Modelica.Clocked.UsersGuide

Library Modelica.Clocked is a Modelica package to precisely define and synchronize sampled data systems with different sampling rates. This package contains the user's 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.
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. Requirements sketches the requirements on a Modelica tool, in order that this library can be utilized.
5. Contact provides information about the authors of the library as well as acknowledgments.

Extends from Modelica.Icons.Information (Icon for general information packages).

Package Content

Name	Description
GettingStarted	Getting started
Clocks	Clocks
Literature	Literature
ReleaseNotes	Release notes
Requirements	Requirements
Contact	Contact

Modelica.Clocked.UsersGuide.GettingStarted

Please explore the Examples, which provide simple models for a broad variety of applications.

A central element of the Modelica.Clocked library is a clock. For an introduction to clocks see UsersGuide.Clocks.

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Modelica.Clocked.UsersGuide.Clocks

A central element of the Modelica.Clocked library is a clock. Below, the most important information for clocks is summarized. For more details, see the Modelica Language Specification, Chapter 16 (for Modelica Language Version ≥ 3.3).

A Clock type is a base data type (introduced in Modelica 3.3, additionally to Real, Integer, Boolean, String) that defines when a particular partition consisting of a set of equations is active. Starting with Modelica Language Version 3.3, every variable and every equation is either continuous-time or is associated exactly to one clock. This feature is visualized in the figure below where c(ti) is a clock that is active at particular time instants ti and r(ti) is a variable that is associated to this clock. A clocked variable has only a value when the corresponding clock is active:

Similarly to RealInput, RealOutput etc., clock input and output connectors, called ClockInput and ClockOutput, are defined in sublibrary ClockSignal.Interfaces in order to propagate clocks via connections. A clock signal can be generated with one of the blocks of sublibrary ClockSignals.Clocks:

The output signals of the blocks in the above figure are clock signals, by default visualized with dotted grey lines.

With the blocks of sublibrary ClockSignals.Sampler a clock signal can be sub-sampled, super-sampled, or shift-sampled to generate a new clock signal. For example, with the following model, a periodic clock signal of 0.1 s is sub-sampled with a factor 3 and therefore a clock signal with a period of 0.3 s is generated:

As usual in synchronous languages, a clock is represented by a true value when the clock is active. The relationship between such derived clocks is exact, so it is guaranteed that at every 3rd tick of clock "periodicRealClock.y", the clock "subSample.y" is active.

If a clock is associated to a clocked continuous-time partition, then an integrator has to be defined that is used to integrate the partition from the previous to the current clock tick. This is performed by setting parameter useSolver = true and defining the integration method as String with parameter solver. Both parameters are in tab Advanced of one of the clock signal generating blocks. The possible integration methods are tool dependent. It is expected that at least the solvers "External" (= use the integrator selected in the simulation environment) and "ExplicitEuler" (= explicit Euler method) are supported by every tool. For an example, see Examples.Systems.ControlledMixingUnit.

A clocked partition is a set of equations that depend on each other and where the boundary variables are marked with sample and hold operators. If a clocked partition contains no operator der, delay, spatialDistribution, no event related operators (with exception of noEvent(…)), and no when-clause with a Boolean condition, it is a clocked discrete-time partition, that is, it is a standard sampled data system that is described by difference equations. If a clocked partition is not a clocked discrete-time partition and it contains neither operator previous nor operator interval, it is a clocked discretized continuous-time partition. Such a partition has to be solved with a solver method. It is an error, if none of the two properties hold, e.g., if operators previous and der are both used in the same partition. In a clocked discrete-time partition all event generating mechanisms do no longer apply. Especially neither relations, nor one of the built-in event triggering operators will trigger an event.

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Modelica.Clocked.UsersGuide.Literature

This library is based on the following references:

The synchronous Modelica language elements allow for the first time to utilize a continuous-time, nonlinear, inverse model in a Modelica sampled-data system, by automatically discretizing this model and providing it as a clocked partition. This allows a convenient definition of certain nonlinear control systems, see example Examples.Systems.ControlledMixingUnit. Several practical details to use nonlinear inverse plant models in a control system are discussed in the following reference:

The synchronous Modelica language elements used in this library are based on the clock calculus and inference system proposed by [Colaco2003] and implemented in Lucid Synchrone version 2 and 3 [Pouzet2006]. However, the Modelica approach also uses multi-rate periodic clocks based on rational arithmetic introduced by [Forget2008], as an extension of the Lucid Synchrone semantics. These approaches belong to the class of synchronous languages [Benveniste2003]:

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Modelica.Clocked.UsersGuide.Requirements

This library is basically a graphical user interface to conveniently operate with the Modelica 3.3 language elements of Chapter 16 "Synchronous Language Elements" of the Modelica Language Specification 3.3. Every tool that supports these language elements, as well as basic language elements of Modelica 3.1, should be able to support this library.

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Modelica.Clocked.UsersGuide.Contact

Main authors

Martin Otter

email: Martin.Otter@dlr.de

Bernhard Thiele

email: Bernhard.Thiele@dlr.de

Address

German Aerospace Center (DLR)
Robotics and Mechatronics Center
Institute of System Dynamics and Control
Postfach 1116
D-82234 Wessling
Germany

Acknowledgements

• The design of the library has been performed in close cooperation and discussion with Hilding Elmqvist from Dassault Systèmes Lund.
• Sven Erik Mattsson from Dassault Systèmes Lund developed the first Dymola prototype supporting the synchronous features of Modelica 3.3. Without this prototype, it would not have been possible to develop the Modelica_Synchronous library (the basis of this library).

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