CLSS
====

Continuous state-space system



Block Screenshot
~~~~~~~~~~~~~~~~





Contents
~~~~~~~~


+ `Continuous state-space system`_
  +

    + `Palette`_
    + `Description`_
    + `Dialog box`_
    + `Default properties`_
    + `Interfacing function`_
    + `Computational function`_
    + `Example`_





Palette
~~~~~~~


+ `Continuous time systems palette`_




Description
~~~~~~~~~~~

This block realizes a continuous-time linear state-space system.



where **x** is the vector of state variables, **u** is the vector of
input functions and **y** is the vector of output variables.

The system is defined by the **(A, B, C, D)** matrices and the initial
state **X0**. The dimensions must be compatible.



Dialog box
~~~~~~~~~~




+ **A matrix** A square matrix. Properties : Type 'mat' of size
  [-1,-1].
+ **B matrix** The **B** matrix, [] if system has no input. Properties
  : Type 'mat' of size ["size(%1,2)","-1"].
+ **C matrix** The **C** matrix , [] if system has no output.
  Properties : Type 'mat' of size ["-1","size(%1,2)"].
+ **D matrix** The **D** matrix, [] if system has no D term.
  Properties : Type 'mat' of size [-1,-1].
+ **Initial state** A vector/scalar initial state of the system.
  Properties : Type 'vec' of size "size(%1,2)".




Default properties
~~~~~~~~~~~~~~~~~~


+ **always active:** yes
+ **direct-feedthrough:** no
+ **zero-crossing:** no
+ **mode:** no
+ **regular inputs:** **- port 1 : size [1,1] / type 1**
+ **regular outputs:** **- port 1 : size [1,1] / type 1**
+ **number/sizes of activation inputs:** 0
+ **number/sizes of activation outputs:** 0
+ **continuous-time state:** yes
+ **discrete-time state:** no
+ **object discrete-time state:** no
+ **name of computational function:** csslti4




Example
~~~~~~~

This sample example illustrates how to use CLSS block to simulate and
display the output waveform **y(t)=Vc(t)** of the RLC circuit shown
below.



The equations for an RLC circuit are the following. They result from
Kirchhoff's voltage law and Newton's law.



The R, L and C are the system's resistance, inductance and capacitor.

We define the capacitor voltage `Vc` and the inductance current `iL`
as the state variables `X1` and `X2.`



thus



Rearranging these equations we get:



These equations can be put into matrix form as follows,



The required output equation is



The following diagram shows these equations modeled in Xcos where
R=10Ω, L=5 mΗ and C=0.1µF; the initial states are x1=0 and x2=0.5.

To obtain the output Vc(t) we use CLSS block from Continuous time
systems Palette.



` `_



Interfacing function
~~~~~~~~~~~~~~~~~~~~


+ SCI/modules/scicos_blocks/macros/Linear/CLSS.sci




Computational function
~~~~~~~~~~~~~~~~~~~~~~


+ SCI/modules/scicos_blocks/src/c/csslti4.c (Type 4)


.. _Example: CLSS.html#Example_CLSS
.. _Continuous state-space system: CLSS.html
.. _Dialog box: CLSS.html#Dialogbox_CLSS
.. _Description: CLSS.html#Description_CLSS
.. _Palette: CLSS.html#Palette_CLSS
.. _Computational
                function: CLSS.html#Computationalfunction_CLSS
.. _Default
                properties: CLSS.html#Defaultproperties_CLSS
.. _Continuous time systems
            palette: Continuous_pal.html
.. _Interfacing
                function: CLSS.html#Interfacingfunction_CLSS