What this book is about

The main aim of this book is to support the use of modelling as a useful knowledge-enhancing exercise, and to propose corresponding modelling methodologies. As a result, the book is concerned with separating out the model development process from the functions for which the model is developed. We use the term metamodelling to emphasise that we are abstracting and describing the thought processes (and corresponding computer-based tools) which lie behind developing specific models of specific systems. Thus we are concerned to abstract the essentials of modelling and thus move attention away from the details of generating specific mathematical models or simulations towards an understanding of the essentials of modelling physical systems in general.

The bond graph   notation was introduced by [4]; its principles and application have been developed since that time and have been expounded in a number of textbooks   including [3] [6] [8] [5] [2] [7] [1]. We have chosen bond graphs to describe systems and to act as the core model   description for computer-based modelling. We hope to convince the reader that this is a good choice.

The book is divided into two parts:

• Part I: general modelling principles,
• Part II: specific modelling applications

• Part I: Principles
  • Chapter 1: Introduction. This chapter. Discusses why models are needed and, using an example industrial process, develops a requirements specification for a modelling tool.
  • Chapter 2: Representation of Elementary Systems. The decomposition of a system into a structure linking elements representing its static and dynamic behaviour is reviewed, first via classical dynamical analysis and then via the energy bond graph notation. Bond graphs are shown to provide a powerful core model representation from which a variety of mathematical models may be derived. This chapter provides the basic ideas of bond graphs and, in so doing, motivates the more detailed work of the remainder of the book.

  • Chapter 3: Causality. Causality is discussed with particular reference to computational causality. The application of bond graphs to causality analysis is detailed. Although causality may, at first, appear to be an abstract notion, this chapter argues that causality is a crucial aspect of system modelling. Links to related areas such as constraint programming and qualitative modelling are drawn.

  • Chapter 4: Derived models. The use of computers to aid modelling is a central theme of this book. This chapter discusses the twin issues of representation and transformation. In particular, model transformations from the core (bond graph) representation to various derived mathematical models (such as differential-algebraic equation, non-linear state-space, linearised state-space, frequency response etc.) are given and illustrated.
  • Chapter 5: System approximation. The art of modelling is, to a large extent, the art of abstracting the simplest model for the required purpose. Chapter 5 shows how a bond-graph methodology for system approximation can aid the system modeller.
  • Chapter 6: System inversion. System inverses are of intrinsic interest as well as relevant to the design of control systems. This chapter shows how to obtain the bond-graph of an inverse system from the bond-graph of the system itself.

• Part II: Modelling Applications
  • Chapter 7: Process engineering. A systematic approach to modelling process systems is developed and illustrated using a progression of examples. The use of systematic approximation is emphasised.
  • Chapter 8: An extrusion process. The process of insulating copper wire using a plasticating extruder, described in this introduction, is modelled using the hierarchical bond graph approach.
  • Chapter 9: Pharmacokinetics. Models for inhaled drug uptake, with particular relevance to anaesthesia, are derived based on physical principles encapsulated in bond graphs.

  • Chapter 10: Mechanical systems and robotics. Bond graphs are used to model the dynamics of a two-dimensional mechanical link. This basic building block is used to systematically create dynamic models for a number of simple systems including a pendulum, a double pendulum and a two-link manipulator. This process is repeated for three-dimensional systems, resulting in models for robotic manipulators, including the PUMA and Stanford arm architectures.
  • Chapter 11: Control Systems. Applications of modelling to control are given. In particular, the use of models in generating physical model-based controllers is emphasised.

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