## Modelica_LinearSystems2.UsersGuide

Library Modelica_LinearSystems2 is a Modelica package providing different representations of linear, time invariant differential and difference equation systems, as well as typical operations on these system descriptions. Additionally, data structures and operations for Complex numbers and for Polynomials are provided. These are utilized above, but are, of course, also useful for other purposes.

This package contains the users guide for the library and has the following content:

1. Getting started contains an introduction to the most important features and how to use them at hand of examples.
2. Literature provides references that have been used to design and implement this library.
3. Release Notes summarizes the differences between different versions of this library.
4. Modelica License 2 is the legal license text und which this library is submitted.
5. Requirements scetches the requirements on a Modelica tool, in order that this library can be utilized.
6. Contact provides information about the author of the library as well as acknowledgments.

### Package Content

Name | Description
--- | ---
GettingStarted | Getting started
Literature | Literature
ReleaseNotes | Release notes
ModelicaLicense2 | Modelica License 2
Requirements | Requirements
Contact | Contact

## Modelica_LinearSystems2.UsersGuide.GettingStarted

In this section, a first introduction to the Modelica_LinearSystems2 library is given at hand of several examples. The library consists of four main parts that are described in the following sections:

1. Section Complex numbers introduces the Modelica_LinearSystems2.Math.Complex record that provides a data struture for Complex numbers and arrays and also the most important (scalar) operations on them. Read this section first, because the structuring of records as well as operator overloading is explained that is also the basis for the other parts of the library.
2. Section Polynomials describes the Modelica_LinearSystems2.Math.Polynomials record that provides a data structure for Polynomials with real coefficients and operations such as evaluation, fitting, integration. The Complex and Polynomial data structures are basic building blocks for the other parts of the library.
3. Linear system data structures are records on the top level of Modelica_LinearSystems2 that define data structures for different representations of linear, time invariant, continuous and discrete systems, e.g., record StateSpace. Furthermore, operations are provided on these data structures, e.g., to connect linear systems together or plot a frequency response.

## Modelica_LinearSystems2.UsersGuide.Literature

This library is based on the following references:

Aström K.J., Wittenmark B. (1997):
  Computer Controlled Systems: Theory and Design. Prentice Hall. 3rd edition.
Datta B. N. (2004):
  Numerical Methods for linear control systems. Elsevier Academic Press
Goloub G.H., Van Loan C.F. (1996):
  Matrix Computations. Johns Hopkins University Press 3rd edition.
Tietze U., and Schenk C. (2002):
  Halbleiter-Schaltungstechnik. Springer Verlag, 12. Auflage, S. 815-852.

## Modelica_LinearSystems2.UsersGuide.ModelicaLicense2

All files in this directory (Modelica_LinearSystems2) and in all subdirectories, especially all files that build package "Modelica_LinearSystems2" are licensed by DLR under the Modelica License 2.

Licensor:
Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
Institut für Robotik und Mechatronik
Postfach 1116
D-82230 Wessling
Germany
email: Martin.Otter@dlr.de

Copyright notices of the files:
Copyright © 2005-2009, DLR Institut für Robotik und Mechatronik.

#### The Modelica License 2

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#### Frequently Asked Questions

This section contains questions/answer to users and/or distributors of Modelica packages and/or documents under Modelica License 2. Note, the answers to the questions below are not a legal interpretation of the Modelica License 2. In case of a conflict, the language of the license shall prevail.

Using or Distributing a Modelica Package under the Modelica License 2

What are the main differences to the previous version of the Modelica License?

1. Modelica License 1 is unclear whether the licensed Modelica package can be distributed under a different license. Version 2 explicitly allows that “Derivative Work” can be distributed under any license of Your choice, see examples in Section 1d) as to what qualifies as Derivative Work (so, version 2 is clearer).

2. If You modify a Modelica package under Modelica License 2 (besides fixing of errors, adding vendor specific Modelica annotations, using a subset of the classes of a Modelica package, or using another representation, e.g., a binary representation), you must rename the root-level name of the package for your distribution. In version 1 you could keep the name (so, version 2 is more restrictive). The reason of this restriction is to reduce the risk that Modelica packages are available that have identical names, but different functionality.

3. Modelica License 1 states that “It is not allowed to charge a fee for the original version or a modified version of the software, besides a reasonable fee for distribution and support“. Version 2 has a similar intention for all Original Work under Modelica License 2 (to remain free of charge and open source) but states this more clearly as “No fee, neither as a copyright-license fee, nor as a selling fee for the copy as such may be charged”. Contrary to version 1, Modelica License 2 has no restrictions on fees for Derivative Work that is provided under a different license (so, version 2 is clearer and has fewer restrictions).

4. Modelica License 2 introduces several useful provisions for the licensee (articles 5, 6, 12), and for the licensor (articles 7, 12, 13, 14) that have no counter part in version 1.

5. Modelica License 2 can be applied to all type of work, including documents, images and data files, contrary to version 1 that was dedicated for software only (so, version 2 is more general).

Can I distribute a Modelica package (under Modelica License 2) as part of my commercial Modelica modeling and simulation environment?

Yes, according to Section 2c). However, you are not allowed to charge a fee for this part of your environment. Of course, you can charge for your part of the environment.

Can I distribute a Modelica package (under Modelica License 2) under a different license?

No. The license of an unmodified Modelica package cannot be changed according to Sections 2c) and 2d). This means that you cannot sell copies of it, any distribution has to be free of charge.

Can I distribute a Modelica package (under Modelica License 2) under a different license when I first encrypt the package?

No. Merely encrypting a package does not qualify for Derivative Work and therefore the encrypted package has to stay under Modelica License 2.

Can I distribute a Modelica package (under Modelica License 2) under a different license when I first add classes to the package?

No. The package itself remains unmodified, i.e., it is Original Work, and therefore the license for this part must remain under Modelica License 2. The newly added classes can be, however, under a different license.

Can I copy a class out of a Modelica package (under Modelica License 2) and include it unmodified in a Modelica package under a commercial/proprietary license?

No, according to article 2c). However, you can include model, block, function, package, record and connector classes in your Modelica package under Modelica License 2. This means that your Modelica package could be under a commercial/proprietary license, but one or more classes of it are under Modelica License 2.
Note, a “type” class (e.g., type Angle = Real(unit=”rad”)) can be copied and included unmodified under a commercial/proprietary license (for details, see the next question).

Can I copy a type class or part of a model, block, function, record, connector class, out of a Modelica package (under Modelica License 2) and include it modified or unmodified in a Modelica package under a commercial/proprietary license

Yes, according to article 2d), since this will in the end usually qualify as Derivative Work. The reasoning is the following: A type class or part of another class (e.g., an equation, a declaration, part of a class description) cannot be utilized “by its own”. In order to make this “usable”, you have to add additional code in order that the class can be utilized. This is therefore usually Derivative Work and Derivative Work can be provided under a different license. Note, this only holds, if the additional code introduced is sufficient to qualify for Derivative Work. Merely, just copying a class and changing, say, one character in the documentation of this class would be no Derivative Work and therefore the copied code would have to stay under Modelica License 2.

Can I copy a class out of a Modelica package (under Modelica License 2) and include it in modified form in a commercial/proprietary Modelica package?

Yes. If the modification can be seen as a “Derivative Work”, you can place it under your commercial/proprietary license. If the modification does not qualify as “Derivative Work” (e.g., bug fixes, vendor specific annotations), it must remain under Modelica License 2. This means that your Modelica package could be under a commercial/proprietary license, but one or more parts of it are under Modelica License 2.

Can I distribute a “save total model” under my commercial/proprietary license, even if classes under Modelica License 2 are included?

Your classes of the “save total model” can be distributed under your commercial/proprietary license, but the classes under Modelica License 2 must remain under Modelica License 2. This means you can distribute a “save total model”, but some parts might be under Modelica License 2.

Can I distribute a Modelica package (under Modelica License 2) in encrypted form?

Yes. Note, if the encryption does not allow “copying” of classes (in to unencrypted Modelica source code), you have to send the Modelica source code of this package to your customer, if he/she wishes it, according to article 6.

Can I distribute an executable under my commercial/proprietary license, if the model from which the executable is generated uses models from a Modelica package under Modelica License 2?

Yes, according to article 2d), since this is seen as Derivative Work. The reasoning is the following: An executable allows the simulation of a concrete model, whereas models from a Modelica package (without pre-processing, translation, tool run-time library) are not able to be simulated without tool support. By the processing of the tool and by its run-time libraries, significant new functionality is added (a model can be simulated whereas previously it could not be simulated) and functionality available in the package is removed (e.g., to build up a new model by dragging components of the package is no longer possible with the executable).

Is my modification to a Modelica package (under Modelica License 2) a Derivative Work?

It is not possible to give a general answer to it. To be regarded as "an original work of authorship", a derivative work must be different enough from the original or must contain a substantial amount of new material. Making minor changes or additions of little substance to a preexisting work will not qualify the work as a new version for such purposes.

Using or Distributing a Modelica Document under the Modelica License 2

This section is devoted especially for the following applications:

1. A Modelica tool extracts information out of a Modelica package and presents the result in form of a “manual” for this package in, e.g., html, doc, or pdf format.

2. The Modelica language specification is a document defining the Modelica language. It will be licensed under Modelica License 2.

3. Someone writes a book about the Modelica language and/or Modelica packages and uses information which is available in the Modelica language specification and/or the corresponding Modelica package.

Can I sell a manual that was basically derived by extracting information automatically from a Modelica package under Modelica License 2 (e.g., a “reference guide” of the Modelica Standard Library):

Yes. Extracting information from a Modelica package, and providing it in a human readable, suitable format, like html, doc or pdf format, where the content is significantly modified (e.g. tables with interface information are constructed from the declarations of the public variables) qualifies as Derivative Work and there are no restrictions to charge a fee for Derivative Work under alternative 2d).

Can I copy a text passage out of a Modelica document (under Modelica License 2) and use it unmodified in my document (e.g. the Modelica syntax description in the Modelica Specification)?

Yes. In case you distribute your document, the copied parts are still under Modelica License 2 and you are not allowed to charge a license fee for this part. You can, of course, charge a fee for the rest of your document.

Can I copy a text passage out of a Modelica document (under Modelica License 2) and use it in modified form in my document?

Yes, the creation of Derivative Works is allowed. In case the content is significantly modified this qualifies as Derivative Work and there are no restrictions to charge a fee for Derivative Work under alternative 2d).

Can I sell a printed version of a Modelica document (under Modelica License 2), e.g., the Modelica Language Specification?

No, if you are not the copyright-holder, since article 2c) does not allow a selling fee for a (in this case physical) copy. However, mere printing and shipping costs may be recovered.

## Modelica_LinearSystems2.UsersGuide.Requirements

This library is implemented with Modelica 3.1 (especially the operator overloading features are utilized) and requires the LAPACK 3.1.1 object library. Furthermore, linearization and plotting is implemented with Dymola API calls. It is planned to move these tool specific calls to the ModelicaServices package (introduced for the Modelica Standard Library 3.1 for these purposes), in order that other Modelica tools can provide the same functionality in a clean way.

## Modelica_LinearSystems2.UsersGuide.Contact

Main Authors:
  Martin Otter and Marcus Baur
  Deutsches Zentrum für Luft und Raumfahrt e.V. (DLR)
  Institut für Robotik und Mechatronik
  Postfach 1116
  D-82230 Wessling
  Germany
  email: Martin.Otter@dlr.de

Acknowledgements:

- Some functionality of Modelica_LinearSystems2 (e.g., linearizing a Modelica model by Modelica_LinearSystems2.StateSpace.Import.fromModel) has been originally developed by Sven Erik Mattsson from Dynasim.
- The Math.Complex, Math.Polynomial, and TransferFunction packages are based on proposals from Hilding Elmqvist, Dynasim, presented at the 33rd Modelica design meeting in Bielefeld (Nov. 2003) and the 37th Modelica design meeting in Lund (Jan. 2004).
- Several functions of package Complex have been provided by Anton Haumer, who also performed a thorough test of the package.
- The design of the records (such as Math.Complex and Math.Polynomial) has been inspired by the discussions about operator overloading at various Modelica design meetings.
- Advice for implementation issues given by Hans Olsson from Dynasim, as well as advice for some numerical algorithms given by Andras Varga and Dieter Joos from DLR is appreciated.
- Financial support of DLR for the development of this library within the European Network of Excellence HYCON (Hybrid Control: taming heterogeneity and complexity of networked embedded systems; contract number: 511368), and within the German BMBF Verbundprojekt PAPAS (Plug-And-Play Antriebs- und Steuerungskonzepte für die Produktion von Morgen; Förderkennzeichen: 02PH2060) is highly appreciated.
- Since Oct. 2007, the library development was partially funded by BMBF within the ITEA2 EUROSYSLIB project.