There is a valve in the brake line of each brake controlled by the ABS. On some

systems, the valve has three positions:

In position one, the valve is open; pressure from the master cylinder is passed

right through to the brake.

In position two, the valve blocks the line, isolating that brake from the master

cylinder. This prevents the pressure from rising further should the driver push

the brake pedal harder.

In position three, the valve releases some of the pressure from the brake.

Pump

Since the valve is able to release pressure from the brakes, there has to be some

way to put that pressure back. That is what the pump does; when a valve

reduces the pressure in a line, the pump is there to get the pressure back up.

Controller

The controller is an ECU type unit in the car which receives information from

each individual wheel speed sensor, in turn if a wheel looses traction the signal

is sent to the controller, the controller will then limit the brakeforce and

activate the ABS modulator which actuates the braking valves on and off.

•The ECU constantly monitors the rotational speed of each wheel.

•When it detects a wheel rotating significantly slower than the others — a condition

indicative of impending wheel lock — it actuates the valves to reduce hydraulic

pressure to the brake at the affected wheel, thus reducing the braking force on that

wheel.

•The wheel then turns faster; when the ECU detects it is turning significantly faster

than the others, brake hydraulic pressure to the wheel is increased so the braking

force is reapplied and the wheel slows.

• This process is repeated continuously, and can be detected by the driver via brake

pedal pulsation.

•Some anti-lock system can apply and release braking pressure 16 times per

second.

•The ECU is programmed to disregard differences in wheel rotative speed below a

critical threshold, because when the car is turning, the two wheels towards the

center of the curve turn slower than the outer two. For this same reason, a

differential is used in virtually all roadgoing vehicles.

Vehicle dynamics and braking systems are complex and behave strongly

non-linear which causes difficulties in developing a classical controller for

ABS.

Fuzzy logic, however facilitates such system designs and improves turning

abilities.

The underlying control philosophy takes into consideration wheel

acceleration as well as wheel slip in order to recognize blocking tendencies.

Fuzzy applied in ABS

The knowledge of the actual vehicle velocity is necessary to

calculate wheel slips.

This is done by means of a good sensor, which weighs the

inputs of a longitudinal acceleration sensor and four wheel

speed sensors.

If lockup tendency is detected, magnetic valves are switched to

reduce brake pressure.

Performance evaluation is based both on computer simulations

and an experimental car.

Wheel model

FZ: Wheel load

R: Wheel radius

w: Angular wheel frequency

v: Velocity of wheel center

FL: Longitudinal force

Figure 1

Calculating the wheel slip by

the longitudinal wheel force results in

At the beginning of an uncontrolled full braking, the

operating point starts at s = 0, then rises steeply and

reaches a peak at s = s max.

After that, the wheel locks within a few milliseconds

because of the declining friction coefficient

characteristic which acts as a positive feedback. At this

moment the wheel force remains constant at the low

level of sliding friction. Steering is not possible any

more.

Therefore a fast and accurate control system is required

to keep wheel slips within the shaded area shown in

Figure 1.

Furthermore Figure 2 depicts the hydraulic unitincluding main brake cylinder, hydraulic lines and wheelbrake cylinders.

By means of two magnetic two-way valves each wheel,braking pressure pi, j is modulated.

Three discrete conditions are possible: decreasepressure, hold pressure firm and increase pressure (upto main brake pressure level only).

Each valve is hydraulically connected to the main brakecylinder, to the wheel brake cylinders and to therecirculation.

CG: Center of gravitiy

ax: Longitudinal acceleration

w i,j: Angular wheel frequency

HU: Hydraulic Unit

pi,j: Wheel brake pressure

i: l=left, r=right

j: f=front, r=rear

Figure 2

The knowledge of the actual vehicle speed over ground is

vital in order to calculate wheel slips correctly.

In this approach the speed estimation uses multi sensor

data fusion that means several sensors measure vehicle

speed independently and the estimator decides which

sensor is most reliable.

Figure 3 represents the schematic structure of the fuzzy

estimator. The signals of the four wheel speed sensors w i,j

are used as well as the signal of the acceleration sensor ax.

Figure 3

In the data pre-processing block the measured signals

are filtered by a lowpass and the inputs for the fuzzy

estimator are calculated.

Four wheels slip , and an acceleration value D va are

calculated. The applied formulas are:

whereby aOffset is a correction value consisting of an

offset and a road slope part. It is derived by

comparing the measured acceleration with the

derivative of the vehicle speed v Fuz.

v Fuz(k-1) is the estimated velocity of the previous

cycle.

A time-delay of T is expressed by the term 1/z.

The fuzzy estimator itself is divided into two parts.

The first (Logic 1) determines which wheel sensor is

most reliable, and the second (Logic 2) decides about

the reliability of the integral of the acceleration

sensor, shown in Figure 4.

This cascade structure is chosen to reduce the

number of rules.

Figure 4

Starting at block “Logic 1" and “Logic 2" the crisp inputs arefuzzificated. Figure 5 shows the input-membership-functions (IMF) with four linguistic values (Negative, Zero,Positive and Very Positive)

Figure 5

The rule base consists of 35 rules altogether. To classify thepresent driving condition vehicle acceleration is taken intoconsideration. This should be explained for three situations:

D va Positive: Braking situation, all wheels are weighted lowbecause of wheel slips appearing.

D va Zero: If wheel speeds tend to constant driving theacceleration signal is low weighted in order to adjust thesensor.

D va Negative: The experimental car was rearwheel driventherefore rear wheels are less weighted than front wheels.

Negative Zero Positive

-50 -40 -30 -20 -10 0 10 20 30 40 50

ax corrected

Here, three linguistic values are sufficient. The output of

the estimation is derived as a weighted sum of the wheel

measurement plus the integrated and corrected

acceleration:

The Fuzzy-Controller uses two input values:

The wheel slip SB:

Wheel acceleration α:

with wheel speed vWheel and vehicle speed vFuz, which is given by

the Sensor.

The input variables are transformed into fuzzy variables slip and dvwheel/dt

by the fuzzification process.

Both variables use seven linguistic values, the slip variable is described by

the terms

slip = {zero, very small, too small, smaller than optimum, optimum, too

large, very large}

and the acceleration dvwheel/dt by

dvwheel/dt = {negative large, negative medium, negative small, negative

few, zero, positive small, positive large}.

As a result of two fuzzy variables, each of them having 7 labels,

49 different conditions are possible.

The rule base is complete that means, all 49 rules are formulated

and all 49 conditions are allowed. These rules create a nonlinear

characteristic surface as shown in Figure 3.

Figure 3

Using this characteristic surface, the two fuzzy input values slip

and dvwheel/dt can be mapped to the fuzzy output value pressure.

The labels for this value are:

pressure = {positive fast, positive slow, zero, negative slow,

negative fast}

The optimal breaking pressure results from the defuzzification of

the linguistic variable pressure.

Finally a three-step controller determines the position of the

magnetic valves, whether the pressure should be increased, hold

firm or decreased.

1 Antilock-Braking System and Vehicle Speed

Estimation using Fuzzy Logic

by Ralf Klein

(Paper presented on 1st Embedded Computing Conference,

October 1996, Paris)

2 On Track 2 program by Bosch conducted in

November 2009.