Tuning proportional-integral controllers based on new analytical methods for finding centroid of stability locus for stable/unstable first-order plus dead-time processes

The simplicity of the proportional-integral controller makes it very popular in many practical engineering applications. In the literature, several approaches have been introduced for tuning proportional-integral controllers by calculating the centroid of the stability region. However, all those approaches depend on graphical plottings which are time-consuming. Also, the design procedure has to be redone as the transfer function changes. Here, two new analytical methods are proposed to obtain the centroid of the stability region for the proportional-integral controllers to control a time delay process which can be modeled by a stable or unstable first-order plus dead-time model. The methods introduced eliminate the compulsory procedure of plotting the stability region. The efficiency of the suggested methods has been studied by conducting a robustness analysis and studying several simulation examples.