Pimpri Chinchwad Education Trust’s

Pimpri Chinchwad college of Engineering

Department of Electronics and Telecommunication

UNIT-3 Vehicle Motion Control

Syllabus:
1. Typical Cruise Control System
2. Digital Cruise Control System
3. Digital Speed Sensor
4. Throttle Actuator
5. Digital Cruise Control Configuration
6. Cruise Control Electronics(Digital Only)
7. Anti-lock Braking system
Vehicle Motion Control
• Vehicle motion refers to the translation along and rotation about all three axes(i.e
longitudinal, lateral, and vertical).
• Longitudinal axes means the axis is parallel to the ground(vehicle at rest) on a
horizontal plane along the length of the car.
• Lateral axis is orthogonal to the longitudinal axis and is also parallel to the
ground(vehicle at rest).
• The vertical axis is orthogonal to both the longitudinal and lateral axes.
• Rotations of the vehicle around these three axes correspond to angular displacement of
the car body in roll, yaw, and pitch.
• Roll refers to angular displacement about the longitudinal axis; Yaw refers to angular
displacement about vertical axis; and pitch refers to angular displacement about lateral
axis.
Typical Cruise Control System
• In cruise control, the variable being regulated is the vehicle speed.
• The driver manually sets the car speed at the desired value via the accelerator
pedal.
• Upon reaching the desired speed the driver activates a momentary contact switch
that sets that speed as the command input to the control system.
• From that point on, the cruise control system maintains the desired speed
automatically by operating the throttle via a throttle actuator.
• which drives the vehicle through the drive axles and wheels.
• The load on this plant includes friction and aerodynamic drag as well as a portion
of the vehicle weight when the car is going up and down hills.
 Cruise Control Configuration
• The momentary contact (push-button) switch that sets the command speed is denoted S1
• A disable switch that completely disengages the cruise control system from the power
supply such that throttle control reverts back to the accelerator pedal.
• This switch is denoted S2 and is a safety feature.
• In an actual cruise control system the disable function can be activated in a variety of
ways, including the master power switch for the cruise control system, and a brake
pedal–activated switch that disables the cruise control any time that the brake pedal is
moved from its rest position.

Fig 1: Cruise Control Configuration

The configuration for a typical automotive cruise control is
shown in the Figure below:
Close loop control configuration
• In a closed loop control system a measurement of a output variable
being controlled is obtained via a sensor and fed back to the controller
• The measured value of the controlled variable is compared with the
desired value for that variable based on the reference input.
• An error signal based on the difference between desired and actual
values of the output signal is created, and the controller generates an
actuator signal u that tends to reduce the error to zero.
• In addition to reducing this error to zero, feedback has other potential
benefits in a control system.
• It can affect control system performance by improving system stability
and suppressing the effects of disturbances in the system.
• Electronic control systems are classified by the way in which the error
signal is processed to generate the control signal.
• The major control systems include proportional, proportional-integral,
and proportional-integral-differential controllers.
 Cruise Control System
• Keeps vehicle's speed constant.
• Prevents driver fatigue.
• Not suitable for all road conditions.
• Ambiguously classified as Non-Safety-Critical.
• Below the set speed, interlocking switches and control logic
prevent the cruise control from being switched ON.
• Above the set speed, the choice to engage cruise control rests with
the driver.
• Kicks out of action immediately a very modest touch of braking is
applied.
• Not considered safe in heavy traffic, on bends, on wet or icy roads
etc.
• https://youtube.com/watch?v=EoA7CAcKkWM
• https://www.youtube.com/watch?v=lTRnRVzs5jk
 Cruise Control System
• The brain of a cruise control system is a small computer that is
normally found under the hood or behind the dashboard. It
connects to the throttle control, as well as several sensors. The
diagram below shows the inputs and outputs of a typical cruise
control system.
• A good cruise control system accelerates aggressively to the
desired speed without overshooting, and then maintains that
speed with little deviation no matter how much weight is in the
car, or how steep the hill you drive up. Controlling the speed of
a car is a classic application of control system theory.
• The cruise control system controls the speed of the car by
adjusting the throttle position, so it needs sensors to tell it the
speed and throttle position. It also needs to monitor the controls
so it can tell what the desired speed is and when to disengage.
Cruise Control Configuration
• When the vehicle reaches the desired speed under normal driver accelerator pedal
regulation of the throttle, to activate cruise control at that speed the driver pushes
a momentary contact switch thereby setting the command speed in the controller.
At this point, control of the throttle position is via the cruise control actuator. The
momentary contact (pushbutton) switch that sets the command speed is denoted
S1.
• A disable switch that completely disengages the cruise control system from the
power supply such that throttle control reverts back to the accelerator pedal. This
switch is denoted S2 is a safety feature.
• In an actual cruise control system, the disable function can be activated in a
variety of ways, including the master power switch for the cruise control system
and a brake pedal-activated switch that disables the cruise control any time that
the brake pedal is moved from its rest position.
• The throttle actuator opens and closes the throttle in response to the error between
the desired and actual speed. Whenever the actual speed is less than the desired
speed, the throttle opening is increased by the actuator, which increases vehicle
speed, until the error is zero at which point the throttle opening remains fixed until
either a disturbance occurs or the driver calls for a new desired speed
 Cruise Control Block Diagram
• The throttle actuator opens and closes the throttle in response to the error between the desired and actual
speed.
• Whenever the actual speed is less than the desired speed the throttle opening is increased by the actuator,
which increases vehicle speed until the error is zero, at which point the throttle opening remains fixed
until either a disturbance occurs or the driver calls for a new desired speed.
• A block diagram of a cruise control system is shown in the figure below:

Fig 2: Cruise Control Block Diagram

 Cruise Control Block Diagram
• In the cruise control depicted in this figure, a proportional integral (PI) control strategy has been
assumed.
• The PI controller is representative of good design for such a control system since it can reduce speed
errors due to disturbances (such as hills) to zero
• In this strategy an error e is formed by subtracting (electronically) the actual speed Va from the
desired speed Vd:

• The controller then electronically generates the actuator signal by combining a term proportional to
the error (KPe) and a term proportional to the integral of the error :

• The actuator signal u is a combination of these two terms:

 Cruise Control Block Diagram
• The throttle opening is proportional to the value of this actuator signal.
• We assume that the driver has reached the desired speed (say, 60 mph) and activated the speed
set switch.
• If the car is traveling on a level road at the desired speed, then the error is zero and the throttle
remains at a fixed position.
• If the car were then to enter a long hill with a steady positive slope (i.e., a hill going up) while
the throttle is set at the cruise position for level road, the engine will produce less power than
required to maintain that speed on the hill.
• The hill represents a disturbance to the cruise control system.
• The vehicle speed will decrease, thereby introducing an error to the control system.
• This error, in turn, results in an increase in the signal to the actuator, causing an increase in
engine power. This increased power results in an increase in speed.
• However, in a proportional control system the speed error is not reduced to zero since a
• The speed response to the disturbance is shown in the Figure below:

Fig 3: Cruise Control Speed Performance

• When the disturbance occurs, the speed drops off and the control system reacts
immediately to increase power.
• However, a certain amount of time is required for the car to accelerate toward the desired
speed.
• As time progresses, the speed reaches a steady value that is less than the desired speed,
thereby accounting for the steady error (es) depicted (i.e., the final speed is less than the
starting 60 mph).
• If we now consider a PI control system, we will see that the steady error when integrated
produces an ever-increasing output from the integrator.
• This increasing output causes the actuator to increase further, with a resulting speed increase.

• In this case the actuator output will increase until the error is reduced to zero. The response of
the cruise control with PI control is shown in figure (b) above.
Cruise Control Block Diagram
• The response characteristics of a PI controller depend
strongly on the choice of the gain parameters KP and KI.
• It is possible to select values for these parameters to
increase the speed of the system response to disturbance.
• If the speed increases too rapidly, however, overshoot will
occur and the actual speed will oscillate around the desired
speed.
• The amplitude of oscillations decreases by an amount
determined by a parameter called the damping ratio
• The damping ratio that produces the fastest response
without overshoot is called critical damping.
• A damping ratio less than critically damped is said to be
under-damped, and one greater than critically damped is
said to be over-damped.
Speed Response Curves
• The curves of Figure ( c) above, show the response of a cruise control system with a PI control
strategy to a sudden disturbance.
• These curves are all for the same car cruising initially at 60 mph along a level road and
encountering an up-sloping hill.
• The only difference in the response of these curves is the controller gain parameters.
• The importance of these performance curves is that they demonstrate how the performance of a
cruise control system is affected by the controller gains.
• These gains are simply parameters that are contained in the control system.
• They determine the relationship between the error, the integral of the error, and the actuator control
signal.
• The system designer chooses the control electronics that provide the following system qualities:
• 1. Quick response
• 2. Relative stability
• 3. Small steady-state error
• 4. Optimization of the control effort required
Adaptive Cruise Control
• The concept of assisting driver in the task of longitudinal vehicle control is known as cruise control.
• The idea of driver assistance was started with the ‘cruise control devices’ first appeared in 1970’s in USA.
• Starting from the cruise control devices of the seventies and eighties, now the technology has reached cooperative
adaptive cruise control.
• Everyday the media brings us the horrible news on road accidents. Once a report said that the damaged property and
other costs may equal 3 % of the world’s gross domestic product.
• The death on the street account for more that 17% of total death around the world.
• The conventional cruise control was capable only to maintain a set speed by accelerating or decelerating the vehicle.
• Adaptive cruise control devices are capable of assisting the driver to keep a safe distance from the preceding vehicle
by controlling the engine throttle and brake according to the sensor data about the vehicle.
 Definition and Physical Overview
• Adaptive Cruise Control (ACC) – An enhancement to a
conventional cruise control system which allows the ACC
vehicle to follow a forward vehicle at an appropriate distance.
• ACC vehicle – the subject vehicle equipped with the ACC
system.
• Active brake control – a function which causes application of
the brakes without driver application of the brake pedal.
• Clearance – distance from the forward vehicle's trailing surface
to the ACC vehicle's leading surface.
• Forward vehicle – any one of the vehicles in front of and
moving in the same direction and traveling on the same roadway
as the ACC vehicle.
• Set speed – the desired cruise control travel speed set by the
driver and is the maximum desired speed of the vehicle while
under ACC control.
 System states
• ACC off state – direct access to the 'ACC active' state is
disabled.
• ACC standby state – system is ready for activation by the
driver.
• ACC active state – the ACC system is in active control of the
vehicle's speed.
• ACC speed control state – a substate of 'ACC active' state in
which no forward vehicles are present such that the ACC system
is controlling vehicle speed to the 'set speed' as is typical with
conventional cruise control systems.
• ACC time gap control state – a substate of 'ACC active' state in
which time gap, or headway, between the ACC vehicle and the
target vehicle is being controlled.
• Target vehicle – one of the forward vehicles in the path of the
ACC vehicle that is closest to the ACC vehicle.
• Time gap – the time interval between the ACC vehicle and the
target vehicle. The 'time gap' is related to the 'clearance' and
vehicle speed by:
time gap = clearance / ACC vehicle speed
How ACC works?
 Adaptive Cruise Control
• Change gear automatically
• Function properly in poor weather condition
• Cannot pick up non-moving objects
• Effective in the speed between 30km-180km/h
► Preset and maintain the car speed
► Measure the distance to the preceding car and the
relative speed
► Adjust the car speed accordingly
► Maximum deceleration = 3.5m/s^2
► ACC automatically adjusts the speed of your car to
match the speed of the car in front of you.
Adaptive Cruise Control System
• Conventional Cruise Control can maintain a steady speed that you set. Adaptive cruise control (ACC) is
an enhancement of conventional cruise control. ACC automatically adjusts the speed of your car to
match the speed of the car in front of you.
• If the car ahead slows down, ACC can automatically match it. Once the car ahead moves out of your
lane or accelerates beyond your car’s set speed, your ACC allows your car to return to the speed that
you have set. Other than setting your speed, you only need to turn on the system and select your
preferred following distance.
• ACC systems use onboard computers and sophisticated sensors, such as radar or laser systems, to
monitor the other vehicles on the road. Because of this, adaptive cruise control is also called radar cruise
control or autonomous cruise control .
• Once the driver locks his or her preferred speed into the ACC system, the vehicle will monitor its
surroundings. The system runs a signal from its radar headway system through a digital signal processor
to determine the distance to the nearest car, and it then uses a longitudinal controller to determine a safe
following distance.
Adaptive Cruise Control System
Adaptive Cruise Control System
• Like standard cruise control systems, ACC keeps your car at
the speed you set, as long as there is nothing in front of you. A
sensor unit is added to determine the distance between your
car and other cars in front you.
• Speed and distance sensors. ACC uses information from two
sensors: a distance sensor that monitors the gap to the car
ahead and a speed sensor that automatically accelerates and
decelerates your car. ACC uses information from these
sensors to adjust your speed and maintain the set distance
from the car in front of you.
• Looking under the hood: Radar-based systems. Let’s take a
look at one ACC technology: radar-based ACC. Some ACC
systems send radar waves that reflect off objects in front of
your car. Based on the radar reflection, ACC uses distance,
direction and relative speed to detect if the car is within the
distance you set. ACC predicts the path of your car and then
decides whether any of the vehicles ahead are within your set
distance.
 Advantages & Disadvantages of ACC
Advantages:
• The driver is relieved from the task of careful acceleration, deceleration and braking in
congested traffics.
• A highly responsive traffic system that adjusts itself to avoid accidents can be developed.
• Since the breaking and acceleration are done in a systematic way, the fuel efficiency of the
vehicle is increased.
Disadvantages:
• A cheap version is not yet realized.
• A high market penetration is required if a society of intelligent vehicles is to be formed.
• Encourages the driver to become careless. It can lead to severe accidents if the system is
malfunctioning.
 Digital Cruise Control System
• Cruise control is now mostly implemented digitally using a microprocessor-based
controller.
• For such a system, proportional and integral control computations are performed
numerically in the computer.
• The vehicle speed sensor is digital
• The digital cruise control is inherently a discrete time system with samples of the vehicle
speed taken at integer multiples of the sample period Ts. The block diagram for a
representative digital cruise control is shown in below figure.
• The system maintains a fixed speed and distance from both your vehicle and the vehicle
in front of you. If the system starts sensing a slow down in traffic the car is able to
progressively slow down the car and bring it to a complete stop and is able to resume the
speed of traffic based on the condition
Digital cruise control system Block Diagram
 Digital Cruise Control System
• The vehicle speed sensor is digital. When the car reaches the desired speed, Sd, the driver
activates the speed set switch. At this time, the output of the vehicle speed sensor is
transferred to a storage register
• The computer continuously reads the actual vehicle speed, V, and generates an error, en,
at the sample time, tn tn : en= Sd–Sa at time tn.
• A control signal, un, is computed that has the following form:
 Digital Cruise Control System
• The vehicle speed sensor and the actuator are analog and can either be modeled as
continuous or discrete time devices and the control system is digital.
• The plant variable being controlled is its forward speed V. The desired speed or set
point for the controller is denoted Vd. The model for the plant as represented by its
transfer function Hp(s) is taken to be the same as that developed above for the analog
version of the cruise control. However, the actuator signal which is the ZOH output u(t)
is a piecewise continuous signal.
• When the car reaches the desired speed, Vd, the driver activates the speed set switch. At
this time, the output of the vehicle speed sensor is sampled, converted to a digital value
and transferred to a storage register. This is the set point for the controller.
•
 Digital Speed Sensor
•In a representative vehicle speed measurement system, the
vehicle speed information is mechanically coupled to the speed
sensor by a flexible cable coming from the driveshaft, which
rotates at an angular speed proportional to vehicle speed.
•A speed sensor driven by this cable generates a pulsed electrical
signal that is processed by the computer to obtain a digital
measurement of speed.
Digital Speed Sensor Configuration
•
Digital Speed Measurement System
• The output pulses are passed through a sample gate to a binary counter.
• The gate is an electronic switch that either passes the pulses to the counter or blocks their
passage depending on whether the switch is closed or open. The time interval during
which the gate is closed is precisely controlled by the computer.
• The digital counter counts the number of pulses from the light detector during time Tg(n)
that the gate is closed and pulses from the sensor are sent to the counter during the nth
speed measurement cycle. The number of pulses P(n) that is counted by the digital counter
is given by
P(n)=Tg(n)NVK
• That is, the number P(n) is proportional to vehicle speed V at speed sample n. The
electrical signal in the binary counter is in a digital format that is suitable for reading by
the cruise control computer.
 Throttle Actuator
• The throttle actuator is an electromechanical device that, in response to an electrical input from
the controller (u), moves the throttle through some appropriate mechanical linkage. Two relatively
common throttle actuators operate either from manifold vacuum or with a stepper motor.
• The throttle opening is either increased or decreased by the stepper motor in response to the
sequences of pulses sent to the two windings depending on the relative phase of the two sets of
pulses.
• This throttle actuator is operated by manifold vacuum through a solenoid valve, which is similar
to that used for the EGR valve. During cruise control operation, the throttle position is set
automatically by the throttle actuator in response to the actuator signal generated in the control
system. This type of manifold-vacuum-operated actuator.
• A pneumatic piston arrangement is driven from the intake manifold vacuum. The piston
connecting rod assembly is attached to the throttle lever. There is also a spring attached to the
lever. If there is no force applied by the piston, the spring pulls the throttle closed.
• When an actuator input signal energizes the electromagnet in the control solenoid, the pressure
control valve is pulled down and changes the actuator cylinder pressure p by providing a path to
manifold pressure pm. Manifold pressure is lower than atmospheric pressure pa, so the actuator
cylinder pressure quickly drops, causing the piston to pull against the throttle lever to open the
throttle.
Vacuum-operated Throttle Actuator
• Although the actuation signal is a binary-valued voltage, the actuator can be considered an
analog device with actuation proportional to the pulse duty cycle.
Vacuum-operated Throttle Actuator
•
Vacuum-operated Throttle Actuator
•
Vacuum-operated Throttle Actuator
•
CRUISE CONTROL ELECTRONICS
• Cruise control can be implemented electronically in various ways, including with a
microcontroller with special-purpose digital electronics or with analog electronics.
• It can also be implemented (in proportional control strategy alone) with an
electromechanical speed governor.
• The physical configuration for a digital, microprocessor-based cruise control is
depicted in figure below:
CRUISE CONTROL ELECTRONICS
• A system such as is depicted in the figure is often called a microcontroller since it is
implemented with a microprocessor operating under program control.
• The actual program that causes the various calculations to be performed is stored in read-only
memory (ROM).
• Typically the ROM also stores parameters that are critical to the correct calculations.
• Normally a relatively small-capacity RAM memory is provided to store the command speed and
to store any temporary calculation results.
• Input from the speed sensor and output to the throttle actuator are handled by the I/O interface
(normally an integrated circuit that is a companion to the microprocessor).
• The output from the controller (i.e., the control signal) is sent via the I/O (on one of its output
ports) to so called driver electronics.
• The latter electronics receives this control signal
• and generates a signal of the correct format and power level to operate the actuator.
• A microprocessor-based cruise control system performs all of the required control law
computations digitally under program control.
 CRUISE CONTROL ELECTRONICS
• For example, a PI control strategy is implemented as explained above, with a
proportional term and an integral term that is formed by a summation.
• In performing this task the controller continuously receives samples of the speed error
en, and where n is a counting index
(n = 1, 2, 3, 4, . . .).
• This sampling occurs at a sufficiently high rate to be able to adjust the control signal to
the actuator in time to compensate for changes in operating condition or to disturbances.
• At each sample the controller reads the most recent error.
• That error is multiplied by a constant KP that is called the proportional gain, yielding
the proportional term in the control law.
• It also computes the sum of a number of previous error samples (the exact sum is chosen
by the control system designer in accordance with the desired steady-state error).
 CRUISE CONTROL ELECTRONICS
• Then this sum is multiplied by a constant KI and added to the proportional
term, yielding the control signal.
• The control signal at this point is simply a number that is stored in a
memory location in the digital controller.
• The use of this number by the electronic circuitry that drives the throttle
actuator to regulate vehicle speed depends on the configuration of the
particular control system and on the actuator used by that system.
1. Stepper Motor-Based Actuator
• In the case of a stepper motor actuator, the actuator driver electronics reads this
number and then generates a sequence of pulses to the pair of windings on the
stepper motor (with the correct relative phasing) to cause the stepper motor to
either advance or retard the throttle setting as required to bring the error toward
zero.
• An illustrative example of driver circuitry for a stepper motor actuator is shown
in Figure below:
Stepper Motor Actuator for Cruise Control
• The basic idea for this circuitry is to continuously drive the stepper motor to advance or
retard the throttle in accordance with the control signal that is stored in memory.
• Just as the controller periodically updates the actuator control signal, the stepper motor
driver electronics continually adjusts the throttle by an amount determined by the
actuator signal.
• This signal is, in effect, a signed number (i.e., a positive or negative numerical value).
• A sign bit indicates the direction of the throttle movement (advance or retard).
• The numerical value determines the amount of advance or retard.
• The magnitude of the actuator signal (in binary format) is loaded into a parallel load
serial down-count binary counter.
• The direction of movement is in the form of the sign bit SB.
• The stepper motor is activated by a pair of quadrature phase signals (i.e., signals that are
a quarter of a cycle out of phase) coming from a pair of oscillators.
• To advance the throttle, phase A signal is applied to coil 1 and phase B to coil 2.
• To retard the throttle these phases are each switched to the opposite coil.
 Stepper Motor Actuator for Cruise Control
• The amount of movement in either direction is determined by the number of cycles of A and B, one step for
each cycle.
• The number of cycles of these two phases is controlled by a logical signal Z.
• This logical signal is switched high, enabling a pair of AND gates (from the set A1, A2, A3, A4).
• The length of time that it is switched high determines the number of cycles and corresponds to the number of
steps of the motor.
• The logical variable Z corresponds to the contents of the binary counter being zero.
• As long as Z is not zero, a pair of AND gates (A1 and A3, or A2 and A4) is enabled, permitting phase A and
phase B signals to be sent to the stepper motor.
• The pair of gates enabled is determined by the sign bit.
• When the sign bit is high, A1 and A3 are enabled and the stepper motor advances the throttle as long as Z is
not zero
 Stepper Motor Actuator for Cruise Control
• Similarly, when the sign bit is low, A2 and A4 are enabled and the stepper motor retards the throttle.
• To control the number of steps, the controller loads a binary value into the binary counter.
• With the contents not zero the appropriate pair of AND gates is enabled.
• When loaded with data, the binary counter counts down at the frequency of a clock Ck.
• When the countdown reaches zero, the gates are disabled and the stepper motor stops moving.
• The time required to count down to zero is determined by the numerical value loaded into the binary
counter.
• By loading signed binary numbers into the binary counter, the cruise controller regulates the amount and
direction of movement of the stepper motor and thereby the corresponding movement of the throttle.
 ANTILOCK BRAKING SYSTEM
• One of the most readily accepted applications of electronics in automobiles has been the antilock brake
system (ABS).
• ABS is a safety-related feature that assists the driver in deceleration of the vehicle in poor or marginal
braking conditions (e.g., wet or icy roads).
• In such conditions, panic braking by the driver (in non-ABS-equipped cars) results in reduced braking
effectiveness and, typically, loss of directional control due to the tendency of the wheels to lock.
• In ABS-equipped cars, the wheel is prevented from locking by a mechanism that automatically regulates
braking force to an optimum for any given low-friction condition.
• The physical configuration for an ABS is shown in Figure below.
• In addition to the normal brake components, including brake pedal, master cylinder, vacuum boost, wheel
cylinders, calipers/disks, and brake lines, this system has a set of angular speed sensors at each wheel, an
electronic control module, and a hydraulic brake pressure modulator (regulator).
• Figure below illustrates the forces applied to the wheel by the road during braking.
ANTILOCK BRAKING SYSTEM
• The car is traveling at a speed U and the wheels are rotating at an angular speed w where

and where RPM is the wheel revolutions per minute.

 ANTILOCK BRAKING SYSTEM
• When the wheel is rolling (no applied brakes),
where R is the radius
• When the brake pedal is depressed, the calipers are forced by hydraulic pressure against the disk,
• This force acts as a torque Tb in opposition to the wheel rotation.
• The actual force that decelerates the car is shown as Fb
ANTILOCK BRAKING SYSTEM
• The lateral force that maintains directional control of the car is shown as FL in Figure.
• The wheel angular speed begins to decrease, causing a difference between the vehicle speed U and the
tire speed over the road (i.e., wR). slips relative to the road surface.
• The amount of slip (S ) determines the braking force and lateral force.
• The slip, as a percentage of car speed, is given by

• Note: A rolling tire has slip S = 0, and a fully locked tire has S = 100%.
ANTILOCK BRAKING SYSTEM
• The braking and lateral forces are proportional to the normal force (from the weight of the car) acting on
the tire/road interface and the friction coefficients for braking force (Fb) and lateral force (FL):

Where μb is the braking friction coefficient, μL is the lateral friction

coefficient.
• These coefficients depend markedly on slip, as shown in Figure
ANTILOCK BRAKING SYSTEM
• The solid curves are for a dry road and the dashed curves for a wet or icy road.
• As brake pedal force is increased from zero, slip increases from zero.
• For increasing slip, μb increases to S = So.
• Further increase in slip actually decreases μb, thereby reducing braking effectiveness.
• On the other hand, μL decreases steadily with increasing S such that for fully locked wheels the lateral
force has its lowest value.
• For wet or icy roads, μL at S = 100% is so low that the lateral force is insufficient to maintain
directional control of the vehicle.
• However, directional control can often be maintained even in poor braking conditions if slip is optimally
controlled.
• This is essentially the function of the ABS, which performs an operation equivalent to pumping the
brakes as done by experienced drivers before the development of ABS.
ANTILOCK BRAKING SYSTEM
• In ABS-equipped cars under marginal or poor braking conditions, the driver simply applies a steady
brake force and the system adjusts tire slip to optimum value automatically.
• In a typical ABS configuration, control over slip is effected by controlling the brake line pressure under
electronic control.
• The configuration for ABS is shown in Figure below:
• This ABS regulates or modulates brake pressure to maintain slip as near to optimum as possible e.g., at
So
• The operation of this ABS is based on estimating the torque Tw applied to the wheel at the road surface
by the braking force Fb:

• In opposition to this torque is the braking torque Tb applied to the disk by the calipers in response to
brake pressure P:

where kb is a constant for the given brakes.

ANTILOCK BRAKING SYSTEM
• The difference between these two torques acts to decelerate the wheel.
• In accordance with basic Newtonian mechanics, the wheel torque Tw is related to braking torque and
wheel deceleration by the following equation:

where Iw is the wheel moment of inertia is the wheel deceleration (dw/dt, that is, the rate of change of
wheel speed)
• During heavy braking under marginal conditions, sufficient braking force is applied to cause wheel
lock-up (in the absence of ABS control).
• As brake pressure is applied, Tb increases and w decreases, causing slip to increase.
• The wheel torque is proportional to μb, which reaches a peak at slip So.
• Consequently, the wheel torque reaches a maximum value (assuming sufficient brake force is applied) at
this level of slip.
ANTILOCK BRAKING SYSTEM
• Figure below is a sketch of wheel torque versus slip illustrating the peak Tw.

• After the peak wheel torque is sensed electronically, the electronic control system commands that brake
pressure be reduced (via the brake pressure modulator).
ANTILOCK BRAKING SYSTEM
• This point is indicated as the limit point of slip for the ABS.
• As the brake pressure is reduced, slip is reduced and the wheel torque again passes through a maximum.
• The wheel torque reaches a value below the peak on the low slip side and at this point brake pressure is
again increased.
• The system will continue to cycle, maintaining slip near the optimal value as long as the brakes are
applied and the braking conditions are poor.
• The mechanism for modulating brake pressure is illustrated in Figure
ANTILOCK BRAKING SYSTEM
• The numbers in figure (a) refer to the following:
• 1. Applied master cylinder pressure
• 2. Bypass brake fluid
• 3. Normally open solenoid valve
• 4. EMB braking action
• 5. DC motor pack
• 6. ESB braking
• 7. Gear assembly
• 8. Ball screw
• 9. Check valve unseated
• 10. Outlet to brake cylinders
• 11. Piston
ANTILOCK BRAKING SYSTEM
• The numbers in figure (b) refer to the following:
• 1. Trapped bypass brake fluid
• 2. Solenoid valve activated
• 3. EMB action released
• 4. DC motor pack
• 5. ESB braking action released
• 6. Gear assembly
• 7. Ball screw
• 8. Check valve seated
• 9. Applied master cylinder pressure
• Under normal braking, brake pressure from the master cylinder passes without reduction
through the passageways associated with check valve 9 and solenoid valve 3 in figure (a).
ANTILOCK BRAKING SYSTEM
• Whenever the wheel slip limit is reached, the solenoid valve is closed and the piston (11) retracts,
closing the check valve.
• This action effectively isolates the brake cylinders from the master cylinder, and brake line pressure is
controlled by the position of piston 11.
• For example, should the driver release the brake pedal, then the pressure at the inlet (1) is reduced.
• At this point, the check valve (9) opens and brake line pressure is also removed.
• The solenoid valve opens and the piston returns to its normal position (fully up) such that the check
valve is held open.
• Figure below illustrates the braking during an ABS action.
• In this illustration, the vehicle is initially traveling at 55 mph and the brakes are applied as indicated by
the rising brake pressure.
ANTILOCK BRAKING SYSTEM
• The wheel speed begins to drop until the slip limit is reached.
• At this point, the ABS reduces brake pressure and the wheel speed increases
• With the high applied brake pressure, the wheels again tend toward lock-up and ABS reduces brake
pressure.
• The cycle continues until the vehicle is stopped.
• It should be noted that by maintaining slip near So, the maximum deceleration is achieved for a given set
of conditions.
ANTILOCK BRAKING SYSTEM
• Some reduction in lateral force occurs from its maximum value by maintaining slip near So.
• However, in most cases the lateral force is large enough to maintain directional control.
• In some antilock brake systems, the slip oscillations are shifted below So, sacrificing some braking
effectiveness to enhance directional control.
• This can be accomplished by adjusting the upper and lower slip limits.
THANK YOU