Bode plot based stability analysis of a fractional-order PI controller with first-order time-delayed plant

The main aim of the paper is to present the stability analysis of a fractional-order PI controller with first order, time-delayed plant based on Bode plot. In the paper there is a comparison, presented between the tuning method based on Hermite-Biehler and Pontryagin theorems with, and without taking the gain and phase margins into consideration. The quality performance is based on two quality indices, namely the Integral of Absolute Error and the Integral of a Squared Error.