\input texinfo
@c %**start of header
@setfilename mtt.info
@settitle MTT: Model Transformation Tools
@c %**end of header
@finalout
@c Here is what I use in the Info `dir' file:
@c * Mtt: (mtt). Model transformation tools.
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@comment Version control history
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@comment $Id$
@comment $Log$
@comment Revision 1.17 2003/08/19 14:20:38 gawthrop
@comment Version 5.0 of MTT
@comment Remove xref errors (spurious spaces)
@comment
@comment Revision 1.16 2003/08/19 14:11:23 gawthrop
@comment Links to legal stuff
@comment
@comment Revision 1.15 2003/08/19 14:01:45 gawthrop
@comment Added legal appendices
@comment
@comment Revision 1.14 2003/08/06 14:50:56 gawthrop
@comment Describe the alias mechanism for invoking mtt options
@comment
@comment Revision 1.13 2002/12/13 10:07:07 gawthrop
@comment Added example in sh section of DIY reps
@comment
@comment Revision 1.12 2002/09/19 08:09:31 gawthrop
@comment Updated documentation documentation
@comment
@comment Revision 1.11 2002/08/20 15:51:17 gawthrop
@comment Update to work with ident DIY rep
@comment
@comment Revision 1.10 2002/07/22 10:45:22 geraint
@comment Fixed gnuplot rep so that it correctly re-runs the simulation if input files have changed.
@comment
@comment Revision 1.9 2002/07/05 13:29:34 geraint
@comment Added notes about generating dynamically linked functions for Octave and Matlab.
@comment
@comment Revision 1.8 2002/07/04 21:34:12 geraint
@comment Updated gnuplot view description to describe Tcl/Tk interface instead of obsolete txt method.
@comment
@comment Revision 1.7 2002/04/23 09:51:54 gawthrop
@comment Changed incorrect statement about searching for components.
@comment
@comment Revision 1.6 2001/10/15 14:29:50 gawthrop
@comment Added documentaton on [1:N] style port labels
@comment
@comment Revision 1.5 2001/07/23 03:35:29 geraint
@comment Updated file structure (mtt/bin).
@comment
@comment Revision 1.4 2001/07/23 03:25:02 geraint
@comment Added notes on -ae hybrd, rk4, ode2odes.cc, .oct dependencies.
@comment
@comment Revision 1.3 2001/07/13 03:02:38 geraint
@comment Added notes on #ICD, gnuplot.txt and odes.sg rep.
@comment
@comment Revision 1.2 2001/07/03 22:59:10 gawthrop
@comment Fixed problems with argument passing for CRs
@comment
@comment Revision 1.1 2001/06/04 08:18:52 gawthrop
@comment Putting documentation under CVS
@comment
@comment Revision 1.66 2000/12/05 14:20:55 peterg
@comment Added the c++ anf m CR info.
@comment
@comment Revision 1.65 2000/11/27 15:36:15 peterg
@comment NOPAR --> NOTPAR
@comment
@comment Revision 1.64 2000/11/16 14:22:48 peterg
@comment added UNITS declaration
@comment
@comment Revision 1.63 2000/11/03 14:41:08 peterg
@comment Added PAR and NOPAR stuff
@comment
@comment Revision 1.62 2000/10/17 17:53:34 peterg
@comment Added some simulation details
@comment
@comment Revision 1.61 2000/09/14 17:13:06 peterg
@comment New options table
@comment
@comment Revision 1.60 2000/09/14 17:09:20 peterg
@comment Tidied up valid name sections
@comment Tidied up defining represnetations table
@comment Verion 4.6
@comment
@comment Revision 1.59 2000/08/30 13:09:00 peterg
@comment Updated option table
@comment
@comment Revision 1.58 2000/08/01 13:30:19 peterg
@comment Version 4.4
@comment updated STEPFACTOR info
@comment describes octave and OCST interfaces
@comment
@comment Revision 1.57 2000/07/20 07:55:44 peterg
@comment Version 4.3
@comment
@comment Revision 1.56 2000/05/19 17:49:17 peterg
@comment Extended the user defined representation section -- new nppp rep.
@comment
@comment Revision 1.55 2000/03/16 13:53:31 peterg
@comment Correct date
@comment
@comment Revision 1.54 2000/03/15 21:22:57 peterg
@comment Updated to 4.1 -- old style SS no longer supported
@comment
@comment Revision 1.53 1999/12/22 05:33:10 peterg
@comment Updated for 4.0
@comment
@comment Revision 1.52 1999/11/23 00:25:11 peterg
@comment Added the sensitivity reps
@comment
@comment Revision 1.51 1999/11/16 04:43:47 peterg
@comment Added start of sensitivity section
@comment
@comment Revision 1.50 1999/11/16 00:30:35 peterg
@comment Updated simulation section
@comment Added vector components
@comment
@comment Revision 1.49 1999/07/20 23:44:58 peterg
@comment V 3.8
@comment
@comment Revision 1.48 1999/07/19 03:08:33 peterg
@comment Added documentation for (new) SS lbl fields
@comment
@comment Revision 1.47 1999/03/09 01:42:22 peterg
@comment Rearranged the User interface section
@comment
@comment Revision 1.46 1999/03/09 01:18:01 peterg
@comment Updated for 3.5 including xmtt
@comment
@comment Revision 1.45 1999/03/03 02:39:26 peterg
@comment Minor updates
@comment
@comment Revision 1.44 1999/02/17 06:52:14 peterg
@comment New level formula dor artwork
@comment
@comment Revision 1.43 1998/11/25 16:49:24 peterg
@comment Put in subs.r documentation (was called params.r)
@comment
@comment Revision 1.42 1998/11/24 12:24:59 peterg
@comment Added section on simulation output
@comment Version 3.4
@comment
@comment Revision 1.41 1998/09/02 12:04:15 peterg
@comment Version 3.2
@comment
@comment Revision 1.40 1998/08/27 08:36:39 peterg
@comment Removed in. methods except Euler anf implicit
@comment
@comment Revision 1.39 1998/08/18 10:44:28 peterg
@comment Typo
@comment
@comment Revision 1.38 1998/08/18 09:16:38 peterg
@comment Version 3.1
@comment
@comment Revision 1.37 1998/08/17 16:14:30 peterg
@comment Version 3.1 - includes documentation on METHOD=IMPLICIT
@comment
@comment Revision 1.36 1998/07/30 17:33:15 peterg
@comment VERSION 3.0
@comment
@comment Revision 1.35 1998/07/22 11:00:53 peterg
@comment Correct date!
@comment
@comment Revision 1.34 1998/07/22 11:00:13 peterg
@comment Version to BAe
@comment
@comment Revision 1.33 1998/07/17 19:32:19 peterg
@comment Added more about aliases
@comment
@comment Revision 1.32 1998/07/05 14:21:56 peterg
@comment Further additions (Carlisle-Glasgow)
@comment
@comment Revision 1.31 1998/07/04 11:35:57 peterg
@comment Strarted new lbl description
@comment
@comment Revision 1.30 1998/07/02 18:39:20 peterg
@comment Started 3.0
@comment Added alias and default sections.
@comment
@comment Revision 1.29 1998/05/19 19:46:58 peterg
@comment Added the odess description
@comment
@comment Revision 1.28 1998/05/14 09:17:22 peterg
@comment Added METHOD variable to the simpar file
@comment
@comment Revision 1.27 1998/05/13 10:03:09 peterg
@comment Added unknown/zero SS label documentation.
@comment
@comment Revision 1.26 1998/04/29 15:12:46 peterg
@comment Version 2.9.
@comment
@comment Revision 1.25 1998/04/12 17:00:26 peterg
@comment Added new port features: coerced direction and top-level behaviour.
@comment
@comment Revision 1.24 1998/04/05 18:27:20 peterg
@comment This was the 2.6 version
@comment
@comment Revision 1.23 1997/08/24 11:17:51 peterg
@comment This is the released version 2.5
@comment
@comment Revision 1.22 1997/08/23 19:38:53 peterg
@comment Added simulation chapter.
@comment
@comment Revision 1.21 1997/08/23 16:50:10 peterg
@comment Added desc section.
@comment Included named and vector ports
@comment Completed list of representations.
@comment
@comment Revision 1.20 1997/06/16 15:39:24 peterg
@comment THis is the released 2.4 document.
@comment
@comment Revision 1.19 1997/06/16 09:48:23 peterg
@comment Back under revision control (elm)
@comment
@comment Revision 1.18 1997/06/14 20:27:41 peterg
@comment Added complex example section.
@comment
@comment Revision 1.18 1997/06/13 14:51:07 peterg
@comment Added report section
@comment
@comment Revision 1.17 1997/05/09 15:06:02 peterg
@comment Changed to version 2.4.
@comment
@comment Revision 1.16 1996/12/05 10:06:25 peterg
@comment Modified .octaverc : 'true' --> 1
@comment
@comment Revision 1.15 1996/11/20 19:02:28 peterg
@comment Added some system admin stuff.
@comment Added section on simple models.
@comment
@comment Revision 1.14 1996/11/12 13:19:04 peterg
@comment Put paths as section, not subsection.
@comment
@comment Revision 1.13 1996/11/11 16:53:14 peterg
@comment Added params documentation
@comment Sorted out table bug.
@comment
@comment Revision 1.12 1996/11/10 20:29:31 peterg
@comment Added section on help -- needs more
@comment
@comment Revision 1.11 1996/11/09 21:15:28 peterg
@comment Rewrite of quick start.
@comment Update of file structure.
@comment
@comment Revision 1.10 1996/11/09 20:25:54 peterg
@comment Final v2.0.
@comment
@comment Revision 1.9 1996/10/01 10:33:02 peter
@comment Cleaned up cross references.
@comment
@comment Revision 1.8 1996/10/01 09:31:00 peter
@comment Added sections written in Hong Kong.
@comment
@comment Revision 1.7 1996/09/16 09:49:47 peter
@comment Added ese section
@comment
@comment Revision 1.6 1996/09/16 08:33:53 peter
@comment Added constitutive relationship section etc.
@comment
@comment Revision 1.5 1996/09/15 20:20:56 peter
@comment Added abg and rbg stuff
@comment
@comment Revision 1.4 1996/08/30 19:07:40 peter
@comment Added some admin stuff.
@comment
@comment Revision 1.3 1996/08/30 07:50:16 peter
@comment Added file structure section.
@comment
@comment Revision 1.2 1996/08/22 14:28:50 peter
@comment Added stuff about labels.
@comment
@comment Revision 1.1 1996/08/22 11:52:59 peter
@comment Initial revision
@comment %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ifinfo
This file documents MTT, a set of Model Transformation Tools.
Copyright (C) Peter J. Gawthrop 1996, 1997, 1998, 1999, 2000, 2001,
2002, 2003
Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.
@ignore
Permission is granted to process this file through TeX and print the
results, provided the printed document carries copying permission
notice identical to this one except for the removal of this paragraph
(this paragraph not being relevant to the printed manual).
@end ignore
Permission is granted to copy and distribute modified versions of this
manual under the conditions for verbatim copying, provided also that the
section entitled ``GNU General Public License'' is included exactly as
in the original, and provided that the entire resulting derived work is
distributed under the terms of a permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual
into another language, under the above conditions for modified versions,
except that the section entitled ``GNU General Public License'' may be
included in a translation approved by the author instead of in the
original English.
@end ifinfo
@titlepage
@title MTT: Model Transformation Tools
@subtitle August 2003
@subtitle For version 5.0.
@author Peter Gawthrop, Geraint Bevan
@page
@vskip 0pt plus 1filll
Copyright @copyright{} 1996,1997,1998,1999,2000,2001,2002,2003 Peter J. Gawthrop
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".
General information about MTT is available at URL www.sf.net. MTT is distributed
under the GNU GENERAL PUBLIC LICENSE (@pxref{Copying}). This manual is
distributed under the GNU Free Documentation License (@pxref{GNU Free
Documentation License}).
@example
http://mtt.sourceforge.net
@end example
@ifhtml
<A
HREF="http://mtt.sourceforge.net"> here</A>.
@end ifhtml
@end titlepage
@ifinfo
@node Top, Introduction, (dir), (dir)
@top MTT
@strong{MTT} is a set of Model Transformation Tools based on bond graphs.
@strong{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:
@itemize @bullet
@item
bicausal bond graphs and
@item
hierarchical bond graphs.
@end itemize
@contents
@end ifinfo
@c @include intro.texi
@c Copyright (C) 1996 Peter J. Gawthrop
@c This is part of the MTT manual.
@c For copying conditions, see the file MTT.texi.
@menu
* Introduction::
* User interface::
* Creating Models::
* Simulation::
* Sensitivity models::
* Representations::
* Extending MTT::
* Documentation::
* Languages::
* Language tools::
* Administration::
* Glossary::
* Index::
@detailmenu
--- The Detailed Node Listing ---
Introduction
* What is a Representation?::
* What is a Transformation?::
* Bond graphs:: What is a bond graph?
* Variables::
* Bonds::
* Components::
* Algebraic loops::
* Switched systems::
Components
* Ports::
* Constitutive relationship::
* Symbolic parameters::
* Numeric parameters::
User interface
* Menu-driven interface::
* Command line interface::
* Options::
* Utilities::
Utilities
* Help::
* Copy::
* Clean::
* Version control::
Help
* help representations::
* help components::
* help examples::
* help crs::
* help <name>::
Creating Models
* Quick start::
* Creating simple models::
* Creating complex models::
Creating complex models
* Top level::
Simulation
* Steady-state solutions::
* Simulation parameters::
* Simulation input::
* Simulation logic::
* Simulation initial state::
* Simulation code::
* Simulation output::
Steady-state solutions
* Steady-state solutions - numerical(odess)::
* Steady-state solutions - symbolic (ss)::
Simulation parameters
* Euler integration::
* Implicit integration::
* Runge Kutta IV integration::
* Hybrd algebraic solver::
Simulation code
* Dynamically linked functions::
Simulation output
* Viewing results with gnuplot::
* Exporting results to SciGraphica::
Representations
* Representation summary::
* Defining representations::
* Verbal description (desc)::
* Acausal bond graph (abg)::
* Stripped acausal bond graph (sabg)::
* Labels (lbl)::
* Structure (struc)::
* Constitutive Relationship (cr)::
* Parameters::
* Causal bond graph (cbg)::
* Elementary system equations::
* Differential-Algebraic Equations::
* Constrained-state Equations::
* Ordinary Differential Equations::
* Descriptor matrices::
* Report::
Acausal bond graph (abg)
* Language fig (abg.fig)::
* Language m (rbg.m)::
* Language m (abg.m)::
* Language tex (abg.tex)::
Language fig (abg.fig)
* icon library::
* bonds::
* strokes::
* components::
* Simple components::
* SS components::
* Simple components - implementation::
* Compound components::
* Named SS components::
* Coerced bond direction::
* Port labels::
* Vector port labels::
* Port label defaults::
* Vector components::
* artwork::
* Valid names::
Simple components
* SS components::
* Simple components - implementation::
Compound components
* Named SS components::
Language m (rbg.m)
* Transformation abg2rbg_fig2m::
Language m (abg.m)
* Arrow-orientated causality::
* Component-orientated causality::
* Transformation rbg2abg_m::
Stripped acausal bond graph (sabg)
* Language fig (sabg.fig)::
* Stripped acausal bond graph (view)::
Labels (lbl)
* SS component labels ::
* Other component labels::
* Component names::
* Component constitutive relationship::
* Component arguments::
* Parameter declarations::
* Units declarations::
* Interface Control Definition::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
* Language tex (desc.tex)::
Other component labels
* Component names::
* Component constitutive relationship::
* Component arguments::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
Aliases
* Port aliases::
* Parameter aliases::
* CR aliases::
* Component aliases::
Old-style labels (lbl)
* SS component labels (old-style)::
* Other component labels (old-style)::
* Parameter passing (old-style)::
Parameter passing (old-style)
* Language tex (desc.tex)::
Structure (struc)
* Language txt (struc.txt)::
* Language tex (struc.tex)::
* Structure (view)::
Constitutive relationship (cr)
* Predefined constitutive relationships::
* DIY constitutive relationships::
* Unresolved constitutive relationships::
* Unresolved constitutive relationships - Octave::
* Unresolved constitutive relationships - c++::
Predefined constitutive relationships
* lin::
* exotherm::
Parameters
* Symbolic parameters (subs.r)::
* Symbolic parameters for simplification (simp.r)::
* Numeric parameters (numpar)::
Numeric parameters (numpar)
* Text form (numpar.txt)::
Causal bond graph (cbg)
* Language fig (cbg.fig)::
* Language m (cbg.m)::
Language m (cbg.m)
* Transformation abg2cbg_m::
Elementary system equations (ese)
* Transformation cbg2ese_m2r::
Differential-Algebraic Equations (dae)
* Differential-Algebraic Equations (reduce)::
* Differential-Algebraic Equations (m)::
Language reduce (dae.r)
* Transformation ese2dae_r::
Language m (dae.m)
* Transformation dae_r2m::
Constrained-state Equations (cse)
* Constrained-state Equations (reduce)::
* Constrained-state Equations (view)::
Language reduce (cse.r)
* Transformation dae2cse_r::
Ordinary Differential Equations
* Ordinary Differential Equations (reduce)::
* Ordinary Differential Equations (m)::
* Ordinary Differential Equations (view)::
Language reduce (ode.r)
* Transformation cse2ode_r::
Language m (ode.m)
* Transformation ode_r2m::
Descriptor matrices (dm)
* Descriptor matrices (reduce)::
* Descriptor matrices (m)::
Report (rep)
* Report (text)::
* Report (view)::
Extending MTT
* Makefiles::
* New (DIY) representations::
* Component library ::
New (DIY) representations
* Makefile (DIY representations)::
* Shell-script (DIY representations)::
* Documentation (DIY representations)::
Documentation
* Manual (Documentation)::
* On-line documentation::
On-line documentation
* Brief::
* Detailed::
Languages
* Fig:: r
* m::
* Reduce::
* c::
Language tools
* Views::
* Xfig::
* Text editors::
* Octave::
* LaTeX::
Octave
* Octave control system toolbox (OCST)::
* Creating GNU Octave .oct files::
* Creating Matlab .mex files::
* Embedding MTT models in Simulink::
Administration
* Software components::
* REDUCE setup::
* Octave setup::
* Paths::
* File structure::
* GNU Free Documentation License::
* Copying::
Octave setup
* .octaverc::
* .oct file dependencies::
Paths
* $MTTPATH::
* $MTT_COMPONENTS::
* $MTT_CRS::
* $MTT_EXAMPLES::
* $OCTAVE_PATH::
@end detailmenu
@end menu
@node Introduction, User interface, Top, Top
@chapter Introduction
@cindex MTT, purpose of
@pindex MTT
@strong{MTT} is a set of Model Transformation Tools based on bond
graphs. @strong{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:
@itemize @bullet
@item
bicausal bond graphs and
@item
hierarchical bond graphs.
@end itemize
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 @strong{MTT} - a set of Model Transformation Tools
each of which implements a single transformation between system
representations.
System representations have two attributes.
@itemize @bullet
@item
A Form: e.g. acausal bond graph, differential algebraic, linear
state-space etc.
@item
A Language: e.g. Fig, Matlab, LaTeX, Reduce, postscript etc.
@end itemize
Transformations in @strong{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.
@menu
* What is a Representation?::
* What is a Transformation?::
* Bond graphs:: What is a bond graph?
* Variables::
* Bonds::
* Components::
* Algebraic loops::
* Switched systems::
@end menu
@node What is a Representation?, What is a Transformation?, Introduction, Introduction
@section What is a representation?
@cindex Representations, what are they?
@pindex Representations
Physical systems have many representations. These include
@itemize @bullet
@item
a schematic diagram,
@item
a block diagram,
@item
a bunch of equations,
@item
a single differential(-algebraic) equation,
@item
simulation code,
@item
linearised state-space (or descriptor) equations,
@item
transfer function (of the linearised system),
@item
frequency response (of the linearised system),
@item
etc...
@end itemize
Each of these representations is related to other representations by an
appropriate transformation (@pxref{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:
@itemize @bullet
@item
simulation,
@item
control system design,
@item
optimisation
@item
etc.
@end itemize
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 (@pxref{What is a Transformation?}.
In this context, the following considerations are relevant.
@itemize @bullet
@item
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.
@item
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.
@item
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.
@item
Representation_1 should be `close' in some sense to the Physical system.
@item
The core representation, and hence the representations leading to it,
must contain enough information to generate all of the required models.
@item
Representations must be easily extensible: it must be possible to add
extra components or attributes without restructuring the representation.
@end itemize
I happen to believe that Bond graphs (@pxref{Bond graphs}) provide the
most convenient and powerful basis for the core representation.
@node What is a Transformation?, Bond graphs, What is a Representation?, Introduction
@comment node-name, next, previous, up
@section What is a transformation?
@cindex Transformations
Each system representation (@pxref{What is a Representation?} is related to other representations by an
appropriate transformation as follows:
@itemize @bullet
@item
Physical system
@item
Transformation_1 ---> Representation_1
@item
Transformation_2 ---> Representation_2
@item
...
@item
Transformation_N ---> Core representation
@item
Transformation_N+1 ---> Representation_N+1
@item
Transformation_N+2 ---> Representation_N+2
@item
...
@item
Transformation_N+M ---> Model
@end itemize
Thus modeling is seen as a sequence of transformations between
representations.
@node Bond graphs, Variables, What is a Transformation?, Introduction
@section What is a bond graph?
@cindex Bond graphs, what are they?
@pindex Bond graphs
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:
@itemize @bullet
@item
Electrical systems
@item
Mechanical systems
@item
Hydraulic systems
@item
Chemical process systems
@end itemize
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 (@pxref{Components}) connected by
bonds (@pxref{Bonds}) which define the relationship between
variables (@pxref{Variables}).
@node Variables, Bonds, Bond graphs, Introduction
@comment node-name, next, previous, up
@section Variables
@cindex Variables
In bond graph terminology there are four sorts of variables:
@itemize @bullet
@item @emph{effort} variables
@item @emph{flow} variables
@item @emph{integrated effort} variables
@item @emph{integrated flow} variables
@end itemize
Examples of @emph{effort} variables are
@itemize @bullet
@item
voltage
@item
pressure
@item
force
@item
torque
@item
temperature
@end itemize
Examples of @emph{flow} variables are
@itemize @bullet
@item
current
@item
volumetric flow rate
@item
velocity
@item
angular velocity
@item
heat flow
@end itemize
Examples of integrated @emph{flow} variables are
@itemize @bullet
@item
charge
@item
volume
@item
momentum
@item
angular momentum
@item
heat
@end itemize
@node Bonds, Components, Variables, Introduction
@comment node-name, next, previous, up
@section Bonds
@cindex Bonds
Bonds connect components (@pxref{Components}) together. Each bond
carries two variables:
@itemize @bullet
@item an effort (@pxref{Variables}) variable and
@item a flow (@pxref{Variables}) variable.
@end itemize
Each bond has three notations associated with it:
@itemize @bullet
@item a half-arrow,
@item a causal stroke and
@item a causal half-stroke.
@end itemize
The half-arrow indicates two things:
@itemize @bullet
@item the direction of power (or pseudo power) flow and
@item the side of the bond associated with the flow variable.
@end itemize
The causal stroke indicates two things:
@itemize @bullet
@item the effort variable is imposed at the same end as the stroke and
@item the flow variable is imposed at the opposite end to the stroke.
@end itemize
The causal half-stoke indicates one thing:
@itemize @bullet
@item if it is on the effort side of the bond, the effort variable is
imposed at the same end as the stroke or
@item if it is on the flow side of the bond, the flow variable is
imposed at the opposite end to the stroke.
@end itemize
@node Components, Algebraic loops, Bonds, Introduction
@comment node-name, next, previous, up
@section Components
@cindex Components
Components provide the building blocks of a dynamic system when
connected by bonds (@pxref{bonds}).
Components have the following attributes:
@vtable @code
@item ports
provide the connections to other components (@pxref{Ports})
@item constitutive relationships
define how the port-variables are related (@pxref{Constitutive
relationship})
@end vtable
@menu
* Ports::
* Constitutive relationship::
* Symbolic parameters::
* Numeric parameters::
@end menu
@node Ports, Constitutive relationship, Components, Components
@comment node-name, next, previous, up
@subsection Ports
@cindex ports
Components have one or more ports. Each port carries two variables,
and effort and a flow variable (@pxref{Variables}). Any pair of ports
can be connected by a bond (@pxref{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 @strong{MTT} using named SS components.
(@pxref{Named SS components}).
The direction of the named SS components.
(@pxref{Named SS components})
is coerced (@pxref{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.
@node Constitutive relationship, Symbolic parameters, Ports, Components
@comment node-name, next, previous, up
@subsection Constitutive relationship
@cindex 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
(@pxref{Symbolic parameters}) which may be replaced, for the purposes
of numerical analysis by numeric parameters
(@pxref{Numeric parameters}).
@node Symbolic parameters, Numeric parameters, Constitutive relationship, Components
@comment node-name, next, previous, up
@subsection Symbolic parameters
@cindex Symbolic parameters
The constitutive relationship of a system component (@pxref{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, @strong{MTT} allows replacement of symbolic parameters by
numeric parameters (@pxref{Numeric parameters}) when appropriate.
@node Numeric parameters, , Symbolic parameters, Components
@comment node-name, next, previous, up
@subsection Numeric parameters
@cindex Numeric parameters
Numerical parameters are needed to give specific values to symbolic
parameters (@pxref{Symbolic parameters}) for the purposes of numeric
analysis;
for example: simulation, graph plotting or use within a numerical
package such as Octave (@pxref{Octave}).
@node Algebraic loops, Switched systems, Components, Introduction
@section Algebraic loops
@cindex 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:
@example
loop SS unknown,zero
@end example
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).
@node Switched systems, , Algebraic loops, Introduction
@comment node-name, next, previous, up
@section Switched systems
@cindex Switched systems
@cindex Hybrid systems
@cindex logic
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.
@strong{MTT} implements a simple pragmatic approach to the modelling and
simulation of such systems via two new Bond Graph components:
@vtable @code
@item ISW
a switched @code{I} component
@item CSW
a switched @code{C} component
@end vtable
These switches are user controlled through the logic representation
(@pxref{Simulation logic}).
@node User interface, Creating Models, Introduction, Top
@comment node-name, next, previous, up
@chapter User interface
@cindex User interface
@pindex User interface
There are two user interfaces to @strong{MTT}: a command line interface
(@pxref{Command line interface}) and a menu-driven interface
(@pxref{Menu-driven interface}).
@menu
* Menu-driven interface::
* Command line interface::
* Options::
* Utilities::
@end menu
@node Menu-driven interface, Command line interface, User interface, User interface
@comment node-name, next, previous, up
@section Menu-driven interface
@cindex Menu-driven interface
@pindex Menu-driven interface
The Menu-driven interface for @strong{MTT} is invoked as:
@example
xmtt
@end example
This will bring up a menu which should be self explanatory :-).
Various messages will be echoed in the window from whence @strong{xMTT}
was invoked.
@node Command line interface, Options, Menu-driven interface, User interface
@comment node-name, next, previous, up
@section Command line interface
@cindex Command line interface
@pindex Command line interface
The command line interface for @strong{MTT} is of the form:
@example
mtt [options] <system_name> <representation> <language>
@end example
@vtable @code
@item [options]
the (optional) option switches (@pxref{Options})
@item <system_name>
the name of the system being transformed
@item <representation>
the mnemonic for the system representation (@pxref{Representation summary})
@item <language>
the mnemonic for language for the representation (@pxref{Languages})
@end vtable
for example
@example
mtt rc rep view
@end example
creates a view of the report describing system rc and
@example
mtt rc sm m
@end example
creates an m file (suitlable for Octave or Matlab) containing state
matrices describing the system rc.
@node Options, Utilities, Command line interface, User interface
@comment node-name, next, previous, up
@section Options
@cindex options
@cindex alias options
@strong{MTT} has a number of optional switches to control its
operation. These are invoked immediately after `mtt' on the command
line; for example:
@example
mtt -o -ss -cc syst cbg view
@end example
invokes the @code{-o}, @code{-ss}, and @code{-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:
@example
alias mtt='mtt -o -ss -cc'
@end example
Means that the previous example can be executed using
@example
mtt syst cbg view
@end example
The available options are:
@vtable @code
@item -q
quiet mode -- suppress MTT banner
@item -A
solve algebraic equations symbolically
@item -ae
<hybrd> solve algebraic equations numerically
(this option requires -cc or -oct)
@item -D
debug -- leave log files etc
@item -I
prints more information
@item -abg
start at abg.m representation
@item -c
c-code generation
@item -cc
C++ code generation
@item -d
<dir> use directory <dir>
@item -dc
Maximise derivative (not integral) causality
@item -dc
Maximise derivative (not integral) causality
@item -i
<implicit|euler|rk4> Use implicit, euler or Runge Kutta IVintegration
@item -o
ode is same as dae
@item -oct
use oct files in place of m files where appropriate
@item -opt
optimise code generation
@item -p
print environment variables
@item -partition
partition hierachical system
@item -r
reset time stamp on representation
@item -s
try to generate sensitivity BG (experimental)
@item -ss
use steady-state info to initialise simulations
@item -stdin
read input data from standard input for simulations
@item -sub
<subsystem> operate on this subsystem
@item -t
tidy mode (default)
@item -u
untidy mode (leaves files in current dir)
@item -v
verbose mode (multiple uses increase the verbosity)
@item -viewlevel
<N> View N levels of hierachy
@item --version
print version and exit
@item --versions
print version of mtt and components and exit
@end vtable
@node Utilities, , Options, User interface
@comment node-name, next, previous, up
@section Utilities
@cindex Utilities
@pindex Utilities
@strong{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:
@ftable @code
@item mtt help
Lists the help/browser commands
@item mtt copy <system>
Copies the system (ie directory and enclosed files) to the
current working directory.
@item mtt rename <old_name> <new_name>
Renames all of the defining representations (@pxref{Defining
representations}) and textually changes each file appropriately.
@item mtt <system> clean
Remove all files generated by @strong{MTT} associated with
system `system'.
@item mtt clean
Remove all files generated by @strong{MTT} associated with
all systems within the current directory.
@item mtt system representation vc
Apply version control to representation `representation' of
system `system'.
@item mtt system vc
Apply version control to all representations (under version control)
system `system'.
@end ftable
These are described in more detail in the following sections.
@menu
* Help::
* Copy::
* Clean::
* Version control::
@end menu
@node Help, Copy, Utilities, Utilities
@comment node-name, next, previous, up
@subsection Help
@cindex Help
@cindex browser
@strong{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:
@example
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>
@end example
@menu
* help representations::
* help components::
* help examples::
* help crs::
* help <name>::
@end menu
@node help representations, help components, Help, Help
@comment node-name, next, previous, up
@subsubsection help representations
@cindex help
@cindex representations
The command
@example
mtt help representations
@end example
lists all of the representations (@pxref{Representations}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help representations <match_string>
@end example
lists those representation which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help representations descriptor
@end example
gives all representations containing the word @code{descriptor}.
@node help components, help examples, help representations, Help
@comment node-name, next, previous, up
@subsubsection help components
@cindex help
@cindex components
The command
@example
mtt help components
@end example
lists all of the components (@pxref{Components}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help components <match_string>
@end example
lists those component which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help components source
@end example
gives all components containing the word @code{component}.
@node help examples, help crs, help components, Help
@comment node-name, next, previous, up
@subsubsection help examples
@cindex help
@cindex examples
This command provides a good way to get started in @strong{MTT}. having
found an interesting example, copy it to your working directory using
@example
mtt copy <example_name>
@end example
(@pxref{Copy})
@example
mtt help examples
@end example
lists all of the examples available in
@strong{MTT}.
This list will change as more examples are added.
The command
@example
mtt help examples <match_string>
@end example
lists those component which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help examples pharmokinetic
@end example
gives all examples containing the word @code{pharmokinetic}.
@node help crs, help <name>, help examples, Help
@comment node-name, next, previous, up
@subsubsection help crs
@cindex help
@cindex crs
The command
@example
mtt help crs
@end example
lists all of the constitutive relationships (@pxref{Constitutive
relationship}) available in
@strong{MTT}. These may change as the version number of @strong{MTT}
increases.
The command
@example
mtt help crs <match_string>
@end example
lists those constitutive relationships which contain the string @code{match_string}.
This string can be any regular expression (see standard Linux
documentation under @code{awk}).
For example
@example
mtt help crs sin
@end example
gives all crs containing the word @code{sin}.
@node help <name>, , help crs, Help
@comment node-name, next, previous, up
@subsubsection help <name>
@cindex help
@cindex <name>
The command
@example
mtt help <name>
@end example
gives a detailed description of the entity called @code{name}.
@node Copy, Clean, Help, Utilities
@comment node-name, next, previous, up
@subsection Copy
@cindex Copy
@strong{MTT} provides a way of copying examples to your working directory:
@example
mtt copy <example_name>
@end example
Use the command
@example
mtt help examples
@end example
(@pxref{help examples}) to find something of interest.
Note that components and constitutive relationships are automatically
copied when required.
@node Clean, Version control, Copy, Utilities
@comment node-name, next, previous, up
@subsection Clean
@cindex Clean
@strong{MTT} generates a lot of representations in a number of
languages.
Some of these you will edit yourself; others can always be recreated by
@strong{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:
@enumerate
@item
@code{mtt system clean}
@item
@code{mtt clean}
@end enumerate
The first removes all files that can be regenerated with @strong{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 (@pxref{Defining representations}).
@node Version control, , Clean, Utilities
@comment node-name, next, previous, up
@subsection Version control
@cindex 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.@strong{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 @strong{MTT}) are the Defining representations
(@pxref{Defining representations}).
All of the files, with the exception of @code{system_abg.fig},
are initially created by @strong{MTT} and contain the RCS header for
version control.
The @strong{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 @strong{MTT} version commands are as follows:
@ftable @code
@item mtt system representation vc
Apply version control to representation `representation' of
system `system'.
@item mtt system vc
Apply version control to all representations (under version control)
system `system'.
@end ftable
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'.
@node Creating Models, Simulation, User interface, Top
@comment node-name, next, previous, up
@chapter Creating Models
@cindex Creating Models
@strong{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 @strong{MTT} aspects of creating a
model. For convenience, this is divided into creating simple models and
creating complex models.
@menu
* Quick start::
* Creating simple models::
* Creating complex models::
@end menu
@node Quick start, Creating simple models, Creating Models, Creating Models
@section Quick start
@cindex Quick start
@pindex Quick start
It is probably worth a quick skim though @strong{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.
@example
mtt copy rc
@end example
@noindent
Move to it.
@example
cd rc
@end example
@noindent
@noindent
View the acausal bond graph (the system is called ``rc'').
@example
mtt rc abg view
@end example
@noindent
View the causal bond graph of the system.
@example
mtt rc cbg view
@end example
@noindent
View the corresponding ordinary differential equations (ode).
@example
mtt rc ode view
@end example
@noindent
View the system (output) step response
@example
mtt rc sro view
@end example
@noindent
An alternative (but more general) way of achieving the same result is
@example
mtt -c rc odeso view
@end example
@noindent
View the system transfer function
@example
mtt rc tf view
@end example
@noindent
View the log modulus frequency response of the system.
@example
mtt rc lmfr view
@end example
@noindent
View the log modulus frequency response of the system for 100
logarithmically spaced frequencies in the range 0.1 to 10
radians per second.
@example
mtt rc lmfr view 'W=logspace(-1,1,100);'
@end example
@strong{MTT} has a report generation ((@pxref{Report}) facility which
can generate a hypertext description of the system.
@example
mtt rc rep hview
@end example
The report contents are specified by the rep representation
(@pxref{Report}), in this case the corresponding file is:
@example
% %% 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
@end example
A non-hypertext version can be viewed using:
@example
mtt rc rep view
@end example
Now have a go at modifying the bond graph.
@example
mtt rc abg fig
@end example
This brings up the bond graph in Xfig (@pxref{Xfig}). Try creating a
system with two rs and 2 cs.
More examples can be found using
@example
mtt help examples
@end example
Details of an example can be found using
@example
mtt help <example_name>
@end example
and copied using
@example
mtt copy <example_name>
@end example
Lots of examples are available.
@example
mtt help examples
@end example
lists them and
@example
mtt copy <name>
@end example
gets you an example.
@ifhtml
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>.
@end ifhtml
@node Creating simple models, Creating complex models, Quick start, Creating Models
@comment node-name, next, previous, up
@section Creating simple models
@cindex 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 (@pxref{Creating complex models}) need to be built
up hierarchically.
The recommended sequence of steps to create a simple model is:
@enumerate
@item Decide on a name for the system; let us call it `syst' for the
purposes of this discussion.
@item Invoke the Bond Graph editor to draw the acausal Bond Graph.
@example
mtt syst abg fig
@end example
@item Draw the Bond Graph (@pxref{Language fig (abg.fig)}), including
the bonds (@pxref{Bonds}), the components (@pxref{Components}) and any
artwork (@pxref{artwork}) to make the Bond Graph more readable. The
graphical editor xfig is (@pxref{Xfig}) is self-explanatory.
The icon library is helpful here (see @pxref{icon library}).
@item Add causal strokes (@pxref{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 @code{SS} components.
(@pxref{SS components}).
Save the bond graph.
@item View the corresponding causal bond graph.
@example
mtt syst cbg view
@end example
@enumerate
@item
At this stage, @strong{MTT} will warn you that the labeled components do
not appear in the label file - this can safely be ignored.
@item
@strong{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.
@item
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.
@item
If the bond graph is causally complete, proceed to the next step,
otherwise think hard and return to the first step.
@end enumerate
@item
At this stage, no constitutive relationships have been
defined. Nevertheless, @strong{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:
@enumerate
@item
View the system Differential-algebraic equations
@example
mtt syst dae view
@end example
@item
View the system state matrices
@example
mtt syst sm view
@end example
@item
View the system transfer function
@example
mtt syst tf view
@end example
@item
View the system step response
@example
mtt syst sro view
@end example
@end enumerate
@item
As well as creating the causal bond graph, @strong{MTT} has also
generated templates for other text files
(@pxref{Defining representations})
used to further specify the
system.
These can now be edited using your favorite text editor (@pxref{Text
editors}).
@item @strong{MTT} will now generate the representations
(@pxref{Representation summary})that you desire.
For example the system can be simulated by
@example
mtt syst odeso view
@end example
@strong{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.
@end enumerate
@node Creating complex models, , Creating simple models, Creating Models
@comment node-name, next, previous, up
@section Creating complex models
@cindex Creating complex models
Complex models -- in distinction to simple models (@pxref{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
(@pxref{Ports}); within each component, ports are represented by
named SS components (@pxref{Named SS components}); outwith
each component, ports are unambiguously identified by
labels (@pxref{Port labels}) and vector labels (@pxref{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 (@pxref{Creating simple models}) is
then followed using the top level system (@pxref{Top level}); @strong{MTT} then recursively
operates on the lower level systems.
The report representation (@pxref{Report}) provides a convenient way of
viewing a complex system.
An example of such a system can be created as follows:
@example
mtt copy twolink
mtt twolink rep hview
@end example
@ifhtml
The result is <A
HREF="./examples/twolink/twolink_rep/twolink_rep.html"> here</A>.
@end ifhtml
@menu
* Top level::
@end menu
@node Top level, , Creating complex models, Creating complex models
@comment node-name, next, previous, up
@subsection Top level
@cindex 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:
@itemize @bullet
@item
its name is used in the mtt command as the system name.
@item
all named SS componenents (@pxref{Named SS components}) are treated as
ordinary SS components (@pxref{SS components}).
@end itemize
@c node next prev up
@node Simulation, Sensitivity models, Creating Models, Top
@chapter Simulation
@cindex Simulation
@pindex Simulation
One purpose of modelling is to simulate the modeled dynamic
system. Although this is just another transformation (@pxref{What is a
Transformation?}) and therefore is covered in the appropriate chapter
(@pxref{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). @strong{MTT} provides a number of alternative routes to
simulation based on the following representations (@pxref{Representations}):
@ftable @code
@item cse
constrained-state differential equation form
@item ode
ordinary differential (or state-space) equations
@c @item dae
@c differential-algebraic (or generalised state-space) equations --
@c these may be linear or nonlinear.
@end ftable
in each case these equations may be
linear or nonlinear.
Special cases of numerical simulation, appropriate to @emph{linear}
systems, are:
@ftable @code
@item ir
impulse response - state
@item iro
impulse response - output
@item sr
impulse response - state
@item sro
impulse response - output
@end ftable
There are a number of languages (@pxref{Languages}) which can be used to describe these
representations for the purposes of numerical simulation:
@ftable @code
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item c
@code{gcc} a c compiler.
@item cc
@code{g++} a C++ front-end to gcc.
@end ftable
There are a number solution algorithms available:
@itemize @bullet
@item
explicit solution via the matrix exponential
@item
backward Euler integration (explicit)
@item
forward Euler integration (implicit)
@item
Runge Kutta IV integration (explicit, fixed step)
@item
Hybrd algebraic solver (MINPACK, Octave fsolve)
@c @item
@c LSODE (Hindmarsh's ODE solver as implemented in Octave)
@c @item
@c DASSL (Petzold's DAE solver as implemented in Octave) (Unavailable just now)
@end itemize
However, all combinations of representation, language and solution
method are not supported by @strong{MTT} at the moment. Given a system
`system', some recommended commands are:
@ftable @code
@item mtt system iro view
creates the impulse response of a @emph{linear} system via the
system_sm.m representation using explicit solution via the matrix exponential.
@item mtt system sro view
creates the step response of a @emph{linear} system via the system_sm.m
representation using explicit solution via the matrix exponential.
@c @item mtt system odeso view
@c creates the step response of a @emph{nonlinear} system via the
@c system_ode.m representation using either METHOD=Euler or
@c METHOD=LSODE in the parameter file (@pxref{Simulation parameters}).
@item mtt -c system odeso view
creates the response of a @emph{nonlinear} system via the
system_ode.c representation using implicit integration.
@item mtt -c -i euler system odeso view
creates the response of a @emph{nonlinear} system via the
system_ode.c representation using euler integration.
@end ftable
Simulation parameters are described in the system_simpar.txt file
(@pxref{Simulation parameters}).
The steady-state solution of a system can also be
``simulated''(@pxref{Steady-state solutions}).
@menu
* Steady-state solutions::
* Simulation parameters::
* Simulation input::
* Simulation logic::
* Simulation initial state::
* Simulation code::
* Simulation output::
@end menu
@node Steady-state solutions, Simulation parameters, Simulation, Simulation
@comment node-name, next, previous, up
@section Steady-state solutions
@cindex Steady-state solutions
@menu
* Steady-state solutions - numerical(odess)::
* Steady-state solutions - symbolic (ss)::
@end menu
@node Steady-state solutions - numerical(odess), Steady-state solutions - symbolic (ss), Steady-state solutions, Steady-state solutions
@comment node-name, next, previous, up
@subsection Steady-state solutions (odess)
@cindex Steady-state solutions - numerical
@strong{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 (@pxref{Simulation
parameters}) is used to provide the time scales.
For example
@example
mtt copy rc
cd rc
mtt rc odess view
@end example
@node Steady-state solutions - symbolic (ss), , Steady-state solutions - numerical(odess), Steady-state solutions
@comment node-name, next, previous, up
@subsection Steady-state solutions (ss)
@cindex Steady-state solutions - symbolic
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 @strong{MTT} using
@example
mtt system ss view
@end example
For example
@example
mtt copy rc
cd rc
mtt rc sspar view
mtt rc ss view
@end example
@node Simulation parameters, Simulation input, Steady-state solutions, Simulation
@comment node-name, next, previous, up
@section Simulation parameters
@cindex Simulation parameters
Simulation parameters are set in the system_simpar.txt file. At the
moment this sets the following variables:
@itemize @bullet
@item LAST
the last simulation time
@item DT
the incremental time (for plotting)
@item STEPFACTOR
the number of integration steps per DT -- thus the integration
interval is DT/STEPFACTOR
@c ; for sparse implicit integration (@pxref{Sparse
@c implicit integration}) the number of conjugate-gradient minimisation
@c steps.
@c @item METHOD
@c The integration methods available appear in the following table
@item WMIN
Minimum frequency = 10^WMIN
@item WMAX
Maximum frequency = 10^WMAX
@item WSTEPS
Number of Frequency steps.
@item INPUT
The input index for frequency response
@end itemize
There are a number of solution algorithms
@itemize @bullet
@item Euler
basic Euler integration (@pxref{Euler integration}). This method
is simple, but not recommended for stiff systems.
@item Implicit
semi-implicit integration (@pxref{Implicit integration}) - uses the smx representation to give
stability.
@item Runge Kutta IV
fixed step Runge Kutta fourth order integration (@pxref{Runge Kutta IV integration}).
@item Hybrd
numerical algebraic equation solver
@c @item ImplicitS
@c Sparse semi-implicit integration (@pxref{Sparse implicit integration})
@c -- takes advantage of the sparsity of the A matrix.
@c @item LSODE
@c the variable step-size method that comes with Octave (@pxref{Octave}).
@end itemize
@menu
* Euler integration::
* Implicit integration::
* Runge Kutta IV integration::
* Hybrd algebraic solver::
@end menu
@node Euler integration, Implicit integration, Simulation parameters, Simulation parameters
@comment node-name, next, previous, up
@subsection Euler integration
@cindex Euler integration
Euler integration approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,u)
@end example
by
@example
x := x + f(x,u)*DDT
@end example
where
@example
DDT = DT/STEPFACTOR
@end example
If the system is linear, stability is ensured if the integer STEPFACTOR
is chosen to be greater than the real number
@example
(maximum eigenvalue of -A)*DT/2
@end example
where A is the nxn matrix appearing in
@example
f(x,u) = Ax + Bu
@end example
If the system is non linear, the linearised system matrix A should act
as a guide to the choice of STEPFACTOR.
@node Implicit integration, Runge Kutta IV integration, Euler integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Implicit integration
@cindex Implicit integration
Implicit integration approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,u)
@end example
by
@example
(I-A*DT)x := (I-A*DT)x + f(x,u)DT
@end example
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:
@example
E(x) dx/dt = f(x,u)
@end example
where E(x) is a state-dependent matrix. The approximate solution is then
given by:
@example
(E(x)-A*DT)x := (E(x)-A*DT)x + f(x,u)DT
@end example
which reduces to the ordinary differential equation case when E(x)=I.
The _smx representation includes the E matrix.
@node Runge Kutta IV integration, Hybrd algebraic solver, Implicit integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Runge Kutta IV integration
Runge Kutta IV approximates the solution of the Ordinary Differential Equation
@example
dx/dt = f(x,t)
@end example
by
@example
x := x + (DT/6)*(k1 + 2*k2 + 2*k3 + k4)
@end example
where
@example
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)
@end example
The @strong{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 @code{u} is not advanced w.r.t. time; the system inputs are
assumed to be constant over the period of the integration step-length.
@node Hybrd algebraic solver, , Runge Kutta IV integration, Simulation parameters
@comment node-name, next, previous, up
@subsection Hybrd algebraic solver
The hybrd algebraic solver of @uref{http://www.netlib.org/minpack/hybrd.f,MINPACK},
which is used by Octave in the @code{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 @strong{MTT} models by use of
@code{unknown} SS Components @pxref{SS component labels}.
This method requires that compiled simulation code is used; either -cc or -oct.
To perform a simulation based on a model @code{sys},
@example
mtt -cc -ae hybrd -i euler sys odeso view
@c XXX: should be daeso view?
@end example
@strong{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.
@c XXX: tolerance option
@c @node Sparse implicit integration, , Implicit integration, Simulation parameters
@c @comment node-name, next, previous, up
@c @subsection Sparse implicit integration
@c @cindex Sparse implicit integration
@c This is an experimental approach for large (N>50) systems.
@c Implicit integration (@pxref{Implicit integration}) requires the
@c solution of N linear equations at each step. This is an O(N^3) operation
@c which can be time consuming for large (N>50) systems. However, the A
@c matrix (and hence the (I-A*DT) matrix) is often sparse - most elements
@c are zero.
@c This method uses a conjugate-gradient optimisation method to solve the
@c linear equations
@c @example
@c (I-A*DT)x := (I-A*DT)x + f(x,u)DT
@c @end example
@c by recasting them as the minimisation of the quadratic function
@c @example
@c [(I-A*DT)x_new - (I-A*DT)x_old + f(x,u)DT]^2
@c @end example
@c with respect to x_new. This is solved by the conjugate gradient method.
@c MTT generates two representations _smxx.m and _smxtx to compute
@c (I-A*DT)x and (I-A*DT)'x respectively making full use of the sparsity of
@c the (I-A*DT) matrices to speed up the minimisation procedure.
@c A fixed number of iterations (STEPFACTOR) are used in each optimisation
@c to give a fixed simulation time. This must be chosen by the user, but
@c between 5N and 10N seems ok. Note that the initial value of the
@c optimisation is x_old.
@node Simulation input, Simulation logic, Simulation parameters, Simulation
@comment node-name, next, previous, up
@section Simulation input
@cindex Simulation input
This is defined in the system_input.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system input txt
@end example
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 (@pxref{Structure (struc)}). They can depend on states (again defined by
name), time (defined by t) and parameters
For example:
@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);
@end example
@node Simulation logic, Simulation initial state, Simulation input, Simulation
@comment node-name, next, previous, up
@section Simulation logic
@cindex Simulation logic
This is defined in the system_logic.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system logic txt
@end example
If the file already exists, the same command checks that the logic
corresponding to all switch states (@pxref{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 (@pxref{Structure
(struc)}) @emph{with `_logic' appended}. They can depend on states (again defined by name), time
(defined by t) and parameters
For example:
@example
bounce_ground_1_mtt_switch_logic = bounce_intf_1_mtt3<0;
@end example
@node Simulation initial state, Simulation code, Simulation logic, Simulation
@comment node-name, next, previous, up
@section Simulation initial state
@cindex Simulation initial state
This is defined in the system_state.txt file. A default file is created
automatically by @strong{MTT}. This is done explicitly by
@example
mtt system state txt
@end example
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 (@pxref{Structure (struc)}). They can depend on parameters.
For example
@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;
@end example
@c The initial state of a simulation of is set in the @code{state}
@c representation with the language @code{txt}.
@c As usual, @strong{MTT} defaults this for you. There are two
@c possibilities
@c @itemize @bullet
@c @item
@c The -ss switch is not present: the states default to zero
@c @item
@c The -ss switch is present: the states default to those set in the
@c sspar.r file.
@c @end itemize
@node Simulation code, Simulation output, Simulation initial state, Simulation
@comment node-name, next, previous, up
@section Simulation code
simulation code can be generated by @strong{MTT} in the form
of the @code{ode2odes} transformation. This can be produced in a number
of languages, including .m, .oct, C and C++ @pxref{Languages}.
To generate simulation code in C:
@example
mtt -c [options] sys ode2odes c
@end example
Similarly, to generate C++ code:
@example
mtt -cc [options] sys ode2odes cc
@end example
To generate an executable based on the C++ representation:
@example
mtt -cc [options] sys ode2odes exe
@end example
@menu
* Dynamically linked functions::
@end menu
@node Dynamically linked functions, , Simulation code, Simulation code
@comment node-name, next, previous, up
@subsection 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 (@pxref{Creating GNU Octave .oct
files}) and .mex files can be generated for use in Matlab
(@pxref{Creating Matlab .mex files}) or Simulink (@pxref{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 @strong{MTT} allows the same code to be
generated as standalone code, Octave .oct files or Matlab .mexglx
files. Although @strong{MTT} usually takes care of the compilation
options, if it is necessary to compile the code on a machine on which
@strong{MTT} is not installed, the appropriate flag should be passed
to the compiler pre-processor:
@itemize @bullet
@item
@code{-DCODEGENTARGET=STANDALONE}
@item
@code{-DCODEGENTARGET=OCTAVEDLD}
@item
@code{-DCODEGENTARGET=MATLABMEX}
@end itemize
@node Simulation output, , Simulation code, Simulation
@comment node-name, next, previous, up
@section Simulation output
@cindex Simulation output
The view (@pxref{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
@ftable @code
@item odes
ordinary differential equation solution (states)
@item odeso
ordinary differential equation solution (output)
@end ftable
Particular output variables can be selected by adding a fourth argument
in one of 2 forms
@ftable @code
@item 'name1;name2;..;namen'
plot the variables with names na1 .. namen against time
@item 'name1:name2'
plot the variable with name2 against that with name 1
@end ftable
An example of plotting a single variable against time is:
@example
mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V'
@end example
An example of plotting one variable against another is:
@example
mtt -o -c -ss OttoCycle odeso ps 'OttoCycle_cycle_V:OttoCycle_cycle_P'
@end example
@menu
* Viewing results with gnuplot::
* Exporting results to SciGraphica::
@end menu
@node Viewing results with gnuplot, Exporting results to SciGraphica, Simulation output, Simulation output
@comment node-name, next, previous, up@subsection
@subsection Viewing results with gnuplot
@cindex gnuplot
Simulation plots may be conveniently selected, viewed with
@uref{http://www.gnuplot.org,gnuplot}
and saved to file (in PostScript format) using the command
@example
mtt [options] rc gnuplot view
@end example
This will cause a menu to be displayed, from which states and outputs may be selected for viewing. Clicking on a @emph{parameter name} will, by default, cause the time history of the selected parameter to be displayed.
As with @strong{xMTT} (@pxref{Menu-driven interface}), the Wish Tcl/Tk interpreter must be installed to make use of this feature.
@node Exporting results to SciGraphica, , Viewing results with gnuplot, Simulation output
@comment node-name, next, previous, up
@subsection Exporting results to SciGraphica
@cindex SciGraphica
Simulation results can be converted into an XML-format
@uref{http://scigraphica.sourceforge.net,SciGraphica} (version 0.61)
@emph{.sg} file with the command
@example
mtt [options] sys odes sg
@end example
The SciGraphica file will contain two worksheets, X_sys and Y_sys, containing
the state and output time-histories from the simulation.
@c node next prev up
@node Sensitivity models, Representations, Simulation, Top
@chapter Sensitivity models
@cindex Sensitivity models
@pindex 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.
@strong{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.
@example
mtt copy rc
cd rc
mtt -s src ode view
mtt -s src odeso view
@end example
The sensitivity system src is automatically created from the system rc
using the predefined sR and sC components together with vector junctions
(@pxref{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:
@ftable @code
@item scse
sensitivity constrained-state equations
@item sm
sensitivity state matrices
@item scsm
sensitivity constrained-state matrices
@end ftable
@c node next prev up
@node Representations, Extending MTT, Sensitivity models, Top
@chapter Representations
@cindex Representations
@pindex Representations
@cindex Defining representations
@cindex Representations, defining
As discussed in @ref{What is a Representation?}, a system has many
representations. The purpose of @strong{MTT} is to provide an easy way to
generate such representation by applying the appropriate sequence of
transformations. The representations supported by @strong{MTT} are
summarised in @ref{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 @emph{defining representations} are listed in
@ref{Defining representations}.
Each representation is implemented in one or more languages depending on
its use. These languages are discussed in @ref{Languages} and are
associated with appropriate tools for modifying or viewing the
representations.
@menu
* Representation summary::
* Defining representations::
* Verbal description (desc)::
* Acausal bond graph (abg)::
* Stripped acausal bond graph (sabg)::
* Labels (lbl)::
* Structure (struc)::
* Constitutive Relationship (cr)::
* Parameters::
* Causal bond graph (cbg)::
* Elementary system equations::
* Differential-Algebraic Equations::
* Constrained-state Equations::
* Ordinary Differential Equations::
* Descriptor matrices::
* Report::
@end menu
@node Representation summary, Defining representations, Representations, Representations
@comment node-name, next, previous, up
@section Representation summary
@cindex Representation summary
Some of the the representations
available in @strong{MTT} are (in alphabetical order):
@ftable @code
@item abg
acausal bond graph
@item cbg
causal bond graph
@item cr
constitutive relationship for each subsystem
@item cse
constrained-state equations
@item csm
constrained-state matrices
@item dae
differential-algebraic equations
@item daes
dae solution - state
@item daeso
dae solution - output
@item def
definitions - system orders etc.
@item desc
Verbal description of system
@item dm
descriptor matrices
@item ese
elementary system equations
@item fr
frequency response
@item input
numerical input declaration
@item ir
impulse response - state
@item iro
impulse response - output
@item lbl
label file
@item lmfr
loglog modulus frequency response
@item lpfr
semilog phase frequency response
@item nifr
Nichols style frequency response
@item numpar
numerical parameter declaration
@item nyfr
Nyquist style frequency response
@item obs
observer equations for CGPC
@item ode
ordinary differential equations
@item odes
ode solution - state
@item odes
ODE simulation header file
@item odeso
ode solution - output
@item odess
ode numerical steady-states - states
@item odesso
ode numerical steady-states - outputs
@item rbg
raw bond graph
@item rep
report
@item rfe
robot-form equations
@item sabg
stripped acausal bond graph
@item simp
simplification information
@item sm
state matrices
@item smx
state matrices containing explicit states and inputs
@item sms
ode
@item smss
SM simulation header file
@item sr
step response - state
@item sro
step response - output
@item ss
steady-state equations
@item sspar
steady-state definition
@item struc
structure - list of inputs, outputs and states
@item sub
Executable subsystem list
@item sub
LaTeX subsystem list
@item sympar
symbolic parameters
@item tf
transfer function
@end ftable
A complete list can be found via the @code{help representations} command
(@pxref{help representations}).
Many of these representations have more than one language (@pxref{Representations}) associated
with them.
Some of these representations define the system (@pxref{Defining
representations}).
@node Defining representations, Verbal description (desc), Representation summary, Representations
@comment node-name, next, previous, up
@section Defining representations
@cindex 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 @strong{MTT} and may then be subsequently edited
(@pxref{Text editors}) viewed or operated on by the appropriate tools
(@pxref{Language tools}).
@vtable @code
@item system_abg.fig
the acausal bond graph (@pxref{Acausal bond graph (abg)})
@item system_lbl.txt
the label file (@pxref{Labels (lbl)})
@item system_desc.tex
the description file (@pxref{Detailed})
@item system_simp.r
algebraic simplifications to make output more readable
(@pxref{Symbolic parameters for simplification (simp.r)})
@item system_subs.r
algebraic substitutions to resolve, eq trig. identities
(@pxref{Symbolic parameters (subs.r)})
@item system_simpar.txt
simulation parameters (@pxref{Simulation parameters})
@item system_numpar.txt
numerical parameters (@pxref{Numeric parameters (numpar)})
@item system_input.txt
the system input for simulations (@pxref{Simulation input})
@item system_logic.txt
the switching logic for simulations (@pxref{Simulation logic})
@item system_sspar.r
defines the system steady-state (@pxref{Steady-state solutions - symbolic (ss)})
@end vtable
@node Verbal description (desc), Acausal bond graph (abg), Defining representations, Representations
@comment node-name, next, previous, up
@section Verbal description (desc)
@cindex Verbal description (desc)
Systems can be documented in LaTeX using the _desc.tex file. This file
is included in the report (@pxref{Report}) if the abg tex option
is included in the rep.txt file. As usual, @strong{MTT} provides a
default text file to be edited by the user (@pxref{Text editors}).
@c node next prev up
@node Acausal bond graph (abg), Stripped acausal bond graph (sabg), Verbal description (desc), Representations
@section Acausal bond graph (abg)
@cindex Acausal bond graph (abg)
@pindex Acausal bond graph (abg)
The acausal bond graph is the main input to @strong{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:
@example
mtt sys abg fig
@end example
To create the acausal bond graph of system `sys' in language m type:
@example
mtt sys abg m
@end example
To view the acausal bond graph of system `sys' type:
@example
mtt sys abg view
@end example
@menu
* Language fig (abg.fig)::
* Language m (rbg.m)::
* Language m (abg.m)::
* Language tex (abg.tex)::
@end menu
@node Language fig (abg.fig), Language m (rbg.m), Acausal bond graph (abg), Acausal bond graph (abg)
@subsection Language fig (abg.fig)
@cindex Language fig (abg.fig)
@pindex Language fig (abg.fig)
A bond graph is made up of:
@ftable @code
@item bonds
To connect components together.
@item strokes
To indicate causality.
@item components
Either simple or compound.
@item artwork
Irrelevant to the system but useful to the user.
@end ftable
An icon library of bonds, components and other symbols is available
within xfig (@pxref{icon library}).
@menu
* icon library::
* bonds::
* strokes::
* components::
* Simple components::
* SS components::
* Simple components - implementation::
* Compound components::
* Named SS components::
* Coerced bond direction::
* Port labels::
* Vector port labels::
* Port label defaults::
* Vector components::
* artwork::
* Valid names::
@end menu
@node icon library, bonds, Language fig (abg.fig), Language fig (abg.fig)
@subsubsection Icon library
@cindex Icon
@cindex library
A number of predefined iconic symbols are available within xfig.
@example
Click onto the library icon
Click onto the library pull-down menu and select BondGraph
Select iconic symbols from the presented list
@end example
@node bonds, strokes, icon library, Language fig (abg.fig)
@subsubsection Bonds
@cindex bonds
@pindex 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:
@itemize @bullet
@item
It points in the direction of power flow; thus a bond normally points
towards C, I and R components.
@item
the corresponding side of the bond indicates flow causality; the other
side represents effort causality. This is significant when using casual
half-strokes (@pxref{strokes}). Please adopt the convention of having
the half-arrows below horizontal bonds and to the right of vertical bonds.
@end itemize
@c node next prev up
@node strokes, components, bonds, Language fig (abg.fig)
@subsubsection Strokes
@cindex strokes
@pindex strokes
Causal strokes are represented by single-segment polylines.
There are two sorts of strokes:
@itemize @bullet
@item
@emph{Full} strokes: these are the usual bond-graph strokes and determine
both the effort and flow causality in the usual way. The @emph{centre} of the
stroke should be at about one end of the bond and be at right angles to
it.
@item
@emph{Half} strokes: these are an innovation in @strong{MTT} and allow you to
specify the effort and flow causality independently. The @emph{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 @emph{same} side as the half-arrow
(@pxref{bonds}) then it determines @emph{flow} causality; if, on the other
hand, it is on the @emph{opposite} side to the half-arrow
(@pxref{bonds}) then it determines @emph{effort} causality.
Two half strokes on the @emph{same}, but on @emph{opposite} sides of the
bond are equivalent to a a full stroke at the same end of the bond.
@end itemize
@strong{MTT} is reasonably forgiving; but a neat diagram will be less ambiguous to
you as well as to @strong{MTT}.
Causality is indicated as follows:
@itemize @bullet
@item
@emph{Effort} is imposed at the @emph{same} end as the stroke.
@item
@emph{Flow} is imposed at the @emph{opposite} end as the stroke.
@end itemize
@c node next prev up
@node components, Simple components, strokes, Language fig (abg.fig)
@subsubsection Components
@cindex components
@pindex 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:
@ftable @code
@item type
Just the type of the component is indicated. Components may be either
Simple components (@pxref{Simple components}) or Compound components
(@pxref{Compound components}). For example:
@example
R
@end example
@item type:label
Both the type and the label of the component are given. The type must be
a valid name (@pxref{Valid names}.The name provides a link to more
information to be found in @xref{Labels (lbl)}. For example:
@example
R:r
@end example
@item 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 (@pxref{Valid names}.The name provides a link to more
information to be found in @xref{Labels (lbl)}. For example:
@example
R:r:flow,r
@end example
@item 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
@example
R:r:mtt_e=r*mtt_f
R:r:mtt_e-r*mtt_f=0
R:r:mtt_f=mtt_e/r
@end example
A non-linear example is:
@example
R:r:mtt_e = sin(mtt_f)
@end example
@item type*n
The name, together with the number @samp{n} of repetitions of the
component, are given. This repetition only makes sense if the component
has an even number of ports (@pxref{Port labels}); n copies of the component
are concatenated with odd Named ports (@pxref{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:
@example
MySystem*25
@end example
@item type:label*n
This complete form and is a combination of the simpler forms. For
example:
@example
MySystem:MyLabel*25
@end example
@end ftable
@node Simple components, SS components, components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Simple components
@cindex Simple components
The following simple components are defined in MTT.
@ftable @code
@item R
Standard one-port R
@item C
Standard one-port I
@item I
Standard one-port I
@item SS
Source-sensor
@item TF
Transformer
@item GY
Gyrator
@item AE
Effort amplifier
@item AF
Flow amplifier
@item CSW
Switched one-port I
@item ISW
Switched one-port I
@end ftable
@menu
* SS components::
* Simple components - implementation::
@end menu
@node SS components, Simple components - implementation, Simple components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection SS components
@cindex SS components
@iftex
$$
@end iftex
@code{SS} components provide input and output variables for a system;
Named SS components (@pxref{Named SS components}) provide this for
subsystems.
@node Simple components - implementation, Compound components, SS components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Simple components - implementation
@cindex Simple components - implementation
Each simple component, with name NAME, is defined by two m files:
@ftable @code
@item NAME_cause.m
defines the possible causal patterns for the component
@item NAME_eqn.m
defines the equations generated
@end ftable
Only the experienced user would normally define simple components -
Compound components (@pxref{Compound components}) are recommended for
DIY components.
@node Compound components, Named SS components, Simple components - implementation, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Compound components
@cindex Compound components
@cindex Named SS
Compound components are systems described by bond graphs and implemented
by MTT. They have special SS components, Named SS components
(@pxref{Named SS components}), to indicate connections to the
encapsulating system.
Like any other system, they are described by a graphical Bond Graph description
(@pxref{Language fig (abg.fig)}), and a label file (@pxref{Labels (lbl)}).
By convention, all of the files describing a component live in a
directory with the same name as the component.
@menu
* Named SS components::
@end menu
@node Named SS components, Coerced bond direction, Compound components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Named SS components
@cindex Named SS components
Named SS components provide the link from the system which @emph{defines}
compound component to the system which @emph{uses} a compound
component @pxref{Compound components}.
A named SS components is of the form
@code{SS:[name]};
Where `name' is a name consisting of alphanumeric characters and
underscore; for example:
@example
SS:[Mechanical_1]
@end example
Each such named SS provides one of the ports
(@pxref{Ports}).
The direction of the named SS components.
(@pxref{Named SS components})
is coerced (@pxref{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 (@pxref{Top level})
and is treated as an
ordinary SS component with the given direction and with the attributes
specified in the label file (@pxref{Labels (lbl)}).
@node Coerced bond direction, Port labels, Named SS components, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Coerced bond direction
@cindex Coerced bond direction
@pindex Coerced bond direction
Named SS components (@pxref{Named SS components}) provide the mechanism
for declaring the ports (@pxref{Ports}) of a component. The
corresponding bond has a direction. However, under some circumstances,
it may be useful to reverse this direction. @strong{MTT} provides a
coercion mechanism for this: the the direction of the bond attached to
the named SS component (@pxref{Named SS components}) is replaced by the
direction of the bond attached to the component port.
@node Port labels, Vector port labels, Coerced bond direction, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Port labels
@cindex ports
@pindex ports
Most multi-port components have ports
@pxref{Ports})which display different
behaviors; the exception to this is the junction (@code{0} and @code{1})
components. For this reason, @strong{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
@code{[name]}, where `name' is a name consisting of alphanumeric
characters and underscore; for example:
@example
[Mechanical_1]
@end example
This provides a label for corresponding to the component to which the
nearest bond-end is attached.
The following rules must be be obeyed:
@itemize @bullet
@item
If a component has any port labels at all, there must be one for each
port of the component.
@c @item
@c If a component is to be used repetitively (see @ref{components}), it
@c must have an even number of ports and the odd ports are connected to the
@c even points within the chain of components.
@end itemize
Port labels may be grouped into vector port labels (@pxref{Vector port
labels}). Components with compatible (ie containing the same number of ports)
vector ports may be connected by a @emph{single} bond
(@pxref{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 @emph{explicit} causal strokes (@pxref{strokes})
@node Vector port labels, Port label defaults, Port labels, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Vector port labels
@cindex vector port labels
@cindex port labels
Port labels (@pxref{Port labels}) may be grouped into vector port
labels of the form @code{[name1,name2,name3]}.
@example
[Mechanical_1,Electrical,Hydraulic_5]
@end example
@node Port label defaults, Vector components, Vector port labels, Language fig (abg.fig)
@comment node-name, next, previous, up
@subsubsection Port label defaults
@cindex Port label defaults
@pindex Port label defaults
Whether impicitly or explicity, all ports of components (with the
exception of 0 and 1 junctions) must have lables (@pxref{Port
labels}). However, these can be omitted from the bond graph in the
following circumstances and default labels are supplied by @strong{MTT}.
@enumerate
@item A single unlabled inport defaults to [in]
@item A single unlabled outport defaults to [out]
@end enumerate
These defaults may, in turn be aliases (@pxref{Aliases}) for port labels
(@pxref{Port labels}) or vector port labels (@pxref{Vector port
labels}). Combining the default and alias mechanism is a powerful tool
for creating uncluttered, yet complex, bond graph models.
@node Vector components, artwork, Port label defaults, Language fig (abg.fig)
@subsubsection Vector Components
@cindex Vector components
@pindex Vector components
Vectors of components can be created in four cases:
@code{0} junctions,
@code{1} junctions,
@code{SS} components and
@code{SS} port components.
In each case, the presence of a vector component is indicated by a
single port label (@pxref{Port labels}) of one of two forms:
@enumerate
@item 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].
@item 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].
@end enumerate
Within the corresponding label file (@pxref{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 (@pxref{Port aliases})
@example
%ALIAS in Electrical_1,Electrical_2,Electrical_3
@end example
@node artwork, Valid names, Vector components, Language fig (abg.fig)
@subsubsection Artwork
@cindex artwork
@pindex 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 (@pxref{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.
@c The recommended way to do this is to @emph{put all artwork at or below
@c Depth 1} in the figure. @strong{MTT} ignores all objects not at depth 0.
For compatibility with earlier versions of @strong{MTT}, the following
objects are ignored even at level 0. However, their use is strongly
discouraged.
@itemize @bullet
@item
Adding text is OK as long as it cannot be confused with components
(@pxref{components}). In particular, you can include invalid component
characters such as white space, @code{"}, @code{'}, @code{!} etc.
@item
Adding boxes, arcs etc is always OK.
@item
Adding dotted or dashes lines is always OK.
@end itemize
The stripped abg file (sabg) (@pxref{Stripped acausal bond graph
(sabg)})
shows only those parts of the diagram recognised by @strong{MTT} and is
therefore useful for distinguishing artwork.
@node Valid names, , artwork, Language fig (abg.fig)
@subsubsection Valid Names
@cindex valid name
@pindex valid name
A valid name is a text string containing alphanumeric characters. It
must @strong{NOT} contain underscore @samp{_}, hyphen @samp{-}, @samp{:}
or @samp{*}.
The following names should be avoided
@example
if endif
@end example
The following reserved words in reduce should also be avoided (with any case)
@example
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
@end example
@node Language m (rbg.m), Language m (abg.m), Language fig (abg.fig), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language m (rbg.m)
The raw bond graph of system `sys' is represented as
an m file with heading:
@example
function [rbonds, rstrokes,rcomponents,rports,n_ports] = sys_rbg
@end example
This representation is a half-way house between the fig
(@pxref{Language fig (abg.fig)}) and m
(@pxref{Language m (abg.m)}) representations. It contains the
geometric information from the fig file in a form digestible by Octave
(@pxref{Octave}).
The five outputs of this function are:
@itemize @bullet
@item
rbonds
@item
rstrokes
@item
rcomponents
@item
rports
@item
n_ports
@end itemize
@emph{rbonds} is a matrix with
@itemize @bullet
@item
one row for each bond (@pxref{bonds})
@item
columns 1 and 2 containing the x,y coordinates for one end of the bond
@item
columns 3 and 4 containing the x,y coordinates for the corner of the bond
@item
columns 5 and 6 containing the x,y coordinates for the other end of the bond
@end itemize
@emph{rstrokes} is a matrix with (@pxref{strokes})
@itemize @bullet
@item
one row for each stroke or half-stroke
@item
columns 1 and 2 containing the x,y coordinates for one end of the stroke
@item
columns 3 and 4 containing the x,y coordinates for the other end of the stroke
@end itemize
@emph{rcomponents} is a matrix with (@pxref{components})
@itemize @bullet
@item
one row for each component
@item
columns 1 and 2 containing the x,y coordinates of the component
@item
the remaining columns containing fig file information
@end itemize
@emph{rports} is a matrix with (@pxref{Port labels})
@itemize @bullet
@item
one row for each component port that is explicitly labeled
@item
columns 1 and 2 containing the x,y coordinates of the port label
@item
column 3 contains the port number.
@end itemize
@emph{n_ports} is the number of ports associated with the system -- i.e. the
number of Named SS components (@pxref{Named SS components}).
@menu
* Transformation abg2rbg_fig2m::
@end menu
@node Transformation abg2rbg_fig2m, , Language m (rbg.m), Language m (rbg.m)
@comment node-name, next, previous, up
@subsubsection Transformation abg2rbg_fig2m
@cindex Transformation abg2rbg_fig2m
This transformation takes the acausal bond graph as a fig file
(@pxref{Language fig (abg.fig)}) and transforms it into a raw bond graph in
m-file format (@pxref{Language m (rbg.m)}).
This transformation is implemented in GNU awk (gawk).
It scans both the fig file (@pxref{Language fig (abg.fig)})
and the label file (@pxref{Labels (lbl)}) and generates the rbg
(@pxref{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.
@node Language m (abg.m), Language tex (abg.tex), Language m (rbg.m), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language m (abg.m)
@cindex Language m (abg.m)
@cindex bonds
@cindex components
@cindex n_ports
The acausal bond graph of system `sys' is represented as
an m file with heading:
@example
function [bonds,components,n_ports] = sys_abg
@end example
The three outputs of this function are:
@itemize @bullet
@item
bonds
@item
components
@item
n_ports
@end itemize
@emph{bonds} is a matrix with
@itemize @bullet
@item
one row for each bond
@item
the first column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{effort} variable.
@item
the second column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{flow} variable.
@end itemize
@emph{components} is a matrix with
@itemize @bullet
@item
one row for each component
@item
one column for each bond impinging on the component. The
@emph{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.
@end itemize
@emph{n_ports} is the number of ports associated with the system -- i.e. the
number of Named SS components (@pxref{Named SS components}).
@menu
* Arrow-orientated causality::
* Component-orientated causality::
* Transformation rbg2abg_m::
@end menu
@node Arrow-orientated causality, Component-orientated causality, Language m (abg.m), Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Arrow-orientated causality
@cindex Arrow-orientated causality
The arrow-orientated causality convention assigns -1, 0 or 1
to both the effort and flow (@pxref{Variables}) sides of a bond
to represent the causal stroke (@pxref{strokes})
as follows:
@vtable @code
@item 0
if there is no causality set.
@item 1
if the causal stroke is at the arrow end of the bond.
@item -1
if the causal stroke is at the other end of the bond.
@end vtable
@pxref{Component-orientated causality}.
@node Component-orientated causality, Transformation rbg2abg_m, Arrow-orientated causality, Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Component-orientated causality
@cindex Component-orientated causality
The component-orientated causality convention assigns -1, 0 or 1
to both the effort and flow (@pxref{Variables}) sides of a bond
to represent the causal stroke (@pxref{strokes})
as follows:
@vtable @code
@item 0
if there is no causality set.
@item 1
if the causal stroke is at the component end of the bond.
@item -1
if the causal stroke is at the other end of the bond.
@end vtable
@pxref{Arrow-orientated causality}.
@node Transformation rbg2abg_m, , Component-orientated causality, Language m (abg.m)
@comment node-name, next, previous, up
@subsubsection Transformation rbg2abg_m
@cindex 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.
@node Language tex (abg.tex), , Language m (abg.m), Acausal bond graph (abg)
@comment node-name, next, previous, up
@subsection Language tex (abg.tex)
@cindex Language tex (abg.tex)
For the purpose of producing a report (@pxref{Report}), @strong{MTT}
generates a LaTeX (@pxref{LaTeX}) file describing the bond graph and its
subsystems. Additional information may be supplied using the description
representation (@pxref{Detailed}).
@c node next prev up
@node Stripped acausal bond graph (sabg), Labels (lbl), Acausal bond graph (abg), Representations
@section Stripped acausal bond graph (sabg)
@cindex Stripped acausal bond graph (sabg)
@pindex Stripped acausal bond graph (sabg)
The stripped acausal bond graph is the acausal bond graph representation
(@pxref{Acausal bond graph (abg)}) without the artwork
(@pxref{artwork}). It is useful to check for mistakes by showing
precisely what is recognised by @strong{MTT}.
@menu
* Language fig (sabg.fig)::
* Stripped acausal bond graph (view)::
@end menu
@node Language fig (sabg.fig), Stripped acausal bond graph (view), Stripped acausal bond graph (sabg), Stripped acausal bond graph (sabg)
@subsection Language fig (sabg.fig)
@cindex Language fig (sabg.fig)
@pindex Language fig (sabg.fig)
The stripped acausal bond graph can be generated as a fig (@pxref{Fig})
file using
@example
mtt syst sabg fig
@end example
@node Stripped acausal bond graph (view), , Language fig (sabg.fig), Stripped acausal bond graph (sabg)
@subsection Stripped acausal bond graph (view)
@cindex Language m (view)
@cindex view Constrained-state Equations
This representation has the standard text view
(@pxref{Views}).
@node Labels (lbl), Structure (struc), Stripped acausal bond graph (sabg), Representations
@comment node-name, next, previous, up
@section Labels (lbl)
@cindex Labels
@cindex 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)
@itemize @bullet
@item Summary - lines beginning with #SUMMARY
@item Description - lines beginning with #DESCRIPTION
@item Alias - lines beginning with #ALIAS
@item Comments - lines beginning with #
@item Labels - other non-blank lines
@end itemize
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:
@enumerate
@item The component name @pxref{Component names}. This must be a valid
name (@pxref{Valid names}.
@item The component constitutive relationship @pxref{Component constitutive relationship}
@item The component arguments @pxref{Component arguments}
@end enumerate
Not each component @pxref{components} needs a label, only those which are explicitly
labeled on the Bond Graph @pxref{Acausal bond graph (abg)}.
@strong{MTT} checks whether all components labelled on the bond graph
have labels and vice versa.
If no lbl file exists, @strong{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
@example
mtt system_name lbl txt
@end example
An example lbl file (for the RC system is):
@example
%% 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
@end example
The old-style lbl files (@pxref{Old-style labels (lbl)}) are NO LONGER
supported -- you are encouraged to convert them ASAP.
@menu
* SS component labels ::
* Other component labels::
* Component names::
* Component constitutive relationship::
* Component arguments::
* Parameter declarations::
* Units declarations::
* Interface Control Definition::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
* Language tex (desc.tex)::
@end menu
@node SS component labels, Other component labels, Labels (lbl), Labels (lbl)
@comment node-name, next, previous, up
@subsection SS component labels
@cindex SS component labels
In addition to the label there are two information fields, @pxref{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
@vtable @code
@item info_field_1
effort
@item info_field_2
flow
@end vtable
Each of these two fields contains one of the following @emph{attributes}:
@vtable @code
@item external
indicates that the corresponding variable is a system input or
output
@item internal
indicates that the variable does not appear as a system output;
it is an error to label an input in this way.
@item a number
the value of the input; or the value of the (imposed) output
@item a symbol
the symbolic value of the input; or the value of the (imposed) output
@item 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.
@item 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.
@end vtable
Some examples are:
@example
%% 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
@end example
@node Other component labels, Component names, SS component labels , Labels (lbl)
@comment node-name, next, previous, up
@subsection Other component labels
@cindex Other component labels
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the constitutive relationship
(see @pxref{Constitutive relationship} and arguments of the
component as follows
@vtable @code
@item info_field_1
constitutive relationship
@item info_field_2
parameters
@end vtable
Some examples are:
@example
%Armature resistance
r_a lin effort,r_a
%Gearbox ratio
n lin effort,n
@end example
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing})
subsystems.
@menu
* Component names::
* Component constitutive relationship::
* Component arguments::
* Aliases::
* Parameter passing::
* Old-style labels (lbl)::
@end menu
@node Component names, Component constitutive relationship, Other component labels, Labels (lbl)
@comment node-name, next, previous, up
@subsection Component names
@cindex Component names
The component name field must contain a valid name (@pxref{Valid names} corresponding to the
name (the bit after the :) of each named component (@pxref{components})
on the bond graph (@pxref{Acausal bond graph (abg)}).
@node Component constitutive relationship, Component arguments, Component names, Labels (lbl)
@comment node-name, next, previous, up
@subsection Component constitutive relationship
@cindex 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 @strong{MTT}:
@enumerate
@item A generic constitutive relationship such as @var{lin} (the generic
linear constitutive relationship.
@item A local constitutive relationship with the same name as the
component type
@item The @var{SS} constitutive relationship reserved for @var{SS}
components.
All labels for @var{SS} components must contain SS in this field.
@end enumerate
@node Component arguments, Parameter declarations, Component constitutive relationship, Labels (lbl)
@comment node-name, next, previous, up
@subsection Component arguments
@cindex Component arguments
@node Parameter declarations, Units declarations, Component arguments, Labels (lbl)
@comment node-name, next, previous, up
@subsection Parameter declarations
@cindex parameter declarations
@pindex parameter declarations
@pindex PAR
@pindex NOTPAR
@pindex VAR
@pindex NOTVAR
It is sometimes useful to use parameters (in addition to those implied by
the Component arguments @pxref{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:
@example
#PAR par1
#PAR par2
@end example
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
@example
#NOTPAR foo
#NOTPAR bar
@end example
For comapability with old code, VAR may be used in place of PAR, but
this usage is deprecated.
@node Units declarations, Interface Control Definition, Parameter declarations, Labels (lbl)
@comment node-name, next, previous, up
@subsection Units declarations
@cindex units declarations
@pindex units declarations
@pindex UNITS
The units and domains of ports (@pxref{Ports}) are declared as:
@example
#UNITS Port_name domain effort_units flow_units
@end example
where "Port_name" is the name of the port, domain is one of:
@vtable @code
@item electrical
the electrical domain
@item translational
the translational mechanical domain
@item rotational
the rotational mechanical domain
@item fluid
the fluid domain
@item thermal
the thermal domain
@end vtable
and effort_units and flow_units are corresponding units for the effort
and the flow.
Allowed units are those defined in the @strong{units} package.
@strong{MTT} checks that units are
@itemize @bullet
@item defined consistently with the domain
@item the same for connected ports when both ports have defined units.
@end itemize
No checks are done if one or both ends of a bond are not connected to a
port with defined units.
@node Interface Control Definition, Aliases, Units declarations, Labels (lbl)
@comment node-name, next, previous, up
@subsection Interface Control Definition
@cindex ICD (label file directive)
It is sometimes useful to be able to automatically generate a set of
assignments mapping @strong{MTT} inputs and outputs to an external interface
definition. This can be achieved with use of the @emph{#ICD} directive.
@example
#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
@end example
The ICD directive consists of 3 whitespace delimited fields:
@enumerate
@item [%|#]ICD
@item component name
@item Four comma (,) or semi-colon (;) delimited fields:
@enumerate
@item name of effort parameter
@item unit of effort parameter
@item name of flow parameter
@item unit of flow parameter
@end enumerate
@end enumerate
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 @pxref{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
@example
mtt sys ICD txt
@end example
will generate a text file containing a list of mappings:
@example
## 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
@end example
A set of assignments can be generated with the command
@example
mtt sys ICD m
@end example
resulting in:
@example
# 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);
@end example
A similar file will be generated by the command
@example
mtt sys ICD cc
@end example
@node Aliases, Parameter passing, Interface Control Definition, Labels (lbl)
@comment node-name, next, previous, up
@subsection Aliases
@cindex aliases
@pindex aliases
Aliases provide a convenient mechanism for relabelling words appearing
in the label file (@pxref{Labels (lbl)}). There are three contexts in
which the alias mechanism is used:
@enumerate
@item renaming ports (@pxref{Port aliases}),
@item renaming parameters (@pxref{Parameter aliases}) and
@item renaming components (@pxref{Component aliases}).
@end enumerate
All three mechanisms use the same form of statement within the label
file
@example
%ALIAS short_label real_label
@end example
@strong{MTT} distinguishes between the three forms as follows:
@itemize @bullet
@item Parameter aliases: `short_label' starts with a `$'
@item Component aliases: `real_label' contains the directory separator
`/'
@item Port aliases: neither of the above
@end itemize
@menu
* Port aliases::
* Parameter aliases::
* CR aliases::
* Component aliases::
@end menu
@node Port aliases, Parameter aliases, Aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Port aliases
@cindex port aliases
@pindex port aliases
Aliases provide a way of refering to (@pxref{Port labels}) or vector port labels (@pxref{Vector
port labels}) on the bond graph using a short-hand notation. With in a
component label file (@pxref{Labels (lbl)}) statements of the following
forms can occur
@example
%ALIAS short_label real_label
@end example
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
@example
%ALIAS short_label_1 real_label
%ALIAS short_label_2 real_label
%ALIAS short_label_3 real_label
@end example
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
@example
%ALIAS short_label_1|short_label_2|short_label_3 real_label
@end example
The alias feature is particularly powerful in conjunction with vector
port labels (@pxref{Vector port labels}) and the port label default
(@pxref{Port label defaults}) mechanisms. For example, a component with
5 ports appearing in the lbl file as:
@example
[Hydraulic_in] external external
[Hydraulic_out] external external
[Power_Shaft] external external
[Thermal_in] external external
[Thermal_out] external external
@end example
together with the following statements in the label file:
@example
%ALIAS in Thermal_in,Hyydraulic_in
%ALIAS out Thermal_out,Hydraulic_out
%ALIAS shaft|power Power_Shaft
@end example
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.
@node Parameter aliases, CR aliases, Port aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Parameter aliases
@cindex parameter aliases
@pindex parameter aliases
Parameter aliases are of the form
@example
%ALIAS $n actual parameter
@end example
where n is an integer (unique within the label file).
For example
@example
%ALIAS $1 c_v
%ALIAS $2 density,ideal_gas,r
%ALIAS $3 alpha
%ALIAS $4 flow,k_p
@end example
Assigns four symbolic parameters to the corresponding strings These four
parameters (@code{$1}--@code{$4}) can then be used for parameter
passing(@pxref{Parameter passing}).
@node CR aliases, Component aliases, Parameter aliases, Aliases
@comment node-name, next, previous, up
@subsubsection CR aliases
@cindex CR aliases
@pindex CR aliases
CR aliases are of the form
@example
%ALIAS $an actual parameter
@end example
where n is an integer (unique within the label file).
For example
@example
%ALIAS $a1 lin
@end example
assigns the symbolic parameter to be lin. This parameter @code{$1} can
then be used for passing a diofferent cr to the
component (@pxref{Parameter passing}).
@node Component aliases, , CR aliases, Aliases
@comment node-name, next, previous, up
@subsubsection Component aliases
@cindex component aliases
@pindex component aliases
Component aliases are of the form
@example
%ALIAS Component_name Component_location
@end example
An example appears in the following label file fragment
@example
...
%ALIAS wPipe CompressibleFlow/wPipe
%ALIAS Poly CompressibleFlow/Poly
....
@end example
The two components `wPipe' and `Poly' are both to be found within the
library `Compressible flow' and the respective subdirectories. This
follows the @strong{MTT} convention that compound components
(@pxref{Compound components}) live within a directory of the same name.
@node Parameter passing, Old-style labels (lbl), Aliases, Labels (lbl)
@comment node-name, next, previous, up
@subsection Parameter passing
@cindex Parameter passing
@strong{MTT} supports parameter-passing to subsystems within label files
(@pxref{Labels (lbl)}). Within a subsystem, explicit constitutive
relationships and parameters (or groups thereof) can be replaced by
postitional parameters such as @code{$1}, @code{$2} etc. Although this
can be done directly, it is recommended that this is done via the alias
mechanism (@pxref{Parameter aliases}).
In a subsystem
@code{$i}, is replaced by the ith field of a colon @code{;} separated
field in the calling label file. This field may include commas @code{,}
and the four arithmetic operators @code{+}, @code{-}, @code{*} and
@code{/}.
For example, consider the following example label file fragment (associated with a
component called Pump:
@example
...
%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
@end example
The 4 parameters @code{$1}, @code{$2}, @code{$3}, and @code{$4} can be
passed from a higher level component as in the following label file
fragment:
@example
% 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
@end example
Thus in component `comp':
@itemize @bullet
@item @code{$1} is replaced by c_v
@item @code{$2} is replaced by rho,ideal_gas
@item @code{$3} is replaced by alpha
@item @code{$4} is replaced by effort,k_c
@end itemize
whereas in component `turb' the first three parameters are the same but
@itemize @bullet
@item @code{$4} is replaced by effort,k_t
@end itemize
@node Old-style labels (lbl), Language tex (desc.tex), Parameter passing, Labels (lbl)
@comment node-name, next, previous, up
@subsection Old-style labels (lbl)
@cindex Old-style labels
@cindex lbl
Old syle labels (mtt version 2.x) are supported by mtt version
3.x. However, you are advised to use the new form (@pxref{Labels
(lbl)}).
Each line of the @code{_label.txt} file is of one of three forms:
@enumerate
@item
Contains three fields (separated by white space) of the form
@example
label field_1 field_2
@end example
@item
Blank
@item
Preceded by %
@end enumerate
Only the first is noticed by @strong{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:
@itemize @bullet
@item
SS components, @pxref{SS components}.
@item
Other components, @pxref{components}.
@end itemize
Named SS component, @pxref{Named SS components} never have labels.
@menu
* SS component labels (old-style)::
* Other component labels (old-style)::
* Parameter passing (old-style)::
@end menu
@node SS component labels (old-style), Other component labels (old-style), Old-style labels (lbl), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection SS component labels (old-style)
@cindex SS component labels (old-style)
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the effort and flow of the components as follows
@vtable @code
@item info_field_1
effort
@item info_field_2
flow
@end vtable
Each of these two fields contains one of the following @emph{attributes}:
@vtable @code
@item
external
indicates that the corresponding variable is a system input or
output
@item internal
indicates that the variable does not appear as a system output;
it is an error to label an input in this way.
@item a number
the value of the input; or the value of the (imposed) output
@item a symbol
the symbolic value of the input; or the value of the (imposed) output
@item 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.
@item 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.
@end vtable
Some examples are:
@example
%Label field1 field2
ss1 external external
ss2 0 external
@end example
@node Other component labels (old-style), Parameter passing (old-style), SS component labels (old-style), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection Other component labels (old-style)
@cindex Other component labels (old-style)
In addition to the label there are two information fields,
@pxref{Labels (lbl)}.
They correspond to the constitutive relationship
(see @pxref{Constitutive relationship} and arguments of the
component as follows
@vtable @code
@item info_field_1
constitutive relationship
@item info_field_2
parameters
@end vtable
Some examples are:
@example
%Armature resistance
r_a lin effort,r_a
%Gearbox ratio
n lin effort,n
@end example
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing (old-style)})
subsystems.
@node Parameter passing (old-style), , Other component labels (old-style), Old-style labels (lbl)
@comment node-name, next, previous, up
@subsubsection Parameter passing (old-style)
@cindex Parameter passing (old-style)
@strong{MTT} supports parameter-passing to (@pxref{Parameter passing (old-style)})
subsystems within label files (@pxref{Labels (lbl)}). Within a subsystem,
explicit constitutive relationships and parameters (or groups thereof)
can be replaced by
@code{$1}, @code{$2}, etc.
In a subsystem
@code{$i}, is replaced by the ith field of a colon @code{;} separated
field in the calling label file. This field may include commas @code{,}.
For example subsystem ROD contains the following lines in the label
file:
@example
%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
@end example
This can be used in a higher-level lbl (@pxref{Labels (lbl)}) file as:
@example
%SUMMARY Pendulum example from Section 10.3 of "Metamodelling"
%Rod parameters
rod none l;l;j;m
@end example
@menu
* Language tex (desc.tex)::
@end menu
@node Language tex (desc.tex), , Old-style labels (lbl), Labels (lbl)
@comment node-name, next, previous, up
@subsection Language tex (desc.tex)
@cindex Language tex (desc.tex)
This file may contain any LaTeX compatible commands. Any mathematics
should conform to the AMSmath package.
@node Structure (struc), Constitutive Relationship (cr), Labels (lbl), Representations
@comment node-name, next, previous, up
@section Structure (struc)
@cindex Structure
@cindex 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.
@menu
* Language txt (struc.txt)::
* Language tex (struc.tex)::
* Structure (view)::
@end menu
@node Language txt (struc.txt), Language tex (struc.tex), Structure (struc), Structure (struc)
@comment node-name, next, previous, up
@subsection Language txt (struc.txt)
@cindex Language txt (struc.txt)
This text tile contains a description of the system structure
(@pxref{Structure (struc)} with 5 tab-separated columns containing the
following information:
@vtable @code
@item type
input, output state or nonstate
@item
index
an integer corresponding to the array index
@item
component name
the name of the component corresponding to the variable
@item system name
the name of the system containing the component
@item repetition
an integer corresponding to the repetition of a repeated subsystem.
@end vtable
An example of such a file (corresponding to rc) (@pxref{Quick start}) is:
@example
input 1 e1 rc 1
output 1 e2 rc 1
state 1 c rc 1
@end example
@node Language tex (struc.tex), Structure (view), Language txt (struc.txt), Structure (struc)
@comment node-name, next, previous, up
@subsection Language tex (struc.tex)
@cindex Language tex (struc.tex)
This LaTeX (@pxref{LaTeX}) file contains a description of the system structure
(@pxref{Structure (struc)} in @code{longtable} format. It is a useful
item to include in a report(@pxref{Report}).
@node Structure (view), , Language tex (struc.tex), Structure (struc)
@subsection Language tex (view)
@cindex Structure (view)
@cindex view Structure
This representation has the standard text view
(@pxref{Views}).
@node Constitutive Relationship (cr), Parameters, Structure (struc), Representations
@comment node-name, next, previous, up
@section Constitutive relationship (cr)
@cindex Constitutive relationship
The constitutive relationship (@pxref{Constitutive relationship})
of a simple component (@pxref{Simple components} is
defined in the symbolic algebra language Reduce (@pxref{Reduce}).
The constitutive relationship of a compound components
(@pxref{Compound components})
is implied by the constitutive relationships of its constituent components.
@menu
* Predefined constitutive relationships::
* DIY constitutive relationships::
* Unresolved constitutive relationships::
* Unresolved constitutive relationships - Octave::
* Unresolved constitutive relationships - c++::
@end menu
@node Predefined constitutive relationships, DIY constitutive relationships, Constitutive Relationship (cr), Constitutive Relationship (cr)
@comment node-name, next, previous, up
@subsection Predefined constitutive relationships
@cindex Predefined constitutive relationships
Some common cr's are predefined by MTT; these are:
@vtable @code
@item lin
a linear constitutive relationship
@item exotherm
an exothermic reaction
@end vtable
@menu
* lin::
* exotherm::
@end menu
@node lin, exotherm, Predefined constitutive relationships, Predefined constitutive relationships
@comment node-name, next, previous, up
@subsubsection lin
@findex lin
The constitutive relationship @code{lin} is predefined for the following
components.
@vtable @code
@item R
(one-port) R component
@item TF
transformer
@item GY
gyrator
@item MTF
modulated transformer
@item MGY
modulated gyrator
@item FMR
flow-modulated resistor
@end vtable
Lin takes two arguments in the form causality,gain
@vtable @code
@item causality
the causality (effort or flow) of the @emph{input} to the
constitutive relationship
@item gain
the gain of the component when the input causality is as
specified in the first argument.
@end vtable
For example the arguments
@example
flow,r
@end example
given to an R component corresponds to
@example
e = rf
@end example
if if the input causality is flow
or
@example
f = e/r
@end example
if if the input causality is effort.
@node exotherm, , lin, Predefined constitutive relationships
@comment node-name, next, previous, up
@subsubsection exotherm
@findex exotherm
@node DIY constitutive relationships, Unresolved constitutive relationships, Predefined constitutive relationships, Constitutive Relationship (cr)
@comment node-name, next, previous, up
@subsection DIY constitutive relationships
@cindex DIY constitutive relationships
You can write your own constitutive relationships using Reduce
(@pxref{Reduce}). This requires some understanding as to how
@strong{MTT} represent the elementary system equations
(@pxref{Elementary system equations}). Looking at the predefined
constitutive relationships is a good way to get started
(@pxref{File structure}).
@node Unresolved constitutive relationships, Unresolved constitutive relationships - Octave, DIY constitutive relationships, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships
@cindex Unresolved constitutive relationships
Consider the following CR file.
@example
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);
@end example
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
(@pxref{Unresolved constitutive relationships - Octave}) or c++ code as
(@pxref{Unresolved constitutive relationships - c++}) appropriate.
@node Unresolved constitutive relationships - Octave, Unresolved constitutive relationships - c++, Unresolved constitutive relationships, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships - Octave
@cindex 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:
@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
@end example
This will be automatically loaded into octave.
@node Unresolved constitutive relationships - c++, , Unresolved constitutive relationships - Octave, Constitutive Relationship (cr)
@subsection Unresolved constitutive relationships - c++
@cindex Unresolved constitutive relationships - Octave
Following the example of the previous section, the unresolved CR `tank'
can be expressed in c++ code. For example:
@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;
@end example
To make sure that this is used in system `model', the model_cr.h file
must be as follows:
@example
// CR headers for system model
#include "tank.c"
@end example
@node Parameters, Causal bond graph (cbg), Constitutive Relationship (cr), Representations
@comment node-name, next, previous, up
@section Parameters
@cindex Parameters
In general, lbl (@pxref{Labels (lbl)}) files contain symbolic
parameters. @strong{MTT} provides three ways of substituting for these
parameters:
@itemize @bullet
@item
symbolic substitution
@item
symbolic substitution for simplification of displayed equations
@item
numeric
@end itemize
@menu
* Symbolic parameters (subs.r)::
* Symbolic parameters for simplification (simp.r)::
* Numeric parameters (numpar)::
@end menu
@node Symbolic parameters (subs.r), Symbolic parameters for simplification (simp.r), Parameters, Parameters
@comment node-name, next, previous, up
@subsection Symbolic parameters (subs.r)
@cindex Symbolic parameters
@vindex subs.r
This file contains reduce statements to symbolically change the
expressions describing the system.
For example, a useful set of trig substitutions is:
@example
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));
@end example
@node Symbolic parameters for simplification (simp.r), Numeric parameters (numpar), Symbolic parameters (subs.r), Parameters
@comment node-name, next, previous, up
@subsection Symbolic parameters for simplification (simp.r)
@cindex Symbolic parameters for simplification
@vindex simp.r
This file contains reduce statements to symbolically change the
expressions describing the system. Unlike the subs.r file
(@pxref{Symbolic parameters (subs.r)}) it does not affect all system
transformations; only those converting to LaTeX form.
@node Numeric parameters (numpar), , Symbolic parameters for simplification (simp.r), Parameters
@comment node-name, next, previous, up
@subsection Numeric parameters (numpar)
@cindex Numeric parameters
When computing time and frequency responses; or when evaluating
functions in Octave (@pxref{Octave}); symbolic parameters need numerical
instantiations.
The numpar representation provides the relevant @emph{numerical}
information. It comes in a number of languages:
@ftable @code
@item txt
a textual description of the parameter values -- this is the
defining representation (@pxref{Defining representations}).
@item m
readable by @code{octave} a high-level interactive language for numerical
computation -- translated by @strong{mtt} from the txt version.
@item c
readable by @code{gcc} a c compiler -- translated by @strong{mtt} from the txt version.
@end ftable
@menu
* Text form (numpar.txt)::
@end menu
@node Text form (numpar.txt), , Numeric parameters (numpar), Numeric parameters (numpar)
@comment node-name, next, previous, up
@subsubsection Text form (numpar.txt)
@cindex Numeric parameters
This is the textual form of the numerical parameters representation
(@pxref{Numeric parameters (numpar)}). Lines are either
@ftable @code
@item assignment statements
variable = value
@item comments
lines beginning with #
@item commented assignment statements
variable = value # comments
@end ftable
An example file is:
@example
# Numerical parameter file (rc_numpar.txt)
# Generated by MTT at Mon Jun 16 15:10:17 BST 1997
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Version control history
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% $Id$
# %% $Log$
# %% 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)
@end example
As usual, @strong{MTT} provides a default text file to be edited by the
user (@pxref{Text editors}).
@node Causal bond graph (cbg), Elementary system equations, Parameters, Representations
@comment node-name, next, previous, up
@section Causal bond graph (cbg)
@cindex Causal bond graph (cbg)
The causal bond graph is the causally complete version of the
Acausal bond graph (@pxref{Acausal bond graph (abg)}).
To create the causal bond graph of system `sys' in language fig type:
@example
mtt sys cbg fig
@end example
To create the causal bond graph of system `sys' in language m type:
@example
mtt sys cbg m
@end example
To view the causal bond graph of system `sys' type:
@example
mtt sys cbg view
@end example
@menu
* Language fig (cbg.fig)::
* Language m (cbg.m)::
@end menu
@node Language fig (cbg.fig), Language m (cbg.m), Causal bond graph (cbg), Causal bond graph (cbg)
@subsection Language fig (cbg.fig)
@cindex Language fig (cbg.fig)
@pindex Language fig (cbg.fig)
The fig file is created by @strong{MTT}. It is identical to the
corresponding acausal representation (@pxref{Language fig (abg.fig)})
except that
@itemize @bullet
@item
the new causal strokes are added (using a double thickness line in blue)
@item
components that are undercausal are bold and green
@item
components that are overcausal are bold and red
@end itemize
@node Language m (cbg.m), , Language fig (cbg.fig), Causal bond graph (cbg)
@comment node-name, next, previous, up
@subsection Language m (cbg.m)
@cindex Language m (cbg.m)
@cindex cbonds
@cindex status
The causal bond graph of system `sys' is represented as
an m file with heading:
@example
function [cbonds,status] = sys_cbg
@end example
The two outputs of this function are:
@itemize @bullet
@item
cbonds
@item
status
@end itemize
@emph{cbonds} is a matrix with
@itemize @bullet
@item
one row for each bond
@item
the first column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{effort} variable.
@item
the second column contains the arrow-orientated
(@pxref{Arrow-orientated causality})
causality of the @emph{flow} variable.
@end itemize
@emph{status} is a matrix with
@itemize @bullet
@item
one row for each component
@item
the first column contains 1 if the component is overcausal; 0 if the
component is causally complete and -1 if the component is undercausal.
@end itemize
A successful model would therefore have all zeros in the status matrix.
@menu
* Transformation abg2cbg_m::
@end menu
@node Transformation abg2cbg_m, , Language m (cbg.m), Language m (cbg.m)
@comment node-name, next, previous, up
@subsubsection Transformation abg2cbg_m
@cindex Transformation abg2cbg_m
This transformation takes the acausal bond graph as an m file
(@pxref{Language m (abg.m)}) and transforms it into a causal bond graph in
m-file format (@pxref{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.
@node Elementary system equations, Differential-Algebraic Equations, Causal bond graph (cbg), Representations
@comment node-name, next, previous, up
@section Elementary system equations (ese)
@cindex Elementary system equations
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 (@pxref{Reduce}) language.
Because these are based on a causally complete system, these assignment
statements are directly soluble by substitution.
Unlike early versions of @strong{MTT}, @strong{MTT} does @emph{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.
@example
cr(arguments,out_causality,outport,
input_1, causality_1, port_1,
....
input_i, causality_i, port_i,
....
input_n, causality_n, port_n
);
@end example
where the symbols have the following meaning
@vtable @code
@item arguments
the constitutive relationship arguments
@item out_causality
the causality (effort or flow) of the output variable
(@pxref{Variables})
@item outport
the number (integer) of the output port of the system
@item input_i
the ith input to the component
@item causality_i
the causality (effort or flow) of the ith input variable
(@pxref{Variables})
@item port_i
the number (integer) of the ith input port of the system
@end vtable
An example for a resistor with linear constitutive relationship is:
@example
rc_1_bond4_flow := lin(flow,r,flow,1,
rc_1_bond4_effort,effort,1
);
@end example
@menu
* Transformation cbg2ese_m2r::
@end menu
@node Transformation cbg2ese_m2r, , Elementary system equations, Elementary system equations
@comment node-name, next, previous, up
@subsubsection Transformation cbg2ese_m2r
@cindex Transformation cbg2ese_m2r
@cindex Structure
@cindex def.r
This transformation takes the causal bond graph as an m file
(@pxref{Language m (cbg.m)}) and transforms it into elementary system
equations
in Reduce (@pxref{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 @file{sys_def.r}.
@node Differential-Algebraic Equations, Constrained-state Equations, Elementary system equations, Representations
@section Differential-Algebraic Equations (dae)
@cindex Differential-Algebraic Equations
@cindex DAE
The system differential algebraic equations describe the system dynamics together
together with any algebraic constraints.
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys dae lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are five sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item z
the system nonstates (corresponding to C and I components with derivative
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item ui
the @emph{internal} system inputs (corresponding to SS components
with internal attribute) used to solve algebraic loops
(@pxref{Algebraic loops}).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
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:
@enumerate
@item
the derivative of x (dx/dt)
@item
z
@item
w=0 (the algebraic equations)
@item
y
@end enumerate
@menu
* Differential-Algebraic Equations (reduce)::
* Differential-Algebraic Equations (m)::
@end menu
@node Differential-Algebraic Equations (reduce), Differential-Algebraic Equations (m), Differential-Algebraic Equations, Differential-Algebraic Equations
@subsection Language reduce (dae.r)
@cindex Differential-Algebraic Equations (reduce)
@cindex dae.r
The system DAEs (@pxref{Differential-Algebraic Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTz
z -- the system nonstates (corresponding to C and I components with derivative
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item mttv
ui -- the @emph{internal} system inputs (corresponding to SS components
with internal attribute) used to solve algebraic loops
(@pxref{Algebraic loops}).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
@menu
* Transformation ese2dae_r::
@end menu
@node Transformation ese2dae_r, , Differential-Algebraic Equations (reduce), Differential-Algebraic Equations (reduce)
@subsubsection Transformation ese2dae_r
@cindex Transformation ese2dae_r
@pindex ese2dae_r
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to combine the elementary system
equations (@pxref{Elementary system equations}) with the
constitutive relationships (@pxref{Constitutive relationship})
and simplify the result.
@node Differential-Algebraic Equations (m), , Differential-Algebraic Equations (reduce), Differential-Algebraic Equations
@subsection Language m (dae.m)
@cindex Differential-Algebraic Equations (m)
@cindex dae.m
The system DAEs (@pxref{Differential-Algebraic Equations})
are represented in the m (@pxref{m}) language as
two m-functions of the form:
@example
function resid = sys_dae(dx,x,t)
function y = sys_dae(dx,x,t)
@end example
Where x is the dae @emph{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.
@menu
* Transformation dae_r2m::
@end menu
@node Transformation dae_r2m, , Differential-Algebraic Equations (m), Differential-Algebraic Equations (m)
@subsubsection Transformation dae_r2m
@cindex Transformation dae_r2m
@pindex dae_r2m
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to rewrite the elementary system
equations (@pxref{Elementary system equations}) in m-file
format (@pxref{m}) . Numerical parameters are declared as global.
@node Constrained-state Equations, Ordinary Differential Equations, Differential-Algebraic Equations, Representations
@section Constrained-state Equations (cse)
@cindex Constrained-state Equations
@cindex ODE
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:
@example
E(x) dx/dt = f(x,u)
y = g(x,u)
@end example
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 @code{lang} for system
@code{sys} by:
@example
mtt sys cse lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are three sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
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:
@enumerate
@item
the derivative of x (dx/dt)
y
@end enumerate
@menu
* Constrained-state Equations (reduce)::
* Constrained-state Equations (view)::
@end menu
@node Constrained-state Equations (reduce), Constrained-state Equations (view), Constrained-state Equations, Constrained-state Equations
@subsection Language reduce (cse.r)
@cindex Constrained-state Equations (reduce)
@cindex cse.r
The system CSEs (@pxref{Constrained-state Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
together with the array containing the elements of the E matrix.
@menu
* Transformation dae2cse_r::
@end menu
@node Transformation dae2cse_r, , Constrained-state Equations (reduce), Constrained-state Equations (reduce)
@subsubsection Transformation dae2cse_r
@cindex Transformation dae2cse_r
@pindex dae2cse_r
This transformation (@pxref{What is a Transformation?})
Reduce (@pxref{Reduce}) to find various Jacobians which are combined to
find the E matrix and the
constrained-state equations (@pxref{Constrained-state Equations}).
@node Constrained-state Equations (view), , Constrained-state Equations (reduce), Constrained-state Equations
@subsection Language m (view)
@cindex Constrained-state Equations (view)
@cindex view Constrained-state Equations
This representation has the standard text view
(@pxref{Views}).
@node Ordinary Differential Equations, Descriptor matrices, Constrained-state Equations, Representations
@section Ordinary Differential Equations
@cindex Ordinary Differential Equations
@cindex ODE
The system ordinary differential equations describe the system dynamics.
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys ode lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
There are three sets of variables describing the system:
@vtable @code
@item x
the system states (corresponding to C and I components with integral
causality.
@item u
the system inputs (corresponding to SS components
with external attribute).
@item y
the system outputs (corresponding to SS components
with external attribute).
@end vtable
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:
@enumerate
@item
the derivative of x (dx/dt)
y
@end enumerate
@menu
* Ordinary Differential Equations (reduce)::
* Ordinary Differential Equations (m)::
* Ordinary Differential Equations (view)::
@end menu
@node Ordinary Differential Equations (reduce), Ordinary Differential Equations (m), Ordinary Differential Equations, Ordinary Differential Equations
@subsection Language reduce (ode.r)
@cindex Ordinary Differential Equations (reduce)
@cindex ode.r
The system ODEs (@pxref{Ordinary Differential Equations})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the algebraic expressions for the
right hand sides of each set of equations. The arrays are:
@vtable @code
@item MTTx
x -- the system states (corresponding to C and I components with integral
causality.
@item MTTu
u -- the system inputs (corresponding to SS components
with external attribute).
@item MTTy
y -- the system outputs (corresponding to SS components
with external attribute).
@end vtable
@menu
* Transformation cse2ode_r::
@end menu
@node Transformation cse2ode_r, , Ordinary Differential Equations (reduce), Ordinary Differential Equations (reduce)
@subsubsection Transformation cse2ode_r
@cindex Transformation cse2ode_r
@pindex cse2ode_r
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to invert the E matrix of the
constrained-state equations (@pxref{Constrained-state Equations})
and simplify the result.
@node Ordinary Differential Equations (m), Ordinary Differential Equations (view), Ordinary Differential Equations (reduce), Ordinary Differential Equations
@subsection Language m (ode.m)
@cindex Ordinary Differential Equations (m)
@cindex ode.m
The system ODEs (@pxref{Ordinary Differential Equations})
are represented in the m (@pxref{m}) language as
two m-functions of the form:
@example
function dx = sys_ODE(x,t)
function y = sys_ODE(dx,x,t)
@end example
Where x is the ODE @emph{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.
@menu
* Transformation ode_r2m::
@end menu
@node Transformation ode_r2m, , Ordinary Differential Equations (m), Ordinary Differential Equations (m)
@subsubsection Transformation ode_r2m
@cindex Transformation ode_r2m
@pindex ode_r2m
This transformation (@pxref{What is a Transformation?})
uses Reduce (@pxref{Reduce}) to rewrite the
ordinary differential equations
(@pxref{Ordinary Differential Equations}) in m-file
format (@pxref{m}) . Numerical parameters are declared as global.
@node Ordinary Differential Equations (view), , Ordinary Differential Equations (m), Ordinary Differential Equations
@subsection Language m (view)
@cindex Ordinary Differential Equations (view)
@cindex view Ordinary Differential Equations
This representation has the standard text view
(@pxref{Views}).
@node Descriptor matrices, Report, Ordinary Differential Equations, Representations
@section Descriptor matrices (dm)
@cindex Descriptor matrices
@cindex dm
The system descriptor matrices A, B, C, D and E describe the
@emph{linearised} system dynamics in the form
@example
E dx/dt = Ax + Bu
y = Cx + Du
@end example
They are generated in language @code{lang} for system
@code{sys} by:
@example
mtt sys dm lang
@end example
Valid languages are:
@vtable @code
@item r
reduce (@pxref{Reduce}).
@item m
m (@pxref{m}).
@item view
reduce (@pxref{Views}).
@end vtable
@menu
* Descriptor matrices (reduce)::
* Descriptor matrices (m)::
@end menu
@node Descriptor matrices (reduce), Descriptor matrices (m), Descriptor matrices, Descriptor matrices
@subsection Language reduce (dm.r)
@cindex Descriptor matrices (reduce)
@cindex dm.r
The system descriptor matrices (@pxref{Descriptor matrices})
are represented in the reduce (@pxref{Reduce}) language as
arrays containing the four matrices. The arrays are:
@vtable @code
@item MTTA
A
@item MTTB
B
@item MTTA
C
@item MTTD
D
@item MTTE
E
@end vtable
@node Descriptor matrices (m), , Descriptor matrices (reduce), Descriptor matrices
@subsection Language m (dm.m)
@cindex Descriptor matrices (m)
@cindex dm.m
The system descriptor matrices (@pxref{Descriptor matrices})
are represented in the m (@pxref{m}) language as
an m-function of the form:
@example
function [A,B,C,D,E] = sys_dm
@end example
System numeric parameters (@pxref{Numeric parameters})
are passed via global variables defined in the _numpar.m file.
@c (@pxref{numpar.m}).
Thus the system descriptor matrices are
typically generated in Octave (@pxref{Octave}) as follows:
@example
sys_numpar
[A,B,C,D,E] = sys_dm
@end example
Parameters can be changed from their default values by entering
their values directly into Octave (@pxref{Octave}) and then invoking
@code{sys_dm}; for example
@example
sys_numpar
par_1 = 25
par_2 = par_1 + 3
[A,B,C,D,E] = sys_dm
@end example
@node Report, , Descriptor matrices, Representations
@section Report (rep)
@cindex Report
@cindex rep
@strong{MTT} has a report-generator feature. The user specifies the
report contents in a text file (@pxref{Report (text)}) using an
appropriate text editor (@pxref{Text editors}).
For example, the report can be viewed by typing
@example
mtt system rep view
@end example
@menu
* Report (text)::
* Report (view)::
@end menu
@node Report (text), Report (view), Report, Report
@subsection Language text (rep.txt)
@cindex Report (text)
@cindex rep.txt
The user specifies the report contents in a text file (@pxref{Report
(text)}) using an appropriate text editor (@pxref{Text editors}).
The text file contains lines which are either comments (indicated by %)
or valid @strong{MTT} commands. The report will then contain appropriate
sections. The following languages are supported by the report generator:
@ftable @code
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item r
@code{reduce} a high-level interactive language for symbolic
computation.
@item tex
@code{latex} a text processor.
@item ps
@code{ghostview} another document viewer.
@item c
@code{gcc} a c compiler.
@end ftable
For example:
@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
@end example
The acausal bond graph (abg) (@pxref{Acausal bond graph (abg)}) with the
tex language is handled in a special way: the acausal Bond Graph in
fig format (@pxref{Language fig (abg.fig)}), the label file (@pxref{Labels (lbl)})
the description file (@pxref{Detailed}), together with
corresponding subsystems are included in the report. It is recommended
that the first (non-comment line) in the file should be:
@example
mtt <system> abg tex
@end example
where @code{<system>} is the name of the (top-level) system.
As usual, @strong{MTT} provides a default text file to be edited by the
user (@pxref{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.
@node Report (view), , Report (text), Report
@subsection Language view
@cindex Report (view)
@cindex view Report
This representation has the standard text view
(@pxref{Views}).
@node Extending MTT, Documentation, Representations, Top
@comment node-name, next, previous, up
@chapter Extending MTT
@cindex Extending MTT
@cindex Make
@strong{MTT} has a number of built-in mechanisms for the user to extend
its capabilities. As @strong{MTT} is based on `Make' it is unsurprising
that some of these involve the creation of `make files'.
@menu
* Makefiles::
* New (DIY) representations::
* Component library ::
@end menu
@node Makefiles, New (DIY) representations, Extending MTT, Extending MTT
@comment node-name, next, previous, up
@section Makefiles
@cindex Makefiles
If a file called `Makefile' exists in the current directory,
@strong{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 @strong{MTT} unaware. Such a function can be
created using the makefile. An example `Makefile' is
@example
# 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
@end example
All of the files in the line stating `all:' are created when
@strong{MTT} is executed (if they don't already exist).
@node New (DIY) representations, Component library , Makefiles, Extending MTT
@comment node-name, next, previous, up
@section New (DIY) representations
@cindex New representations
@cindex DIY representations
It may be convenient to create new representations for @strong{MTT}; in
particular, it is nice to be able to include the result of some
numerical or symbolic computations within an @strong{MTT} report
(@pxref{Report}). Therefore @strong{MTT} provides a mechanism for doing
this.
Future extensions of @strong{MTT} will use such representations stored
in $MTT_REP.
There are three parts to creating a DIY representation called myrep
@enumerate
@item Creating a make file in Make format called myrep_rep.make
@item Optionally creating a shell script called myrep_rep.sh
@item Optionally creating a documentation file in LaTeX format called myrep_rep.tex
@end enumerate
@menu
* Makefile (DIY representations)::
* Shell-script (DIY representations)::
* Documentation (DIY representations)::
@end menu
@node Makefile (DIY representations), Shell-script (DIY representations), New (DIY) representations, New (DIY) representations
@comment node-name, next, previous, up
@subsection Makefile
@cindex New representations
@cindex DIY representations
@cindex Makefile
To create a new representation `myrep' in a language `mylang', create a
file with the name
@example
myrep_rep.make
@end example
This file must contain text in `make' syntax. It is executed by
@strong{MTT} and the two arguments `SYS' (the system name) and `LANG'
(the language) are passed to it by @strong{MTT}. Note that @strong{MTT}
cannot know of any prerequisites, but these can be explicitly included in
the makefile (which may include execution of @strong{MTT} itself.
The following example declares the new representation `ident' which is
created in conjunction with the shell-script ident_rep.sh (@pxref{Shell-script (DIY
representations)}).
@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
@end verbatim
@node Shell-script (DIY representations), Documentation (DIY representations), Makefile (DIY representations), New (DIY) representations
@comment node-name, next, previous, up
@subsection Shell-script
@cindex New representations
@cindex DIY representations
@cindex Shell-script
For more complex DIY representations, it is convenient to define new
commands to be used by the Makefile (@pxref{Makefile (DIY
representations)}).
The following example shows this in the context of the DIY
representation `ident' used as an example in the previous section
(@pxref{Makefile (DIY representations)}).
@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
@end verbatim
@node Documentation (DIY representations), , Shell-script (DIY representations), New (DIY) representations
@comment node-name, next, previous, up
@subsection Documentation
@cindex New representations
@cindex DIY representations
@cindex Documentation
@node Component library, , New (DIY) representations, Extending MTT
@comment node-name, next, previous, up
@section Component library
@cindex Component library
@cindex component
@cindex Component library
If @strong{MTT} does not recognise a component (eg named MyComponent) as
a simple component (@pxref{Simple components}) or as already existing,
it searches the library search path $MTT_COMPONENTS
(@pxref{$MTT_COMPONENTS}) for a directory called MyComponent containing
MyComponent_lbl.txt. It then copies the @emph{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.
@c node next prev up
@node Documentation, Languages, Extending MTT, Top
@chapter Documentation
@cindex Documentation
@menu
* Manual (Documentation)::
* On-line documentation::
@end menu
@node Manual (Documentation), On-line documentation, Documentation, Documentation
@section Manual
@cindex Manual
MTT is documented in this manual. The manual can be invoked in various
ways:
@vtable @code
@item mtt manual
Brings up a pdf version of the manual
@item mtt info
Brings up an xterm containing an info version of the manual
@item mtt hinfo
Brings up an html browser containing the manual
@item emacs
type ^h^i followed by mmtt in the command window
@item browser
point browser to mtt.sf.netb
@end vtable
@node On-line documentation, , Manual (Documentation), Documentation
@section On-line documentation
@cindex Components
@cindex Examples
@cindex Documentation
@cindex On-line documentation
@strong{MTT} components, constitutive relations, examples and representations in libraries
(@pxref{Component library}) are documented in two ways:
@enumerate
@item brief
@item verbose
@end enumerate
@menu
* Brief::
* Detailed::
@end menu
@node Brief, Detailed, On-line documentation, On-line documentation
@subsection Brief on-line documentation
@cindex Brief documentation
Documentation of DIY components, examples, constitutive relationships
and representations is provides by the programmer by inserting code of
the form
@example
#SUMMARY One line summary
#DESCRIPTION Multi-line
#DESCRIPTION More detailed description
@end example
within the appropriate file (usually at or near the top):
@vtable @code
@item components
_lbl.txt (@pxref{Labels (lbl)})
@item examples
_lbl.txt (@pxref{Labels (lbl)})
@item constitutive relations
_cr.r (@pxref{DIY constitutive relationships})
@item representations
_rep.make (@pxref{Makefile (DIY representations)})
@end vtable
This documentation is accessed by the user in various ways
@vtable @code
@item mtt help name
prints basic information on the screen
@item mtt system lbl view
gives formatted information about the component or example
@item Including mtt system abg tex in the _rep.txt file
gives formatted information about the component or example
within the report
@end vtable
@node Detailed, , Brief, On-line documentation
@subsection Detailed on-line documentation
@cindex Detailed documentation
@cindex Description
@cindex desc
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 (@pxref{Language tex (abg.tex)}) of the acausal bond
graph representation (@pxref{Acausal bond graph (abg)}).
The file may contain any LaTeX commands
valis for the ``article'' document type but must @strong{not} contain:
@itemize @bullet
@item documentclass commands
@item document environments
@end itemize
@c node next prev up
@node Languages, Language tools, Documentation, Top
@chapter Languages
@cindex Languages
@pindex Languages
@c node next prev up
@menu
* Fig:: r
* m::
* Reduce::
* c::
@end menu
These are a number of languages used by @strong{MTT} to implement the
various representations.
Each has associated Language tools (@pxref{Language tools}) to
manipulate and/or view the representation.
@ftable @code
@item fig
@code{Fig} a graphical description language.
@item m
@code{octave} a high-level interactive language for numerical
computation.
@item r
@code{reduce} a high-level interactive language for symbolic
computation.
@item tex
@code{latex} a text processor.
@item dvi
@code{xdvi} a document viewer.
@item ps
@code{ghostview} another document viewer.
@item gdat
@code{gnuplot} a data viewer.
@item c
@code{gcc} a c compiler.
@item sg
@code{scigraphica} a plotting package.
@end ftable
These tools are automatically invoked as appropriate by @strong{MTT};
but for more advanced use, these tools can be used directly on files
(with the appropriate suffix) generated by @strong{MTT}.
@node Fig, m, Languages, Languages
@section Fig
@cindex Fig
@pindex Fig
Please see xfig documentation.
@node m, Reduce, Fig, Languages
@section m
@cindex m
@pindex m
Please see Octave documentation
@ifhtml
<A HREF="http://www.che.wisc.edu/octave/">Octave</A> documentation.
<A HREF="http://www.mathworks.com/homepage.html">Matlab</A> documentation.
@end ifhtml
@node Reduce, c, m, Languages
@section Reduce
@cindex Reduce
@pindex Reduce
Please see the reduce documentation.
@node c, , Reduce, Languages
@comment node-name, next, previous, up
@section c
@cindex c
@pindex c
Please see the gcc documentation.
@node Language tools, Administration, Languages, Top
@comment node-name, next, previous, up
@chapter Language tools
@cindex Language tools
@menu
* Views::
* Xfig::
* Text editors::
* Octave::
* LaTeX::
@end menu
@node Views, Xfig, Language tools, Language tools
@comment node-name, next, previous, up
@section Views
@cindex views
A number of representations (@pxref{Representations}) have a language
representation which is particularly useful for viewing by the
user. These views are
invoked, where appropriate by the command:
@example
mtt sys rep view
@end example
where @code{sys} is the system name and @code{rep} a corresponding representation.
@node Xfig, Text editors, Views, Language tools
@comment node-name, next, previous, up
@section Xfig
@cindex Xfig
@node Text editors, Octave, Xfig, Language tools
@comment node-name, next, previous, up
@section Text editors
@cindex Text editors
All representations live in text files and thus may be edited using your
favourite text editor; however, the Fig (@pxref{Fig}) representation is
pretty meaningless in this form and so you should use Xfig
(@pxref{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 @strong{MTT} out of an emacs shell window and keep the
rest of the files in emacs buffers.
@node Octave, LaTeX, Text editors, Language tools
@comment node-name, next, previous, up
@section Octave
@cindex Octave
@cindex Matlab
@cindex m-files
@cindex Octave interface
@cindex mtt.m
Octave is a numerical matrix-based language @xref{Top,
,Octave,Octave,Octave}. It is similar to Matlab in many ways. In most
cases, m-files generated by @strong{MTT} can be understood by both
Matlab and Octave (and no doubt other Matlab lookalikes).
@strong{MTT} provides the octave function @code{mtt}. The octave
command
@example
help mtt
@end example
gives the following information:
@example
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
@end example
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.
@example
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>
@end example
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:
@example
step(rc);
bode(rc);
@end example
@menu
* Octave control system toolbox (OCST)::
* Creating GNU Octave .oct files::
* Creating Matlab .mex files::
* Embedding MTT models in Simulink::
@end menu
@node Octave control system toolbox (OCST), Creating GNU Octave .oct files, Octave, Octave
@comment node-name, next, previous, up
@subsection Octave control system toolbox (OCST)
@cindex Octave
@cindex toolbox
@cindex OCST
@cindex control systems
@cindex mtt2sys
@strong{MTT} provides an interface to the Octave control system toolbox
(OCST) using the mfile @code{mtt2sys}. the octave command
@example
help mtt2sys
@end example
gives the following information.
@example
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
@end example
Thus for example, if octave is in the directory containing the system
rc:
@example
rc = mtt2sys("rc");
@end example
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:
@example
step(rc);
bode(rc);
@end example
@node Creating GNU Octave .oct files, Creating Matlab .mex files, Octave control system toolbox (OCST), Octave
@comment node-name, next, previous, up
@subsection Creating GNU Octave .oct files
@cindex Creating GNU Octave .oct files
GNU Octave dynamically loaded functions (.oct files) can be created by
instructing @strong{MTT} to create the ``oct'' representation:
@example
mtt [options] sys ode oct
@end example
This will cause @strong{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:
@example
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
@end example
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:
@example
mtt -oct rc odeso view
@end example
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 (@pxref{.oct file dependencies}).
@node Creating Matlab .mex files, Embedding MTT models in Simulink, Creating GNU Octave .oct files, Octave
@comment node-name, next, previous, up
@subsection Creating Matlab .mex files
@cindex Creating Matlab .mex files
On GNU/Linux systems, Matlab dynamically linked executables (.mexglx
files) can created by instructing @strong{MTT} to create the
``mexglx'' representation:
@example
mtt [options] sys ode mexglx
@end example
This will cause @strong{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.
@example
mtt_machine:
mtt -cc rc ode cc
matlab_machine:
matlab> mex -DCODEGENTARGET=MATLABMEX rc_ode.cc
@end example
@node Embedding MTT models in Simulink, , Creating Matlab .mex files, Octave
@comment node-name, next, previous, up
@subsection Embedding MTT models in Simulink
@cindex Embedding MTT models in Simulink
It is possible to embed @strong{MTT} functions or entire @strong{MTT}
models within Simulink simulations as Sfun blocks. If the zip package
is installed on the system, the command
@example
mtt sys sfun zip
@end example
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,
@itemize @bullet
@item
sys_sfun.c
model state and output equations
@item
sys_sfun_ae.c
model algebraic equations
@item
sys_sfun_input.c
model inputs
@item
sys_sfun_interface.c
interface between MTT model and Simulink
@end itemize
The last of these files must be edited to correctly map the inputs and
outputs between the @strong{MTT} and Simulink models. The two sections
to edit are clearly marked with
@example
@code{/* Start EDIT */}
@code{....}
@code{/* End EDIT */}
@end example
These four files should then be compiled with the Matlab ``mex''
compiler as described in the @emph{README} file in the archive.
If it is desired to compile the .mex files directly from within
@strong{MTT} on a machine which has the Matlab header files installed,
this may be done with the command
@example
mtt sys sfun mexglx
@end example
which will generated the four .mex files and the .mdl file. In this
case, the user must ensure that @emph{sys_sfun_interface.c} has been
correctly edited prior to compilation.
Note that solution of algebraic equations within Simulink is not
possible unless the @emph{Matlab Optimisation Toolbox} is installed.
@node LaTeX, , Octave, Language tools
@comment node-name, next, previous, up
@section LaTeX
@cindex LaTeX
LaTeX is a powerful text processor which @strong{MTT} uses to provide
visual output.
@node Administration, Glossary, Language tools, Top
@comment node-name, next, previous, up
@chapter Administration
@cindex Administration
@menu
* Software components::
* REDUCE setup::
* Octave setup::
* Paths::
* File structure::
* GNU Free Documentation License::
* Copying::
@end menu
@node Software components, REDUCE setup, Administration, Administration
@comment node-name, next, previous, up
@section Software components
@cindex Software components
@strong{MTT} is built from a set of readily-available software tools.
These are:
@itemize @bullet
@item General purpose software tools.
@item Octave (@pxref{Octave setup})
@item REDUCE (@pxref{REDUCE setup})
@end itemize
The General purpose tools are (these will all be available with a
standard Linux distribution):
@vtable @code
@item sh
Bourne shell
@item gmake
Gnu make
@item gawk
Gnu awk
@item sed
Gnu sed
@item grep
Gnu grep
@item comm
Gnu Compare sorted files by line
@item xfig
Figure editor, version 3 or greater.
@item fig2dev
Fig file conversion, version 3 or greater.
@item ghostview
postscript viewer
@item xdvi
dvi viewer
@item dvips
dvi to postscript conversion
@item latex
the text processor (LaTeX2e needed)
@item latex2html
converts latex to html
@item perl
needed for latex2html
@item gnuplot
a graph plotting program
@item gnuscape
or other web/html browser such as netscape, Red Baron etc.
@item gcc
GNU c compiler
@end vtable
@ifhtml
<A HREF="http://home.pages.de/~GNU/">GNU</A> documentation.
@end ifhtml
@node REDUCE setup, Octave setup, Software components, Administration
@comment node-name, next, previous, up
@section REDUCE setup
@cindex 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:
@quotation
ZIB ( http://www.zib.de )
@end quotation
@ifhtml
<A HREF="http://www.rrz.uni-koeln.de/REDUCE/">REDUCE</A> documentation.
<A HREF="http://www.zib.de">ZIB</A> documentation.
@end ifhtml
@node Octave setup, Paths, REDUCE setup, Administration
@comment node-name, next, previous, up
@section Octave setup
@cindex Octave setup
Octave is available at various web sites including:
@uref{http://www.octave.org}
@menu
* .octaverc::
* .oct file dependencies::
@end menu
@node .octaverc, .oct file dependencies, Octave setup, Octave setup
@comment node-name, next, previous, up
@subsection .octaverc
@vindex .octaverc
The @file{.octaverc} file should contain the following lines:
@example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Startup file for Octave for use with MTT
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
implicit_str_to_num_ok = 1;
empty_list_elements_ok = 1;
@end example
@node .oct file dependencies, , .octaverc, Octave setup
@comment node-name, next, previous, up Additionally, it is necessary to
@subsection .oct file dependencies
Successful compilation of .oct code requires that Octave has been
configured to use dynamically linked libraries and that the Octave
libraries @code{liboctave}, @code{libcruft} and @code{liboctinterp}
are available on the system.
This can be acheived by compiling Octave from the source code, configured
with the options @code{--enable-shared} and @code{--enable-dl}.
A number of additional libraries and headers are also required to be
installed on a system. These include,
@itemize @bullet
@item
@emph{ncurses} and @emph{readline}
terminal control routines
@item
@emph{blas} or @emph{altas}
basic linear algebra subprograms, usually optimised for the specific processor
@item
@emph{fftw}
fast Fourier transform routines
@item
@emph{g2c}
GNU Fortran to C conversion routines
@item
@emph{kpathsea}
TeX path search routines
@end itemize
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
@uref{http://www.octave.org/docs.html,Octave documentation}.
@node Paths, File structure, Octave setup, Administration
@comment node-name, next, previous, up
@section Paths
@cindex paths
@cindex mttrc
There are a number of paths that must be set correctely for @strong{MTT}
to work. These are normally set up by sourcing the file @code{mttrc} that
lives in the @strong{MTT} home directory.
@menu
* $MTTPATH::
* $MTT_COMPONENTS::
* $MTT_CRS::
* $MTT_EXAMPLES::
* $OCTAVE_PATH::
@end menu
@node $MTTPATH, $MTT_COMPONENTS, Paths, Paths
@comment node-name, next, previous, up
@subsection $MTTPATH
@vindex $MTTPATH
The environment variable $MTTPATH points to the mtt home directory.
This is usually @code{/usr/local/lib/mtt}.
@node $MTT_COMPONENTS, $MTT_CRS, $MTTPATH, Paths
@comment node-name, next, previous, up
@subsection $MTT_COMPONENTS
@vindex $MTT_COMPONENTS
The environment variable $MTT_COMPONENTS is a colon-separated path
pointing to directories containing components and subsystems.
By default
@example
MTT_COMPONENTS=.:$MTT_LIB/lib/comp/
@end example
but you may wish to add your own component libraries:
@example
MTT_COMPONENTS=my_library_path:$MTT_COMPONENTS
@end example
@node $MTT_CRS, $MTT_EXAMPLES, $MTT_COMPONENTS, Paths
@comment node-name, next, previous, up
@subsection $MTT_CRS
@vindex $MTT_CRS
The environment variable $MTT_CRS is a colon-separated path
pointing to directories containing constitutive relationships.
By default
@example
MTT_CRS=$MTTPATH/lib/cr
@end example
but you may wish to add your own component libraries:
@example
MTT_CRS=my_cr_path:$MTT_CRS
@end example
@node $MTT_EXAMPLES, $OCTAVE_PATH, $MTT_CRS, Paths
@comment node-name, next, previous, up
@subsection $MTT_EXAMPLES
@vindex $MTT_EXAMPLES
The environment variable $MTT_EXAMPLES is a colon-separated path
pointing to directories containing EXAMPLES and subsystems.
By default
@example
MTT_EXAMPLES=$MTTPATH/lib/examples
@end example
but you may wish to add your own component libraries:
@example
MTT_EXAMPLES=my_examples_path:$MTT_EXAMPLES
@end example
@node $OCTAVE_PATH, , $MTT_EXAMPLES, Paths
@comment node-name, next, previous, up
@subsection $OCTAVE_PATH
@vindex $OCTAVE_PATH
The @code{$OCTAVE_PATH} path must include the relevant paths for mtt to
work properly. In particular, it must include:
@example
$MTTPATH/trans/m
$MTTPATH/lib/comp/simple
$MTTPATH/lib/comp/compound
@end example
@node File structure, GNU Free Documentation License, Paths, Administration
@comment node-name, next, previous, up
@section File structure
@cindex File structure
The recommended installation of @strong{MTT} uses the following
directory structure with corresponding contents. Normally, each of the
listed directories is a subdirectory of @file{/usr/local}. The directory
@code{mtt} is pointed to by $MTTPATH (@pxref{$MTTPATH}).
@vtable @file
@item mtt/bin
This is the home directory for @strong{MTT}. @strong{MTT} itself lives
here along with @file{mttrc}.
@item mtt/bin/trans
The transformations executed by @strong{MTT}.
@item mtt/bin/trans/m
The @code{m-files} associated with the transformations.
@item mtt/bin/trans/awk
The @code{awk} scripts associated with the transformations.
@item mtt/lib
The place for components, examples and CRs which will be updated.
@item mtt/lib/comp/simple
@cindex simple components
The @code{m-files} defining the simple components.
@cindex compound components
@item mtt/lib/comp/compound
The @code{m-files} defining the compound components.
@item mtt/lib/cr/r
constitutive relationship definitions
@item mtt/lib/examples
Some examples.
@item mtt/examples/metamodelling
Examples from the book.
@item mtt/doc
The documentation files for @strong{MTT}.
@item mtt/doc/Examples
Examples used in the documentation.
@end vtable
@appendix Legal stuff
@node GNU Free Documentation License, Copying, File structure, Administration
@appendixsec GNU Free Documentation License
@cindex FDL, GNU Free Documentation License
@center Version 1.2, November 2002
@display
Copyright @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.
@end display
@enumerate 0
@item
PREAMBLE
The purpose of this License is to make a manual, textbook, or other
functional and useful document @dfn{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.
@item
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
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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
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@acronym{DTD}, and standard-conforming simple @acronym{HTML},
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of transparent image formats include @acronym{PNG}, @acronym{XCF} and
@acronym{JPG}. Opaque formats include proprietary formats that can be
read and edited only by proprietary word processors, @acronym{SGML} or
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not generally available, and the machine-generated @acronym{HTML},
PostScript or @acronym{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.
@item
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.
@item
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.
@item
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:
@enumerate A
@item
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.
@item
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.
@item
State on the Title page the name of the publisher of the
Modified Version, as the publisher.
@item
Preserve all the copyright notices of the Document.
@item
Add an appropriate copyright notice for your modifications
adjacent to the other copyright notices.
@item
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.
@item
Preserve in that license notice the full lists of Invariant Sections
and required Cover Texts given in the Document's license notice.
@item
Include an unaltered copy of this License.
@item
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.
@item
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.
@item
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.
@item
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.
@item
Delete any section Entitled ``Endorsements''. Such a section
may not be included in the Modified Version.
@item
Do not retitle any existing section to be Entitled ``Endorsements'' or
to conflict in title with any Invariant Section.
@item
Preserve any Warranty Disclaimers.
@end enumerate
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.
@item
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.''
@item
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.
@item
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.
@item
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.
@item
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.
@item
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
@uref{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.
@end enumerate
@page
@appendixsubsec 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:
@smallexample
@group
Copyright (C) @var{year} @var{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''.
@end group
@end smallexample
If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the ``with...Texts.'' line with this:
@smallexample
@group
with the Invariant Sections being @var{list their titles}, with
the Front-Cover Texts being @var{list}, and with the Back-Cover Texts
being @var{list}.
@end group
@end smallexample
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.
@c Local Variables:
@c ispell-local-pdict: "ispell-dict"
@c End:
@page
@node Copying, , GNU Free Documentation License, Administration
@appendixsec GNU GENERAL PUBLIC LICENSE
@center Version 2, June 1991
@c This file is intended to be included in another file.
@display
Copyright @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.
@end display
@page
@appendixsubsec 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.
@iftex
@appendixsubsec TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
@end iftex
@ifinfo
@center TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
@end ifinfo
@enumerate 0
@item
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.
@item
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.
@item
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:
@enumerate a
@item
You must cause the modified files to carry prominent notices
stating that you changed the files and the date of any change.
@item
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.
@item
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.)
@end enumerate
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.
@item
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:
@enumerate a
@item
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,
@item
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,
@item
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.)
@end enumerate
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.
@item
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.
@item
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.
@item
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.
@item
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.
@item
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.
@item
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.
@item
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.
@iftex
@heading NO WARRANTY
@end iftex
@ifinfo
@center NO WARRANTY
@end ifinfo
@item
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.
@item
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.
@end enumerate
@iftex
@heading END OF TERMS AND CONDITIONS
@end iftex
@ifinfo
@center END OF TERMS AND CONDITIONS
@end ifinfo
@page
@appendixsubsec 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.
@smallexample
@var{one line to give the program's name and a brief idea of what it does.}
Copyright (C) @var{yyyy} @var{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.
@end smallexample
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:
@smallexample
Gnomovision version 69, Copyright (C) 19@var{yy} @var{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.
@end smallexample
The hypothetical commands @samp{show w} and @samp{show c} should show
the appropriate parts of the General Public License. Of course, the
commands you use may be called something other than @samp{show w} and
@samp{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:
@example
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
@var{signature of Ty Coon}, 1 April 1989
Ty Coon, President of Vice
@end example
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.
@node Glossary, Index, Administration, Top
@comment node-name, next, previous, up
@unnumbered Glossary
@printindex fn
@node Index, , Glossary, Top
@comment node-name, next, previous, up
@unnumbered Index
@printindex cp
@contents
@bye