New tuning rules for PID controllers based on IMC with minimum IAE for inverse response processes

Abstract

In this paper new tuning rules for Proportional Integral Derivative (PID) are presented, which are based on Internal Model Control (IMC). This set of equations minimizes the performance index, in this case, the Integral Absolute Error (IAE). Furthermore, a correlation is proposed in order to calculate the tuning parameter of the method, where a holding oscillation response is obtained regarding changes in the set point. This value represents a stability limit for the IMC method. The overall development is then applied to an Inverse Response System of second order and with dead time.