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Vehicle Dynamics and Control

of: Rajesh Rajamani

Springer-Verlag, 2006

ISBN: 9780387288239 , 472 Pages

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Vehicle Dynamics and Control


 

Contents

11

Acknowledgments

24

1 INTRODUCTION

25

1.1 DRIVER ASSISTANCE SYSTEMS

26

1.2 ACTIVE STABILITY CONTROLSYSTEMS

26

1.3 RIDE QUALITY

28

1.4 TECHNOLOGIES FOR ADDRESSING TRAFFIC CONGESTION

29

1.4.1 Automated highway systems

30

1.4.2 "Traffic-friendly"adaptive cruise control

30

1.4.3 Narrow tilt-controlled commuter vehicles

31

1.5 EMISSIONS AND FUEL ECONOMY

33

1.5.1 Hybrid electric vehicles

34

1.5.2 Fuel cell vehicles

35

REFERENCES

35

2 LATERAL VEHICLE DYNAMICS

38

2.1 LATERAL SYSTEMS UNDER COMMERCIAL DEVELOPMENT

38

2.1.1 Lane departure warning

39

2.1.2 Lane keeping systems

40

2.1.3 Yaw stability control systems

41

2.2 KINEMATIC MODEL OF LATERAL VEHICLE MOTION

43

2.3 BICYCLE MODEL OF LATERAL VEHICLE DYNAMICS

50

2.4 MOTION OFA PARTICLE RELATIVE TO A ROTATING FRAME

56

2.5 DYNAMIC MODEL IN TERMS OF ERROR WITH RESPECT TO ROAD

58

2.6 DYNAMIC MODEL IN TERMS OF YAW RATE AND SLIPANGLE

62

2.7 FROM BODY FIXED TO GLOBAL COORDINATES

64

2.8 ROAD MODEL

66

2.9 CHAPTER SUMMARY

69

NOMENCLATURE

70

REFERENCES

71

3 STEERING CONTROL FOR AUTOMATED LANE KEEPING

73

3.1 STATE FEEDBACK

73

3.2 STEADY STATE ERROR FROM DYNAMIC EQUATIONS

77

3.3 UNDERSTANDING STEADY STATE CORNERING

81

3.3.1 Steering angle for steady state cornering

81

3.3.2 Can the yaw-angleerror be zero ?

86

3.3.3 Is non-zero yaw angle error a concern ?

87

3.4 CONSIDERATION OF VARYING LONGITUDINAL VELOCITY

88

3.5 OUTPUT FEEDBACK

90

3.6 UNITY FEEDBACK LOOP SYSTEM

92

3.7 LOOP ANALYSIS WITH A PROPORTIONAL CONTROLLER

94

3.8 LOOP ANALYSIS WITH A LEAD COMPENSATOR

101

3.9 SIMULATION OF PERFORMANCE WITH LEAD COMPENSATOR

105

3.10 ANALYSIS OF CLOSED-LOOPPERFORMANCE

106

3.10.1 Performance variation with vehicle speed

106

3.10.2 Performance variation with sensor location

108

3.11 COMPENSATOR DESIGN WITH LOOK-AHEAD SENSOR MEASUREMENT

110

3.12 CHAPTER SUMMARY

112

NOMENCLATURE

112

REFERENCES

114

4 LONGITUDINAL VEHICLE DYNAMICS

116

4.1 LONGITUDINALVEHICLE DYNAMICS

116

4.1.1 Aerodynamic drag force

118

4.1.2 Longitudinal tire force

120

4.1.3 Why does longitudinal tire force depend on slip ?

122

4.1.4 Rolling resistance

125

4.1.5 Calculation of normal tire forces

127

4.1.6 Calculation of effective tire radius

129

4.2 DRIVELINE DYNAMICS

132

4.2.1 Torque converter

133

4.2.2 Transmission dynamics

135

4.2.3 Engine dynamics

137

CHAPTER SUMMARY

141

NOMENCLATURE

141

REFERENCES

143

5 INTRODUCTION TO LONGITUDINAL CONTROL

144

5.1 INTRODUCTION

144

5.1.1 Adaptive cruise control

145

5.1.2 Collision avoidance

146

5.1.3 Automated highway systems

146

5.2 BENEFITS OF LONGITUDINALAUTOMATION

147

5.3 CRUISE CONTROL

149

5.4 UPPER LEVEL CONTROLLER FOR CRUISE CONTROL

151

5.5 LOWER LEVEL CONTROLLER FOR CRUISE CONTROL

154

5.5.1 Engine Torque Calculation for Desired Acceleration

155

5.5.2 Engine Control

158

5.6 ANTI-LOCK BRAKE SYSTEMS

158

5.6.1 Motivation

158

5.6.2 ABS Functions

162

5.6.3 Deceleration Threshold Based Algorithms

163

5.6.4 Other Logic Based ABS Control Systems

167

5.6.5 Recent Research Publications on ABS

169

5.7 CHAPTER SUMMARY

169

NOMENCLATURE

170

REFERENCES

171

6 ADAPTIVE CRUISE CONTROL

174

6.1 INTRODUCTION

174

6.2 VEHICLE FOLLOWING SPECIFICATIONS

176

6.3 CONTROLARCHITECTURE

177

6.4 STRING STABILITY

179

6.5 AUTONOMOUS CONTROL WITH CONSTANT SPACING

180

6.6 AUTONOMOUS CONTROL WITH THE CONSTANT TIME-GAPPOLICY

183

6.6.1 String stability of the CTG spacing policy

185

6.6.2 Typical delay values

188

6.7 TRANSITIONAL TRAJECTORIES

190

6.7.1 The need for a transitional controller

190

6.7.2 Transitional controller design through diagrams

193

6.8 LOWER LEVEL CONTROLLER

199

6.9 CHAPTER SUMMARY

201

NOMENCLATURE

201

REFERENCES

202

APPENDIX 6.A

204

7 LONGITUDINAL CONTROL FOR VEHICLE PLATOONS

208

7.1 AUTOMATED HIGHWAY SYSTEMS

208

7.2 VEHICLE CONTROL ON AUTOMATED HIGHWAY SYSTEMS

209

7.3 LONGITUDINAL CONTROLARCHITECTURE

210

7.4 VEHICLE FOLLOWING SPECIFICATIONS

212

7.5 BACKGROUND ON NORMS OF SIGNALSAND SYSTEMS

214

7.5.1 Norms of signals

214

7.5.2 System norms

215

7.6 DESIGN APPROACH FOR ENSURING STRING STABILITY

219

7.7 CONSTANT SPACING WITH AUTONOMOUS CONTROL

221

7.8 CONSTANT SPACING WITH WIRELESS COMMUNICATION

224

7.9 EXPERIMENTALRESULTS

227

7.10 LOWER LEVEL CONTROLLER

229

7.11 ADAPTIVE CONTROL FOR UNKNOWN VEHICLE PARAMETERS

230

7.11.1 Redefined notation

230

7.11.2 Adaptive controller

232

7.12 CHAPTER SUMMARY

235

NOMENCLATURE

236

REFERENCES

237

APPENDIX 7.A

239

8 ELECTRONIC STABILITY CONTROL

241

8.1 INTRODUCTION

241

8.1.1 The functioning of a stability control system

241

8.1.2 Systems developed by automotive manufacturers

243

8.1.3 Types of stability control systems

243

8.2 DIFFERENTIAL BRAKING SYSTEMS

244

8.2.1 Vehicle model

244

8.2.2 Control architecture

249

8.2.3 Desired yaw rate

250

8.2.4 Desired side-slip angle

251

8.2.5 Upper bounded values of target yaw rate and slip angle

253

8.2.6 Upper controller design

255

8.2.7 Lower controller design

258

8.3 STEER-BY-WIRESYSTEMS

260

8.3.1 Introduction

260

8.3.2 Choice of output for decoupling

261

8.3.3 Controller Design

264

8.4 INDEPENDENT ALL WHEEL DRIVE TORQUE DISTRIBUTION

267

8.4.1 Traditional four wheel drive systems

267

8.4.2 Torque transfer between left and right wheels using

268

8.4.3 Active Control of Torque Transfer To All Wheels

269

8.5 CHAPTER SUMMARY

271

NOMENCLATURE

272

REFERENCES

275

9 MEAN VALUE MODELING OF SI AND DIESEL ENGINES

277

9.1 SI ENGINE MODEL USING PARAMETRIC EQUATIONS

278

9.1.1 Engine rotational dynamics

279

9.1.2 Indicated combustion torque

280

9.1.3 Friction and pumping losses

281

9.1.4 Manifold pressure equation

282

9.1.5 Outflow rate from intake manifold

283

9.1.6 Inflow rate into intake manifold

283

9.2 SI ENGINE MODEL USING LOOK-UP MAPS

285

9.2.1 Introduction to engine maps

286

9.2.2 Second order engine model using engine maps

290

9.2.3 First order engine model using engine maps

291

9.3 INTRODUCTION TO TURBOCHARGED DIESEL ENGINES

293

9.4 MEAN VALUE MODELING OF TURBOCHARGED DIESEL ENGINES

294

9.4.1 Intake manifold dynamics

295

9.4.2 Exhaust manifold dynamics

295

9.4.3 Turbocharger dynamics

296

9.4.4 Engine crankshaft dynamics

297

9.4.5 Control system objectives

298

9.5 LOWER LEVEL CONTROLLER WITH SI ENGINES

299

CHAPTER SUMMARY

301

NOMENCLATURE

302

REFERENCES

304

10 DESIGN AND ANALYSIS OF PASSIVE AUTOMOTIVE SUSPENSIONS

306

10.1 INTRODUCTION TO AUTOMOTIVE SUSPENSIONS

306

10.1.1 Full, half and quarter car suspension models

306

10.1.2 Suspensionfunctions

308

10.1.3 Dependent and independent suspensions

310

10.2 MODAL DECOUPLING

312

10.3 PERFORMANCE VARIABLES FOR A QUARTER CAR SUSPENSION

314

10.4 NATURAL FREQUENCIES AND MODE SHAPES FOR THE QUARTER CAR

316

10.5 APPROXIMATE TRANSFER FUNCTIONS USING DECOUPLING

318

10.6 ANALYSIS OF VIBRATIONS IN THE SPRUNG MASS MODE

324

10.7 ANALYSIS OF VIBRATIONS IN THE UNSPRUNG MASS MODE

326

10.8 VERIFICATION USING THE COMPLETE QUARTER CAR MODEL

327

10.8.1 Verification of the influence of suspension stiffness

327

10.8.2 Verification of the influence of suspension damping

329

10.8.3 Verification of the influence of tire stiffness

332

10.9 HALF-CAR AND FULL-CAR SUSPENSION MODELS

334

10.10 CHAPTER SUMMARY

340

NOMENCLATURE

341

REFERENCES

342

11 ACTIVE AUTOMOTIVE SUSPENSIONS

343

11.1 INTRODUCTION

343

11.2 ACTIVE CONTROL :TRADE-OFFS AND LIMITATIONS

346

11.2.1 Transfer functions of interest

346

11.2.2 Use of the LQR formulation and its Relation to optimal control

346

11.2.3 LQR formulation for active suspension design

348

11.2.4 Performance studies of the LQR controller

350

11.3 ACTIVE SYSTEM ASYMPTOTES

357

11.4 INVARIANT POINTS AND THEIR INFLUENCE ON THE SUSPENSION PROBLEM

359

11.5 ANALYSIS OF TRADE-OFFS USING INVARIANT POINTS

361

11.5.1 Ride quality1road holding trade-offs

362

11.5.2 Ride quality1rattle space trade-offs

363

11.6 CONCLUSIONS ON ACHIEVABLE ACTIVE SYSTEM PERFORMANCE

364

11.7 PERFORMANCE OFA SIMPLE VELOCITY FEEDBACK CONTROLLER

366

11.8 HYDRAULIC ACTUATORS FOR ACTIVE SUSPENSIONS

368

11.9 CHAPTER SUMMARY

370

NOMENCLATURE

371

REFERENCES

372

12 SEMI-ACTIVE SUSPENSIONS

374

12.1 INTRODUCTION

374

12.2 SEMI-ACTIVE SUSPENSION MODEL

376

12.3 THEORETICAL RESULTS: OPTIMAL SEMI-ACTIVE SUSPENSIONS

379

12.3.1 Problem formulation

379

12.3.2 Problem definition

381

12.3.3 Optimal solution with no constraints on damping

382

12.3.4 Optimal solution in the presence of constraints

385

12.4 INTERPRETATION OF THE OPTIMAL SEMI-ACTIVE CONTROL LAW

386

12.5 SIMULATION RESULTS

389

12.6 CALCULATION OF TRANSFER FUNCTION PLOTS WITH SEMI-ACTIVE SYSTEMS

392

12.7 PERFORMANCE OF SEMI-ACTIVESYSTEMS

395

12.7.1 Moderately weighted ride quality

395

12.7.2 Sky hook damping

397

12.8 CHAPTER SUMMARY

400

NOMENCLATURE

400

REFERENCES

401

13 LATERAL AND LONGITUDINAL TIRE FORCES

403

13.1 TIRE FORCES

403

13.2 TIRE STRUCTURE

406

13.3 LONGITUDINALTIRE FORCE AT SMALL SLIP RATIOS

407

13.4 LATERAL TIRE FORCE AT SMALL SLIP ANGLES

411

13.5 INTRODUCTION TO THE MAGIC FORMULA TIRE MODEL

414

13.6 DEVELOPMENT OF LATERAL TIRE MODEL FOR UNIFORM NORMAL FORCE DISTRIBUTION

416

13.6.1 Lateral forces at small slip angles

418

13.6.2 Lateral forces at large slip angles

421

13.7 DEVELOPMENT OF LATERAL TIRE MODEL FOR PARABOLIC NORMAL PRESSURE DISTRIBUTION

425

13.8 COMBINED LATERALAND LONGITUDINAL TIRE FORCE GENERATION

433

13.9 THE MAGIC FORMULA TIRE MODEL

437

13.10 DUGOFF'S TIRE MODEL

441

13.10.1 Introduction

441

13.10.2 Model equations

442

13.10.3 Friction circle interpretation of Dugoff's model

443

13.11 DYNAMIC TIRE MODEL

445

13.12 CHAPTER SUMMARY

446

NOMENCLATURE

446

REFERENCES

448

14 TIRE-ROAD FRICTION MEASUREMENT ON HIGHWAY VEHICLES

449

14.1 INTRODUCTION

449

14.1.1 Definition of tire-road friction coefficient

449

14.1.2 Benefits of tire-roadfriction estimation

450

14.1.3 Review of results on tire-road friction coefficient estimation

451

14.1.4 Review of results on slip-slope based approach to friction estimation

452

14.2 LONGITUDINAL VEHICLE DYNAMICS AND

454

14.2 TIRE MODELFOR FRICTION ESTIMATION

454

14.2.1 Vehicle longitudinal dynamics

454

14.2.2 Determination of the normal force

455

14.2.3 Tire model

456

14.2.4 Friction coefficient estimation for both traction and braking

458

14.3 SUMMARY OF LONGITUDINAL FRICTION IDENTIFICATIONAPPROACH

462

14.4 IDENTIFICATION ALGORITHM DESIGN

463

14.4.1 Recursive least-squares (RLS) identification

463

14.4.2 RLS with gain switching

465

14.4.3 Conditions for parameter updates

466

14.5 ESTIMATION OF ACCELEROMETER BIAS

467

14.6 EXPERIMENTALRESULTS

470

14.6.1 System hardware and software

470

14.6.2 Tests on dry concrete road surface

471

14.6.3 Tests on concrete surface with loose snow covering

473

14.6.4 Tests on surface consistingof two different friction levels

475

14.6.5 Hard braking test

476

14.7 CHAPTER SUMMARY

477

NOMENCLATURE

478

REFERENCES

480

Index

482