Mechatronic Modeling and Simulation Using Bond Graphs » (New Edition)

Bond graphs are especially well-suited for mechatronic systems, as engineering system modeling is best handled using a multidisciplinary approach. Bond graphing permits one to see the separate components of an engineering system as a unified whole, and allows these components to be categorized under a few generalized elements, even when they come from different disciplines. In addition to those advantages, the bond graph offers a visual representation of a system from which derivation of the governing equations is algorithmic. This makes the design process accessible to beginning readers, providing them with a practical understanding of mechatronic systems.

Mechatronic Modeling and Simulation Using Bond Graphs is written for those who have some hands-on experience with mechatronic systems, enough to appreciate the value of computer modeling and simulation. Avoiding elaborate mathematical derivations and proofs, the book is written for modelers seeking practical results in addition to theoretical confirmations. Key concepts are revealed step-by-step, supported by the application of rudimentary examples that allow readers to develop confidence in their approach right from the start.

For those who take the effort to master its application, the use of bond graph methodology in system modeling can be very satisfying in the way it unifies information garnered from different disciplines.

In the second half of the book after readers have learned how to develop bond graph models, the author provides simulation results for engineering examples that encourage readers to model, simulate, and practice as they progress through the chapters. Although the models can be simulated using any number of software tools, the text employs 20Sim for all the simulation work in this text. A free version of the software can be downloaded from the 20Sim Web site.

Preface xiii

Acknowledgments xvii

Author xix

Chapter 1 Introduction to Mechatronics and System Modeling 1

1.1 What Is Mechatronics? 1

1.2 What Is a System and Why Model Systems? 4

1.3 Mathematical Modeling Techniques Used in Practice 7

1.4 Software 10

Problems 11

Chapter 2 Bond Graphs: What Are They? 13

2.1 Engineering Systems 14

2.2 Ports 16

2.3 Generalized Variables 20

2.3.1 Power Variables 20

2.3.2 Energy Variables 20

2.3.3 Tetrahedron of State 21

2.4 Bond Graphs 23

2.4.1 Word Bond Graphs 23

2.5 Basic Components in Systems 26

2.5.1 1-Port Components 26

2.5.1.1 1-Port Resistor: Energy Dissipating Device 27

2.5.1.2 1-Port Capacitor: 1-Port Energy Storage Device 28

2.5.1.3 1-Port Inductor/Inertia: 1-Port Energy Storage Device 30

2.5.1.4 Other 1-Port Elements 33

2.5.2 2-Port Components 35

2.5.2.1 Transformer Element 35

2.5.2.2 Gyrator Element 39

2.5.3 3-Port (or Higher-Port) Components 41

2.5.3.1 Flow Junction, Parallel Junction, O Junction, and Common Effort Junction 42

2.5.3.2 Effort Junction, Series Junction, 1 Junction, and Common Flow Junction 43

2.5.4 Modulated Components: Transformers, Gyrators, Resistances, and More 46

2.6 A Brief Note about Bond Graph Power Directions 46

2.7 Summary of Bond Direction Rules 47

Problems 48

Chapter 3 Drawing Bond Graphs for Simple Systems: Electrical and Mechanical 55

3.1 Simplification Rules for Junction Structure 56

3.2 Drawing Bond Graphs for Electrical Systems 62

3.2.1 Formal Method of Drawing Bond Graphs for Electrical Systems 65

3.3 Drawing Bond Graphs for Mechanical Systems 69

3.3.1 Formal Method of Drawing Bond Graphs for Mechanical Systemsin Translation and Rotation 72

3.3.2 A Note about Gravitational Forces on Objects 73

3.3.3 Examples of Systems in Rotational Motion 79

3.4 Causality 83

3.4.1 Transformer 85

3.4.2 Gyrator 86

3.4.3 Junctions 86

3.4.4 Storage Elements: I, C 87

3.4.4.1 I, for Mass Elements or Inductances 88

3.4.4.2 C, for Capacitive or Spring Elements 89

3.4.5 R, for Resistive Elements 91

3.4.6 Algorithm for Assigning Causality in a Bond Graph Model 92

3.4.7 Integral Causality versus Differential Causality for Storage Elements 100

3.4.8 Final Discussion of Integral and Differential Causality 105

3.4.9 Causality Summary 106

Problems 107

Chapter 4 Drawing Bond Graphs for Hydraulic and Electronic Components and Systems 113

4.1 Some Basic Properties and Concepts for Fluids 114

4.1.1 Mass Density 114

4.1.2 Force, Pressure, and Head 115

4.1.3 Bulk Modulus 115

4.1.4 Mass Conservation for Steady, Irrotational, Nonviscous Flows 115

4.1.5 Energy Conservation for Steady, Irrotational, Nonviscous Flows 116

4.2 Bond Graph Model of Hydraulic Systems 117

4.2.1 Fluid Compliance, C Element 117

4.2.2 Fluid Inertia, I Element 118

4.2.3 Fluid Resistances, R Element 119

4.2.4 Sources (Effort and Flow) 121

4.2.5 Transformer Elements 121

4.2.6 Gyrator Elements 122

4.2.7 Bond Graph Models of Hydraulic Systems 122

4.3 Electronic Systems 127

4.3.1 Operational Amplifiers 128

4.3.2 Diodes 133

Problems 136

Chapter 5 Deriving System Equations from Bond Graphs 145

5.1 System Variables 145

5.2 Deriving System Equations 146

5.2.1 Review 147

5.2.2 Junction Power Direction and Its Interpretation 147

5.3 Tackling Differential Causality 159

5.4 Algebraic Loops 162

Problems 166

Chapter 6 Solution of Model Equations and Their Interpretation 173

6.1 Zeroth Order Systems 174

6.2 First Order Systems 176

6.2.1 Solution of the First-Order Differential Equation 178

6.3 Second Order System 180

6.3.1 System Response for Step Input 189

6.3.2 System Response to Sinusoidal Inputs 191

6.3.3 System Response Study Using State-Space Representation 194

6.4 Transfer Functions and Frequency Responses 197

6.4.1 System Response in the Frequency Domain 199

6.5 Summary 206

Problems 206

Chapter 7 Numerical Solution Fundamentals 211

7.1 Techniques for Solving Ordinary Differential Equations 211

7.2 Euler's Method 212

7.3 Implicit Euler and Trapezoidal Method 215

7.4 Runge-Kutta Method 217

7.5 Adaptive Methods 219

7.6 Summary 223

Problems 224

Chapter 8 Transducers: Sensor Models 227

8.1 Resistive Sensors 228

8.2 Capacitive Sensors 233

8.2.1 Multiport Storage Fields: C-Field 235

8.3 Magnetic Sensors 242

8.3.1 Magnetic Circuits and Fields 242

8.3.1.1 Faraday's Law of Electromagnetic Induction 243

8.3.1.2 Ampere's Law 243

8.3.1.3 Gauss's Law for Magnetism 243

8.3.2 Simple Magnetic Circuit 245

8.3.2.1 Magnetic Circuit with Air Gap 247

8.3.2.2 Magnetic Bond Graph Elements 249

8.3.2.3 Inside C-Field 257

8.4 Hall Effect Sensors 266

8.5 Piezo-Electric Sensors 271

8.6 MEMS Devices 277

8.6.1 MEMS Examples 279

8.6.1.1 Microcantilever-Based Capacitive Sensors 279

8.6.1.2 Comb Drives 281

8.6.1.3 MEMS Gyroscopic Sensors 281

8.7 Sensor Design for Desired Performance-Mechanical Transducers 287

8.8 Signal Conditioning 295

8.9 Summary 297

Problems 297

Chapter 9 Modeling Transducers: Actuators 303

9.1 Electromagnetic Actuators 303

9.1.1 Linear 303

9.1.2 Rotational Actuators: Motors 314

9.1.2.1 Permanent Magnet DC Motor 316

9.1.2.2 Motor Load 322

9.1.2.3 Parallel Wound Motor (Shunt) 323

9.1.2.4 Series Wound Motor 327

9.1.2.5 Separately Excited DC Motors 332

9.1.3 Example of a Motor That Is Driving a Load 332

9.2 Hydraulic Actuators 336

9.2.1 Hydraulic Cylinders 336

9.2.2 Pumps 337

9.2.3 Hydraulic Valves 338

9.3 Summary 345

Problems 345

Chapter 10 Modeling Vehicle Systems 351

10.1 Vehicle Systems 352

10.2 Vehicle Dynamics 358

10.2.1 Ride: Heave and Pitch Motion 358

10.2.1.1 Transformer Parameter Calculation 362

10.2.1.2 Active Dampers 369

10.2.2 Handling: Bicycle Model 371

10.3 Vehicle Systems 374

10.3.1 Electric Braking 374

10.3.2 Power Steering Model 377

10.3.3 Steer-by-Wire System (SBW) 380

10.4 Energy Regeneration in Vehicles 386

10.4.1 First Square Wave Generator 388

10.4.2 Second Square Wave Generator 390

10.5 Planar Rigid Body Motion 390

10.6 Simple Engine Model: A Different Approach 399

10.7 Summary 402

Problems 403

Chapter 11 Control System Modeling 405

11.1 PID Control 407

11.1.1 Proportional Control 407

11.1.2 Proportional Integral Control 411

11.1.3 Proportional Derivative Control 413

11.1.4 Proportional Integral Derivative Control 416

11.1.5 Ziegler-Nichols Closed Loop Method 422

11.2 Control Examples 422

11.3 Nonlinear Control Examples 427

11.3.1 Inverted Pendulum 428

11.3.2 Motor 432

11.3.3 Controller 433

11.4 Summary 441

Problems 441

Chapter 12 Other Applications 443

12.1 Case Study 1: Modeling CNC Feed-Drive System 444

12.1.1 Bond Graph Modeling of an Open and Closed Loop System 446

12.1.2 Backlash, Stick-Slip, and Cutting Force 451

12.1.2.1 Backlash 451

12.1.2.2 Stick-Slip Friction 453

12.1.2.3 Cutting Force Model 454

12.2 Case Study 2: Developing a System Model for a MEMS Electrothermal Actuator 458

12.2.1 FEA Analysis 460

12.2.1.1 Steps Involved in the FEA Analysis 460

12.2.2 Simulation of ETM Actuator Using 20Sim 462

References 469

Bibliography 475

Index 477