Stabilization using FO-PI controllers for first-order time delay systems

This paper presents a new tuning method for frational PI^λ controllers. The main contribution is based on Hermite-Biehler theorem for time delay systems. A solution to the problem of stabilizing a given first order time delay plant is offered. The set of admissible (k_p, k_i) gain values is determined for the various values of λ and plotted in (k_p, k_i, λ) plane. The viability of the method is verified using two examples where λ ∈ [0.1 : 0.1 : 1] and λ ∈ ]1 : 0.1 : 2[. The comparison results show the effect of the fractional order integral.