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    Vehicle Dynamicsand Control
    Preface
    Acknowledgments
    Contents
    Chapter 1 INTRODUCTION
    1.1 DRIVER ASSISTANCE SYSTEMS
    1.2 ACTIVE STABILITY CONTROL SYSTEMS
    1.3 RIDE QUALITY
    1.4 TECHNOLOGIES FOR ADDRESSING TRAFFIC CONGESTION
    1.4.1 Automated highway systems
    1.4.2 “Traffic-friendly” adaptive cruise control
    1.4.3 Narrow tilt-controlled commuter vehicles
    1.5 EMISSIONS AND FUEL ECONOMY
    1.5.1 Hybrid electric vehicles
    1.5.2 Fuel cell vehicles
    REFERENCES
    Chapter 2 LATERAL VEHICLE DYNAMICS
    2.1 LATERAL SYSTEMS UNDER COMMERCIAL DEVELOPMENT
    2.1.1 Lane departure warning
    2.1.2 Lane keeping systems
    2.1.3 Yaw stability control systems
    2.2 KINEMATIC MODEL OF LATERAL VEHICLE MOTION
    2.3 BICYCLE MODEL OF LATERAL VEHICLE DYNAMICS
    2.4 MOTION OF A PARTICLE RELATIVE TO A ROTATING FRAME
    2.5 DYNAMIC MODEL IN TERMS OF ERROR WITH RESPECT TO ROAD
    2.6 DYNAMIC MODEL IN TERMS OF YAW RATE AND SLIP ANGLE
    2.7 FROM BODY FIXED TO GLOBAL COORDINATES
    2.8 ROAD MODEL
    2.9 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 3 STEERING CONTROL FOR AUTOMATED LANE KEEPING
    3.1 STATE FEEDBACK
    3.2 STEADY STATE ERROR FROM DYNAMIC EQUATIONS
    3.3 UNDERSTANDING STEADY STATE CORNERING
    3.3.1 Steering angle for steady state cornering
    3.3.2 Can the yaw-angle error be zero ?
    3.3.3 Is non-zero yaw angle error a concern ?
    3.4 CONSIDERATION OF VARYING LONGITUDINAL VELOCITY
    3.5 OUTPUT FEEDBACK
    3.6 UNITY FEEDBACK LOOP SYSTEM
    3.7 LOOP ANALYSIS WITH A PROPORTIONAL CONTROLLER
    3.8 LOOP ANALYSIS WITH A LEAD COMPENSATOR
    3.9 SIMULATION OF PERFORMANCE WITH LEAD COMPENSATOR
    3.10 ANALYSIS OF CLOSED-LOOP PERFORMANCE
    3.10.1 Performance variation with vehicle speed
    3.10.2 Performance variation with sensor location
    3.11 COMPENSATOR DESIGN WITH LOOK-AHEAD SENSOR MEASUREMENT
    3.12 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 4 LONGITUDINAL VEHICLE DYNAMICS
    4.1 LONGITUDINAL VEHICLE DYNAMICS
    4.1.1 Aerodynamic drag force
    4.1.2 Longitudinal tire force
    4.1.3 Why does longitudinal tire force depend on slip ?
    4.1.4 Rolling resistance
    4.1.5 Calculation of normal tire forces
    4.1.6 Calculation of effective tire radius
    4.2 DRIVELINE DYNAMICS
    4.2.1 Torque converter
    4.2.2 Transmission dynamics
    4.2.3 Engine dynamics
    4.2.4 Wheel Dynamics
    4.3 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 5 INTRODUCTION TO LONGITUDINAL CONTROL
    5.1 INTRODUCTION
    5.1.1 Adaptive cruise control
    5.1.2 Collision avoidance
    5.1.3 Automated highway systems
    5.2 BENEFITS OF LONGITUDINAL AUTOMATION
    5.3 CRUISE CONTROL
    5.4 UPPER LEVEL CONTROLLER FOR CRUISE CONTROL
    5.5 LOWER LEVEL CONTROLLER FOR CRUISE CONTROL
    5.5.1 Engine Torque Calculation for Desired Acceleration
    5.5.2 Engine Control
    5.6 ANTI-LOCK BRAKE SYSTEMS
    5.6.1 Motivation
    5.6.2 ABS Functions
    5.6.3 Deceleration Threshold Based Algorithms
    5.6.4 Other Logic Based ABS Control Systems
    5.6.5 Recent Research Publications on ABS
    5.7 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 6 ADAPTIVE CRUISE CONTROL
    6.1 INTRODUCTION
    6.2 VEHICLE FOLLOWING SPECIFICATIONS
    6.3 CONTROL ARCHITECTURE
    6.4 STRING STABILITY
    6.5 AUTONOMOUS CONTROL WITH CONSTANT SPACING
    6.6 AUTONOMOUS CONTROL WITH THE CONSTANT TIME-GAP POLICY
    6.6.1 String stability of the CTG spacing policy
    6.6.2 Typical delay values
    6.7 TRANSITIONAL TRAJECTORIES
    6.7.1 The need for a transitional controller
    6.7.2 Transitional controller design through R . R. diagrams
    6.8 LOWER LEVEL CONTROLLER
    6.9 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    APPENDIX 6.A
    Chapter 7 LONGITUDINAL CONTROL FOR VEHICLE PLATOONS
    7.1 AUTOMATED HIGHWAY SYSTEMS
    7.2 VEHICLE CONTROL ON AUTOMATED HIGHWAY SYSTEMS
    7.3 LONGITUDINAL CONTROL ARCHITECTURE
    7.4 VEHICLE FOLLOWING SPECIFICATIONS
    7.5 BACKGROUND ON NORMS OF SIGNALS AND SYSTEMS
    7.5.1 Norms of signals
    7.5.2 System norms
    7.5.3 Use of induced norms to study signal amplification
    7.6 DESIGN APPROACH FOR ENSURING STRING STABILITY
    7.7 CONSTANT SPACING WITH AUTONOMOUS CONTROL
    7.8 CONSTANT SPACING WITH WIRELESS COMMUNICATION
    7.9 EXPERIMENTAL RESULTS
    7.10 LOWER LEVEL CONTROLLER
    7.11 ADAPTIVE CONTROL FOR UNKNOWN VEHICLE PARAMETERS
    7.11.1 Redefined notation
    7.11.2 Adaptive controller
    7.12 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    APPENDIX 7.A
    Chapter 8 ELECTRONIC STABILITY CONTROL
    8.1 INTRODUCTION 8.1.1 The functioning of a stability control system
    8.1.2 Systems developed by automotive manufacturers
    8.1.3 Types of stability control systems
    8.2 DIFFERENTIAL BRAKING SYSTEMS
    8.2.1 Vehicle model
    8.2.2 Control architecture
    8.2.3 Desired yaw rate
    8.2.4 Desired side-slip angle
    8.2.5 Upper bounded values of target yaw rate and slip angle
    8.2.6 Upper controller design
    8.2.7 Lower controller design
    8.3 STEER-BY-WIRE SYSTEMS
    8.3.1 Introduction
    8.3.2 Choice of output for decoupling
    8.3.3 Controller Design
    8.4 INDEPENDENT ALL WHEEL DRIVE TORQUE DISTRIBUTION
    8.4.1 Traditional four wheel drive systems
    8.4.2 Torque transfer between left and right wheels using a differential
    8.4.3 Active Control of Torque Transfer To All Wheels
    8.5 NEED FOR SLIP ANGLE CONTROL
    8.6 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 9 MEAN VALUE MODELING OF SI AND DIESEL ENGINES
    9.1 SI ENGINE MODEL USING PARAMETRIC EQUATIONS
    9.1.1 Engine rotational dynamics
    9.1.2 Indicated combustion torque
    9.1.3 Friction and pumping losses
    9.1.4 Manifold pressure equation
    9.1.5 Outflow rate ao m. from intake manifold
    9.1.6 Inflow rate m. ai into intake manifold
    9.2 SI ENGINE MODEL USING LOOK-UP MAPS
    9.2.1 Introduction to engine maps
    9.2.2 Second order engine model using engine maps
    9.2.3 First order engine model using engine maps
    9.3 INTRODUCTION TO TURBOCHARGED DIESEL ENGINES
    9.4 MEAN VALUE MODELING OF TURBOCHARGED DIESEL ENGINES
    9.4.1 Intake manifold dynamics
    9.4.2 Exhaust manifold dynamics
    9.4.3 Turbocharger dynamics
    9.4.4 Engine crankshaft dynamics
    9.4.5 Control system objectives
    9.5 LOWER LEVEL CONTROLLER WITH SI ENGINES
    9.6 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 10 DESIGN AND ANALYSIS OF PASSIVE AUTOMOTIVE SUSPENSIONS
    10.1 INTRODUCTION TO AUTOMOTIVE SUSPENSIONS
    10.1.1 Full, half and quarter car suspension models
    10.1.2 Suspension functions
    10.1.3 Dependent and independent suspensions
    10.2 MODAL DECOUPLING
    10.3 PERFORMANCE VARIABLES FOR A QUARTER CAR SUSPENSION
    10.4 NATURAL FREQUENCIES AND MODE SHAPES FOR THE QUARTER CAR
    10.5 APPROXIMATE TRANSFER FUNCTIONS USING DECOUPLING
    10.6 ANALYSIS OF VIBRATIONS IN THE SPRUNG MASS MODE
    10.7 ANALYSIS OF VIBRATIONS IN THE UNSPRUNG MASS MODE
    10.8 VERIFICATION USING THE COMPLETE QUARTER CAR MODEL
    10.8.1 Verification of the influence of suspension stiffness
    10.8.2 Verification of the influence of suspension damping
    10.8.3 Verification of the influence of tire stiffness
    10.9 HALF-CAR AND FULL-CAR SUSPENSION MODELS
    10.10 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 11 ACTIVE AUTOMOTIVE SUSPENSIONS
    11.1 INTRODUCTION
    11.2 ACTIVE CONTROL : TRADE-OFFS AND LIMITATIONS
    11.2.1 Transfer functions of interest
    11.2.2 Use of the LQR formulation and its Relation to H2 -optimal control
    11.2.3 LQR formulation for active suspension design
    11.2.4 Performance studies of the LQR controller
    11.3 ACTIVE SYSTEM ASYMPTOTES
    11.4 INVARIANT POINTS AND THEIR INFLUENCE ON THE SUSPENSION PROBLEM
    11.5 ANALYSIS OF TRADE-OFFS USING INVARIANT POINTS
    11.5.1 Ride quality/ road holding trade-offs
    11.5.2 Ride quality/ rattle space trade-offs
    11.6 CONCLUSIONS ON ACHIEVABLE ACTIVE SYSTEM PERFORMANCE
    11.7 PERFORMANCE OF A SIMPLE VELOCITY FEEDBACK CONTROLLER
    11.8 HYDRAULIC ACTUATORS FOR ACTIVE SUSPENSIONS
    11.9 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 12 SEMI-ACTIVE SUSPENSIONS
    12.1 INTRODUCTION
    12.2 SEMI-ACTIVE SUSPENSION MODEL
    12.3 THEORETICAL RESULTS: OPTIMAL SEMI-ACTIVE SUSPENSIONS
    12.3.1 Problem formulation
    12.3.2 Problem definition
    12.3.3 Optimal solution with no constraints on damping
    12.3.4 Optimal solution in the presence of constraints
    12.4 INTERPRETATION OF THE OPTIMAL SEMIACTIVE CONTROL LAW
    12.5 SIMULATION RESULTS
    12.6 CALCULATION OF TRANSFER FUNCTION PLOTS WITH SEMI-ACTIVE SYSTEMS
    12.7 PERFORMANCE OF SEMI-ACTIVE SYSTEMS
    12.7.1 Moderately weighted ride quality
    12.7.2 Sky hook damping
    12.8 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 13 LATERAL AND LONGITUDINAL TIRE FORCES
    13.1 TIRE FORCES
    13.2 TIRE STRUCTURE
    13.3 LONGITUDINAL TIRE FORCE AT SMALL SLIP RATIOS
    13.4 LATERAL TIRE FORCE AT SMALL SLIP ANGLES
    13.5 INTRODUCTION TO THE MAGIC FORMULA TIRE MODEL
    13.6 DEVELOPMENT OF LATERAL TIRE MODEL FOR UNIFORM NORMAL FORCE DISTRIBUTION
    13.6.1 Lateral forces at small slip angles
    13.6.2 Lateral forces at large slip angles
    13.7 DEVELOPMENT OF LATERAL TIRE MODEL FOR PARABOLIC NORMAL PRESSURE DISTIRBUTION
    13.8 COMBINED LATERAL AND LONGITUDINAL TIRE FORCE GENERATION
    13.9 THE MAGIC FORMULA TIRE MODEL
    13.10 DUGOFF’S TIRE MODEL
    13.10.1 Introduction
    13.10.2 Model equations
    13.10.3 Friction circle interpretation of Dugoff’s model
    13.11 DYNAMIC TIRE MODEL
    13.12 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 14 TIRE-ROAD FRICTION MEASUREMENT ON HIGHWAY VEHICLES
    14.1 INTRODUCTION
    14.1.1 Definition of tire-road friction coefficient
    14.1.2 Benefits of tire-road friction estimation
    14.1.3 Review of results on tire-road friction coefficient estimation
    14.1.4 Review of results on slip-slope based approach to friction estimation
    14.2 LONGITUDINAL VEHICLE DYNAMICS AND TIRE MODEL FOR FRICTION ESTIMATION
    14.2.1 Vehicle longitudinal dynamics
    14.2.2 Determination of the normal force
    14.2.3 Tire model
    14.2.4 Friction coefficient estimation for both traction and braking
    14.3 SUMMARY OF LONGITUDINAL FRICTION IDENTIFICATION APPROACH
    14.4 IDENTIFICATION ALGORITHM DESIGN
    14.4.2 Recursive least-squares (RLS) identification
    14.4.3 RLS with gain switching
    14.4.4 Conditions for parameter updates
    14.5 ESTIMATION OF ACCELEROMETER BIAS
    14.6 EXPERIMENTAL RESULTS
    14.6.2 System hardware and software
    14.6.3 Tests on dry concrete road surface
    14.6.4 Tests on concrete surface with loose snow covering
    14.6.5 Tests on surface consisting of two different friction levels
    14.6.6 Hard braking test
    14.7 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 15 ROLL DYNAMICS AND ROLLOVER PREVENTION
    15.1 ROLLOVER RESISTANCE RATING FOR VEHICLES
    15.2 ONE DEGREE OF FREEDOM ROLL DYNAMICS MODEL
    15.3 FOUR DEGREES OF FREEDOM ROLL DYNAMICS MODEL
    15.4 ROLLOVER INDEX
    15.5 ROLLOVER PREVENTION
    15.6 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Chapter 16 DYNAMICS AND CONTROL OF HYBRID GAS ELECTRIC VEHICLES
    16.1 TYPES OF HYBRID POWERTRAINS
    16.2 POWERTRAIN DYNAMIC MODEL
    16.2.1 Dynamic Model for Simulation of a Parallel Gas-Electric Hybrid Vehicle
    16.2.2 Dynamic Model for Simulation of a Power-Split Hybrid Vehicle
    16.3 BACKGROUND ON CONTROL DESIGN TECHNIQUES FOR ENERGY MANAGEMENT
    16.3.1 Dynamic Programming Overview
    16.3.2 Model Predictive Control Overview
    16.3.3 Equivalent Consumption Minimization Strategy
    16.4 DRIVING CYCLES
    16.5 PERFORMANCE INDEX, CONSTRAINTS AND SYSTEM MODEL DETAILS FOR CONTROL DESIGN
    16.6 ILLUSTRATION OF CONTROL SYSTEM DESIGN FOR A PARALLEL HYBRID VEHICLE
    16.7 CHAPTER SUMMARY
    NOMENCLATURE
    REFERENCES
    Index
    MechanicalEngineeringSeriesFrederickF.LingEditor-in-ChiefTheMechanicalEngineeringSeriesfeaturesgraduatetextsandresearchmonographstoaddresstheneedforinformationincontemporarymechanicalengineering,includingareasofconcentrationofappliedmechanics,biomechanics,computa-tionalmechanics,dynamicalsystemsandcontrol,energetics,mechanicsofmaterials,processing,productionsystems,thermalscience,andtribology.AdvisoryBoard/SeriesEditorsAppliedMechanicsF.A.LeckieUniversityofCalifornia,SantaBarbaraD.GrossTechnicalUniversityofDarmstadtBiomechanicsV.C.MowColumbiaUniversityComputationalMechanicsH.T.YangUniversityofCalifornia,SantaBarbaraDynamicSystemsandControl/MechatronicsD.BryantUniversityofTexasatAustinEnergeticsJ.R.WeltyUniversityofOregon,EugeneMechanicsofMaterialsI.FinnieUniversityofCalifornia,BerkeleyProcessingK.K.WangCornellUniversityProductionSystemsG.-A.KlutkeTexasA&MUniversityThermalScienceA.E.BerglesRensselaerPolytechnicInstituteTribologyW.O.WinerGeorgiaInstituteofTechnologyForfurthervolumes:http://www.springer.com/series/1161
    Second Edition RajeshRajamaniVehicleDynamicsandControl
    Dr.RajeshRajamaniDepartmentofMechanicalEngineeringUniversityofMinnesotaMinneapolis,MN55455,USArajamani@me.umn.eduISSN0941-5122e-ISSN2192-063XISBN978-1-4614-1432-2e-ISBN978-1-4614-1433-9DOI10.1007/978-1-4614-1433-9SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2011940692#Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScienceþBusinessMedia(www.springer.com)RajeshRajamani2012
    For Priya
    Preface As a research advisor to graduate students working on automotive projects, I have frequently felt the need for a textbook that summarizes common vehicle control systems and the dynamic models used in the development of these control systems. While a few different textbooks on ground vehicle dynamics are already available in the market, they do not satisfy all the needs of a control systems engineer. A controls engineer needs models that are both simple enough to use for control system design but at the same time rich enough to capture all the essential features of the dynamics. This book attempts to present such models and actual automotive control systems from literature developed using these models. The control system applications covered in the book include cruise control, adaptive cruise control, anti-lock brake systems, automated lane keeping, automated highway systems, yaw stability control, engine control, passive, active and semi-active suspensions, tire-road friction coefficient estimation, rollover prevention, and hybrid electric vehicles. A special effort has been made to explain the several different tire models commonly used in literature and to interpret them physically. In the second edition, the topics of roll dynamics, rollover prevention and hybrid electric vehicles have been added as Chapters 15 and 16 of the book. Chapter 8 on electronic stability control has been significantly enhanced. As the worldwide use of automobiles increases rapidly, it has become ever more important to develop vehicles that optimize the use of highway and fuel resources, provide safe and comfortable transportation and at the same time have minimal impact on the environment. To meet these diverse and often conflicting requirements, automobiles are increasingly relying on electromechanical systems that employ sensors, actuators and feedback control. It is hoped that this textbook will serve as a useful resource to researchers who work on the development of such control systems, both in vii
    May 2005 and June 2011 Rajesh Rajamani Minneapolis, Minnesota Preface viii the automotive industry and at universities. The book can also serve as a textbook for a graduate level course on Vehicle Dynamics and Control. An up-to-date errata for typographic and other errors found in the book after it has been published will be maintained at the following web-site: http://www.menet.umn.edu/~rajamani/vdc.html I will be grateful for reports of such errors from readers.
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