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*uy=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.

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 |

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