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.

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Interfacing function

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

Computational function

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