Discussed so far has been Math Model PD3(PI) control. E.g. a known 3rd order process transfer function could be controlled best using PD3 feedforward when the set point has been moved by steps. Disturbances have been controlled by feedback PI action.
It is also easily possible to compensate feedforward the disturbances if the process is known. Let's call it PD3(PID)Z. PID will just do the fine work and adjust the system if necessary, e.g. for nonlinearities to be settled.
See Math Control Modelling:
formatting link
Diagrams Page 1 PD3(PID) Page 2 (t = 0.25 disturbance) PD3(PID)Z Pade 3 (t = 0.25 disturbance can't be recognized!)This is in compliance with the Control Theory. The accuracy of control depends on the accuracy of the process transfer function!