Understanding Automotive
Electronics
An Engineering Perspective


I would like to thank my wife for her outstanding help in preparing this book.
Without her dedication in editing/proofing and correcting errors,
this book would not have been completed. I dedicate this work to her.


Understanding Automotive
Electronics
An Engineering Perspective
Seventh edition
William Ribbens

AMSTERDAM • BOSTON • HEIDELBERG • LONDON
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Contents
Preface .......................................................................................................... xiii
Introduction ..................................................................................................... xv
Chapter 1: The Systems Approach to Control and Instrumentation ........................ 1

Chapter Overview .......................................................................................................1
Concept of a System ...................................................................................................2
Block Diagram Representation of a System .......................................................... 3
Analog (Continuous Time) Systems ....................................................................... 5
Linear System Theory: Continuous Time ..................................................................5
First-Order System .................................................................................................. 9
Second-Order System ........................................................................................... 11
Steady-State Sinusoidal Frequency Response of a System .....................................16
State Variable Formulation of Models .....................................................................17
Control Theory ..........................................................................................................20
Open-Loop Control ............................................................................................... 20
Closed-Loop Control ............................................................................................ 21
Stability of Control System ......................................................................................28
Root-Locus Techniques ........................................................................................ 29
Robustness of Control-System Stability ............................................................... 31
Closed-Loop Limit-Cycle Control ............................................................................34
Instrumentation .........................................................................................................35
Measurement ......................................................................................................... 36
Issues ..................................................................................................................... 36
Systematic Errors .................................................................................................. 37
Basic Measurement System ......................................................................................39
Sensor .................................................................................................................... 40
Random Errors ...................................................................................................... 42
Signal Processing .................................................................................................. 45
Filtering .....................................................................................................................45
Filter-Design Techniques ...................................................................................... 46

v



vi

Contents

Chapter 2: Discrete Time Systems Theory ......................................................... 51
Digital Subsystem .....................................................................................................55
Sinusoidal Frequency Response ...............................................................................56
Discrete Time Control System .................................................................................63
Closed Loop Control .................................................................................................68
Example Discrete Time Control System ..................................................................72
Summary ...................................................................................................................77

Chapter 3: Electronics Fundamentals ................................................................ 79
Semiconductor Devices ............................................................................................80
Diodes ................................................................................................................... 83
Rectifier Circuit ..................................................................................................... 85
Transistors .................................................................................................................87
Field-Effect Transistors ......................................................................................... 96
Integrated Circuits .....................................................................................................99
Operational Amplifiers ...........................................................................................100
Use of Feedback in Op Amps ................................................................................101
Summing Mode Amplifier .................................................................................. 103
Phase-Locked Loop ................................................................................................104
Sample and Zero-Order Hold Circuits ............................................................... 106
Digital Circuits ........................................................................................................111
Binary Number System ...........................................................................................113
Logic Circuits (Combinatorial) ..............................................................................114
NOT Gate ............................................................................................................ 114
AND Gate ........................................................................................................... 115
OR Gate .............................................................................................................. 117

Combination Logic Circuits ............................................................................... 117
Logic Circuits with Memory (Sequential) .............................................................119
ReS Flip-Flop ..................................................................................................... 119
JK Flip-Flop ........................................................................................................ 119
Synchronous Counter ..............................................................................................120
Register Circuits .................................................................................................. 121
Shift Register ...................................................................................................... 122
Integrated Circuits ...................................................................................................124
The Microprocessor ................................................................................................124

Chapter 4: Microcomputer Instrumentation and Control ................................... 127
Microcomputer Fundamentals ................................................................................128
Digital versus Analog Computers ...................................................................... 128


Contents vii
Parts of a Computer ............................................................................................ 129
Microcomputers versus Mainframe Computers ................................................. 130
Programs ............................................................................................................. 130
Microcomputer Tasks ..............................................................................................131
Microcomputer Operations .....................................................................................132
Buses ................................................................................................................... 132
Memory Read/Write ........................................................................................... 133
Timing ................................................................................................................. 134
Addressing Peripherals ....................................................................................... 135
CPU Registers .........................................................................................................135
Accumulator Register ......................................................................................... 136
Condition Code Register ..................................................................................... 136
Microprocessor Architecture .............................................................................. 138
Reading Instructions ...............................................................................................140

Initialization ........................................................................................................ 141
Operation Codes .................................................................................................. 141
Program Counter ................................................................................................. 142
Branch Instruction ............................................................................................... 143
Jump Instruction .................................................................................................. 144
Jump-to-Subroutine Instruction .......................................................................... 144
Example Use of a Microcomputer .........................................................................147
Buffer .................................................................................................................. 147
Programming Languages ........................................................................................148
Assembly Language ............................................................................................ 148
Logic Functions .................................................................................................. 150
Shift ..................................................................................................................... 150
Programming the AND Function ....................................................................... 152
Masking ............................................................................................................... 153
Shift and AND .................................................................................................... 153
Use of Subroutines .............................................................................................. 153
Microcomputer Hardware .......................................................................................154
Central Processing Unit ...................................................................................... 154
Memory: ROM .................................................................................................... 155
Memory: RAM .................................................................................................... 156
I/O Parallel Interface .......................................................................................... 156
Digital-to-Analog Converter ............................................................................... 156
Analog-to-Digital Converter ............................................................................... 159
Sampling ............................................................................................................. 162
Polling ................................................................................................................. 162


viii

Contents

Interrupts ............................................................................................................. 163
Vectored Interrupts .............................................................................................. 163
Microcomputer Applications in Automotive Systems ...........................................164
Instrumentation Applications of Microcomputers .................................................166
Digital Filters ...................................................................................................... 168
Microcomputers in Control Systems ......................................................................170
Closed-Loop Control System ............................................................................. 171
Limit-Cycle Controller ....................................................................................... 171
Feedback Control Systems ................................................................................. 171
Table Lookup ...................................................................................................... 173
Multivariable and Multiple Task Systems .......................................................... 175

Chapter 5: The Basics of Electronic Engine Control .......................................... 177
Motivation for Electronic Engine Control .............................................................178
Exhaust Emissions ..................................................................................................178
Fuel Economy .........................................................................................................179
Federal Government Test Procedures .....................................................................180
Fuel Economy Requirements .............................................................................. 181
Meeting the Requirements .................................................................................. 183
The Role of Electronics ...................................................................................... 184
Concept of an Electronic Engine Control System .................................................184
Inputs to Controller ............................................................................................. 187
Output from Controller ....................................................................................... 188
Definition of Engine Performance Terms ...............................................................193
Torque ................................................................................................................. 193
Power ................................................................................................................... 196
Fuel Consumption ............................................................................................... 198
Engine Overall Efficiency ................................................................................... 200
Calibration ........................................................................................................... 201
Engine Mapping .................................................................................................. 201

Effect of Air/Fuel Ratio on Performance ........................................................... 202
Effect of Spark Timing on Performance ............................................................ 203
Effect of Exhaust Gas Recirculation on Performance ....................................... 204
Exhaust Catalytic Converters .................................................................................206
Oxidizing Catalytic Converter ............................................................................ 206
The Three-Way Catalyst ..................................................................................... 207
Electronic Fuel-Control System .............................................................................209
Engine Control Sequence ................................................................................... 212
Open-Loop Control ............................................................................................. 213


Contents ix
Closed-Loop Control .......................................................................................... 213
Closed-Loop Operation ....................................................................................... 215
Analysis of Intake Manifold Pressure ....................................................................219
Measuring Air Mass ........................................................................................... 220
Influence of Valve System on Volumetric Efficiency ........................................ 223
Idle Speed Control ..................................................................................................224
Electronic Ignition ..................................................................................................230

Chapter 6: Sensors and Actuators .................................................................. 233
Automotive Control System Applications of Sensors and Actuators ....................234
Variables to be Measured .................................................................................... 236
Airflow Rate Sensor ............................................................................................ 236
Pressure Measurements ....................................................................................... 242
Engine Crankshaft Angular Position Sensor ...................................................... 245
Magnetic Reluctance Position Sensor ................................................................ 247
Hall-Effect Position Sensor ................................................................................ 259
Optical Crankshaft Position Sensor .................................................................... 263
Throttle Angle Sensor .............................................................................................265

Temperature Sensors ...............................................................................................268
Typical Coolant Sensor ...........................................................................................268
Sensors for Feedback Control ................................................................................270
Exhaust Gas Oxygen Sensor ............................................................................... 270
Oxygen Sensor Improvements ............................................................................ 274
Knock Sensors ........................................................................................................276
Automotive Engine Control Actuators ...................................................................279
Fuel Injection ...................................................................................................... 284
Exhaust Gas Recirculation Actuator .................................................................. 286
Variable Valve Timing ............................................................................................288
VVP Mechanism Model ..................................................................................... 290
Electric Motor Actuators ........................................................................................292
Brushless DC Motors .......................................................................................... 301
Stepper Motors .................................................................................................... 304
Ignition System .......................................................................................................304
Ignition Coil Operations ..................................................................................... 305

Chapter 7: Digital Powertrain Control Systems ............................................... 309
Introduction .............................................................................................................310
Digital Engine Control ............................................................................................310
Digital Engine Control Features .............................................................................312


x

Contents
Control Modes for Fuel Control .............................................................................316
Engine Start ......................................................................................................... 317
Open-Loop Mode ................................................................................................ 317
Acceleration/Deceleration ................................................................................... 317

Engine Crank ...................................................................................................... 319
Engine Warm-Up ................................................................................................ 320
Open-Loop Control ............................................................................................. 322
Closed-Loop Control .......................................................................................... 323
Acceleration Enrichment .................................................................................... 328
Deceleration Leaning .......................................................................................... 328
Idle Speed Control .............................................................................................. 329
Discrete Time Idle Speed Control ..........................................................................329
EGR Control ...........................................................................................................335
Variable Valve Timing Control ...............................................................................337
Electronic Ignition Control .....................................................................................343
Closed-Loop Ignition Timing ............................................................................. 347
Spark Advance Correction Scheme .................................................................... 353
Integrated Engine Control System ..........................................................................354
Secondary Air Management ............................................................................... 354
Evaporative Emissions Canister Purge ............................................................... 355
Automatic System Adjustment ........................................................................... 356
System Diagnosis ................................................................................................ 356
Summary of Control Modes ...................................................................................357
Engine Crank (Start) ........................................................................................... 357
Engine Warm-Up ................................................................................................ 357
Open-Loop Control ............................................................................................. 357
Closed-Loop Control .......................................................................................... 358
Hard Acceleration ............................................................................................... 358
Deceleration and Idle .......................................................................................... 359
Automatic Transmission Control ........................................................................ 359
Torque Converter Lock-Up Control ................................................................... 366
Differential and Traction Control ....................................................................... 366
Hybrid Electric Vehicle Powertrain Control ...................................................... 368


Chapter 8: Vehicle-Motion Controls ................................................................ 381
Representative Cruise Control System ...................................................................382
Digital Cruise Control ........................................................................................ 390
Hardware Implementation Issues ....................................................................... 394
Throttle Actuator ................................................................................................. 396
Cruise Control Electronics ......................................................................................400


Contents xi
Stepper Motor-based Actuator Electronics ........................................................ 401
Vacuum-Operated Actuator ................................................................................ 403
Advanced Cruise Control ................................................................................... 406
Antilock Braking System ........................................................................................410
Tire-Slip Controller ............................................................................................. 420
Electronic Suspension System ................................................................................420
Variable Damping via Variable Strut Fluid Viscosity ........................................ 442
Variable Spring Rate ........................................................................................... 443
Electronic Suspension Control System .............................................................. 444
Electronic Steering Control ....................................................................................446
Four-Wheel Steering ...............................................................................................449
Summary .................................................................................................................457

Chapter 9: Automotive Instrumentation and Telematics .................................... 459
Modern Automotive Instrumentation .....................................................................460
Input and Output Signal Conversion ......................................................................463
Multiplexing ........................................................................................................ 465
Multirate Sampling ............................................................................................. 468
Advantages of Computer-Based Instrumentation ..................................................469
Display Devices ......................................................................................................470
LED ..................................................................................................................... 474

LCD ..................................................................................................................... 476
Transmissive LCD .............................................................................................. 480
VFD ..................................................................................................................... 480
Flat Panel Display ...................................................................................................483
Fuel Quantity Measurement ...................................................................................491
Coolant Temperature Measurement ........................................................................497
Oil Pressure Measurement ......................................................................................498
Vehicle Speed Measurement ...................................................................................500
High-Speed Digital Communications (CAN) ........................................................502
CAN Network ..................................................................................................... 504
Trip Information Computer ....................................................................................507
Telematics ...............................................................................................................510
GPS Navigation ......................................................................................................511
The GPS System Structure .....................................................................................516
Automotive Diagnostics ..........................................................................................519

Chapter 10: Diagnostics and Occupant Protection ............................................ 521
Electronic Control System Diagnostics ..................................................................522


xii

Contents
Service Bay Diagnostic Tool ..................................................................................524
Onboard Diagnostics ...............................................................................................525
Model-Based Sensor Failure Detection ..................................................................526
Diagnostic Fault Codes ...........................................................................................529
Onboard Diagnosis (OBD II) .................................................................................543
Model-Based Misfire Detection System .................................................................544
Expert Systems in Automotive Diagnosis ..............................................................555

Occupant Protection Systems .................................................................................561

Glossary ....................................................................................................... 569
Quiz questions .............................................................................................. 573
Index ........................................................................................................... 589


Preface
The present edition of this book is an extensive revision of the previous editions based upon
suggestions of reviewers. The present edition has a strong engineering focus including
analytical models and quantitative performance analysis of electronic components/
subsystems and systems found in contemporary automobiles. However, the largely qualitative
explanations of automotive electronic systems from previous editions has been retained and,
in some cases, expanded wherever it has been possible to do so.
It has been the intention in writing this book to make it accessible to readers who have not had
the formal training in physical sciences and mathematics (as well as those who have) to
understand the functional operation of automotive electronic systems. The author
recommends that such individuals lacking the science background skip over the mathematical
portions of the text and concentrate on the qualitative discussion and verbal explanations
preceding and following the mathematical sections of the book.
It is hoped that the mathematical models and performance analyses presented throughout this
book will be informative to readers with backgrounds in the sciences, engineering and/or
mathematics. There may even be engineers/scientists working within the automotive industry
for whom a detailed discussion of electronic subsystems and components will be useful.
The first chapter in previous editions presented an overview of basic functional components
of an automobile. This chapter has been removed, although a shortened version of the
explanation of certain automotive components and subsystems (e.g., engine, drivetrain,
braking, steering etc.) is presented as deemed necessary in the new chapters of this edition.
There are some topics in the present edition of this book that were not covered in detail in any
of the previous editions. These include the theory of electric motors, which find application in

hybrid/electric vehicles. Telematics, which is an increasingly important automotive
technology, is covered in considerable detail (including the theory of GPS navigation
systems). In addition, the theory of onboard diagnosis of problems with exhaust emission
control systems is presented for the first time in any of the editions of this book.
It has been the intent in writing this book to emphasize the fundamental aspects of the
application of electronics to automobiles. Ideally, if this objective has been achieved, the
reader should understand evolving technologies as well as totally new automotive electronic
technologies as they occur in future vehicles.
xiii


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Introduction
This book covers the general topic of the application of electronics in automobiles and light
trucks. Some of the technology described herein is also found in large trucks and other land
vehicles, although these applications are not explicitly discussed.
The only important use of electronics in automobiles through the late 1950s was the broadcast
band radio receiver, which was based upon vacuum tube technology. The development of
solid-state electronics, from the first transistors through the latest high performance integrated
circuits, came at a time that permitted the very sophisticated electronic systems discussed in
this book to be applied to solving automotive control and instrumentation problems.
The book is organized in a way that allows the reader to select his/her own desired starting
point depending upon background and/or experience. The first two chapters provide a review
of linear system theory at the level found throughout the remainder of the book.
The new first and second chapters present a survey of various aspects of linear system theory.
The new first chapter discuses continuous time (analog) theory and the new second chapter
discuses discrete time (digital) system theory. Neither of these two chapters has sufficient
breadth or depth to serve as a full ab initio presentation of system theory. For many readers,

they will be redundant. Nevertheless, they provide a review of linear system theory and
introduce notation that is used throughout this book.
Chapter 3 discusses the basics of solid-state active elements (e.g. diodes and various types of
transistors) along with circuits that form the basic building blocks of automotive electronic
systems. Chapter 4 discusses microprocessors/microcontrollers and certain fundamental
aspects of their application in automotive electronic systems. Chapter 5 presents the
fundamentals of electronic engine control. Chapter 6 surveys sensors and actuators found in
automotive electronic control or instrumentation systems that are arguably the most important
components in such systems. The remaining chapters discuss specific automotive systems
that incorporate electronics for control or instrumentation purposes. The automotive
components/systems covered include engine, drivetrain, suspension, steering, brakes,
instrumentation, telematics and diagnostics as well as motion control. All of the mathematical
models and performance analyses are given in terms of the theory and methods of the first and
second chapters. Extensive use is made of contemporary computer simulation.
xv


xvi

Introduction

Specific examples are presented for most electronic systems/components for which
component models and performance analyses are given. These examples are based upon
simplified models and linear system theory such that the basic principles involved are
illustrated without the cumbersome mathematical details (and nonlinearities) that are often
found in the analysis of practical production vehicle systems.
Furthermore, the examples given in this book of any component/system are representative of
those found in any production vehicle. Proprietary issues prohibit the detailed discussion of
such production items. In addition, the technology of automotive electronics found in
production vehicles is constantly evolving and any detailed discussion of a given vehicle

electronic system as of the writing of this book might well be obsolete in the next model year.
There is an important notational issue concerning the analytical portions of this book. There
are many variables and parameters involved in the various components/systems discussed in
each chapter. The symbols used in this book include upper and lower case Roman and Greek
(often subscripted) letters. However, the reader should be aware that these symbols do not
have a global definition throughout the book. Rather, each symbol is defined for the section of
the book in which it is used.
The units and dimensions for variables discussed in this book are English in keeping with
earlier editions, even though the worldwide automotive industry uses essentially all metric
units. However, conversion tables from English to metric units are readily available.
Moreover, those readers in the USA, having relatively limited backgrounds in the physical
sciences, are likely to be more familiar with English rather than metric units. Readers having
backgrounds in the sciences will find unit conversion straightforward.


CHAPTER 1

The Systems Approach to Control
and Instrumentation
Chapter Outline
Chapter Overview 1
Concept of a System 2
Block Diagram Representation of a System 3
Analog (Continuous Time) Systems 5

Linear System Theory: Continuous Time

5

First-Order System 9

Second-Order System 11

Steady-State Sinusoidal Frequency Response of a System
State Variable Formulation of Models 17
Control Theory 20

16

Open-Loop Control 20
Closed-Loop Control 21

Stability of Control System

28

Root-Locus Techniques 29
Robustness of Control-System Stability

Closed-Loop Limit-Cycle Control
Instrumentation 35

31

34

Measurement 36
Issues 36
Systematic Errors 37

Basic Measurement System


39

Sensor 40
Random Errors 42
Signal Processing 45

Filtering 45
Filter-Design Techniques

46

Chapter Overview
This book discusses the application of electronics in automobiles from the standpoint of
electronic systems and subsystems. In a sense, the systems approach to describing automotive
electronics is a way of organizing the subject into its component parts based on functional
Understanding Automotive Electronics. />Copyright Ó 2012 Elsevier Inc. All rights reserved.

1


2

Chapter 1

groups. This chapter will lay the foundation for this discussion by explaining the concepts of
a system and a subsystem and how such systems function and interact with one another. The
means for characterizing the performance of any system will be explained so that the reader
will understand some of the relative benefits and limitations of automotive electronic systems.
This chapter will explain, generally, what a system is and, more precisely, what an electronic

system is. In addition, basic concepts of electronic systems that are applicable to all
automotive electronic systems, such as structure (architecture) and quantitative performance
analysis principles, will be discussed. In the general field of electronic systems (including
automotive systems), there are three major categories of function, including control,
measurement, and communication.
Two major classes of electronic systems e analog or continuous time and digital or discrete
time e will be explained. In most cases, it is theoretically possible to implement a given
electronic system as either an analog or a digital system. The relatively low cost of digital
electronics coupled with the high performance achievable relative to analog electronics has
led modern automotive electronic system designers to choose digital rather than analog
realizations for new systems.

Concept of a System
A system is a collection of components that function together to perform a specific task.
Various systems are encountered in everyday life. It is common practice to refer to the bones
of the human body as the skeletal system. The collection of highways linking the country’s
population centers is known as the interstate freeway system.
Electronic systems are similar in the sense that they consist of collections of electronic and
electrical parts interconnected in such a way as to perform a specific function. The
components of an electronic system include transistors, diodes, resistors, and capacitors, as
well as standard electrical parts such as switches and connectors among others. All these
components are interconnected with individual wires or with printed circuit boards. In
addition, many automotive electronic systems incorporate specialized components known as
sensors or actuators that enable the electronic system to interface with the appropriate
automotive mechanical systems. Systems can often be broken down into subsystems. The
subsystems also consist of a number of individual parts.
Any electronic system can be described at various levels of abstraction, from a pictorial
description or a schematic drawing at the lowest level to a block diagram at the highest level.
For the purposes of this chapter, this higher-level abstraction is preferable. At this level, each
functional subsystem is characterized by inputs, outputs, and the relationship between input

and output. Normally, only the system designer or maintenance technician would be
concerned with detailed schematics and the internal workings of the system. Furthermore, the


The Systems Approach to Control and Instrumentation 3
only practical way to cover the vast range of automotive electronic systems is to limit our
discussion to this so-called system level of abstraction. It is important for the reader to realize
that there are typically many different circuit configurations capable of performing a given
function.

Block Diagram Representation of a System
At the level of abstraction appropriate for the present discussion, a block diagram will
represent the electronic system. Depending on whether a given electronic system application
is to (a) control, (b) measure, or (c) communicate, it will have one of the three block diagram
configurations shown in Figure 1.1. The designer of a system often begins with a block
diagram, in which major components are represented as blocks.
In block diagram architecture, each functional component or subsystem is represented by an
appropriately labeled block. The inputs and outputs for each block are identified. In electronic
systems, these input and output variables are electrical signals, except for the system input
and system output. One benefit of this approach is that the subsystem operation can be

(a)

(b)

(c)

Figure 1.1:
Electronic system block diagrams variable being controlled.



4

Chapter 1

described by functional relationships between input and output. There is no need to describe
the operation of individual transistors and components within the blocks at this block diagram
level.
In the performance analysis of an existing system or in the design of a new one, the system or
subsystem is represented by a mathematical model that is derived from its physical
configuration. Normally, this model is derived from known models of each of its constituent
parts, i.e., its basic physics. Initially, this chapter will consider components, subsystems, and
system blocks that can be represented by a linear mathematical model. Later in the chapter,
the treatment of nonlinearities is discussed.
For a block having input x(t) and output y(t) that can be represented by a linear model, the
model is of the form of a differential equation of the form
ao y þ a1

dy
dn y
dx
dm x
þ . an n ¼ bo x þ b1 . bm m
dt
dt
dt
dt

(1)


Typically, n ! m and such a system block or component is said to be of order n. Analysis of
this block is accomplished by calculating its output y(t) for an arbitrary (but physically
realizable) input x(t). The performance of such a block in an automotive system normally
involves finding its response to certain physically meaningful inputs. Such analysis is
explained later in this chapter.
Figure 1.1a depicts the architecture or configuration for a control application electronic system.
In such a system, control of a physical subsystem (called the plant) occurs by regulating some
physical variable (or variables) through an actuator. An actuator is an energy conversion device
having an electrical input and an output of the physical form required to vary the plant (e.g.,
mechanical energy) as required to perform the desired system function output. Thus, an
actuator has an electrical input and an output that may be mechanical, pneumatic, hydraulic,
chemical, or so forth. The plant being controlled varies in response to changes in the actuator
output. The control is determined by electronic signal processing based on measurement of
some variable (or variables) by a sensor in relationship to a command input by the operator of
the system (i.e., by the driver in an automotive application).
In an electronic control system, the output of the sensor is always an electrical signal (denoted
e1 in Figure 1.1). The input is the desired value of the physical variable in the plant being
controlled. The electronic signal processing generates an output electrical signal (denoted e2
in Figure 1.1) that operates the actuator. The signal processing is designed to achieve the
desired control of the plant in relation to the variable being measured by the sensor. The
operation of such a control system is described later in this chapter. At this point, we are
interested only in describing the control-system architecture. A redundant explanation of
electronic control is presented later in this chapter.


The Systems Approach to Control and Instrumentation 5
The architecture for electronic measurement (also known as instrumentation) is similar to that
for a control system in the sense that both structures incorporate a sensor and electronic signal
processing. However, instead of an actuator, the measurement architecture incorporates
a display device. A display is an electromechanical or electro-optical device capable of

presenting numerical values to the user (driver). In automotive electronic measurement, the
display is sometimes simply a fixed message rather than a numeric display. Nevertheless, the
architecture is as shown in Figure 1.1b. It should be noted that both control and
instrumentation electronic systems use one or more sensors as well as electronic signal
processing.
Figure 1.1c depicts a block diagram for a communication system. In such a system, data or
messages are sent from a source to a receiver over a communication channel. This particular
architecture is sufficiently general that it can accommodate all communication systems from
ordinary car radios to digital data buses between multiple electronic systems on cars, as well
as extravehicular communication. Communication systems are described in detail later in this
chapter.

Analog (Continuous Time) Systems
Modern automotive digital electronic systems have virtually completely replaced analog
systems. Whereas digital systems are represented by discrete time models, analog systems are
represented by continuous time models having a form such as is given in Eqn (1). Normally
automotive electronic systems incorporate components (e.g., sensors and actuators) that are
best characterized by continuous time models. Typically, only the electronic portion is best
characterized by discrete time models. Furthermore, even the digital electronics can be
represented by an equivalent continuous time model, which can be converted to a discrete
time equivalent readily. Consequently, this discussion begins with a brief overview of linear
continuous time system theory. The discrete time system theory is reviewed in the next
chapter.

Linear System Theory: Continuous Time
The performance of a continuous time block (i.e., component/system) is found from the
solution to the differential equation Eqn (1) for a specific input. One straightforward method
of solving this equation is to take the Laplace transform of each term. The Laplace transform
(also denoted xðsÞ ¼ L ½xðtÞŠÞ of the input is denoted x(s) and is defined as following the
linear integral transform of its time domain representation:

ZN
xðsÞ ¼
o


e Àst xðtÞdt þ xðtÞt¼0

(2)


6

Chapter 1

where
s ¼ s þ ju ¼ complex frequency
and where
j¼

pffiffiffiffiffiffiffi
À1

(3)

Similarly, the Laplace transform of the block output is denoted y(s) and is given by
ZN
yðsÞ ¼


e Àst yðtÞdt þ yðtÞt¼0


(4)

o

The differential equation model for a given continuous time block includes time derivatives of
the input and output. The Laplace transform of the time derivative of order m of a variable
(e.g., the input) is given by
ZN

e Àst

dm x
dt ¼ sm xðsÞ
dtm

m ¼ 1; 2.

(5)

o

Assuming for simplicity that the initial conditions for both input and output are zero,

yðtÞ t¼0 ¼ 0


xðtÞ t¼0 ¼ 0;

the Laplace transform of the differential equation (Eqn (1)) for the block yields

Â

Ã
a0 þ a1 s þ a2 s2 / an sn yðsÞ ¼ ½b0 þ b1 s þ / bm sm ŠxðsÞ

(6)

It is conventional for the purpose of conducting analysis for continuous time systems to define
the transfer function (H(s)) for each block:
HðsÞ ¼

yðsÞ
xðsÞ

b0 þ b1 s þ / bm sm
¼
a0 þ a1 s þ / an sn

(7)

The transfer function concept is highly useful for continuous time linear system analysis
since the transfer function for any such system made up of a cascade connection of K blocks
(e.g., as depicted in Figure 1.2) is the product of the transfer functions of the individual
blocks.


The Systems Approach to Control and Instrumentation 7

Figure 1.2:
System cascade connection block diagram.


Denoting the transfer function of the kth block Hk(s), and for the complete system H(s), the
latter is given by
K
Y
Hk ðsÞ
(8)
HðsÞ ¼
k¼1

An alternate, highly useful, formulation of the transfer function is based on the roots of
equations formed from its numerator and denominator polynomials. The roots zj of the
numerator polynomial (PN(s)) are the m solutions to the equation
PN ðsÞ ¼ b0 þ b1 s þ / bm sm ¼ 0

(9)

where
PN ðzj Þ ¼ 0

j ¼ 1; 2.m

are called the zeros of the transfer function. Similarly, the roots pi of the denominator
polynomial (PD(s)) are the n solutions to the equation
PD ðsÞ ¼ a0 þ a1 s þ / an sn ¼ 0

(10)

where
PD ðpi Þ ¼ 0


i ¼ 1; 2.n

are called the poles of the transfer function. For a system that is stable, all poles and zeros
have negative real parts (i.e., s < 0) or, equivalently, all poles and zeros of a stable system lie
in the left half of the complex s-plane. The dynamic response of the block to any input is
determined by its poles and zeros.
The alternate form for H(s) in terms of its poles and zeros is given by
m
Q

HðsÞ ¼

j¼1
n
Q
i¼1

ðs À zj Þ
(11)
ðs À pi Þ


8

Chapter 1

The time domain response of a continuous time block to any given input is given by the
inverse Laplace transform of Y(s). One method of computing this inverse Laplace transform
uses the residue theorem of complex analysis. The block output Y(s) is given as

YðsÞ ¼ HðsÞXðsÞ

(12)

The residue theorem expresses the output time domain in terms of the poles and zeros of the
product H(s)X(s) and includes the poles and zeros of H(s) as well as any zeros and poles of the
input:
m
Q
ðs À zj Þ
YðsÞ ¼

j¼1
n
Q

i¼1

(13)
ðs À pi Þ

Assuming that all of the poles are distinct (i.e., pj 6¼ pk unless j ¼ k), the time domain output
is given by
N

X

ðs À pk ÞHðsÞXðsÞ e pk t
(14)
yðtÞ ¼

s/pk

k¼1

In evaluating this expression, the pole at s ¼ pk is canceled by the term (s À pk) in the
remaining portion of H(s)X(s). That is, each pole of the product contributes an exponential
term to the output.
The above formula for calculating the output time domain is, in fact, the inverse Laplace
transform of y(s) denoted:
yðtÞ ¼ L

À1

½Yðsފ

(15)

The formula given above for calculating the inverse transform is known as the residue
theorem.
The inverse Laplace transform of a system transfer function H(s) is known as its impulse
response. It is denoted h(t) and is given by the inverse Laplace transform of H(s):
hðtÞ ¼ L

À1

½Hðsފ

(16)

It is the response of a linear system to a unit impulse. The output of a linear system can be

found from its impulse response by the so-called convolution theorem which is given as
follows:
ZN
hðsÞ x ðt À sÞds
(17)
yðtÞ ¼
ÀN