Considerations on PI/PID controller design: application to a continuous stirred tank reactor

This paper addresses the problem of tuning a PID controller on the basis of a model reference specification and posterior inclusion of robustness considerations. The tuning is based upon a first order plus time delay (FOPTD) model and aims to achieve a desired closed loop transfer function. The specific point tackled in the paper is about the advantages of using a PID instead of a PI controller. From a generic tuning rule the optimum settings from an integral squared error 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