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

b	Value: {1} Type: Real[:] Description: Numerator coefficients of transfer function.
a	Value: Type: Real[:] Description: Denominator coefficients of transfer function.

x	Type: Real[size(a, 1) - 1] Description: State vector of controller canonical form