Integrated Vehicle Dynamics and Control
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Wuwei Chen is a Professor at the School of Mechanical and Automotive Engineering, Hefei University of Technology, China. Dr. Chen has been working in the area of vehicle system dynamics, particularly in integrated control of vehicle dynamic systems, for more than 20 years. He has been recognized as a leading researcher in developing integrated vehicle dynamic control systems through both theoretical analysis and experimental investigation.
Dr. Chen was a guest editor of International Journal of Vehicle Design for a special issue on "Vehicle Control Systems". He is also a member of the editorial boards of Journal of Vibration Engineering (in Chinese) and Transactions of the Chinese Society for Agricultural Machinery. Dr. Chen has authored and co-authored over 150 journal and conference papers, and has made numerous presentations at scientific and engineering conferences.
Hansong Xiao is now working with Hanergy Product Development Group, China. He received his Ph.D.in Mechanical Engineering at the University of Toronto, Canada. His current research interests include Engineering Optimization, Dynamic Analysis, and Automotive Electronic Control.
Qidong Wang, Ph.D, Professor at School of Mechanical and Automotive Engineering, Hefei University of Technology. Wang has been doing research in the field of vehicle dynamics and control for over 20 years and has published over 80 papers. Linfeng Zhao, Ph.D, Associate Professor at School of Mechanical and Automotive Engineering, Hefei University of Technology. Zhao's interest is vehicle dynamics and control technologies, he has published over 10 journal papers.
Maofei Zhu, Hefei Institutes of Physical Science, Chinese Academy of Sciences.
Content
Preface xi
1 Basic Knowledge of Vehicle System Dynamics 1
1.1 Traditional Methods of Formulating Vehicle Dynamics Equations 1
1.1.1 Newtonian Mechanics 2
1.1.2 Analytical Mechanics 3
1.2 Dynamics of Rigid Multibody Systems 3
1.2.1 Birth and Development 3
1.2.2 Theories and Methods of Multi-Rigid Body System Dynamics 5
1.2.3 An Example of the Application of Multi-Rigid Body Dynamics Method in Vehicle System Modeling 8
1.3 Flexible Multibody Dynamics 12
References 13
2 Tyre Dynamics 15
2.1 Tyre Models 15
2.1.1 Terminology and Concepts 15
2.1.2 Tyre Model 17
2.2 Tyre Longitudinal Mechanical Properties 19
2.2.1 Tyre Rolling Resistance 20
2.2.2 Road Resistance 21
2.2.3 Tyre Slip Resistance 23
2.2.4 Overall Rolling Resistance of the Tyres 23
2.2.5 Rolling Resistance Coefficient 24
2.3 Vertical Mechanical Properties of Tyres 26
2.4 Lateral Mechanical Properties of Tyres 29
2.5 Mechanical Properties of Tyres in Combined Conditions 30
References 32
3 Longitudinal Vehicle Dynamics and Control 33
3.1 Longitudinal Vehicle Dynamics Equations 33
3.1.1 Longitudinal Force Analysis 33
3.1.2 Longitudinal Vehicle Dynamics Equation 34
3.2 Driving Resistance 35
3.2.1 Aerodynamic Drag 36
3.2.2 Ramp Resistance 36
3.2.3 Inertial Resistance 37
3.3 Anti-lock Braking System 38
3.3.1 Introduction 38
3.3.2 Basic Structure and Working Principle 38
3.3.3 Design of an Anti-lock Braking System 40
3.4 Traction Control System 48
3.4.1 Introduction 48
3.4.2 Control Techniques of TCS 49
3.4.3 TCS Control Strategy 51
3.4.4 Traction Control System Modeling and Simulation 53
3.5 Vehicle Stability Control 54
3.5.1 Basic Principle of VSC 55
3.5.2 Structure of a VSC System 56
3.5.3 Control Methods to Improve Vehicle Stability 59
3.5.4 Selection of the Control Variables 60
3.5.5 Control System Structure 64
3.5.6 The Dynamics Models 64
3.5.7 Setting of the Target Values for the Control Variables 67
3.5.8 Calculation of the Nominal Yaw Moment and Control 68
Appendix 75
References 75
4 Vertical Vehicle Dynamics and Control 77
4.1 Vertical Dynamics Models 77
4.1.1 Introduction 77
4.1.2 Half-vehicle model 78
4.2 Input Models of the Road's Surface 81
4.2.1 Frequency-domain Models 81
4.2.2 Time Domain Models 83
4.3 Design of a Semi-active Suspension System 84
4.3.1 Dynamic Model of a Semi-active Suspension System 85
4.3.2 Integrated Optimization Design of a Semi-active Suspension System 87
4.3.3 The Realization of the Integrated Optimization Method 88
4.3.4 Implementation of the Genetic Algorithm 90
4.3.5 LQG Controller Design 91
4.3.6 Simulations and Result Analysis 92
4.4 Time-lag Problem and its Control of a Semi-active Suspension 95
4.4.1 Causes and Impacts of Time-lag 96
4.4.2 Time-lag Variable Structure Control of an MR (Magneto-Rheological) Semi-active Suspension 98
4.4.3 Simulation Results and Analysis 103
4.4.4 Experiment Validation 108
4.5 Design of an Active Suspension System 110
4.5.1 The Dynamic Model of an Active Suspension System 111
4.5.2 Design of the Control Scheme 112
4.5.3 Multi-objective Mixed H2/H8 Control 114
4.5.4 Simulation Study 116
4.6 Order-reduction Study of an Active Suspension Controller 119
4.6.1 Full Vehicle Model with 7 Degrees of Freedom 122
4.6.2 Controller Design 124
4.6.3 Controller Order-reduction 125
4.6.4 Simulation Analysis 129
References 133
5 Lateral Vehicle Dynamics and Control 135
5.1 General Equations of Lateral Vehicle Dynamics 135
5.2 Handling and Stability Analysis 137
5.2.1 Steady State Response (Steady Steering) 137
5.2.2 Transient Response 140
5.2.3 The Frequency Response Characteristics of Yaw Rate 144
5.3 Handling Stability Evaluations 144
5.3.1 Subjective Evaluation Contents 144
5.3.2 Experimental Evaluation Contents 144
5.4 Four-wheel Steering System and Control 145
5.4.1 Control Objectives of the Four-wheel Steering Vehicle 146
5.4.2 Design of a Four-wheel Steering Control System 146
5.4.3 Multi-body Dynamics Modeling of a Four-wheel Steering Vehicle 150
5.4.4 Simulation Results and Analysis 152
5.5 Electric Power Steering System and Control Strategy 152
5.5.1 EPS Model 154
5.5.2 Steering Torque Model of the Steering Pinion 155
5.5.3 The Estimation Algorithm of the Road Adhesion Coefficient 159
5.5.4 Design of the Control Strategy 160
5.5.5 Simulation and Analysis 163
5.5.6 Experimental Study 165
5.6 Automatic Lane Keeping System 167
5.6.1 Control System Design 167
5.6.2 Desired Yaw Rate Generation 168
5.6.3 Desired Yaw Rate Tracking Control 171
5.6.4 Simulation and Analysis 173
5.6.5 Experimental Verification 175
References 180
6 System Coupling Mechanism and Vehicle Dynamic Model 183
6.1 Overview of Vehicle Dynamic Model 183
6.2 Analysis of the Chassis Coupling Mechanisms 184
6.2.1 Coupling of Tyre Forces 184
6.2.2 Coupling of the Dynamic Load Distribution 185
6.2.3 Coupling of Movement Relationship 185
6.2.4 Coupling of Structure Parameters and Control Parameters 186
6.3 Dynamic Model of the Nonlinear Coupling for the Integrated Controls of a Vehicle 186
6.4 Simulation Analysis 191
6.4.1 Simulation 191
6.4.2 Results Analysis 192
References 199
7 Integrated Vehicle Dynamics Control: Centralized Control Architecture 201
7.1 Principles of Integrated Vehicle Dynamics Control 201
7.2 Integrated Control of Vehicle Stability Control Systems (VSC) 204
7.2.1 Sideslip Angle Control 204
7.2.2 Estimation of the Road Adhesion Coefficient 218
7.3 Integrated Control of Active Suspension System (ASS) and Vehicle Stability Control System (VSC) using Decoupling Control Method 226
7.3.1 Vehicle Dynamic Model 227
7.3.2 2-DOF Reference Model 228
7.3.3 Lateral Force Model 229
7.3.4 Integrated System Control Model 229
7.3.5 Design of the Decoupling Control System 230
7.3.6 Calculation of the Relative Degree 230
7.3.7 Design of the Input/Output Decoupling Controller 232
7.3.8 Design of the Disturbance Decoupling Controller 233
7.3.9 Design of the Closed Loop Controller 233
7.3.10 Design of the ASS Controller 233
7.3.11 Design of the VSC Controller 234
7.3.12 Simulation Investigation 236
7.3.13 Experimental Study 240
7.4 Integrated Control of an Active Suspension System (ASS) and Electric Power Steering System (EPS) using H Control Method 240
7.4.1 Vehicle Dynamic Model 243
7.4.2 EPS Model 243
7.4.3 Design of Integrated Control System 245
7.4.4 Simulation Investigation 246
7.5 Integrated Control of Active Suspension System (ASS) and Electric Power Steering System (EPS) using the Predictive Control Method 249
7.5.1 Designing a Predictive Control System 249
7.5.2 Boundary Conditions 250
7.5.3 Simulation Investigation 251
7.6 Integrated Control of the Active Suspension System (ASS) and Electric Power Steering System (EPS) using a Self-adaptive Control Method 253
7.6.1 Parameter Estimation of a Multivariable System 253
7.6.2 Design of the Multivariable Generalized Least Square Controller 254
7.6.3 Design of the Multivariable Self-adaptive Integrated Controller 255
7.6.4 Simulation Investigation 255
7.7 Integrated Control of an Active Suspension System (ASS) and Electric Power Steering System (EPS) using a Centralized Control Method 256
7.7.1 Centralized Controller Design 256
7.7.2 Simulation Investigation 259
7.8 Integrated Control of the Electric Power Steering System (EPS) and Vehicle Stability Control (VSC) System 264
7.8.1 Interactions Between EPS and VSC 264
7.8.2 Control System Design 264
7.8.3 Dynamic Distribution of Tyre Forces 265
7.8.4 Design of a Self-aligning Torque Controller 267
7.8.5 Simulation Investigation 270
7.9 Centralized Control of Integrated Chassis Control Systems using the Artificial Neural Networks (ANN) Inverse System Method 271
7.9.1 Vehicle Dynamic Model 272
7.9.2 Design of the Centralized Control System 273
7.9.3 Simulation Investigation 278
References 281
8 Integrated Vehicle Dynamics Control: Multilayer Coordinating Control Architecture 283
8.1 Multilayer Coordinating Control of Active Suspension System (ASS) and Active Front Steering (AFS) 283
8.1.1 AFS Model 284
8.1.2 Controller Design 285
8.1.3 Simulation Investigation 289
8.2 Multilayer Coordinating Control of Active Suspension System (ASS) and Electric Power Steering System (EPS) 291
8.2.1 System Modeling 291
8.2.2 Controller Design 295
8.2.3 Simulation Investigation 298
8.3 Multilayer Coordinating Control of an Active Suspension System (ASS) and Anti-lock Brake System (ABS) 299
8.3.1 Coordinating Controller Design 300
8.3.2 Simulation Investigation 301
8.4 Multilayer Coordinating Control of the Electric Power Steering System (EPS) and Anti-lock Brake System (ABS) 303
8.4.1 Interactions between the EPS System and ABS 304
8.4.2 Coordinating Controller Design 305
8.4.3 Simulation Investigation 306
8.5 Multi-layer Coordinating Control of the Active Suspension System (ASS) and Vehicle Stability Control (VSC) System 308
8.5.1 System Model 308
8.5.2 Multilayer Coordinating Controller Design 308
8.5.3 Simulation Investigation 313
8.6 Multilayer Coordinating Control of an Active Four-wheel Steering System (4WS) and Direct Yaw Moment Control System (DYC) 315
8.6.1 Introduction 315
8.6.2 Coordinating Control of DYC and 4WS 316
8.6.3 Simulation Investigation 320
8.7 Multilayer Coordinating Control of Integrated Chassis Control Systems 321
8.7.1 Introduction 321
8.7.2 Controller Design 322
8.7.3 Simulation and Experiment Investigations 327
8.8 Multilayer Coordinating Control of Integrated Chassis Control Systems using Game Theory and Function Distribution Methods 330
8.8.1 Structure of the Chassis Control System 331
8.8.2 Design of the Suspension Subsystem Controller 331
8.8.3 Design of the Steering Subsystem Controller 332
8.8.4 Design of the Braking Subsystem Controller 333
8.8.5 Design of the Upper Layer Controller 333
8.8.6 Simulation Investigation 335
References 337
9 Perspectives 339
9.1 Models of Full Vehicle Dynamics 339
9.2 Multi-sensor Information Fusion 340
9.3 Fault-tolerant Control 340
9.4 Active and Passive Safety Integrated Control Based on the Function Allocation Method 341
9.5 Design of System Integration for a Vehicle 344
9.6 Assumption about the Vehicle of the Future 345
References 346
Index 347
1
Basic Knowledge of Vehicle System Dynamics
1.1 Traditional Methods of Formulating Vehicle Dynamics Equations
Traditional methods of formulating vehicle dynamics equations are based on the theories of Newtonian mechanics and analytical mechanics. Some of the definitions used in dynamics are presented first.
- Generalized coordinates
Any set of parameters that uniquely define the configuration (position and orientation) of the system relative to the reference configuration is called a set of generalized coordinates. Generalized coordinates may be dependent or independent. To a system in motion, the generalized coordinates that specify the system may vary with time. In this text, column vector is used to designate generalized coordinates, where n is the total number of generalized coordinates.
In Cartesian coordinates, to describe a planar system which consists of b bodies, coordinates are needed. For a spatial system with b bodies, (or ) coordinates are needed.
The overall vector of coordinates of the system is denoted by , where vector qi is the vector of coordinates for the ith body in the system.
- Constraints and constraint equations
Normally, a mechanical system that is in motion can be subjected to some geometry or movement restrictions. These restrictions are called constraints. When these restrictions are expressed as mathematical equations, they are referred to as constraint equations. Usually these constraint equations are denoted as follows:
(1.1)If the time variable appears explicitly in the constraint equations, they are expressed as:
(1.2) - Holonomic constraints and nonholonomic constraints
Holonomic and nonholonomic constraints are classical mechanics concepts that are used to classify constraints and systems. If constraint equations do not contain derivative terms, or the derivative terms are integrable, these constraints are said to be called holonomic. They are geometric constraints. However, if the constraint equations contain derivative terms that are not integrable in closed form, these constraints are said to be nonholonomic. They are movement constraints, such as the velocity or acceleration conditions imposed on the system.
- Degrees of freedom
The generalized coordinates that satisfy the constraint equations in a system may not be independent. Thus, the minimum number of coordinates required to describe the system is called the number of degrees of freedom (DOF).
- Virtual displacement
Virtual displacement is an assumed infinitesimal displacement of a system at a certain position with constraints satisfied while time is held constant. Conditions imposed on the virtual displacement by the constraint equations are called virtual displacement equations. A virtual displacement may be a linear or an angular displacement, and it is normally denoted by the variational symbol d. Virtual displacement is a different concept from actual displacement. Actual displacement can only take place with the passage of time; however, virtual displacement has nothing to do with any other conditions but the constraint conditions.
1.1.1 Newtonian Mechanics
The train of thought used to establish the vehicle dynamics equations using Newton's law can be summarized in a few steps. According to the characteristics of the problem at hand, first, we need to simplify the system and come up with a suitable mathematical model by representing the practical system with rigid bodies and lumped masses which are connected to each other by springs and dampers. Then, we isolate the masses and bodies and draw the free-body diagrams. Finally, we apply the following formulas to the masses and bodies shown by free-body diagrams.
The dynamic equations of a planar rigid body are:
(1.3) (1.4)where m is the mass of the body, r is the displacement of the center of gravity, Fi is the ith force acting on the body, J is the mass moment of inertia of the body about the axis through the center of gravity, ? is the angular velocity of the body, and Mi is the moment of the ith force acting on the center of gravity of the body.
1.1.2 Analytical Mechanics
In solving the dynamics problems of simple rigid body systems, Newtonian mechanics theories have some obvious advantages; however, the efficiency will be low if dealing with constrained systems and deformable bodies. Analytical mechanics theories have been proven to be a useful method in solving these problems. This theory contains mainly the methods of general equations of dynamics, the Lagrange equation of the first kind, and the Lagrange equation of the second kind; the latter being the most widely used.
For a system with b particles (or bodies), and n DOF, q1, q2, ., qn is a set of generalized coordinates. Then, the Lagrange equation of the second kind can be expressed as
(1.5)where T is the kinetic energy, and V the potential energy of the system.
1.2 Dynamics of Rigid Multibody Systems
1.2.1 Birth and Development
The history of the development of classical mechanics goes back more than 200 years. In the past two centuries, classical mechanics has been successfully used in the theoretical study and engineering practice of relatively simple systems. However, most modern practical engineering problems are quite complicated systems consisting of many parts. Since the middle of the 20th century, the rapid development of aerospace, robotics, automotive and other industries has brought new challenges to classical mechanics. The kinematics and dynamics analysis of complicated systems becomes difficult. Thus, there was an urgent need to develop new theories to accomplish this task.
In the late 1960s and early 1970s, Roberson[1], Kane[2], Haug[3], Witternburg[4], Popov[5] and other scholars put forward methods of their own to solve the dynamic problems of complex systems. Although there were some differences between these methods in describing the position and orientation of the systems, and formulating and solving the equations, one characteristic was common among them: recurring formularization was adopted in all these methods. Computers, which help engineers to model, form, and solve differential equations of motion, were used analyze and synthesize complex systems. Thus, a new branch of mechanics called multibody dynamics was born. This developing and crossing discipline arises from the combination of rigid mechanics, analytical mechanics, elastic mechanics, matrix theory, graph theory, computational mathematics, and automatic control. It is one of the most active fields in applied mechanics, machinery, and vehicle engineering.
Multibody systems are composed of rigid and/or flexible bodies interconnected by joints and force elements such as springs and dampers. In the last few decades, remarkable advances have been made in the theory of multibody system dynamics with wide applications. An enormous number of results have been reported in the fields of vehicle dynamics, spacecraft control, robotics, and biomechanics. With the development and perfection of the multibody formalisms, multibody dynamics has received growing attention and a considerable amount of commercial software is now available. The first International Symposium on multibody system dynamics was held in Munich in 1977 by IUTAM. The second was held in Udine in 1985 by IUTAM/IFTOMM. After the middle of the 1980s, multibody dynamics entered a period of fast development. A wealth of literature has been published[6,7].
The first book about multibody system dynamics was titled Dynamics of System of Rigid Bodies[4] written by Wittenburg, was published in 1977. Dynamics: Theory and applications by Kaneand Levinson came out in 1985. In Dynamics of Multibody System[8], printed in 1989, Shabanacomprhensively discusses many aspects of multibody system dynamics, with a second edition of this book appearing in 1998. In Computer-aided Analysis of Mechanical Systems[9], Nikravesh introduces theories and numerical methods for use in computational mechanics. These theories and methods can be used to develop computer programs for analyzing the response of simple and complex mechanical systems. Using the Cartesian coordinate approach, Haug presented basic methods for the analysis of the kinematics and dynamics of planar and spatial mechanical systems in Computer Aided Kinematics and Dynamics of Mechanical Systems[3].
The work of three scholars will also be reviewed in the following section.
- Schiehlen, from the University of Stuttgart, published his two books in 1977 and 1993 respectively. Multibody System Handbook[10] was an international collection of programs and software which included theory research results and programs from 17 research groups. Advanced Multibody Dynamics[11] collected research achievements of the project supported by The German Research Council from 1987 to 1992, and the latest developments in the field of multibody system dynamics worldwide at that time. The content of this book was of an interdisciplinary nature.
- In Computational Methods in Multibody Dynamics[12], Amirouche Farid offered an in-depth...
