.Modelica_LinearSystems2

Information

Library Modelica_LinearSystems2 is a Modelica package providing different representations of linear, time invariant differential and difference equation systems. For example, record StateSpace defines a linear time invariant differential equation system in state space form:

der(x) = A * x + B * u
    y  = C * x + D * u

Operators are overloaded to work conveniently with these system descriptions in an interactive environment, e.g. to multiply transfer functions or to operate on complex numbers. About 230 functions are provided to operate on these data structures, e.g. to compute eigenvalues, zeros, step responses, to design pole-placement and LQG controllers, to plot step responses, frequency responses, eigenvalues, to convert between different description forms, or to generate a linear system description by linearization of a Modelica model.

Furthermore, in subpackage Controllers about 20 input/output blocks of linear systems are provided that are based on the different representation forms, e.g. PID, StateSpace or Filter blocks. A unique feature of these blocks is that it is very convenient to quickly switch between a continuous and a discrete block representation. Also, templates are provided to quickly built-up standard controller structures.

For an introduction, have especially a look at:

• Getting started provides an overview of the Library in the User's Guide.
• Release Notes summarizes the changes of new versions of this package.
• Contact gives the contact information for this library.
• In an interactive environment, it is useful to run the script "_abbreviations.mos" in directory "Modelica_LinearSystems2/Resources/Scripts" first, in order to set useful abbreviations for e.g. ss, tf, zp, poly, j, etc. It is not necessary to import the package Complex since it is handled as a built-in complex number type within Dymola. See also ComplexNumbers in the User's Guide.

It is planned to include this library in a future version of the Modelica Standard Library.

For copyright and BSD 3-clause license, see Copyright and License agreement.

Modelica® is a registered trademark of the Modelica Association.

Contents

Name	Description
UsersGuide	User's Guide
ModelAnalysis	Package of functions to perform analysis on Modelica models (nonlinear models are linearized)
Examples	Package of examples to demonstrate the usage of functions from the library
StateSpace	Continuous state space description of a linear, time invariant differential equation system (data + operations)
ZerosAndPoles	Continuous zeros and poles description of a single input, single output system (data + operations)
TransferFunction	Continuous transfer function description of a single input, single output system (data + operations)
DiscreteStateSpace	Discrete state space description of a linear, time invariant difference equation system (data + operations)
DiscreteZerosAndPoles	Discrete zeros and poles description of a single input, single output system (data + operations)
DiscreteTransferFunction	Discrete transfer function description of a single input, single output system (data + operations)
Controllers	Package of continuous and discrete input/output blocks
Math	Package of additional functions for Modelica.Math
ComplexMathAdds	Library of additional complex mathematical functions and of functions operating on complex vectors and matrices
Utilities	Package of utility elements used in the library
Internal	Package of internal utilities of the library (for advanced users only)
Records	Package of records, especially to build menus
WorkInProgress	Package for developments and internal models