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

摘要

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