Synthesis of a fractional PI controller for a first-order time delay system

Abstract

This paper considers the problem of stabilizing a first-order plants with known time delay using a fractional-order proportional–integral controller [Formula: see text]. Using a generalization of the Hermite–Biehler theorem applicable to quasi-polynomials, a complete analytical characterization of all stabilizing gain values ([Formula: see text]) is provided. The widespread industrial use of fractional PI controllers justifies a timely interest in [Formula: see text] tuning techniques.