# System Dynamics: Modeling, Simulation, and Control of Mechatronic Systems, 5th Edition

ISBN: 978-0-470-88908-4
648 pages
February 2012
For Instructors

## Description

An expanded new edition of the bestselling system dynamics book using the bond graph approach

A major revision of the go-to resource for engineers facing the increasingly complex job of dynamic systems design, System Dynamics, Fifth Edition adds a completely new section on the control of mechatronic systems, while revising and clarifying material on modeling and computer simulation for a wide variety of physical systems.

This new edition continues to offer comprehensive, up-to-date coverage of bond graphs, using these important design tools to help readers better understand the various components of dynamic systems. Covering all topics from the ground up, the book provides step-by-step guidance on how to leverage the power of bond graphs to model the flow of information and energy in all types of engineering systems. It begins with simple bond graph models of mechanical, electrical, and hydraulic systems, then goes on to explain in detail how to model more complex systems using computer simulations. Readers will find:

• New material and practical advice on the design of control systems using mathematical models
• New chapters on methods that go beyond predicting system behavior, including automatic control, observers, parameter studies for system design, and concept testing
• Coverage of electromechanical transducers and mechanical systems in plane motion
• Formulas for computing hydraulic compliances and modeling acoustic systems
• A discussion of state-of-the-art simulation tools such as MATLAB and bond graph software

Complete with numerous figures and examples, System Dynamics, Fifth Edition is a must-have resource for anyone designing systems and components in the automotive, aerospace, and defense industries. It is also an excellent hands-on guide on the latest bond graph methods for readers unfamiliar with physical system modeling.

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Preface xi

1 Introduction 1

1.1 Models of Systems, 4

1.2 Systems, Subsystems, and Components, 7

1.3 State-Determined Systems, 9

1.4 Uses of Dynamic Models, 10

1.5 Linear and Nonlinear Systems, 11

1.6 Automated Simulation, 12

References, 13

Problems, 14

2 Multiport Systems and Bond Graphs 17

2.1 Engineering Multiports, 17

2.2 Ports, Bonds, and Power, 24

2.3 Bond Graphs, 27

2.4 Inputs, Outputs, and Signals, 30

Problems, 33

3 Basic Bond Graph Elements 37

3.1 Basic 1-Port Elements, 37

3.2 Basic 2-Port Elements, 50

3.3 The 3-Port Junction Elements, 57

3.4 Causality Considerations for the Basic Elements, 63

3.4.1 Causality for Basic 1-Ports, 64

3.4.2 Causality for Basic 2-Ports, 65

3.4.3 Causality for Basic 3-Ports, 66

3.5 Causality and Block Diagrams, 67

Reference, 71

Problems, 71

4 System Models 77

4.1 Electrical Systems, 78

4.1.1 Electrical Circuits, 78

4.1.2 Electrical Networks, 84

4.2 Mechanical Systems, 91

4.2.1 Mechanics of Translation, 91

4.2.2 Fixed-Axis Rotation, 100

4.2.3 Plane Motion, 106

4.3 Hydraulic and Acoustic Circuits, 121

4.3.1 Fluid Resistance, 122

4.3.2 Fluid Capacitance, 125

4.3.3 Fluid Inertia, 130

4.3.4 Fluid Circuit Construction, 132

4.3.5 An Acoustic Circuit Example, 135

4.4 Transducers and Multi-Energy-Domain Models, 136

4.4.1 Transformer Transducers, 137

4.4.2 Gyrator Transducers, 139

4.4.3 Multi-Energy-Domain Models, 142

References, 144

Problems, 144

5 State-Space Equations and Automated Simulation 162

5.1 Standard Form for System Equations, 165

5.2 Augmenting the Bond Graph, 168

5.3 Basic Formulation and Reduction, 175

5.4 Extended Formulation Methods—Algebraic Loops, 183

5.4.1 Extended Formulation Methods—Derivative Causality, 188

5.5 Output Variable Formulation, 196

5.6 Nonlinear and Automated Simulation, 198

5.6.1 Nonlinear Simulation, 198

5.6.2 Automated Simulation, 202

Reference, 207

Problems, 207

6 Analysis and Control of Linear Systems 218

6.1 Introduction, 218

6.2 Solution Techniques for Ordinary Differential Equations, 219

6.3 Free Response and Eigenvalues, 222

6.3.1 A First-Order Example, 223

6.3.2 Second-Order Systems, 225

6.3.3 Example: The Undamped Oscillator, 230

6.3.4 Example: The Damped Oscillator, 232

6.3.5 The General Case, 236

6.4 Transfer Functions, 239

6.4.1 The General Case for Transfer Functions, 241

6.5 Frequency Response, 244

6.5.1 Example Transfer Functions and Frequency Responses, 249

6.5.2 Block Diagrams, 255

6.6 Introduction to Automatic Control, 258

6.6.1 Basic Control Actions, 259

6.6.2 Root Locus Concept, 273

6.6.3 General Control Considerations, 285

6.7 Summary, 310

References, 311

Problems, 311

7 Multiport Fields and Junction Structures 326

7.1 Energy-Storing Fields, 327

7.1.1 C-Fields, 327

7.1.2 Causal Considerations for C-Fields, 333

7.1.3 I -Fields, 340

7.1.4 Mixed Energy-Storing Fields, 348

7.2 Resistive Fields, 350

7.3 Modulated 2-Port Elements, 354

7.4 Junction Structures, 357

7.5 Multiport Transformers, 359

References, 364

Problems, 365

8 Transducers, Amplifiers, and Instruments 371

8.1 Power Transducers, 372

8.2 Energy-Storing Transducers, 380

8.3 Amplifiers and Instruments, 385

8.4 Bond Graphs and Block Diagrams for Controlled Systems, 392

References, 397

Problems, 397

9 Mechanical Systems with Nonlinear Geometry 411

9.1 Multidimensional Dynamics, 412

9.1.1 Coordinate Transformations, 416

9.2 Kinematic Nonlinearities in Mechanical Dynamics, 420

9.2.1 The Basic Modeling Procedure, 422

9.2.2 Multibody Systems, 433

9.2.3 Lagrangian or Hamiltonian IC -Field Representations, 440

9.3 Application to Vehicle Dynamics, 445

9.4 Summary, 452

References, 452

Problems, 453

10 Distributed-Parameter Systems 470

10.1 Simple Lumping Techniques for Distributed Systems, 471

10.1.1 Longitudinal Motions of a Bar, 471

10.1.2 Transverse Beam Motion, 476

10.2 Lumped Models of Continua through Separation of Variables, 482

10.2.1 The Bar Revisited, 483

10.2.2 Bernoulli–Euler Beam Revisited, 491

10.3 General Considerations of Finite-Mode Bond Graphs, 499

10.3.1 How Many Modes Should Be Retained?, 499

10.3.2 How to Include Damping, 503

10.3.3 Causality Consideration for Modal Bond Graphs, 503

10.4 Assembling Overall System Models, 508

10.5 Summary, 512

References, 512

Problems, 512

11 Magnetic Circuits and Devices 519

11.1 Magnetic Effort and Flow Variables, 519

11.2 Magnetic Energy Storage and Loss, 524

11.3 Magnetic Circuit Elements, 528

11.4 Magnetomechanical Elements, 532

11.5 Device Models, 534

References, 543

Problems, 544

CONTENTS ix

12 Thermofluid Systems 548

12.1 Pseudo-Bond Graphs for Heat Transfer, 548

12.2 Basic Thermodynamics in True Bond Graph Form, 551

12.3 True Bond Graphs for Heat Transfer, 558

12.3.1 A Simple Example of a True Bond Graph Model, 561

12.3.2 An Electrothermal Resistor, 563

12.4 Fluid Dynamic Systems Revisited, 565

12.4.1 One-Dimensional Incompressible Flow, 569

12.4.2 Representation of Compressibility Effects in True Bond Graphs, 573

12.4.3 Inertial and Compressibility Effects in One-Dimensional Flow, 576

12.5 Pseudo-Bond Graphs for Compressible Gas Dynamics, 578

12.5.1 The Thermodynamic Accumulator—A Pseudo-Bond Graph Element, 579

12.5.2 The Thermodynamic Restrictor—A Pseudo-Bond Graph Element, 584

12.5.3 Constructing Models with Accumulators and Restrictors, 587

12.5.4 Summary, 590

References, 592

Problems, 592

13 Nonlinear System Simulation 600

13.1 Explicit First-Order Differential Equations, 601

13.2 Differential Algebraic Equations Caused by Algebraic Loops, 604

13.3 Implicit Equations Caused by Derivative Causality, 608

13.4 Automated Simulation of Dynamic Systems, 612

13.4.1 Sorting of Equations, 613

13.4.2 Implicit and Differential Algebraic Equation Solvers, 614

13.4.3 Icon-Based Automated Simulation, 614

13.5 Example Nonlinear Simulation, 616

13.5.1 Some Simulation Results, 620

13.6 Summary, 623

References, 624

Problems, 624

Appendix: Typical Material Property Values Useful in Modeling

Mechanical, Acoustic, and Hydraulic Elements 630

Index 633

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## Author Information

DEAN C. KARNOPP and DONALD L. MARGOLIS are Professors of Mechanical Engineering at the University of California, Davis. RONALD C. ROSENBERG is Professor of Mechanical Engineering at Michigan State University. The authors have extensive experience in teaching system dynamics at the graduate and undergraduate levels and have published numerous papers on the industrial applications of the subject.

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