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

**by**Karnopp, Dean C.; Margolis, Donald L.; Rosenberg, Ronald C.

5th

### 9780470889084

047088908X

Hardcover

2/28/2012

Wiley

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## Summary

This is a revision of a book currently in its fourth edition which deals with the modeling of physical systems. With this edition (as with prior editions) one of the key features is the extensive use of bond graphs to illustrate and model physical systems. Dynamic systems are taught either using bond graph or not - so the market for Karnopp's book is clearly defined. Bond graphs are a graphical breakdown of a system which illustrates the structure of the system focusing on the flow of information and energy. In this way engineers can better understand the overall system, the various components, and whether they are electrical, chemical, mechanical, etc. The book includes coverage of electromechanical transducers, mechanical systems in plane motion, and formulas for computing hydraulic compliances and for modeling acoustic systems. New chapters and sections are being added that cover the use of physical system models beyond simply predicting system performance - including automatic control, observers, parameter studies for system design, and concept testing. As with the previous editions there will be a solutions manual to accompany this edition.

## Author Biography

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.

## Table of Contents

Preface | p. xi |

Introduction | p. 1 |

Models of Systems | p. 4 |

Systems, Subsystems, and Components | p. 7 |

State-Determined Systems | p. 9 |

Uses of Dynamic Models | p. 10 |

Linear and Nonlinear Systems | p. 11 |

Automated Simulation | p. 12 |

References | p. 13 |

Problems | p. 14 |

Multiport Systems and Bond Graphs | p. 17 |

Engineering Multiports | p. 17 |

Ports, Bonds, and Power | p. 24 |

Bond Graphs | p. 27 |

Inputs, Outputs, and Signals | p. 30 |

Problems | p. 33 |

Basic Bond Graph Elements | p. 37 |

Basic 1-Port Elements | p. 37 |

Basic 2-Port Elements | p. 50 |

The 3-Port Junction Elements | p. 57 |

Causality Considerations for the Basic Elements | p. 63 |

Causality for Basic 1-Ports | p. 64 |

Causality for Basic 2-Ports | p. 65 |

Causality for Basic 3-Ports | p. 66 |

Causality and Block Diagrams | p. 67 |

Reference | p. 71 |

Problems | p. 71 |

System Models | p. 77 |

Electrical Systems | p. 78 |

Electrical Circuits | p. 78 |

Electrical Networks | p. 84 |

Mechanical Systems | p. 91 |

Mechanics of Translation | p. 91 |

Fixed-Axis Rotation | p. 100 |

Plane Motion | p. 106 |

Hydraulic and Acoustic Circuits | p. 121 |

Fluid Resistance | p. 122 |

Fluid Capacitance | p. 125 |

Fluid Inertia | p. 130 |

Fluid Circuit Construction | p. 132 |

An Acoustic Circuit Example | p. 135 |

Transducers and Multi-Energy-Domain Models | p. 136 |

Transformer Transducers | p. 137 |

Gyrator Transducers | p. 139 |

Multi-Energy-Domain Models | p. 142 |

References | p. 144 |

Problems | p. 144 |

State-Space Equations and Automated Simulation | p. 162 |

Standard Form for System Equations | p. 165 |

Augmenting the Bond Graph | p. 168 |

Basic Formulation and Reduction | p. 175 |

Extended Formulation Methods-Algebraic Loops | p. 183 |

Extended Formulation Methods-Derivative Causality | p. 188 |

Output Variable Formulation | p. 196 |

Nonlinear and Automated Simulation | p. 198 |

Nonlinear Simulation | p. 198 |

Automated Simulation | p. 202 |

Reference | p. 207 |

Problems | p. 207 |

Analysis and Control of Linear Systems | p. 218 |

Introduction | p. 218 |

Solution Techniques for Ordinary Differential Equations | p. 219 |

Free Response and Eigenvalues | p. 222 |

A First-Order Example | p. 223 |

Second-Order Systems | p. 225 |

Example: The Undamped Oscillator | p. 230 |

Example: The Damped Oscillator | p. 232 |

The General Case | p. 236 |

Transfer Functions | p. 239 |

The General Case for Transfer Functions | p. 241 |

Frequency Response | p. 244 |

Example Transfer Functions and Frequency Responses | p. 249 |

Block Diagrams | p. 255 |

Introduction to Automatic Control | p. 258 |

Basic Control Actions | p. 259 |

Root Locus Concept | p. 273 |

General Control Considerations | p. 285 |

Summary | p. 310 |

References | p. 311 |

Problems | p. 311 |

Multiport Fields and Junction Structures | p. 326 |

Energy-Storing Fields | p. 327 |

C-Fields | p. 327 |

Causal Considerations for C-Fields | p. 333 |

I-Fields | p. 340 |

Mixed Energy-Storing Fields | p. 348 |

Resistive Fields | p. 350 |

Modulated 2-Port Elements | p. 354 |

Junction Structures | p. 357 |

Multiport Transformers | p. 359 |

References | p. 364 |

Problems | p. 365 |

Transducers, Amplifiers, and Instruments | p. 371 |

Power Transducers | p. 372 |

Energy-Storing Transducers | p. 380 |

Amplifiers and Instruments | p. 385 |

Bond Graphs and Block Diagrams for Controlled Systems | p. 392 |

References | p. 397 |

Problems | p. 397 |

Mechanical Systems with Nonlinear Geometry | p. 411 |

Multidimensional Dynamics | p. 412 |

Coordinate Transformations | p. 416 |

Kinematic Norlinearities in Mechanical Dynamics | p. 420 |

The Basic Modeling Procedure | p. 422 |

Multibody Systems | p. 433 |

Lagrangian or Hamiltonian IC-Field Representations | p. 440 |

Application to Vehicle Dynamics | p. 445 |

Summary | p. 452 |

References | p. 452 |

Problems | p. 453 |

Distributed-Parameter Systems | p. 470 |

Simple Lumping Techniques for Distributed Systems | p. 471 |

Longitudinal Motions of a Bar | p. 471 |

Transverse Beam Motion | p. 476 |

Lumped Models of Continua through Separation of Variables | p. 482 |

The Bar Revisited | p. 483 |

Bernoulli-Euler Beam Revisited | p. 491 |

General Considerations of Finite-Mode Bond Graphs | p. 499 |

How Many Modes Should Be Retained? | p. 499 |

How to Include Damping | p. 503 |

Causality Consideration for Modal Bond Graphs | p. 503 |

Assembling Overall System Models | p. 508 |

Summary | p. 512 |

References | p. 512 |

Problems | p. 512 |

Magnetic Circuits and Devices | p. 519 |

Magnetic Effort and Flow Variables | p. 519 |

Magnetic Energy Storage and Loss | p. 524 |

Magnetic Circuit Elements | p. 528 |

Magnetomechanical Elements | p. 532 |

Device Models | p. 534 |

References | p. 543 |

Problems | p. 544 |

Thermofluid Systems | p. 548 |

Pseudo-Bond Graphs for Heat Transfer | p. 548 |

Basic Thermodynamics in True Bond Graph Form | p. 551 |

True Bond Graphs for Heat Transfer | p. 558 |

A Simple Example of a True Bond Graph Model | p. 561 |

An Electrothermal Resistor | p. 563 |

Fluid Dynamic Systems Revisited | p. 565 |

One-Dimensional Incompressible Flow | p. 569 |

Representation of Compressibility Effects in True Bond Graphs | p. 573 |

Inertial and Compressibility Effects in One-Dimensional Flow | p. 576 |

Pseudo-Bond Graphs for Compressible Gas Dynamics | p. 578 |

The Thermodynamic Accumulator-A Pseudo-Bond Graph Element | p. 579 |

The Thermodynamic Restrictor-A Pseudo-Bond Graph Element | p. 584 |

Constructing Models with Accumulators and Restrictors | p. 587 |

Summary | p. 590 |

References | p. 592 |

Problems | p. 592 |

Nonlinear System Simulation | p. 600 |

Explicit First-Order Differential Equations | p. 601 |

Differential Algebraic Equations Caused by Algebraic Loops | p. 604 |

Implicit Equations Caused by Derivative Causality | p. 608 |

Automated Simulation of Dynamic Systems | p. 612 |

Sorting of Equations | p. 613 |

Implicit and Differential Algebraic Equation Solvers | p. 614 |

Icon-Based Automated Simulation | p. 614 |

Example Nonlinear Simulation | p. 616 |

Some Simulation Results | p. 620 |

Summary | p. 623 |

References | p. 624 |

Problems | p. 624 |

Appendix: Typical Material Property Values Useful in Modeling Mechanical, Acoustic, and Hydraulic Elements | p. 630 |

Index | p. 633 |

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