blockTransferFunction

Information

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. 

Example:

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

results in the following transfer function:

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

This block differs from the one of the same name in the Modelica Standard Library in one respect : the initial equations are absent since Dynawo ignores them, start values are given for y and for x_scaled instead.

Three initialization options are available :

• NoInit : x, x_scaled and y are initialized at 0;
• SteadyState : the initial values of x, x_scaled and y depend on u_start (a parameter for the initial input value) with the goal of having derivative values equal to 0;
• InitialState or InitialOutput : x and x_scaled are initialized on the basis of x_start, y is initialized at y_start.

Parameters

Connectors

Components