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ADDED README.md Index: README.md ================================================================== --- /dev/null +++ README.md @@ -0,0 +1,22 @@ +# MTT + +## Model Transformation Tools + +### Bond-graph based modeling tools + +MTT is a set of tools for modeling dynamic physical systems using the bond-graph methodology and transforming these models into representations suitable for analysis, control, and simulation. + +---- + +## Introduction + +- MTT uses and generates `.m` files for [GNU Octave](https://www.octave.org/). +- MTT is mainly built on the [GNU](https://gnu.org/) set of tools. +- MTT uses the algebraic package [REDUCE](https://reduce-algebra.sourceforge.io/). +- MTT is based on the bond graph language; general bond graph information is available from [The Bond Graph Compendium](https://www2.engr.arizona.edu/~cellier/bg.html) homepage. + +## Authors + +- [Peter Gawthrop](http://www.gawthrop.net/) [\](mailto:peter.gawthrop@unimelb.edu.au) +- [Geraint Paul Bevan](https://www.gcu.ac.uk/cebe/staff/geraint%20bevan/) [\](mailto:Geraint.Bevan@gcu.ac.uk) + - [Alternate Contact](https://www.enchant.me.uk/) [\](mailto:geraint@enchant.me.uk) ADDED mtt/doc/13873950500069078.pdf Index: mtt/doc/13873950500069078.pdf ================================================================== --- /dev/null +++ mtt/doc/13873950500069078.pdf cannot compute difference between binary files ADDED mtt/doc/293854591.pdf Index: mtt/doc/293854591.pdf ================================================================== --- /dev/null +++ mtt/doc/293854591.pdf cannot compute difference between binary files ADDED mtt/doc/BreedveldChapter.pdf Index: mtt/doc/BreedveldChapter.pdf ================================================================== --- /dev/null +++ mtt/doc/BreedveldChapter.pdf cannot compute difference between binary files ADDED mtt/doc/GawSmi96.pdf Index: mtt/doc/GawSmi96.pdf ================================================================== --- /dev/null +++ mtt/doc/GawSmi96.pdf cannot compute difference between binary files ADDED mtt/doc/PN10J72L665H44JN.pdf Index: mtt/doc/PN10J72L665H44JN.pdf ================================================================== --- /dev/null +++ mtt/doc/PN10J72L665H44JN.pdf cannot compute difference between binary files ADDED mtt/doc/bbm_978-3-662-04181-9-1.pdf Index: mtt/doc/bbm_978-3-662-04181-9-1.pdf ================================================================== --- /dev/null +++ mtt/doc/bbm_978-3-662-04181-9-1.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/AlgebraicLoops_rep.pdf Index: mtt/doc/example_out/AlgebraicLoops_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/AlgebraicLoops_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Anaesthesia_rep.pdf Index: mtt/doc/example_out/Anaesthesia_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Anaesthesia_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Chemical_rep.pdf Index: mtt/doc/example_out/Chemical_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Chemical_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Components_rep.pdf Index: mtt/doc/example_out/Components_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Components_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Electrical_rep.pdf Index: mtt/doc/example_out/Electrical_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Electrical_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Electromechanical_rep.pdf Index: mtt/doc/example_out/Electromechanical_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Electromechanical_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/GasDynamics_rep.pdf Index: mtt/doc/example_out/GasDynamics_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/GasDynamics_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Hybrid_rep.pdf Index: mtt/doc/example_out/Hybrid_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Hybrid_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Identification_rep.pdf Index: mtt/doc/example_out/Identification_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Identification_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Inverse_rep.pdf Index: mtt/doc/example_out/Inverse_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Inverse_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Mechanical_rep.pdf Index: mtt/doc/example_out/Mechanical_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Mechanical_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Sensitivity_rep.pdf Index: mtt/doc/example_out/Sensitivity_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Sensitivity_rep.pdf cannot compute difference between binary files ADDED mtt/doc/example_out/Simulation_rep.pdf Index: mtt/doc/example_out/Simulation_rep.pdf ================================================================== --- /dev/null +++ mtt/doc/example_out/Simulation_rep.pdf cannot 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[Top][Contents][Index][ ? + ]
+

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 + Figr
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
+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

1.5 Bonds

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << + ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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>
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

2.4.1.5 help <name>

+

The command

+ + + + + +
+ 
mtt help <name>
+
+
gives a detailed description of the entity called + name. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. mtt clean
    3. +
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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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'.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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>.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. Invoke the Bond Graph editor to draw the acausal Bond Graph. + + + + + +
    + 
      mtt syst abg fig
+
    +
    +
    3. +
  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. +
  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. +
  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. +
    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. +
    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. +
    4. If the bond graph is causally complete, proceed to the next step, + otherwise think hard and return to the first step.
      5. +
    +
    6. +
  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. +
    2. View the system state matrices + + + + + +
      + 
      mtt syst sm view
+
      +
      +
      3. +
    3. View the system transfer function + + + + + +
      + 
      mtt syst tf view
+
      +
      +
      4. +
    4. View the system step response + + + + + +
      + 
      mtt syst sro view
+
      +
      +
      5. +
    +
    7. +
  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. +
  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. +
    9. +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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: + +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

4.1 Steady-state solutions

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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);
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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;
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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;
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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))
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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]
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. A single unlabled outport defaults to [out]
    3. +
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  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].
    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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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

+ +

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.5.2 Stripped acausal bond graph (view)

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. The component constitutive relationship see section 6.6.4 Component constitutive relationship
    3. +
  3. The component arguments see section 6.6.5 + Component arguments
    4. +
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. A local constitutive relationship with the same name as the component + type
    3. +
  3. The SS constitutive relationship reserved for + SS components. All labels for SS components must + contain SS in this field.
    4. +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.6.5 Component arguments

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. component name
    3. +
  3. Four comma (,) or semi-colon (;) delimited fields: +
      +
    1. name of effort parameter
      2. +
    2. unit of effort parameter
      3. +
    3. name of flow parameter
      4. +
    4. unit of flow parameter
      5. +
    +
    4. +
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. renaming parameters (see section 6.6.9.2 + Parameter aliases) and
    3. +
  3. renaming components (see section 6.6.9.4 + Component aliases).
    4. +
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. Blank
    3. +
  3. Preceded by %
    4. +
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:

+ 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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.6.12 Language tex (desc.tex)

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.7.3 Language tex (view)

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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++
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.8.1.2 exotherm

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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"
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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));
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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

+ +

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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'.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. z
    3. +
  3. w=0 (the algebraic equations)
    4. +
  4. y
    5. +
+ + + + + + + + + + + +
6.12.1 Language + reduce (dae.r)
6.12.2 Language + m (dae.m)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    2. +
+ + + + + + + + + + + +
6.13.1 Language + reduce (cse.r)
6.13.2 Language + m (view)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.13.2 Language m (view)

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    2. +
+ + + + + + + + + + + + + + + + +
6.14.1 Language + reduce (ode.r)
6.14.2 Language + m (ode.m)
6.14.3 Language + m (view)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.14.3 Language m (view)

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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)
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

6.16.2 Language view

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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). +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. Optionally creating a shell script called myrep_rep.sh
    3. +
  3. Optionally creating a documentation file in LaTeX format called + myrep_rep.tex
    4. +
+ + + + + + + + + + + + + + + + +
7.2.1 + Makefile
7.2.2 + Shell-script
7.2.3 + Documentation
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

7.2.3 Documentation

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

8. Documentation

+ + + + + + + + + + + +
8.1 + Manual
8.2 On-line + documentation
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  2. verbose
    3. +
+ + + + + + + + + + + +
8.2.1 Brief + on-line documentation
8.2.2 Detailed + on-line documentation
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
    • +
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

9. Languages

+ + + + + + + + + + + + + + + + + + + + + +
9.1 + Figr
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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

9.1 Fig

+ Please see xfig documentation. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

9.3 Reduce

+ Please see the reduce documentation. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

9.4 c

+ Please see the gcc documentation. +
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

10. Language tools

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

10.2 Xfig

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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);
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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).

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

10.5 LaTeX

+

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

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

11.1 Software components

+

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

+ +

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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;
+
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

11.4.1 $MTTPATH

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

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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
+
+
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.
+
+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

A. Legal stuff

+ +
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  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. +
  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. +
  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. +
  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. +
    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. +
    3. State on the Title page the name of the publisher of the Modified + Version, as the publisher.
      4. +
    4. Preserve all the copyright notices of the Document.
      5. +
    5. Add an appropriate copyright notice for your modifications + adjacent to the other copyright notices.
      6. +
    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. +
    7. Preserve in that license notice the full lists of Invariant + Sections and required Cover Texts given in the Document's license + notice.
      8. +
    8. Include an unaltered copy of this License.
      9. +
    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. +
    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. +
    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. +
    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. +
    13. Delete any section Entitled "Endorsements". Such a section may + not be included in the Modified Version.
      14. +
    14. Do not retitle any existing section to be Entitled "Endorsements" + or to conflict in title with any Invariant Section.
      15. +
    15. Preserve any Warranty Disclaimers.
      16. +
    +

    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. +
  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. +
  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. +
  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. +
  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. +
  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. +
  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.

    +
    12. +
+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.
+
+
+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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. +
  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. +
  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. +
    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. +
    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.)
      4. +
    +

    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. +
  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. +
    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. +
    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.)
      4. +
    +

    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. +
  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. +
  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. +
  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. +
  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. +
  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. +
  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. +
  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. +
  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. +
  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.
    14. +
+
+ END OF TERMS AND CONDITIONS +
+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

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.

+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > + ][ << ][ Up + ][ >> ][Top][Contents][Index][ ? + ]
+

Glossary

+ + + + + +
Jump to:'
+ A B C D E F G I L M N O P R S T
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Index EntrySection
+
+
'
'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
abg6.1 Representation + summary
abg6.1 Representation + summary
AE6.4.1.5 Simple + components
AE6.4.1.5 Simple + components
AF6.4.1.5 Simple + components
AF6.4.1.5 Simple + components
artwork6.4.1 Language fig + (abg.fig)
artwork6.4.1 Language fig + (abg.fig)
assignment + statements6.9.3.1 Text form + (numpar.txt)
assignment + statements6.9.3.1 Text form + (numpar.txt)
+
+
B
bonds6.4.1 Language fig + (abg.fig)
bonds6.4.1 Language fig + (abg.fig)
+
+
C
C6.4.1.5 Simple + components
c4. Simulation
C6.4.1.5 Simple + components
c4. Simulation
c6.9.3 Numeric parameters + (numpar)
c6.9.3 Numeric parameters + (numpar)
c6.16.1 Language text + (rep.txt)
c6.16.1 Language text + (rep.txt)
c9. Languages
c9. Languages
cbg6.1 Representation + summary
cbg6.1 Representation + summary
cc4. Simulation
cc4. Simulation
commented assignment + statements6.9.3.1 Text form + (numpar.txt)
commented assignment + statements6.9.3.1 Text form + (numpar.txt)
comments6.9.3.1 Text form + (numpar.txt)
comments6.9.3.1 Text form + (numpar.txt)
components6.4.1 Language fig + (abg.fig)
components6.4.1 Language fig + (abg.fig)
cr6.1 Representation + summary
cr6.1 Representation + summary
cse4. Simulation
cse4. Simulation
cse6.1 Representation + summary
cse6.1 Representation + summary
csm6.1 Representation + summary
csm6.1 Representation + summary
CSW6.4.1.5 Simple + components
CSW6.4.1.5 Simple + components
+
+
D
dae6.1 Representation + summary
dae6.1 Representation + summary
daes6.1 Representation + summary
daes6.1 Representation + summary
daeso6.1 Representation + summary
daeso6.1 Representation + summary
def6.1 Representation + summary
def6.1 Representation + summary
desc6.1 Representation + summary
desc6.1 Representation + summary
dm6.1 Representation + summary
dm6.1 Representation + summary
dvi9. Languages
dvi9. Languages
+
+
E
ese6.1 Representation + summary
ese6.1 Representation + summary
exotherm6.8.1.2 exotherm
+
+
F
fig9. Languages
fig9. Languages
fr6.1 Representation + summary
fr6.1 Representation + summary
+
+
G
gdat9. Languages
gdat9. Languages
GY6.4.1.5 Simple + components
GY6.4.1.5 Simple + components
+
+
I
I6.4.1.5 Simple + components
I6.4.1.5 Simple + components
input6.1 Representation + summary
input6.1 Representation + summary
ir4. Simulation
ir4. Simulation
ir6.1 Representation + summary
ir6.1 Representation + summary
iro4. Simulation
iro4. Simulation
iro6.1 Representation + summary
iro6.1 Representation + summary
ISW6.4.1.5 Simple + components
ISW6.4.1.5 Simple + components
+
+
L
lbl6.1 Representation + summary
lbl6.1 Representation + summary
lin6.8.1.1 lin
lmfr6.1 Representation + summary
lmfr6.1 Representation + summary
lpfr6.1 Representation + summary
lpfr6.1 Representation + summary
+
+
M
m4. Simulation
m4. Simulation
m6.9.3 Numeric parameters + (numpar)
m6.9.3 Numeric parameters + (numpar)
m6.16.1 Language text + (rep.txt)
m6.16.1 Language text + (rep.txt)
m9. Languages
m9. Languages
mtt + &lt;system&gt; clean2.4 Utilities
mtt + &lt;system&gt; clean2.4 Utilities
mtt -c -i euler system + odeso view4. Simulation
mtt -c -i euler system + odeso view4. Simulation
mtt -c system odeso + view4. Simulation
mtt -c system odeso + view4. Simulation
mtt + clean2.4 Utilities
mtt + clean2.4 Utilities
mtt copy + &lt;system&gt;2.4 Utilities
mtt copy + &lt;system&gt;2.4 Utilities
mtt + help2.4 Utilities
mtt + help2.4 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 + view4. Simulation
mtt system iro + view4. Simulation
mtt system + representation vc2.4 Utilities
mtt system + representation vc2.4 Utilities
mtt system + representation vc2.4.4 Version + control
mtt system + representation vc2.4.4 Version + control
mtt system sro + view4. Simulation
mtt system sro + view4. Simulation
mtt system + vc2.4 Utilities
mtt system + vc2.4 Utilities
mtt system + vc2.4.4 Version + control
mtt system + vc2.4.4 Version + control
+
+
N
NAME_cause.m6.4.1.7 Simple components - + implementation
NAME_cause.m6.4.1.7 Simple components - + implementation
NAME_eqn.m6.4.1.7 Simple components - + implementation
NAME_eqn.m6.4.1.7 Simple components - + implementation
nifr6.1 Representation + summary
nifr6.1 Representation + summary
numpar6.1 Representation + summary
numpar6.1 Representation + summary
nyfr6.1 Representation + summary
nyfr6.1 Representation + summary
+
+
O
obs6.1 Representation + summary
obs6.1 Representation + summary
ode4. Simulation
ode4. Simulation
ode6.1 Representation + summary
ode6.1 Representation + summary
odes4.7 Simulation + output
odes4.7 Simulation + output
odes6.1 Representation + summary
odes6.1 Representation + summary
odes6.1 Representation + summary
odes6.1 Representation + summary
odeso4.7 Simulation + output
odeso4.7 Simulation + output
odeso6.1 Representation + summary
odeso6.1 Representation + summary
odess6.1 Representation + summary
odess6.1 Representation + summary
odesso6.1 Representation + summary
odesso6.1 Representation + summary
+
+
P
ps6.16.1 Language text + (rep.txt)
ps6.16.1 Language text + (rep.txt)
ps9. Languages
ps9. Languages
+
+
R
R6.4.1.5 Simple + components
r6.16.1 Language text + (rep.txt)
R6.4.1.5 Simple + components
r6.16.1 Language text + (rep.txt)
r9. Languages
r9. Languages
rbg6.1 Representation + summary
rbg6.1 Representation + summary
rep6.1 Representation + summary
rep6.1 Representation + summary
rfe6.1 Representation + summary
rfe6.1 Representation + summary
+
+
S
sabg6.1 Representation + summary
sabg6.1 Representation + summary
scse5. Sensitivity + models
scse5. Sensitivity + models
scsm5. Sensitivity + models
scsm5. Sensitivity + models
sg9. Languages
sg9. Languages
simp6.1 Representation + summary
simp6.1 Representation + summary
sm5. Sensitivity + models
sm5. Sensitivity + models
sm6.1 Representation + summary
sm6.1 Representation + summary
sms6.1 Representation + summary
sms6.1 Representation + summary
smss6.1 Representation + summary
smss6.1 Representation + summary
smx6.1 Representation + summary
smx6.1 Representation + summary
sr4. Simulation
sr4. Simulation
sr6.1 Representation + summary
sr6.1 Representation + summary
sro4. Simulation
sro4. Simulation
sro6.1 Representation + summary
sro6.1 Representation + summary
SS6.4.1.5 Simple + components
ss6.1 Representation + summary
ss6.1 Representation + summary
SS6.4.1.5 Simple + components
sspar6.1 Representation + summary
sspar6.1 Representation + summary
strokes6.4.1 Language fig + (abg.fig)
strokes6.4.1 Language fig + (abg.fig)
struc6.1 Representation + summary
struc6.1 Representation + summary
sub6.1 Representation + summary
sub6.1 Representation + summary
sub6.1 Representation + summary
sub6.1 Representation + summary
sympar6.1 Representation + summary
sympar6.1 Representation + summary
+
+
T
tex6.16.1 Language text + (rep.txt)
tex6.16.1 Language text + (rep.txt)
tex9. Languages
tex9. Languages
TF6.4.1.5 Simple + components
tf6.1 Representation + summary
TF6.4.1.5 Simple + components
tf6.1 Representation + summary
txt6.9.3 Numeric parameters + (numpar)
txt6.9.3 Numeric parameters + (numpar)
type6.4.1.4 Components
type6.4.1.4 Components
type*n6.4.1.4 Components
type*n6.4.1.4 Components
type:label6.4.1.4 Components
type:label6.4.1.4 Components
type:label*n6.4.1.4 Components
type:label*n6.4.1.4 Components
type:label:cr6.4.1.4 Components
type:label:cr6.4.1.4 Components
type:label:expression6.4.1.4 Components
type:label:expression6.4.1.4 Components
+
+
+ + + + + +
Jump to:'
+ A B C D E F G I L M N O P R S T
+

+
+ + + + + + + + + + + + + + + + + + +
[ < + ][ > ][ << ][ 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 EntrySection
+
+
<
<name>2.4.1.5 help + <name>
+
+
A
Acausal bond graph + (abg)6.4 Acausal bond graph + (abg)
Administration11. Administration
Algebraic loops1.7 Algebraic loops
alias options2.3 Options
aliases6.6.9 Aliases
Arrow-orientated + causality6.4.3.1 Arrow-orientated + causality
artwork6.4.1.15 Artwork
+
+
B
Bond graphs, what are + they?1.3 What is a bond + graph?
Bonds1.5 Bonds
bonds6.4.1.2 Bonds
bonds6.4.3 Language m + (abg.m)
Brief documentation8.2.1 Brief on-line + documentation
browser2.4.1 Help
+
+
C
c9.4 c
Causal bond graph + (cbg)6.10 Causal bond graph + (cbg)
cbonds6.10.2 Language m + (cbg.m)
Clean2.4.3 Clean
Coerced bond + direction6.4.1.10 Coerced bond + direction
Command line + interface2.2 Command line + interface
component7.3 Component + library
component aliases6.6.9.4 Component + aliases
Component arguments6.6.5 Component + arguments
Component constitutive + relationship6.6.4 Component constitutive + relationship
Component library7.3 Component + library
Component library7.3 Component + library
Component names6.6.3 Component + names
Component-orientated + causality6.4.3.2 Component-orientated + causality
Components1.6 Components
components2.4.1.2 help + components
Components8.2 On-line + documentation
components6.4.1.4 Components
components6.4.3 Language m + (abg.m)
compound components11.5 File structure
Compound components6.4.1.8 Compound + components
Constitutive + Relationship1.6.2 Constitutive + relationship
Constitutive + relationship6.8 Constitutive + relationship (cr)
Constrained-state + Equations6.13 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 systems10.4.1 Octave control system + toolbox (OCST)
Copy2.4.2 Copy
CR aliases6.6.9.3 CR aliases
Creating complex + models3.3 Creating complex + models
Creating GNU Octave .oct + files10.4.2 Creating GNU Octave + .oct files
Creating Matlab .mex + files10.4.3 Creating Matlab .mex + files
Creating Models3. Creating Models
Creating simple + models3.2 Creating simple + models
crs2.4.1.4 help crs
cse.r6.13.1 Language reduce + (cse.r)
+
+
D
DAE6.12 Differential-Algebraic + Equations (dae)
dae.m6.12.2 Language m + (dae.m)
dae.r6.12.1 Language reduce + (dae.r)
def.r6.11.0.1 Transformation + cbg2ese_m2r
Defining + representations6. Representations
Defining + representations6.2 Defining + representations
desc8.2.2 Detailed on-line + documentation
Description8.2.2 Detailed on-line + documentation
Descriptor matrices6.15 Descriptor matrices + (dm)
Descriptor matrices + (m)6.15.2 Language m + (dm.m)
Descriptor matrices + (reduce)6.15.1 Language reduce + (dm.r)
Detailed + documentation8.2.2 Detailed on-line + documentation
Differential-Algebraic + Equations6.12 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 + relationships6.8.2 DIY constitutive + relationships
DIY representations7.2 New (DIY) + representations
DIY representations7.2.1 Makefile
DIY representations7.2.2 Shell-script
DIY representations7.2.3 Documentation
dm6.15 Descriptor matrices + (dm)
dm.m6.15.2 Language m + (dm.m)
dm.r6.15.1 Language reduce + (dm.r)
Documentation7.2.3 Documentation
Documentation8. Documentation
Documentation8.2 On-line + documentation
+
+
E
Elementary system + equations6.11 Elementary system + equations (ese)
Embedding MTT models in + Simulink10.4.4 Embedding MTT models + in Simulink
Euler integration4.2.1 Euler + integration
Examples8.2 On-line + documentation
examples2.4.1.3 help + examples
Extending MTT7. Extending MTT
+
+
F
FDL, GNU Free Documentation + LicenseA.1 GNU Free Documentation + License
Fig9.1 Fig
File structure11.5 File structure
+
+
G
gnuplot4.7.1 Viewing results with + gnuplot
+
+
H
help2.4.1.1 help + representations
Help2.4.1 Help
help2.4.1.2 help + components
help2.4.1.3 help + examples
help2.4.1.4 help crs
help2.4.1.5 help + <name>
Hybrid systems1.8 Switched systems
+
+
I
ICD (label file + directive)6.6.8 Interface Control + Definition
Icon6.4.1.1 Icon library
Implicit integration4.2.2 Implicit + integration
+
+
L
Labels6.6 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 tools10. Language tools
Language txt + (struc.txt)6.7.1 Language txt + (struc.txt)
Languages9. Languages
LaTeX10.5 LaTeX
lbl6.6 Labels (lbl)
lbl6.6.11 Old-style labels + (lbl)
library6.4.1.1 Icon library
logic1.8 Switched systems
+
+
M
m9.2 m
m-files10.4 Octave
Make7. Extending MTT
Makefile7.2.1 Makefile
Makefiles7.1 Makefiles
Manual8.1 Manual
Matlab10.4 Octave
Menu-driven + interface2.1 Menu-driven + interface
MTT, purpose of1. Introduction
mtt.m10.4 Octave
mtt2sys10.4.1 Octave control system + toolbox (OCST)
mttrc11.4 Paths
+
+
N
n_ports6.4.3 Language m + (abg.m)
Named SS6.4.1.8 Compound + components
Named SS components6.4.1.9 Named SS + components
New representations7.2 New (DIY) + representations
New representations7.2.1 Makefile
New representations7.2.2 Shell-script
New representations7.2.3 Documentation
Numeric parameters1.6.4 Numeric + parameters
Numeric parameters6.9.3 Numeric parameters + (numpar)
Numeric parameters6.9.3.1 Text form + (numpar.txt)
+
+
O
OCST10.4.1 Octave control system + toolbox (OCST)
Octave10.4 Octave
Octave10.4.1 Octave control system + toolbox (OCST)
Octave interface10.4 Octave
Octave setup11.3 Octave setup
ODE6.13 Constrained-state + Equations (cse)
ODE6.14 Ordinary Differential + Equations
ode.m6.14.2 Language m + (ode.m)
ode.r6.14.1 Language reduce + (ode.r)
Old-style labels6.6.11 Old-style labels + (lbl)
On-line + documentation8.2 On-line + documentation
options2.3 Options
Ordinary Differential + Equations6.14 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 + labels6.6.2 Other component + labels
Other component labels + (old-style)6.6.11.2 Other component + labels (old-style)
+
+
P
parameter aliases6.6.9.2 Parameter + aliases
parameter + declarations6.6.6 Parameter + declarations
Parameter passing6.6.10 Parameter + passing
Parameter passing + (old-style)6.6.11.3 Parameter passing + (old-style)
Parameters6.9 Parameters
paths11.4 Paths
port aliases6.6.9.1 Port aliases
Port label defaults6.4.1.13 Port label + defaults
port labels6.4.1.12 Vector port + labels
ports1.6.1 Ports
ports6.4.1.11 Port labels
Predefined constitutive + relationships6.8.1 Predefined + constitutive relationships
+
+
Q
Quick start3.1 Quick start
+
+
R
Reduce9.3 Reduce
REDUCE setup11.2 REDUCE setup
rep6.16 Report (rep)
rep.txt6.16.1 Language text + (rep.txt)
Report6.16 Report (rep)
Report (text)6.16.1 Language text + (rep.txt)
Report (view)6.16.2 Language + view
Representation + summary6.1 Representation + summary
Representations6. Representations
representations2.4.1.1 help + representations
Representations, + defining6. Representations
Representations, what are + they?1.1 What is a + representation?
+
+
S
SciGraphica4.7.2 Exporting results to + SciGraphica
Sensitivity models5. Sensitivity + models
Shell-script7.2.2 Shell-script
Simple components6.4.1.5 Simple + components
simple components11.5 File structure
Simple components - + implementation6.4.1.7 Simple components - + implementation
Simulation4. Simulation
Simulation initial + state4.5 Simulation initial + state
Simulation input4.3 Simulation input
Simulation logic4.4 Simulation logic
Simulation output4.7 Simulation + output
Simulation + parameters4.2 Simulation + parameters
Software components11.1 Software + components
SS component labels6.6.1 SS component + labels
SS component labels + (old-style)6.6.11.1 SS component labels + (old-style)
SS components6.4.1.6 SS + components
status6.10.2 Language m + (cbg.m)
Steady-state + solutions4.1 Steady-state + solutions
Steady-state solutions - + numerical4.1.1 Steady-state solutions + (odess)
Steady-state solutions - + symbolic4.1.2 Steady-state solutions + (ss)
Stripped acausal bond graph + (sabg)6.5 Stripped acausal bond + graph (sabg)
strokes6.4.1.3 Strokes
struc6.7 Structure + (struc)
Structure6.7 Structure + (struc)
Structure6.11.0.1 Transformation + cbg2ese_m2r
Structure (view)6.7.3 Language tex + (view)
Switched systems1.8 Switched systems
Symbolic parameters1.6.3 Symbolic + parameters
Symbolic parameters6.9.1 Symbolic parameters + (subs.r)
Symbolic parameters for + simplification6.9.2 Symbolic parameters + for simplification (simp.r)
+
+
T
Text editors10.3 Text editors
toolbox10.4.1 Octave control system + toolbox (OCST)
Top level3.3.1 Top level
Transformation + abg2cbg_m6.10.2.1 Transformation + abg2cbg_m
Transformation + abg2rbg_fig2m6.4.2.1 Transformation + abg2rbg_fig2m
Transformation + cbg2ese_m2r6.11.0.1 Transformation + cbg2ese_m2r
Transformation + cse2ode_r6.14.1.1 Transformation + cse2ode_r
Transformation + dae2cse_r6.13.1.1 Transformation + dae2cse_r
Transformation + dae_r2m6.12.2.1 Transformation + dae_r2m
Transformation + ese2dae_r6.12.1.1 Transformation + ese2dae_r
Transformation + ode_r2m6.14.2.1 Transformation + ode_r2m
Transformation + rbg2abg_m6.4.3.3 Transformation + rbg2abg_m
Transformations1.2 What is a + transformation?
+
+
U
units declarations6.6.7 Units + declarations
Unresolved constitutive + relationships6.8.3 Unresolved + constitutive relationships
Unresolved constitutive + relationships - Octave6.8.4 Unresolved + constitutive relationships - Octave
Unresolved constitutive + relationships - Octave6.8.5 Unresolved + constitutive relationships - c++
User interface2. User interface
Utilities2.4 Utilities
+
+
V
valid name6.4.1.16 Valid Names
Variables1.4 Variables
Vector components6.4.1.14 Vector + Components
vector port labels6.4.1.12 Vector port + labels
Verbal description + (desc)6.3 Verbal description + (desc)
Version control2.4.4 Version + control
view Constrained-state + Equations6.5.2 Stripped acausal bond + graph (view)
view Constrained-state + Equations6.13.2 Language m + (view)
view Ordinary Differential + Equations6.14.3 Language m + (view)
view Report6.16.2 Language + view
view Structure6.7.3 Language tex + (view)
views10.1 Views
+
+
X
Xfig10.2 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][ ? + ]
+

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