Vehicle Dynamics and Control (eBook)

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

Chapter 4 LONGITUDINAL VEHICLE DYNAMICS (p. 95)

The control of longitudinal vehicle motion has been pursued at many different levels by researchers and automotive manufacturers. Common systems involving longitudinal control available on today's passenger cars include cruise control, anti-lock brake systems and traction control systems. Other advanced longitudinal control systems that have been the topic of intense research include radar-based collision avoidance systems, adaptive cruise control systems, individual wheel torque control with active differentials and longitudinal control systems for the operation of vehicles in platoons on automated highway systems.

This chapter presents dynamic models for the longitudinal motion of the vehicle. The two major elements of the longitudinal vehicle model are the vehicle dynamics and the powertrain dynamics. The vehicle dynamics are influenced by longitudinal tire forces, aerodynamic drag forces, rolling resistance forces and gravitational forces. Models for these forces are discussed in section 4.1. The longitudinal powertrain system of the vehicle consists of the internal combustion engine, the torque converter, the transmission and the wheels. Models for these components are discussed in section 4.2.

4.1 LONGITUDINAL VEHICLE DYNAMICS
Consider a vehicle moving on an inclined road as shown in Figure 4-1. The external longitudinal forces acting on the vehicle include aerodynamic drag forces, gravitational forces, longitudinal tire forces and rolling resistance forces. These forces are described in detail in the sub-sections that follow.