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. 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 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.