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

This block defines the transfer function between the input u and the output y as (nb = dimension of b, na = dimension of a):

        b[1]*s^[nb-1] + b[2]*s^[nb-2] + ... + b[nb]
y(s) = --------------------------------------------- * u(s)
        a[1]*s^[na-1] + a[2]*s^[na-2] + ... + a[na]

State variables x are defined according to controller canonical form. Internally, vector x is scaled to improve the numerics (the states in versions before version 3.0 of the Modelica Standard Library have been not scaled). This scaling is not visible from the outside of this block because the non-scaled vector x is provided as output signal and the start value is with respect to the non-scaled vector x. Initial values of the states x can be set via parameter x_start.

Example:

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

results in the following transfer function:

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