Written by a professor with extensive teaching experience, System Dynamics and Control with Bond Graph Modeling treats system dynamics from a bond graph perspective. Using an approach that combines bond graph concepts and traditional approaches, the author presents an integrated approach to system dynamics and automatic controls.
The textbook guides students from the process of modeling using bond graphs, through dynamic systems analysis in the time and frequency domains, to classical and state-space controller design methods. Each chapter contains worked examples, review exercises, problems that assess students' grasp of concepts, and open-ended "challenges" that bring in real-world engineering practices. It also includes innovative vodcasts and animated examples, to motivate student learners and introduce new learning technologies.

This text was written for those who teach/learn System Dynamics using bond graphs. It was designed from the onset to be undergraduate focused. As such the material is a synergy of bond graph concepts and a traditional System Dynamics curriculum. The intent was to present bond graphs as a more inte-grated tool within System Dynamics. Moreover, the intention was to develop a text that makes the bond graph methodology more accessible to undergrad-uate Engineering students. The text is purposefully designed to cater to a third or fourth year undergraduate Engineering student.
The prerequisites for this text include Linear Algebra, Ordinary Differ-ential Equations, Engineering Mechanics, and Electrical Circuits. The reader may also benefit from exposure to Fluid Mechanics and Thermodynamics. The text includes ten chapters and can be divided into four parts-bond graph modeling, mathematical representations, analysis, and automatic control.
The first part, Chapters 1-3, focuses on synthesizing models of dynamic systems using the bond graph methodology. The first chapter is an intro-duction to model decomposition based on energy formalisms. This chapter introduces the reader to the needs and uses of System Dynamics. Further, the reader is shown how systems can be broken down into more basic compo-nents. The reader learns that energy and power are two unifying concepts that exist regardless of the energy domain. They are introduced to bonds, signals, and causality. In Chapter 2, the reader learns about basic bond graph elements and discover show elements can be categorized based on their energy usage. Chapter 2 also explains the differences between linear and nonlinear systems. Since the text primarily targets linear systems, the chapter covers lineariza-tion. Finally, in Chapter 3 students learn how to synthesize bond graphs and derive differential equations.
Chapters 4-6 compose the second part which addresses state-space and transfer function representations of dynamic systems. Chapter 4 covers state-space representations. The readers learn how to convert the system of first-order differential equations derived using the bond graph model into a state-space representation. At this point, students are introduced to the use of MATLAB® for numerically simulating basic dynamic responses. (MAT-LAB is used through the second, third, and fourth parts of the text.) Using the state-space model, they simulate impulse, step, and ramp responses. Through Chapter 4, the focus is on time-domain representations. In Chapter 5, the stu-dents review Laplace Transforms in preparation for impedance methods and transfer function representations, which are introduced in Chapter 6. Chap-ter 6 covers some unique material on impedance bond graphs. The chapter is influenced by the unpublished work of Beaman and Paynter (Beaman and Paynter 1993). Students also learn how to simulate responses using transfer function representations derived from impedance bond graphs.
In Chapters 7-8, the text covers analysis, including time-and frequency-domain methods. Time-domain analysis is discussed in detail in Chapter 7. The chapter covers the characteristics of first-and second-order systems and explains how higher-order systems have responses that are the combinations of lower-order responses. In preparation for the introduction to classical con-trol methods in Chapter 9, students learn about pole-zero analysis. Chapter 8 covers the frequency domain. Students discover methods used in the analysis of vibrating systems, AC circuits, and the like. They learn about concepts including phasor analysis, modal analysis, and bode plots.
In the final part, Chapters 9-10, the reader is introduced to automatic con-trol methods that vary from traditional to more modern approaches. The focus in Chapter 9ison classical methods of designing lead-lag and proportional-integral-derivative type compensators. The methods covered include the root locus method and bode plot analysis. Chapter 10, the final chapter, is in-tended to introduce the reader to more modern state-space approaches. The students learn how to assess controllability and observability using the state-space model. They discover how to design a compensator through pole place-ment and linear quadratic regulation. Additionally, they learn about the use and design of state observers.
Each chapter includes three types of exercises. The first are "review" problems or questions. These measure the reader's mastery or understanding of content. The second are simply "problems" like those commonly found in textbooks. These are designed so that the reader practices the concepts introduced in each chapter. They assess the reader's ability to implement the concepts to solve problems similar to examples in the chapter. The third and final type of exercises are "challenges" Challenges are semi-open-ended problems that require the student to transfer the knowledge learned in a man-ner more indicative of "real-world" problems. These challenges do not have one right answer; rather, the solution may vary based on the assumptions made by the student.
Though much of the text is unique material, it brings to bear concepts from Bond Graph Modeling, System Dynamics, and Automatic Controls. It has been influenced by several works including those of Paynter, Beaman, Ogata, Karnoop, Margolis, and Rosenburg (Beaman and Paynter 1993; Payn-ter 1961; Ogata 2002, 2004; Karnopp, Margolis, and Rosenberg 2000). This work has also been impacted by the course notes of Raul G. Longoria and Joseph Beaman from the Mechanical Engineering Department at the Univer-sity of Texas at Austin. It is based primarily on my personal course notes for the System Dynamics course in the Mechanical Engineering Department at the University of Texas-Pan American where I have been teaching dynamic systems related courses for over a decade.
Additional material is available from the CRC Website:
http://www.crcpress.com/product/isbn/9781466560758
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Preface xi

Author Biography xv

Nomenclature xvii

1 Introduction to System Dynamics 1

1.1 Introduction 2

1.2 System Decomposition and Model Complexity 4

1.3 Mathematical Modeling of Dynamic Systems 6

1.4 Analysis and Design of Dynamic Systems 8

1.5 Control of Dynamic Systems 9

1.6 Diagrams of Dynamic Systems 12

1.7 A Graph-Centered Approach to Modeling 13

1.8 Power and Energy Variables 13

1.9 Bonds, Ports, Signals, Inputs, and Outputs 16

1.10 Word Bond Graphs 17

1.11 Summary 19

1.12 Review 20

1.13 Problems 20

1.14 Challenges 24

2 Basic Bond Graph Elements 27

2.1 Introduction 27

2.2 Basic 1-Port Elements 28

      2.2.1 R-Elements 29

      2.2.2 C-Elements 31

      2.2.3 I-Elements 33

      2.2.4 R-, C-, and I-Elements and the Tetrahedron of State 36

      2.2.5 Effort and Flow Sources 37

2.3 Basic 2-Port Elements 39

      2.3.1 Transformers (TF-Elements) 39

      2.3.2 Gyrators (GY-Elements) 42

2.4 Junction Elements 43

2.5 Simple Bond Graph Examples 48

2.6 Linear versus Nonlinear Systems and Linearization 52

2.7 Summary 56

2.8 Review 57

2.9 Problems 58

2.10 Challenges 60

3 Bond Graph Synthesis and Equation Derivation 63

3.1 Introduction 63

3.2 General Guidelines 64

3.3 Mechanical Translation 66

3.4 Mechanical Rotation 74

3.5 Electrical Circuits 78

3.6 Hydraulic Circuits 86

3.7 Mixed Systems 91

3.8 State Equation Derivation 93

3.9 Algebraic Loops and Derivative Causality 107

3.10 Summary 113

3.11 Review 114

3.12 Problems 115

3.13 Challenges 118

4 The State Space and Numerical Simulation 119

4.1 Introduction 119

4.2 The State Space 120

4.3 Composing State-Space Representations 121

4.4 Basic Transient Responses 128

      4.4.1 The Unit Impulse 129

      4.4.2 The Unit Step 130

      4.4.3 The Unit Ramp 131

4.5 State-Space Simulations Using MATLAB 132

4.6 Applications 134

4.7 State Transformations 141

4.8 Summary 145

4.9 Review 146

4.10 Problems 146

4.11 Challenges 149

5 Laplace Transforms 151

5.1 Introduction 151

5.2 Complex Numbers, Variables, and Functions 152

      5.2.1 Complex Numbers 153

      5.2.2 Euler's Theorem 154

      5.2.3 Complex Algebra 156

      5.2.4 Complex Variables and Functions 158

5.3 The Laplace Transform 159

5.4 Common Functions and Their Transforms 160

5.5 Advanced Transforms and Theorems 164

5.6 Inverse Laplace Transforms 173

5.7 Poles, Zeros, Partial Fraction Expansions, and MATLAB 181

5.8 Summary 185

5.9 Review 185

5.10 Problems 186

5.11 Challenges 188

6 Impedance Bond Graphs 191

6.1 Introduction 191

6.2 Laplace Transform of the State-Space Equation 192

6.3 Basic 1-Port Impedances 197

6.4 Impedance Bond Graph Synthesis 200

6.5 Junctions, Transformers, and Gyrators 203

6.6 Effort and Flow Dividers 206

6.7 Sign Changes 208

6.8 Transfer Function Derivation 212

6.9 Alternate Derivation of a Transfer Function 225

6.10 Model Transformations using MATLAB 228

6.11 Summary 231

6.12 Review 233

6.13 Problems 233

6.14 Challenges 236

7 Time Domain Analysis 237

7.1 Introduction 237

7.2 Transient Responses of First-Order Systems 238

      7.2.1 The Natural Response 239

      7.2.2 The Impulse Response 239

      7.2.3 The Step Response 240

      7.2.4 The Ramp Response 243

7.3 Transient Responses of Second-Order Systems 245

      7.3.1 The Natural Response 246

      7.3.2 The Natural Frequency, Damping Ratio, and Pole Placement 255

      7.3.3 The Impulse Response 258

      7.3.4 The Step Response 261

      7.3.5 The Ramp Response 264

7.4 Transient Responses of Higher-Order Systems 266

7.5 An Introduction to Pole-Zero Analysis 269

7.6 Pole-Zero Analysis Using MATLAB 272

7.7 Pole-Zero Analysis in the State Space 276

7.8 Steady-State Space Analysis 279

7.9 Summary 281

7.10 Review 283

7.11 Problems 284

7.12 Challenges 287

8 Frequency Domain Analysis 289

8.1 Introduction 289

8.2 Properties of Sinusoids 291

8.3 The Sinusoidal Transfer Function 292

8.4 Complex Operations Using MATLAB 298

8.5 Mechanical Vibration 301

      8.5.1 Transmissibility 301

      8.5.2 Modal Analysis of Free Vibration 307

8.6 AC Circuits 314

8.7 The Bode Diagram 322

      8.7.1 Frequency Responses of First-Order Factors 324

      8.7.2 Frequency Responses of Second-Order Factors 332

      8.7.3 Frequency Responses of Higher-Order Systems 336

8.8 Summary 341

8.9 Review 343

8.10 Problems 344

8.11 Challenges 347

9 Classical Control Systems 349

9.1 Introduction 349

9.2 Block Diagram Algebra 351

9.3 Proportional, Integral, and Derivative Control Actions 354

9.4 Higher-Order Systems and Dominant Closed-Loop Poles 359

9.5 Static Error Constants 362

9.6 Stability Analysis 367

9.7 Root-Locus Analysis 378

9.8 Plotting the Root Locus Using MATLAB 398

9.9 Tuning PID Compensators 402

9.10 Relating the Transient and Frequency Responses 410

      9.10.1 Stability Analysis in Frequency Domain 411

      9.10.2 Resonance and the Damping Ratio 412

      9.10.3 Phase Margin and the Damping Ratio 415

      9.10.4 Cutoff Frequency and Bandwidth 417

9.11 Compensator Design Using Bode Plot Analysis 418

      9.11.1 Design of Lead Compensators 419

      9.11.2 Design of Lag Compensators 425

      9.11.3 Design of Lead-Lag Compensators 430

      9.11.4 Gain and Phase Margins Using MATLAB 437

9.12 Summary 439

9.13 Review 442

9.14 Problems 443

9.15 Challenges 446

10 Modern Control Systems 447

10.1 Introduction 448

10.2 State Feedback Control 449

10.3 Control System Analysis in the State Space 452

10.4 Control Design Using Pole Placement 458

10.5 Ackermann's Formula 467

10.6 Optimal Control and the Linear Quadratic Regulator 468

10.7 State Observers 472

10.8 State-Space Control Design Using MATLAB 477

10.9 MIMO Control 483

10.10 Summary 488

10.11 Review 489

10.12 Problems 490

10.13 Challenges 492

Bibliography 493

Index 495

Javier A. Ky puros is a professor of mechanical engineering at the University of Texas-Pan American. He earned his PhD in mechanical engineering in 2001at the University of Texas at Austin under the guidance of Dr. Raul Longoria, and his BSE in mechanical engineering from Princeton University in 1996. He has taught courses in the area of dynamic systems and control for over a decade, and has been awarded numerous grants from the National Science Foundation to develop and implement pedagogical innovations for engineering mechanics and system dynamics curricula.

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