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Ajuda do Scilab >> Xcos > palettes > Continuous time systems palette > CLSS


Continuous state-space system

Block Screenshot


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


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.


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)

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Last updated:
Wed Apr 01 10:24:22 CEST 2015