An Introduction to Bond Graph Modeling with Applications

J. A. Tenreiro Machado, Vitor M. R. Cunha

• Publisher: Chapman and Hall/CRC
• Year: 2021
• ISBN:
  9781000395501
• Edition: 1
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

An Introduction to Bond Graph Modeling with Applications presents a collection of exercises on dynamical systems, modeling and control for university students in the areas of engineering, physics and applied mathematics. We can find several books on bond graphs, but most merely a small set of exercises and, in a few cases, some commands for computer packages like MATLAB or Mathematica. It is difficult to find books with a broad set of solved exercises and proposed exercises with solutions, guiding researchers starting their work with bond graphs, or students who are just beginning their study of the topic. This book aims to fill that gap, and provide a comprehensive, reader-friendly introduction to the Bond Graph modeling tool. Features

• Gives in-depth theoretical background coupled with practical, hands-on instructions.
• Provides a clear pedagogical framework, with numerous exercises and problems.
• Suitable for students and researchers who work with bond graphs: principally such as applied mathematicians, physicist and engineers.

CHAPTER 1

Mathematical Models of Dynamical Systems

1.1 Introduction

In the study of dynamical systems, both for understanding, describing, predicting and controlling its behavior, we need a model. In general, a mathematical model consists of a set of differential equations that try to represent the dynamics of the system reasonably well. However, a mathematical model is not unique. A given system may be represented in different ways and, therefore, may have several mathematical models, depending on the adopted approach and the final purposes. Hereafter, we consider systems described by a set of ordinary differential equations that may be obtained by following the governing physical laws. The analysis and design of control systems for many applications use linear models, or eventually linearized versions of nonlinear models, not only because they are well established, but also because the treatment of nonlinear systems is considerably more complex.

In this textbook we consider that the principle of causality apply, meaning that the output of the system (i.e., the output at the time instant $t=0$) depends on the past input (i.e., $t\le 0$) but does not depend on the future (i.e., $t>0$). Moreover, it is assumed that readers have the fundamental knowledge of Laplace transform, transfer functions and block diagrams.

The Laplace transform is given by:

$$\begin{array}{l}\mathcal{L}\left\{f(t)\right\}={\displaystyle {\int }_{0^{-}}^{+\infty }f}(t)e^{-st}\text{d}t,\hfill \end{array}$$ (1.1)

where f is a signal evolving in time t, $\mathcal{L}$ denotes the Laplace operator and $s=\sigma +j\omega$ stands for the Laplace variable with $j=\sqrt{-1}$.

The transfer function between the input and output signals, $x(t)$ and $y(t)$, corresponds to the ratio $\frac{Y(s)}{X(s)}$, where $X(s)=\mathcal{L}\left\{x(t)\right\}$ and $Y(s)=\mathcal{L}\left\{y(t)\right\}$ and zero initial conditions are assumed.

Hereafter, the notations $\dot{x}$ and $\ddot{x}$, or $\frac{\text{d}x}{\text{d}t}$ and $\frac{{\text{d}}^{2}x}{\text{d}{t}^2}$, will be considered interchangeably. Id...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• Chapter 1 ▪  Mathematical Models of Dynamical Systems
• Chapter 2 ▪  Bond Graph Modeling
• Chapter 3 ▪  Electrical Systems
• Chapter 4 ▪  Mechanical Systems
• Chapter 5 ▪  Hydraulic Systems
• Chapter 6 ▪  Thermal Systems
• Chapter 7 ▪  Multi-domain Systems
• Chapter 8 ▪  Bond Graph Modeling and Simulation Using \unhbox \voidb@x \hbox {20-sim}
• Solutions
• Appendix A
• Appendix B
• References
• Index