WOLFRAM SYSTEM MODELER

TransferFunction

Discrete-time Transfer Function block

Wolfram Language

In[1]:=
SystemModel["Modelica.Clocked.RealSignals.Periodic.TransferFunction"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

The discrete transfer function block defines the transfer function between the input signal u and the output signal y. The numerator has the order nb-1, the denominator has the order na-1.

       b(1)*z^(nb-1) + b(2)*z^(nb-2) + … + b(nb)
y(z) = -------------------------------------------- * u(z)
       a(1)*z^(na-1) + a(2)*z^(na-2) + … + a(na)

State variables x are defined according to controller canonical form. Initial values of the states can be set as start values of x.

Example:

TransferFunction g(b = {2,4}, a = {1,3});

results in the following transfer function:

     2*z + 4
y = --------- * u
      z + 3

Parameters (2)

b

Value: {1}

Type: Real[:]

Description: Numerator coefficients of transfer function.
a

Value:

Type: Real[:]

Description: Denominator coefficients of transfer function.

Outputs (1)

x

Type: Real[size(a, 1) - 1]

Description: State vector of controller canonical form

Connectors (2)

u

Type: RealInput

Description: Connector of clocked, Real input signal
y

Type: RealOutput

Description: Connector of clocked, Real output signal

Revisions

Release Notes:

  • August 13, 2012 by Bernhard Thiele:
    Used the original code from Blocks.Discrete.TransferFunction and converted it into the Modelica 3.3 clocked equation style.
  • November 15, 2000 by Hans Olsson:
    Converted to when-semantics of Modelica 1.4 with special care to avoid unnecessary algebraic loops.
  • June 18, 2000 by Martin Otter:
    Realized based on a corresponding model of Dieter Moormann and Hilding Elmqvist.