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# Understanding Automotive Electronics 8th - Chapter 7

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The term vehicle motion refers to the translation along and rotation about all three axes (i.e., longitudinal, lateral, and vertical) for a vehicle. By the term longitudinal axis, we mean the axis that is parallel to the ground (vehicle at rest) on a horizontal plane along the length of the car. The 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.

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CHAPTER

VEHICLE MOTION CONTROLS

7

CHAPTER OUTLINE

Representative Cruise Control System ................................................................................................. 344

Digital Cruise Control ........................................................................................................... 351

Hardware Implementation Issues .......................................................................................... 354

Throttle Actuator ................................................................................................................. 356

Cruise Control Electronics .................................................................................................................. 359

Stepper Motor-Based Actuator Electronics ............................................................................. 360

Vacuum-Operated Actuator ................................................................................................... 362

Advanced Cruise Control ...................................................................................................... 364

Antilock Braking System .................................................................................................................... 368

Tire Slip Controller .............................................................................................................. 377

Electronic Suspension System ............................................................................................................ 377

Variable Damping via Variable Strut Fluid Viscosity ................................................................ 395

Variable Spring Rate ............................................................................................................ 396

Electronic Suspension Control System ................................................................................................. 397

Electronic Steering Control ................................................................................................... 398

Four-Wheel Steering Car .................................................................................................................... 401

Summary ........................................................................................................................................... 408

The term vehicle motion refers to the translation along and rotation about all three axes (i.e., longitu-

dinal, lateral, and vertical) for a vehicle. By the term longitudinal axis, we mean the axis that is parallel

to the ground (vehicle at rest) on a horizontal plane along the length of the car. The 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 the vertical axis; and pitch refers to angular displacement about the

lateral axis.

In characterizing the vehicle dynamic motion, it is common practice to define a body-centered

Cartesian coordinate system in which the x-axis is the longi tudinal axis with positive forward. The

y-axis is the lateral axis and is taken as the lateral axis with the positive sense to the right-hand side

(RHS). The vertical axis is taken as the z-axis with the positive sense up.

Understanding Automotive Electronics. http://dx.doi.org/10.1016/B978-0-12-810434-7.00007-7

Copyright # 2017 Elsevier Inc. All rights reserved.

343

The vehicle dynamic motion is represented as displacement, velocity, and acceleration of the ve-

hicle relative to an earth-centered, earth-fixed (ECEF) inertial coordinate system (as will be explained

later in this chapter) in response to forces acting on it. Although strictly speak ing, the ECEF coordinate

system is not tru ly an inertial reference, with respect to the types of motion of interest in most vehicle

dynamics, it is essentially an inertial reference system.

Electronic controls have been recently developed with the capability of regulating the motion along

and about all three axes. Individual car models employ variou s selected combinations of these controls.

This chapter discusses motion control electronics beginning with control of motion along the longitu-

dinal axis in the form of a cruise control system.

The forces and moments/torque that influence vehicle motion along the longitudinal axis include

those due to the power train (including, in selected models and traction control), the brakes, the aero-

dynamic drag, and the tire-rolling resistance, as well as the influence of gravity when the car is moving

on a road with a nonzero inclination (or grade). In a traditional cruise control system, the tractive force

due to the power train is balanced against all resisting forces to maintain a constant speed. In an

advanced cruise control (ACC) system, brakes are also automatically applied as required to maintain

speed when going down a hill of sufficiently steep grade . Longitudinal vehicle motion refers to trans-

lation of the vehicle in an ECEF y-z plane.

REPRESENTATIVE CRUISE CONTROL SYSTEM

Automotive cruise control is an excellent example of the type of electronic feedback control system

that is discussed in general terms in Appendix A. It is explained in Appendix A that the components of a

closed-loop control system include the plant or system being controlled and a sensor for measuring the

plant variable being regulated. It also includes an electronic control system that receives inputs in the

form of the desired value of the regulated variable and the measured value of that variable from the

sensor. The control system generates an error signal constituting the difference between the desired

and actual values of this variable. It then generates an output from this error signal that drives an elec-

tromechanical actuat or. The actuator controls the input to the plant in such a way that the regulated

plant variable is moved toward the desired value.

We begin with a simplified traditional cruise control for a vehicle traveling along a straight road

(along the x-axis in our ECEF coordinate system). An ACC is explained in a later section of this

chapter. In the case of a traditional cruise control, the variable being regulated is the vehicle speed:

V ¼

dx

dt

where x is the translation of the vehicle in the ECEF frame.

The driver manually sets the car speed at the desired value via the accelerator pedal. Upon reaching

the desired speed (V

d

), the driver activates a momentary contact switch that sets that speed as the com-

mand input to the control system. From that point on, the cruise control system maintai ns the desired

speed automatically by operating the throttle via a throttle actuator.

Under normal driving circumstances, the total external forces acting on the vehicle are such that a

net positive traction force (from the power train) is required to maintain a constant vehicle speed. The

total external forces acting on the vehicle include rolling resistance of the tires, aerodynamic drag, and a

component of vehicle weight whenever the vehicle is traveling on a road with a slope relative to level.

344 CHAPTER 7 VEHICLE MOTION CONTROLS

However, when the car is on a downward sloping road of sufficient grade, drag, and tire-rolling resis-

tance are insufficient to prevent vehicle acceleration (i.e.,

_

V > 0) and maintaining a constant vehicle

speed requires a negative tractive force that the power train cannot deliver. In this case, the car will

accelerate unless brakes are applied. For our initial discussion, we assume this latter condition does

not occur and that no braking is required. It is further assumed that the power train has sufficient power

capability of maintaining constant vehicle speed on an up-sloping grade.

The plant being controlled consists of the power train (i.e., engine and drivetrain), which propels the

vehicle through the drive axles and wheels. As described above, the load on this plant include s friction

and aerodynamic drag as well as a portion of the vehicle weight when the car is going up- and

downhills.

For an understanding of the dynamic performance of a cruise control, it is helpful to devel op a

model for vehicle motion along a road. The basic performance of a cruise control can be presented

with a few simplifying assumptions. In the interest of safety, a typical traditional cruise control cannot

be activated below a certain speed (e.g., 40 mph). For the purposes of presenting the present somewhat

simplified model, it is assumed that the vehicle is traveling along a straight road at a cruise speed with

the automatic transmission in torque converter lockup mode (see Chapter 6). This assumption removes

some power train dynamics from the model. It is further assumed that the transmission is in direct drive

such that its gear ratio is 1. The total gear ratio is given by the differential/transaxle gear ratio g

A

where

typically 2:8 g

A

4:0. Under this assumption, the torque applied to the drive wheels T

w

is given by

T

w

¼g

A

T

b

(7.1)

where T

b

is the engine brake torque.

The cruise control system employs an actuator that moves the throttle in response to the control

signal. Of course whenever the cruise control is disconnected (e.g., by brake application), this actuator

must release control of the throttle such that the driver controls throttle angular position via the accel-

erator pedal and associated linkage. Except for roads with relatively steep grades, normally, once cruise

control is activated relatively small, changes in throttle position are required to maintain selected

vehicle speed. For our simplified model, we assume that T

b

varies linearly with cruise control output

electrical signal u:

T

b

¼K

a

u (7.2)

where K

a

is a constant for the engine/throttle actuator. This assumption, though not strictly valid,

permits a system performance analysis using the discussion of linear control theory of Appendix A

without any serious loss of generality.

A vehicle traveling along a straight road at speed V experiences forces due to the wheel torque T

w

,

aerodynamic drag D tire-rolling resistance F

rr

, and inertial forces. A dynamic model for the vehicle

longitudinal speed in m/s or ft/s (i.e., along the direction of travel and vehicle fore/aft axis) is given by

M

_

V + D + F

rr

¼

g

A

T

b

r

w

W

V

sinθ (7.3)

where

M ¼vehicle mass

W

V

¼vehicle weight (Mg)

g ¼gravitational constant (e.g., 9.81 m/s

2

or 32 ft/s

2

)

r

w

¼drive wheel effective radius

345REPRESENTATIVE CRUISE CONTROL SYSTEM

F

rr

¼μ

rr

W

V

μ

rr

¼coefficient of tire-rolling resistance

0:02 μ

rr

0:04 typically

θ ¼angle of the road surface relative to a horizontal plane

Drag force D ¼

ρ

2

C

D

S

ref

V + V

w

ðÞ

2

ρ ¼air density

C

D

¼drag coefficient

S

ref

¼reference area

V

w

¼the component of wind along vehicle longitudinal axis (positive for head wind negative

for tail wind).

In specifying a drag coefficient for a car, it is necessary to specify a reference area. Although the choice

of S

ref

is somewhat arbitrary, conventional practice takes the largest vehicle cross-sectional area

projected in a body y-z plane. In the above nonlinear differential Eq. (7.3), the first term on the

RHS is the force acting on the vehicle due to the applied road torque acting at the tire/road interface

due to the power train, and g

A

is the combined gear ratio from the engine to the drive axle. The second

term on the RHS is the component of force along the vehicle axis due to its weight and any road slope

expressed by θ.

For a car traveling at constant cruise speed V

C

(i.e.,

_

V ¼0) along a level, horizontal road (i.e., θ ¼0)

with zero wind, the differential equation above reduces to an algebra ic expression in terms of the engine

brake torque and speed V

C

:

ρ

C

D

S

ref

2

V

2

C

+ μ

rr

W

V

¼g

A

T

b

r

w

(7.4)

This equation permits a determination of engine brake torque versus cruise speed for a level road.

If the vehicle is traveling at a steady speed along a hill with slope angle θ, then the T

b

is determined

from the following equation:

g

A

T

b

r

w

¼ρ

C

D

S

ref

V

2

C

2

+ μ

rr

W

V

+ Mgsinθ (7.5)

For the operation of the cruise control system, it is normally sufficient to model vehicle dynamics with a

linearized version of the nonlinear differential equation. The drag term can be linearized by represent-

ing vehicle instantane ous speed (V(t)) with the approximate model assuming for simplicity that V

w

¼0:

D ¼D

C

+ δD

VtðÞ¼V

C

+ δV

(7.6)

where D

C

is the drag at speed V

C

:

δD ¼

dD

dV

V

C

δV

¼ρC

D

S

ref

V

C

δV

¼K

D

δV

346 CHAPTER 7 VEHICLE MOTION CONTROLS

where K

D

is a constant for a given initial steady cruise speed V

C

and constant ρ and δV is the variation in

speed about V

C

.

In modeling the cruise control system, it is helpful to consider the influence of road grade (θ)asa

disturbance. This distur bance can be linearized to a close approximation by the substitution (provided

that the slope of the hill is sufficiently small):

sinθ θ

The linearized equation of motion is given by

Mδ

_

V + ρC

D

S

ref

V

C

δV Mgθ ¼g

A

δT

b

r

w

(7.7)

The operational transfer function H

p

(s) for the “plant” for zero disturbance (i.e., θ ¼0) is given by

H

p

sðÞ¼

δVsðÞ

δT

b

sðÞ

¼

g

A

= Mr

w

ðÞ

s + ρ

C

D

S

ref

V

C

M

(7.8)

The configuration for a representative automotive cruise control is shown in Fig. 7.1.

When the vehicle reaches the desired speed V

d

under normal driver accelerator pedal regulation of

the throttle, to activate cruise control at that speed the driver pushes a momentary contact switch S

1

in

Fig. 7.1, 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 (push-button) switch that sets the

command speed (V

d

) is denoted S

1

in Fig. 7.1 .

Also shown in this figure is a disengage 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 S

2

in Fig. 7.1 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 disengages the cruise control any time that the brake pedal is moved

from its rest position.

Actual

speed

Command

speed

Electrical

power

Air

Throttle

Controller

Engine

drivetrain

Control

signal

Throttle

actuator

Speed

sensor

To drive

axles

V

S

1

S

2

FIG. 7.1 Cruise control configuration.

347REPRESENTATIVE CRUISE CONTROL SYSTEM

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