Revisiting IMC based design of PI/PID controllers for FOPTD Models

This communication addresses the tuning of PI and PID controllers on the basis of the IMC approach. The tuning is based upon a first order plus time delay (FOPTD) model and aims to achieve a step response specification. It is analyzed that by using the IMC approach we get a PI or a PID depending on the kind of approximation used for the time delay term. This paper raises the question that the use of a PID instead of a PI controller should obey to another reason more related to the control objectives rather than the use of a better approximation for the time delay. An alternative tuning is presented that, even got within the IMC formulation is based on a min-max optimization. From the tuning rule provided by this approach the optimum settings from an integral squared error (ISE) criterion point of view are derived. The optimal controller results to be a PI controller. From this optimal controller as the starting point, the introduction of the derivative action can be seen as a detuning procedure that can increase the controller robustness. The approach provides further insight into the tuning of PI and PID controllers giving the (alternative) parameters a precise and engineering meaning.