On the consideration of FOPTD and SOPTD responses ab bounds of PI tuning

This document presents a new model-based approach to tune a PI controller for first-order plus time delay (FOPTD) plants using second-order plus time delay (SOPTD) and FOPTD responses. The main emphasis of this paper is on the analytical demonstration that the response of a PI-controlled FOPTD plant has two bounds characterized by pure SOPTD and FOPTD transfer functions. Since the desired specifications for a SISO system in the time domain may be easily modelled by these transfer function, PI tuning as a balance of properties of such responses presents more advantages than other procedures