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

This blocks defines the transfer function between the input u and the output y as PI system:

                 1
   y = k * (1 + ---) * u
                T*s
           T*s + 1
     = k * ------- * u
             T*s

If you would like to be able to change easily between different transfer functions (FirstOrder, SecondOrder, ... ) by changing parameters, use the general model class TransferFunction instead and model a PI SISO system with parameters
b = {k*T, k}, a = {T, 0}.

Example:

   parameter: k = 0.3,  T = 0.4

   results in:
               0.4 s + 1
      y = 0.3 ----------- * u
                 0.4 s

It might be difficult to initialize the PI component in steady state due to the integrator part. This is discussed in the description of package Continuous.