Hello Steve,
You can have a look in Aspen HYSYS Operations Guide at chapter Control Ops.
These parameters calculation is futile because they are determined based on ultimate gain (Kc,u) and ultimate period (Pu), values specific to control loop and which in turn are not calculated, but found from a feed-back relay test (in case of a HYSYS simulation, this is done by auto-tuning). Based on them, the values of controller parameters are established: Kc=Kc,u/3.2, Ti=2.2*Pu, Td=Pu/6.3 (in case of Tyreus-Luyben method).
They have a big impact on controller performance when faced with a disturbance, e.g. the control may not be tight enough (i.e., settle time of controlled variable is too long or/and offset from set point) because of untunned parameters.
I hope this was helpful,
Lucian