Vehicle Dynamics and Control

Contents

Acknowledgments

1 INTRODUCTION

1.1 DRIVER ASSISTANCE SYSTEMS

1.2 ACTIVE STABILITY CONTROLSYSTEMS

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

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 OFA 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 SLIPANGLE

2.7 FROM BODY FIXED TO GLOBAL COORDINATES

2.8 ROAD MODEL

2.9 CHAPTER SUMMARY

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REFERENCES

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-angleerror 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-LOOPPERFORMANCE

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

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REFERENCES

4 LONGITUDINAL VEHICLE DYNAMICS

4.1 LONGITUDINALVEHICLE 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

CHAPTER SUMMARY

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REFERENCES

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 LONGITUDINALAUTOMATION

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

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REFERENCES

6 ADAPTIVE CRUISE CONTROL

6.1 INTRODUCTION

6.2 VEHICLE FOLLOWING SPECIFICATIONS

6.3 CONTROLARCHITECTURE

6.4 STRING STABILITY

6.5 AUTONOMOUS CONTROL WITH CONSTANT SPACING

6.6 AUTONOMOUS CONTROL WITH THE CONSTANT TIME-GAPPOLICY

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 diagrams

6.8 LOWER LEVEL CONTROLLER

6.9 CHAPTER SUMMARY

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REFERENCES

APPENDIX 6.A

7 LONGITUDINAL CONTROL FOR VEHICLE PLATOONS

7.1 AUTOMATED HIGHWAY SYSTEMS

7.2 VEHICLE CONTROL ON AUTOMATED HIGHWAY SYSTEMS

7.3 LONGITUDINAL CONTROLARCHITECTURE

7.4 VEHICLE FOLLOWING SPECIFICATIONS

7.5 BACKGROUND ON NORMS OF SIGNALSAND SYSTEMS

7.5.1 Norms of signals

7.5.2 System norms

7.6 DESIGN APPROACH FOR ENSURING STRING STABILITY

7.7 CONSTANT SPACING WITH AUTONOMOUS CONTROL

7.8 CONSTANT SPACING WITH WIRELESS COMMUNICATION

7.9 EXPERIMENTALRESULTS

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

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REFERENCES

APPENDIX 7.A

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-WIRESYSTEMS

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

8.4.3 Active Control of Torque Transfer To All Wheels

8.5 CHAPTER SUMMARY

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REFERENCES

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 from intake manifold

9.1.6 Inflow rate 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

CHAPTER SUMMARY

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REFERENCES

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 Suspensionfunctions

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

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REFERENCES

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 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 quality1road holding trade-offs

11.5.2 Ride quality1rattle space trade-offs

11.6 CONCLUSIONS ON ACHIEVABLE ACTIVE SYSTEM PERFORMANCE

11.7 PERFORMANCE OFA SIMPLE VELOCITY FEEDBACK CONTROLLER

11.8 HYDRAULIC ACTUATORS FOR ACTIVE SUSPENSIONS

11.9 CHAPTER SUMMARY

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REFERENCES

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 SEMI-ACTIVE CONTROL LAW

12.5 SIMULATION RESULTS

12.6 CALCULATION OF TRANSFER FUNCTION PLOTS WITH SEMI-ACTIVE SYSTEMS

12.7 PERFORMANCE OF SEMI-ACTIVESYSTEMS

12.7.1 Moderately weighted ride quality

12.7.2 Sky hook damping

12.8 CHAPTER SUMMARY

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REFERENCES

13 LATERAL AND LONGITUDINAL TIRE FORCES

13.1 TIRE FORCES

13.2 TIRE STRUCTURE

13.3 LONGITUDINALTIRE 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 DISTRIBUTION

13.8 COMBINED LATERALAND 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

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REFERENCES

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-roadfriction 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

14.2 TIRE MODELFOR 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 IDENTIFICATIONAPPROACH

14.4 IDENTIFICATION ALGORITHM DESIGN

14.4.1 Recursive least-squares (RLS) identification

14.4.2 RLS with gain switching

14.4.3 Conditions for parameter updates

14.5 ESTIMATION OF ACCELEROMETER BIAS

14.6 EXPERIMENTALRESULTS

14.6.1 System hardware and software

14.6.2 Tests on dry concrete road surface

14.6.3 Tests on concrete surface with loose snow covering

14.6.4 Tests on surface consistingof two different friction levels

14.6.5 Hard braking test

14.7 CHAPTER SUMMARY

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REFERENCES

Index