Fractional-order PI stabilization of first order systems with time delay via Hermite-Biehler theorem: an analytical approach

This work finds sufficient bounds on fractional-order PI coefficients that guarantee closed-loop stability of the first order systems with time delay. To find these stabilizing ranges, the order of the fractional integration is assumed to be known. The boundaries are obtained by using the generalization of Hermite-Biehler theorem. The fractional-order PI controller has been applied to stable and unstable First-Order-Plus-Dead-Time (FOPDT) processes. The comparison between the fractional-order PI controller and the conventional integer-order PI reveals that the fractional controller outperforms the integer one