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# MTT: Model Transformation Tools

MTT is a set of Model Transformation Tools based on bond graphs. MTT implements the theory to be found in the book "Metamodelling: Bond Graphs and Dynamic Systems" by Peter Gawthrop and Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).

It implements two features not discussed in that book:

- bicausal bond graphs and
- hierarchical bond graphs.

1. Introduction |  |
2. User interface |  |
3. Creating Models |  |
4. Simulation |  |
5. Sensitivity models |  |
6. Representations |  |
7. Extending MTT |  |
8. Documentation |  |
9. Languages |  |
10. Language tools |  |
11. Administration |  |
Glossary |  |
Index |  |
-- The Detailed Node Listing ---
Introduction
1.1 What is a representation? |  |
1.2 What is a transformation? |  |
1.3 What is a bond graph? |  |
1.4 Variables |  |
1.5 Bonds |  |
1.6 Components |  |
1.7 Algebraic loops |  |
1.8 Switched systems |  |
Components
1.6.1 Ports |  |
1.6.2 Constitutive relationship |  |
1.6.3 Symbolic parameters |  |
1.6.4 Numeric parameters |  |
User interface
2.1 Menu-driven interface |  |
2.2 Command line interface |  |
2.3 Options |  |
2.4 Utilities |  |
Utilities
2.4.1 Help |  |
2.4.2 Copy |  |
2.4.3 Clean |  |
2.4.4 Version control |  |
Help
2.4.1.1 help representations |  |
2.4.1.2 help components |  |
2.4.1.3 help examples |  |
2.4.1.4 help crs |  |
2.4.1.5 help <name> |  |
Creating Models
3.1 Quick start |  |
3.2 Creating simple models |  |
3.3 Creating complex models |  |
Creating complex models
3.3.1 Top level |  |
Simulation
4.1 Steady-state solutions |  |
4.2 Simulation parameters |  |
4.3 Simulation input |  |
4.4 Simulation logic |  |
4.5 Simulation initial state |  |
4.6 Simulation code |  |
4.7 Simulation output |  |
Steady-state solutions
4.1.1 Steady-state solutions (odess) |  |
4.1.2 Steady-state solutions (ss) |  |
Simulation parameters
4.2.1 Euler integration |  |
4.2.2 Implicit integration |  |
4.2.3 Runge Kutta IV integration |  |
4.2.4 Hybrd algebraic solver |  |
Simulation code
4.6.1 Dynamically linked functions |  |
Simulation output
4.7.1 Viewing results with gnuplot |  |
4.7.2 Exporting results to SciGraphica |  |
Representations
6.1 Representation summary |  |
6.2 Defining representations |  |
6.3 Verbal description (desc) |  |
6.4 Acausal bond graph (abg) |  |
6.5 Stripped acausal bond graph (sabg) |  |
6.6 Labels (lbl) |  |
6.7 Structure (struc) |  |
6.8 Constitutive relationship (cr) |  |
6.9 Parameters |  |
6.10 Causal bond graph (cbg) |  |
6.11 Elementary system equations (ese) |  |
6.12 Differential-Algebraic Equations (dae) |  |
6.13 Constrained-state Equations (cse) |  |
6.14 Ordinary Differential Equations |  |
6.15 Descriptor matrices (dm) |  |
6.16 Report (rep) |  |
Acausal bond graph (abg)
6.4.1 Language fig (abg.fig) |  |
6.4.2 Language m (rbg.m) |  |
6.4.3 Language m (abg.m) |  |
6.4.4 Language tex (abg.tex) |  |
Language fig (abg.fig)
6.4.1.1 Icon library |  |
6.4.1.2 Bonds |  |
6.4.1.3 Strokes |  |
6.4.1.4 Components |  |
6.4.1.5 Simple components |  |
6.4.1.6 SS components |  |
6.4.1.7 Simple components - implementation |  |
6.4.1.8 Compound components |  |
6.4.1.9 Named SS components |  |
6.4.1.10 Coerced bond direction |  |
6.4.1.11 Port labels |  |
6.4.1.12 Vector port labels |  |
6.4.1.13 Port label defaults |  |
6.4.1.14 Vector Components |  |
6.4.1.15 Artwork |  |
6.4.1.16 Valid Names |  |
Simple components
6.4.1.6 SS components |  |
6.4.1.7 Simple components - implementation |  |
Compound components
6.4.1.9 Named SS components |  |
Language m (rbg.m)
6.4.2.1 Transformation abg2rbg_fig2m |  |
Language m (abg.m)
6.4.3.1 Arrow-orientated causality |  |
6.4.3.2 Component-orientated causality |  |
6.4.3.3 Transformation rbg2abg_m |  |
Stripped acausal bond graph (sabg)
6.5.1 Language fig (sabg.fig) |  |
6.5.2 Stripped acausal bond graph (view) |  |
Labels (lbl)
6.6.1 SS component labels |  |
6.6.2 Other component labels |  |
6.6.3 Component names |  |
6.6.4 Component constitutive relationship |  |
6.6.5 Component arguments |  |
6.6.6 Parameter declarations |  |
6.6.7 Units declarations |  |
6.6.8 Interface Control Definition |  |
6.6.9 Aliases |  |
6.6.10 Parameter passing |  |
6.6.11 Old-style labels (lbl) |  |
6.6.12 Language tex (desc.tex) |  |
Other component labels
6.6.3 Component names |  |
6.6.4 Component constitutive relationship |  |
6.6.5 Component arguments |  |
6.6.9 Aliases |  |
6.6.10 Parameter passing |  |
6.6.11 Old-style labels (lbl) |  |
Aliases
6.6.9.1 Port aliases |  |
6.6.9.2 Parameter aliases |  |
6.6.9.3 CR aliases |  |
6.6.9.4 Component aliases |  |
Old-style labels (lbl)
6.6.11.1 SS component labels (old-style) |  |
6.6.11.2 Other component labels (old-style) |  |
6.6.11.3 Parameter passing (old-style) |  |
Parameter passing (old-style)
6.6.12 Language tex (desc.tex) |  |
Structure (struc)
6.7.1 Language txt (struc.txt) |  |
6.7.2 Language tex (struc.tex) |  |
6.7.3 Language tex (view) |  |
Constitutive relationship (cr)
6.8.1 Predefined constitutive relationships |  |
6.8.2 DIY constitutive relationships |  |
6.8.3 Unresolved constitutive relationships |  |
6.8.4 Unresolved constitutive relationships - Octave |  |
6.8.5 Unresolved constitutive relationships - c++ |  |
Predefined constitutive relationships
6.8.1.1 lin |  |
6.8.1.2 exotherm |  |
Parameters
6.9.1 Symbolic parameters (subs.r) |  |
6.9.2 Symbolic parameters for simplification (simp.r) |  |
6.9.3 Numeric parameters (numpar) |  |
Numeric parameters (numpar)
6.9.3.1 Text form (numpar.txt) |  |
Causal bond graph (cbg)
6.10.1 Language fig (cbg.fig) |  |
6.10.2 Language m (cbg.m) |  |
Language m (cbg.m)
6.10.2.1 Transformation abg2cbg_m |  |
Elementary system equations (ese)
6.11.0.1 Transformation cbg2ese_m2r |  |
Differential-Algebraic Equations (dae)
6.12.1 Language reduce (dae.r) |  |
6.12.2 Language m (dae.m) |  |
Language reduce (dae.r)
6.12.1.1 Transformation ese2dae_r |  |
Language m (dae.m)
6.12.2.1 Transformation dae_r2m |  |
Constrained-state Equations (cse)
6.13.1 Language reduce (cse.r) |  |
6.13.2 Language m (view) |  |
Language reduce (cse.r)
6.13.1.1 Transformation dae2cse_r |  |
Ordinary Differential Equations
6.14.1 Language reduce (ode.r) |  |
6.14.2 Language m (ode.m) |  |
6.14.3 Language m (view) |  |
Language reduce (ode.r)
6.14.1.1 Transformation cse2ode_r |  |
Language m (ode.m)
6.14.2.1 Transformation ode_r2m |  |
Descriptor matrices (dm)
6.15.1 Language reduce (dm.r) |  |
6.15.2 Language m (dm.m) |  |
Report (rep)
6.16.1 Language text (rep.txt) |  |
6.16.2 Language view |  |
Extending MTT
7.1 Makefiles |  |
7.2 New (DIY) representations |  |
7.3 Component library |  |
New (DIY) representations
7.2.1 Makefile |  |
7.2.2 Shell-script |  |
7.2.3 Documentation |  |
Documentation
8.1 Manual |  |
8.2 On-line documentation |  |
On-line documentation
8.2.1 Brief on-line documentation |  |
8.2.2 Detailed on-line documentation |  |
Languages
9.1 Fig |  | r
9.2 m |  |
9.3 Reduce |  |
9.4 c |  |
Language tools
10.1 Views |  |
10.2 Xfig |  |
10.3 Text editors |  |
10.4 Octave |  |
10.5 LaTeX |  |
Octave
10.4.1 Octave control system toolbox (OCST) |  |
10.4.2 Creating GNU Octave .oct files |  |
10.4.3 Creating Matlab .mex files |  |
10.4.4 Embedding MTT models in Simulink |  |
Administration
11.1 Software components |  |
11.2 REDUCE setup |  |
11.3 Octave setup |  |
11.4 Paths |  |
11.5 File structure |  |
A.1 GNU Free Documentation License |  |
A.2 GNU GENERAL PUBLIC LICENSE |  |
Octave setup
11.3.1 .octaverc |  |
11.3.2 .oct file dependencies |  |
Paths
11.4.1 $MTTPATH |  |
11.4.2 $MTT_COMPONENTS |  |
11.4.3 $MTT_CRS |  |
11.4.4 $MTT_EXAMPLES |  |
11.4.5 $OCTAVE_PATH |  |

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# 1. Introduction

MTT is a set of Model Transformation Tools based on bond graphs. MTT implements the theory to be found in the book "Metamodelling: Bond Graphs and Dynamic Systems" by Peter Gawthrop and Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).

It implements two features not discussed in that book:

- bicausal bond graphs and
- hierarchical bond graphs.

In the context of software, it has been said that one good tool is worth many packages. UNIX is a good example of this philosophy: the user can put together applications from a range of ready made tools. This manual describes the application of this philosophy to dynamic system modeling embodied in MTT - a set of Model Transformation Tools each of which implements a single transformation between system representations.

System representations have two attributes.

- A Form: e.g. acausal bond graph, differential algebraic, linear state-space etc.
- A Language: e.g. Fig, Matlab, LaTeX, Reduce, postscript etc.

Transformations in MTT are accomplished using appropriate software (e.g. Octave/Matlab, Reduce) encapsulated in UNIX Bourne shell scripts. The relationships between the tools are encoded in a Make File; thus the user can specify a final representation and all the necessary intermediate transformations are automatically generated.

1.1 What is a representation? |  |
1.2 What is a transformation? |  |
1.3 What is a bond graph? |  |
1.4 Variables |  |
1.5 Bonds |  |
1.6 Components |  |
1.7 Algebraic loops |  |
1.8 Switched systems |  |

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## 1.1 What is a representation?

Physical systems have many representations. These include

- a schematic diagram,
- a block diagram,
- a bunch of equations,
- a single differential(-algebraic) equation,
- simulation code,
- linearised state-space (or descriptor) equations,
- transfer function (of the linearised system),
- frequency response (of the linearised system),
- etc...

Each of these representations is related to other representations by an appropriate transformation (see section 1.2 What is a transformation?. In many cases, a modeler is presented with a physical system and needs to make a model. In particular, a model, in this context, is a representation of the system appropriate to a particular use, for example:

- simulation,
- control system design,
- optimisation
- etc.

Indeed, for a given physical system, the modeler would need to derive a number of models. This process can be viewed as a series of steps; each involving a transformation between representations (see section 1.2 What is a transformation?.

In this context, the following considerations are relevant.

- There is a unique `core' representation of any system. There are many routes from this core representation, each leading to an appropriate model. There are many possible routes to this core representation from the physical system: the route chosen is a matter of convenience.
- Because the core representation is unique, it is easy to expand the tool-box to include additional transformations from the physical system to the core representation and additional transformations from the core representation to the mode.
- Transformation_1 probably cannot, and certainly should not, be completely automated. Engineering insight, knowledge and experience is essential to capture the essence (with respect to the particular use) of the physical system whilst discarding irrelevant form.
- Representation_1 should be `close' in some sense to the Physical system.
- The core representation, and hence the representations leading to it, must contain enough information to generate all of the required models.
- Representations must be easily extensible: it must be possible to add extra components or attributes without restructuring the representation.

I happen to believe that Bond graphs (see section 1.3 What is a bond graph?) provide the most convenient and powerful basis for the core representation.

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## 1.2 What is a transformation?

Each system representation (see section 1.1 What is a representation? is related to other representations by an appropriate transformation as follows:

- Physical system
- Transformation_1 ---> Representation_1
- Transformation_2 ---> Representation_2
- ...
- Transformation_N ---> Core representation
- Transformation_N+1 ---> Representation_N+1
- Transformation_N+2 ---> Representation_N+2
- ...
- Transformation_N+M ---> Model

Thus modeling is seen as a sequence of transformations between representations.

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## 1.3 What is a bond graph?

Bond graphs provide a graphical high-level language for describing dynamic systems in a precise and unambiguous fashion. They make a clear distinction between structure (how components are connected together), and behavior (the particular constitutive relationships, or physical laws, describing each component.

They can describe a range of physical systems including:

- Electrical systems
- Mechanical systems
- Hydraulic systems
- Chemical process systems

More importantly, they can describe systems which contain subsystems drawn from all of these domains in a uniform manner.

Bond graphs are made up of components (see section 1.6 Components) connected by bonds (see section 1.5 Bonds) which define the relationship between variables (see section 1.4 Variables).

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## 1.4 Variables

In bond graph terminology there are four sorts of variables:

- effort variables
- flow variables
- integrated effort variables
- integrated flow variables

Examples of effort variables are

- voltage
- pressure
- force
- torque
- temperature

Examples of flow variables are

- current
- volumetric flow rate
- velocity
- angular velocity
- heat flow

Examples of integrated flow variables are

- charge
- volume
- momentum
- angular momentum
- heat

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## 1.5 Bonds

Bonds connect components (see section 1.6 Components) together. Each bond carries two variables:

- an effort (see section 1.4 Variables) variable and
- a flow (see section 1.4 Variables) variable.

Each bond has three notations associated with it:

- a half-arrow,
- a causal stroke and
- a causal half-stroke.

The half-arrow indicates two things:

- the direction of power (or pseudo power) flow and
- the side of the bond associated with the flow variable.

The causal stroke indicates two things:

- the effort variable is imposed at the same end as the stroke and
- the flow variable is imposed at the opposite end to the stroke.

The causal half-stoke indicates one thing:

- if it is on the effort side of the bond, the effort variable is imposed at the same end as the stroke or
- if it is on the flow side of the bond, the flow variable is imposed at the opposite end to the stroke.

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## 1.6 Components

Components provide the building blocks of a dynamic system when connected by bonds (see section 6.4.1.2 Bonds). Components have the following attributes:

`ports`
  provide the connections to other components (see section 1.6.1 Ports)
`constitutive relationships`
  define how the port-variables are related (see section 1.6.2 Constitutive relationship)

1.6.1 Ports |  |
1.6.2 Constitutive relationship |  |
1.6.3 Symbolic parameters |  |
1.6.4 Numeric parameters |  |

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### 1.6.1 Ports

Components have one or more ports. Each port carries two variables, and effort and a flow variable (see section 1.4 Variables). Any pair of ports can be connected by a bond (see section 1.5 Bonds); this connection is equivalent to saying that the effort variables at each port are identical and that the flow variables at each port are identical.

Ports are implemented in MTT using named SS components. (see section 6.4.1.9 Named SS components).

The direction of the named SS components. (see section 6.4.1.9 Named SS components) is coerced (see section 6.4.1.10 Coerced bond direction) to have the same direction as the bons connected to the corresponding port. Thus the direction of the direction of the named SS components has no significance unless the component is at the top level.

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### 1.6.2 Constitutive relationship

The constitutive relationship of a component defines how the port variables are related. This relationship may be linear or non-linear. This typically contains symbolic parameters (see section 1.6.3 Symbolic parameters) which may be replaced, for the purposes of numerical analysis by numeric parameters (see section 1.6.4 Numeric parameters).

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### 1.6.3 Symbolic parameters

The constitutive relationship of a system component (see section 1.6 Components) typically contains symbolic parameters. For example a resistor may have a symbolic resistance r. It is convenient to leave such parameters as symbols when viewing equations or when performing symbolic analysis such as differentiation.

However, MTT allows replacement of symbolic parameters by numeric parameters (see section 1.6.4 Numeric parameters) when appropriate.

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### 1.6.4 Numeric parameters

Numerical parameters are needed to give specific values to symbolic parameters (see section 1.6.3 Symbolic parameters) for the purposes of numeric analysis; for example: simulation, graph plotting or use within a numerical package such as Octave (see section 10.4 Octave).

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## 1.7 Algebraic loops

Following Chapter 3 of the book, algebraic loops appear as under-causal components in the bond graph. It is up to the modeler to indicate how these loops are to be resolved by adding appropriate SS elements.

In particular if zero junction is undercausal an SS:loop component (with effort output indicated by a causal stroke) with the following label file entry:

      loop SS unknown,zero

For more information, refer to: "Metamodelling: Bond Graphs and Dynamic Systems" by Peter Gawthrop and Lorcan Smith published by Prentice Hall in 1996 (ISBN 0-13-489824-9).

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## 1.8 Switched systems

Some systems contain switch-like components. For example an electrical system may contain on-off switches and diodes and a hydraulic system may shut-off valves and non-return valves.

Such systems are sometimes called hybrid systems. The modelling an simulation of such systems is the subject of current research. MTT implements a simple pragmatic approach to the modelling and simulation of such systems via two new Bond Graph components:

`ISW`
  a switched `I` component
`CSW`
  a switched `C` component

These switches are user controlled through the logic representation (see section 4.4 Simulation logic).

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# 2. User interface

There are two user interfaces to MTT: a command line interface (see section 2.2 Command line interface) and a menu-driven interface (see section 2.1 Menu-driven interface).

2.1 Menu-driven interface |  |
2.2 Command line interface |  |
2.3 Options |  |
2.4 Utilities |  |

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## 2.1 Menu-driven interface

The Menu-driven interface for MTT is invoked as:

    xmtt

This will bring up a menu which should be self explanatory :-). Various messages will be echoed in the window from whence xMTT was invoked.

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## 2.2 Command line interface

The command line interface for MTT is of the form:

    mtt [options] <system_name> <representation> <language>

`[options]`
  the (optional) option switches (see section 2.3 Options)
`<system_name>`
  the name of the system being transformed
`<representation>`
  the mnemonic for the system representation (see section 6.1 Representation summary)
`<language>`
  the mnemonic for language for the representation (see section 9. Languages)

for example

    mtt rc rep view

creates a view of the report describing system rc and

    mtt rc sm m

creates an m file (suitlable for Octave or Matlab) containing state matrices describing the system rc.

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## 2.3 Options

MTT has a number of optional switches to control its operation. These are invoked immediately after `mtt' on the command line; for example:

    mtt -o -ss -cc syst cbg view

invokes the `-o`, `-ss`, and `-cc` options.

If you wish to use an option all the time, use the alias function appropriate to the shell you are using. For example, using bash:

    alias mtt='mtt -o -ss -cc'

Means that the previous example can be executed using

    mtt syst cbg view

The available options are:

`-q`
  quiet mode -- suppress MTT banner
`-A`
  solve algebraic equations symbolically
`-ae`
  <hybrd> solve algebraic equations numerically (this option requires -cc or -oct)
`-D`
  debug -- leave log files etc
`-I`
  prints more information
`-abg`
  start at abg.m representation
`-c`
  c-code generation
`-cc`
  C++ code generation
`-d`
  <dir> use directory <dir>
`-dc`
  Maximise derivative (not integral) causality
`-dc`
  Maximise derivative (not integral) causality
`-i`
  <implicit|euler|rk4> Use implicit, euler or Runge Kutta IVintegration
`-o`
  ode is same as dae
`-oct`
  use oct files in place of m files where appropriate
`-opt`
  optimise code generation
`-p`
  print environment variables
`-partition`
  partition hierachical system
`-r`
  reset time stamp on representation
`-s`
  try to generate sensitivity BG (experimental)
`-ss`
  use steady-state info to initialise simulations
`-stdin`
  read input data from standard input for simulations
`-sub`
  <subsystem> operate on this subsystem
`-t`
  tidy mode (default)
`-u`
  untidy mode (leaves files in current dir)
`-v`
  verbose mode (multiple uses increase the verbosity)
`-viewlevel`
  <N> View N levels of hierachy
`--version`
  print version and exit
`--versions`
  print version of mtt and components and exit

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## 2.4 Utilities

MTT provides some utilities to help you keep track of model building and to keep things clean and tidy. The commands, and there purpose are:

`mtt help`
  Lists the help/browser commands
`mtt copy <system>`
  Copies the system (ie directory and enclosed files) to the current working directory.
`mtt rename <old_name> <new_name>`
  Renames all of the defining representations (see section 6.2 Defining representations) and textually changes each file appropriately.
`mtt <system> clean`
  Remove all files generated by MTT associated with system `system'.
`mtt clean`
  Remove all files generated by MTT associated with all systems within the current directory.
`mtt system representation vc`
  Apply version control to representation `representation' of system `system'.
`mtt system vc`
  Apply version control to all representations (under version control) system `system'.

These are described in more detail in the following sections.

2.4.1 Help |  |
2.4.2 Copy |  |
2.4.3 Clean |  |
2.4.4 Version control |  |

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### 2.4.1 Help

MTT implements a browser to keep track of all the systems, subsystems and constitutive relationships that you, and others may write. It is invoked in the following ways:

           mtt help representations
           mtt help components
           mtt help examples
           mtt help crs
           mtt help representations <match_string>
           mtt help components <match_string>
           mtt help examples  <match_string>
           mtt help crs <match_string>
           mtt help <component_or_example_or_CR_name>

2.4.1.1 help representations |  |
2.4.1.2 help components |  |
2.4.1.3 help examples |  |
2.4.1.4 help crs |  |
2.4.1.5 help <name> |  |

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#### 2.4.1.1 help representations

The command

    mtt help representations

lists all of the representations (see section 6. Representations) available in MTT. These may change as the version number of MTT increases.

The command

    mtt help representations <match_string>

lists those representation which contain the string `match_string`. This string can be any regular expression (see standard Linux documentation under `awk`). For example

    mtt help representations descriptor

gives all representations containing the word `descriptor`.

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#### 2.4.1.2 help components

The command

    mtt help components

lists all of the components (see section 1.6 Components) available in MTT. These may change as the version number of MTT increases.

The command

    mtt help components <match_string>

lists those component which contain the string `match_string`. This string can be any regular expression (see standard Linux documentation under `awk`). For example

    mtt help components source

gives all components containing the word `component`.

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#### 2.4.1.3 help examples

This command provides a good way to get started in MTT. having found an interesting example, copy it to your working directory using

    mtt copy <example_name>

(see section 2.4.2 Copy)

    mtt help examples

lists all of the examples available in MTT. This list will change as more examples are added.

The command

    mtt help examples <match_string>

lists those component which contain the string `match_string`. This string can be any regular expression (see standard Linux documentation under `awk`). For example

    mtt help examples pharmokinetic

gives all examples containing the word `pharmokinetic`.

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#### 2.4.1.4 help crs

The command

    mtt help crs

lists all of the constitutive relationships (see section 1.6.2 Constitutive relationship) available in MTT. These may change as the version number of MTT increases.

The command

    mtt help crs <match_string>

lists those constitutive relationships which contain the string `match_string`. This string can be any regular expression (see standard Linux documentation under `awk`). For example

    mtt help crs sin

gives all crs containing the word `sin`.

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#### 2.4.1.5 help <name>

The command

    mtt help <name>

gives a detailed description of the entity called `name`.

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### 2.4.2 Copy

MTT provides a way of copying examples to your working directory:

    mtt copy <example_name>

Use the command

    mtt help examples

(see section 2.4.1.3 help examples) to find something of interest.

Note that components and constitutive relationships are automatically copied when required.

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### 2.4.3 Clean

MTT generates a lot of representations in a number of languages. Some of these you will edit yourself; others can always be recreated by MTT. It makes sense, therefore to have a utility that removes all of these other files when you have finished actively working with a particular system. These are two versions:

1. `mtt system clean`
2. `mtt clean`

The first removes all files that can be regenerated with MTT associated with system `system'; the second removes all such files associated with all systems in the current working directory.

The files which remain after such a clean are the Defining representations (see section 6.2 Defining representations).

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### 2.4.4 Version control

When you are working on a modeling project, it is easy to forget what changes you made to a system and why you made them. Sometimes, you may regret some changes and wish to revert to an earlier version: even if you use .old files this may be difficult to achieve safely.

These are very similar problems to those faced by software developers and can be solved in the same way: using version control.MTT provides version control using the standard GNU Revision Control System (RCS). This is hidden from the user, but is fully complementary to direct use of RCS (e.g. via emacs vc commands) to the more experienced user who wishes to do so.

The only files that you should ever change (i.e. the ones never overwritten by MTT) are the Defining representations (see section 6.2 Defining representations).

All of the files, with the exception of `system_abg.fig`, are initially created by MTT and contain the RCS header for version control.

The MTT version control will automatically expand this part of the text to include all change comments that you give it -- so will direct use of RCS (e.g. via emacs vc commands)

The MTT version commands are as follows:

`mtt system representation vc`
  Apply version control to representation `representation' of system `system'.
`mtt system vc`
  Apply version control to all representations (under version control) system `system'.

The first is appropriate after you have made a revision to a single file. It will prompt you for a change comment; this will be automatically included in the file header. In addition, enough information will be saved to enable any version to be retrieved via RCS.

The second is appropriate to record the state of the entire model. This assumes that all relevant files have been recorded by the first version of the command. Once again, old versions of the entire model can be retrieved using the relevant RCS commands.

A subdirectory `RCS' is created to hold this information. You need not bother about the contents, except that you must not delete any files within `RCS'.

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# 3. Creating Models

MTT helps you to analyse and transform system models -- ultimately the process of capturing the real world in a model is up to you. This chapter discusses the MTT aspects of creating a model. For convenience, this is divided into creating simple models and creating complex models.

3.1 Quick start |  |
3.2 Creating simple models |  |
3.3 Creating complex models |  |

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## 3.1 Quick start

It is probably worth a quick skim though MTT to get a flavour of what it can do before plunging into the detail of the rest of this document. Here is a series of commands to do this.

Copy an initial set of files describing the bond graph.

    mtt copy rc

Move to it.

    cd rc

View the acausal bond graph (the system is called "rc").

    mtt rc abg view

View the causal bond graph of the system.

    mtt rc cbg view

View the corresponding ordinary differential equations (ode).

    mtt rc ode view

View the system (output) step response

    mtt rc sro view

An alternative (but more general) way of achieving the same result is

    mtt -c rc odeso view

View the system transfer function

    mtt rc tf view

View the log modulus frequency response of the system.

    mtt rc lmfr view

View the log modulus frequency response of the system for 100 logarithmically spaced frequencies in the range 0.1 to 10 radians per second.

    mtt rc lmfr view 'W=logspace(-1,1,100);'

MTT has a report generation ((see section 6.16 Report (rep)) facility which can generate a hypertext description of the system.

    mtt rc rep hview

The report contents are specified by the rep representation (see section 6.16 Report (rep)), in this case the corresponding file is:

    % %% Outline report file for system rc (rc_rep.txt)

    mtt rc abg tex
    mtt rc struc tex
    mtt rc cbg ps
    mtt rc ode tex
    mtt rc ode dvi
    mtt rc sm tex
    mtt rc tf tex
    mtt rc tf dvi
    mtt rc sro ps
    mtt rc lmfr ps
    mtt rc odes h
    mtt rc numpar txt
    mtt rc input txt
    mtt -c rc odeso ps
    mtt rc rep txt

A non-hypertext version can be viewed using:

    mtt rc rep view

Now have a go at modifying the bond graph.

    mtt rc abg fig

This brings up the bond graph in Xfig (see section 10.2 Xfig). Try creating a system with two rs and 2 cs.

More examples can be found using

    mtt help examples

Details of an example can be found using

    mtt help <example_name>

and copied using

    mtt copy <example_name>

Lots of examples are available.

    mtt help examples

lists them and

    mtt copy <name>

gets you an example.

A number of examples are to be found <A HREF="http://www.mech.gla.ac.uk/~peterg/software/MTT/examples/Examples/Examples.html"> here</A>.

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## 3.2 Creating simple models

For then purposes of this section, simple models are those which are built up from bond graphs involving predefined components. In contrast, more complex systems (see section 3.3 Creating complex models) need to be built up hierarchically.

The recommended sequence of steps to create a simple model is:

1. Decide on a name for the system; let us call it `syst' for the purposes of this discussion.
2. Invoke the Bond Graph editor to draw the acausal Bond Graph.

         mtt syst abg fig

3. Draw the Bond Graph (see section 6.4.1 Language fig (abg.fig)), including the bonds (see section 1.5 Bonds), the components (see section 1.6 Components) and any artwork (see section 6.4.1.15 Artwork) to make the Bond Graph more readable. The graphical editor xfig is (see section 10.2 Xfig) is self-explanatory. The icon library is helpful here (see see section 6.4.1.1 Icon library).
4. Add causal strokes (see section 6.4.1.3 Strokes) where needed to define causality. As a general rule, use the minimum number of strokes needed to define the problem; this will often be only on the `SS` components. (see section 6.4.1.6 SS components). Save the bond graph.
5. View the corresponding causal bond graph.

         mtt syst cbg view

   1. At this stage, MTT will warn you that the labeled components do not appear in the label file - this can safely be ignored.
   2. MTT will indicate the percentage of components which are causally complete -- ideally this will be 100\%. Components which are not causally complete will be listed.
   3. A view of the causal bond graph will be created. The added causal strokes are indicated in blue, undercausal components in green and overcausal components in red.
   4. If the bond graph is causally complete, proceed to the next step, otherwise think hard and return to the first step.
6. At this stage, no constitutive relationships have been defined. Nevertheless, MTT will proceed in a semi-qualitative fashion by assuming that all constitutive relationships are unity (and therefore linear). It may be useful at this stage to view various derived representations to check the overall model properties before proceeding further. For example:
   1. View the system Differential-algebraic equations

          mtt syst dae view

   2. View the system state matrices

          mtt syst sm view

   3. View the system transfer function

          mtt syst tf view

   4. View the system step response

          mtt syst sro view

7. As well as creating the causal bond graph, MTT has also generated templates for other text files (see section 6.2 Defining representations) used to further specify the system. These can now be edited using your favorite text editor (see section 10.3 Text editors).
8. MTT will now generate the representations (see section 6.1 Representation summary)that you desire. For example the system can be simulated by

       mtt syst odeso view

   MTT will complain if a component is named in the bond graph but not in the label file and vice versa. This mainly to catch typing errors.

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## 3.3 Creating complex models

Complex models -- in distinction to simple models (see section 3.2 Creating simple models) -- have a hierarchical structure. In particular, bond graph components can be created by specifying their bond graph. Typically, such components will have more than one port (see section 1.6.1 Ports); within each component, ports are represented by named SS components (see section 6.4.1.9 Named SS components); outwith each component, ports are unambiguously identified by labels (see section 6.4.1.11 Port labels) and vector labels (see section 6.4.1.12 Vector port labels).

Complex models are thus created by conceptually decomposing the system into simple subsystems, and then creating the corresponding bond graphs. The procedure for simple systems (see section 3.2 Creating simple models) is then followed using the top level system (see section 3.3.1 Top level); MTT then recursively operates on the lower level systems.

The report representation (see section 6.16 Report (rep)) provides a convenient way of viewing a complex system.

An example of such a system can be created as follows:

    mtt copy twolink
    mtt twolink rep hview

The result is <A HREF="./examples/twolink/twolink_rep/twolink_rep.html"> here</A>.

3.3.1 Top level |  |

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### 3.3.1 Top level

The top level of a complex model contains subsystems but is not, itself, contained by other systems. It has the following special features:

- its name is used in the mtt command as the system name.
- all named SS componenents (see section 6.4.1.9 Named SS components) are treated as ordinary SS components (see section 6.4.1.6 SS components).

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# 4. Simulation

One purpose of modelling is to simulate the modeled dynamic system. Although this is just another transformation (see section 1.2 What is a transformation?) and therefore is covered in the appropriate chapter (see section 6. Representations), it is important enough to be given its own chapter.

Simulation is typically performed using an appropriate simulation language (which is often inappropriately conflated with modelling tools). MTT provides a number of alternative routes to simulation based on the following representations (see section 6. Representations):

`cse`
  constrained-state differential equation form
`ode`
  ordinary differential (or state-space) equations

in each case these equations may be linear or nonlinear.

Special cases of numerical simulation, appropriate to linear systems, are:

`ir`
  impulse response - state
`iro`
  impulse response - output
`sr`
  impulse response - state
`sro`
  impulse response - output

There are a number of languages (see section 9. Languages) which can be used to describe these representations for the purposes of numerical simulation:

`m`
  `octave` a high-level interactive language for numerical computation.
`c`
  `gcc` a c compiler.
`cc`
  `g++` a C++ front-end to gcc.

There are a number solution algorithms available:

- explicit solution via the matrix exponential
- backward Euler integration (explicit)
- forward Euler integration (implicit)
- Runge Kutta IV integration (explicit, fixed step)
- Hybrd algebraic solver (MINPACK, Octave fsolve)

However, all combinations of representation, language and solution method are not supported by MTT at the moment. Given a system `system', some recommended commands are:

`mtt system iro view`
  creates the impulse response of a linear system via the system_sm.m representation using explicit solution via the matrix exponential.
`mtt system sro view`
  creates the step response of a linear system via the system_sm.m representation using explicit solution via the matrix exponential.
`mtt -c system odeso view`
  creates the response of a nonlinear system via the system_ode.c representation using implicit integration.
`mtt -c -i euler system odeso view`
  creates the response of a nonlinear system via the system_ode.c representation using euler integration.

Simulation parameters are described in the system_simpar.txt file (see section 4.2 Simulation parameters).

The steady-state solution of a system can also be "simulated"(see section 4.1 Steady-state solutions).

4.1 Steady-state solutions |  |
4.2 Simulation parameters |  |
4.3 Simulation input |  |
4.4 Simulation logic |  |
4.5 Simulation initial state |  |
4.6 Simulation code |  |
4.7 Simulation output |  |

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## 4.1 Steady-state solutions

4.1.1 Steady-state solutions (odess) |  |
4.1.2 Steady-state solutions (ss) |  |

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### 4.1.1 Steady-state solutions (odess)

MTT can compute the steady-state solutions of an ordinary differential equation; this used the octave function `fsolve'. The solution is computed as a function of time using the input specified in the input file. The simulation parameter file (see section 4.2 Simulation parameters) is used to provide the time scales.

For example

    mtt copy rc
    cd rc
    mtt rc odess view

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### 4.1.2 Steady-state solutions (ss)

A rudimentary form of steady-state solution exists in mtt. The steady states and inouts are supplied by the user in the file system_simpar.r and the corresponding output and sate derivative computed by MTT using

    mtt system ss view

For example

    mtt copy rc
    cd rc
    mtt rc sspar view
    mtt rc ss view

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## 4.2 Simulation parameters

Simulation parameters are set in the system_simpar.txt file. At the moment this sets the following variables:

- LAST the last simulation time
- DT the incremental time (for plotting)
- STEPFACTOR the number of integration steps per DT -- thus the integration interval is DT/STEPFACTOR
- WMIN Minimum frequency = 10^WMIN
- WMAX Maximum frequency = 10^WMAX
- WSTEPS Number of Frequency steps.
- INPUT The input index for frequency response

There are a number of solution algorithms

- Euler basic Euler integration (see section 4.2.1 Euler integration). This method is simple, but not recommended for stiff systems.
- Implicit semi-implicit integration (see section 4.2.2 Implicit integration) - uses the smx representation to give stability.
- Runge Kutta IV fixed step Runge Kutta fourth order integration (see section 4.2.3 Runge Kutta IV integration).
- Hybrd numerical algebraic equation solver

4.2.1 Euler integration |  |
4.2.2 Implicit integration |  |
4.2.3 Runge Kutta IV integration |  |
4.2.4 Hybrd algebraic solver |  |

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### 4.2.1 Euler integration

Euler integration approximates the solution of the Ordinary Differential Equation

    dx/dt = f(x,u)

by

    x := x + f(x,u)*DDT

where

    DDT = DT/STEPFACTOR

If the system is linear, stability is ensured if the integer STEPFACTOR is chosen to be greater than the real number

    (maximum eigenvalue of -A)*DT/2

where A is the nxn matrix appearing in

    f(x,u) = Ax + Bu

If the system is non linear, the linearised system matrix A should act as a guide to the choice of STEPFACTOR.

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### 4.2.2 Implicit integration

Implicit integration approximates the solution of the Ordinary Differential Equation

    dx/dt = f(x,u)

by

    (I-A*DT)x := (I-A*DT)x + f(x,u)DT

where A is the linearised system matrix. This implies the solution of N (=number of states) linear equations at each sample interval. The OCTAVE version used the `\' operator to solve the set of linear equations, the C version uses LU decomposition.

If the system is linear, stability is ensured unconditionaly. If the system is non-linear, then the method still works well.

This method is nice in that choice of DT trades of accuracy against computation time without compromising stability. In addition, the correct stready-state values are achieved.

This approach can also be used for constrained state equations of the form:

    E(x) dx/dt = f(x,u)

where E(x) is a state-dependent matrix. The approximate solution is then given by:

    (E(x)-A*DT)x := (E(x)-A*DT)x + f(x,u)DT

which reduces to the ordinary differential equation case when E(x)=I.

The _smx representation includes the E matrix.

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### 4.2.3 Runge Kutta IV integration

Runge Kutta IV approximates the solution of the Ordinary Differential Equation

    dx/dt = f(x,t)

by

    x := x + (DT/6)*(k1 + 2*k2 + 2*k3 + k4)

where

    k1 := f(x,t)
    k2 := f(x+(1/2)*k1,t+(1/2)*DT)
    k3 := f(x+(1/2)*k2,t+(1/2)*DT)
    k4 := f(x+k3,t+DT)

The MTT implementation of Runge-Kutta integration is a fourth order, fixed-step, explicit integration method.

For some systems of equations, the increased accuracy of using a fourth order method can allow larger step-lengths to be used than would allowed by the lower order Euler integration method.

It should be noted that during the interemediate calculations (k1...k4), the input vector `u` is not advanced w.r.t. time; the system inputs are assumed to be constant over the period of the integration step-length.

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### 4.2.4 Hybrd algebraic solver

The hybrd algebraic solver of MINPACK, which is used by Octave in the `fsolve` routine, may be used in conjunction with one of the other integration methods to solve semi-explicit, index 1, differential algebraic equations; these may be generated in MTT models by use of `unknown` SS Components see section 6.6.1 SS component labels.

This method requires that compiled simulation code is used; either -cc or -oct. To perform a simulation based on a model `sys`,

    mtt -cc -ae hybrd -i euler sys odeso view

MTT will attempt to minimise the residual error at each integration time-step using the hybrd routine.

This method of simulation is particularly well suited to stiff systems where very fast dynamics are of little interest. Care must be taken to ensure that an acceptable level of convergence is achieved by the solver for the system under investigation.

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## 4.3 Simulation input

This is defined in the system_input.txt file. A default file is created automatically by MTT. This is done explicitly by

    mtt system input txt

If the file already exists, the same command checks that all inputs are defined and that all defined inputs exist in the system and promts the user to correct discrepancies.

Inputs are defined by the full system name appearing in the structure file (see section 6.7 Structure (struc)). They can depend on states (again defined by name), time (defined by t) and parameters

For example:

    system_pump_l_1_u      = 4e5*atm;
    system_pump_r_1_u       = 4e5*(t<10)*atm;
    system_ss_i             = 0*kg;
    system_ss_o             = 3e-3*kg;
    system_v_1_u            = (t>10);
    system_v_ll_1_u         = 1;
    system_v_lr_1_u         = (t<10);
    system_v_ul_1_u         = 0;
    system_v_ur_1_u         = (t>10);

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## 4.4 Simulation logic

This is defined in the system_logic.txt file. A default file is created automatically by MTT. This is done explicitly by

    mtt system logic txt

If the file already exists, the same command checks that the logic corresponding to all switch states (see section 1.8 Switched systems) are defined and that all defined logic exists in the system and promts the user to correct discrepancies.

Logical inputs are defined by the full system name corresponding to MTT_switch components appearing in the structure file (see section 6.7 Structure (struc)) with `_logic' appended. They can depend on states (again defined by name), time (defined by t) and parameters

For example:

    bounce_ground_1_mtt_switch_logic       = bounce_intf_1_mtt3<0;

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## 4.5 Simulation initial state

This is defined in the system_state.txt file. A default file is created automatically by MTT. This is done explicitly by

    mtt system state txt

If the file already exists, the same command checks that all states are defined and that all defined states exist in the system and prompts the user to correct discrepancies.

States are defined by the full system name appearing in the structure file (see section 6.7 Structure (struc)). They can depend on parameters. For example

    system_c_l     = (1e4/k_l)/kg;
    system_c_ll     = (1e4/k_s)/kg;
    system_c_lr     = (1e4/k_s)/kg;
    system_c_u      = (1e4/k_l)/kg;

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## 4.6 Simulation code

simulation code can be generated by MTT in the form of the `ode2odes` transformation. This can be produced in a number of languages, including .m, .oct, C and C++ see section 9. Languages.

To generate simulation code in C:

    mtt -c [options] sys ode2odes c

Similarly, to generate C++ code:

    mtt -cc [options] sys ode2odes cc

To generate an executable based on the C++ representation:

    mtt -cc [options] sys ode2odes exe

4.6.1 Dynamically linked functions |  |

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### 4.6.1 Dynamically linked functions

Some model representations can be compiled into dynamically loaded code (shared objects) which are compiled prior to use in other modelling and simulation environments; in particular, .oct files can be generated for use in GNU Octave (see section 10.4.2 Creating GNU Octave .oct files) and .mex files can be generated for use in Matlab (see section 10.4.3 Creating Matlab .mex files) or Simulink (see section 10.4.4 Embedding MTT models in Simulink). The use of compiled (and possibly compiler-optimised) code can offer significant processing speed advantages over equivalent interpreted functions (e.g. .m files) for computationally intensive procedures.

The C++ code generated by MTT allows the same code to be generated as standalone code, Octave .oct files or Matlab .mexglx files. Although MTT usually takes care of the compilation options, if it is necessary to compile the code on a machine on which MTT is not installed, the appropriate flag should be passed to the compiler pre-processor:

- `-DCODEGENTARGET=STANDALONE`
- `-DCODEGENTARGET=OCTAVEDLD`
- `-DCODEGENTARGET=MATLABMEX`

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## 4.7 Simulation output

The view (see section 10.1 Views) representation provides a graphical representation of the results of a simulation; the postscript language provides the same thing in a form that can be included in a document.

These are two simulation output representations

`odes`
  ordinary differential equation solution (states)
`odeso`
  ordinary differential equation solution (output)

Particular output variables can be selected by adding a fourth argument in one of 2 forms

`'name1;name2;..;namen'`
  plot the variables with names na1 .. namen against time
`'name1:name2'`
  plot the variable with name2 against that with name 1

An example of plotting a single variable against time is:

    mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V'

An example of plotting one variable against another is:

    mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V:OttoCycle_cycle_P'

4.7.1 Viewing results with gnuplot |  |
4.7.2 Exporting results to SciGraphica |  |

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### 4.7.1 Viewing results with gnuplot

Simulation plots may be conveniently selected, viewed with gnuplot and saved to file (in PostScript format) using the command

    mtt [options] rc gnuplot view

This will cause a menu to be displayed, from which states and outputs may be selected for viewing. Clicking on a parameter name will, by default, cause the time history of the selected parameter to be displayed.

As with xMTT (see section 2.1 Menu-driven interface), the Wish Tcl/Tk interpreter must be installed to make use of this feature.

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### 4.7.2 Exporting results to SciGraphica

Simulation results can be converted into an XML-format SciGraphica (version 0.61) .sg file with the command

    mtt [options] sys odes sg

The SciGraphica file will contain two worksheets, X_sys and Y_sys, containing the state and output time-histories from the simulation.

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# 5. Sensitivity models

The sensitivity model of a system is a set of equations giving the sensitivity of the system outputs with respect to system parameters. MTT has built in methods for assisting with the development of such models.

This feature is experimental at the moment, but the following example gives an idea of what can be achieved.

    mtt copy rc
    cd rc
    mtt -s src ode view
    mtt -s src odeso view

The sensitivity system src is automatically created from the system rc using the predefined sR and sC components together with vector junctions (see section 6.4.1.14 Vector Components). The four outputs are the two system outputs plus the two sensitivity functions.

An alternative route is to create the sensitivity functions by symbolic differentiation. The following sensitivity representations are available:

`scse`
  sensitivity constrained-state equations
`sm`
  sensitivity state matrices
`scsm`
  sensitivity constrained-state matrices

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# 6. Representations

As discussed in 1.1 What is a representation?, a system has many representations. The purpose of MTT is to provide an easy way to generate such representation by applying the appropriate sequence of transformations. The representations supported by MTT are summarised in 6.1 Representation summary.

There is a two-fold division of representations into those with which the user defines the system and its various attributes, and those which are derived from these. The defining representations are listed in 6.2 Defining representations.

Each representation is implemented in one or more languages depending on its use. These languages are discussed in 9. Languages and are associated with appropriate tools for modifying or viewing the representations.

6.1 Representation summary |  |
6.2 Defining representations |  |
6.3 Verbal description (desc) |  |
6.4 Acausal bond graph (abg) |  |
6.5 Stripped acausal bond graph (sabg) |  |
6.6 Labels (lbl) |  |
6.7 Structure (struc) |  |
6.8 Constitutive relationship (cr) |  |
6.9 Parameters |  |
6.10 Causal bond graph (cbg) |  |
6.11 Elementary system equations (ese) |  |
6.12 Differential-Algebraic Equations (dae) |  |
6.13 Constrained-state Equations (cse) |  |
6.14 Ordinary Differential Equations |  |
6.15 Descriptor matrices (dm) |  |
6.16 Report (rep) |  |

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## 6.1 Representation summary

Some of the the representations available in MTT are (in alphabetical order):

`abg`
  acausal bond graph
`cbg`
  causal bond graph
`cr`
  constitutive relationship for each subsystem
`cse`
  constrained-state equations
`csm`
  constrained-state matrices
`dae`
  differential-algebraic equations
`daes`
  dae solution - state
`daeso`
  dae solution - output
`def`
  definitions - system orders etc.
`desc`
  Verbal description of system
`dm`
  descriptor matrices
`ese`
  elementary system equations
`fr`
  frequency response
`input`
  numerical input declaration
`ir`
  impulse response - state
`iro`
  impulse response - output
`lbl`
  label file
`lmfr`
  loglog modulus frequency response
`lpfr`
  semilog phase frequency response
`nifr`
  Nichols style frequency response
`numpar`
  numerical parameter declaration
`nyfr`
  Nyquist style frequency response
`obs`
  observer equations for CGPC
`ode`
  ordinary differential equations
`odes`
  ode solution - state
`odes`
  ODE simulation header file
`odeso`
  ode solution - output
`odess`
  ode numerical steady-states - states
`odesso`
  ode numerical steady-states - outputs
`rbg`
  raw bond graph
`rep`
  report
`rfe`
  robot-form equations
`sabg`
  stripped acausal bond graph
`simp`
  simplification information
`sm`
  state matrices
`smx`
  state matrices containing explicit states and inputs
`sms`
  ode
`smss`
  SM simulation header file
`sr`
  step response - state
`sro`
  step response - output
`ss`
  steady-state equations
`sspar`
  steady-state definition
`struc`
  structure - list of inputs, outputs and states
`sub`
  Executable subsystem list
`sub`
  LaTeX subsystem list
`sympar`
  symbolic parameters
`tf`
  transfer function

A complete list can be found via the `help representations` command (see section 2.4.1.1 help representations).

Many of these representations have more than one language (see section 6. Representations) associated with them.

Some of these representations define the system (see section 6.2 Defining representations).

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## 6.2 Defining representations

The following representations define the system and therefore must, ultimately, be defined by the user. However, all of these are assigned default values by MTT and may then be subsequently edited (see section 10.3 Text editors) viewed or operated on by the appropriate tools (see section 10. Language tools).

`system_abg.fig`
  the acausal bond graph (see section 6.4 Acausal bond graph (abg))
`system_lbl.txt`
  the label file (see section 6.6 Labels (lbl))
`system_desc.tex`
  the description file (see section 8.2.2 Detailed on-line documentation)
`system_simp.r`
  algebraic simplifications to make output more readable (see section 6.9.2 Symbolic parameters for simplification (simp.r))
`system_subs.r`
  algebraic substitutions to resolve, eq trig. identities (see section 6.9.1 Symbolic parameters (subs.r))
`system_simpar.txt`
  simulation parameters (see section 4.2 Simulation parameters)
`system_numpar.txt`
  numerical parameters (see section 6.9.3 Numeric parameters (numpar))
`system_input.txt`
  the system input for simulations (see section 4.3 Simulation input)
`system_logic.txt`
  the switching logic for simulations (see section 4.4 Simulation logic)
`system_sspar.r`
  defines the system steady-state (see section 4.1.2 Steady-state solutions (ss))

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## 6.3 Verbal description (desc)

Systems can be documented in LaTeX using the _desc.tex file. This file is included in the report (see section 6.16 Report (rep)) if the abg tex option is included in the rep.txt file. As usual, MTT provides a default text file to be edited by the user (see section 10.3 Text editors).

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## 6.4 Acausal bond graph (abg)

The acausal bond graph is the main input to MTT. It is up to you, as a system modeler, to distill the essential aspects of the system that you wish to model and capture this information in the form of a bond graph.

The inexperienced modeler may wish to look in one of the standard textbooks and copy some bond graphs of systems to get going.

To create the acausal bond graph of system `sys' in language fig type:

    mtt sys abg fig

To create the acausal bond graph of system `sys' in language m type:

    mtt sys abg m

To view the acausal bond graph of system `sys' type:

    mtt sys abg view

6.4.1 Language fig (abg.fig) |  |
6.4.2 Language m (rbg.m) |  |
6.4.3 Language m (abg.m) |  |
6.4.4 Language tex (abg.tex) |  |

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### 6.4.1 Language fig (abg.fig)

A bond graph is made up of:

`bonds`
  To connect components together.
`strokes`
  To indicate causality.
`components`
  Either simple or compound.
`artwork`
  Irrelevant to the system but useful to the user.

An icon library of bonds, components and other symbols is available within xfig (see section 6.4.1.1 Icon library).

6.4.1.1 Icon library |  |
6.4.1.2 Bonds |  |
6.4.1.3 Strokes |  |
6.4.1.4 Components |  |
6.4.1.5 Simple components |  |
6.4.1.6 SS components |  |
6.4.1.7 Simple components - implementation |  |
6.4.1.8 Compound components |  |
6.4.1.9 Named SS components |  |
6.4.1.10 Coerced bond direction |  |
6.4.1.11 Port labels |  |
6.4.1.12 Vector port labels |  |
6.4.1.13 Port label defaults |  |
6.4.1.14 Vector Components |  |
6.4.1.15 Artwork |  |
6.4.1.16 Valid Names |  |

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#### 6.4.1.1 Icon library

A number of predefined iconic symbols are available within xfig.

    Click onto the library icon
    Click onto the library pull-down menu and select BondGraph
    Select iconic symbols from the presented list

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#### 6.4.1.2 Bonds

Bonds are represented by polylines with two segments. They must be the default style (i.e. plain not dashed or dotted). The shortest segment is taken to be the half-arrow. its positioning is significant because:

- It points in the direction of power flow; thus a bond normally points towards C, I and R components.
- the corresponding side of the bond indicates flow causality; the other side represents effort causality. This is significant when using casual half-strokes (see section 6.4.1.3 Strokes). Please adopt the convention of having the half-arrows below horizontal bonds and to the right of vertical bonds.

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#### 6.4.1.3 Strokes

Causal strokes are represented by single-segment polylines. There are two sorts of strokes:

- Full strokes: these are the usual bond-graph strokes and determine both the effort and flow causality in the usual way. The centre of the stroke should be at about one end of the bond and be at right angles to it.
- Half strokes: these are an innovation in MTT and allow you to specify the effort and flow causality independently. The end of the stroke should be at about one end of the bond and be at right angles to it. If the causal half-stroke is on the same side as the half-arrow (see section 6.4.1.2 Bonds) then it determines flow causality; if, on the other hand, it is on the opposite side to the half-arrow (see section 6.4.1.2 Bonds) then it determines effort causality. Two half strokes on the same, but on opposite sides of the bond are equivalent to a a full stroke at the same end of the bond.

MTT is reasonably forgiving; but a neat diagram will be less ambiguous to you as well as to MTT.

Causality is indicated as follows:

- Effort is imposed at the same end as the stroke.
- Flow is imposed at the opposite end as the stroke.

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#### 6.4.1.4 Components

Components are represented by a text string in fig. The recommended style is: 20pt, Times-Roman and centre justified.

The component text string can be of the following forms:

`type`
  Just the type of the component is indicated. Components may be either Simple components (see section 6.4.1.5 Simple components) or Compound components (see section 6.4.1.8 Compound components). For example:

      R

`type:label`
  Both the type and the label of the component are given. The type must be a valid name (see section 6.4.1.16 Valid Names.The name provides a link to more information to be found in See section 6.6 Labels (lbl). For example:

      R:r

`type:label:cr`
  Not only are the type and the label of the component given, but also the component cr argument. The type must be a valid name (see section 6.4.1.16 Valid Names.The name provides a link to more information to be found in See section 6.6 Labels (lbl). For example:

      R:r:flow,r

`type:label:expression`
  Expression is a mathematical expression relating the effort (called mtt_e) to the flow (called mtt_f). For example the following three forms are equivalent

      R:r:mtt_e=r*mtt_f
      R:r:mtt_e-r*mtt_f=0
      R:r:mtt_f=mtt_e/r

  A non-linear example is:

      R:r:mtt_e = sin(mtt_f)

`type*n`
  The name, together with the number ``n`' of repetitions of the component, are given. This repetition only makes sense if the component has an even number of ports (see section 6.4.1.11 Port labels); n copies of the component are concatenated with odd Named ports (see section 6.4.1.11 Port labels) of the component being connected to the even Named ports of the previous component in the chain in numerical order. This feature is particularly useful if the component is compound and can be used for, example to give a lumped approximation of a distributed system. For example:

      MySystem*25

`type:label*n`
  This complete form and is a combination of the simpler forms. For example:

      MySystem:MyLabel*25

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#### 6.4.1.5 Simple components

The following simple components are defined in MTT.

`R`
  Standard one-port R
`C`
  Standard one-port I
`I`
  Standard one-port I
`SS`
  Source-sensor
`TF`
  Transformer
`GY`
  Gyrator
`AE`
  Effort amplifier
`AF`
  Flow amplifier
`CSW`
  Switched one-port I
`ISW`
  Switched one-port I

6.4.1.6 SS components |  |
6.4.1.7 Simple components - implementation |  |

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#### 6.4.1.6 SS components

`SS` components provide input and output variables for a system; Named SS components (see section 6.4.1.9 Named SS components) provide this for subsystems.

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#### 6.4.1.7 Simple components - implementation

Each simple component, with name NAME, is defined by two m files:

`NAME_cause.m`
  defines the possible causal patterns for the component
`NAME_eqn.m`
  defines the equations generated

Only the experienced user would normally define simple components - Compound components (see section 6.4.1.8 Compound components) are recommended for DIY components.

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#### 6.4.1.8 Compound components

Compound components are systems described by bond graphs and implemented by MTT. They have special SS components, Named SS components (see section 6.4.1.9 Named SS components), to indicate connections to the encapsulating system.

Like any other system, they are described by a graphical Bond Graph description (see section 6.4.1 Language fig (abg.fig)), and a label file (see section 6.6 Labels (lbl)).

By convention, all of the files describing a component live in a directory with the same name as the component.

6.4.1.9 Named SS components |  |

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#### 6.4.1.9 Named SS components

Named SS components provide the link from the system which defines compound component to the system which uses a compound component see section 6.4.1.8 Compound components. A named SS components is of the form `SS:[name]`;

Where `name' is a name consisting of alphanumeric characters and underscore; for example:

    SS:[Mechanical_1]

Each such named SS provides one of the ports (see section 1.6.1 Ports). The direction of the named SS components. (see section 6.4.1.9 Named SS components) is coerced (see section 6.4.1.10 Coerced bond direction) to have the same direction as the bond connected to the corresponding port. Thus the direction of the direction of the named SS components has no significance unless the component is at the top level of a system.

If a named SS component exists at the top level (see section 3.3.1 Top level) and is treated as an ordinary SS component with the given direction and with the attributes specified in the label file (see section 6.6 Labels (lbl)).

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#### 6.4.1.10 Coerced bond direction

Named SS components (see section 6.4.1.9 Named SS components) provide the mechanism for declaring the ports (see section 1.6.1 Ports) of a component. The corresponding bond has a direction. However, under some circumstances, it may be useful to reverse this direction. MTT provides a coercion mechanism for this: the the direction of the bond attached to the named SS component (see section 6.4.1.9 Named SS components) is replaced by the direction of the bond attached to the component port.

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#### 6.4.1.11 Port labels

Most multi-port components have ports see section 1.6.1 Ports)which display different behaviors; the exception to this is the junction (`0` and `1`) components. For this reason, MTT provides a method for unambiguously identifying the ports of a multi-port component by port labels.

A port label is indicated by a name within parentheses of the form `[name]`, where `name' is a name consisting of alphanumeric characters and underscore; for example:

    [Mechanical_1]

This provides a label for corresponding to the component to which the nearest bond-end is attached.

The following rules must be be obeyed:

- If a component has any port labels at all, there must be one for each port of the component.

Port labels may be grouped into vector port labels (see section 6.4.1.12 Vector port labels). Components with compatible (ie containing the same number of ports) vector ports may be connected by a single bond (see section 1.5 Bonds); such a bond implies the corresponding number of bonds (one for each element of the vector port label). All such bonds inherit the same direction and any explicit causal strokes (see section 6.4.1.3 Strokes)

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#### 6.4.1.12 Vector port labels

Port labels (see section 6.4.1.11 Port labels) may be grouped into vector port labels of the form `[name1,name2,name3]`.

    [Mechanical_1,Electrical,Hydraulic_5]

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#### 6.4.1.13 Port label defaults

Whether impicitly or explicity, all ports of components (with the exception of 0 and 1 junctions) must have lables (see section 6.4.1.11 Port labels). However, these can be omitted from the bond graph in the following circumstances and default labels are supplied by MTT.

1. A single unlabled inport defaults to [in]
2. A single unlabled outport defaults to [out]

These defaults may, in turn be aliases (see section 6.6.9 Aliases) for port labels (see section 6.4.1.11 Port labels) or vector port labels (see section 6.4.1.12 Vector port labels). Combining the default and alias mechanism is a powerful tool for creating uncluttered, yet complex, bond graph models.

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#### 6.4.1.14 Vector Components

Vectors of components can be created in four cases: `0` junctions, `1` junctions, `SS` components and `SS` port components.

In each case, the presence of a vector component is indicated by a single port label (see section 6.4.1.11 Port labels) of one of two forms:

1. containing numerals from 1 to the order of the vector. Thus a vector of 3 components is indicated by a port label of the form [1,2,3].
2. 1: followed by the order of the vector. Thus a vector of 3 components is indicated by a port label of the form [1:3].

Within the corresponding label file (see section 6.6 Labels (lbl)), the components of a vector port can be accessed using _i where i is the corresponding index. Thus a port SS:[Electrical] appearing near the port label [1,2,3] could contain the port alias (see section 6.6.9.1 Port aliases)

    %ALIAS  in Electrical_1,Electrical_2,Electrical_3

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#### 6.4.1.15 Artwork

You are encouraged to annotate your bond graphs extensively - this makes them an immediately readable document whilst retaining the precise and unambiguous expressive power of the bond graph.

You may add any Fig (see section 9.1 Fig) object to the bond graph as long as it will not be interpreted as part of the bond graph. The reccommended way to acheive this is to put the Bond Graph at depth 0,10,20 etc (ie depth modulo 10 is zero) and artwork at any other depth.

For compatibility with earlier versions of MTT, the following objects are ignored even at level 0. However, their use is strongly discouraged.

- Adding text is OK as long as it cannot be confused with components (see section 6.4.1.4 Components). In particular, you can include invalid component characters such as white space, `"`, `'`, `!` etc.
- Adding boxes, arcs etc is always OK.
- Adding dotted or dashes lines is always OK.

The stripped abg file (sabg) (see section 6.5 Stripped acausal bond graph (sabg)) shows only those parts of the diagram recognised by MTT and is therefore useful for distinguishing artwork.

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#### 6.4.1.16 Valid Names

A valid name is a text string containing alphanumeric characters. It must NOT contain underscore ``_`', hyphen ``-`', ``:`' or ``*`'.

The following names should be avoided

    if endif

The following reserved words in reduce should also be avoided (with any case)

    Commands ALGEBRAIC ANTISYMMETRIC ARRAY BYE CLEAR CLEARRULES COMMENT
    CONT DECOMPOSE DEFINE DEPEND DISPLAY ED EDITDEF END EVEN FACTOR FOR
    FORALL FOREACH GO GOTO IF IN INDEX INFIX INPUT INTEGER KORDER LET
    LINEAR LISP LISTARGP LOAD LOAD PACKAGE MASS MATCH MATRIX MSHELL
    NODEPEND NONCOM NONZERO NOSPUR ODD OFF ON OPERATOR ORDER OUT PAUSE
    PRECEDENCE PRINT PRECISION PROCEDURE QUIT REAL REMFAC REMIND RETRY
    RETURN SAVEAS SCALAR SETMOD SHARE SHOWTIME SHUT SPUR SYMBOLIC
    SYMMETRIC VECDIM VECTOR WEIGHT WRITE WTLEVEL

    Boolean Operators EVENP FIXP FREEOF NUMBERP ORDP PRIMEP

    Infix Operators := = >= > <= < => + * / ^ ** . WHERE SETQ OR AND
    MEMBER MEMQ EQUAL NEQ EQ GEQ GREATERP LEQ LESSP PLUS DIFFERENCE MINUS
    TIMES QUOTIENT EXPT CONS Numerical Operators ABS ACOS ACOSH ACOT ACOTH
    ACSC ACSCH ASEC ASECH ASIN ASINH ATAN ATANH ATAN2 COS COSH COT COTH
    CSC CSCH EXP FACTORIAL FIX FLOOR HYPOT LN LOG LOGB LOG10 NEXTPRIME
    ROUND SEC SECH SIN SINH SQRT TAN TANH

    Prefix Operators APPEND ARGLENGTH CEILING COEFF COEFFN COFACTOR CONJ
    DEG DEN DET DF DILOG EI EPS ERF FACTORIZE FIRST GCD G IMPART INT
    INTERPOL LCM LCOF LENGTH LHS LINELENGTH LTERM MAINVAR MAT MATEIGEN MAX
    MIN MKID NULLSPACE NUM PART PF PRECISION RANDOM RANDOM NEW SEED RANK
    REDERR REDUCT REMAINDER REPART REST RESULTANT REVERSE RHS SECOND SET
    SHOWRULES SIGN SOLVE STRUCTR SUB SUM THIRD TP TRACE VARNAME

    Reserved Variables CARD NO E EVAL MODE FORT WIDTH HIGH POW I INFINITY
    K!* LOW POW NIL PI ROOT MULTIPLICITY T

    Switches ADJPREC ALGINT ALLBRANCH ALLFAC BFSPACE COMBINEEXPT
    COMBINELOGS COMP COMPLEX CRAMER CREF DEFN DEMO DIV ECHO ERRCONT
    EVALLHSEQP EXP EXPANDLOGS EZGCD FACTOR FORT FULLROOTS GCD IFACTOR INT
    INTSTR LCM LIST LISTARGS MCD MODULAR MSG MULTIPLICITIES NAT NERO
    NOSPLIT OUTPUT PERIOD PRECISE PRET PRI RAT RATARG RATIONAL RATIONALIZE
    RATPRI REVPRI RLISP88 ROUNDALL ROUNDBF ROUNDED SAVESTRUCTR
    SOLVESINGULAR TIME TRA TRFAC TRIGFORM TRINT

    Other Reserved Ids BEGIN DO EXPR FEXPR INPUT LAMBDA LISP MACRO PRODUCT
    REPEAT SMACRO SUM UNTIL WHEN WHILE WS

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### 6.4.2 Language m (rbg.m)

The raw bond graph of system `sys' is represented as an m file with heading:

    function [rbonds, rstrokes,rcomponents,rports,n_ports] = sys_rbg

This representation is a half-way house between the fig (see section 6.4.1 Language fig (abg.fig)) and m (see section 6.4.3 Language m (abg.m)) representations. It contains the geometric information from the fig file in a form digestible by Octave (see section 10.4 Octave).

The five outputs of this function are:

- rbonds
- rstrokes
- rcomponents
- rports
- n_ports

rbonds is a matrix with

- one row for each bond (see section 6.4.1.2 Bonds)
- columns 1 and 2 containing the x,y coordinates for one end of the bond
- columns 3 and 4 containing the x,y coordinates for the corner of the bond
- columns 5 and 6 containing the x,y coordinates for the other end of the bond

rstrokes is a matrix with (see section 6.4.1.3 Strokes)

- one row for each stroke or half-stroke
- columns 1 and 2 containing the x,y coordinates for one end of the stroke
- columns 3 and 4 containing the x,y coordinates for the other end of the stroke

rcomponents is a matrix with (see section 6.4.1.4 Components)

- one row for each component
- columns 1 and 2 containing the x,y coordinates of the component
- the remaining columns containing fig file information

rports is a matrix with (see section 6.4.1.11 Port labels)

- one row for each component port that is explicitly labeled
- columns 1 and 2 containing the x,y coordinates of the port label
- column 3 contains the port number.

n_ports is the number of ports associated with the system -- i.e. the number of Named SS components (see section 6.4.1.9 Named SS components).

6.4.2.1 Transformation abg2rbg_fig2m |  |

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#### 6.4.2.1 Transformation abg2rbg_fig2m

This transformation takes the acausal bond graph as a fig file (see section 6.4.1 Language fig (abg.fig)) and transforms it into a raw bond graph in m-file format (see section 6.4.2 Language m (rbg.m)).

This transformation is implemented in GNU awk (gawk). It scans both the fig file (see section 6.4.1 Language fig (abg.fig)) and the label file (see section 6.6 Labels (lbl)) and generates the rbg (see section 6.4.2 Language m (rbg.m)) with components sorted according to the label file. It also generates a file sys_fig.fig containing details of the bond graph with the components removed.

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### 6.4.3 Language m (abg.m)

The acausal bond graph of system `sys' is represented as an m file with heading:

    function [bonds,components,n_ports] = sys_abg

The three outputs of this function are:

- bonds
- components
- n_ports

bonds is a matrix with

- one row for each bond
- the first column contains the arrow-orientated (see section 6.4.3.1 Arrow-orientated causality) causality of the effort variable.
- the second column contains the arrow-orientated (see section 6.4.3.1 Arrow-orientated causality) causality of the flow variable.

components is a matrix with

- one row for each component
- one column for each bond impinging on the component. The magnitude of each entry corresponds to the bond number (the appropriate row index of` bonds'); the sign is positive if the bond arrow points into the component and negative otherwise.

n_ports is the number of ports associated with the system -- i.e. the number of Named SS components (see section 6.4.1.9 Named SS components).

6.4.3.1 Arrow-orientated causality |  |
6.4.3.2 Component-orientated causality |  |
6.4.3.3 Transformation rbg2abg_m |  |

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#### 6.4.3.1 Arrow-orientated causality

The arrow-orientated causality convention assigns -1, 0 or 1 to both the effort and flow (see section 1.4 Variables) sides of a bond to represent the causal stroke (see section 6.4.1.3 Strokes) as follows:

`0`
  if there is no causality set.
`1`
  if the causal stroke is at the arrow end of the bond.
`-1`
  if the causal stroke is at the other end of the bond.

see section 6.4.3.2 Component-orientated causality.

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#### 6.4.3.2 Component-orientated causality

The component-orientated causality convention assigns -1, 0 or 1 to both the effort and flow (see section 1.4 Variables) sides of a bond to represent the causal stroke (see section 6.4.1.3 Strokes) as follows:

`0`
  if there is no causality set.
`1`
  if the causal stroke is at the component end of the bond.
`-1`
  if the causal stroke is at the other end of the bond.

see section 6.4.3.1 Arrow-orientated causality.

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#### 6.4.3.3 Transformation rbg2abg_m

This transformation takes the raw bond graph and, by doing some geometrical computation, determines the topology of the bond graph -- ie what is close to what.

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### 6.4.4 Language tex (abg.tex)

For the purpose of producing a report (see section 6.16 Report (rep)), MTT generates a LaTeX (see section 10.5 LaTeX) file describing the bond graph and its subsystems. Additional information may be supplied using the description representation (see section 8.2.2 Detailed on-line documentation).

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## 6.5 Stripped acausal bond graph (sabg)

The stripped acausal bond graph is the acausal bond graph representation (see section 6.4 Acausal bond graph (abg)) without the artwork (see section 6.4.1.15 Artwork). It is useful to check for mistakes by showing precisely what is recognised by MTT.

6.5.1 Language fig (sabg.fig) |  |
6.5.2 Stripped acausal bond graph (view) |  |

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### 6.5.1 Language fig (sabg.fig)

The stripped acausal bond graph can be generated as a fig (see section 9.1 Fig) file using

    mtt syst sabg fig

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### 6.5.2 Stripped acausal bond graph (view)

This representation has the standard text view (see section 10.1 Views).

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## 6.6 Labels (lbl)

Bond graph components have optional labels. These provide pointers to further information relating to the component; this avoids clutter on the bond graph.

The label file contains the following non-blank lines (blank lines are ignored)

- Summary - lines beginning with #SUMMARY
- Description - lines beginning with #DESCRIPTION
- Alias - lines beginning with #ALIAS
- Comments - lines beginning with #
- Labels - other non-blank lines

Note, for compatability with old versions, % may be used in place of #; but the use of % is deprecated. Each lable contains three fields (in the following order) separated by white space and on one line:

1. The component name see section 6.6.3 Component names. This must be a valid name (see section 6.4.1.16 Valid Names.
2. The component constitutive relationship see section 6.6.4 Component constitutive relationship
3. The component arguments see section 6.6.5 Component arguments

Not each component see section 6.4.1.4 Components needs a label, only those which are explicitly labeled on the Bond Graph see section 6.4 Acausal bond graph (abg). MTT checks whether all components labelled on the bond graph have labels and vice versa.

If no lbl file exists, MTT will create a valid one for you; including a default set of arguments and crs for both simplae and compound components.

If wish to create one to edit yourself, type

    mtt system_name lbl txt

An example lbl file (for the RC system is):

    %% Label file for system RC (RC_lbl.txt)
    %SUMMARY RC
    %DESCRIPTION <Detailed description here>
    % Port aliases
    %ALIAS  in      in
    %ALIAS  out     out

    % Argument aliases
    %ALIAS  $1      c
    %ALIAS  $2      r

    %% Each line should be of one of the following forms:
    %            a comment (ie starting with %)
    %            component-name     cr_name arg1,arg2,..argn
    %            blank

    % ---- Component labels ----

    % Component type C
            c               lin     effort,c

    % Component type R
            r               lin     flow,r

    % Component type SS
            [in]    SS              external,external
            [out]   SS              external,external

The old-style lbl files (see section 6.6.11 Old-style labels (lbl)) are NO LONGER supported -- you are encouraged to convert them ASAP.

6.6.1 SS component labels |  |
6.6.2 Other component labels |  |
6.6.3 Component names |  |
6.6.4 Component constitutive relationship |  |
6.6.5 Component arguments |  |
6.6.6 Parameter declarations |  |
6.6.7 Units declarations |  |
6.6.8 Interface Control Definition |  |
6.6.9 Aliases |  |
6.6.10 Parameter passing |  |
6.6.11 Old-style labels (lbl) |  |
6.6.12 Language tex (desc.tex) |  |

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### 6.6.1 SS component labels

In addition to the label there are two information fields, see section 6.6 Labels (lbl). The first must be `SS', the second contains two information fields of the form info_field_1,info_field_2.

These two information fields correspond to the effort and flow variables of the of the SS components as follows

`info_field_1`
  effort
`info_field_2`
  flow

Each of these two fields contains one of the following attributes:

`external`
  indicates that the corresponding variable is a system input or output
`internal`
  indicates that the variable does not appear as a system output; it is an error to label an input in this way.
`a number`
  the value of the input; or the value of the (imposed) output
`a symbol`
  the symbolic value of the input; or the value of the (imposed) output
`unknown`
  used for the SS method of solving algebraic loops. This indicates that the corresponding system input (SS output) is to be chosen to set the corresponding system output (SS input) to zero.
`zero`
  used for the SS method of solving algebraic loops. This indicates that the corresponding system output (SS input) is to be set to zero using the variable indicted by the corresponding `unknown' label.

Some examples are:

    %% ss1 is both a source and sensor
    ss1     SS              external,external
    %% ss1 acts as a flow sensor - it imposes zero effort.
    ss2     SS              0,external

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### 6.6.2 Other component labels

In addition to the label there are two information fields, see section 6.6 Labels (lbl). They correspond to the constitutive relationship (see see section 1.6.2 Constitutive relationship and arguments of the component as follows

`info_field_1`
  constitutive relationship
`info_field_2`
  parameters

Some examples are:

    %Armature resistance
    r_a     lin     effort,r_a

    %Gearbox ratio
    n       lin     effort,n

MTT supports parameter-passing to (see section 6.6.10 Parameter passing) subsystems.

6.6.3 Component names |  |
6.6.4 Component constitutive relationship |  |
6.6.5 Component arguments |  |
6.6.9 Aliases |  |
6.6.10 Parameter passing |  |
6.6.11 Old-style labels (lbl) |  |

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### 6.6.3 Component names

The component name field must contain a valid name (see section 6.4.1.16 Valid Names corresponding to the name (the bit after the :) of each named component (see section 6.4.1.4 Components) on the bond graph (see section 6.4 Acausal bond graph (abg)).

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### 6.6.4 Component constitutive relationship

The constitutive relationship field contains the name of a constitutive relationship for the component. There are three sorts of constitutive relationship recognised by MTT:

1. A generic constitutive relationship such as lin (the generic linear constitutive relationship.
2. A local constitutive relationship with the same name as the component type
3. The SS constitutive relationship reserved for SS components. All labels for SS components must contain SS in this field.

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### 6.6.5 Component arguments

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### 6.6.6 Parameter declarations

It is sometimes useful to use parameters (in addition to those implied by the Component arguments see section 6.6.5 Component arguments) to compute values in, for example the numpar file. These can be declared in the label file; for examples , the two parameters par1 and par 2 can be declared as:

    #PAR par1
    #PAR par2

On the other hand, some CR arguments (eg foo and bar) may not correspond to parameters. These can be excluded from the sympar list using the NOTPAR declaration

    #NOTPAR foo
    #NOTPAR bar

For comapability with old code, VAR may be used in place of PAR, but this usage is deprecated.

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### 6.6.7 Units declarations

The units and domains of ports (see section 1.6.1 Ports) are declared as:

    #UNITS Port_name domain effort_units flow_units

where "Port_name" is the name of the port, domain is one of:

`electrical`
  the electrical domain
`translational`
  the translational mechanical domain
`rotational`
  the rotational mechanical domain
`fluid`
  the fluid domain
`thermal`
  the thermal domain

and effort_units and flow_units are corresponding units for the effort and the flow.

Allowed units are those defined in the units package.

MTT checks that units are

- defined consistently with the domain
- the same for connected ports when both ports have defined units.

No checks are done if one or both ends of a bond are not connected to a port with defined units.

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### 6.6.8 Interface Control Definition

It is sometimes useful to be able to automatically generate a set of assignments mapping MTT inputs and outputs to an external interface definition. This can be achieved with use of the #ICD directive.

    #ICD    PressureSensor         PUMP1_PRESSURE_SENSOR,Pa;null,none
    #ICD    Electrical              PUMP1_VOLTAGE,volt;PUMP1_CURRENT,amp

    % Component type De
            PressureSensor  SS      external

    % Component type SS
            Electrical      SS      external,external

The ICD directive consists of 3 whitespace delimited fields:

1. [%|#]ICD
2. component name
3. Four comma (,) or semi-colon (;) delimited fields:
   1. name of effort parameter
   2. unit of effort parameter
   3. name of flow parameter
   4. unit of flow parameter

If no parameter name is required, a value of "null" should be used. If the parameter does not have any units, a value of "none" should be used.

ICD parameters may be aliased see section 6.6.9 Aliases in the same way as normal parameters, thus it is possible to define some or all of the ICD in higher level components.

The command

    mtt sys ICD txt

will generate a text file containing a list of mappings:

    ## Interface Control Definition for System sys
    ## sys_ICD.txt: Generated by MTT Thu Jul 12 21:21:21 CDT 2001

    Input:  PUMP1_VOLTAGE           sys_P1_1_Electrical      Causality: Effort   Units: volt
    Output: PUMP1_CURRENT           sys_P1_1_Electrical      Causality: Flow     Units: amp
    Output: PUMP1_PRESSURE_SENSOR   sys_P1_1_PressureSensor  Causality: Effort   Units: Pa

A set of assignments can be generated with the command

    mtt sys ICD m

resulting in:

    # Interface Control Definition mappings for system sys
    # sys_ICD.m: Generated by MTT Thu Jul 12 21:26:56 CDT 2001

    # Inputs

            mttu(1) = PUMP1_VOLTAGE;

    # Outputs

            PUMP1_CURRENT                  = mtty(1);
            PUMP1_PRESSURE_SENSOR          = mtty(2);

A similar file will be generated by the command

    mtt sys ICD cc

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### 6.6.9 Aliases

Aliases provide a convenient mechanism for relabelling words appearing in the label file (see section 6.6 Labels (lbl)). There are three contexts in which the alias mechanism is used:

1. renaming ports (see section 6.6.9.1 Port aliases),
2. renaming parameters (see section 6.6.9.2 Parameter aliases) and
3. renaming components (see section 6.6.9.4 Component aliases).

All three mechanisms use the same form of statement within the label file

    %ALIAS short_label       real_label

MTT distinguishes between the three forms as follows:

- Parameter aliases: `short_label' starts with a `$'
- Component aliases: `real_label' contains the directory separator `/'
- Port aliases: neither of the above

6.6.9.1 Port aliases |  |
6.6.9.2 Parameter aliases |  |
6.6.9.3 CR aliases |  |
6.6.9.4 Component aliases |  |

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#### 6.6.9.1 Port aliases

Aliases provide a way of refering to (see section 6.4.1.11 Port labels) or vector port labels (see section 6.4.1.12 Vector port labels) on the bond graph using a short-hand notation. With in a component label file (see section 6.6 Labels (lbl)) statements of the following forms can occur

    %ALIAS short_label       real_label

When the component is used within another component, the short_lable may be used in place of the real_label. More than one alias per label can be used, for example

    %ALIAS short_label_1       real_label
    %ALIAS short_label_2       real_label
    %ALIAS short_label_3       real_label

The port can then be refered to in four ways: as real_label, short_label_1, short_label_2 or short_label_3. An alternative notation for the ALIAS statement in this case is

    %ALIAS short_label_1|short_label_2|short_label_3       real_label

The alias feature is particularly powerful in conjunction with vector port labels (see section 6.4.1.12 Vector port labels) and the port label default (see section 6.4.1.13 Port label defaults) mechanisms. For example, a component with 5 ports appearing in the lbl file as:

            [Hydraulic_in]  external        external
            [Hydraulic_out] external        external
            [Power_Shaft]           external        external
            [Thermal_in]    external        external
            [Thermal_out]   external        external

together with the following statements in the label file:

    %ALIAS  in              Thermal_in,Hyydraulic_in
    %ALIAS  out             Thermal_out,Hydraulic_out
    %ALIAS  shaft|power     Power_Shaft

can appear in the bond graph containing that component with one bond labeled either [shaft] or [power] or [Power_Shaft], one unlabeled vector bond pointing in and one unlabeled vector bond pointing out.

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#### 6.6.9.2 Parameter aliases

Parameter aliases are of the form

    %ALIAS $n       actual parameter

where n is an integer (unique within the label file). For example

    %ALIAS  $1              c_v
    %ALIAS  $2              density,ideal_gas,r
    %ALIAS  $3              alpha
    %ALIAS  $4              flow,k_p

Assigns four symbolic parameters to the corresponding strings These four parameters (`$1`--`$4`) can then be used for parameter passing(see section 6.6.10 Parameter passing).

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#### 6.6.9.3 CR aliases

CR aliases are of the form

    %ALIAS $an       actual parameter

where n is an integer (unique within the label file). For example

    %ALIAS  $a1  lin

assigns the symbolic parameter to be lin. This parameter `$1` can then be used for passing a diofferent cr to the component (see section 6.6.10 Parameter passing).

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#### 6.6.9.4 Component aliases

Component aliases are of the form

    %ALIAS Component_name   Component_location

An example appears in the following label file fragment

    ...
    %ALIAS  wPipe   CompressibleFlow/wPipe
    %ALIAS  Poly    CompressibleFlow/Poly
    ....

The two components `wPipe' and `Poly' are both to be found within the library `Compressible flow' and the respective subdirectories. This follows the MTT convention that compound components (see section 6.4.1.8 Compound components) live within a directory of the same name.

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### 6.6.10 Parameter passing

MTT supports parameter-passing to subsystems within label files (see section 6.6 Labels (lbl)). Within a subsystem, explicit constitutive relationships and parameters (or groups thereof) can be replaced by postitional parameters such as `$1`, `$2` etc. Although this can be done directly, it is recommended that this is done via the alias mechanism (see section 6.6.9.2 Parameter aliases).

In a subsystem `$i`, is replaced by the ith field of a colon `;` separated field in the calling label file. This field may include commas `,` and the four arithmetic operators `+`, `-`, `*` and `/`.

For example, consider the following example label file fragment (associated with a component called Pump:

    ...

    %ALIAS  $1              c_v
    %ALIAS  $2              density,ideal_gas,r
    %ALIAS  $3              alpha
    %ALIAS  $4              flow,k_p

    %ALIAS  wPipe   CompressibleFlow/wPipe
    %ALIAS  Poly    CompressibleFlow/Poly

    % Component type wPipe
            pipe    none                    c_v;density,ideal_gas,r

    % Component type Poly
            poly            Poly            alpha

The 4 parameters `$1`, `$2`, `$3`, and `$4` can be passed from a higher level component as in the following label file fragment:

    % Component type Pump
            comp            none            c_v;rho,ideal_gas,r;alpha;effort,k_c
            turb            none            c_v;rho,ideal_gas,r;alpha;effort,k_t

Thus in component `comp':

- `$1` is replaced by c_v
- `$2` is replaced by rho,ideal_gas
- `$3` is replaced by alpha
- `$4` is replaced by effort,k_c

whereas in component `turb' the first three parameters are the same but

- `$4` is replaced by effort,k_t

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### 6.6.11 Old-style labels (lbl)

Old syle labels (mtt version 2.x) are supported by mtt version 3.x. However, you are advised to use the new form (see section 6.6 Labels (lbl)).

Each line of the `_label.txt` file is of one of three forms:

1. Contains three fields (separated by white space) of the form

       label   field_1   field_2

2. Blank
3. Preceded by %

Only the first is noticed by MTT; the second and third are for providing helpful commenting.

The role of the two information fields depends on the component with the corresponding label. In particular the classes of components are:

- SS components, see section 6.4.1.6 SS components.
- Other components, see section 6.4.1.4 Components.

Named SS component, see section 6.4.1.9 Named SS components never have labels.

6.6.11.1 SS component labels (old-style) |  |
6.6.11.2 Other component labels (old-style) |  |
6.6.11.3 Parameter passing (old-style) |  |

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#### 6.6.11.1 SS component labels (old-style)

In addition to the label there are two information fields, see section 6.6 Labels (lbl). They correspond to the effort and flow of the components as follows

`info_field_1`
  effort
`info_field_2`
  flow

Each of these two fields contains one of the following attributes:

  external indicates that the corresponding variable is a system input or output
`internal`
  indicates that the variable does not appear as a system output; it is an error to label an input in this way.
`a number`
  the value of the input; or the value of the (imposed) output
`a symbol`
  the symbolic value of the input; or the value of the (imposed) output
`unknown`
  used for the SS method of solving algebraic loops. This indicates that the corresponding system input (SS output) is to be chosen to set the corresponding system output (SS input) to zero.
`zero`
  used for the SS method of solving algebraic loops. This indicates that the corresponding system output (SS input) is to be set to zero using the variable indicted by the corresponding `unknown' label.

Some examples are:

    %Label  field1          field2
    ss1     external        external
    ss2     0               external

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#### 6.6.11.2 Other component labels (old-style)

In addition to the label there are two information fields, see section 6.6 Labels (lbl). They correspond to the constitutive relationship (see see section 1.6.2 Constitutive relationship and arguments of the component as follows

`info_field_1`
  constitutive relationship
`info_field_2`
  parameters

Some examples are:

    %Armature resistance
    r_a     lin     effort,r_a

    %Gearbox ratio
    n       lin     effort,n

MTT supports parameter-passing to (see section 6.6.11.3 Parameter passing (old-style)) subsystems.

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#### 6.6.11.3 Parameter passing (old-style)

MTT supports parameter-passing to (see section 6.6.11.3 Parameter passing (old-style)) subsystems within label files (see section 6.6 Labels (lbl)). Within a subsystem, explicit constitutive relationships and parameters (or groups thereof) can be replaced by `$1`, `$2`, etc.

In a subsystem `$i`, is replaced by the ith field of a colon `;` separated field in the calling label file. This field may include commas `,`.

For example subsystem ROD contains the following lines in the label file:

    %DESCRIPTION    Parameter 1:    length from end 1 to mass centre
    %DESCRIPTION    Parameter 2:    length from end 2 to mass centre
    %DESCRIPTION    Parameter 3:    inertia about mass centre
    %DESCRIPTION    Parameter 4:    mass
    %DESCRIPTION    See Section 10.2 of "Metamodelling"

    %Inertias
    J       lin     flow,$3
    m_x     lin     flow,$4
    m_y     lin     flow,$4

    %Integrate angular velocity to get angle
    th

    %Modulated transformers
    s1      lsin    flow,$1
    s2      lsin    flow,$2
    c1      lcos    flow,$1
    c2      lcos    flow,$2

This can be used in a higher-level lbl (see section 6.6 Labels (lbl)) file as:

    %SUMMARY Pendulum example from Section 10.3 of "Metamodelling"

    %Rod parameters
    rod     none    l;l;j;m

6.6.12 Language tex (desc.tex) |  |

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### 6.6.12 Language tex (desc.tex)

This file may contain any LaTeX compatible commands. Any mathematics should conform to the AMSmath package.

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## 6.7 Structure (struc)

The causal bond graph implies a set of equations describing the system. The Structure (struc) representation describes the structure of these equations in terms of the input, outputs, states and non-states of the system.

6.7.1 Language txt (struc.txt) |  |
6.7.2 Language tex (struc.tex) |  |
6.7.3 Language tex (view) |  |

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### 6.7.1 Language txt (struc.txt)

This text tile contains a description of the system structure (see section 6.7 Structure (struc) with 5 tab-separated columns containing the following information:

`type`
  input, output state or nonstate
  index an integer corresponding to the array index
  component name the name of the component corresponding to the variable
`system name`
  the name of the system containing the component
`repetition`
  an integer corresponding to the repetition of a repeated subsystem.

An example of such a file (corresponding to rc) (see section 3.1 Quick start) is:

    input           1       e1      rc      1
    output          1       e2      rc      1
    state           1       c       rc      1

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### 6.7.2 Language tex (struc.tex)

This LaTeX (see section 10.5 LaTeX) file contains a description of the system structure (see section 6.7 Structure (struc) in `longtable` format. It is a useful item to include in a report(see section 6.16 Report (rep)).

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### 6.7.3 Language tex (view)

This representation has the standard text view (see section 10.1 Views).

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## 6.8 Constitutive relationship (cr)

The constitutive relationship (see section 1.6.2 Constitutive relationship) of a simple component (see section 6.4.1.5 Simple components is defined in the symbolic algebra language Reduce (see section 9.3 Reduce). The constitutive relationship of a compound components (see section 6.4.1.8 Compound components) is implied by the constitutive relationships of its constituent components.

6.8.1 Predefined constitutive relationships |  |
6.8.2 DIY constitutive relationships |  |
6.8.3 Unresolved constitutive relationships |  |
6.8.4 Unresolved constitutive relationships - Octave |  |
6.8.5 Unresolved constitutive relationships - c++ |  |

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### 6.8.1 Predefined constitutive relationships

Some common cr's are predefined by MTT; these are:

`lin`
  a linear constitutive relationship
`exotherm`
  an exothermic reaction

6.8.1.1 lin |  |
6.8.1.2 exotherm |  |

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#### 6.8.1.1 lin

The constitutive relationship `lin` is predefined for the following components.

`R`
  (one-port) R component
`TF`
  transformer
`GY`
  gyrator
`MTF`
  modulated transformer
`MGY`
  modulated gyrator
`FMR`
  flow-modulated resistor

Lin takes two arguments in the form causality,gain

`causality`
  the causality (effort or flow) of the input to the constitutive relationship
`gain`
  the gain of the component when the input causality is as specified in the first argument.

For example the arguments

    flow,r

given to an R component corresponds to

    e = rf

if if the input causality is flow or

    f = e/r

if if the input causality is effort.

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#### 6.8.1.2 exotherm

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### 6.8.2 DIY constitutive relationships

You can write your own constitutive relationships using Reduce (see section 9.3 Reduce). This requires some understanding as to how MTT represent the elementary system equations (see section 6.11 Elementary system equations (ese)). Looking at the predefined constitutive relationships is a good way to get started (see section 11.5 File structure).

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### 6.8.3 Unresolved constitutive relationships

Consider the following CR file.

    FOR ALL rho,g,vol,h,topt,bott,flowin,press
    LET tktf2(rho,g,vol,h,topt,bott,effort,2,press,effort,1)
            = tank(rho,g,vol,h,topt,bott,press);

Assuming that `tank' is not defined in a reduce file, MTT will leave it unresolved when generating m or c code.

The resulting function can then be expressed as octave (see section 6.8.4 Unresolved constitutive relationships - Octave) or c++ code as (see section 6.8.5 Unresolved constitutive relationships - c++) appropriate.

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### 6.8.4 Unresolved constitutive relationships - Octave

Following the example of the previous section, the unresolved CR `tank' can be expressed as an Octave m-file. For example:

    function p = tank (rho,g,vol,h,topt,bott,press)

      ## usage:  p = tank (vol,h,topt,bott,press)
      ##
      ##

       val = press; zt = topt; zb = bott;
       zval = 0.5*(abs(zb+(zt-zb)*val-h)+(zb+(zt-zb)*val-h));

       p = rho*g*zval + 0.5*(1+tanh((press-0.98)*500))*100000;

    endfunction

This will be automatically loaded into octave.

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### 6.8.5 Unresolved constitutive relationships - c++

Following the example of the previous section, the unresolved CR `tank' can be expressed in c++ code. For example:

    inline double tank(const double rho,
                       const double g,
                       const double vol,
                       const double h,
                       const double topt,
                       const double bott,
                       const double press)

      /*  ## usage:  p = tank (vol,h,topt,bott,press)
        ##
        ##
      */
      double p, val, zval, zt, zb;

      val = press;
      zt = topt;
      zb = bott;
      zval = 0.5 * (abs(zb + (zt - zb) * val - h) + zb + (zt - zb) * val - h);

      p = rho * g * zval + 0.5 * (1 + tanh((press - 0.98) * 500)) * 100000L;

      return p;

To make sure that this is used in system `model', the model_cr.h file must be as follows:

    // CR headers for system model
    #include "tank.c"

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## 6.9 Parameters

In general, lbl (see section 6.6 Labels (lbl)) files contain symbolic parameters. MTT provides three ways of substituting for these parameters:

- symbolic substitution
- symbolic substitution for simplification of displayed equations
- numeric

6.9.1 Symbolic parameters (subs.r) |  |
6.9.2 Symbolic parameters for simplification (simp.r) |  |
6.9.3 Numeric parameters (numpar) |  |

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### 6.9.1 Symbolic parameters (subs.r)

This file contains reduce statements to symbolically change the expressions describing the system. For example, a useful set of trig substitutions is:

    LET cos(~x)*cos(~y) = (cos(x+y)+cos(x-y))/2;
    LET cos(~x)*sin(~y) = (sin(x+y)-sin(x-y))/2;
    LET sin(~x)*sin(~y) = (cos(x-y)-cos(x+y))/2;
    LET cos(~x)^2       = (1+cos(2*x))/2;
    LET sin(~x)^2       = (1-cos(2*x));

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### 6.9.2 Symbolic parameters for simplification (simp.r)

This file contains reduce statements to symbolically change the expressions describing the system. Unlike the subs.r file (see section 6.9.1 Symbolic parameters (subs.r)) it does not affect all system transformations; only those converting to LaTeX form.

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### 6.9.3 Numeric parameters (numpar)

When computing time and frequency responses; or when evaluating functions in Octave (see section 10.4 Octave); symbolic parameters need numerical instantiations.

The numpar representation provides the relevant numerical information. It comes in a number of languages:

`txt`
  a textual description of the parameter values -- this is the defining representation (see section 6.2 Defining representations).
`m`
  readable by `octave` a high-level interactive language for numerical computation -- translated by mtt from the txt version.
`c`
  readable by `gcc` a c compiler -- translated by mtt from the txt version.

6.9.3.1 Text form (numpar.txt) |  |

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#### 6.9.3.1 Text form (numpar.txt)

This is the textual form of the numerical parameters representation (see section 6.9.3 Numeric parameters (numpar)). Lines are either

`assignment statements`
  variable = value
`comments`
  lines beginning with #
`commented assignment statements`
  variable = value # comments

An example file is:

    # Numerical parameter file (rc_numpar.txt)
    # Generated by MTT at Mon Jun 16 15:10:17 BST 1997

    # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    # %% Version control history
    # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    # %% $Id: mtt.texi,v 1.18 2003/09/07 20:41:19 geraint Exp $
    # %% $Log: mtt.texi,v $
    # %% Revision 1.18  2003/09/07 20:41:19  geraint
    # %% *** empty log message ***
    # %%
    # %% Revision 1.17  2003/08/19 14:20:38  gawthrop
    # %% Version 5.0 of MTT
    # %% Remove xref errors (spurious spaces)
    # %%
    # %% Revision 1.16  2003/08/19 14:11:23  gawthrop
    # %% Links to legal stuff
    # %%
    # %% Revision 1.15  2003/08/19 14:01:45  gawthrop
    # %% Added legal appendices
    # %%
    # %% Revision 1.14  2003/08/06 14:50:56  gawthrop
    # %% Describe the alias mechanism for invoking mtt options
    # %%
    # %% Revision 1.13  2002/12/13 10:07:07  gawthrop
    # %% Added example in sh section of DIY reps
    # %%
    # %% Revision 1.12  2002/09/19 08:09:31  gawthrop
    # %% Updated documentation documentation
    # %%
    # %% Revision 1.11  2002/08/20 15:51:17  gawthrop
    # %% Update to work with ident DIY rep
    # %%
    # %% Revision 1.10  2002/07/22 10:45:22  geraint
    # %% Fixed gnuplot rep so that it correctly re-runs the simulation if input files have changed.
    # %%
    # %% Revision 1.9  2002/07/05 13:29:34  geraint
    # %% Added notes about generating dynamically linked functions for Octave and Matlab.
    # %%
    # %% Revision 1.8  2002/07/04 21:34:12  geraint
    # %% Updated gnuplot view description to describe Tcl/Tk interface instead of obsolete txt method.
    # %%
    # %% Revision 1.7  2002/04/23 09:51:54  gawthrop
    # %% Changed incorrect statement about searching for components.
    # %%
    # %% Revision 1.6  2001/10/15 14:29:50  gawthrop
    # %% Added documentaton on  [1:N] style port labels
    # %%
    # %% Revision 1.5  2001/07/23 03:35:29  geraint
    # %% Updated file structure (mtt/bin).
    # %%
    # %% Revision 1.4  2001/07/23 03:25:02  geraint
    # %% Added notes on -ae hybrd, rk4, ode2odes.cc, .oct dependencies.
    # %%
    # %% Revision 1.3  2001/07/13 03:02:38  geraint
    # %% Added notes on #ICD, gnuplot.txt and odes.sg rep.
    # %%
    # %% Revision 1.2  2001/07/03 22:59:10  gawthrop
    # %% Fixed problems with argument passing for CRs
    # %%
    # %% Revision 1.1  2001/06/04 08:18:52  gawthrop
    # %% Putting documentation under CVS
    # %%
    # %% Revision 1.66  2000/12/05 14:20:55  peterg
    # %% Added the c++  anf m CR info.
    # %%
    # %% Revision 1.65  2000/11/27 15:36:15  peterg
    # %% NOPAR --> NOTPAR
    # %%
    # %% Revision 1.64  2000/11/16 14:22:48  peterg
    # %% added UNITS declaration
    # %%
    # %% Revision 1.63  2000/11/03 14:41:08  peterg
    # %% Added PAR and NOTPAR stuff
    # %%
    # %% Revision 1.62  2000/10/17 17:53:34  peterg
    # %% Added some simulation details
    # %%
    # %% Revision 1.61  2000/09/14 17:13:06  peterg
    # %% New options table
    # %%
    # %% Revision 1.60  2000/09/14 17:09:20  peterg
    # %% Tidied up valid name sections
    # %% Tidied up defining represnetations table
    # %% Verion 4.6
    # %%
    # %% Revision 1.59  2000/08/30 13:09:00  peterg
    # %% Updated option table
    # %%
    # %% Revision 1.58  2000/08/01 13:30:19  peterg
    # %% Version 4.4
    # %% updated STEPFACTOR info
    # %% describes octave and OCST interfaces
    # %%
    # %% Revision 1.57  2000/07/20 07:55:44  peterg
    # %% Version 4.3
    # %%
    # %% Revision 1.56  2000/05/19 17:49:17  peterg
    # %% Extended the user defined representation section -- new nppp rep.
    # %%
    # %% Revision 1.55  2000/03/16 13:53:31  peterg
    # %% Correct date
    # %%
    # %% Revision 1.54  2000/03/15 21:22:57  peterg
    # %% Updated to 4.1 -- old style SS no longer supported
    # %%
    # %% Revision 1.53  1999/12/22 05:33:10  peterg
    # %% Updated for 4.0
    # %%
    # %% Revision 1.52  1999/11/23 00:25:11  peterg
    # %% Added the sensitivity reps
    # %%
    # %% Revision 1.51  1999/11/16 04:43:47  peterg
    # %% Added start of sensitivity section
    # %%
    # %% Revision 1.50  1999/11/16 00:30:35  peterg
    # %% Updated simulation section
    # %% Added vector components
    # %%
    # %% Revision 1.49  1999/07/20 23:44:58  peterg
    # %% V 3.8
    # %%
    # %% Revision 1.48  1999/07/19 03:08:33  peterg
    # %% Added documentation for (new) SS lbl fields
    # %%
    # %% Revision 1.47  1999/03/09 01:42:22  peterg
    # %% Rearranged the User interface section
    # %%
    # %% Revision 1.46  1999/03/09 01:18:01  peterg
    # %% Updated for 3.5 including xmtt
    # %%
    # %% Revision 1.45  1999/03/03 02:39:26  peterg
    # %% Minor updates
    # %%
    # %% Revision 1.44  1999/02/17 06:52:14  peterg
    # %% New level formula dor artwork
    # %%
    # %% Revision 1.43  1998/11/25 16:49:24  peterg
    # %% Put in subs.r documentation (was called params.r)
    # %%
    # %% Revision 1.42  1998/11/24 12:24:59  peterg
    # %% Added section on simulation output
    # %% Version 3.4
    # %%
    # %% Revision 1.41  1998/09/02 12:04:15  peterg
    # %% Version 3.2
    # %%
    # %% Revision 1.40  1998/08/27 08:36:39  peterg
    # %% Removed in. methods except Euler anf implicit
    # %%
    # %% Revision 1.39  1998/08/18 10:44:28  peterg
    # %% Typo
    # %%
    # %% Revision 1.38  1998/08/18 09:16:38  peterg
    # %% Version 3.1
    # %%
    # %% Revision 1.37  1998/08/17 16:14:30  peterg
    # %% Version 3.1 - includes documentation on METHOD=IMPLICIT
    # %%
    # %% Revision 1.36  1998/07/30 17:33:15  peterg
    # %% VERSION 3.0
    # %%
    # %% Revision 1.35  1998/07/22 11:00:53  peterg
    # %% Correct date!
    # %%
    # %% Revision 1.34  1998/07/22 11:00:13  peterg
    # %% Version to BAe
    # %%
    # %% Revision 1.33  1998/07/17 19:32:19  peterg
    # %% Added more about aliases
    # %%
    # %% Revision 1.32  1998/07/05 14:21:56  peterg
    # %% Further additions (Carlisle-Glasgow)
    # %%
    # %% Revision 1.31  1998/07/04 11:35:57  peterg
    # %% Strarted new lbl description
    # %%
    # %% Revision 1.30  1998/07/02 18:39:20  peterg
    # %% Started 3.0
    # %% Added alias and default sections.
    # %%
    # %% Revision 1.29  1998/05/19 19:46:58  peterg
    # %% Added the odess description
    # %%
    # %% Revision 1.28  1998/05/14 09:17:22  peterg
    # %% Added METHOD variable to the simpar file
    # %%
    # %% Revision 1.27  1998/05/13 10:03:09  peterg
    # %% Added unknown/zero SS label documentation.
    # %%
    # %% Revision 1.26  1998/04/29 15:12:46  peterg
    # %% Version 2.9.
    # %%
    # %% Revision 1.25  1998/04/12 17:00:26  peterg
    # %% Added new port features: coerced direction and top-level behaviour.
    # %%
    # %% Revision 1.24  1998/04/05 18:27:20  peterg
    # %% This was the 2.6 version
    # %%
    # Revision 1.23  1997/08/24  11:17:51  peterg
    # This is the released  version 2.5
    #
    # %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    # Parameters
    c =     1.0; # Default value
    r =     1.0; # Default value
    # Initial states
    x(1) =  0.0; # Initial state for rc (c)

As usual, MTT provides a default text file to be edited by the user (see section 10.3 Text editors).

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## 6.10 Causal bond graph (cbg)

The causal bond graph is the causally complete version of the Acausal bond graph (see section 6.4 Acausal bond graph (abg)).

To create the causal bond graph of system `sys' in language fig type:

    mtt sys cbg fig

To create the causal bond graph of system `sys' in language m type:

    mtt sys cbg m

To view the causal bond graph of system `sys' type:

    mtt sys cbg view

6.10.1 Language fig (cbg.fig) |  |
6.10.2 Language m (cbg.m) |  |

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### 6.10.1 Language fig (cbg.fig)

The fig file is created by MTT. It is identical to the corresponding acausal representation (see section 6.4.1 Language fig (abg.fig)) except that

- the new causal strokes are added (using a double thickness line in blue)
- components that are undercausal are bold and green
- components that are overcausal are bold and red

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### 6.10.2 Language m (cbg.m)

The causal bond graph of system `sys' is represented as an m file with heading:

    function [cbonds,status] = sys_cbg

The two outputs of this function are:

- cbonds
- status

cbonds is a matrix with

- one row for each bond
- the first column contains the arrow-orientated (see section 6.4.3.1 Arrow-orientated causality) causality of the effort variable.
- the second column contains the arrow-orientated (see section 6.4.3.1 Arrow-orientated causality) causality of the flow variable.

status is a matrix with

- one row for each component
- the first column contains 1 if the component is overcausal; 0 if the component is causally complete and -1 if the component is undercausal.

A successful model would therefore have all zeros in the status matrix.

6.10.2.1 Transformation abg2cbg_m |  |

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#### 6.10.2.1 Transformation abg2cbg_m

This transformation takes the acausal bond graph as an m file (see section 6.4.3 Language m (abg.m)) and transforms it into a causal bond graph in m-file format (see section 6.10.2 Language m (cbg.m)).

It is based on the m-function abg2cbg.m which iteratively tries to complete causality whilst recursively searching the bond graph structure. If causality is incomplete, it picks the first acausal dynamic (C or I) component, asserts integral causality, and tries again.

This is essentially the sequential causality assignment procedure of Karnopp and Rosenberg.

The transformation informs the user of the final status in terms of the percentage of causally complete components; a successful model will yield 100% here.

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## 6.11 Elementary system equations (ese)

The elementary system equations are a complete set of assignment statements describing the dynamic system corresponding to the bond graph. They are in the Reduce (see section 9.3 Reduce) language.

Because these are based on a causally complete system, these assignment statements are directly soluble by substitution.

Unlike early versions of MTT, MTT does not sort the equations in order of solution, but rather leaves them sorted by component and subsystem.

These are not supposed to be read by the user, so there is no view facility as such. However, you may read these with your favourite text editor and, to this end, helpful comment lines have been added.

Wherever components have an explicit constitutive relationship, the corresponding RHS of the equation has a standard form.

    cr(arguments,out_causality,outport,
            input_1, causality_1, port_1,
            ....
            input_i, causality_i, port_i,
            ....
            input_n, causality_n, port_n
            );

where the symbols have the following meaning

`arguments`
  the constitutive relationship arguments
`out_causality`
  the causality (effort or flow) of the output variable (see section 1.4 Variables)
`outport`
  the number (integer) of the output port of the system
`input_i`
  the ith input to the component
`causality_i`
  the causality (effort or flow) of the ith input variable (see section 1.4 Variables)
`port_i`
  the number (integer) of the ith input port of the system

An example for a resistor with linear constitutive relationship is:

    rc_1_bond4_flow := lin(flow,r,flow,1,
            rc_1_bond4_effort,effort,1
            );

6.11.0.1 Transformation cbg2ese_m2r |  |

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#### 6.11.0.1 Transformation cbg2ese_m2r

This transformation takes the causal bond graph as an m file (see section 6.10.2 Language m (cbg.m)) and transforms it into elementary system equations in Reduce (see section 9.3 Reduce) form.

It is based on the m-function cbg2ese.m which iteratively traverses the causal bond graph writing equations as it goes.

It also writes out the system structure as the file ``sys_def.r`'.

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## 6.12 Differential-Algebraic Equations (dae)

The system differential algebraic equations describe the system dynamics together together with any algebraic constraints.

They are generated in language `lang` for system `sys` by:

    mtt sys dae lang

Valid languages are:

`r`
  reduce (see section 9.3 Reduce).
`m`
  m (see section 9.2 m).
`view`
  reduce (see section 10.1 Views).

There are five sets of variables describing the system:

`x`
  the system states (corresponding to C and I components with integral causality.
`z`
  the system nonstates (corresponding to C and I components with derivative causality.
`u`
  the system inputs (corresponding to SS components with external attribute).
`ui`
  the internal system inputs (corresponding to SS components with internal attribute) used to solve algebraic loops (see section 1.7 Algebraic loops).
`y`
  the system outputs (corresponding to SS components with external attribute).

In general there are four sets of equations. The right-hand side of each is a function of x, dz/dt, u and ui and the left hand sides are:

1. the derivative of x (dx/dt)
2. z
3. w=0 (the algebraic equations)
4. y

6.12.1 Language reduce (dae.r) |  |
6.12.2 Language m (dae.m) |  |

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### 6.12.1 Language reduce (dae.r)

The system DAEs (see section 6.12 Differential-Algebraic Equations (dae)) are represented in the reduce (see section 9.3 Reduce) language as arrays containing the algebraic expressions for the right hand sides of each set of equations. The arrays are:

`MTTx`
  x -- the system states (corresponding to C and I components with integral causality.
`MTTz`
  z -- the system nonstates (corresponding to C and I components with derivative causality.
`MTTu`
  u -- the system inputs (corresponding to SS components with external attribute).
`mttv`
  ui -- the internal system inputs (corresponding to SS components with internal attribute) used to solve algebraic loops (see section 1.7 Algebraic loops).
`MTTy`
  y -- the system outputs (corresponding to SS components with external attribute).

6.12.1.1 Transformation ese2dae_r |  |

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#### 6.12.1.1 Transformation ese2dae_r

This transformation (see section 1.2 What is a transformation?) uses Reduce (see section 9.3 Reduce) to combine the elementary system equations (see section 6.11 Elementary system equations (ese)) with the constitutive relationships (see section 1.6.2 Constitutive relationship) and simplify the result.

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### 6.12.2 Language m (dae.m)

The system DAEs (see section 6.12 Differential-Algebraic Equations (dae)) are represented in the m (see section 9.2 m) language as two m-functions of the form:

    function resid = sys_dae(dx,x,t)
    function y  = sys_dae(dx,x,t)

Where x is the dae descriptor vector and dx its time derivative; t is the time. The first function is of a form suitable for solution by DASSL; the second function can then be used to find the coresponding system output.

6.12.2.1 Transformation dae_r2m |  |

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#### 6.12.2.1 Transformation dae_r2m

This transformation (see section 1.2 What is a transformation?) uses Reduce (see section 9.3 Reduce) to rewrite the elementary system equations (see section 6.11 Elementary system equations (ese)) in m-file format (see section 9.2 m) . Numerical parameters are declared as global.

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## 6.13 Constrained-state Equations (cse)

The system constrained-state equations describe the system dynamics for a special class of systems (see the book for details). The resuting equations are of the form:

    E(x) dx/dt = f(x,u)
    y = g(x,u)

They typically occure where two or more states are constrained to be equal, or proportional, to each other. For example, two capacitors in parallel or two inertias connected by a stiff shaft.

They are generated in language `lang` for system `sys` by:

    mtt sys cse lang

Valid languages are:

`r`
  reduce (see section 9.3 Reduce).
`m`
  m (see section 9.2 m).
`view`
  reduce (see section 10.1 Views).

There are three sets of variables describing the system:

`x`
  the system states (corresponding to C and I components with integral causality.
`u`
  the system inputs (corresponding to SS components with external attribute).
`y`
  the system outputs (corresponding to SS components with external attribute).

In general there are two sets of equations. The right-hand side of each is a function of x and u and the left hand sides are:

1. the derivative of x (dx/dt) y

6.13.1 Language reduce (cse.r) |  |
6.13.2 Language m (view) |  |

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### 6.13.1 Language reduce (cse.r)

The system CSEs (see section 6.13 Constrained-state Equations (cse)) are represented in the reduce (see section 9.3 Reduce) language as arrays containing the algebraic expressions for the right hand sides of each set of equations. The arrays are:

`MTTx`
  x -- the system states (corresponding to C and I components with integral causality.
`MTTu`
  u -- the system inputs (corresponding to SS components with external attribute).
`MTTy`
  y -- the system outputs (corresponding to SS components with external attribute).

together with the array containing the elements of the E matrix.

6.13.1.1 Transformation dae2cse_r |  |

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#### 6.13.1.1 Transformation dae2cse_r

This transformation (see section 1.2 What is a transformation?) Reduce (see section 9.3 Reduce) to find various Jacobians which are combined to find the E matrix and the constrained-state equations (see section 6.13 Constrained-state Equations (cse)).

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### 6.13.2 Language m (view)

This representation has the standard text view (see section 10.1 Views).

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## 6.14 Ordinary Differential Equations

The system ordinary differential equations describe the system dynamics.

They are generated in language `lang` for system `sys` by:

    mtt sys ode lang

Valid languages are:

`r`
  reduce (see section 9.3 Reduce).
`m`
  m (see section 9.2 m).
`view`
  reduce (see section 10.1 Views).

There are three sets of variables describing the system:

`x`
  the system states (corresponding to C and I components with integral causality.
`u`
  the system inputs (corresponding to SS components with external attribute).
`y`
  the system outputs (corresponding to SS components with external attribute).

In general there are two sets of equations. The right-hand side of each is a function of x and u and the left hand sides are:

1. the derivative of x (dx/dt) y

6.14.1 Language reduce (ode.r) |  |
6.14.2 Language m (ode.m) |  |
6.14.3 Language m (view) |  |

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### 6.14.1 Language reduce (ode.r)

The system ODEs (see section 6.14 Ordinary Differential Equations) are represented in the reduce (see section 9.3 Reduce) language as arrays containing the algebraic expressions for the right hand sides of each set of equations. The arrays are:

`MTTx`
  x -- the system states (corresponding to C and I components with integral causality.
`MTTu`
  u -- the system inputs (corresponding to SS components with external attribute).
`MTTy`
  y -- the system outputs (corresponding to SS components with external attribute).

6.14.1.1 Transformation cse2ode_r |  |

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#### 6.14.1.1 Transformation cse2ode_r

This transformation (see section 1.2 What is a transformation?) uses Reduce (see section 9.3 Reduce) to invert the E matrix of the constrained-state equations (see section 6.13 Constrained-state Equations (cse)) and simplify the result.

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### 6.14.2 Language m (ode.m)

The system ODEs (see section 6.14 Ordinary Differential Equations) are represented in the m (see section 9.2 m) language as two m-functions of the form:

    function dx = sys_ODE(x,t)
    function y  = sys_ODE(dx,x,t)

Where x is the ODE state vector and dx its time derivative; t is the time. The first function is of a form suitable for solution by odesol; the second function can then be used to find the corresponding system output.

6.14.2.1 Transformation ode_r2m |  |

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#### 6.14.2.1 Transformation ode_r2m

This transformation (see section 1.2 What is a transformation?) uses Reduce (see section 9.3 Reduce) to rewrite the ordinary differential equations (see section 6.14 Ordinary Differential Equations) in m-file format (see section 9.2 m) . Numerical parameters are declared as global.

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### 6.14.3 Language m (view)

This representation has the standard text view (see section 10.1 Views).

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## 6.15 Descriptor matrices (dm)

The system descriptor matrices A, B, C, D and E describe the linearised system dynamics in the form

    E dx/dt = Ax + Bu
    y = Cx + Du

They are generated in language `lang` for system `sys` by:

    mtt sys dm lang

Valid languages are:

`r`
  reduce (see section 9.3 Reduce).
`m`
  m (see section 9.2 m).
`view`
  reduce (see section 10.1 Views).

6.15.1 Language reduce (dm.r) |  |
6.15.2 Language m (dm.m) |  |

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### 6.15.1 Language reduce (dm.r)

The system descriptor matrices (see section 6.15 Descriptor matrices (dm)) are represented in the reduce (see section 9.3 Reduce) language as arrays containing the four matrices. The arrays are:

`MTTA`
  A
`MTTB`
  B
`MTTA`
  C
`MTTD`
  D
`MTTE`
  E

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### 6.15.2 Language m (dm.m)

The system descriptor matrices (see section 6.15 Descriptor matrices (dm)) are represented in the m (see section 9.2 m) language as an m-function of the form:

    function [A,B,C,D,E] = sys_dm

System numeric parameters (see section 1.6.4 Numeric parameters) are passed via global variables defined in the _numpar.m file. Thus the system descriptor matrices are typically generated in Octave (see section 10.4 Octave) as follows:

    sys_numpar
    [A,B,C,D,E] = sys_dm

Parameters can be changed from their default values by entering their values directly into Octave (see section 10.4 Octave) and then invoking `sys_dm`; for example

    sys_numpar
    par_1 = 25
    par_2 = par_1 + 3
    [A,B,C,D,E] = sys_dm

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## 6.16 Report (rep)

MTT has a report-generator feature. The user specifies the report contents in a text file (see section 6.16.1 Language text (rep.txt)) using an appropriate text editor (see section 10.3 Text editors).

For example, the report can be viewed by typing

    mtt system rep view

6.16.1 Language text (rep.txt) |  |
6.16.2 Language view |  |

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### 6.16.1 Language text (rep.txt)

The user specifies the report contents in a text file (see section 6.16.1 Language text (rep.txt)) using an appropriate text editor (see section 10.3 Text editors). The text file contains lines which are either comments (indicated by %) or valid MTT commands. The report will then contain appropriate sections. The following languages are supported by the report generator:

`m`
  `octave` a high-level interactive language for numerical computation.
`r`
  `reduce` a high-level interactive language for symbolic computation.
`tex`
  `latex` a text processor.
`ps`
  `ghostview` another document viewer.
`c`
  `gcc` a c compiler.

For example:

    mtt rc abg tex
    mtt rc cbg ps
    mtt rc struc tex
    mtt rc ode tex
    mtt rc sro ps
    mtt rc tf tex
    mtt rc lmfr ps

The acausal bond graph (abg) (see section 6.4 Acausal bond graph (abg)) with the tex language is handled in a special way: the acausal Bond Graph in fig format (see section 6.4.1 Language fig (abg.fig)), the label file (see section 6.6 Labels (lbl)) the description file (see section 8.2.2 Detailed on-line documentation), together with corresponding subsystems are included in the report. It is recommended that the first (non-comment line) in the file should be:

    mtt <system> abg tex

where `<system>` is the name of the (top-level) system.

As usual, MTT provides a default text file to be edited by the user (see section 10.3 Text editors).

In the special case that the first argument to mtt (normally the system) is a directory, a default text file is provided which generates a report for all systems to be found in that directory tree.

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### 6.16.2 Language view

This representation has the standard text view (see section 10.1 Views).

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# 7. Extending MTT

MTT has a number of built-in mechanisms for the user to extend its capabilities. As MTT is based on `Make' it is unsurprising that some of these involve the creation of `make files'.

7.1 Makefiles |  |
7.2 New (DIY) representations |  |
7.3 Component library |  |

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## 7.1 Makefiles

If a file called `Makefile' exists in the current directory, MTT executes it using make before doing anything else. This is useful if one of the .txt files contains a reference to, for example, an octave function of which MTT unaware. Such a function can be created using the makefile. An example `Makefile' is

    # Makefile for the Two link GMV example

    all: msdP_tf.m TwoLinkP_obs.m TwoLinkP_sm.m twolinkp_sm.m TwoLinkGMV_numpar.m

    msdP_tf.m: msdP_abg.fig
            mtt -q msdP tf m

    TwoLinkP_obs.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
            mtt -q TwoLinkP obs m

    TwoLinkP_sm.m: TwoLinkP_abg.fig TwoLinkP_lbl.txt
            mtt -q TwoLinkP sm m

    twolinkp_sm.m: TwoLinkP_sm.m
            cp -v TwoLinkP_sm.m twolinkp_sm.m

    TwoLinkGMV_numpar.m: TwoLinkGMV_numpar.txt
            mtt -q TwoLinkGMV numpar m

All of the files in the line stating `all:' are created when MTT is executed (if they don't already exist).

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## 7.2 New (DIY) representations

It may be convenient to create new representations for MTT; in particular, it is nice to be able to include the result of some numerical or symbolic computations within an MTT report (see section 6.16 Report (rep)). Therefore MTT provides a mechanism for doing this.

Future extensions of MTT will use such representations stored in $MTT_REP.

There are three parts to creating a DIY representation called myrep

1. Creating a make file in Make format called myrep_rep.make
2. Optionally creating a shell script called myrep_rep.sh
3. Optionally creating a documentation file in LaTeX format called myrep_rep.tex

7.2.1 Makefile |  |
7.2.2 Shell-script |  |
7.2.3 Documentation |  |

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### 7.2.1 Makefile

To create a new representation `myrep' in a language `mylang', create a file with the name

    myrep_rep.make

This file must contain text in `make' syntax. It is executed by MTT and the two arguments `SYS' (the system name) and `LANG' (the language) are passed to it by MTT. Note that MTT cannot know of any prerequisites, but these can be explicitly included in the makefile (which may include execution of MTT itself.

The following example declares the new representation `ident' which is created in conjunction with the shell-script ident_rep.sh (see section 7.2.2 Shell-script).

@verbatim # -*-makefile-*-

#SUMMARY Identification #DESCRIPTION Partially know system identification using #DESCRIPTION using bond graphs

# Makefile for representation ident # File ident_rep.make

#Copyright (C) 2000,2001,2002 by Peter J. Gawthrop

## Model targets model_reps = ${SYS}_sympar.m ${SYS}_simpar.m ${SYS}_state.m model_reps += ${SYS}_numpar.m ${SYS}_input.m ${SYS}_ode2odes.m model_reps += ${SYS}_def.m

## Prepend s to get the sensitivity targets sensitivity_reps = ${model_reps:%=s%}

## Model prerequisites model_pre = ${SYS}_abg.fig ${SYS}_lbl.txt model_pre += ${SYS}_rdae.r ${SYS}_numpar.txt

## Prepend s to get the sensitivity targets sensitivity_pre = ${model_pre:%=s%}

## Simulation targets sims = ${SYS}_sim.m s${SYS}_ssim.m

## m-files needed for ident ident_m = ${SYS}_ident.m ${SYS}_ident_numpar.m

## Targets for the ident simulation ident_reps = ${ident_m} ${sims} ${model_reps} ${sensitivity_reps}

## ps output files etc psfiles = ${SYS}_ident.ps ${SYS}_ident.comparison.ps figfiles = ${psfiles:%.ps=%.fig} gdatfiles = ${psfiles:%.ps=%.gdat} datfiles = ${psfiles:%.ps=%.dat2}

## LaTeX files etc latexfiles = ${SYS}_ident_par.tex

all: ${SYS}_ident.${LANG}

echo: echo "sims: ${sims}" echo "model_reps: ${model_reps}" echo "sensitivity_reps: ${sensitivity_reps}" echo "ident_reps: ${ident_reps}"

${SYS}_ident.view: ${psfiles} ident_rep.sh ${SYS} view

${psfiles}: ${figfiles} ident_rep.sh ${SYS} ps

${figfiles}: ${gdatfiles} ident_rep.sh ${SYS} fig

${gdatfiles}: ${datfiles} ident_rep.sh ${SYS} gdat

${datfiles} ${latexfiles}: ${ident_reps} ident_rep.sh ${SYS} dat2

${SYS}_ident.m: ident_rep.sh ${SYS} m

${SYS}_ident_numpar.m: ident_rep.sh ${SYS} numpar.m

## System model reps ## Generic txt files ${SYS}_%.txt: mtt ${OPTS} -q -stdin ${SYS} $* txt

## Specific m files ${SYS}_ode2odes.m: ${model_pre} mtt -q -stdin ${OPTS} ${SYS} ode2odes m

${SYS}_sim.m: ${SYS}_ode2odes.m mtt ${OPTS} -q -stdin ${SYS} sim m

## Numpar files ${SYS}_numpar.m: mtt ${SYS} numpar m

## Sympar files ${SYS}_sympar.m: mtt ${SYS} sympar m

## Generic txt to m ${SYS}_%.m: ${SYS}_%.txt mtt ${OPTS} -q -stdin ${SYS} $* m

## r files ${SYS}_def.r: ${SYS}_abg.fig mtt ${OPTS} -q -stdin ${SYS} def r

${SYS}_rdae.r: mtt ${OPTS} -q -stdin ${SYS} rdae r

## Sensitivity model reps ## Generic txt files s${SYS}_%.txt: mtt ${OPTS} -q -stdin -s s${SYS} $* txt

## Specific m files ## Numpar files s${SYS}_numpar.m: mtt -s s${SYS} numpar m

## Sympar files s${SYS}_sympar.m: mtt -s s${SYS} sympar m

s${SYS}_ode2odes.m: ${sensitivity_pre} mtt -q -stdin ${OPTS} -s s${SYS} ode2odes m

s${SYS}_ssim.m: mtt -q -stdin ${OPTS} -s s${SYS} ssim m

s${SYS}_def.m: mtt -q -stdin ${OPTS} -s s${SYS} def m

## Generic txt to m s${SYS}_%.m: s${SYS}_%.txt mtt ${OPTS} -q -stdin s${SYS} $* m

## r files s${SYS}_rdae.r: mtt ${OPTS} -q -stdin -s s${SYS} rdae r

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### 7.2.2 Shell-script

For more complex DIY representations, it is convenient to define new commands to be used by the Makefile (see section 7.2.1 Makefile).

The following example shows this in the context of the DIY representation `ident' used as an example in the previous section (see section 7.2.1 Makefile).

@verbatim #! /bin/sh

## ident_rep.sh ## DIY representation "ident" for mtt # Copyright (C) 2002 by Peter J. Gawthrop

ps=ps

sys=$1 rep=ident lang=$2 mtt_parameters=$3 rep_parameters=$4

## Some names target=${sys}_${rep}.${lang} def_file=${sys}_def.r dat2_file=${sys}_ident.dat2 dat2s_file=${sys}_idents.dat2 ident_numpar_file=${sys}_ident_numpar.m option_file=${sys}_ident_mtt_options.txt

## Get system information if [ -f "${def_file}" ]; then echo Using ${def_file} else mtt -q ${sys} def r fi

ny=`mtt_getsize $1 y` nu=`mtt_getsize $1 u`

check_new_options() { if [ -f "${option_file}" ]; then old_options=`cat ${option_file}` if [ "${mtt_options}" != "${old_options}" ]; then echo ${mtt_options} > ${option_file} fi else echo ${mtt_options} > ${option_file} fi }

## Make the _ident.m file make_ident() { filename=${sys}_${rep}.m date=`date` echo Creating ${filename}

cat > ${filename} <<EOF function [epar,Y] = ${sys}_ident (y,u,t,par_names,Q,extras)

## usage: [epar,Y] = ${sys}_ident (y,u,t,par_names,Q,extras) ## ## last last time in run ## ppp_names Column vector of names of ppp params ## par_names Column vector of names of estimated params ## extras Structure containing additional info ## ## Created by MTT on ${date} ## Sensitivity system name system_name = "s${sys}"

##Sanity check if nargin<3 printf("Usage: [y,u,t] = ${sys}_ident(y,u,t,par_names,Q,extras);"); return endif

if nargin<6 ## Set up optional parameters extras.criterion = 1e-3; extras.emulate_timing = 0; extras.max_iterations = 10; extras.simulate = 2; extras.v = 1e-2; extras.verbose = 1; extras.visual = 1; endif ## System info [n_x,n_y,n_u,n_z,n_yz] = ${sys}_def; sympar = ${sys}_sympar; simpar = ${sys}_simpar; sympars = s${sys}_sympar; simpars = s${sys}_simpar;

## Parameter indices i_par = ppp_indices (par_names,sympar,sympars);

## Initial model state x_0 = zeros(2*n_x,1);

## Initial model parameters par_0 = s${sys}_numpar;

## Reset simulation parameters [n_data,m_data] = size(y); dt = t(2)-t(1); simpars.last = (n_data-1)*dt; simpars.dt = dt;

## Identification [epar,Par,Error,Y,iterations,x] = ppp_optimise(system_name,x_0,par_0,simpars,u,y,i_par,Q,extras); ## Do some plots figure(1); title("Comparison of data"); xlabel("t"); ylabel("y"); [N,M] = size(Y); plot(t,Y(:,M-n_y+1:M),"1;Estimated;", t,y,"3;Actual;"); figfig("${sys}_ident_comparison");

## Create a table of the parameters [n_par,m_par] = size(i_par); fid = fopen("${sys}_ident_par.tex", "w"); fprintf(fid,"\\\\begin{table}[htbp]\\n"); fprintf(fid," \\\\centering\\n"); fprintf(fid," \\\\begin{tabular}{|l|l|}\\n"); fprintf(fid," \\\\hline\\n"); fprintf(fid," Name & Value \\\\\\\\ \\n"); fprintf(fid," \\\\hline\\n"); for i = 1:n_par fprintf(fid,"$%s$ & %4.2f \\\\\\\\ \\n", par_names(i,:), epar(i_par(i,1))); endfor fprintf(fid," \\\\hline\\n"); fprintf(fid,"\\\\end{tabular}\\n"); fprintf(fid,"\\\\caption{Estimated Parameters}\\n"); fprintf(fid,"\\\\end{table}\\n"); fclose(fid);

endfunction EOF }

make_ident_numpar() { echo Creating ${ident_numpar_file} cat > ${sys}_ident_numpar.m <<EOF function [y,u,t,par_names,Q,extras] = ${sys}_ident_numpar;

## usage: [y,u,t,par_names,Q,extras] = ${sys}_ident_numpar; ## Edit for your own requirements ## Created by MTT on ${date}

## This section sets up the data source ## simulate = 0 Real data (you supply ${sys}_ident_data.dat) ## simulate = 1 Real data input, simulated output ## simulate = 2 Unit step input, simulated output simulate = 2;

## System info [n_x,n_y,n_u,n_z,n_yz] = ${sys}_def; simpars = s${sys}_simpar;

## Access or create data if (simulate<2) # Get the real data if (exist("${sys}_ident_data.dat")==2) printf("Loading ${sys}_ident_data.dat\n"); load ${sys}_ident_data.dat else printf("Please create a loadable file ${sys}_ident_data.dat containing y,u and t\n"); return endif else switch simulate case 2 # Step simulation t = [0:simpars.dt:simpars.last]'; u = ones(size(t)); otherwise error(sprintf("simulate = %i not implemented", simulate)); endswitch endif if (simulate>0) par = ${sys}_numpar(); x_0 = ${sys}_state(par); dt = t(2)-t(1); simpars.dt = dt; simpars.last = t(length(t)); y = ${sys}_sim(zeros(n_x,1), par, simpars, u); endif

## Default parameter names - Put in your own here sympar = ${sys}_sympar; # Symbolic params as structure par_names = struct_elements (sympar); # Symbolic params as strings [n,m] = size(par_names); # Size the string list

## Sort by index for [i,name] = sympar par_names(i,:) = sprintf("%s%s",name, blanks(m-length(name))); endfor ## Output weighting vector Q = ones(n_y,1); ## Extra parameters extras.criterion = 1e-5; extras.emulate_timing = 0; extras.max_iterations = 10; extras.simulate = simulate; extras.v = 1e-2; extras.verbose = 1; extras.visual = 1;

endfunction EOF }

make_dat2() {

## Inform user echo Creating ${dat2_file}

## Use octave to generate the data octave -q <<EOF [y,u,t,par_names,Q,extras] = ${sys}_ident_numpar; [epar,Y] = ${sys}_ident (y,u,t,par_names,Q,extras); [N,M] = size(Y); y_est = Y(:,M); data = [t,y_est,u]; save -ascii ${dat2_file} data EOF

## Tidy up the latex stuff - convert foo_123 to foo_{123} cat ${sys}_ident_par.tex > mtt_junk sed -e "s/_\([a-z0-9,]*\)/_{\1}/g" < mtt_junk >${sys}_ident_par.tex rm mtt_junk }

case ${lang} in numpar.m) ## Make the numpar stuff make_ident_numpar; ;; m) ## Make the code make_ident; ;; dat2) ## The dat2 language (output data) & fig file make_dat2; ;; gdat) cp ${dat2_file} ${dat2s_file} dat22dat ${sys} ${rep} dat2gdat ${sys} ${rep} ;; fig) gdat2fig ${sys}_${rep} ;; ps) figs=`ls ${sys}_ident*.fig | sed -e 's/\.fig//'` for fig in ${figs}; do fig2dev -Leps ${fig}.fig > ${fig}.ps done texs=`ls ${sys}_ident*.tex | sed -e 's/\.tex//'` for tex in ${texs}; do makedoc "" "${sys}" "ident_par" "tex" "" "" "$ps" doc2$ps ${sys}_ident_par "$documenttype" done ;; view) pss=`ls ${sys}_ident*.ps` echo Viewing ${pss} for ps in ${pss}; do gv ${ps}& done ;; *) echo Language ${lang} not supported by ${rep} representation exit 3 esac

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### 7.2.3 Documentation

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## 7.3 Component library

If MTT does not recognise a component (eg named MyComponent) as a simple component (see section 6.4.1.5 Simple components) or as already existing, it searches the library search path $MTT_COMPONENTS (see section 11.4.2 $MTT_COMPONENTS) for a directory called MyComponent containing MyComponent_lbl.txt. It then copies the entire directory into the current working directory. Thus, for example, the directory could contain MyComponent_desc.tex MyComponent_abg.fig MyComponent_lbl.txt and MyComponent_cr.r in addition to MyComponent_lbl.txt.

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# 8. Documentation

8.1 Manual |  |
8.2 On-line documentation |  |

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## 8.1 Manual

MTT is documented in this manual. The manual can be invoked in various ways:

`mtt manual`
  Brings up a pdf version of the manual
`mtt info`
  Brings up an xterm containing an info version of the manual
`mtt hinfo`
  Brings up an html browser containing the manual
`emacs`
  type ^h^i followed by mmtt in the command window
`browser`
  point browser to mtt.sf.netb

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## 8.2 On-line documentation

MTT components, constitutive relations, examples and representations in libraries (see section 7.3 Component library) are documented in two ways:

1. brief
2. verbose

8.2.1 Brief on-line documentation |  |
8.2.2 Detailed on-line documentation |  |

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### 8.2.1 Brief on-line documentation

Documentation of DIY components, examples, constitutive relationships and representations is provides by the programmer by inserting code of the form

    #SUMMARY     One line summary
    #DESCRIPTION Multi-line
    #DESCRIPTION More detailed description

within the appropriate file (usually at or near the top):

`components`
  _lbl.txt (see section 6.6 Labels (lbl))
`examples`
  _lbl.txt (see section 6.6 Labels (lbl))
`constitutive relations`
  _cr.r (see section 6.8.2 DIY constitutive relationships)
`representations`
  _rep.make (see section 7.2.1 Makefile)

This documentation is accessed by the user in various ways

`mtt help name`
  prints basic information on the screen
`mtt system lbl view`
  gives formatted information about the component or example
`Including mtt system abg tex in the _rep.txt file`
  gives formatted information about the component or example within the report

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### 8.2.2 Detailed on-line documentation

DIY components, examples, constitutive relationships can be described textually in LaTeX (.tex) description file; this is the only language for this representation. This representation is used by the LaTeX language version (see section 6.4.4 Language tex (abg.tex)) of the acausal bond graph representation (see section 6.4 Acausal bond graph (abg)).

The file may contain any LaTeX commands valis for the "article" document type but must not contain:

- documentclass commands
- document environments

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# 9. Languages

9.1 Fig |  | r
9.2 m |  |
9.3 Reduce |  |
9.4 c |  |

These are a number of languages used by MTT to implement the various representations. Each has associated Language tools (see section 10. Language tools) to manipulate and/or view the representation.

`fig`
  `Fig` a graphical description language.
`m`
  `octave` a high-level interactive language for numerical computation.
`r`
  `reduce` a high-level interactive language for symbolic computation.
`tex`
  `latex` a text processor.
`dvi`
  `xdvi` a document viewer.
`ps`
  `ghostview` another document viewer.
`gdat`
  `gnuplot` a data viewer.
`c`
  `gcc` a c compiler.
`sg`
  `scigraphica` a plotting package.

These tools are automatically invoked as appropriate by MTT; but for more advanced use, these tools can be used directly on files (with the appropriate suffix) generated by MTT.

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## 9.1 Fig

Please see xfig documentation.

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## 9.2 m

Please see Octave documentation <A HREF="http://www.che.wisc.edu/octave/">Octave</A> documentation. <A HREF="http://www.mathworks.com/homepage.html">Matlab</A> documentation.

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## 9.3 Reduce

Please see the reduce documentation.

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## 9.4 c

Please see the gcc documentation.

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# 10. Language tools

10.1 Views |  |
10.2 Xfig |  |
10.3 Text editors |  |
10.4 Octave |  |
10.5 LaTeX |  |

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## 10.1 Views

A number of representations (see section 6. Representations) have a language representation which is particularly useful for viewing by the user. These views are invoked, where appropriate by the command:

    mtt sys rep view

where `sys` is the system name and `rep` a corresponding representation.

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## 10.2 Xfig

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## 10.3 Text editors

All representations live in text files and thus may be edited using your favourite text editor; however, the Fig (see section 9.1 Fig) representation is pretty meaningless in this form and so you should use Xfig (see section 10.2 Xfig) for representation in this language.

Its up to you which text editor to use. I recommend emacs, but simpler (and less powerful) editors such as xedit, textedit and vi are also ok.

I usually run MTT out of an emacs shell window and keep the rest of the files in emacs buffers.

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## 10.4 Octave

Octave is a numerical matrix-based language See section `Octave' in Octave. It is similar to Matlab in many ways. In most cases, m-files generated by MTT can be understood by both Matlab and Octave (and no doubt other Matlab lookalikes).

MTT provides the octave function `mtt`. The octave command

    help mtt

gives the following information:

     usage:  mtt (system[,representation,language])

     Invokes mtt from octave to generate system_representation.language
     Ie equivalent to "mtt system representation language" at the shell
     Representation and language defualt to "sm" and "m" respectively

Thus for example, if octave is in the directory containing the system rc the following session generates the state matrices of the system "rc" with the defaut capacitance but resitance r=0.1.

    octave> mtt("rc");
    Creating rc_rbg.m
    Creating rc_cmp.m
    Creating rc_fig.fig
    Creating rc_sabg.fig
    Creating rc_alias.txt
    Creating rc_alias.m
    Creating rc_sub.sh
    Creating rc_abg.m
    Creating rc_cbg.m (maximise integral causality)
    Creating rc_type.sh
    Creating rc_ese.r
    Creating rc_def.r
    Creating rc_struc.txt
    Creating rc_rdae.r
    Creating rc_subs.r
    Creating rc_cr.txt
    Creating rc_cr.r
    Copying CR SS to here from
    Copying CR lin to here from
    Creating rc_dae.r
    Creating rc_sympar.txt
    Creating rc_sympar.r
    Creating rc_cse.r
    Creating rc_sspar.r
    Creating rc_csm.r
    Creating rc_ode.r
    Creating rc_ss.r
    Creating rc_sm.r
    Creating rc_switch.txt
    0 switches found
    Creating rc_sympars.txt
    Creating rc_sm.m
    Copying rc_sm.m
    octave> mtt("rc","numpar");
    Creating rc_numpar.txt
    Creating rc_numpar.m
    Copying rc_numpar.m
    octave> mtt("rc","sympar");
    Creating rc_sympar.m
    Copying rc_sympar.m
    octave> par = rc_numpar
    par =

      1
      1

    octave> sym = rc_sympar;

    octave> par(sym.r) = 0.1;
    octave> [A,B,C,D] = rc_sm(par)
    A = -10

    B = 10

    C = 1

    D = 0

    octave>

generates the data structure rc corresponding the the bond graph of the system called `rc'. The following octave commands then generate the step reponse and bode diagram respectively:

    step(rc);
    bode(rc);

10.4.1 Octave control system toolbox (OCST) |  |
10.4.2 Creating GNU Octave .oct files |  |
10.4.3 Creating Matlab .mex files |  |
10.4.4 Embedding MTT models in Simulink |  |

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### 10.4.1 Octave control system toolbox (OCST)

MTT provides an interface to the Octave control system toolbox (OCST) using the mfile `mtt2sys`. the octave command

    help mtt2sys

gives the following information.

     usage:  sys = mtt2sys (Name[,par])

     Creates a sys structure for the Octave Control Systems Toolbox
     from an MTT system with name "Name"
     Optional second argument is system parameter list
     Assumes that Name_sm.m, Name_struc.m and Name_numpar.m exist

Thus for example, if octave is in the directory containing the system rc:

    rc = mtt2sys("rc");

generates the data structure rc corresponding the the bond graph of the system called `rc'. The following octave commands then generate the step reponse and bode diagram respectively:

    step(rc);
    bode(rc);

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### 10.4.2 Creating GNU Octave .oct files

GNU Octave dynamically loaded functions (.oct files) can be created by instructing MTT to create the "oct" representation:

      mtt [options] sys ode oct

This will cause MTT to create the C++ representation of the system (sys_ode.cc) and to then compile it as a shared object suitable for use within Octave. The resultant file may be used in an identical manner to the equivalent, but generally slower, interpreted .m file.

Usage information for the function may be obtained within Octave in the usual manner:

      octave:1> help rc_ode

      rc_ode is the dynamically-linked function from the file
      /home/mttuser/rc/rc_ode.oct

      Usage: [mttdx] = rc_ode(mttx,mttu,mttt,mttpar)
      Octave ode representation of system rc
      Generated by MTT on Fri Jul  5 11:23:08 BST 2002

Note that the first line of output from Octave identifies whether the compiled or interpreted function is being used.

Alternatively, standard representations may be generated using the Octave DLDs by use of the "-oct" switch:

      mtt -oct rc odeso view

In order to successfully generate .oct files, Octave must be correctly configured prior to compilation and certain headers and libraries must be correctly installed on the system (see section 11.3.2 .oct file dependencies).

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### 10.4.3 Creating Matlab .mex files

On GNU/Linux systems, Matlab dynamically linked executables (.mexglx files) can created by instructing MTT to create the "mexglx" representation:

      mtt [options] sys ode mexglx

This will cause MTT to create the C++ representation of the system (sys_ode.cc) and to then compile it as a shared object suitable for use within Matlab.

If it is necessary to compile mex files for another platform, then the usual C++ representation (generated with the -cc flag) can be created and the resultant file compiled with the -DCODEGENTARGET=MATLABMEX flag on the target platform.

      mtt_machine:
      mtt -cc rc ode cc

      matlab_machine:
      matlab> mex -DCODEGENTARGET=MATLABMEX rc_ode.cc

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### 10.4.4 Embedding MTT models in Simulink

It is possible to embed MTT functions or entire MTT models within Simulink simulations as Sfun blocks. If the zip package is installed on the system, the command

      mtt sys sfun zip

will create a compressed archive containing sys.mdl, which may be embedded into a larger Simulink model. Also contained within the archive will be four sys_sfun*.c files,

- sys_sfun.c model state and output equations
- sys_sfun_ae.c model algebraic equations
- sys_sfun_input.c model inputs
- sys_sfun_interface.c interface between MTT model and Simulink

The last of these files must be edited to correctly map the inputs and outputs between the MTT and Simulink models. The two sections to edit are clearly marked with

      /* Start EDIT */
      ....
      /* End EDIT */

These four files should then be compiled with the Matlab "mex" compiler as described in the README file in the archive.

If it is desired to compile the .mex files directly from within MTT on a machine which has the Matlab header files installed, this may be done with the command

      mtt sys sfun mexglx

which will generated the four .mex files and the .mdl file. In this case, the user must ensure that sys_sfun_interface.c has been correctly edited prior to compilation.

Note that solution of algebraic equations within Simulink is not possible unless the Matlab Optimisation Toolbox is installed.

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## 10.5 LaTeX

LaTeX is a powerful text processor which MTT uses to provide visual output.

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# 11. Administration

11.1 Software components |  |
11.2 REDUCE setup |  |
11.3 Octave setup |  |
11.4 Paths |  |
11.5 File structure |  |
A.1 GNU Free Documentation License |  |
A.2 GNU GENERAL PUBLIC LICENSE |  |

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## 11.1 Software components

MTT is built from a set of readily-available software tools. These are:

- General purpose software tools.
- Octave (see section 11.3 Octave setup)
- REDUCE (see section 11.2 REDUCE setup)

The General purpose tools are (these will all be available with a standard Linux distribution):

`sh`
  Bourne shell
`gmake`
  Gnu make
`gawk`
  Gnu awk
`sed`
  Gnu sed
`grep`
  Gnu grep
`comm`
  Gnu Compare sorted files by line
`xfig`
  Figure editor, version 3 or greater.
`fig2dev`
  Fig file conversion, version 3 or greater.
`ghostview`
  postscript viewer
`xdvi`
  dvi viewer
`dvips`
  dvi to postscript conversion
`latex`
  the text processor (LaTeX2e needed)
`latex2html`
  converts latex to html
`perl`
  needed for latex2html
`gnuplot`
  a graph plotting program
`gnuscape`
  or other web/html browser such as netscape, Red Baron etc.
`gcc`
  GNU c compiler

<A HREF="http://home.pages.de/~GNU/">GNU</A> documentation.

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## 11.2 REDUCE setup

Symbolic algebra is performed by REDUCE, which although not free software is the the result of international collaboration. The version I use is obtained from:

> ZIB ( http://www.zib.de )

<A HREF="http://www.rrz.uni-koeln.de/REDUCE/">REDUCE</A> documentation. <A HREF="http://www.zib.de">ZIB</A> documentation.

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## 11.3 Octave setup

Octave is available at various web sites including: http://www.octave.org

11.3.1 .octaverc |  |
11.3.2 .oct file dependencies |  |

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### 11.3.1 .octaverc

The ``.octaverc`' file should contain the following lines:

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %% Startup file for Octave for use with MTT
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    implicit_str_to_num_ok = 1;
    empty_list_elements_ok = 1;

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### 11.3.2 .oct file dependencies

Successful compilation of .oct code requires that Octave has been configured to use dynamically linked libraries and that the Octave libraries `liboctave`, `libcruft` and `liboctinterp` are available on the system.

This can be acheived by compiling Octave from the source code, configured with the options `--enable-shared` and `--enable-dl`.

A number of additional libraries and headers are also required to be installed on a system. These include,

- ncurses and readline terminal control routines
- blas or altas basic linear algebra subprograms, usually optimised for the specific processor
- fftw fast Fourier transform routines
- g2c GNU Fortran to C conversion routines
- kpathsea TeX path search routines

Note that on many GNU/Linux distributions, the necessary headers are contained in development packages which must be installed in addition to the standard library package.

Further information on configuring and installing Octave to handle dynamic libraries (DLDs) can be found in the Octave documentation.

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## 11.4 Paths

There are a number of paths that must be set correctely for MTT to work. These are normally set up by sourcing the file `mttrc` that lives in the MTT home directory.

11.4.1 $MTTPATH |  |
11.4.2 $MTT_COMPONENTS |  |
11.4.3 $MTT_CRS |  |
11.4.4 $MTT_EXAMPLES |  |
11.4.5 $OCTAVE_PATH |  |

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### 11.4.1 $MTTPATH

The environment variable $MTTPATH points to the mtt home directory. This is usually `/usr/local/lib/mtt`.

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### 11.4.2 $MTT_COMPONENTS

The environment variable $MTT_COMPONENTS is a colon-separated path pointing to directories containing components and subsystems. By default

    MTT_COMPONENTS=.:$MTT_LIB/lib/comp/

but you may wish to add your own component libraries:

    MTT_COMPONENTS=my_library_path:$MTT_COMPONENTS

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### 11.4.3 $MTT_CRS

The environment variable $MTT_CRS is a colon-separated path pointing to directories containing constitutive relationships. By default

    MTT_CRS=$MTTPATH/lib/cr

but you may wish to add your own component libraries:

    MTT_CRS=my_cr_path:$MTT_CRS

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### 11.4.4 $MTT_EXAMPLES

The environment variable $MTT_EXAMPLES is a colon-separated path pointing to directories containing EXAMPLES and subsystems. By default

    MTT_EXAMPLES=$MTTPATH/lib/examples

but you may wish to add your own component libraries:

    MTT_EXAMPLES=my_examples_path:$MTT_EXAMPLES

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### 11.4.5 $OCTAVE_PATH

The `$OCTAVE_PATH` path must include the relevant paths for mtt to work properly. In particular, it must include:

    $MTTPATH/trans/m
    $MTTPATH/lib/comp/simple
    $MTTPATH/lib/comp/compound

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## 11.5 File structure

The recommended installation of MTT uses the following directory structure with corresponding contents. Normally, each of the listed directories is a subdirectory of ``/usr/local`'. The directory `mtt` is pointed to by $MTTPATH (see section 11.4.1 $MTTPATH).

``mtt/bin`'
  This is the home directory for MTT. MTT itself lives here along with ``mttrc`'.
``mtt/bin/trans`'
  The transformations executed by MTT.
``mtt/bin/trans/m`'
  The `m-files` associated with the transformations.
``mtt/bin/trans/awk`'
  The `awk` scripts associated with the transformations.
``mtt/lib`'
  The place for components, examples and CRs which will be updated.
``mtt/lib/comp/simple`'
  The `m-files` defining the simple components.
``mtt/lib/comp/compound`'
  The `m-files` defining the compound components.
``mtt/lib/cr/r`'
  constitutive relationship definitions
``mtt/lib/examples`'
  Some examples.
``mtt/examples/metamodelling`'
  Examples from the book.
``mtt/doc`'
  The documentation files for MTT.
``mtt/doc/Examples`'
  Examples used in the documentation.

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# A. Legal stuff

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## A.1 GNU Free Documentation License

Version 1.2, November 2002

    Copyright © 2000,2001,2002 Free Software Foundation, Inc.
    59 Temple Place, Suite 330, Boston, MA  02111-1307, USA

    Everyone is permitted to copy and distribute verbatim copies
    of this license document, but changing it is not allowed.

1. PREAMBLE

   The purpose of this License is to make a manual, textbook, or other functional and useful document free in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

   This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

   We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

2. APPLICABILITY AND DEFINITIONS

   This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

   A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

   A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

   The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

   The "Cover Texts" are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

   A "Transparent" copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not "Transparent" is called "Opaque".

   Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

   The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

   A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications", "Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ" according to this definition.

   The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

3. VERBATIM COPYING

   You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

   You may also lend copies, under the same conditions stated above, and you may publicly display copies.

4. COPYING IN QUANTITY

   If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

   If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

   If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

   It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

5. MODIFICATIONS

   You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

   1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
   2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
   3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
   4. Preserve all the copyright notices of the Document.
   5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
   6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
   7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
   8. Include an unaltered copy of this License.
   9. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
   10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
   11. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
   12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
   13. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified Version.
   14. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.
   15. Preserve any Warranty Disclaimers.

   If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.

   You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties--for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

   You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

   The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

6. COMBINING DOCUMENTS

   You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

   The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

   In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements."

7. COLLECTIONS OF DOCUMENTS

   You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

   You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

8. AGGREGATION WITH INDEPENDENT WORKS

   A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

   If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

9. TRANSLATION

   Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

   If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

10. TERMINATION

    You may not copy, modify, sublicense, or distribute the Document except as expressly provided for under this License. Any other attempt to copy, modify, sublicense or distribute the Document is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.

11. FUTURE REVISIONS OF THIS LICENSE

    The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

    Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation.

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### A.1.1 ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

      Copyright (C)  year  your name.
      Permission is granted to copy, distribute and/or modify this document
      under the terms of the GNU Free Documentation License, Version 1.2
      or any later version published by the Free Software Foundation;
      with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
      Texts.  A copy of the license is included in the section entitled ``GNU
      Free Documentation License''.

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this:

        with the Invariant Sections being list their titles, with
        the Front-Cover Texts being list, and with the Back-Cover Texts
        being list.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

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## A.2 GNU GENERAL PUBLIC LICENSE

Version 2, June 1991

    Copyright © 1989, 1991 Free Software Foundation, Inc.
    59 Temple Place - Suite 330, Boston, MA  02111-1307, USA

    Everyone is permitted to copy and distribute verbatim copies
    of this license document, but changing it is not allowed.

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### A.2.1 Preamble

The licenses for most software are designed to take away your freedom to share and change it. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change free software--to make sure the software is free for all its users. This General Public License applies to most of the Free Software Foundation's software and to any other program whose authors commit to using it. (Some other Free Software Foundation software is covered by the GNU Library General Public License instead.) You can apply it to your programs, too.

When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for this service if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs; and that you know you can do these things.

To protect your rights, we need to make restrictions that forbid anyone to deny you these rights or to ask you to surrender the rights. These restrictions translate to certain responsibilities for you if you distribute copies of the software, or if you modify it.

For example, if you distribute copies of such a program, whether gratis or for a fee, you must give the recipients all the rights that you have. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.

We protect your rights with two steps: (1) copyright the software, and (2) offer you this license which gives you legal permission to copy, distribute and/or modify the software.

Also, for each author's protection and ours, we want to make certain that everyone understands that there is no warranty for this free software. If the software is modified by someone else and passed on, we want its recipients to know that what they have is not the original, so that any problems introduced by others will not reflect on the original authors' reputations.

Finally, any free program is threatened constantly by software patents. We wish to avoid the danger that redistributors of a free program will individually obtain patent licenses, in effect making the program proprietary. To prevent this, we have made it clear that any patent must be licensed for everyone's free use or not licensed at all.

The precise terms and conditions for copying, distribution and modification follow.

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

1. This License applies to any program or other work which contains a notice placed by the copyright holder saying it may be distributed under the terms of this General Public License. The "Program", below, refers to any such program or work, and a "work based on the Program" means either the Program or any derivative work under copyright law: that is to say, a work containing the Program or a portion of it, either verbatim or with modifications and/or translated into another language. (Hereinafter, translation is included without limitation in the term "modification".) Each licensee is addressed as "you".

   Activities other than copying, distribution and modification are not covered by this License; they are outside its scope. The act of running the Program is not restricted, and the output from the Program is covered only if its contents constitute a work based on the Program (independent of having been made by running the Program). Whether that is true depends on what the Program does.

2. You may copy and distribute verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice and disclaimer of warranty; keep intact all the notices that refer to this License and to the absence of any warranty; and give any other recipients of the Program a copy of this License along with the Program.

   You may charge a fee for the physical act of transferring a copy, and you may at your option offer warranty protection in exchange for a fee.

3. You may modify your copy or copies of the Program or any portion of it, thus forming a work based on the Program, and copy and distribute such modifications or work under the terms of Section 1 above, provided that you also meet all of these conditions:
   1. You must cause the modified files to carry prominent notices stating that you changed the files and the date of any change.
   2. You must cause any work that you distribute or publish, that in whole or in part contains or is derived from the Program or any part thereof, to be licensed as a whole at no charge to all third parties under the terms of this License.
   3. If the modified program normally reads commands interactively when run, you must cause it, when started running for such interactive use in the most ordinary way, to print or display an announcement including an appropriate copyright notice and a notice that there is no warranty (or else, saying that you provide a warranty) and that users may redistribute the program under these conditions, and telling the user how to view a copy of this License. (Exception: if the Program itself is interactive but does not normally print such an announcement, your work based on the Program is not required to print an announcement.)

   These requirements apply to the modified work as a whole. If identifiable sections of that work are not derived from the Program, and can be reasonably considered independent and separate works in themselves, then this License, and its terms, do not apply to those sections when you distribute them as separate works. But when you distribute the same sections as part of a whole which is a work based on the Program, the distribution of the whole must be on the terms of this License, whose permissions for other licensees extend to the entire whole, and thus to each and every part regardless of who wrote it.

   Thus, it is not the intent of this section to claim rights or contest your rights to work written entirely by you; rather, the intent is to exercise the right to control the distribution of derivative or collective works based on the Program.

   In addition, mere aggregation of another work not based on the Program with the Program (or with a work based on the Program) on a volume of a storage or distribution medium does not bring the other work under the scope of this License.

4. You may copy and distribute the Program (or a work based on it, under Section 2) in object code or executable form under the terms of Sections 1 and 2 above provided that you also do one of the following:
   1. Accompany it with the complete corresponding machine-readable source code, which must be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
   2. Accompany it with a written offer, valid for at least three years, to give any third party, for a charge no more than your cost of physically performing source distribution, a complete machine-readable copy of the corresponding source code, to be distributed under the terms of Sections 1 and 2 above on a medium customarily used for software interchange; or,
   3. Accompany it with the information you received as to the offer to distribute corresponding source code. (This alternative is allowed only for noncommercial distribution and only if you received the program in object code or executable form with such an offer, in accord with Subsection b above.)

   The source code for a work means the preferred form of the work for making modifications to it. For an executable work, complete source code means all the source code for all modules it contains, plus any associated interface definition files, plus the scripts used to control compilation and installation of the executable. However, as a special exception, the source code distributed need not include anything that is normally distributed (in either source or binary form) with the major components (compiler, kernel, and so on) of the operating system on which the executable runs, unless that component itself accompanies the executable.

   If distribution of executable or object code is made by offering access to copy from a designated place, then offering equivalent access to copy the source code from the same place counts as distribution of the source code, even though third parties are not compelled to copy the source along with the object code.

5. You may not copy, modify, sublicense, or distribute the Program except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense or distribute the Program is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance.
6. You are not required to accept this License, since you have not signed it. However, nothing else grants you permission to modify or distribute the Program or its derivative works. These actions are prohibited by law if you do not accept this License. Therefore, by modifying or distributing the Program (or any work based on the Program), you indicate your acceptance of this License to do so, and all its terms and conditions for copying, distributing or modifying the Program or works based on it.
7. Each time you redistribute the Program (or any work based on the Program), the recipient automatically receives a license from the original licensor to copy, distribute or modify the Program subject to these terms and conditions. You may not impose any further restrictions on the recipients' exercise of the rights granted herein. You are not responsible for enforcing compliance by third parties to this License.
8. If, as a consequence of a court judgment or allegation of patent infringement or for any other reason (not limited to patent issues), conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot distribute so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not distribute the Program at all. For example, if a patent license would not permit royalty-free redistribution of the Program by all those who receive copies directly or indirectly through you, then the only way you could satisfy both it and this License would be to refrain entirely from distribution of the Program.

   If any portion of this section is held invalid or unenforceable under any particular circumstance, the balance of the section is intended to apply and the section as a whole is intended to apply in other circumstances.

   It is not the purpose of this section to induce you to infringe any patents or other property right claims or to contest validity of any such claims; this section has the sole purpose of protecting the integrity of the free software distribution system, which is implemented by public license practices. Many people have made generous contributions to the wide range of software distributed through that system in reliance on consistent application of that system; it is up to the author/donor to decide if he or she is willing to distribute software through any other system and a licensee cannot impose that choice.

   This section is intended to make thoroughly clear what is believed to be a consequence of the rest of this License.

9. If the distribution and/or use of the Program is restricted in certain countries either by patents or by copyrighted interfaces, the original copyright holder who places the Program under this License may add an explicit geographical distribution limitation excluding those countries, so that distribution is permitted only in or among countries not thus excluded. In such case, this License incorporates the limitation as if written in the body of this License.
10. The Free Software Foundation may publish revised and/or new versions of the General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.

    Each version is given a distinguishing version number. If the Program specifies a version number of this License which applies to it and "any later version", you have the option of following the terms and conditions either of that version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of this License, you may choose any version ever published by the Free Software Foundation.

11. If you wish to incorporate parts of the Program into other free programs whose distribution conditions are different, write to the author to ask for permission. For software which is copyrighted by the Free Software Foundation, write to the Free Software Foundation; we sometimes make exceptions for this. Our decision will be guided by the two goals of preserving the free status of all derivatives of our free software and of promoting the sharing and reuse of software generally.
    NO WARRANTY
12. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
13. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

END OF TERMS AND CONDITIONS

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### A.2.2 Appendix: How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found.

    one line to give the program's name and a brief idea of what it does.
    Copyright (C) yyyy  name of author

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this when it starts in an interactive mode:

    Gnomovision version 69, Copyright (C) 19yy name of author
    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands ``show w`' and ``show c`' should show the appropriate parts of the General Public License. Of course, the commands you use may be called something other than ``show w`' and ``show c`'; they could even be mouse-clicks or menu items--whatever suits your program.

You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the program, if necessary. Here is a sample; alter the names:

    Yoyodyne, Inc., hereby disclaims all copyright interest in the program
    `Gnomovision' (which makes passes at compilers) written by James Hacker.

    signature of Ty Coon, 1 April 1989
    Ty Coon, President of Vice

This General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Library General Public License instead of this License.

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# Glossary

Jump to: | ' A B C D E F G I L M N O P R S T

| Index Entry | Section

' |  |
| `'name1:name2'` | 4.7 Simulation output
| `'name1:name2'` | 4.7 Simulation output
| `'name1;name2;..;namen'` | 4.7 Simulation output
| `'name1;name2;..;namen'` | 4.7 Simulation output

A |  |
| `abg` | 6.1 Representation summary
| `abg` | 6.1 Representation summary
| `AE` | 6.4.1.5 Simple components
| `AE` | 6.4.1.5 Simple components
| `AF` | 6.4.1.5 Simple components
| `AF` | 6.4.1.5 Simple components
| `artwork` | 6.4.1 Language fig (abg.fig)
| `artwork` | 6.4.1 Language fig (abg.fig)
| `assignment statements` | 6.9.3.1 Text form (numpar.txt)
| `assignment statements` | 6.9.3.1 Text form (numpar.txt)

B |  |
| `bonds` | 6.4.1 Language fig (abg.fig)
| `bonds` | 6.4.1 Language fig (abg.fig)

C |  |
| `C` | 6.4.1.5 Simple components
| `c` | 4. Simulation
| `C` | 6.4.1.5 Simple components
| `c` | 4. Simulation
| `c` | 6.9.3 Numeric parameters (numpar)
| `c` | 6.9.3 Numeric parameters (numpar)
| `c` | 6.16.1 Language text (rep.txt)
| `c` | 6.16.1 Language text (rep.txt)
| `c` | 9. Languages
| `c` | 9. Languages
| `cbg` | 6.1 Representation summary
| `cbg` | 6.1 Representation summary
| `cc` | 4. Simulation
| `cc` | 4. Simulation
| `commented assignment statements` | 6.9.3.1 Text form (numpar.txt)
| `commented assignment statements` | 6.9.3.1 Text form (numpar.txt)
| `comments` | 6.9.3.1 Text form (numpar.txt)
| `comments` | 6.9.3.1 Text form (numpar.txt)
| `components` | 6.4.1 Language fig (abg.fig)
| `components` | 6.4.1 Language fig (abg.fig)
| `cr` | 6.1 Representation summary
| `cr` | 6.1 Representation summary
| `cse` | 4. Simulation
| `cse` | 4. Simulation
| `cse` | 6.1 Representation summary
| `cse` | 6.1 Representation summary
| `csm` | 6.1 Representation summary
| `csm` | 6.1 Representation summary
| `CSW` | 6.4.1.5 Simple components
| `CSW` | 6.4.1.5 Simple components

D |  |
| `dae` | 6.1 Representation summary
| `dae` | 6.1 Representation summary
| `daes` | 6.1 Representation summary
| `daes` | 6.1 Representation summary
| `daeso` | 6.1 Representation summary
| `daeso` | 6.1 Representation summary
| `def` | 6.1 Representation summary
| `def` | 6.1 Representation summary
| `desc` | 6.1 Representation summary
| `desc` | 6.1 Representation summary
| `dm` | 6.1 Representation summary
| `dm` | 6.1 Representation summary
| `dvi` | 9. Languages
| `dvi` | 9. Languages

E |  |
| `ese` | 6.1 Representation summary
| `ese` | 6.1 Representation summary
| `exotherm` | 6.8.1.2 exotherm

F |  |
| `fig` | 9. Languages
| `fig` | 9. Languages
| `fr` | 6.1 Representation summary
| `fr` | 6.1 Representation summary

G |  |
| `gdat` | 9. Languages
| `gdat` | 9. Languages
| `GY` | 6.4.1.5 Simple components
| `GY` | 6.4.1.5 Simple components

I |  |
| `I` | 6.4.1.5 Simple components
| `I` | 6.4.1.5 Simple components
| `input` | 6.1 Representation summary
| `input` | 6.1 Representation summary
| `ir` | 4. Simulation
| `ir` | 4. Simulation
| `ir` | 6.1 Representation summary
| `ir` | 6.1 Representation summary
| `iro` | 4. Simulation
| `iro` | 4. Simulation
| `iro` | 6.1 Representation summary
| `iro` | 6.1 Representation summary
| `ISW` | 6.4.1.5 Simple components
| `ISW` | 6.4.1.5 Simple components

L |  |
| `lbl` | 6.1 Representation summary
| `lbl` | 6.1 Representation summary
| `lin` | 6.8.1.1 lin
| `lmfr` | 6.1 Representation summary
| `lmfr` | 6.1 Representation summary
| `lpfr` | 6.1 Representation summary
| `lpfr` | 6.1 Representation summary

M |  |
| `m` | 4. Simulation
| `m` | 4. Simulation
| `m` | 6.9.3 Numeric parameters (numpar)
| `m` | 6.9.3 Numeric parameters (numpar)
| `m` | 6.16.1 Language text (rep.txt)
| `m` | 6.16.1 Language text (rep.txt)
| `m` | 9. Languages
| `m` | 9. Languages
| `mtt &lt;system&gt; clean` | 2.4 Utilities
| `mtt &lt;system&gt; clean` | 2.4 Utilities
| `mtt -c -i euler system odeso view` | 4. Simulation
| `mtt -c -i euler system odeso view` | 4. Simulation
| `mtt -c system odeso view` | 4. Simulation
| `mtt -c system odeso view` | 4. Simulation
| `mtt clean` | 2.4 Utilities
| `mtt clean` | 2.4 Utilities
| `mtt copy &lt;system&gt;` | 2.4 Utilities
| `mtt copy &lt;system&gt;` | 2.4 Utilities
| `mtt help` | 2.4 Utilities
| `mtt help` | 2.4 Utilities
| `mtt rename &lt;old_name&gt; &lt;new_name&gt;` | 2.4 Utilities
| `mtt rename &lt;old_name&gt; &lt;new_name&gt;` | 2.4 Utilities
| `mtt system iro view` | 4. Simulation
| `mtt system iro view` | 4. Simulation
| `mtt system representation vc` | 2.4 Utilities
| `mtt system representation vc` | 2.4 Utilities
| `mtt system representation vc` | 2.4.4 Version control
| `mtt system representation vc` | 2.4.4 Version control
| `mtt system sro view` | 4. Simulation
| `mtt system sro view` | 4. Simulation
| `mtt system vc` | 2.4 Utilities
| `mtt system vc` | 2.4 Utilities
| `mtt system vc` | 2.4.4 Version control
| `mtt system vc` | 2.4.4 Version control

N |  |
| `NAME_cause.m` | 6.4.1.7 Simple components - implementation
| `NAME_cause.m` | 6.4.1.7 Simple components - implementation
| `NAME_eqn.m` | 6.4.1.7 Simple components - implementation
| `NAME_eqn.m` | 6.4.1.7 Simple components - implementation
| `nifr` | 6.1 Representation summary
| `nifr` | 6.1 Representation summary
| `numpar` | 6.1 Representation summary
| `numpar` | 6.1 Representation summary
| `nyfr` | 6.1 Representation summary
| `nyfr` | 6.1 Representation summary

O |  |
| `obs` | 6.1 Representation summary
| `obs` | 6.1 Representation summary
| `ode` | 4. Simulation
| `ode` | 4. Simulation
| `ode` | 6.1 Representation summary
| `ode` | 6.1 Representation summary
| `odes` | 4.7 Simulation output
| `odes` | 4.7 Simulation output
| `odes` | 6.1 Representation summary
| `odes` | 6.1 Representation summary
| `odes` | 6.1 Representation summary
| `odes` | 6.1 Representation summary
| `odeso` | 4.7 Simulation output
| `odeso` | 4.7 Simulation output
| `odeso` | 6.1 Representation summary
| `odeso` | 6.1 Representation summary
| `odess` | 6.1 Representation summary
| `odess` | 6.1 Representation summary
| `odesso` | 6.1 Representation summary
| `odesso` | 6.1 Representation summary

P |  |
| `ps` | 6.16.1 Language text (rep.txt)
| `ps` | 6.16.1 Language text (rep.txt)
| `ps` | 9. Languages
| `ps` | 9. Languages

R |  |
| `R` | 6.4.1.5 Simple components
| `r` | 6.16.1 Language text (rep.txt)
| `R` | 6.4.1.5 Simple components
| `r` | 6.16.1 Language text (rep.txt)
| `r` | 9. Languages
| `r` | 9. Languages
| `rbg` | 6.1 Representation summary
| `rbg` | 6.1 Representation summary
| `rep` | 6.1 Representation summary
| `rep` | 6.1 Representation summary
| `rfe` | 6.1 Representation summary
| `rfe` | 6.1 Representation summary

S |  |
| `sabg` | 6.1 Representation summary
| `sabg` | 6.1 Representation summary
| `scse` | 5. Sensitivity models
| `scse` | 5. Sensitivity models
| `scsm` | 5. Sensitivity models
| `scsm` | 5. Sensitivity models
| `sg` | 9. Languages
| `sg` | 9. Languages
| `simp` | 6.1 Representation summary
| `simp` | 6.1 Representation summary
| `sm` | 5. Sensitivity models
| `sm` | 5. Sensitivity models
| `sm` | 6.1 Representation summary
| `sm` | 6.1 Representation summary
| `sms` | 6.1 Representation summary
| `sms` | 6.1 Representation summary
| `smss` | 6.1 Representation summary
| `smss` | 6.1 Representation summary
| `smx` | 6.1 Representation summary
| `smx` | 6.1 Representation summary
| `sr` | 4. Simulation
| `sr` | 4. Simulation
| `sr` | 6.1 Representation summary
| `sr` | 6.1 Representation summary
| `sro` | 4. Simulation
| `sro` | 4. Simulation
| `sro` | 6.1 Representation summary
| `sro` | 6.1 Representation summary
| `SS` | 6.4.1.5 Simple components
| `ss` | 6.1 Representation summary
| `ss` | 6.1 Representation summary
| `SS` | 6.4.1.5 Simple components
| `sspar` | 6.1 Representation summary
| `sspar` | 6.1 Representation summary
| `strokes` | 6.4.1 Language fig (abg.fig)
| `strokes` | 6.4.1 Language fig (abg.fig)
| `struc` | 6.1 Representation summary
| `struc` | 6.1 Representation summary
| `sub` | 6.1 Representation summary
| `sub` | 6.1 Representation summary
| `sub` | 6.1 Representation summary
| `sub` | 6.1 Representation summary
| `sympar` | 6.1 Representation summary
| `sympar` | 6.1 Representation summary

T |  |
| `tex` | 6.16.1 Language text (rep.txt)
| `tex` | 6.16.1 Language text (rep.txt)
| `tex` | 9. Languages
| `tex` | 9. Languages
| `TF` | 6.4.1.5 Simple components
| `tf` | 6.1 Representation summary
| `TF` | 6.4.1.5 Simple components
| `tf` | 6.1 Representation summary
| `txt` | 6.9.3 Numeric parameters (numpar)
| `txt` | 6.9.3 Numeric parameters (numpar)
| `type` | 6.4.1.4 Components
| `type` | 6.4.1.4 Components
| `type*n` | 6.4.1.4 Components
| `type*n` | 6.4.1.4 Components
| `type:label` | 6.4.1.4 Components
| `type:label` | 6.4.1.4 Components
| `type:label*n` | 6.4.1.4 Components
| `type:label*n` | 6.4.1.4 Components
| `type:label:cr` | 6.4.1.4 Components
| `type:label:cr` | 6.4.1.4 Components
| `type:label:expression` | 6.4.1.4 Components
| `type:label:expression` | 6.4.1.4 Components

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[ < ] | [ > ] |  | [ << ] | [ Up ] | [ >> ] |  |  |  |  | [Top] | [Contents] | [Index] | [ ? ]

# Index

Jump to: | < A B C D E F G H I L M N O P Q R S T U V X

| Index Entry | Section

< |  |
| <name> | 2.4.1.5 help <name>

A |  |
| Acausal bond graph (abg) | 6.4 Acausal bond graph (abg)
| Administration | 11. Administration
| Algebraic loops | 1.7 Algebraic loops
| alias options | 2.3 Options
| aliases | 6.6.9 Aliases
| Arrow-orientated causality | 6.4.3.1 Arrow-orientated causality
| artwork | 6.4.1.15 Artwork

B |  |
| Bond graphs, what are they? | 1.3 What is a bond graph?
| Bonds | 1.5 Bonds
| bonds | 6.4.1.2 Bonds
| bonds | 6.4.3 Language m (abg.m)
| Brief documentation | 8.2.1 Brief on-line documentation
| browser | 2.4.1 Help

C |  |
| c | 9.4 c
| Causal bond graph (cbg) | 6.10 Causal bond graph (cbg)
| cbonds | 6.10.2 Language m (cbg.m)
| Clean | 2.4.3 Clean
| Coerced bond direction | 6.4.1.10 Coerced bond direction
| Command line interface | 2.2 Command line interface
| component | 7.3 Component library
| component aliases | 6.6.9.4 Component aliases
| Component arguments | 6.6.5 Component arguments
| Component constitutive relationship | 6.6.4 Component constitutive relationship
| Component library | 7.3 Component library
| Component library | 7.3 Component library
| Component names | 6.6.3 Component names
| Component-orientated causality | 6.4.3.2 Component-orientated causality
| Components | 1.6 Components
| components | 2.4.1.2 help components
| Components | 8.2 On-line documentation
| components | 6.4.1.4 Components
| components | 6.4.3 Language m (abg.m)
| compound components | 11.5 File structure
| Compound components | 6.4.1.8 Compound components
| Constitutive Relationship | 1.6.2 Constitutive relationship
| Constitutive relationship | 6.8 Constitutive relationship (cr)
| Constrained-state Equations | 6.13 Constrained-state Equations (cse)
| Constrained-state Equations (reduce) | 6.13.1 Language reduce (cse.r)
| Constrained-state Equations (view) | 6.13.2 Language m (view)
| control systems | 10.4.1 Octave control system toolbox (OCST)
| Copy | 2.4.2 Copy
| CR aliases | 6.6.9.3 CR aliases
| Creating complex models | 3.3 Creating complex models
| Creating GNU Octave .oct files | 10.4.2 Creating GNU Octave .oct files
| Creating Matlab .mex files | 10.4.3 Creating Matlab .mex files
| Creating Models | 3. Creating Models
| Creating simple models | 3.2 Creating simple models
| crs | 2.4.1.4 help crs
| cse.r | 6.13.1 Language reduce (cse.r)

D |  |
| DAE | 6.12 Differential-Algebraic Equations (dae)
| dae.m | 6.12.2 Language m (dae.m)
| dae.r | 6.12.1 Language reduce (dae.r)
| def.r | 6.11.0.1 Transformation cbg2ese_m2r
| Defining representations | 6. Representations
| Defining representations | 6.2 Defining representations
| desc | 8.2.2 Detailed on-line documentation
| Description | 8.2.2 Detailed on-line documentation
| Descriptor matrices | 6.15 Descriptor matrices (dm)
| Descriptor matrices (m) | 6.15.2 Language m (dm.m)
| Descriptor matrices (reduce) | 6.15.1 Language reduce (dm.r)
| Detailed documentation | 8.2.2 Detailed on-line documentation
| Differential-Algebraic Equations | 6.12 Differential-Algebraic Equations (dae)
| Differential-Algebraic Equations (m) | 6.12.2 Language m (dae.m)
| Differential-Algebraic Equations (reduce) | 6.12.1 Language reduce (dae.r)
| DIY constitutive relationships | 6.8.2 DIY constitutive relationships
| DIY representations | 7.2 New (DIY) representations
| DIY representations | 7.2.1 Makefile
| DIY representations | 7.2.2 Shell-script
| DIY representations | 7.2.3 Documentation
| dm | 6.15 Descriptor matrices (dm)
| dm.m | 6.15.2 Language m (dm.m)
| dm.r | 6.15.1 Language reduce (dm.r)
| Documentation | 7.2.3 Documentation
| Documentation | 8. Documentation
| Documentation | 8.2 On-line documentation

E |  |
| Elementary system equations | 6.11 Elementary system equations (ese)
| Embedding MTT models in Simulink | 10.4.4 Embedding MTT models in Simulink
| Euler integration | 4.2.1 Euler integration
| Examples | 8.2 On-line documentation
| examples | 2.4.1.3 help examples
| Extending MTT | 7. Extending MTT

F |  |
| FDL, GNU Free Documentation License | A.1 GNU Free Documentation License
| Fig | 9.1 Fig
| File structure | 11.5 File structure

G |  |
| gnuplot | 4.7.1 Viewing results with gnuplot

H |  |
| help | 2.4.1.1 help representations
| Help | 2.4.1 Help
| help | 2.4.1.2 help components
| help | 2.4.1.3 help examples
| help | 2.4.1.4 help crs
| help | 2.4.1.5 help <name>
| Hybrid systems | 1.8 Switched systems

I |  |
| ICD (label file directive) | 6.6.8 Interface Control Definition
| Icon | 6.4.1.1 Icon library
| Implicit integration | 4.2.2 Implicit integration

L |  |
| Labels | 6.6 Labels (lbl)
| Language fig (abg.fig) | 6.4.1 Language fig (abg.fig)
| Language fig (cbg.fig) | 6.10.1 Language fig (cbg.fig)
| Language fig (sabg.fig) | 6.5.1 Language fig (sabg.fig)
| Language m (abg.m) | 6.4.3 Language m (abg.m)
| Language m (cbg.m) | 6.10.2 Language m (cbg.m)
| Language m (view) | 6.5.2 Stripped acausal bond graph (view)
| Language tex (abg.tex) | 6.4.4 Language tex (abg.tex)
| Language tex (desc.tex) | 6.6.12 Language tex (desc.tex)
| Language tex (struc.tex) | 6.7.2 Language tex (struc.tex)
| Language tools | 10. Language tools
| Language txt (struc.txt) | 6.7.1 Language txt (struc.txt)
| Languages | 9. Languages
| LaTeX | 10.5 LaTeX
| lbl | 6.6 Labels (lbl)
| lbl | 6.6.11 Old-style labels (lbl)
| library | 6.4.1.1 Icon library
| logic | 1.8 Switched systems

M |  |
| m | 9.2 m
| m-files | 10.4 Octave
| Make | 7. Extending MTT
| Makefile | 7.2.1 Makefile
| Makefiles | 7.1 Makefiles
| Manual | 8.1 Manual
| Matlab | 10.4 Octave
| Menu-driven interface | 2.1 Menu-driven interface
| MTT, purpose of | 1. Introduction
| mtt.m | 10.4 Octave
| mtt2sys | 10.4.1 Octave control system toolbox (OCST)
| mttrc | 11.4 Paths

N |  |
| n_ports | 6.4.3 Language m (abg.m)
| Named SS | 6.4.1.8 Compound components
| Named SS components | 6.4.1.9 Named SS components
| New representations | 7.2 New (DIY) representations
| New representations | 7.2.1 Makefile
| New representations | 7.2.2 Shell-script
| New representations | 7.2.3 Documentation
| Numeric parameters | 1.6.4 Numeric parameters
| Numeric parameters | 6.9.3 Numeric parameters (numpar)
| Numeric parameters | 6.9.3.1 Text form (numpar.txt)

O |  |
| OCST | 10.4.1 Octave control system toolbox (OCST)
| Octave | 10.4 Octave
| Octave | 10.4.1 Octave control system toolbox (OCST)
| Octave interface | 10.4 Octave
| Octave setup | 11.3 Octave setup
| ODE | 6.13 Constrained-state Equations (cse)
| ODE | 6.14 Ordinary Differential Equations
| ode.m | 6.14.2 Language m (ode.m)
| ode.r | 6.14.1 Language reduce (ode.r)
| Old-style labels | 6.6.11 Old-style labels (lbl)
| On-line documentation | 8.2 On-line documentation
| options | 2.3 Options
| Ordinary Differential Equations | 6.14 Ordinary Differential Equations
| Ordinary Differential Equations (m) | 6.14.2 Language m (ode.m)
| Ordinary Differential Equations (reduce) | 6.14.1 Language reduce (ode.r)
| Ordinary Differential Equations (view) | 6.14.3 Language m (view)
| Other component labels | 6.6.2 Other component labels
| Other component labels (old-style) | 6.6.11.2 Other component labels (old-style)

P |  |
| parameter aliases | 6.6.9.2 Parameter aliases
| parameter declarations | 6.6.6 Parameter declarations
| Parameter passing | 6.6.10 Parameter passing
| Parameter passing (old-style) | 6.6.11.3 Parameter passing (old-style)
| Parameters | 6.9 Parameters
| paths | 11.4 Paths
| port aliases | 6.6.9.1 Port aliases
| Port label defaults | 6.4.1.13 Port label defaults
| port labels | 6.4.1.12 Vector port labels
| ports | 1.6.1 Ports
| ports | 6.4.1.11 Port labels
| Predefined constitutive relationships | 6.8.1 Predefined constitutive relationships

Q |  |
| Quick start | 3.1 Quick start

R |  |
| Reduce | 9.3 Reduce
| REDUCE setup | 11.2 REDUCE setup
| rep | 6.16 Report (rep)
| rep.txt | 6.16.1 Language text (rep.txt)
| Report | 6.16 Report (rep)
| Report (text) | 6.16.1 Language text (rep.txt)
| Report (view) | 6.16.2 Language view
| Representation summary | 6.1 Representation summary
| Representations | 6. Representations
| representations | 2.4.1.1 help representations
| Representations, defining | 6. Representations
| Representations, what are they? | 1.1 What is a representation?

S |  |
| SciGraphica | 4.7.2 Exporting results to SciGraphica
| Sensitivity models | 5. Sensitivity models
| Shell-script | 7.2.2 Shell-script
| Simple components | 6.4.1.5 Simple components
| simple components | 11.5 File structure
| Simple components - implementation | 6.4.1.7 Simple components - implementation
| Simulation | 4. Simulation
| Simulation initial state | 4.5 Simulation initial state
| Simulation input | 4.3 Simulation input
| Simulation logic | 4.4 Simulation logic
| Simulation output | 4.7 Simulation output
| Simulation parameters | 4.2 Simulation parameters
| Software components | 11.1 Software components
| SS component labels | 6.6.1 SS component labels
| SS component labels (old-style) | 6.6.11.1 SS component labels (old-style)
| SS components | 6.4.1.6 SS components
| status | 6.10.2 Language m (cbg.m)
| Steady-state solutions | 4.1 Steady-state solutions
| Steady-state solutions - numerical | 4.1.1 Steady-state solutions (odess)
| Steady-state solutions - symbolic | 4.1.2 Steady-state solutions (ss)
| Stripped acausal bond graph (sabg) | 6.5 Stripped acausal bond graph (sabg)
| strokes | 6.4.1.3 Strokes
| struc | 6.7 Structure (struc)
| Structure | 6.7 Structure (struc)
| Structure | 6.11.0.1 Transformation cbg2ese_m2r
| Structure (view) | 6.7.3 Language tex (view)
| Switched systems | 1.8 Switched systems
| Symbolic parameters | 1.6.3 Symbolic parameters
| Symbolic parameters | 6.9.1 Symbolic parameters (subs.r)
| Symbolic parameters for simplification | 6.9.2 Symbolic parameters for simplification (simp.r)

T |  |
| Text editors | 10.3 Text editors
| toolbox | 10.4.1 Octave control system toolbox (OCST)
| Top level | 3.3.1 Top level
| Transformation abg2cbg_m | 6.10.2.1 Transformation abg2cbg_m
| Transformation abg2rbg_fig2m | 6.4.2.1 Transformation abg2rbg_fig2m
| Transformation cbg2ese_m2r | 6.11.0.1 Transformation cbg2ese_m2r
| Transformation cse2ode_r | 6.14.1.1 Transformation cse2ode_r
| Transformation dae2cse_r | 6.13.1.1 Transformation dae2cse_r
| Transformation dae_r2m | 6.12.2.1 Transformation dae_r2m
| Transformation ese2dae_r | 6.12.1.1 Transformation ese2dae_r
| Transformation ode_r2m | 6.14.2.1 Transformation ode_r2m
| Transformation rbg2abg_m | 6.4.3.3 Transformation rbg2abg_m
| Transformations | 1.2 What is a transformation?

U |  |
| units declarations | 6.6.7 Units declarations
| Unresolved constitutive relationships | 6.8.3 Unresolved constitutive relationships
| Unresolved constitutive relationships - Octave | 6.8.4 Unresolved constitutive relationships - Octave
| Unresolved constitutive relationships - Octave | 6.8.5 Unresolved constitutive relationships - c++
| User interface | 2. User interface
| Utilities | 2.4 Utilities

V |  |
| valid name | 6.4.1.16 Valid Names
| Variables | 1.4 Variables
| Vector components | 6.4.1.14 Vector Components
| vector port labels | 6.4.1.12 Vector port labels
| Verbal description (desc) | 6.3 Verbal description (desc)
| Version control | 2.4.4 Version control
| view Constrained-state Equations | 6.5.2 Stripped acausal bond graph (view)
| view Constrained-state Equations | 6.13.2 Language m (view)
| view Ordinary Differential Equations | 6.14.3 Language m (view)
| view Report | 6.16.2 Language view
| view Structure | 6.7.3 Language tex (view)
| views | 10.1 Views

X |  |
| Xfig | 10.2 Xfig

Jump to: | < A B C D E F G H I L M N O P Q R S T U V X

[Top] | [Contents] | [Index] | [ ? ]

# Table of Contents

> 1. Introduction

> > 1.1 What is a representation?
> > 1.2 What is a transformation?
> > 1.3 What is a bond graph?
> > 1.4 Variables
> > 1.5 Bonds
> > 1.6 Components

> > > 1.6.1 Ports
> > > 1.6.2 Constitutive relationship
> > > 1.6.3 Symbolic parameters
> > > 1.6.4 Numeric parameters

> > 1.7 Algebraic loops
> > 1.8 Switched systems

> 2. User interface

> > 2.1 Menu-driven interface
> > 2.2 Command line interface
> > 2.3 Options
> > 2.4 Utilities

> > > 2.4.1 Help

> > > > 2.4.1.1 help representations
> > > > 2.4.1.2 help components
> > > > 2.4.1.3 help examples
> > > > 2.4.1.4 help crs
> > > > 2.4.1.5 help <name>

> > > 2.4.2 Copy
> > > 2.4.3 Clean
> > > 2.4.4 Version control

> 3. Creating Models

> > 3.1 Quick start
> > 3.2 Creating simple models
> > 3.3 Creating complex models

> > > 3.3.1 Top level

> 4. Simulation

> > 4.1 Steady-state solutions

> > > 4.1.1 Steady-state solutions (odess)
> > > 4.1.2 Steady-state solutions (ss)

> > 4.2 Simulation parameters

> > > 4.2.1 Euler integration
> > > 4.2.2 Implicit integration
> > > 4.2.3 Runge Kutta IV integration
> > > 4.2.4 Hybrd algebraic solver

> > 4.3 Simulation input
> > 4.4 Simulation logic
> > 4.5 Simulation initial state
> > 4.6 Simulation code

> > > 4.6.1 Dynamically linked functions

> > 4.7 Simulation output

> > > 4.7.1 Viewing results with gnuplot
> > > 4.7.2 Exporting results to SciGraphica

> 5. Sensitivity models
> 6. Representations

> > 6.1 Representation summary
> > 6.2 Defining representations
> > 6.3 Verbal description (desc)
> > 6.4 Acausal bond graph (abg)

> > > 6.4.1 Language fig (abg.fig)

> > > > 6.4.1.1 Icon library
> > > > 6.4.1.2 Bonds
> > > > 6.4.1.3 Strokes
> > > > 6.4.1.4 Components
> > > > 6.4.1.5 Simple components
> > > > 6.4.1.6 SS components
> > > > 6.4.1.7 Simple components - implementation
> > > > 6.4.1.8 Compound components
> > > > 6.4.1.9 Named SS components
> > > > 6.4.1.10 Coerced bond direction
> > > > 6.4.1.11 Port labels
> > > > 6.4.1.12 Vector port labels
> > > > 6.4.1.13 Port label defaults
> > > > 6.4.1.14 Vector Components
> > > > 6.4.1.15 Artwork
> > > > 6.4.1.16 Valid Names

> > > 6.4.2 Language m (rbg.m)

> > > > 6.4.2.1 Transformation abg2rbg_fig2m

> > > 6.4.3 Language m (abg.m)

> > > > 6.4.3.1 Arrow-orientated causality
> > > > 6.4.3.2 Component-orientated causality
> > > > 6.4.3.3 Transformation rbg2abg_m

> > > 6.4.4 Language tex (abg.tex)

> > 6.5 Stripped acausal bond graph (sabg)

> > > 6.5.1 Language fig (sabg.fig)
> > > 6.5.2 Stripped acausal bond graph (view)

> > 6.6 Labels (lbl)

> > > 6.6.1 SS component labels
> > > 6.6.2 Other component labels
> > > 6.6.3 Component names
> > > 6.6.4 Component constitutive relationship
> > > 6.6.5 Component arguments
> > > 6.6.6 Parameter declarations
> > > 6.6.7 Units declarations
> > > 6.6.8 Interface Control Definition
> > > 6.6.9 Aliases

> > > > 6.6.9.1 Port aliases
> > > > 6.6.9.2 Parameter aliases
> > > > 6.6.9.3 CR aliases
> > > > 6.6.9.4 Component aliases

> > > 6.6.10 Parameter passing
> > > 6.6.11 Old-style labels (lbl)

> > > > 6.6.11.1 SS component labels (old-style)
> > > > 6.6.11.2 Other component labels (old-style)
> > > > 6.6.11.3 Parameter passing (old-style)

> > > 6.6.12 Language tex (desc.tex)

> > 6.7 Structure (struc)

> > > 6.7.1 Language txt (struc.txt)
> > > 6.7.2 Language tex (struc.tex)
> > > 6.7.3 Language tex (view)

> > 6.8 Constitutive relationship (cr)

> > > 6.8.1 Predefined constitutive relationships

> > > > 6.8.1.1 lin
> > > > 6.8.1.2 exotherm

> > > 6.8.2 DIY constitutive relationships
> > > 6.8.3 Unresolved constitutive relationships
> > > 6.8.4 Unresolved constitutive relationships - Octave
> > > 6.8.5 Unresolved constitutive relationships - c++

> > 6.9 Parameters

> > > 6.9.1 Symbolic parameters (subs.r)
> > > 6.9.2 Symbolic parameters for simplification (simp.r)
> > > 6.9.3 Numeric parameters (numpar)

> > > > 6.9.3.1 Text form (numpar.txt)

> > 6.10 Causal bond graph (cbg)

> > > 6.10.1 Language fig (cbg.fig)
> > > 6.10.2 Language m (cbg.m)

> > > > 6.10.2.1 Transformation abg2cbg_m

> > 6.11 Elementary system equations (ese)

> > > > 6.11.0.1 Transformation cbg2ese_m2r

> > 6.12 Differential-Algebraic Equations (dae)

> > > 6.12.1 Language reduce (dae.r)

> > > > 6.12.1.1 Transformation ese2dae_r

> > > 6.12.2 Language m (dae.m)

> > > > 6.12.2.1 Transformation dae_r2m

> > 6.13 Constrained-state Equations (cse)

> > > 6.13.1 Language reduce (cse.r)

> > > > 6.13.1.1 Transformation dae2cse_r

> > > 6.13.2 Language m (view)

> > 6.14 Ordinary Differential Equations

> > > 6.14.1 Language reduce (ode.r)

> > > > 6.14.1.1 Transformation cse2ode_r

> > > 6.14.2 Language m (ode.m)

> > > > 6.14.2.1 Transformation ode_r2m

> > > 6.14.3 Language m (view)

> > 6.15 Descriptor matrices (dm)

> > > 6.15.1 Language reduce (dm.r)
> > > 6.15.2 Language m (dm.m)

> > 6.16 Report (rep)

> > > 6.16.1 Language text (rep.txt)
> > > 6.16.2 Language view

> 7. Extending MTT

> > 7.1 Makefiles
> > 7.2 New (DIY) representations

> > > 7.2.1 Makefile
> > > 7.2.2 Shell-script
> > > 7.2.3 Documentation

> > 7.3 Component library

> 8. Documentation

> > 8.1 Manual
> > 8.2 On-line documentation

> > > 8.2.1 Brief on-line documentation
> > > 8.2.2 Detailed on-line documentation

> 9. Languages

> > 9.1 Fig
> > 9.2 m
> > 9.3 Reduce
> > 9.4 c

> 10. Language tools

> > 10.1 Views
> > 10.2 Xfig
> > 10.3 Text editors
> > 10.4 Octave

> > > 10.4.1 Octave control system toolbox (OCST)
> > > 10.4.2 Creating GNU Octave .oct files
> > > 10.4.3 Creating Matlab .mex files
> > > 10.4.4 Embedding MTT models in Simulink

> > 10.5 LaTeX

> 11. Administration

> > 11.1 Software components
> > 11.2 REDUCE setup
> > 11.3 Octave setup

> > > 11.3.1 .octaverc
> > > 11.3.2 .oct file dependencies

> > 11.4 Paths

> > > 11.4.1 $MTTPATH
> > > 11.4.2 $MTT_COMPONENTS
> > > 11.4.3 $MTT_CRS
> > > 11.4.4 $MTT_EXAMPLES
> > > 11.4.5 $OCTAVE_PATH

> > 11.5 File structure

> A. Legal stuff

> > A.1 GNU Free Documentation License

> > > A.1.1 ADDENDUM: How to use this License for your documents

> > A.2 GNU GENERAL PUBLIC LICENSE

> > > A.2.1 Preamble
> > > A.2.2 Appendix: How to Apply These Terms to Your New Programs

> Glossary
> Index

[Top] | [Contents] | [Index] | [ ? ]

# Short Table of Contents

> 1. Introduction
> 2. User interface
> 3. Creating Models
> 4. Simulation
> 5. Sensitivity models
> 6. Representations
> 7. Extending MTT
> 8. Documentation
> 9. Languages
> 10. Language tools
> 11. Administration
> A. Legal stuff
> Glossary
> Index

[Top] | [Contents] | [Index] | [ ? ]

# About this document

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