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:

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

results in the following transfer function:

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

samplePeriod	Value: Type: Time (s) Description: Sample period of component
startTime	Value: 0 Type: Time (s) Description: First sample time instant
b	Value: {1} Type: Real[:] Description: Numerator coefficients of transfer function.
a	Value: {1} Type: Real[:] Description: Denominator coefficients of transfer function.

sampleTrigger	Type: Boolean Description: True, if sample time instant
firstTrigger	Type: Boolean Description: Rising edge signals first sample instant
x	Type: Real[size(a, 1) - 1] Description: State of transfer function from controller canonical form